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Preface

You want to do your best on the ACT® test, and this book can help. It supplements our free booklet, Preparing for the ACT, and our ACT Online Prep™ (a web-based preparation program for the ACT). This book features six actual ACT tests—all of which include the optional writing test—which you can use for practice, and it gives detailed explanatory answers to every question to help you review.

Using this book will help you become familiar with the following:

The content of the ACT

The procedures you’ll follow when you’re actually taking the ACT

The types of questions you can expect to find on the ACT

Suggestions on how to approach the questions

General test-taking strategies

This book is intended to help you know what to expect when you take the ACT so you can relax and concentrate on doing your best. The more you know about what to expect on any test you take, the more likely it is that your performance on that test will accurately reflect your overall preparation and achievement in the areas it measures. Knowing what to expect can help reduce any nervousness you may feel as you approach the test.

The ACT measures your understanding of what you’ve been taught in core high school courses that you should have completed by the time you finish high school. Because it has taken you years to learn all this material, it might take you some time to review for the ACT. You can’t expect to cram for the ACT in a night or two. However, any review should be helpful to you, even if it just makes you more comfortable when you actually sit down to take the ACT. We hope this book helps you to gauge how much reviewing you feel you need to do and identify subject areas on which to focus your efforts.

How This Book Is Arranged

This book is divided into five parts:

Part One: Getting Acquainted with the ACT. Chapters in this part introduce the ACT, explain how to prepare, and present general test-taking techniques and strategies for you to consider.

Part Two: Taking and Evaluating Your First Practice Test. This part includes a practice test along with guidance on how to use the test to identify areas where you may need to invest more time and effort.

Part Three: Improving Your Score. Chapters in this part present test-taking strategies tailored for each subject test—English, math, reading, and science—along with suggestions for taking the optional writing test.

Part Four: Taking Additional Practice Tests. In this part, you have the opportunity to take five additional practice tests, see the results, and interpret your scores to determine how well prepared you are to take the ACT.

Part Five: Moving Forward to Test Day. This part prepares you for test day by explaining how to register for the ACT and describing what to expect on the day of the test, so you show up on time with everything you need.

The parts are identified by bars on the edge of their right-hand pages.

Before You Begin

There is no standardized way to prepare for the ACT. Everyone learns and prepares differently. Some people prepare best when they are by themselves. Others need to work with fellow students to do their best. Still others function best in a structured class with a teacher leading them through their work. Use whatever method works best for you. Keep in mind, though, that when you actually take the ACT, it will be just you and the test.

As you use this book to prepare for the ACT, consider working in 1-hour segments (except when you’re taking the timed practice tests, of course). If you want to invest more than 1 hour a day, that’s fine, but take breaks to stretch and give your mind a chance to absorb the material. Toiling to the point of burnout is counterproductive.

Part One:
Getting Acquainted with the ACT Test

In This Part

This part introduces you to the ACT, the five tests that it is composed of (English, mathematics, reading, science, and the optional writing test), and testing procedures. It also features test-taking strategies and skills that apply to all of the component tests. Specifically, you will do the following:

Find out what is covered on the tests.

Determine when you can use a calculator and the types of calculators you are permitted to use and prohibited from using.

Get a preview of what you can expect on test day.

Obtain guidance on how to prepare for test day.

Learn test-taking strategies that may improve your scores on all of the tests.

Chapter 1:
About the ACT

The ACT® measures your achievement in core academic areas important for your college and career success: English, math, reading, science, and (optionally) writing. It isn’t an IQ test—it doesn’t measure your basic intelligence. It’s an achievement test that’s been carefully designed—using surveys of classroom teachers, reviews of curriculum guides for schools all over the country, and advice from curriculum specialists and college faculty members—to be one of several effective tools for evaluating your college and career readiness.

The individual tests that make up the ACT consist of questions that measure your knowledge and skills. You’re not required to memorize facts or vocabulary to do well on the ACT. Of course, all the terms, formulas, and other information you learned in your classes will be useful to you when you take the ACT. However, last-minute cramming (such as memorizing 5,000 vocabulary words or the entire periodic table of elements) won’t directly improve your performance on the ACT.

Description of the Full ACT Test

The full ACT consists of four multiple-choice tests—English, mathematics, reading, and science—and an optional writing test. Topics covered on these five tests correspond very closely to topics covered in typical high school classes. Table 1.1 gives you a snapshot of all five tests.

Table 1.1: ACT Tests

Test

Questions

Time

Content Covered

English

75 questions

45 minutes

Measures standard written English knowledge and skills along with English language conventions

Mathematics

60 questions

60 minutes

Measures mathematical skills students have typically acquired in courses taken up to the beginning of grade 12

Reading

40 questions

35 minutes

Measures reading comprehension

Science

40 questions

35 minutes

Measures the interpretation, analysis, evaluation, reasoning, and problem-solving skills required in the natural sciences

Writing (optional)

1 prompt

40 minutes

Measures writing skills emphasized in high school English classes and in entry-level college composition courses

Questions on the tests are intended to help assess college and career readiness. The following sections provide an overview of what you should know to perform well on each test. For additional details, check out the ACT College and Career Readiness Standards presented in chapter 12.

English Test

75 questions, 45 minutes

The English test consists of five essays or passages, each of which is accompanied by a sequence of multiple-choice test questions. Different passage types are employed to provide a variety of rhetorical situations. Passages are chosen not only for their appropriateness in assessing writing skills but also to reflect students’ interests and experiences.

You will receive four scores for the ACT English test: a total test score based on all 75 questions and three reporting category scores based on the following:

Production of Writing

Knowledge of Language

Conventions of Standard English

Production of Writing

Production of Writing questions test knowledge and skills in two areas of English composition:

Topic development in terms of purpose and focus

Organization, unity, and cohesion

Topic Development in Terms of Purpose and Focus

Examples of knowledge and skills tested include the following:

Determine the relevance of material to the topic or the focus of the passage or paragraph.

Identify the purpose of a word or phrase (for example, to identify a person, to define a term, or to help describe an object).

Determine whether a passage has met a specific goal.

Use a word, phrase, or sentence to accomplish a specific purpose, such as to convey a feeling or attitude or to illustrate a given statement.

Organization, Unity, and Cohesion

Examples of knowledge and skills tested include the following:

Determine the need for transition words or phrases to define relationships in terms of time or logic.

Determine the most logical place for a sentence in a paragraph or in the passage as a whole.

Provide a suitable conclusion for a paragraph or passage.

Provide a suitable introduction for a paragraph or passage.

Rearrange sentences in a paragraph or rearrange paragraphs in a passage to establish a logical flow.

Determine the most logical place to divide a paragraph to achieve a stated goal.

Knowledge of Language

Knowledge of Language questions test your ability to clearly and succinctly express yourself in written English. Knowledge and skills tested include the following:

Revise unclear, clumsy, and confusing writing.

Delete redundant and wordy material.

Revise an expression to make it conform to the style and tone used throughout the passage.

Determine logical connections between clauses.

Choose the most appropriate word or phrase in terms of the sentence content.

Conventions of Standard English

Conventions of Standard English questions test knowledge and skills such as the following:

Determine the need for punctuation or conjunctions to join clauses or to correct awkward-sounding fragments, fused sentences, and faulty subordination and coordination of clauses.

Recognize and correct inappropriate shifts in verb tense.

Recognize and correct disturbances in sentence structure, such as faulty placement of adjectives, participial phrase fragments, missing or incorrect relative pronouns, dangling or misplaced modifiers, faulty parallelism, and run-on sentences.

Maintain consistent and logical verb tense and voice and pronoun person within a paragraph or passage.

Note: Spelling and the rote recall of grammar rules are not tested.

Mathematics Test

60 questions, 60 minutes

The mathematics test presents multiple-choice questions that require you to use reasoning skills to solve practical math problems. The material covered on the test emphasizes the major content areas that are prerequisites to successful performance in entry-level courses in college mathematics. Some questions may belong to a set of several questions (for example, several questions about the same graph or chart).

Conceptual knowledge and computational skills are assumed as background for the problems, but recall of complex formulas and extensive computation is not required.

Nine scores are reported for the ACT mathematics test: a total test score based on all 60 questions and eight reporting category scores based on specific mathematical knowledge and skills. The reporting categories are:

Preparing for Higher Mathematics, which includes separate scores for Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability

Integrating Essential Skills

Modeling

Preparing for Higher Mathematics

This category captures the more recent mathematics that students are learning, starting when they begin using algebra as a general way of expressing and solving equations. This category is divided into the following five subcategories:

Number and Quantity

Algebra

Functions

Geometry

Statistics and Probability

Number and Quantity

Math questions in this category test your knowledge of numbers and fundamental math concepts and operations, including the following:

Perform calculations on whole numbers and decimals.

Recognize equivalent fractions and fractions in lowest terms.

Locate rational numbers (whole numbers, fractions, decimals, and mixed numbers) on the number line.

Recognize single-digit factors of a number.

Identify a digit’s place value.

Demonstrate knowledge of elementary number concepts, including rounding, ordering of decimals, pattern identification, primes, and greatest common factor.

Write powers of 10 using exponents.

Comprehend the concept of length on the number line, and find the distance between two points.

Understand absolute value in terms of distance.

Find the distance between two points with the same x-coordinate or y-coordinate in the coordinate plane.

Add, subtract, and multiply matrices (tables of numbers).

Order fractions.

Find and use the least common multiple.

Demonstrate knowledge of complex numbers and multiply two complex numbers.

Comprehend the concept of irrational numbers, such as π.

Apply properties of rational exponents.

Use relations involving addition, subtraction, and scalar multiplication of vectors and matrices.

Analyze and draw conclusions based on number concepts.

Algebra and Functions

The mathematics test contains questions that require knowledge of and skills in algebra, functions, or both. Algebra involves formulas and equations in which letters and other symbols are used to represent unknown or unspecified values. A function is a rule, equation, or expression that produces exactly one output for any given input; for example, 2x is a function in that any input used for x results in an output that is twice the input’s value.

Algebra

Algebra knowledge and skills tested include the following:

Demonstrate knowledge of basic expressions, such as b + g to identify a total.

Solve equations in the form x + a = b, where a and b are whole numbers or decimals.

Use substitution to evaluate mathematical expressions.

Combine like terms, such as 2x + 5x.

Add and subtract algebraic expressions.

Multiply two binomials.

Match inequalities with their graphs on the number line.

Demonstrate knowledge of slope.

Solve real-world problems by using first-degree equations.

Solve inequalities.

Match linear or compound inequalities with their graphs on the number line.

Add, subtract, and multiply polynomials.

Solve quadratic equations.

Factor quadratics.

Work with squares/square roots and cubes/cube roots of numbers.

Work with scientific notation.

Solve problems involving positive integer exponents.

Determine the slope of a line from an equation.

Solve linear inequalities when the method involves reversing the inequality sign.

Solve systems of two linear equations.

Solve absolute value equations and inequalities.

Match quadratic inequalities with their graphs on the number line.

Functions

Questions that involve functions test your ability to do the following:

Understand the concept of a function having a well-defined output value at each valid input value.

Extend a given pattern by a few terms for patterns that have a constant increase or decrease between terms or that have a constant factor between terms.

Evaluate linear, quadratic, and polynomial functions expressed in function notation at the integer level.

Interpret statements that use function notation in terms of their context.

Find the domain of polynomial functions and rational functions.

Find the range of polynomial functions.

Find where a rational function’s graph has a vertical asymptote.

Use function notation for simple functions of two variables.

Relate a graph to a situation described qualitatively in terms of faster change or slower change.

Build functions for relations that are inversely proportional or exponential.

Find a recursive expression for the general term in a sequence described recursively.

Evaluate composite functions of integer values.

Compare actual values and the values of a modeling function to judge model fit and compare models.

Demonstrate knowledge of geometric sequences.

Demonstrate knowledge of unit circle trigonometry.

Match graphs of basic trigonometric functions with their equations.

Use trigonometric concepts and basic identities to solve problems.

Demonstrate knowledge of logarithms.

Write an expression for the composite of two simple functions.

Algebra and Functions

Questions that involve both algebra and functions test your ability to do the following:

Solve problems using whole numbers and decimals in the context of money.

Solve one- or two-step arithmetic problems using positive rational numbers, such as percent.

Relate a graph to a situation described quantitatively.

Solve two- or three-step arithmetic problems involving concepts such as rate and proportion, sales tax, percentage off, and estimation.

Perform word-to-symbol translations.

Solve multistep arithmetic problems that involve planning or converting units of measure (for example, feet per second to miles per hour).

Build functions and write expressions, equations, or inequalities with a single variable for common pre-algebra settings, such as rate and distance problems and problems that involve proportions.

Match linear equations with their graphs in the coordinate plane.

Solve word problems containing several rates, proportions, or percentages.

Build functions and write expressions, equations, and inequalities for common algebra settings.

Interpret and use information from graphs in the coordinate plane.

Solve complex math problems involving percent of increase or decrease or requiring integration of several concepts.

Build functions and write expressions, equations, and inequalities when the process requires planning and/or strategic manipulation.

Analyze and draw conclusions based on properties of algebra and/or functions.

Analyze and draw conclusions based on information from graphs in the coordinate plane.

Identify characteristics of graphs based on a set of conditions or on a general equation, such as y = ax² + c.

Given an equation or function, find an equation or function whose graph is a translation by specified amounts up or down.

Geometry

Geometry questions are based primarily on the mathematical properties and relationships of points, lines, angles, two-dimensional shapes, and three-dimensional objects. Knowledge and skills tested include the following:

Estimate the length of a line segment based on other lengths in a geometric figure.

Calculate the length of a line segment based on the lengths of other line segments that go in the same direction (for example, overlapping line segments and parallel sides of polygons with only right angles).

Perform common conversions of money and of length, weight, mass, and time within a measurement system (for example, inches to feet and hours to minutes).

Compute the area and perimeter of triangles, rectangles, and other polygons.

Use properties of parallel lines to find the measure of an angle.

Exhibit knowledge of basic angle properties and special sums of angle measures (for example, 90°, 180°, and 360°).

Use geometric formulas when all necessary information is given.

Locate points in the coordinate plane.

Translate points up, down, left, and right in the coordinate plane.

Use several angle properties to find an unknown angle measure.

Count the number of lines of symmetry of a geometric figure.

Use symmetry of isosceles triangles to find unknown side lengths or angle measures.

Recognize that real-world measurements are typically imprecise and that an appropriate level of precision is related to the measuring device and procedure.

Compute the perimeter of composite geometric figures with unknown side lengths.

Compute the area and circumference of circles.

Given the length of two sides of a right triangle, find the length of the third side.

Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths.

Determine the slope of a line from points or a graph.

Find the midpoint of a line segment.

Find the coordinates of a point rotated 180° around a given center point.

Use relationships involving area, perimeter, and volume of geometric figures to compute another measure (for example, surface area for a cube of a given volume and simple geometric probability).

Use the Pythagorean theorem.

Apply properties of 30°–60°–90°, 45°–45°–90°, similar, and congruent triangles.

Apply basic trigonometric ratios to solve right-triangle problems.

Use the distance formula.

Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point.

Find the coordinates of a point reflected across a vertical or horizontal line or across y = x.

Find the coordinates of a point rotated 90° across a vertical.

Recognize special characteristics of parabolas and circles (for example, the vertex of a parabola and the center or radius of a circle).

Use relationships among angles, arcs, and distances in a circle.

Compute the area of composite geometric figures when planning and/or visualization is required.

Use scale factors to determine the magnitude of a size change.

Analyze and draw conclusions based on a set of conditions.

Solve multistep geometry problems that involve integrating concepts, planning, and/or visualization.

Statistics and Probability

Statistics is a branch of mathematics that involves the collection and analysis of large quantities of numerical data. Probability is a branch of mathematics that involves calculating the likelihood of an event occurring or a condition existing. Statistics and Probability questions test your ability to do the following:

Calculate averages.

Read and extract relevant data from a basic table or chart, and use the data in a computation.

Use the relationship between the probability of an event and the probability of its complement.

Calculate the missing data value given the average and all other data values.

Translate from one representation of data to another (for example, from a bar graph to a circle graph).

Compute probabilities.

Describe events as combinations of other events (for example, using and, or, and not).

Demonstrate knowledge of and apply counting techniques.

Calculate the average given the frequency counts of all the data values.

Manipulate data from tables and charts.

Use Venn diagrams in counting.

Recognize that when data summaries are reported in the real world, results are often rounded and must be interpreted as having appropriate precision.

Recognize that when a statistical model is used, model values typically differ from actual values.

Calculate or use a weighted average.

Interpret and use information from tables and charts, including two-way frequency tables.

Recognize the concepts of conditional and joint probability and of independence expressed in real-world contexts.

Distinguish among mean, median, and mode for a list of numbers.

Analyze and draw conclusions based on information from tables and charts, including two-way frequency tables.

Understand the role of randomization in surveys, experiments, and observational studies.

Demonstrate knowledge of conditional and joint probability.

Recognize that part of the power of statistical modeling comes from looking at regularity in the differences between actual values and model values.

Integrating Essential Skills

Students learn some of the most useful mathematics before grade 8: rates and percentages; proportional relationships; area, surface area, and volume; average and median; expressing numbers in different ways; using expressions to represent quantities and equations to capture relationships; and other topics. Each year, students should grow in what they can accomplish using learning from prior years. Students should be able to solve problems of increasing complexity, combine skills in longer chains of steps, apply skills in more varied contexts, understand more connections, and increase fluency. In order to assess whether students have had appropriate growth, all questions in this reporting category focus on the higher-level cognitive skills, such as making decisions on how to approach a problem, comparing, reasoning, planning, applying algebra strategically, drawing conclusions, solving novel problems, and the like.

Modeling

Modeling uses mathematics to represent with a model an analysis of an actual, empirical situation. Models often help us predict or understand the actual. However, sometimes knowledge of the actual helps us understand the model, such as when addition is introduced to students as a model of combining two groups. The Modeling reporting category represents all questions that involve producing, interpreting, understanding, evaluating, and improving models. Each modeling question is also counted in the other appropriate reporting categories previously identified. Thus, the Modeling reporting category is an overall measure of how well a student uses modeling skills across mathematical topics.

Reading Test

40 questions, 35 minutes

The reading test comprises four sections, each containing one long or two shorter prose passages that are representative of the level and kinds of text commonly encountered in first-year college curricula. Passages include literary narratives and informational texts from the humanities, natural sciences, and social sciences. One informational passage may include a mixed-information format—visual and quantitative elements (like graphs, diagrams, tables) that acccompany the passage and contain additional information related to the passage topic. The passages vary in terms of how challenging and complex they are.

Four scores are reported for the ACT reading test: a total test score based on all 40 questions, and three reporting category scores based on specific knowledge and skills. You will also see an Understanding Complex Texts indicator.

The reading test measures your reading comprehension in three general areas:

Key Ideas and Details

Craft and Structure

Integration of Knowledge and Ideas

Key Ideas and Details

These questions focus primarily on identifying key details in the passage and grasping the overall meaning of the passage. Reading skills tested fall into these categories:

Close reading

Central ideas, themes, and summaries

Close Reading

Close-reading skills involve your ability to do the following:

Locate and interpret facts or details in a passage.

Draw logical conclusions.

Paraphrase statements.

Identify the sequence of events or place events in their correct sequence.

Identify stated or implied cause-effect relationships.

Identify stated or implied comparative relationships.

Central Ideas, Themes, and Summaries

Questions that focus on central ideas, themes, and summaries challenge your ability to do the following:

Identify or infer the main idea of a paragraph.

Identify or infer the central idea or theme of a passage.

Differentiate key ideas from secondary ideas.

Summarize key ideas and information.

Craft and Structure

Some reading questions go beyond the meaning of the passage to challenge your understanding of how the author crafted and structured the passage. Reading skills tested in this area are divided into three categories:

Word meanings and word choice

Text structure

Purpose and point of view

Word Meanings and Word Choice

Reading questions may focus on the meaning or impact of a word or phrase, challenging your ability to do the following:

Use context to determine the meaning of a word or phrase, including determining technical, academic, and connotative meanings.

Understand the implication of a word or phrase and of descriptive language.

Determine the meaning of figurative language in context.

Text Structure

Text-structure questions ask you to analyze how various structural elements function to serve a specific purpose in the passage. To answer such questions, you may need to do one of the following:

Analyze the overall structure of a passage.

Analyze how one or more sentences in a passage relate to the whole passage.

Identify or infer the function of one or more paragraphs in a passage.

Determine the function or effect of specific words or phrases in a passage.

Purpose and Point of View

The reading test may include questions that challenge your ability to do the following:

Identify or infer the author’s or narrator’s purpose or intent.

Determine how an author’s or narrator’s purpose or intent shapes the content and style of the passage.

Recognize an author’s or narrator’s point of view.

Integration of Knowledge and Ideas

Reading questions may require that you go beyond simply reading and understanding a passage. Some questions will require analyzing two passages. Others may ask you to integrate information from different formats (like graphs, diagrams, and tables). Reading skills tested in the area of Integration of Knowledge and Ideas are divided into three categories:

Arguments

Multiple texts

Mixed-information format

Arguments

Questions in this category may test your ability to do the following:

Identify or infer the central claim being presented in the passage.

Analyze how one or more sentences offer reasons for or support the claim.

Differentiate between fact and opinion.

Recognize errors in reasoning or identify information that would strengthen or weaken a claim in the passage.

Multiple Texts

Multiple-text questions involve reading two passages and may test your ability to do the following:

Make connections between people, relationships, and ideas across the two passages.

Draw logical conclusions using information from the two passages.

Compare text structure, purpose, and perspective in the two passages.

Mixed-Information Format

Though these questions are not as common as questions about arguments and multiple texts, you may also encounter questions that ask you to understand mixed-information formats. These questions test your ability to do the following:

Identify and interpret information represented in quantitative or graphic formats (e.g., graphs, diagrams, tables).

Draw conclusions and compare information across a passage and graphic element.

Science Test

40 questions, 35 minutes

The science test measures the interpretation, analysis, evaluation, reasoning, and problem-solving skills required in the natural sciences: life science/biology; physical science/chemistry, physics; and earth and space science.

The test assumes that students are in the process of taking the core science course of study (three years or more) that will prepare them for college-level work and have completed a course in earth science and/or physical science and a course in biology. The test presents several sets of scientific information, each followed by a number of multiple-choice test questions. The scientific information is conveyed in the form of reading passages and graphic representations—graphs (charts), tables, and illustrations.

Four scores are reported for the ACT science test: a total test score based on all 40 questions and three reporting category scores based on scientific knowledge, skills, and practices. The reporting categories are:

Interpretation of Data

Scientific Investigation

Evaluation of Models, Inferences, and Experimental Results

Interpretation of Data

Interpretation of Data involves the following skills:

Select data from a data presentation (for example, a food web diagram, a graph, a table, or a phase diagram).

Identify features of a table, graph, or diagram (for example, units of measurement).

Find information in text that describes a data presentation.

Understand scientific terminology.

Determine how the values of variables change as the value of another variable changes in a data presentation.

Compare or combine data from one or more data presentations (for example, order or sum data from a table).

Translate information into a table, graph, or diagram.

Perform an interpolation or extrapolation using data in a table or graph (for example, categorize data from a table using a scale from another table).

Determine and/or use a mathematical relationship that exists between data.

Analyze presented information when given new information.

Scientific Investigation

Questions that apply to scientific investigation are typically related to experiments and other research. Such questions challenge your ability to do the following:

Find information in text that describes an experiment.

Understand the tools and functions of tools used in an experiment.

Understand the methods used in an experiment.

Understand experimental design.

Identify a control in an experiment.

Identify similarities and differences between experiments.

Determine which experiments use a given tool, method, or aspect of design.

Predict the results of an additional trial or measurement in an experiment.

Determine the experimental conditions that would produce specified results.

Determine the hypothesis for an experiment.

Determine an alternate method for testing a hypothesis.

Understand precision and accuracy issues.

Predict the effects of modifying the design or methods of an experiment.

Determine which additional trial or experiment could be performed to enhance or evaluate experimental results.

Evaluation of Models, Inferences, and Experimental Results

Some questions on the science test challenge your ability to evaluate models, inferences, and experimental results. (A model is a description of an object or phenomenon intended to explain and predict its behavior.) To answer such questions, you must be able to do the following:

Find basic information in a model.

Identify implications in a model.

Determine which models present certain information.

Determine which hypothesis, prediction, or conclusion is, or is not, consistent with one or more data presentations, models, or pieces of information in text.

Identify key assumptions in a model.

Identify similarities and differences between models.

Determine whether presented information or new information supports or contradicts (or weakens) a hypothesis or conclusion and why.

Identify the strengths and weaknesses of models.

Determine which models are supported or weakened by new information.

Determine which experimental results or models support or contradict a hypothesis, prediction, or conclusion.

Use new information to make a prediction based on a model.

Writing Test (Optional)

1 prompt, 40 minutes

The writing test is a 40-minute essay test that measures your writing skills—specifically those writing skills emphasized in high school English classes and in entry-level college composition courses.

The test asks you to produce an essay in response to a contemporary issue. You will be given a prompt that presents the issue and provides three different perspectives on it. Your task is to write an essay in which you develop a perspective on the issue, providing a convincing rationale through discussion of your perspective’s strengths and weaknesses, and explore how it relates to at least one other perspective, recognizing relationships between or among conflicting views.

Trained readers will evaluate your essay for the evidence it provides of a number of core writing skills. You will receive a total of five scores for this test: four domain scores (provided by two readers) based on an analytic scoring rubric and a single subject-level writing score reported on a scale of 2–12 (reflecting a rounded average of the four domain scores). The four domain scores are

Ideas and Analysis

Development and Support

Organization

Language Use and Conventions

Ideas and Analysis

Effective writing depends on effective ideas. It is important to think carefully about the issue in the prompt and compose an argument that addresses the issue meaningfully, allowing any reader to understand why your argument is worth considering. In evaluating the ideas and analysis in your essay, readers will look for your ability to do the following:

Generate a clear main idea that establishes your perspective on the issue and the thesis that will direct your essay.

Engage with multiple perspectives on the issue by analyzing the relationship between your perspective and at least one other perspective.

Clarify your understanding of the issue and differing perspectives on it by providing a relevant context for discussion, describing the circumstances surrounding the issue and connecting the specific issue in the prompt to a broader situation.

Analyze critical elements such as implications (potential effects of decisions) and complexities (factors that complicate an issue or challenge a perspective).

Development and Support

No single idea should be left to speak for itself. Even the best ideas must be developed and supported to be effective in a written argument. By explaining and illustrating your points, you help the reader understand your thinking. In evaluating this dimension of your essay, readers will look for your ability to do the following:

Clarify your ideas by explaining your reasoning.

Bolster your claims with persuasive examples.

Convey the significance of your perspective by exploring reasons why your ideas are worth considering; address why your argument might be more compelling than another.

Extend your argument by considering qualifications, exceptions, counterarguments, and complicating factors. Convey your understanding of the limitations of your argument, demonstrating to the reader that you have considered its potential weaknesses.

Organization

Organizational choices are essential to effective writing. Guide the reader through your discussion by arranging your ideas according to the logic of your argument, making sure that the connections among ideas are clear. As readers evaluate the organization of your essay, they will look for your ability to do the following:

Unify your essay by making strategic use of a controlling idea, ensuring all ideas are working in service of the thesis, and employing other organizational techniques (e.g., theme or motif).

Group ideas clearly, with each paragraph limited to the discussion of related ideas while still linked to the argument as a whole.

Produce a sequence of ideas that follows a clear logic, both in terms of the argument’s overall structure (e.g., introduction, body, conclusion) and within the argument itself, with each point following logically from the last.

Use transitions to connect ideas, both within paragraphs (e.g., relating claims to support) and across paragraphs (e.g., moving from discussion of one point to that of another).

Language Use and Conventions

Skillful language use enhances argumentative writing. Strategic choices in the vocabulary you use and the style you employ can make your essay more effective. To evaluate your use of language, readers will look for your ability to do the following:

Make precise word choices that communicate your ideas with clarity. Use specific rather than vague terms that enhance understanding (e.g., “a lot of free music is available today” vs. “the endless volumes of free music available today can be overwhelming”).

Demonstrate control over a variety of sentence structures. Use a mixture of simple and complex sentences, exhibiting as much grammatical control over longer sentences as shorter ones.

Match the style of your writing to the audience and purpose (e.g., more evocative language to convey emotional appeals versus a more neutral voice to convey an argument based on reason).

Accurately apply the conventions of grammar, word usage, syntax, and mechanics.

The Fifth Test

ACT is dedicated to meeting professional testing standards. To accomplish this, ACT includes additional questions on the test that do not count toward your score. This practice ensures that ACT develops questions that are fair and of the highest possible quality.

If you are taking the full ACT test, you should expect to take a 20-minute fifth test that includes additional questions.

ACT Test Formats: Paper and Online

The ACT is available as a paper test and as an online test in certain states and educational districts. Some sections may look slightly different online than they do on paper. For example, English items may be indicated by highlighted text instead of underlining, or you may see highlighted asterisks in brackets in the essay instead of numbers in boxes. Likewise, reading items may refer to highlighting in the passage instead of containing line references. Regardless of format, what is most important is the knowledge and skills you have developed over your course of study. If you know the material, whether you choose answers by marking them on paper or clicking an option on a computer screen will likely make little difference.

Using a Calculator

You may use a permitted calculator only on the mathematics test, but you are not required to do so. All math problems on the test can be solved without a calculator, and you may be able to perform some of the math more quickly in your head or on scratch paper.

Note: You may use any four-function, scientific, or graphing calculator as long as it is a permitted calculator modified, if necessary, as described in the following. For additional details and ACT’s most current calculator policy, visit www.act.org/the-act/testday.

Certain types of calculators, including the following, are prohibited:

Calculators with built-in or downloaded computer algebra system (CAS) functionality, including the TI-89, TI-92, TI-Nspire CAS, HP Prime, HP 48GII, HP 40G, HP 49G, HP 50G, fx-ClassPad 400, ClassPad 300, ClassPad 330, and all Casio models that start with CFX-9970G. (Using the TI-89 is the most common reason students are dismissed from the ACT for prohibited calculator use.)

Handheld, tablet, or laptop computers, including PDAs.

Electronic writing pads or pen-input devices (the Sharp EL 9600 is permitted).

Calculators built into cell phones or any other electronic communication devices.

Calculators with a typewriter keypad (letter keys in QWERTY format). This does not apply to calculators that are provided in a secure test delivery platform. Letter keys not in QWERTY format are permitted.

The following types of calculators are permitted but only after they are modified as noted:

Calculators that can hold programs or documents (remove all documents and all programs that have CAS functionality).

Calculators with paper tape (remove the tape).

Calculators that make noise (mute the device).

Calculators with an infrared data port (completely cover the infrared data port with heavy opaque material, such as duct tape or electrician’s tape). These calculators include the Hewlett-Packard HP 38G series, HP 39G series, and HP 48G.

Calculators that have power cords (remove all power and electrical cords).

Accessible calculators (such as audio-talking or braille calculators) may be allowed under the accessibility policies for the ACT test. (Visit www.act.org for details.)

If you choose to use a calculator during the mathematics test, follow these guidelines:

Use a calculator you are accustomed to using. A more powerful, but unfamiliar, calculator may be a disadvantage. If you are unaccustomed to using a calculator, practice using it when you take the practice tests in this book, so you are comfortable with using it in a test situation.

Sharing calculators during the test is not permitted.

Make sure your calculator works properly. If your calculator uses batteries, the batteries should be strong enough to last throughout the testing session.

Bring a spare calculator and/or extra batteries.

In a computer-based testing environment:

An on-screen calculator may be available.

Calculators may not be connected in any way to the computer or device being used for testing.

Taking the Test

Knowing what to expect on test day can alleviate any anxiety you may feel. The following list describes the steps you will take through the testing day:

You must report to the test center by the reporting time.

If you are testing on a national test date and are taking the full ACT test, the reporting time is 8:00 AM.

You will need to bring the following:

A printed copy of your ACT admission ticket, which contains important match information that cannot be found anywhere else. Failure to bring your admission ticket will delay your scores.

Acceptable photo ID; if you do not bring acceptable photo ID, you will not be allowed to take the test.

Sharpened no. 2 soft-lead pencils with good erasers (no mechanical pencils or ink pens).

A permitted calculator, if you would like to use one.

If you are testing during the week day at your school through state and district testing, the reporting time will be at the same time you usually report for school.

You will need to bring the following:

Acceptable photo ID

Sharpened no. 2 soft-lead pencils with good erasers (no mechanical pencils or ink pens)

A permitted calculator, if you would like to use one

(Note: You will not be admitted to test if you are late or if your ID does not meet ACT’s requirements.)

When all examinees present at the reporting time are checked in and seated, wait until you are notified to start the test.

A short break is scheduled after the first two tests. You are prohibited from using a cell phone or any electronic device during the break, and you may not eat or drink anything in the test room. (If you take the ACT with writing, you will have time before the writing test to relax and sharpen your pencils.)

When time has expired, paper tests are collected. Online tests must be submitted prior to your dismissal.

Note: If you do not complete all your tests for any reason, tell a member of the testing staff whether or not you want your answer document or online test to be scored before you leave the test center. If you do not, all tests attempted will be scored.

Summary

This book should help you to understand how to get ready to take the ACT. Knowing the basics should get you started. By now, you should have a fair idea of what to expect at the test center and know where to find more information: on ACT’s website at www.act.org. Now that you know the basic information, you should be ready to start preparing for the ACT.

Prep Online!

Want even more ways to prep? Go to act.wiley.com to access our online platform or use our companion app. Take online practice tests and track your progress, create your own question sets, and use flash cards to practice. Flag difficult or confusing questions for review. To get started, go to act.wiley.com, and register with the PIN on the back of the front cover of this book. Once registered, you can also use our companion app if you prefer to study from your mobile device.

Chapter 2:
Preparation, Skills, and Strategies

Performance on the ACT is largely influenced by two factors: the knowledge and skills you acquire over your many years of formal education and your familiarity with the test format and questions.

The best preparation for the ACT is taking rigorous high school classes. If you’ve taken challenging courses, paid attention in class, and completed your assignments satisfactorily, you’ve already done much of the preparation required to do well on the ACT.

Your familiarity with the test format and questions and your comfort and confidence in tackling the ACT also play an important role in how well you do on the test. Of course, no test-taking strategy can help you choose the correct answer when you don’t understand the question or don’t have the knowledge and skills to answer it, but certain strategies and skills can help you avoid common mistakes that will lower your score, such as misreading an answer choice or spending too much time on any given question.

The suggestions in this chapter are designed to help you build on the preparation that you have already completed. They’re taken from advice gathered over years—from education specialists, testing specialists, and people who, similar to you, have taken lots of tests. Read the advice, try it out, and see whether it helps. Realize that you can choose how you will take the ACT. Then make intelligent choices about what will work for you.

Mental Preparation

The best mental preparation for the ACT is rigorous course work, but mental preparation also involves confidence and clear thinking. The following tips will help make you feel calmer and more confident so that you’ll do your very best on the ACT.

Identify Strengths and Address Areas of Improvement

One of the best ways to prepare mentally for the test is to identify your strengths and areas of improvement, then work toward addressing the areas that may hamper your performance on the test. For example, if time expires before you have a chance to answer all of the questions on a practice test, you need to work on pacing. If you struggle to comprehend word problems in math, you need to practice solving more word problems. However, if you breeze through reading comprehension questions, you might not need to spend time improving your reading comprehension skills.

The following sections explain how to identify strengths and areas of improvement and address issues that may hamper your performance on the test.

Take the First Practice Test

To evaluate your ACT readiness take the first practice test in chapter 3 and analyze the results, as instructed in chapter 4. The test-taking experience and the results will help reveal your strengths and areas of improvement. If you do well on the first practice test, you can be confident that you know the material and are comfortable with the test format. You may decide to take additional practice tests for confirmation or review the test-taking skills in this chapter and in chapters 5 through 9 to see whether they can help you do even better.

If your performance on the first practice test falls short of your goal, you may need to do additional course work in certain subject areas or invest additional time and effort developing effective test-taking strategies and skills. Do not be discouraged if you do not meet your goal on the practice test. Be thankful that your areas for improvement were identified prior to test day and that you now have the information you need to formulate your improvement plan.

Identify Subject Areas to Review

Some students do better in certain subjects than in others. The practice tests in this book will help you identify your stronger and weaker subjects. As you take and score the practice tests, create a list of the subject areas and types of questions you struggle to answer. For example, if you had trouble answering math questions about angles in a triangle, the circumference of a circle, the volume of a cube, the relationships among parallel and perpendicular lines, and so forth, you may need a refresher course in plane geometry.

When taking practice tests on the online platform (act.wiley.com), you can flag questions that you found difficult or confusing. Then, on the Metrics tab, you can click on any assessment to view a list of flagged questions. Use this list to look for patterns and prioritize subjects to review and practice.

Chapter 1 includes a list of subject areas covered on each portion of the ACT to help you categorize the questions you answered incorrectly and identify subject areas you need to study or review.

Plan Your Practice and Study Time

To stay on track leading up to test day, set up a reasonable schedule to practice and study for the ACT. Set aside small amounts of time for studying over an extended period—days, weeks, or even months—so you won’t feel the need to cram in the days leading up to the test.

Make your schedule flexible enough to allow for a surprise homework assignment or some unexpected fun. And find a way to reward yourself as you get the work done, even if it’s just a checklist you can mark to show your progress. A flexible schedule with regular rewards will prevent burnout while keeping you motivated.

Develop a Positive Mental Attitude

Approach the ACT confident that you will do your best. Although confidence alone obviously isn’t enough to ensure good performance on a test, doubt and fear can hurt your performance. Be confident in your ability to do well on the ACT. You will do well! You just need to be prepared.

Some small changes can make a surprising difference. For example, how you imagine yourself taking the exam may affect how well you actually do. Negative thoughts have a way of generating negative results. So practice positive thinking; imagine yourself meeting the challenge of the exam with ease. The day of the test, tell yourself you intend to do your best, and believe it.

Keep the Test in Perspective

Remembering that the ACT is only one part of the process of your education and training will help you keep it in perspective. So will remembering that the ACT and tests similar to it are designed to provide you with feedback and direction. Your scores can help make decisions about your future education and career choices. Think of the test as an opportunity to get to know more about yourself, not as a potential barrier to your future plans.

Another way to keep the ACT in perspective is to use the test as an opportunity to identify careers that match your interests, abilities, and values; explore suitable college majors; and start choosing high school courses that align with your future education and career goals.

General Test-Taking Strategies and Skills

How you approach the ACT and various types of questions, how well you manage your time, whether you change answers, and other factors may affect how well you do on the ACT. The following sections present a few test-taking strategies and skills to help you perform to the best of your ability.

Remain Calm

When you’re under pressure during a test, an unexpected question or a minor incident such as breaking a pencil can be very upsetting. For many students, the natural tendency at such times is to panic. Panic detracts from test performance by causing students to become confused and discouraged and to have trouble recalling information they know.

It’s a good idea to have a strategy ready for dealing with incidents that might rattle your nerves. One effective strategy is to take a brief time out to center yourself. Take slow, deep breaths and let yourself relax. Put the test temporarily out of mind. Close your eyes if you want. Visualize yourself confidently resuming work on the test, turning in a completed answer document, and leaving the room with a feeling of having done your best work. Allow 20 to 30 seconds for your time out, which is probably all you’ll need to regain your composure.

Pace Yourself

The ACT, similar to many tests, must be completed within a specific and limited amount of time. Working quickly and efficiently is one of the skills necessary for conveying how much you’ve learned in the subject area being tested.

To develop an effective, efficient pace, time yourself as you take the practice tests. If time expires before you have a chance to answer all the questions, you know that you need to work faster next time. If you rushed through the test, had time remaining at the end, and made careless mistakes, you know that you will need to work at a more relaxed pace and be more careful in answering questions.

Warning: Don’t try to push yourself to work so fast that you make errors. Answering 50 questions carefully and correctly and leaving 10 unanswered is better than answering 60 questions too quickly and missing 20 because of mistakes.

Although you won’t want to lose time by being distracted, you shouldn’t obsess about time either. Use all of the time available so you can do your very best on the test.

Some people suggest more formal methods for pacing yourself by allocating a certain amount of time per question or set of questions, as in the following examples:

Divide the available time by the number of questions. For example, on the mathematics test, divide 60 minutes by 60 questions, and you know you have 1 minute per question.

Divide the available time into different stages of the writing process. If you’re taking the optional writing test, you may want to allocate the time to planning, writing, and revising/editing your essay. Keep in mind that you probably won’t have enough time to fully draft, revise, and then recopy your essay, so spending a few minutes planning your essay before you start writing it is usually wise.

Keep in mind that these strategies are not foolproof, that some questions will take you longer to answer than others, and that doing the math to calculate your time allocations takes time. You may be better off developing a feel for the time and occasionally checking the clock to make sure you’re on track to finish, perhaps with a few minutes remaining at the end to check answers you were unsure of. If you want to keep track of your pace while taking the ACT, bring a watch. Not all testing centers have wall clocks.

Know the Directions Ahead of Time

You can save yourself precious moments on the ACT by being familiar with the directions ahead of time. Then, when taking the test, you can read the directions to refresh your memory instead of having to spend time and mind power processing those directions. For example, the ACT English, reading, and science tests ask for the “best” answer, and the mathematics test asks for the “correct” answer. This simple difference in the instructions signals an important distinction to keep in mind as you’re working through those tests. Because only one answer is “correct” in the mathematics test, you’ll want to be sure your understanding of the question and your calculations are precise—so that your answer matches one, and only one, of the possible answers. In the other tests, more than one of the possible answers may be correct to some degree, and you’ll need to be careful to select the “best” answer among those potentially “correct” ones. You’ll find the directions for each test in the practice ACT tests in this book.

The directions for the writing test are also very important, because they spell out the aspects of writing that will be evaluated. They also tell you where in the test booklet you can plan your essay and where you should write your final version. The directions for the writing test and a sample answer document appear in the practice ACT tests in this book.

Before you take the ACT, become familiar with the answer document. Knowing in advance how to use the answer document will save you time and prevent worry when you take the actual ACT.

Read Carefully and Thoroughly

Just as it’s important to read and understand the directions for a test, it’s also important to read and understand each question and answer choice on the test. As you’ve probably discovered somewhere along the line, you can miss even the simplest test question by reading carelessly and overlooking an important word or detail. Some questions on the ACT, for instance, require more than one step, and the answer to each preliminary step may be included as an answer choice. If you read these questions too quickly, you can easily make the mistake of choosing a plausible answer that relates to a preliminary step but is the incorrect answer to the question.

Take the time to read each question carefully and thoroughly before choosing your answer. Make sure you understand exactly what the question asks and what you are to do to answer it. You may want to underline or circle key words in the test booklet (see the later section “Write Notes in Your Test Booklet”). Reread the item if you are confused.

Watch the question’s wording. Look for words such as not or least, especially when they are not clearly set off with underlining, capital letters, or bold type. Don’t make careless errors because you only skimmed the question or the answer choices. Pay close attention to qualifying words such as all, most, some, none; always, usually, seldom, sometimes, never; best, worst; highest, lowest; smaller, larger. (There are many other qualifying words; these are only a few examples of related groups.) When you find a qualifier in one of the responses to a question, a good way to determine whether or not the response is the best answer is to substitute related qualifiers and see which makes the best statement. For example, if a response says, “Tests are always difficult,” you might test the truth of the word always by substituting sometimes and the other words related to always. If any of the words other than the one in the answer makes the best statement, then the response is not the best answer.

Pay close attention to modifying or limiting phrases in the statement. For instance, a question in the reading test might have the following as a possible answer: “Lewis and Clark, the great British explorers, began their historic trip to the West Coast by traveling up the Mississippi.” The answer is incorrect because Lewis and Clark were not British but were US citizens. (You would not be expected to know from memory that Lewis and Clark were US citizens; that information would be included in the passage.)

Read all the answer choices before selecting one. Questions on the ACT often include answer choices that seem plausible but aren’t quite correct. Even though the first answer choice may appeal to you, the correct or best answer may be farther down the list.

When taking the writing test, read the writing prompt carefully. Before you start to plan your essay, make sure you understand the writing prompt and the specific issue it asks you to respond to.

Choose Strategies for Answering Easier and More Difficult Questions

A strategy for taking the ACT is to answer the easy questions first and skip the questions you find difficult. After answering all of the easy questions, go back and answer the more difficult questions, as time permits. When you skip a question, mark it in the test booklet (but not on the answer document), so you can quickly flip back to it later. Also, make absolutely sure that on the answer document, you skip the set of answer choices that correspond to the question you skipped.

Use Logic on More Difficult Questions

When you return to more difficult questions, use logic to eliminate incorrect answer choices. Compare the remaining answer choices and note how they differ. Such differences may provide clues as to what the question requires. Eliminate as many incorrect answer choices as you can, then make an educated selection from the remaining choices. See the next section for additional guidance.

Choose a Strategy for Guessing on Multiple-Choice Questions

On some standardized tests, you’re penalized for each incorrect answer. On the ACT multiple-choice tests, however, your raw score is based on the number of questions you answer correctly—nothing is deducted for wrong answers.

Because you’re not penalized for guessing on the ACT, answering every question is advantageous. Here’s a good way to proceed:

If a question stumps you, try to eliminate wrong choices. Narrowing your choices increases your odds of guessing the correct answer.

If you still aren’t sure about the answer, take your best guess.

You don’t need a perfect reason to eliminate one answer and choose another. Sometimes an intelligent guess is based on a hunch—on something you may know but don’t have time to consciously recognize in a timed-test situation.

Maybe you’ve heard some advice about how to answer questions when you don’t know the correct answer, such as “When in doubt, choose ‘C,’ ” or “When in doubt, select the longest (or shortest) alternative,” or “If ‘none of the above’ (or a similar response) is among the answer choices, select it.” Although these bits of advice may hold true now and then, the questions on the ACT have been carefully written to make these strategies ineffective.

Choose a Strategy for Changing Answers

You think you marked the wrong answer choice on a certain question. Do you go with your original answer or change it to the new answer? Some people advise always going with your first response. And surely everyone has had the experience of agonizing over a response, trying to decide whether to change it, then doing so only to find out later that the first answer was the correct one.

However, some research by education and testing specialists suggests that you should change your answer when you change your mind. If you’re like the test-takers in the study, your second answer is more likely to be the correct one.

So, how can you decide what to do? Before you change an answer, think about how you approached the question in the first place. Give some weight to the reasons why you now believe another answer is better. Don’t mechanically follow an arbitrary rule just because it works for somebody else. Know yourself; then trust yourself to make intelligent, informed decisions.

Write Notes in Your Test Booklet

You’re allowed to write in the test booklet, so feel free to write notes in the test booklet to flag key details or to work out a problem on paper.

Mark Your Answers Carefully

Only answers marked on the answer document during the time allowed for a particular test will count. Carefully mark your answers on the answer document as you work through the questions on each test.

Remember that during an actual test you may not fill in answers or alter answers on your answer document after “stop” is called.

For the writing test, writing (or printing) legibly in English in the correct place in the test booklet is vital. If readers cannot read what you have written, they will be unable to score your essay. You are allowed to write in cursive or print your essay, but you must do so clearly. Keep in mind, you must write your essay using a soft-lead pencil (not a mechanical pencil). You must write on the lined pages in the answer folder. If you make corrections, do so thoroughly. You may write corrections or additions neatly between the lines of your essay, but you may not write in the margins.

Plan to Check Your Answers

When you reach the end of one of the ACT tests with several minutes to spare, you may feel you’ve done quite enough. Resist the temptation to rest. Use the remaining time to check your work, as follows:

For the multiple-choice tests, be sure you’ve marked all your answers in the proper section on the answer document.

Be certain you’ve answered all the questions on your answer document, even the ones you weren’t sure about. (Of course, you must be very careful to stop marking ovals when time is called.)

When you reach the end of the mathematics test, check your calculations. You may check your calculations using the test booklet or scratch paper, or using a permitted calculator (see chapter 1).

Check your answer document for stray pencil marks that may be misread by the scoring machine. Erase any such marks cleanly and completely.

Be sure you’ve marked only one answer on your answer document for each question.

If there are too many questions for you to check all of your answers, be sure to check those that you feel most uncertain about first, then any others that you have time for on that test.

At the end of the writing test, take a few minutes to read over your essay. Correct any mistakes in spelling, grammar, usage, or punctuation. If you see any words that are difficult to read, rewrite them so they’re legible. Make any revisions neatly between the lines (but do not write in the margins).

Learn Strategies for Specific Tests

In addition to the general test-taking strategies presented in the preceding sections there are specific strategies for each of the ACT tests. For example, on the mathematics test, if a question includes an illustration, you may want to write dimensions given in the question on the illustration to help you visualize what the question is asking. In part 3 of this book, the chapters provide test-taking tips for each of the ACT tests along with additional information that reveals the types of questions you can expect to encounter on each test.

Summary

All the strategies outlined in this chapter are merely suggestions intended to give you ideas about good preparation habits and strategies for getting through the ACT in the best, most efficient manner possible. Some of the strategies will work for you, others won’t. Feel free to pick and choose from among all the strategies in this chapter, as well as the more specific strategies in part 3, so that you have a test-taking plan that works best for you.

Prep Online!

Want even more ways to prep? Go to act.wiley.com to access our online platform or use our companion app. Take online practice tests and track your progress, create your own question sets, and use flash cards to practice. Flag difficult or confusing questions for review. To get started, go to act.wiley.com, and register with the PIN on the back of the front cover of this book. Once registered, you can also use our companion app if you prefer to study from your mobile device.

NOTES

Part Two:
Taking and Evaluating Your First Practice Test

In This Part

In this part, you have the opportunity to take, score, and evaluate your first practice test. This exercise enables you to identify your strengths and weaknesses, so you can develop an efficient study plan that focuses on areas where you need the most improvement. In this part, you will do the following:

Simulate testing conditions, so you become acclimated to the conditions you will experience on test day.

Take a complete practice test comprising all five ACT tests—English, mathematics, reading, science, and the optional writing test.

Score your test to gauge your overall performance.

Review explanatory answers to understand why you answered each question correctly or incorrectly.

Determine whether you need to work more on subject matter or on test-taking strategies and skills.

Analyze your performance on each test to gain better insight on the knowledge and skills in greatest need of improvement.

Chapter 3:
Taking and Scoring Your First ACT Practice Test

In this chapter, you take the first of the six practice tests in this book, score the test, and review the answers with explanations. We encourage you to take the test under conditions similar to those you will encounter on test day and to try your very best.

After you take and score the test and review the answers, you will be well poised to analyze your performance in chapter 4. The results of this first practice test will help you identify subject areas you may need to review and test-taking strategies, such as pacing, that you may want to work on prior to test day.

Simulating Testing Conditions

Taking the practice tests can help you become familiar with the ACT. We recommend that you take the tests under conditions that are as similar as possible to those you will experience on the actual test day. The following tips will help you make the most of the practice tests:

The four multiple-choice tests require a total of 2 hours and 55 minutes. Try an entire practice test in one sitting, with a 10-minute break between the mathematics test and the reading test. (If you are taking the writing test, you may also take a break of roughly 5 minutes after the science test.)

Sit at a desk with good lighting. You will need sharpened no. 2 pencils with good erasers. You may not use mechanical pencils or highlight pens. Remove all books and other aids from your desk. On test day, you will not be allowed to use references or notes. Scratch paper is not needed as each page of the mathematics test has a blank column that you can use for scratch work. In some circumstances you are not permitted to write in your test booklet. In those circumstances, you’ll be given scratch paper, and you can use it to jot down the numbers of the questions you skip.

If you plan to use a calculator on the mathematics test, review the details about permissible calculators on ACT’s website, www.act.org. Use a calculator with which you are familiar for both the practice test and on the test day. You may use any four-function, scientific, or graphing calculator on the mathematics test, except as specified on ACT’s website and in chapter 1.

Use a digital timer or clock to time yourself on each test. Set your timer for 5 minutes less than the allotted time for each test so you can get used to the 5-minute warning. (Students approved for self-paced extended time should set a timer for 60-minute warnings up to the total time allowed—5 hours for the multiple-choice tests. If you take the optional writing test, you will then have an additional hour to complete that test.)

Did you know? Our online platform practice tests time you automatically! Go to act.wiley.com to prep online or use our companion app.

Allow yourself only the time permitted for each test.

Detach and use one sample multiple-choice answer document.

Read the general test directions on the first page of the practice test. After reading the directions, start your timer and begin with the English test. Continue through the science test, taking a short break between the mathematics test and the reading test. If you do not plan to take the ACT writing test, score your multiple-choice tests using the information beginning on page 101.

If you plan to take the writing test, take a short break after the science test. Detach (or photocopy) the writing test answer document that follows the writing test planning pages. Then read the test directions on the first page of the practice ACT writing test. After reading the directions, start your timer, then carefully read the prompt. After you have considered what the prompt is asking you to do, use the pages provided to plan your essay, and then write your essay on the answer document. After you have finished, score your essay using the information beginning on page 108.

Scoring Your Practice Test

After taking your first ACT practice test, you are ready to score the test to see how you did overall. In this chapter, you learn how to determine your raw score, convert raw scores to scale scores, compute your Composite score, determine your estimated percentile ranks for each of your scale scores, and score your practice writing test.

Prep Online!

Practice tests taken on the online platform are scored automatically, allowing you to review your performance and see important areas to focus on right away.

When scoring each practice test and reviewing your scores, remember that your scores on the practice tests are only estimates of the scores that you will obtain on the ACT. If your score isn’t as high as you expected, it could mean a number of things. Maybe you need to review important content and skills. Maybe you should work a little faster when taking the test. Perhaps you simply weren’t doing your best work on the test. Or maybe you need to take more challenging courses to be better prepared. Keep in mind that a test score is just one indicator of your level of academic knowledge and skills. You know your own strengths and weaknesses better than anyone else, so keep them in mind as you evaluate your performance.

On each of the four multiple-choice tests (English, mathematics, reading, and science), the number of questions you answer correctly is called a raw score. To figure out your raw scores for the practice tests in this book, count all your correct answers for each test using the scoring keys provided in the next section, “Scoring Your Multiple-Choice Practice Tests.” Then you can convert your raw scores into scale scores.

A raw score is converted to a scale score to enhance score interpretation and allow comparability across different forms. Scale scores are the scores that ACT reports to students, high schools, colleges, and scholarship agencies. One of the reasons ACT uses scale scores is to adjust for small differences among different forms of the ACT. After you’ve converted your raw scores for the practice tests to scale scores, you’ll want to convert your scale scores to percentile ranks. Percentile ranks, which are explained in the following pages, are useful for interpreting your scores relative to the scores of others who have taken the ACT.

If you took the optional practice writing test, the later section “Scoring Your Practice Writing Test Essay” includes an analytic rubric for evaluating your essay and estimating your writing test score. Although it is difficult to be objective about one’s own work, it is to your advantage to read your own writing critically. Becoming your own editor helps you grow as a writer and as a reader, so it makes sense for you to evaluate your own practice essay. However, it likely will be helpful for you to give your practice essay to another reader to get another perspective: perhaps that of a classmate, a parent, or an English teacher, for example. To rate your essay, you and your reader should read the analytic rubric on pages 109–110 and the examples on pages 299–325, and then assign your practice essay a score of 1 (low) through 6 (high) in each of the four writing domains (Ideas and Analysis, Development and Support, Organization, and Language Use and Conventions).

Your writing test domain scores are based on the analytic rubric used to score the essays, whereas the overall score is calculated from the four domain scores.

Finally, convert your writing test score to percentile ranks using the procedures described. Percentile ranks enable you to compare your writing test score to those of others who have taken the writing test.

Scoring Your Multiple-Choice Practice Tests

To score your multiple-choice practice tests, follow these eight steps:

STEP 1. Write a “1” in the blank for each English test question that you answered correctly. An example is provided in the box below:

Key

Your answer was

1.

A

Incorrect

2.

J

1

Correct

3.

B

1

Correct

4.

G

Incorrect

English ■ Scoring Key ■ Practice Test 1

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

C

G

A

J

A

F

C

F

C

J

B

F

B

J

D

G

A

G

D

G

A

J

C

F

D

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

H

C

G

D

G

D

G

B

F

A

G

A

F

C

J

D

G

C

J

B

J

A

H

D

J

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

A

H

A

J

B

F

C

G

C

J

A

H

A

G

C

J

D

H

D

G

C

H

D

F

B

STEP 2. Compute your total number correct for the English test by adding the numbers you entered in Step 1. Write this total in the blank in the shaded box below. This is your raw score.

Number Correct (Raw Score) for:

Total Number Correct for English Test (75 questions)

STEP 3. Repeat Steps 1 and 2 for the ACT mathematics, reading, and science tests using the scoring keys on this page and the following page,

Mathematics ■ Scoring Key ■ Practice Test 1

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

C

H

E

H

E

G

E

F

C

H

B

J

B

G

B

F

B

K

D

G

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

A

G

C

G

C

F

C

H

D

J

D

F

B

H

B

J

E

H

A

H

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

C

G

A

J

D

J

B

H

A

F

B

F

A

K

A

J

C

F

A

J

Number Correct (Raw Score) for:

Total Number Correct for Math Test (60 questions)

Reading ■ Scoring Key ■ Practice Test 1

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

C

F

B

H

A

J

B

J

D

G

C

F

B

H

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

A

H

B

J

A

F

B

G

D

G

D

H

C

G

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

A

G

A

H

C

F

A

J

C

G

D

J

Number Correct (Raw Score) for:

Total Number Correct for Reading Test (40 questions)

Science ■ Scoring Key ■ Practice Test 1

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

B

G

B

F

D

J

B

J

A

G

A

F

B

F

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

C

G

C

F

B

G

A

F

D

H

D

J

B

H

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

B

F

C

J

D

H

C

G

D

H

D

H

Number Correct (Raw Score) for:

Total Number Correct for Science Test (40 questions)

STEP 4. On each of the four tests, the total number of correct responses yields a raw score. Use the conversion table on the following page to convert your raw scores to scale scores. For each of the four tests, locate and circle your raw score or the range of raw scores that includes it in the conversion table. Then, read across to either outside column of the table and circle the scale score that corresponds to that raw score. As you determine your scale scores, enter them in the blanks provided below. The highest possible scale score for each test is 36. The lowest possible scale score for any of the four tests is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

STEP 5. Compute your Composite score by averaging the four scale scores. To do this, add your four scale scores and divide the sum by 4. If the resulting number ends in a fraction, round it off to the nearest whole number. (Round down any fraction less than one-half; round up any fraction that is one-half or more.) Enter this number in the appropriate blank below. This is your Composite score. The highest possible Composite score is 36. The lowest possible Composite score is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

Composite Score (sum ÷ 4)

Scale Score Conversion Table: Practice Test 1

Scale Score

Raw Score

Scale Score

English

Mathematics

Reading

Science

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

73–75

69–72

68

67

65–66

64

63

62

60–61

59

57–58

55–56

52–54

49–51

46–48

43–45

40–42

38–39

37

35–36

32–34

29–31

27–28

25–26

23–24

20–22

17–19

15–16

12–14

10–11

8–9

6–7

5

3–4

2

0–1

58–60

55–57

54

52–53

51

50

48–49

46–47

44–45

42–43

40–41

38–39

36–37

34–35

32–33

31

29–30

27–28

25–26

22–24

18–21

15–17

11–14

9–10

7–8

6

5

4

–

3

2

–

1

–

–

0

39–40

38

37

36

35

34

33

–

32

31

30

29

28

26–27

25

23–24

22

20–21

19

17–18

16

14–15

13

11–12

9–10

8

7

6

5

4

–

3

2

–

1

0

39–40

38

37

36

35

34

33

32

31

30

29

27–28

25–26

23–24

22

20–21

19

17–18

16

14–15

12–13

11

10

9

8

7

6

5

4

–

3

2

–

1

–

0

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

STEP 6. Use the table on page 107 to determine your estimated percentile ranks (percent at or below) for each of your scale scores. In the far left column of the table, circle your scale score for the English test (from page 105). Then read across to the percentile rank column for that test; circle or put a checkmark beside the corresponding percentile rank. Use the same procedure for the other three tests (from page 105). Using the right-hand column of scale scores for your science test and Composite scores may be easier. As you mark your percentile ranks, enter them in the blanks provided. You may also find it helpful to compare your performance with the national mean (average) score for each of the four tests and the Composite as shown at the bottom of the table.

National Norms for ACT Test Scores Reported During the 2020–2021 Reporting Year

Score

English

Math

Reading

Science

Composite

STEM

Score

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

100

99

96

94

92

91

89

88

86

84

82

79

75

71

65

60

55

49

45

41

37

32

25

19

15

11

7

3

2

1

1

1

1

1

1

1

100

99

99

98

97

96

94

93

91

88

84

79

74

70

65

61

58

54

49

42

33

21

11

4

1

1

1

1

1

1

1

1

1

1

1

1

100

98

96

94

91

89

86

84

82

80

77

74

71

66

61

55

50

44

39

34

29

24

19

14

10

5

3

1

1

1

1

1

1

1

1

1

100

99

98

97

96

95

93

92

90

88

85

82

77

71

64

58

51

45

39

32

26

19

14

10

7

4

3

1

1

1

1

1

1

1

1

1

100

99

99

98

96

95

93

90

88

85

82

78

74

70

64

59

53

47

41

35

28

22

16

10

5

2

1

1

1

1

1

1

1

1

1

1

100

99

99

98

97

96

94

92

90

87

84

80

75

70

65

60

54

48

41

33

26

18

11

5

2

1

1

1

1

1

1

1

1

1

1

1

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Mean:

20.1

20.4

21.2

20.6

20.7

20.7

SD:

7.1

5.6

6.9

5.8

5.9

5.5

Note: These national norms are the source of U.S. Ranks, for multiple-choice tests, displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 5,368,134, are based on 2018, 2019 and 2020 graduates.

Scoring Your Practice Writing Test Essay

To score your practice writing test essay, follow these steps:

STEP 1. Use the analytic rubric on the following two pages to score your essay. Because many essays do not fit the exact description at each score point, read each description and try to determine which paragraph in the rubric best describes most of the characteristics of your essay.

Critiquing your own writing can be difficult. If possible, ask a trusted source to help you use the rubric and determine your score. If you must evaluate your essay on your own, try to be as objective as you can and remember that any reader of your essay would understand only what you wrote, not what you meant to write. In either case, you may find it useful to consult chapters 4 and 9 for additional information regarding the rubric and sample essays to which you can compare your own.

The ACT Writing Test Analytic Rubric

Ideas and Analysis

Development and Support

Organization

Language Use and Conventions

Score 6:

Responses at this scorepoint demonstrate effective skill in writing an argumentative essay.

The writer generates an argument that critically engages with multiple perspectives on the given issue. The argument’s thesis reflects nuance and precision in thought and purpose. The argument establishes and employs an insightful context for analysis of the issue and its perspectives. The analysis examines implications, complexities and tensions, and/or underlying values and assumptions.

Development of ideas and support for claims deepen insight and broaden context. An integrated line of skillful reasoning and illustration effectively conveys the significance of the argument. Qualifications and complications enrich and bolster ideas and analysis.

The response exhibits a skillful organizational strategy. The response is unified by a controlling idea or purpose, and a logical progression of ideas increases the effectiveness of the writer’s argument. Transitions between and within paragraphs strengthen the relationships among ideas.

The use of language enhances the argument. Word choice is skillful and precise. Sentence structures are consistently varied and clear. Stylistic and register choices, including voice and tone, are strategic and effective. While a few minor errors in grammar, usage, and mechanics may be present, they do not impede understanding.

Score 5:

Responses at this scorepoint demonstrate well-developed skill in writing an argumentative essay.

The writer generates an argument that productively engages with multiple perspectives on the given issue. The argument’s thesis reflects precision in thought and purpose. The argument establishes and employs a thoughtful context for analysis of the issue and its perspectives. The analysis addresses implications, complexities and tensions, and/or underlying values and assumptions.

Development of ideas and support for claims deepen understanding. A mostly integrated line of purposeful reasoning and illustration capably conveys the significance of the argument. Qualifications and complications enrich ideas and analysis.

The response exhibits a productive organizational strategy. The response is mostly unified by a controlling idea or purpose, and a logical sequencing of ideas contributes to the effectiveness of the argument. Transitions between and within paragraphs consistently clarify the relationships among ideas.

The use of language works in service of the argument. Word choice is precise. Sentence structures are clear and varied often. Stylistic and register choices, including voice and tone, are purposeful and productive. While minor errors in grammar, usage, and mechanics may be present, they do not impede understanding.

Score 4:

Responses at this scorepoint demonstrate adequate skill in writing an argumentative essay.

The writer generates an argument that engages with multiple perspectives on the given issue. The argument’s thesis reflects clarity in thought and purpose. The argument establishes and employs a relevant context for analysis of the issue and its perspectives. The analysis recognizes implications, complexities and tensions, and/or underlying values and assumptions.

Development of ideas and support for claims clarify meaning and purpose. Lines of clear reasoning and illustration adequately convey the significance of the argument. Qualifications and complications extend ideas and analysis.

The response exhibits a clear organizational strategy. The overall shape of the response reflects an emergent controlling idea or purpose. Ideas are logically grouped and sequenced. Transitions between and within paragraphs clarify the relationships among ideas.

The use of language conveys the argument with clarity. Word choice is adequate and sometimes precise. Sentence structures are clear and demonstrate some variety. Stylistic and register choices, including voice and tone, are appropriate for the rhetorical purpose. While errors in grammar, usage, and mechanics are present, they rarely impede understanding.

Score 3:

Responses at this scorepoint demonstrate some developing skill in writing an argumentative essay.

The writer generates an argument that responds to multiple perspectives on the given issue. The argument’s thesis reflects some clarity in thought and purpose. The argument establishes a limited or tangential context for analysis of the issue and its perspectives. Analysis is simplistic or somewhat unclear.

Development of ideas and support for claims are mostly relevant but are overly general or simplistic. Reasoning and illustration largely clarify the argument but may be somewhat repetitious or imprecise.

The response exhibits a basic organizational structure. The response largely coheres, with most ideas logically grouped. Transitions between and within paragraphs sometimes clarify the relationships among ideas.

The use of language is basic and only somewhat clear. Word choice is general and occasionally imprecise. Sentence structures are usually clear but show little variety. Stylistic and register choices, including voice and tone, are not always appropriate for the rhetorical purpose. Distracting errors in grammar, usage, and mechanics may be present, but they generally do not impede understanding.

Score 2:

Responses at this scorepoint demonstrate weak or inconsistent skill in writing an argumentative essay.

The writer generates an argument that weakly responds to multiple perspectives on the given issue. The argument’s thesis, if evident, reflects little clarity in thought and purpose. Attempts at analysis are incomplete, largely irrelevant, or consist primarily of restatement of the issue and its perspectives.

Development of ideas and support for claims are weak, confused, or disjointed. Reasoning and illustration are inadequate, illogical, or circular, and fail to fully clarify the argument.

The response exhibits a rudimentary organizational structure. Grouping of ideas is inconsistent and often unclear. Transitions between and within paragraphs are misleading or poorly formed.

The use of language is inconsistent and often unclear. Word choice is rudimentary and frequently imprecise. Sentence structures are sometimes unclear. Stylistic and register choices, including voice and tone, are inconsistent and are not always appropriate for the rhetorical purpose. Distracting errors in grammar, usage, and mechanics are present, and they sometimes impede understanding.

Score 1:

Responses at this scorepoint demonstrate little or no skill in writing an argumentative essay.

The writer fails to generate an argument that responds intelligibly to the task. The writer’s intentions are difficult to discern. Attempts at analysis are unclear or irrelevant.

Ideas lack development, and claims lack support. Reasoning and illustration are unclear, incoherent, or largely absent.

The response does not exhibit an organizational structure. There is little grouping of ideas. When present, transitional devices fail to connect ideas.

The use of language fails to demonstrate skill in responding to the task. Word choice is imprecise and often difficult to comprehend. Sentence structures are often unclear. Stylistic and register choices are difficult to identify. Errors in grammar, usage, and mechanics are pervasive and often impede understanding.

STEP 2. Because your writing test domain scores are the sum of two readers’ ratings of your essay, multiply your own 1–6 rating from step 1 by 2. Or, have both you and someone else read and score your practice essay, add those ratings together, and record the total in the Domain Score column in step 3.

STEP 3. Enter your writing test domain scores in the following box.

Domain Score

Ideas and Analysis

× 2 =

Development and Support

× 2 =

Organization

× 2 =

Language Use and Conventions

× 2 =

STEP 4. Enter the sum of the second-column scores here __________.

STEP 5. Divide sum by 4† (range 2–12). This is your writing test score.

†Round value to the nearest whole number. Round down any fraction less than one-half; round up any fraction that is one-half or more.

STEP 6. Use the table on page 112 to determine your estimated percentile rank (percent at or below) for your writing test score.

National Norms for ACT Writing Scores Reported During the 2020–2021 Reporting Year

Score

Writing

12

11

10

9

8

7

6

5

4

3

2

1

100

99

99

96

90

66

51

28

15

5

2

Mean:

6.5

SD:

1.8

Note: These national norms are the source of the U.S. Ranks for the ACT Writing scores displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 2,370,670, are based on 2018, 2019 and 2020 graduates. Writing scores earned prior to September 2016 are not represented by this table.

Reviewing Explanatory Answers

After scoring your test, review the questions and answers to gain a better understanding of why each correct answer is correct and why the other choices for each question are wrong. We encourage you to review the explanatory answers for all questions, not just those you missed. As you read through the explanations, note any subject matter or concepts you don’t fully understand, such as subject-verb agreement on the English test or how to calculate the volume of three-dimensional objects on the mathematics test.

When taking practice tests on the online platform (act.wiley.com), you can flag questions that you found difficult or confusing. By clicking on each question, you can review the explanation, and you can even add notes to help you keep track of what you have learned and where you need to focus.

The following sections give the correct answers for each question along with an explanation of why each correct answer is correct, why each of the other choices is wrong, and (in some cases) insight into why certain wrong answers may have been tempting choices. For more guidance on how to identify subject areas or skills you may need to work on, turn to chapter 4.

ENGLISH • PRACTICE TEST 1 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is C because it is the only option that has correct sentence structure. It uses a preposition to begin an introductory dependent clause that links to an independent clause, which creates a complete sentence.

The best answer is NOT:

A because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

B because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

D because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

Question 2. The best answer is G because it is the only option that has correct sentence structure. It creates a complete sentence with a main subject and main verb.

The best answer is NOT:

F because it adds the relative pronoun which before the verb, resulting in a sentence fragment.

H because it creates a long clause that is a sentence fragment.

J because, like H, it creates a long clause that is a sentence fragment.

Question 3. The best answer is A because it provides the appropriate punctuation (dashes) to set off the nonessential element “up to twenty-five feet wide.”

The best answer is NOT:

B because a colon is not used to introduce a nonessential element.

C because the punctuation used to set off a nonessential element must match; since the nonessential element ends with a dash, it cannot be set off with a comma at the beginning.

D because a colon is not used to complete a nonessential element.

Question 4. The best answer is J because it does not include any unnecessary punctuation.

The best answer is NOT:

F because it has an unnecessary comma after variations.

G because it has an unnecessary dash after variations.

H because it has two unnecessary commas that incorrectly set off “in the mantas” from the rest of the sentence.

Question 5. The best answer is A because it clearly explains why the sentence should be deleted. The information about Marshall’s beachside lodgings in Mozambique is not relevant to the paragraph’s discussion of how Marshall came to investigate the possibility that there were two manta ray species.

The best answer is NOT:

B because the information about why Marshall did her research in Mozambique is not relevant to the discussion of how Marshall came to investigate the possibility that there were two manta ray species.

C because the sentence refers to Marshall’s beachside lodgings in Mozambique, which are not related to how Marshall, who started as a lone researcher, ended up creating a large scientific institution.

D because the sentence refers to Marshall’s beachside lodgings in Mozambique, which are not related to Marshall’s role at the Marine Megafauna Center.

Question 6. The best answer is F because it is the only option with correct subject-verb agreement. The singular subject skin must have a singular verb.

The best answer is NOT:

G because happen is a plural verb, and the subject of the sentence is singular.

H because were is a plural verb, and the subject of the sentence is singular.

J because are is a plural verb, and the subject of the sentence is singular.

Question 7. The best answer is C because it does not include any unnecessary punctuation.

The best answer is NOT:

A because it has an unnecessary colon after the word was.

B because it has two unnecessary commas that incorrectly set off the word that from the rest of the sentence.

D because it has an unnecessary comma after the word was.

Question 8. The best answer is F because after Sentence 1 is the only logical place to add information that refers to the basic data Marshall began collecting.

The best answer is NOT:

G because Sentence 2 begins with “Other data,” which refers back to the phrase “Some of the data” in the new sentence, so it would be illogical to place the new sentence after Sentence 2.

H because to place the sentence after Sentence 3 would interrupt the discussion of the manta denticles.

J because to place the sentence after Sentence 4 would interrupt the introduction of another discovery Marshall made in regard to the mantas.

Question 9. The best answer is C because it best expresses the idea specified in the stem. The word choice in this option (evidence) best conveys that the announcement was backed by scientific data.

The best answer is NOT:

A because the wording doesn’t clearly indicate that the announcement was backed by scientific data.

B because the wording doesn’t clearly indicate that the announcement was backed by scientific data.

D because the wording doesn’t clearly indicate that the announcement was backed by scientific data.

Question 10. The best answer is J because it is the only option with correct subject-verb agreement. The plural subject “two manta species” must have a plural verb.

The best answer is NOT:

F because is is a singular verb, and the subject of the sentence is plural.

G because exists is a singular verb, and the subject of the sentence is plural.

H because was is a singular verb, and the subject of the sentence is plural.

Question 11. The best answer is B because it maintains the overall style and tone of the essay. The language here is neither overly informal nor too formal.

The best answer is NOT:

A because the wording is too informal compared to the rest of the essay.

C because the wording introduces a tone that is not consistent with the rest of the essay.

D because the wording is too informal compared to the rest of the essay.

Question 12. The best answer is F because it creates a sentence that is structurally sound and has proper subordination.

The best answer is NOT:

G because whether is not the correct subordinating conjunction to use in this context and creates an illogical sentence.

H because which is not the correct subordinating conjunction to use in this context and creates an illogical sentence.

J because how is not the correct subordinating conjunction to use in this context and creates an illogical sentence.

Question 13. The best answer is B because it creates a logical sentence with correctly placed modifiers. The phrase “for so long” refers to the amount of time large animals went undifferentiated and so is correctly placed after that word.

The best answer is NOT:

A because the phrase “for so long” is incorrectly placed so that it appears to modify know, creating an illogical sentence.

C because the phrase “for so long” is incorrectly placed so that it appears to modify highlights, creating an illogical sentence.

D because the phrase “for so long” is incorrectly placed so that it appears to modify how, creating an illogical sentence.

Question 14. The best answer is J because it is the only option that clearly supports the suggestion that the scientific study of manta rays will continue: it is because Dr. Marshall, an expert researcher, is so devoted to manta rays.

The best answer is NOT:

F because the fact that the current manta ray population faces an array of threats across the world does not support the suggestion that the scientific study of manta rays will continue.

G because the fact that a documentary film about Dr. Marshall was released in 2009 does not support the suggestion that the scientific study of manta rays will continue.

H because the fact that Dr. Marshall once described the manta ray as a large and beautiful underwater bird does not support the suggestion that the scientific study of manta rays will continue.

Question 15. The best answer is D because this option clearly indicates why the essay does not meet the writer’s primary purpose. The main focus of the essay is on how Marshall’s research led to the discovery of the two manta species; it is not about surveying the scientific community’s response to the identification of the two species.

The best answer is NOT:

A because the fact that the scientific community accepted the identification of the two species is not the main focus of the essay.

B because the fact that Marshall’s research was thorough and well documented is not the main focus of the essay.

C because the essay does not present any scientific responses to Marshall’s identification of the two species.

Passage II

Question 16. The best answer is G because it is the only option that has correct sentence structure. It correctly uses a comma to connect the independent clause to the participial phrase.

The best answer is NOT:

F because it inserts a semicolon after temperature, which creates a sentence fragment because what comes after the semicolon is a participial phrase.

H because the comma after temperature is separating two independent clauses, which creates a run-on sentence.

J because it inserts a period after temperature, which creates a sentence fragment because what comes after the period is a participial phrase.

Question 17. The best answer is A because it provides the appropriate punctuation (commas) to set off the adverbial phrase “particularly in the bark of the willow tree.”

The best answer is NOT:

B because it contains misplaced and inconsistent punctuation, creating an unclear sentence. The second dash after bark interrupts the adverbial phrase. In addition, an adverbial phrase should be set off by the same punctuation on both sides, either commas or dashes, but not both.

C because a colon is not used to introduce an adverbial phrase.

D because it contains misplaced punctuation, creating an unclear sentence. The first comma should precede, not follow, the word particularly.

Question 18. The best answer is G because it creates a sentence that is structurally sound; it has a subject and uses the correct preposition.

The best answer is NOT:

F because it has no subject.

H because on is not the right preposition to show the relationship between willow and the other plants.

J because it has no subject.

Question 19. The best answer is D because it provides the clearest, most concise wording.

The best answer is NOT:

A because it is redundant; approximately and about essentially have the same meaning.

B because “an estimation of” is both wordy and awkward.

C because “in the region of” is both wordy and vague.

Question 20. The best answer is G because it is the only option that provides a logical transition to the information presented in the paragraph it introduces.

The best answer is NOT:

F because the information in this clause does not logically connect to the information in the rest of the paragraph.

H because the information in this clause does not logically connect to the information in the rest of the paragraph.

J because the information in this clause does not logically connect to the information in the rest of the paragraph.

Question 21. The best answer is A because it is the only option that has consistent verb tense. The verb preferred should match the tense in the rest of the paragraph.

The best answer is NOT:

B because “would of” is an incorrect verb form of “would have,” which creates a sentence that is both unclear and lacks consistent verb tense.

C because the verb “will prefer” creates a sentence that lacks consistent verb tense.

D because the verb prefer creates a sentence that lacks consistent verb tense.

Question 22. The best answer is J because it provides the clearest, most concise wording.

The best answer is NOT:

F because it is redundant; “high cost” and expensive essentially have the same meaning.

G because it is redundant; “high price tag” and expensive essentially have the same meaning, and the phrasing is wordy and awkward.

H because it is redundant; “high importation cost of” and expensive essentially have the same meaning, and the phrasing is wordy and awkward.

Question 23. The best answer is C because it provides the appropriate punctuation (commas) to set off the conjunctive adverb however.

The best answer is NOT:

A because it lacks a comma before however.

B because a colon creates a sentence fragment.

D because it lacks a comma after however.

Question 24. The best answer is F because it provides the most logical transition word to connect this sentence with the preceding one. The word consequently provides a resolution to the earlier word however in the previous sentence, helping to explain the pivot away from cinchona bark to willow bark.

The best answer is NOT:

G because the word nevertheless is illogical in relation to the previous sentence.

H because the word furthermore is illogical in relation to the previous sentence.

J because the word likewise is illogical in relation to the previous sentence.

Question 25. The best answer is D because the word began, the simple past tense, is the correct form of the verb as is it used in this sentence.

The best answer is NOT:

A because the past tense is appropriate here, not the past perfect. Additionally, the past-perfect tense is “had begun,” not “had began.”

B because the past tense is appropriate here, not the past-perfect subjunctive mood. Additionally, the past-perfect subjunctive mood is “would have begun,” not “would have began.”

C because began is the correct form of the past tense, not begun.

Question 26. The best answer is H because it is the only option that provides a logical transition from the information presented in the previous sentence.

The best answer is NOT:

F because this phrase is illogical in relation to the previous sentence and what follows in this sentence.

G because this phrase is illogical in relation to the previous sentence and what follows in this sentence.

J because this phrase is illogical in relation to the previous sentence and what follows in this sentence.

Question 27. The best answer is C because it is the only choice that uses the correct verb tense and the correct form of the possessive pronoun its.

The best answer is NOT:

A because adds is the incorrect tense of the verb as it is used in this sentence.

B because it’s is the incorrect form of the possessive pronoun.

D because adds is the incorrect tense of the verb as its used in this sentence, and it’s is the incorrect form of the possessive pronoun.

Question 28. The best answer is G because it best expresses the idea specified in the stem. Tested emphasizes that the medicine was experimental in nature.

The best answer is NOT:

F because the wording doesn’t clearly indicate that the medicine was experimental in nature.

H because the wording doesn’t clearly indicate that the medicine was experimental in nature.

J because the wording doesn’t clearly indicate that the medicine was experimental in nature.

Question 29. The best answer is D because it is the only option that has correct sentence structure. It creates two independent sentences.

The best answer is NOT:

A because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

B because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

C because a comma is needed before a nonrestrictive relative clause introduced by which.

Question 30. The best answer is G because this option clearly indicates why the essay does fulfill the writer’s primary purpose. The essay outlines the development of a common medicine by documenting the historical use of willow bark as a medicine and tracing its gradual refinement into modern aspirin.

The best answer is NOT:

F because the essay does not focus on how the Egyptians and Sumerians administered willow bark.

H because the essay does not focus on the function of salicylates and how aspirin affects the human body.

J because the essay does not focus on comparing the use of willow bark to that of cinchona bark in the eighteenth century.

Passage III

Question 31. The best answer is D because it is the only option that has correct sentence structure. It correctly places “painter Martin Klimas” immediately after the introductory phrase “in his studio in Dusseldorf, Germany,” which correctly modifies the word his.

The best answer is NOT:

A because it introduces a dangling modifier. The logical referent for his is Klimas, not the paint.

B because it introduces a dangling modifier. The independent clause begins with “there is,” which leaves no logical subject for his to modify.

C because, like A and B, it introduces a dangling modifier. The logical referent for his is Klimas, not the paint.

Question 32. The best answer is G because it provides appropriate punctuation (a colon) to set off examples of the information that precedes the colon. The sentence refers to the paint that collects in a “puddle of colors” and is followed by a list of those colors. G also includes a comma to separate the two pairs of hues in the sentence.

The best answer is NOT:

F because a semicolon should not be used to introduce a list.

H because a semicolon should not be used to separate items in a list where commas can be used instead. It also omits a comma after blues.

J because a semicolon should not be used to introduce a list or to separate items in a list where commas can be used instead.

Question 33. The best answer is B because it includes two independent clauses that are joined only by and, which results in a run-on sentence.

The best answer is NOT:

A because it correctly inserts a comma and the conjunction and between the two independent clauses.

C because it correctly ends the first independent clause with a period and begins the second one with a capital letter.

D because it correctly uses a semicolon to join two closely related independent clauses.

Question 34. The best answer is F because “level with” is precise and appropriately conveys how the camera is positioned relative to the paint puddle.

The best answer is NOT:

G because the phrase “eye-to-eye with” isn’t appropriate in this context, as neither the camera nor the puddle has eyes.

H because “the same as” falsely equates the camera to the paint puddle. They are different things.

J because the phrase “equal to” indicates that the camera and the paint puddle are somehow equal, which doesn’t make sense.

Question 35. The best answer is A because it best expresses the idea specified in the stem. The word choice in this option is the most dramatic, which is what the question asks for. Crank indicates an aggressive movement, and ten is often the highest level that volume can be turned to.

The best answer is NOT:

B because the wording isn’t as dramatic as the wording in A. “A bit higher” is a small increase.

C because the wording isn’t as dramatic as the wording in A. “Increases the volume of the output” is straightforward and undramatic.

D because the wording isn’t as dramatic as the wording in A. “Adjusts the speaker’s output level” is straightforward and undramatic.

Question 36. The best answer is G because it is the only option with correct subject-verb agreement. The plural subject vibrations must have a plural verb.

The best answer is NOT:

F because “has caused” is a singular verb, and the subject of the sentence is plural.

H because “is causing” is a singular verb, and the subject of the sentence is plural.

J because causes is a singular verb, and the subject of the sentence is plural.

Question 37. The best answer is A because it maintains the overall style and tone of the essay. The language here is neither overly informal nor too formal.

The best answer is NOT:

B because the phrase “frozen in time’s embrace” is too flowery compared with the rest of the essay, and the words pic and snapped are too casual.

C because the wording is too informal compared with the rest of the essay.

D because the wording is too informal compared with the rest of the essay.

Question 38. The best answer is F because at this point, the writer is discussing how Klimas’s photos are unique to each song. The quotation about letting the sound of the music create the picture is therefore the most relevant.

The best answer is NOT:

G because this quotation is about how annoying it was to clean up after each shot, which is not relevant at this point in the essay.

H because a quotation about using normal photographic equipment and common music is less relevant at this point than the quotation in F is.

J because this quotation is about the repetitive nature of the process, which is less relevant at this point than the quotation in F is.

Question 39. The best answer is C because it is the only option with correct subject-verb agreement. The singular subject idea must have a singular verb.

The best answer is NOT:

A because were is a plural verb, and the subject of the sentence is singular.

B because “have been” is a plural verb, and the subject of the sentence is singular.

D because are is a plural verb, and the subject of the sentence is singular.

Question 40. The best answer is J because it does not include any unnecessary punctuation.

The best answer is NOT:

F because it has two unnecessary commas that incorrectly set off “of Swiss scientist” from the rest of the sentence.

G because it has an unnecessary comma after experiments.

H because it has an unnecessary comma after Swiss.

Question 41. The best answer is D because it is the only option that has correct sentence structure. It creates a complete sentence with a main subject and main verb.

The best answer is NOT:

A because it creates a long phrase that is a sentence fragment. The phrase has no verb.

B because it adds the subordinating conjunction while before the subject and verb, resulting in a long dependent clause that is a sentence fragment.

C because, like A, it creates a long phrase that is a sentence fragment. The phrase has no verb.

Question 42. The best answer is G because the essay does shift at this point from information about Jenny’s experiments to the music Klimas uses in his work. Dividing the paragraph at this point makes sense.

The best answer is NOT:

F because even though it makes sense to divide the paragraph, the essay is not discussing harmonics or Klimas’s taste in music at this point.

H because dividing the paragraph here would not interrupt an analysis of Jenny’s experiments, as those are not being analyzed at this point in the essay.

J because dividing the paragraph here would not interrupt a description of Klimas’s scientific background, as that is not discussed in the essay.

Question 43. The best answer is C because it is the only option that has correct sentence structure. It correctly uses a comma to connect the introductory dependent clause to the independent clause of the sentence.

The best answer is NOT:

A because it inserts a period after sculptures, which creates a sentence fragment because what comes before the period is a dependent clause.

B because it adds the conjunction and between the dependent clause and independent clause of the sentence, which results in incorrect subordination.

D because it inserts a semicolon after sculptures, which creates a sentence fragment because what comes before the semicolon is a dependent clause.

Question 44. The best answer is J because this sentence links the idea of using dynamic and percussive music to the idea that Klimas needs the paint to “get up and dance.”

The best answer is NOT:

F because a sentence speculating that such music would impress Jenny is not an effective transition here.

G because a sentence stating that Klimas’s music selection is a matter of taste is not an effective transition here.

H because a sentence saying that dynamic and percussive music is an unwise choice is illogical and is not an effective transition here.

Question 45. The best answer is B because this option clearly indicates why the essay does fulfill the writer’s primary purpose. The essay explains how Klimas creates his art by photographing the effects of music on paint.

The best answer is NOT:

A because the essay does not focus on the artistic process that Jenny used.

C because the essay does not focus on the cultural significance of Klimas’s photos.

D because the essay does not give an overview of how Jenny’s experiments have inspired other artists.

Passage IV

Question 46. The best answer is J because it creates a sentence that is structurally sound and is parallel in grammatical structure to the surrounding phrases.

The best answer is NOT:

F because the clause “there are tree-covered bluffs” disrupts the parallel structure of the series phrases.

G because the clause “tree-covered bluffs flank the river” disrupts the parallel structure of the series of phrases.

H because the phrase “featuring tree-covered bluffs” disrupts the parallel structure of the series of phrases.

Question 47. The best answer is A because it best expresses the idea specified in the stem. The phrase “daunted would-be” best indicates that the builders who intended to construct the highway were intimidated by the features of the gorge.

The best answer is NOT:

B because the wording doesn’t clearly indicate that the builders who intended to construct the highway were intimidated by the features of the gorge.

C because the wording doesn’t clearly indicate that the builders who intended to construct the highway were intimidated by the features of the gorge.

D because the wording doesn’t clearly indicate that the builders who intended to construct the highway were intimidated by the features of the gorge.

Question 48. The best answer is H because it provides appropriate punctuation (a colon) to connect two independent clauses and indicate the relationship between them. In this sentence, the information in the second clause (“showcased the scenic grandeur”) illustrates and expands upon information in the first clause (“design went beyond practicalities”).

The best answer is NOT:

F because no punctuation between two independent clauses creates a run-on sentence.

G because the coordinating conjunction and is not used with a colon to join two independent clauses.

J because a comma between two independent clauses creates a run-on sentence.

Question 49. The best answer is D because it provides the clearest, most concise wording.

The best answer is NOT:

A because it is redundant; “Columbia River” is referenced earlier in the paragraph.

B because it is redundant; the length of the gorge is referenced earlier in the paragraph.

C because it is redundant and wordy; the gorge’s scenery is referenced earlier in the sentence.

Question 50. The best answer is J because deleting the underlined portion provides the clearest, most concise wording.

The best answer is NOT:

F because it is redundant and wordy; the location of the benches is referenced earlier in the sentence, and benches are typically for sitting.

G because it is redundant and wordy; the location of the benches is referenced earlier in the sentence.

H because it is redundant; that the benches were for travelers’ use is referenced later in the sentence.

Question 51. The best answer is A because it is the only option that creates a standard English idiom (“take in a view”).

The best answer is NOT:

B because the phrase “take up a view” is not idiomatic standard English.

C because the phrase “take on a view” is not idiomatic standard English.

D because the phrase “take a view” is not idiomatic standard English.

Question 52. The best answer is H because it is the only option that is clear. The word road clearly indicates that the distinction that was blurred was between “road and environment,” which prevents ambiguity regarding what the writer is referring to at this point in the sentence.

The best answer is NOT:

F because the pronoun that is ambiguous, lacking a clear antecedent.

G because the pronoun this is ambiguous, lacking a clear antecedent.

J because the pronoun it is ambiguous, lacking a clear antecedent. In addition, the word it’s is the incorrect form of the possessive pronoun.

Question 53. The best answer is A because it clearly explains why the phrase should be added to the sentence. The detail helps develop and support the overarching idea in the paragraph that the design of the Columbia River Highway was impressive, with five tunnels previously being unheard of in such a design.

The best answer is NOT:

B because the phrase, though it should be added, does not imply how the engineers were able to make openings in the tunnel.

C because the phrase, which should be added, makes clear that there were several openings in the side of one tunnel; this relates to information in the sentence about motorists’ ability to glimpse the river below.

D because the phrase, which should be added, does not suggest that creating intricate tunnels was easy for engineers.

Question 54. The best answer is J because it is the only option that has correct sentence structure. It creates a grammatically correct sentence by using a comma to separate an independent clause from a participial phrase.

The best answer is NOT:

F because it inserts a semicolon after tunnel, which creates a sentence fragment because what follows the semicolon is a participial phrase.

G because, like F, it inserts a semicolon after tunnel, which creates a sentence fragment because what follows the semicolon is a participial phrase.

H because the comma after tunnel is separating two independent clauses, which creates a run-on sentence.

Question 55. The best answer is B because it is the only option that has correct sentence structure. It uses a subordinating conjunction to begin the introductory dependent clause that links to an independent clause, which creates a complete sentence.

The best answer is NOT:

A because it creates a run-on sentence. “In time” is a prepositional phrase, not a subordinating conjunction. “In time, Oregon built a new road along the Columbia” is an independent clause.

C because it creates a run-on sentence. The word soon is an adverb, not a subordinating conjunction. “Soon Oregon built a new road along the Columbia” is an independent clause.

D because it creates a run-on sentence. “Oregon built a new road along the Columbia” is an independent clause.

Question 56. The best answer is F because it maintains the overall style and tone of the essay.

The best answer is NOT:

G because the wording introduces a wordy, pretentious tone that is not consistent with the rest of the essay.

H because the wording introduces an elevated, formal tone that is not consistent with the rest of the essay. In addition, the phrase “was completed in 1922” is redundant with information presented in the previous paragraph.

J because the wording introduces an elevated, formal tone that is not consistent with the rest of the essay.

Question 57. The best answer is C because it best expresses the idea specified in the stem. The word rekindled clearly conveys that people’s interest in the Columbia River Highway in the 1980s was a renewal of earlier interest in the original highway.

The best answer is NOT:

A because the wording doesn’t clearly convey that people’s interest in the Columbia River Highway in the 1980s was a renewal of earlier interest in the original highway.

B because the wording doesn’t clearly convey that people’s interest in the Columbia River Highway in the 1980s was a renewal of earlier interest in the original highway.

D because the wording doesn’t clearly convey that people’s interest in the Columbia River Highway in the 1980s was a renewal of earlier interest in the original highway.

Question 58. The best answer is G because it maintains the sentence pattern the writer has established in the previous two sentences by using simple sentence structure, passive voice, present-perfect tense, and similar ordering of words and phrases. This approach creates a sense of repetition and emphasis for stylistic effect.

The best answer is NOT:

F because it does not maintain the sentence pattern the writer has established in the previous two sentences.

H because it does not maintain the sentence pattern the writer has established in the previous two sentences.

J because it does not maintain the sentence pattern the writer has established in the previous two sentences.

Question 59. The best answer is C because it is the only option that clearly refers back to information in the first paragraph, which mentions that Hill and Lancaster began constructing the road in 1913 and that their design showcased the splendor of the gorge.

The best answer is NOT:

A because the first paragraph does not state that the site became a National Historic Landmark in 2000.

B because the first paragraph does not discuss uses for sections of the road where it was not feasible to restore motor traffic.

D because the idea that the Historic Columbia River Highway Trail has become a popular tourist destination is not referred to in the first paragraph.

Question 60. The best answer is J because Point D in Paragraph 3 is the most logical place to add information about the eventual disrepair of what remained of the original Columbia River Highway. Paragraph 3 as a whole focuses on the highway’s decrease in use and resulting decline, so a sentence about the highway’s condition fits logically at Point D and helps the overall understanding of the paragraph.

The best answer is NOT:

F because placing the sentence at Point A would interrupt the discussion of Hill and Lancaster’s role in the design and construction of the original Columbia River Highway.

G because placing the sentence at Point B would interrupt the introduction of the discussion of particular design features of the original Columbia River Highway.

H because placing the sentence at Point C would interrupt the list of design features of the original Columbia River Highway.

Passage V

Question 61. The best answer is A because the name “Sylvia Robinson” is an essential element and should not be set off in the sentence.

The best answer is NOT:

B because “Sylvia Robinson” is an essential element and should not be set off with commas.

C because “Sylvia Robinson” is an essential element and should not be set off with commas.

D because it adds a comma after singer, which is incorrect.

Question 62. The best answer is H because it is the only option with correct subject-verb agreement. The singular subject subculture must have a singular verb.

The best answer is NOT:

F because were is a plural verb, and the subject of the sentence is singular.

G because have is a plural verb, and the subject of the sentence is singular.

J because are is a plural verb, and the subject of the sentence is singular.

Question 63. The best answer is A because it provides the clearest, most concise wording.

The best answer is NOT:

B because it is redundant; the sentence already indicates the action people were taking when they obeyed the directive from the DJ.

C because it is redundant; “heeded the DJ’s call” and “obeyed him” are redundant phrases.

D because it is redundant; “did what he said” is redundant with obeyed.

Question 64. The best answer is G because it provides the appropriate punctuation (a dash) to set off the nonessential element “Big Bank Hank, Master Gee, and Wonder Mike” and also because the element ends with a dash.

The best answer is NOT:

F because a colon is not used to introduce a nonessential element.

H because a semicolon is not used to introduce a nonessential element.

J because the punctuation used to set off a nonessential element must match; since the nonessential element ends with a dash, it cannot be set off with a comma at the beginning.

Question 65. The best answer is C because it clearly explains why the new sentence should not be added. The information about Robinson and her husband forming other record labels is not relevant to the paragraph’s discussion of how “Rapper’s Delight” was created.

The best answer is NOT:

A because the suggested addition refers to the future labels Robinson would form, which logically would have no bearing on where the Sugarhill Gang would choose to record at the time being referenced.

B because the suggested addition refers to the future labels Robinson would form, and since the three rappers had already signed with Robinson at the time being referenced, it would be illogical to say Robinson’s future labels had any effect on why they decided to record with her.

D because the time period in which Robinson and her husband started other record labels is not relevant to the paragraph’s discussion of how “Rapper’s Delight” was created.

Question 66. The best answer is J because it is the only option that has correct sentence structure. The introductory phrase correctly modifies Robinson, because Robinson wanted to “re-create the feel-good vibe of the music.”

The best answer is NOT:

F because the introductory phrase incorrectly modifies “an upbeat disco record” as if the record were “wanting to re-create the feel-good vibe of the music.”

G because the introductory phrase incorrectly modifies “an upbeat disco record” as if the record were “wanting to re-create the feel-good vibe of the music.”

H because the introductory phrase incorrectly modifies rhymes as if the rhymes were “wanting to re-create the feel-good vibe of the music.”

Question 67. The best answer is D because no transition word or phrase is necessary at this point.

The best answer is NOT:

A because the word Nevertheless suggests that the idea in this sentence is in opposition with the idea in the preceding sentence, which is incorrect.

B because the phrase “On the other hand” suggests that the idea in this sentence is in opposition with the idea in the preceding sentence, which is incorrect.

C because the phrase “As a result” indicates that Robinson’s instincts having served her well was directly caused by her producing a successful rap record, which is illogical.

Question 68. The best answer is H because it does not include any unnecessary punctuation.

The best answer is NOT:

F because it has an unnecessary comma after instincts.

G because it has two unnecessary commas that incorrectly set off the word and from the rest of the sentence.

J because it has an unnecessary comma after savvy.

Question 69. The best answer is D because it is the only option that has correct sentence structure. It uses a gerund to begin the introductory dependent clause that links to an independent clause, which creates a complete sentence.

The best answer is NOT:

A because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

B because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

C because it creates two independent clauses that are separated by a comma, which creates a run-on sentence.

Question 70. The best answer is G because it best expresses the idea specified in the stem. The word option in this choice (persuaded) most effectively indicates that Robinson had to be convincing.

The best answer is NOT:

F because the wording doesn’t effectively indicate that Robinson had to be convincing.

H because the wording doesn’t effectively indicate that Robinson had to be convincing.

J because the wording doesn’t effectively indicate that Robinson had to be convincing.

Question 71. The best answer is C because it is the only option that creates a standard English idiom (“covered new ground”).

The best answer is NOT:

A because the phrase “encountered new ground” is not an idiomatically sound expression in standard English.

B because the phrase “protected new ground” is not an idiomatically sound expression in standard English.

D because the phrase “filled new ground” is not an idiomatically sound expression in standard English.

Question 72. The best answer is H because it provides the most logical conjunction to connect the ideas presented in this sentence. The song’s focus was weightier and very different from other singles the group had released, and this caused them to be hesitant to record it.

The best answer is NOT:

F because the subordinating conjunction because is not logical in context; the song wasn’t different than previous singles because of the rappers’ hesitancy to record it.

G because the subordinating conjunction although is not logical in context; the song wasn’t different than previous singles in spite of the rappers’ hesitancy to record it.

J because the coordinating conjunction for is not logical in context; the song wasn’t different than previous singles because of the rappers’ hesitancy to record it.

Question 73. The best answer is D because it provides the most logical transitional phrase in context. The preceding sentences describe the tension between Robinson’s determination to record “The Message” and the group’s hesitancy to record it. But eventually, or “in the end,” two group members recorded the song, and it became a success.

The best answer is NOT:

A because the phrase “in the opposite fashion” signals that what follows in the sentence presents a contrast to the idea in the preceding sentences, which is incorrect.

B because the phrase “in the first place” is illogical when the sentence is in fact describing the outcome of the situation described in the preceding sentences.

C because the phrase “in the same way” indicates that what follows in the sentence is similar to the idea described in the preceding sentences, which is incorrect.

Question 74. The best answer is F because the possessive adjective Its and the adjective conscious are the correct words to use in this context.

The best answer is NOT:

G because the noun conscience is incorrect in this context. It should be the adjective conscious.

H because the contraction It’s is incorrect in this context. It should be the possessive adjective its.

J because the noun conscience and the contraction It’s are both incorrect in this context.

Question 75. The best answer is B because it fails to correctly subordinate the sentence’s second clause; it incorrectly uses a coordinating conjunction (and) to connect an independent clause and a dependent clause.

The best answer is NOT:

A because it creates an acceptable sentence construction in that it uses a coordinating conjunction and a comma to connect two independent clauses.

C because it creates an acceptable sentence construction in that it uses and to connect two parallel verb phrases.

D because it creates an acceptable sentence construction in that it uses a comma and a gerund to connect an independent clause and a dependent clause.

MATHEMATICS • PRACTICE TEST 1 • EXPLANATORY ANSWERS

Question 1. The correct answer is C. Substitute for and for to get 27 − 8, or . If you answered A, you may have substituted for and for to get , or . If you answered B, you may have substituted for and for and multiplied the exponent to get , or . If you answered D, you may have substituted for and for , and then squared the product of and before applying the exponent to get , or . If you answered E, you may have substituted for and for , and then squared the product of and before applying the exponent to get , or .

Question 2. The correct answer is H. Use the exterior angle theorem to determine that the measure of is the sum of the measures of the interior angles and or . If you answered F, you may have thought and have the same measure. If you answered G, you may have added . If you answered J, you may have added . If you answered K, you may have subtracted the measure of from to get , or .

Question 3. The correct answer is E. First, divide the constants to get or , and then apply the exponent rule for division to get , or . By combining the constant and the variable expression, the fraction is equivalent to . If you answered A, you may have added the constants, , and correctly applied the exponent rule for division to get . If you answered B, you may have subtracted the constants, and correctly applied the exponent rule for division to get . If you answered C, you may have correctly calculated the constant as , and then, you may have incorrectly applied the exponent rule for division and added exponents to get , or , thus obtaining . If you answered D, you may have correctly calculated the constant as , and then, you may have thought the exponents in the denominator of the fraction were both 0 and applied the exponent rule for division to get , or , thus obtaining .

Question 4. The correct answer is H. Find how many batches of mileage points are in , , multiply that by , and then add to get . If you answered F, you may have incorrectly found as , multiplied the by to get , and then added to get . If you answered G, you may have found how many batches of mileage points were in 7,000, , added and to get , and then multiplied by to get . If you answered J, you may have multiplied by to get . If you answered K, you may have multiplied by to get and then added to get .

Question 5. The correct answer is E. Substitute for to get 4(25) + 55 = 100 + 55 = 155. If you answered A, you may have correctly substituted but then simplified as to get . If you answered B, you may have correctly substituted but then simplified as to get . If you answered C, you may have correctly substituted but then simplified as to get . If you answered D, you may have correctly substituted but then simplified as to get 84.

Question 6. The correct answer is G. Set up an expression that represents the sum of regular pay and overtime pay, with one addend for the regular hourly rate and one addend for the over--hours rate, , to get , or . If you answered F, you may have multiplied the regular hour rate by the total number of hours, , to get . If you answered H, you may have multiplied the total number of hours by the sum of and to get , or . If you answered J, you may have used instead of for the regular hourly rate and then multiplied the total number of hours by the over--hours rate to get , or . If you answered K, you may have multiplied the over--hour rate by the total number of hours, 11(1.5)(50), to get $.

Question 7. The correct answer is E. Since a junior has already been chosen that leaves students— seniors and juniors. The probability of choosing a senior is the number of seniors divided by the total number of students left, or . If you answered A, you may have thought the probability was the number of students you were picking divided by the total number of students left, or . If you answered B, you may have thought the probability was how many students were being picked over the number of seniors, or . If you answered C, you thought the first student picked was a senior, resulting in seniors and total students, or a probability of . If you answered D, you may have thought the first student picked was a senior and the probability was how many students were being picked over the number of seniors left, or .

Question 8. The correct answer is F. The change in temperature is equal to the ending temperature minus the beginning temperature, or F. If you answered G, you may have added the temperatures and attached a negative sign since the temperature decreased to get or F. If you answered H, you may have added the temperatures and divided by to get or F. If you answered J, you may have added the temperatures to get or F. If you answered K, you may have subtracted the ending temperature from the beginning temperature to get or F.

Question 9. The correct answer is C. The total cost of the car rental is equal to the sum of the total daily rental fee (the product of the number of days rented and the daily rental fee) and the total mileage fee (the product of the number of miles the car is driven and the per-mile fee), , or . If you answered A, you may have added to the product of the number of miles the car is driven and the per-mile fee to get , or . If you answered B, you may have multiplied by the sum of and to get , or . If you answered D, you may have found twice the product of and to get , or . If you answered E, you may have found the total cost of the car rental using for the per-mile fee to get , or .

Question 10. The correct answer is H. The slope is defined as . For these points, it is , or . If you answered F, you may have added instead of subtracted to get , or . If you answered G, you may have subtracted the terms and added the terms to get , or . If you answered J, you may have subtracted the terms in one order and the terms in the opposite order to get , or . If you answered K, you may have subtracted the terms and added the terms to get , or .

Question 11. The correct answer is B. To find the probability of the selected customer having ordered regular coffee without milk, first find the number in the cell where the “Regular” column and the “Without milk” row meet. Then place that number over the total number of customers to get , or . If you answered A, you may have found the cell where the “Decaf” column and the “Without milk” row meet and then put that number over the total number of customers to get , or . If you answered C, you may have found the cell where the “Regular” column and the “Without milk” row meet; you then put that number over the customer total minus that number to get , or . If you answered D, you may have found the cell where the “Regular” column and the “Total” row meet and then put that number over the total number of customers to get , or . If you answered E, you may have found the cell where the “Regular” column and the “Without milk” row meet and then found the cell where the “Total” column and the “Without milk” row meet. You then put the first number over the second to get , or .

Question 12. The correct answer is J. To solve the inequality, you subtract 2x and add 5 to both sides to get , or . If you answered F, you may have subtracted 2x and added to get , or . If you answered G, you may have added 2x and to get , or , or . If you answered H, you may have added 2x and 5 to get , or , or . If you answered K, you may have subtracted 2x and added 5 and then switched the inequality sign to get , or .

Question 13. The correct answer is B. To simplify the expression, you distribute the multiplication inside the parentheses to get , or , which factors to . If you answered A, you may have added all the terms to get , or . If you answered C, you may have distributed and added all the expressions to get , or , and then you factored incorrectly to get or . If you answered D, you may have distributed and added all the expressions to get , or . If you answered E, you may have combined the expressions in the parentheses and then multiplied to get , or .

Question 14. The correct answer is G. Convert the percentage to a decimal and the scientific notation to standard form, and then multiply to get 544. If you answered F, you may have divided by 4 to get , or 0.34; decreased the exponent by 1; and then multiplied the exponential part to get 0.34(1,000), or 340. If you answered H, you may have divided by 0.4 to get , or 3.4; decreased the exponent by 1; and then multiplied to get 3.4(1,000), or 3,400. If you answered J, you may have multiplied by 0.4 to get 0.4(13,600), or 5,440. If you answered K, you may have converted to standard form and then multiplied by 4 to get 4(13,600), or 54,400.

Question 15. The correct answer is B. Factor the denominators as 5(7), 7(11), and 2(11). Accounting for duplicates, you get (5)(7)(11)(2), or 770. If you answered A, you may have multiplied to get 5(11)(2), or 110. If you answered C, you may have multiplied to get 35(77), or 2,695. If you answered D, you may have missed the duplicate 7 after you factored the denominators as 5(7), 7(11), and 2(11); you then multiplied to get 35(11)(22), or 8,470. If you answered E, you may have multiplied all 3 denominators to get 35(77)(22), or 59,290.

Question 16. The correct answer is F. A move 3 coordinate units to the left means you subtract 3 from the x-coordinate to get , or . If you answered G, you may have subtracted 3 from the y-coordinate to get , or . If you answered H, you may have thought that a translation does not change a graph, so would still be on the graph. If you answered J, you may have added 3 to the y-coordinate to get , or . If you answered K, you may have added 3 to the x-coordinate to get , or .

Question 17. The correct answer is B. To find the midpoint, you average the x-coordinates and the y-coordinates to get , or . If you answered A, you may have subtracted the first point’s coordinates from the second point’s coordinates but thought that a negative number, when subtracted, is still negative, yielding , or . If you answered C, you may have added the coordinates of each point and divided by 2 to get , or . If you answered D, you may have subtracted the first point’s coordinates from the second point’s coordinates and divided by 2 to get , or . If you answered E, you may have subtracted the first point’s coordinates from the second point’s coordinates to get , or .

Question 18. The correct answer is K. You simplified the fraction on the left to x, so you got , or x = 2. If you answered F, you may have multiplied wrong to get and then subtracted wrong to get . Then you factored the left side as . Setting the factor equal to 0 and solving, you got . If you answered G, you may have rewritten the equation as to get , or . If you answered H, you may have set the denominator equal to 0 to get , or . If you answered J, you may have rewritten the left side as . Then, you set that side equal to the right side to get , or .

Question 19. The correct answer is D. The total number of moviegoers surveyed is 5,000. To find the average, you need to divide 5,000 by the number of categories, 4, to get 1,250 moviegoers. If you answered A, you may have mistakenly and incorrectly added the numbers in the top 2 rows in the table to get , then divided by 4 to get , or 610 moviegoers. If you answered B, you may have found the difference between the greatest and least numbers in the table and divided by 2 to get , or 1,060 moviegoers. If you answered C, you may have mistakenly calculated the average of the 4 numbers as , or 1,240 movie goers. If you answered E, you may have averaged the 2 greatest numbers in the table to get , or 1,985 moviegoers.

Question 20. The correct answer is G. Let m be the number of matinee moviegoers. Set up the equation by multiplying the number of moviegoers by the cost per type of movie attendance to get → → , or moviegoers. If you answered F, you may have set up the equation → → to get moviegoers. If you answered H, you may have divided 5,000 by 2 (the number of different prices) to get 2,500 moviegoers. If you answered J, you may have set up the equation → → to get moviegoers. If you answered K, you may have set up the equation → → to get . Then you subtracted to get 4,500 moviegoers.

Question 21. The correct answer is A. You divided each age group number by 5,000 and then multiplied by 100 to get , , , and . These match the percentages in A. If you answered B, you may have estimated the percentages. If you answered C, you may have calculated the percentage for 21–30 and then rounded the other 3 percentages to the nearest 5%. If you answered D, you may have estimated the percentages. If you answered E, you may have tried to have the circle graph represent both tables.

Question 22. The correct answer is G. You can decompose the composite figure into 2 rectangles. If you extend the vertical line segment on the right of the 6-centimeter side, you have a 6 by 9 rectangle and a 3 by 7 rectangle (see Figure 1). The 7-centimeter side is found by calculating 13 – 6 = 7. The area of the 6 by 9 rectangle is 54 square centimeters, and the area of the 3 by 7 rectangle is 21 square centimeters. The total area is then 75 square centimeters, because 54 + 21 = 75. Alternatively, you could have found the area of the larger 9 by 13 rectangle and then subtracted the area of a 6 by 7 rectangle (see Figure 2). The 6-centimeter side of the rectangle shown shaded is found by calculating 9 – 3 = 6. The total area is then 75 square centimeters, because 9(13) – 6(7) = 75. If you selected F, you may have reasoned that the composite figure was a 9 by 13 rectangle with a 6 by 7 rectangle removed and found the area of the removed rectangle instead of the composite rectangle. If you selected H, you may have added the areas of a 6 by 9 rectangle and a 13 by 3 rectangle, not accounting for the overlap: 54 + 39 = 93. If you selected J, you may have estimated that the area of the composite figure was the same as that of a rectangle with width 9 centimeters and length 11 centimeters: 9(11) = 99. If you selected K, you may have found the area of a 9 by 13 rectangle, not accounting for the removed 6 by 7 rectangle: 9(13) = 117.

Question 23. The correct answer is C. Because and form a line, . Solving for gives us that . By angle addition . After substitution of known angles, we have . Solving for results in . If you selected A, you may have found instead of . If you selected B, you may have incorrectly thought that bisected then calculated . If you selected D, you may have known the angle appeared to be between and based on the diagram but may not have known how to calculate it exactly. If you selected E, you may have thought that the item didn’t give you enough information to answer the question.

Question 24. The correct answer is G. Let . Since 5 sin(x) − 14 = , we can write the image of after the transformation to be . This is a translation of down 7 coordinate units. If you selected F, you may have confused y – 7 = f (x) with y = . If you selected H, you may have confused the negative direction on the x-axis with the negative direction on the y-axis. If you selected J, you may have confused y = with y = . If you selected K, you may not have compared the subtracted 14 and the subtracted 7 and confused y = with y = .

Question 25. The correct answer is C. Because and , . If you selected A, you may have found correctly but not squared the result. If you selected B, you may have you may have added the bases to get and then simplified If you selected D, you may have incorrectly simplified to be and then calculated . If you selected E, you may have incorrectly simplified then calculated .

Question 26. The correct answer is F. The sine of an angle in a right triangle is the ratio of the length of the side opposite that angle to the length of the hypotenuse of the triangle. To find the sine, we need to calculate the length of the side opposite the angle using the Pythagorean theorem, . For the given triangle, so . The length of the side opposite angle θ is 5 inches. Therefore, the sine of θ is . If you selected G, you may have found tan θ, the ratio of the lengths of the opposite and adjacent sides. If you selected H, you may have found cos θ, the ratio of the length of the adjacent side to the length of the hypotenuse. If you selected J, you may have found sec θ, the ratio of the length of the hypotenuse to the length of the adjacent side. If you selected K, you may have found csc θ, the ratio of the length of the hypotenuse to the length of the opposite side.

Question 27. The correct answer is C. The shaded region is made up of 2 triangles. The smaller triangle has a base of 2 inches and a height of 4 inches. The larger triangle has a base of 4 inches and a height of 6 inches. Therefore, the total number of shaded square inches is . The shaded area is 16 square inches, and the total area is 36 square inches. The fractional part that is shaded is then . If you selected A, you may have thought that both shaded triangles had an area of 12 square inches: . If you selected B, you may have divided the area of the shaded region by the area of the unshaded region instead of the total area: . If you selected D, you may have found the fractional part of the square that is unshaded instead of shaded: . If you selected E, you may have not multiplied by when finding the area of the shaded triangles: .

Question 28. The correct answer is H. By the communitive property of multiplication, . Because and , . Because , we know that . If you selected F, you may have incorrectly thought that and then found the solution to . If you selected G, you may have incorrectly thought that and then found the solution to . If you selected J, you may have incorrectly thought that and then found the solution to . If you selected K, you may have incorrectly thought that and then found the solution to .

Question 29. The correct answer is D. The value of m + 1 is always 1 more than m, thus m + 1 is always greater than m. If you selected one of the other choices, you may not have been able to produce a counter example. We know that (choice A) is false because . We know that (choice B) is false because . We know that (choice C) is false because . We know that (choice E) is false because .

Question 30. The correct answer is J. The volume of the cylinder is cubic meters. Since each cubic meter is 2,205 pounds, using the approximation , the total weight is pounds, which is between 500,000 pounds and 1,000,000 pounds. If you selected F, you may have not multiplied by pi when calculating the volume and found the total weight as pounds. If you selected G, you may have incorrectly calculated cubic meters as the volume, then found the weight as pounds. If you selected H, you may have mixed up the radius and the height of the cylinder and thought the volume was cubic meters. You may then have calculated the weight as pounds. If you selected K, you may have incorrectly calculated cubic meters as the volume, then found the weight as pounds.

Question 31. The correct answer is D. The length of the horizontal leg is 40 coordinate units, found by subtracting 0 – (–40). The length of the vertical leg is 30 coordinate units, found by subtracting 30 – 0. To find the length of a hypotenuse, c, when you know the lengths of 2 legs, a and b, use the Pythagorean theorem: . So and , which simplifies to c = 50. If you chose A, you may have found the length of the vertical leg. If you chose B, you may have found the mean of both leg lengths: . If you chose C, you may have found the length of the horizontal leg. If you chose E, you may have found the sum of the leg lengths: 40 + 30.

Question 32. The correct answer is F. Every circle has a vertical line of symmetry about its center (among infinitely many lines of symmetry). Any rotation of a circle about its center maps the circle onto itself. So, no matter where and how you draw a circle, it has a vertical line of symmetry. We can eliminate choices G, H, J, and K with counterexamples. This graphic gives all the lines of symmetry for a square, an ellipse, an equilateral triangle, and a rectangle. In the top row, they are oriented so 1 line of symmetry is vertical. In the bottom row, they are oriented so they do not have a vertical line of symmetry.

If you chose G, you may have done so because every square has 4 lines of symmetry, so 4 different orientations would result in a vertical line of symmetry; however, you didn’t consider the orientations that do not result in a vertical line of symmetry. If you chose H, J, or K, you may have done so because ellipses, triangles, and rectangles are often drawn with vertical lines of symmetry, and you didn’t consider counterexamples such as those shown in the bottom row of the graphic.

Question 33. The correct answer is B. The equation of this parabola is almost given in vertex form. Vertex form of a parabola is , where (h,k) is the vertex of the parabola. The given equation is equivalent to , which means h = –17 and k = –42. Therefore, the vertex is given by (–17, –42). If you chose A, (–a,k), you may have thought the x-coordinate of the vertex is equal to the opposite of a, the coefficient of the squared term. If you chose C, (–h,k), you may have forgotten that h, the x-coordinate of the vertex, is subtracted from x, so you forgot to divide 17 by –1. If you chose D, (–h,–k), you may have divided –42 by –1 instead of dividing 17 by –1. If you chose E, (a,–k), you may have used a instead of h and –k instead of k.

Question 34. The correct answer is H. First, find the area of square ABCD. For any square, all sides are congruent, so the length and width of square ABCD are both 15 meters. The area of any square or rectangle is the product of its length and width, so the area of square ABCD is 15(15) = 225 square meters. We are told that the area of the rectangle is equal to the area of the square, so it is also 225 square meters. We divide the area of the rectangle by its width, 10 meters, to get 225 ÷ 10 = 22.5 meters.

If you chose F, you may have assumed the length of the rectangle was equal to the length of the square. If you chose G, you may have thought the perimeters, not the areas, of the square and rectangle were equal: 2(15 + 15) = 2(10 + 20). If you chose J, you may have found the sum of the given lengths: 15 + 10. If you chose K, you may have found the product of the given lengths and then divided by 4: .

Question 35. The correct answer is B. Because the average of the 10 weights is 77 pounds, the total of the 10 weights is 77(10) = 770 pounds. The average of the weights of the 9 oldest boys is 78 pounds, so the total of those 9 weights is 78(9) = 702 pounds. The difference in totals gives the weight, in pounds, of the youngest boy: 770 – 702 = 68.

If you chose A, you may have thought the youngest boy was the lightest of the group and chosen the least option among the choices. If you chose C, you may have estimated well but not known how to find the exact value. If you chose D, you may have thought the youngest boy weighed the same as the average of the 9 remaining boys. If you chose E, you may have added the total number of boys and their average weight: 10 + 77.

Question 36. The correct answer is J. Substituting 10 and 100 for A and A₀, we have . To solve for h, first divide both sides by 10 to isolate the power: . Rewrite this exponential equation as an equivalent equation in logarithmic form: log₂10 . Finally, multiply both sides by 5: 5 log₂10 = h.

If you chose F, you may have rewritten by taking 10² first, resulting in and then solved correctly for h from this incorrect equation. If you chose G, you may have rewritten as if the exponent were a factor, resulting in and then solved correctly for h from this incorrect equation. If you chose H, you may have thought the product of 5 and log₂10 was log₂50. If you chose K, you may have multiplied the 10 and 2 on the right before rewriting the equation in logarithmic form: → log₂₀100 ; you then solved correctly for h from this incorrect equation.

Question 37. The correct answer is E. Both the numerator and the denominator of the given fraction can be factored into 2 binomials: . The identical binomials (x – 3) cancel, leaving . If you chose A, you may have thought you could cancel the identical terms x², even though they aren’t factors. If you chose B, you may have factored incorrectly: . If you chose C, you may have factored incorrectly: . If you chose D, you may have factored incorrectly: .

Question 38. The correct answer is H. We must find half of 9 feet 4 inches. To do this, we can find half of 9 feet, find half of 4 inches, and then add the results. Half of 9 feet is 4.5 feet, which is equivalent to 4 feet 6 inches (because there are 12 inches in 1 foot). Half of 4 inches is 2 inches. Now we can add 4 feet 6 inches plus 2 inches to get 4 feet 8 inches. Alternatively, we can convert 9 feet 4 inches to 112 inches. This comes from (9 feet)(12 inches per foot) + (4 inches). We divide 112 inches by 2 to get 56 inches and then convert 56 inches by finding how many whole groups of 12 inches go into 56 inches. There are 4 groups of 12 inches plus 8 inches left over. That is 4 feet 8 inches.

If you chose F, you may have taken half of 9 feet, which is 4.5 feet, and thought it was equivalent to 4 feet 5 inches. If you chose G, you may have thought 4.5 feet (half of 9 feet) was equivalent to 4 feet 5 inches and then added the 2 inches (half of 4 inches) to get 4 feet 7 inches. If you chose J, you may have converted 9 feet to 108 inches, divided 108 by 2, and then thought 54 inches was 5 feet 4 inches.

Question 39. The correct answer is A. Order of operations instructs us to perform the multiplication and division before the addition. Also, dividing by is equivalent to multiplying by 5. After multiplying and and 5, we have . Because is equal to , we have . Because 11 and 12 are relatively prime, x = 11 and y = 12. Therefore, x + y = 23.

If you chose B, you may have added + to get before multiplying: ; you then chose the numerator of the result, x = 25. If you chose C, you may have added + to get before multiplying: ; you then added x + y: 25 + 24 = 49. If you chose D, you may have multiplied by instead of multiplying by its reciprocal: ; you then added x + y: 31 + 60 = 91. If you chose E, you may have correctly solved for x and y but found the product xy instead of the sum x + y: 11(12) = 132.

Question 40. The correct answer is H. First, note that there are 4 repeating digits. This means than the 5th, 9th, 13th, etc., digits after the decimal point will be the same as the 1st digit after the decimal point, which is 3. In other words, any digit in a position corresponding to 1 mod 4 (has a remainder of 1 when divided by 4) will be 3. Similarly, any digit in a position corresponding to 2 mod 4 will be 1 (the 2nd digit). When we divide 358 by 4, we have a remainder of 2. Therefore, the 358th digit after the decimal point will be the same as the 2nd digit after the decimal point. This digit is 1.

If you chose F, you may have assumed the decimal terminated before position 358. If you chose G, you may have divided 358 by 5 instead of 4 (because there are 5 digits shown in the decimal, counting the 0) and chosen the remainder of that division. If you chose J, you may have divided 358 by 5 instead of 4 (because there are 5 digits shown in the decimal, counting the 0), and because the remainder of that division is 3, you chose the 3rd digit after the decimal point. If you chose K, you may have thought the digit must occur in both the given repeating decimal and 358.

Question 41. The correct answer is C. To answer this question, calculate the expected value of a random variable. The random variable is the discount amount per customer, measured in dollars. The value of the random variable depends on the color of the ball selected: for red, for white, and for green.

To calculate the expected value, multiply each of the possible values by its probability of occurring (the fraction of all balls that are a certain color), and then add the products. There is a probability of a red selection (a $6 discount), a probability of a white selection (an $18 discount), and a probability of a green selection (a $36 discount). So, the expected value is .

If you chose A, you likely multiplied the shoe price by the discount percentage for the color of the ball most likely to be selected (). If you chose B, you likely divided the sum of the possible discount amounts by the number of balls in the jar: . If you chose D, you likely found the average of the possible discount amounts: . If you chose E, you likely multiplied the discount percentage by $100 instead of $60 when finding the 3 possible discount amounts ().

Question 42. The correct answer is G. To find , the percentage of large animals that were lions, first divide the number of lions by the total number of animals. Then multiply that result by 100 to convert the decimal into a percentage: , which rounds down to 8%. So, the choice that is closest to the value of is 8.

If you chose F, you likely found the percentage of all animals that were lions: . If you chose H, you may have rounded up to 9. If you chose J, you may have found the ratio of animals that are NOT lions to animals that are lions: . If you chose K, you likely divided the number of large animals by the number of lions: .

Question 43. The correct answer is A. Only A and B are possible answers, since they are the only matrix products that result in a 1-by-1 matrix that represents the average daily total number of gallons of water consumed by all elephants, lions, and giraffes. The order of the entries in each matrix in A confirms that it is the correct choice. Since the left-to-right order of entries in the left matrix is the number of elephants (600), lions (200), and giraffes (800), the top-to-bottom order of entries in the right matrix must be the gallons of water for elephants (50), lions (5), and giraffes (10).

If you chose B, you likely didn’t notice that the left-to-right order of entries in the left matrix (elephants, giraffes, lions) failed to correspond the top-to-bottom order of entries in the right matrix (elephants, lions, giraffes). If the entries in the left and right matrices are not ordered consistently, the value of the entry in the 1-by-1 matrix product will be incorrect. If you chose C or D, you did not recognize that a 3-by-1 matrix multiplied by a 1-by-3 matrix results in a 3-by-3 matrix, not a 1-by-1 matrix. If you chose E, you likely forgot that a 3-by-1 matrix cannot be multiplied by a 3-by-1 matrix. For matrices and , the product exists only if the number of columns of equal the number of rows of .

Question 44. The correct answer is J. Populations that grow by a fixed percentage each year for years can be modeled with an exponential expression of the form , where is the starting size of the population and is the annual growth rate of the population. The growth rate should be rewritten as a decimal or fraction if it is given as a percentage. In this situation, and . So, the number of protected park animals years after the beginning of 2014 is .

If you chose F or G, you likely didn’t realize that linear expressions (expressions of the form ) do not model populations that grow in the way described. Choice G also shows an incorrect conversion of a percentage to a decimal (). If you chose H, you may not have realized that is not equivalent to . The location of the right parenthesis matters! If you chose K, you likely made the same incorrect percentage-to-decimal conversion mentioned for G.

Question 45. The correct answer is D. Anela will arrive in 5.5 hours. To see why, add her driving time of 5 hours to her break time of 0.5 hour (30 minutes is half an hour). As for Jacob, before his break he will drive 180 kilometers: . This leaves him with 420 kilometers left to drive: 600 – 180. It will take him 6 hours to drive that distance: . Adding his driving times to his break time shows that Jacob will arrive in 9 hours: 2 + 1 + 6. So, Anela and Jacob will arrive at the same time if Jacob leaves 3.5 hours earlier than Anela: 9 – 5.5.

If you chose A, you likely divided Jacob’s starting distance from Brady by his speed before the break , added his break time (), then subtracted from that Anela’s total travel time: 7.7 – 5.5. If you chose B, you likely forgot to add Jacob’s break time to his travel time: 8 – 5.5. If you chose C, you likely divided Jacob’s starting distance from Brady by his speed after the break , and subtracted from that Anela’s total travel time: 8.6 – 5.5. If you chose E, you likely forgot to add Anela’s break time to her driving time, and so subtracted only 5 hours from Jacob’s arrival time: 9 – 5.

Question 46. The correct answer is J. Rational expressions with the same denominator are subtracted the same way as fractions with the same denominator. The numerator of the result is the difference of the 2 numerators, while the denominator of the result is identical to the common denominator. The result is . The two terms in the numerator have a common factor of 2, meaning the result can be rewritten as . The common factors of 2 can be canceled. So, the result is .

If you chose F, you likely found the difference of the numerators () but thought the denominators cancel, since they are identical. If you chose G, you likely subtracted 3 instead of –3 when finding the difference of the numerators (), and thought the denominators cancel. If you chose H, your work may have looked like this: . This work reflects 2 errors: the subtraction error mentioned for G, and the deletion of in the denominator when the common factor of 2 is canceled. If you chose K, you likely canceled the variables in each fraction and evaluated the resulting expression: .

Question 47. The correct answer is B. To find the area of the rectangular stage in square yards, first convert its length and width from feet to yards. Since there are 3 feet per yard, the stage is 30 yards long () and 10 yards wide (). The area of a rectangle is its length times its width. So, the area of the stage is square yards.

If you chose A, you likely calculated the area in square feet and then found its square root since the unit of measure is a square unit: . If you chose C, you likely divided the area in square feet by the number of sides of the stage: . If you chose D, you likely divided the area in square feet by the number of feet in 1 yard to convert square feet into square yards: . If you chose E, you likely calculated the area in square feet, not square yards: .

Question 48. The correct answer is H. There are 15 lattice points inside the rectangle: (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3). Seven of those lattice points have coordinates whose sum is odd: (1,2), (2,1), (2,3), (3,2), (4,1), (4,3), (5,2). So, the probability that the chosen lattice point will have coordinates with an odd-numbered sum is .

If you chose F, you likely divided the number of lattice points randomly chosen (1) by the number of different odd -coordinates and -coordinates ( and ) of lattice points inside the rectangle. If you chose G, you likely counted only 6 of the 7 lattice points inside the rectangle with an odd-numbered sum: . If you chose J, you likely divided the number of lattice points on and inside the rectangle with an odd-numbered sum (17) by the number of lattice points on and inside the rectangle (35). If you chose K, you likely thought that since an integer is either odd or even, then half the lattice points would have odd-numbered sums, and half the lattice points would have even-numbered sums.

Question 49. The correct answer is A. One method for finding the answer starts with solving the system of equations . The top equation is the given formula rewritten to describe the third term, while the bottom equation describes the sixth term. Subtracting the bottom equation from the top equation gives , or . Adding the common difference of to the sixth term results in the seventh term. So, the seventh term is .

If you chose B, you may have noticed that the progression decreases from the third term and the sixth term. Since A and B are the only choices less than the sixth term, you may have incorrectly guessed which of them was correct. If you chose C, you likely subtracted the sixth term from the opposite of : . If you chose D, you likely selected the fraction that resembled the common difference, though it is missing the negative sign. If you chose E, you likely omitted the negative sign on when adding the common difference to the sixth term: .

Question 50. The correct answer is F. The event for which you need to find the odds in favor is “Jamie will be chosen to bat first.” The probability that Jamie will be chosen is . The probability that Jamie will NOT be chosen is . So, the odds in favor of Jamie being chosen to bat first is .

If you chose G, you may have thought the probability of Jamie being chosen was equal to the odds in favor of Jamie being chosen. If you chose H, you likely found the probability of Jamie NOT being chosen to be and built the odds ratio with that value: . If you chose J, you likely found the odds against Jamie being chosen: . If you chose K, you may have thought odds in favor was the reciprocal of the probability of Jamie being chosen.

Question 51. The correct answer is B. Find the total amount of salt by adding 5% of 120 liters and 15% of 80 liters: 0.05(120) + 0.15(80) = 6 + 12 = 18. Divide the 18 liters of salt by the 200-liter total: 18/200 = 0.09. Finally, convert 0.09 to a percentage. If you chose A, you may have reasoned correctly that because there is more of the 5% solution than the 15% solution, the combined solution must be less than 10% salt (the average of 5% and 15%), but you were not able to find the exact percentage. If you chose C, you may have found the average of the given percentages: . If you chose E, you may have found the average of the salt amounts from the original solutions: .

Question 52. The correct answer is F. Draw a trapezoid to represent a cross section of the pool: vertical bases of 3 feet and 10 feet representing the shallow end and deep end of the pool, extend down from a 50-foot horizontal representing the length of the pool. The sloped bottom side of the trapezoid represents the sloped bottom of the pool. Find the point where the sloped bottom meets the 3-foot vertical base and label it X. Beginning at X, draw a 50-foot horizontal line segment through the trapezoid to the 10-foot base to form a right triangle. The acute angle X is opposite the side of length 7 feet (from 10 − 3) and is adjacent to the side of length 50 feet. Therefore, . To solve for X, take the inverse tangent of both sides of the equation.

If you chose G, you may have added 10 feet and 3 feet instead of subtracting them. If you chose H, you may have made a ratio of the difference in depths to the greater depth: . If you chose J, you may have added 10 feet and 3 feet instead of subtracting them and thought the tangent ratio is the adjacent side over the opposite side instead of the opposite side over the adjacent side. If you chose K, you may have thought the tangent ratio is the adjacent side over the opposite side instead of the opposite side over the adjacent side.

Question 53. The correct answer is A. The standard form of a hyperbola is , where the center of the hyperbola is (h,k). The center of the given hyperbola is (2,2), so our answer should look like . So, among the answer choices, only A and B are possible. Rewrite A and B in standard form as and , respectively. Recall that the asymptotes of a hyperbola are lines that intersect at the center, forming an X shape, and that the branches of the hyperbola approach but do not intersect. The slope of the asymptote with positive slope is given by . If you draw the asymptote with positive slope, you will realize it must be greater than 1. Therefore, b > a. For the equations in both A and B, the value of a is 1, so we want the equation where b > 1. This is true only of the equation in answer choice A. If you chose B, you may have forgotten to move the coefficients of the 2nd fraction’s numerator to the denominator. If you chose C, you may have forgotten that h and k are subtracted from x and y. If you chose D, you may have forgotten that the 2nd fraction in standard form is subtracted instead of added. If you chose E, you may have made the 3 errors described in B, C, and D.

Question 54. The correct answer is K. Note that we are asked to find the length of the side opposite the obtuse angle of the triangle. The obtuse angle forms a linear pair with the 25° angle, so the measure of the obtuse angle must be 180° – 25° = 155°. To find the 3rd side length of a triangle when we know the opposite angle measure and the other 2 side lengths, we can use the law of cosines: . Substitute 700 for a, 250 for b, and 155° for C to get °. Finally, take the square root of both sides to isolate c, the unknown side length. If you chose F, you may have added the given side lengths and used the given angle. If you chose G, you may have just chosen an expression that uses the given side lengths and angle measure. If you chose H, you may have found the relevant obtuse angle, but you didn’t know how to proceed. If you chose J, you may have known to use the law of cosines, but you used the given 25° instead of the relevant interior angle measure of 155°.

Question 55. The correct answer is A. Because b > 0, b is positive. Because a > b, a is also positive. For any positive number, the absolute value of the number is equal to the number. Therefore, the first numbered inequality, |a| > |b|, is always true. We know that c is less than b, so c could be positive or negative. A counterexample shows that neither of the last 2 inequalities is always true: consider a = 5, b = 3, and c = –7. Then |a| = 5, |b| = 3, and |c| = 7, in which case |c| is greater than both |a| and |b|. Thus, B, C, and D are not always true. If you chose E, you may have ignored the absolute value bars in the given numbered inequalities.

Question 56. The correct answer is J. The committee is made up of Kenji, Mary, and 4 others. Imagine that Mary is seated. Someone will be randomly seated to her right. The probability that the person seated to Mary’s right is not Kenji is because 4 of the 5 people not seated yet are not Kenji. Now imagine that someone who is not Kenji is seated to Mary’s right, and someone will now be randomly seated to Mary’s left. The probability that the person seated to Mary’s left is not Kenji is because 3 of the 4 people not seated yet are not Kenji. Recall P(A and B) = P(A) · P(B|A); the probability that events A and B occur is equal to the probability of A times the probability of B given that A has occurred. Therefore, we find the product of and . Alternately, we can find the probability of the complement, that Kenji and Mary are seated next to each other and subtract that probability from 1. Imagine that Mary is seated. There are 5 positions in which Kenji can sit, 2 of which are next to Mary. So the probability that Kenji is seated next to Mary is . Therefore, the probability that Kenji is not seated next to Mary is 1 – . If you chose F, you may have considered Mary seated and made a fraction of 1 person (Kenji) over the total number of people who are not yet seated. If you chose G, you may have made a fraction of 2 people (Kenji and Mary) over the total number of people. If you chose H, you may have found the probability that Kenji and Mary are seated next to each other, but you did not subtract from 1. If you chose K, you may have thought that the probability that Kenji is seated next to Mary is . You then subtracted from 1.

Question 57. The correct answer is C. Note that 2⁹⁰ is the product of 2⁸⁸ and 2². That means that we can multiply 2⁸⁸ by 4 to get 2⁹⁰. We know that 2⁸⁸ has a 6 in the ones place. When we multiply the 6 in the ones place by 4, we get 24, which will result in a 4 in the ones place. If you chose A, you may have thought that you could add (instead of multiplying) 4 to 2⁸⁸ to get 2⁹⁰. Adding 4 to 6 gives 10, which results in a 0 in the ones place. If you chose B, D, or E, you may have chosen one of the other possible digits that could be in the ones place of a power of 2.

Question 58. The correct answer is F. The area of a triangle with base b and height h is given by . Recall that b and h must be perpendicular. The bottom side of the given triangle is horizontal because the endpoints both have a y-coordinate of d. Consider this side to be the base of the triangle, b, and find the length of this base by subtracting the x-coordinates: c – a. Now imagine the altitude of the triangle drawn from the point (b,e) down to our base at the point (b,d). The altitude would be vertical, making the x-coordinates of the endpoints both b. To find the altitude’s length or height, h, subtract the y-coordinates: e – d. In the expression , substitute (c – a) for b and (e – d) for h. If you chose H, you may have used just e for the height instead of e – d. If you chose J, you may have assumed sides and were perpendicular and tried to use the distance formula to represent their lengths, but you forgot to take the square root of the sums of the squares. If you chose K, you may have assumed sides and were perpendicular and used the distance formula to represent their lengths.

Question 59. The correct answer is A. To solve for x, divide both sides of the equation by (2 + 3i). This gives the solution . To find which of the given answer choices is equivalent to our solution, multiply the numerator and denominator of our fraction by 2 – 3i, the conjugate of the denominator: . Distribute to get , and simplify the denominator: . Finally, decompose the fraction into addends using the numerator addends. If you chose B, you may have simplified as instead of . If you chose C, you may have thought the number to the right of the equal sign of the given equation was the solution. If you chose D, you may have thought i = –1 and simplified as . If you chose E, you may have evaluated correctly until but then thought this was equivalent to .

Question 60. The correct answer is J. The shaded rectangular face of the dividing wall has an area of 39 square inches. Divide 39 square inches by the 13-inch length to find that the height of the dividing wall and container must be 3 inches. The base of the larger compartment is a trapezoid with parallel bases of 15 inches and 10 inches (from 15 – 5). The height of the trapezoid is 12 inches. The area of a trapezoid is given by . Substituting correctly gives , which is equal to 150. The area of the trapezoidal base of the larger compartment is 150 square inches. Finally, multiply the area of the base times the height of 3 inches to get a volume of 450 cubic inches.

If you chose F, you may have tried to find the volume of the smaller triangular compartment, multiplying side lengths of 5 inches and 12 inches to get 60 square inches and then multiplying by the 3-inch height. If you chose G, you may have multiplied 15 times 13. If you chose H, you may have thought you could find the area of the trapezoidal base of the larger compartment by multiplying the 13-inch side length by the 10-inch side length to get 130 square inches, and then you multiplied by the 3-inch height. If you chose K, you may have found the volume of the entire container: (15)(12)(3).

READING • PRACTICE TEST 1 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is C because the paragraphs that follow describe Murali and Vani’s growing closeness with each other as they become a “couple” (line 61). The passage implies that the two were “talking” (line 72) about their future plans for marriage. Lines 76–92 recount the negative reactions of their respective families.

The best answer is NOT:

A because the passage does not depict a time in which Murali is yet married.

B because although the passage alludes to Murali’s previously “thinking about widows or about repeating his own father’s collapse” (lines 33–34), nowhere does the passage indicate that Murali has specific reservations about marriage.

D because although Murali is indirectly characterized in the narration, this is not the main focus of the paragraphs that follow. Murali’s family conflicts are not specifically characterized in the passage.

Question 2. The best answer is F because the paragraph describes Vani’s “reserve” (line 17). The passage also notes that “she did not speak softly” (Line 20), denoting her certainty about speaking and indicating that her reserve was not caused by a lack of confidence. The description of Vani sewing her own clothes (lines 22–25) suggests a determined self-reliance.

The best answer is NOT:

G because although Murali anticipates that Vani’s face may take on an “austere severity” (line 15) when older, her manner is not described as being harsh or severe. Nowhere does the paragraph indicate that Vani is impolite.

H because the paragraph does not directly characterize Vani’s intelligence, nor does it describe Vani as apologetic. The paragraph notes her avoidance of “admitting she was wrong” (line 28), which suggests that Vani may be unlikely to be especially apologetic.

J because although the paragraph describes qualities Murali admires, no specific claims are made about Vani’s beauty. There is no support in the passage for the idea that Vani’s appearance was unkempt. Murali notes Vani’s “precision in even the smallest of tasks” (lines 15–16), which may extend to indicate precision in her personal style, as well.

Question 3. The best answer is B because, in recounting who “was responsible” (line 39) for the introduction, the paragraph indicates that the friend’s suggestion that Murali drive Vani home provided the introduction that drew the two together.

The best answer is NOT:

A because the elders were “eager to play parents” (line 61) only after Murali and Vani were known as a “couple” (line 61).

C because Vani smiled with her teeth (lines 57–59) after she’d exited Murali’s car at the conclusion of the drive to her home.

D because Vani’s brother burst into Murali’s brother’s home after learning that Murali wanted to marry his sister (lines 87–89).

Question 4. The best answer is H because the quoted dialogue immediately follows the description of Vani’s manner of speaking (lines 19–20), and the italicized portion serves to exemplify her calmly confident speech in public.

The best answer is NOT:

F because the passage does not provide any information that suggests Murali rehearses comments to himself in advance of speaking with someone previously unknown to him.

G because as the passage indicates, before Murali drove Vani home, the two had admired each other but hadn’t yet been introduced (lines 34–39). During the car ride home, which served as their introduction to each other, “they were silent” (line 48).

J because although Murali thought Vani “might be full of secrets and wanted to know them” (lines 19–20), he does not speculate about what those secrets are.

Question 5. The best answer is A because as the passage states, Vani “liked her food steaming and spicy” (lines 21–22), as Murali did.

The best answer is NOT:

B because although the passage states that Vani and Murali met in New York City (line 1), it does not indicate that they were born there.

C because the passage doesn’t indicate if either Vani or Murali had a passion for cooking.

D because although the passage states that “Vani had a job” (lines 62–63), it does not indicate where she worked. The passage describes Murali as a “bachelor-doctor” (line 66) but does not specifically indicate his place of work.

Question 6. The best answer is J because, as the passage indicates in lines 34–42, neither Murali nor Vani initiated direct contact with the other, and therefore neither of them would falsely claim or “admit” (line 39) responsibility.

The best answer is NOT:

F because the passage does not indicate that either Murali or Vani have forgotten, but rather that “no one else” (line 38) other than Murali and Vani remembers.

G because the passage doesn’t indicate that a friend claims responsibility; aside from Murali and Vani, “no one else really remembers” (line 38).

H because Murali did not initiate contact with Vani, but rather, as the passage relates in lines 39–42, Murali and Vani had their first direct contact after a friend suggested that Murali could give Vani a ride home.

Question 7. The best answer is B because as the passage states, Vani “did not ask him in for a cup of coffee; it was not her house” (lines 54–55).

The best answer is NOT:

A because the silence of their ride home is described as “comfortable” (line 49), and there is no evidence to suggest Vani was self-conscious or uncomfortable.

C because the passage does not indicate at what time Vani and Murali left the party or whether it was late.

D because as the passage states, Murali gave Vani a ride home in response to a friend’s suggestion (lines 41–42), rather than from a request from Vani.

Question 8. The best answer is J because the description of Vani serves to illustrate why the elders may have been “eager to play parents to the couple” (lines 60–61).

The best answer is NOT:

F because although Murali admired Vani, he was drawn by specific traits outlined in the second paragraph (lines 9–32), rather than the more generic virtues of being polite or being a good cook (line 62).

G because although the passage describes Vani’s family’s negative reaction to news of Murali’s interest in Vani (lines 76–82), the passage does not indicate how the family regards Vani herself.

H because the passage’s indication that a friend of Murali’s suggested Murali could give Vani a ride home (lines 41–42) is the passage’s only reference to a New York friend of Murali.

Question 9. The best answer is D because it can be inferred from the passage (lines 71–73) that Vani and Murali are “directly” (line 73) discussing plans to marry, which is confirmed by the passage’s description of Vani’s brother’s angry reaction after learning of “this doctor who wants to marry” (line 89) his sister. Vani’s family almost doesn’t agree to the marriage because of their discomfort with Murali’s “failure to observe certain formalities” (line 79). The passage indicates that it was unusual for a couple to discuss romantic feelings, that “these were not words they were used to saying” (lines 91–92).

The best answer is NOT:

A because as the passage states, Vani’s family found their discussion “improper” (line 78).

B because there is no support in the passage for the idea that their direct discussion of marriage was considered sensible by the Sri Lankan community.

C because as the passage states, “oceans away, families exploded” (line 76) with shock and anger at the news, which suggests they understood the serious, committed intent of Vani and Murali’s discussions.

Question 10. The best answer is G because “follow” is a synonym of “observe” in the context of adhering to certain traditions and practices. In this usage, the passage describes the family’s perception that Murali has failed to follow the rules required by “certain formalities” (line 79).

The best answer is NOT:

F because although “study” can be a synonym for “observe,” the passage describes that the family is disappointed by Murali’s failure to act in a traditional way (lines 77–80), rather than by a failure to study certain traditions.

H because “express” and “observe” have different meanings, and “express” would not make sense in the context of the passage.

J because although “perceive” can be a synonym for “observe,” the passage describes that the family is disappointed by Murali’s failure to act in a traditional way (lines 77–80), rather than by a failure of his perception.

Passage II

Question 11. The best answer is C because the first paragraph of Passage A states that “for most of human history, the phrase ‘light pollution’ would have made no sense” (lines 1–2). The details that follow describing the darkness of London, “Earth’s most populous city” (line 4) in 1800, support this idea that light pollution created by artificial light is a relatively recent phenomenon.

The best answer is NOT:

A because although the paragraph relates the invitation to “imagine walking toward London on a moonlit night” (lines 2–3), it does not include a specific claim about travel difficulty, nor does it include a claim about the impact of electricity.

B because although the paragraph mentions the use of gas lighting (lines 6–9), these details serve to further emphasize how dark London was in 1800.

D because although the paragraph describes London as “Earth’s most populous city” (line 4) in 1800, the darkness of such a populous city further illustrates the overall lack of light pollution.

Question 12. The best answer is F because the third paragraph of Passage A begins by stating that “in most cities the sky looks as though it has been emptied of stars, leaving behind a vacant haze” (lines 21–22). The third paragraph of Passage A concludes by describing the universe above “the city’s pale ceiling” (line 27) as “a bright shoal of stars and planets and galaxies, shining in seemingly infinite darkness” (lines 28–30).

The best answer is NOT:

G because the paragraph does not describe the colors of stars.

H because although the paragraph refers to the planet Venus in lines 25–26, this reference serves to illustrate the darkness of the sky, and no comparison of the brightness of Venus to that of the stars is made.

J because although the paragraph states that people have “grown so used to this pervasive orange haze” (lines 23–24), it does not mention people’s lost appreciation for stars or a pervasive apathy for stars today.

Question 13. The best answer is B because Passage A describes light as “a powerful biological force” (lines 34–35) that can act “as a magnet” (line 35). Passage A gives the example of songbirds and seabirds “circling and circling in the thousands” (lines 40–41) as a result of being drawn by the artificial light emitted by searchlights and gas flares.

The best answer is NOT:

A because Passage A does not refer to any animal’s food-searching abilities, nor does it indicate that darkness would diminish those abilities.

C because Passage A states that light “is a powerful biological force” (lines 34–35) that can act “as a magnet” (line 35) that draws animals. It does not indicate whether light levels drive animals to dark areas.

D because Passage A does not refer to the natural habitats of animals or to urban expansion.

Question 14. The best answer is H because the author of Passage B states: “I love the story this painting tells, of a small dark town, a few yellow-orange gaslights in house windows, under a giant swirling and waving blue-green sky” (lines 54–57). In contrast, Joseph doesn’t mention the story of the painting. “It’s beautiful” (line 52), Joseph states, adding, “What more can you say than that?” (lines 52–53).

The best answer is NOT:

F because although the author of Passage B notes the “yellow-orange” (line 56) and “blue-green” (line 57) colors in the painting, the author focuses in greater detail on “the story this painting tells” (lines 54–55).

G because Passage B indicates in lines 52–54 that both the author and Joseph admire the painting’s beauty.

J because Passage B does not include any information about the technique Van Gogh used to paint The Starry Night.

Question 15. The best answer is A because the first paragraph of Passage B describes The Starry Night as a “scene of stars and moon and sleeping town” (line 47). In addition, the first paragraph indicates the painting’s popularity, noting that “fifty million people pass by every year” (lines 45–46).

The best answer is NOT:

B because the paragraph does not establish that the author of Passage B is seeing The Starry Night for the first time.

C because the paragraph does not provide examples of people’s expectations about The Starry Night.

D because the paragraph does not establish why Van Gogh painted The Starry Night.

Question 16. The best answer is H because the author of Passage B states, “Does Van Gogh use his imagination? Of course, but this is an imagined sky inspired by a real sky” (lines 68–70). The excerpt from Van Gogh’s letter in lines 79–87 then describes the bright and colorful night sky that he observed in 1888.

The best answer is NOT:

F because Passage B does not establish the time of day in which Van Gogh painted.

G because the excerpt from Van Gogh’s 1888 letter establishes that the artist witnessed a night sky with such vibrant colors that he compared the stars to jewels: “opals you might call them, emeralds, lapis lazuli, rubies, sapphires” (lines 86–87).

J because the author of Passage B argues that Van Gogh did use his imagination to paint The Starry Night, stating, “Does Van Gogh use his imagination? Of course, but this is an imagined sky inspired by a real sky” (lines 68–70).

Question 17. The best answer is B because in Passage B, Van Gogh’s description of the stars as “more brilliant, more sparkling gemlike than at home—even in Paris” (lines 84–85) indicates that the stars over Paris would have been quite bright even in that “time before electric light” (lines 75–76). That this brightness would be “remarkable to modern eyes” (line 88) helps establish that in recent times, the night sky in Paris is much duller. Therefore, no one has recently seen “anything like” the night sky over Paris mentioned in Van Gogh’s letter.

The best answer is NOT:

A because Passage B establishes a stark contrast between the two night skies in Paris rather than a strong similarity between them.

C because Passage B does not establish a spatial relationship between the two night skies in Paris.

D because Passage B does not establish a spatial relationship between the two night skies in Paris.

Question 18. The best answer is J because Passage A explores the issue of light at night, noting how “most of humanity” (line 11) lives beneath artificial light, positing that “in most cities the sky looks as though it has been emptied of stars” (lines 21–22) and that “we’ve lit up the night as if it were an unoccupied country” (lines 31–32). Passage B presents the issue of light at night by discussing the depiction of the night sky in Van Gogh’s The Starry Night, describing it as “a painting of our world from before night had been pushed back to the forest and the seas, from back when sleepy towns slept without streetlights” (lines 57–60).

The best answer is NOT:

F because Passage A does not present a summary of the circumstances that led to light being common at night.

G because Passage A does not offer suggestions for restoring darkness to today’s night. Additionally, Passage B provides information only about Van Gogh’s The Starry Night.

H because Passage B does not provide an explanation for how people in Van Gogh’s time used light at night.

Question 19. The best answer is A because the first paragraph of Passage A discusses the darkness of night in London in 1800. From the references to the bright stars of Paris in lines 83–91 of Passage B, it can be inferred that the night sky over the city of Paris was dark during Van Gogh’s lifetime.

The best answer is NOT:

B because neither of the passage authors discuss the opinions of scientific researchers.

C because the author of Passage A does not discuss any well-known works of art.

D because neither of the passage authors discuss personal memories of when night was darker.

Question 20. The best answer is F because the last paragraph of Passage A describes the effects of artificial light on animals in lines 33–41, whereas Passage B does not mention animals at all.

The best answer is NOT:

G because in lines 79–91, Passage B provides information on the colorful appearance of stars prior to electric lights, whereas Passage A does not refer to star color at all.

H because Passage B makes the argument that Van Gogh’s The Starry Night is both a reflection of nature and a work of imagination in lines 68–73, whereas Passage A does not refer to the imagination at all.

J because Passage B refers to night having “been pushed back to the forest and the seas” (lines 58–59), places where night’s original darkness remains.

Passage III

Question 21. The best answer is B because the passage begins in lines 1–19 by recounting the author’s experience returning to a once-familiar place and experiencing memories. This first paragraph provides an example of how “places hold memories” (line 20). The author proceeds to consider how personal memories can be affected by photographs and other factors.

The best answer is NOT:

A because although the passage alludes to a childhood experience in lines 3–4, the passage does not describe a specific incident.

C because although the author self-identifies as belonging to the “image-makers and consumers” (lines 75–76), the passage does not relate a specific narrative of the author’s lifelong hobby of photography.

D because the passage does not indicate that the author’s opinions on a topic have changed.

Question 22. The best answer is G because the author claims that “places hold memories better than people and better than photographs” (lines 20–21). Lines 24–29 describe how conversations may alter or replace memories, and the passage continues by exploring how “photographs do not preserve memory” (line 47) but instead “replace memory” (line 48).

The best answer is NOT:

F because the author claims in lines 24–29 that conversations may alter or replace memories and states that “photographs inaccurately reflect experience from the start” (lines 35–36).

H because the passage makes no claim that a person’s memory of an event has any effect on the truth of a photograph depicting that event.

J because the passage does not establish that conversation, photographs, and visits to places are the exclusive sustainers of memories.

Question 23. The best answer is D because the author states, “I loved this place” (line 4) and describes himself as “amazed” (line 5). The reference to “this ritual” (line 19) also suggests an earnest seriousness.

The best answer is NOT:

A because the author’s tone is sincere, rather than joking, in recounting how the place remains “startingly unchanged” (line 8).

B because the waterfall reminds the author of positive childhood memories, and he describes his “mixture of apprehension and pleasure” (line 15).

C because the author does not make a request.

Question 24. The best answer is G because the details in the second paragraph support the claim that conversations about shared memories may “alter or even replace our own memories with those of another” (lines 27–28).

The best answer is NOT:

F because instead of focusing on the loss of the memory, the second paragraph focuses on how memories may be changed as a result of interactions with others.

H because in lines 27–28, reminiscing is portrayed as an activity that alters or replaces memories, rather than preserving them.

J because although the second paragraph identifies both “family” (line 21) and “people from our past who may remind us of events in our lives and with whom we may reminisce” (lines 21–23), it makes no distinction between how well family members or non-family members evoke memories.

Question 25. The best answer is D because the prior sentence describes how “snapshots are most commonly a break from the event” (lines 64–65), in which people pause to allow a photo to be taken. The moment captured in the photograph, therefore, “is experienced as a moment taking a photograph” (lines 66–67) rather than a moment in the experience being documented.

The best answer is NOT:

A because the quotation focuses on the act of photography itself, rather than the skill of the photographer.

B because the author’s description of a photograph being taken in lines 64–70 focuses on the experience of being photographed and does not focus on the photographer as a participant in the action.

C because the author questions the degree to which photographs can be considered accurate records of experience, noting that “photographs only tell such a small part of any story” (lines 56–57) and that “they deceive” (line 58).

Question 26. The best answer is H because in the first paragraph the author states that he was “getting ready to jump” (line 16), leaning over the edge of the cliff to “prepare myself for what I am about to do” (lines 17–18). He describes the action he is about to take as “this ritual” (line 19), suggesting the repetition of the childhood action of when the author “used to jump from those cliffs” (lines 3–4).

The best answer is NOT:

F because the first paragraph does not mention the possibility of hiking back down, and the author instead describes “getting ready to jump” (line 16) from the cliff.

G because the first paragraph does not mention the possibility of sitting, and the author instead describes “getting ready to jump” (line 16) from the cliff.

J because the first paragraph does not indicate whether the author was in possession of a camera or intended to take a photograph.

Question 27. The best answer is C because in the third paragraph the author states that “photographs inaccurately reflect experience” (lines 35–36), partly as a result of “elimin[ating] . . . time” (line 38).

The best answer is NOT:

A because the author makes no reference to the age of people taking photographs.

B because although the author provides examples in lines 42–44 of different events a photograph might depict, the author does not indicate that there is a best way to photograph an event.

D because the author does not make a comparison between the ability of the human eye to capture detail and that of a photograph.

Question 28. The best answer is G because the information helps illuminate what kinds of experiences people try to capture in photographs, providing specific examples of the “family outings” and “vacations” mentioned in line 42.

The best answer is NOT:

F because the author makes no distinction between trivial and meaningful pictures, but instead uses these examples to support the claim that photographs are taken “in the hope of freezing time” (lines 44–45).

H because although the details in lines 43–44 are used as examples, they are utilized to support the claim that photographs are taken “in the hope of freezing time” (lines 44–45).

J because although the author states that “we fill scrapbooks and hard drives” (lines 41–42), the context makes clear that he means “we” in the collective sense, referring to people in general, rather than to himself, specifically. The author’s statement, “I do it, too” (line 46) helps clarify that he was not referring specifically to himself in his use of the word “we” in line 41.

Question 29. The best answer is A because “objective truth” has a similar meaning as “irrefutable factuality” (lines 52–53) and “seemingly” (line 52) suggests something that appears to be true but isn’t necessarily so—something that “conveys an impression.” Further clarity is provided by the statement that “a photograph’s version of events did happen” (lines 54–55) but only tells a “small part of any story” (line 57).

The best answer is NOT:

B because the author argues that “photographs are an abstraction of experience” (lines 48–49) and “an abstraction of memory” (lines 49–50), which, it can be inferred, would serve to make events less clear.

C because although the passage states that “a photograph’s version of events did happen” (line 54–55), lines 56–58 state that the image can be deceptive by telling only a small part of the story.

D because the author claims that photographic depictions “only tell such a small part of any story” (lines 56–57) and “deceive” (line 58), rather than imply a story beyond the actual depiction.

Question 30. The best answer is G because “essence” is a synonym of “nature” in the context of the author’s defining key qualities of memory in lines 82–83.

The best answer is NOT:

F because although “temperament” can be a synonym for “nature,” the word is usually used to describe the mood or behavior of a living entity, making this a contextually inappropriate choice to modify “memory” in lines 82–83.

H because although “scenery” may sometimes be used to refer to natural surroundings or landscapes, the word would not make sense in the context of defining the key qualities or “nature” of memory in lines 82–83.

J because although “scenery” may sometimes be used to refer to natural settings, the word would not make sense in the context of defining the key qualities or “nature” of memory in lines 82–83.

Passage IV

Question 31. The best answer is A because lines 65–78 describe how a certain type of solar technology that uses electrolyzers demonstrates that the technology could work, “in principle” (line 75). The passage notes, however, that the models are “bulky” (line 65), and key components such as silicon crystals (line 80) and platinum (lines 81–82) are too expensive for use in large-scale implementation.

The best answer is NOT:

B because although the seventh paragraph states that an electrolyzer “uses the solar electricity to break water molecules” (lines 69–70), this detail is given in support of the paragraph’s overall explanation of the technology.

C because although the seventh and eighth paragraphs (lines 65–82) describe a prototype made by a Japanese automaker, they do not indicate that the United States and Japan are working collaboratively on research.

D because although the seventh and eighth paragraphs (lines 65–82) describe a prototype made by a Japanese automaker, they do not question any aspect of the auto industry.

Question 32. The best answer is H because Nathan S. Lewis is identified as the speaker “giving a lecture” (line 1), and lines 4–6 present a paraphrase of the lecture’s key claim.

The best answer is NOT:

F because although the passage mentions that “other researchers” (line 22) are researching uses of algae, this is given as an example of alternate research approaches, and the researchers’ location is not given.

G because the passage attributes the claim in lines 4–6 to “the chemist” (lines 3–4) that is giving the lecture. Nathan S. Lewis was introduced in the preceding sentence (lines 1–2) as the speaker giving the lecture.

J because the passage author prefaces the claim in lines 4–6 with “the chemist says” (lines 3–4), indicating that what follows is the opinion of “the chemist,” Nathan S. Lewis, and not the opinion of the author.

Question 33. The best answer is C because the passage states that “humankind needs a radical breakthrough in solar fuel technology” (lines 11–12), indicating that a technological breakthrough is necessary but has not yet occurred. The passage then indicates that such a breakthrough would involve using solar technology to “create heat or generate electricity” (lines 14–16) and “store the fuel for use when the sun is down” (lines 16–17).

The best answer is NOT:

A because the passage states that “humankind needs a radical breakthrough in solar fuel technology” (lines 11–12), indicating that a technological breakthrough has not yet occurred. The description of Lewis’s research that follows in lines 18–22 suggests early progress toward the goal of “artificial leaves” (lines 13–14), but this work is too preliminary to have a broad impact.

B because the passage does not indicate that Lewis believes that either the breakthrough or the capabilities are misguided. The passage does not refer to the energy industry having a focus on consumption.

D because the passage states that “humankind needs a radical breakthrough in solar fuel technology” (lines 11–12), indicating that the breakthrough has not yet occurred. In addition, the passage suggests that the capabilities described in lines 14–17 will be the result of the radical breakthrough, not the cause.

Question 34. The best answer is F because the passage states that “commercial solar cells contain expensive silicon crystals” (lines 79–80) and that platinum is “to date the best material for catalyzing the water-splitting reaction, but it costs $1,500 an ounce” (lines 81–82). The passage goes on to explain that, according to Lewis, “future solar-fuel devices would have to cost less than $1 per square foot of sun-collecting surface” (lines 84–85), suggesting that cheaper materials will be needed to implement solar technology on a large scale.

The best answer is NOT:

G because the passage relates that a device called an “electrolyzer” (line 58) can “split water into oxygen and hydrogen” (lines 58–59). The passage then goes on to explain that “electrolyzers are used in various commercial processes” (lines 62–63), indicating that a device capable of splitting water into hydrogen and oxygen already exists.

H because the passage does not refer to federal funding research for solar technology research, nor does it specifically indicate that Lewis lacks the federal funding necessary for his research.

J because the passage does not indicate that the public is reluctant to embrace new technology. Rather, it claims that “with a new energy and climate crunch looming, solar fuel is suddenly gaining attention” (lines 47–48).

Question 35. The best answer is A because, as the passage indicates in a paraphrase of Lewis’s lectures, he tells his crowds that “the sun pours more energy onto the earth every hour than humankind uses in a year” (lines 9–11).

The best answer is NOT:

B because, as the passage indicates in a paraphrase of Lewis’s lectures, he tells his crowds that “the sun pours more energy onto the earth every hour than humankind uses in a year” (lines 9–11).

C because, as the passage indicates in a paraphrase of Lewis’s lectures, he tells his crowds that “the sun pours more energy onto the earth every hour than humankind uses in a year” (lines 9–11).

D because, as the passage indicates in a paraphrase of Lewis’s lectures, he tells his crowds that “the sun pours more energy onto the earth every hour than humankind uses in a year” (lines 9–11).

Question 36. The best answer is J because the passage states that Lewis’s lab is crafting prototype leaves that are “not much larger than computer chips” (line 19).

The best answer is NOT:

F because the passage does not compare the size of Lewis’s prototype leaves to that of a human hand. Rather, the passage states that Lewis’s lab is crafting prototype leaves that are “not much larger than computer chips” (line 19).

G because although the passage describes Lewis’s solar technology as “artificial leaves” (lines 13–14), the passage goes on to explain that the prototype leaves crafted at Lewis’s lab are “not much larger than computer chips” (line 19).

H because although the passage refers to films as “cheap as wall-to-wall carpeting” (line 41), the passage does not compare the size of Lewis’s prototype leaves to that of a carpet square. Rather, the passage states that Lewis’s lab is crafting prototype leaves that are “not much larger than computer chips” (line 19).

Question 37. The best answer is C because lines 24–26 describe projects that seek to “capture solar rays and churn out chemical fuel” (lines 13–14) and “turn sunlight into chemical energy that can be stored” (lines 27– 28). In this context, when the passage states that the algae “has been genetically altered to pump out biofuels” (lines 24–25), it can be inferred that to “pump out” means “to produce.”

The best answer is NOT:

A because when the passage states that the algae “has been genetically altered to pump out biofuels” (lines 24–25), it can be inferred that the goal is for the algae to produce, rather than to remove, fuel to use as an energy source.

B because when the passage states that the algae “has been genetically altered to pump out biofuels” (lines 24–25), it can be inferred that the goal is for the algae to produce, rather than to drain or diminish, fuel to use as an energy source.

D because when the passage states that the algae “has been genetically altered to pump out biofuels” (lines 24–25), it can be inferred that the goal is for the algae to produce, rather than to siphon or drain away, fuel to use as an energy source.

Question 38. The best answer is G because the passage states that Lewis estimates the need to “manufacture thin, flexible solar-fuel films” (lines 37–38) that would “roll off high-speed production lines the way newsprint does” (lines 39– 40).

The best answer is NOT:

F because, although the passage describes Lewis’s initial prototypes as “not much larger than computer chips” (line 19), it paraphrases Lewis’s prediction of the need for “thin, flexible solar-fuel films, instead of discrete chip-like devices” (lines 38–39).

H because the passage does not indicate that Lewis imagines small, rigid solar panels as the ideal, but rather “thin, flexible solar-fuel films” (line 38).

J because, although the passage does describe a Japanese prototype that is “taller than a refrigerator and is covered with photovoltaic cells” (lines 68–69), the passage does not relate this research to Lewis’s ideals for energy innovation. Instead, the passage states that Lewis argues that “the man-made leaf option is most likely” (line 29) to provide a large-scale solar energy solution, which he imagines as being manufactured as “thin, flexible solar-fuel films” (line 38).

Question 39. The best answer is D because the passage states that Lewis’s artificial leaf technology “requires two principal elements: a collector that converts solar energy (photons) into electrical energy (electrons) and an electrolyzer” (lines 55–59).

The best answer is NOT:

A because the passage does not indicate that either ambient air or fuel cells are the principal elements of Lewis’s artificial leaves. Rather, the passage explains that the principal elements of Lewis’s leaves are a collector and an electrolyzer (lines 55–59).

B because, while the passage indicates that a catalyst is needed to help an electrolyzer split oxygen and hydrogen (lines 59–60) and explains that an electrolyzer uses solar electricity to break water molecules (line 70), it does not indicate that these are the principal elements of Lewis’s artificial leaves. Rather, the passage explains that the principal elements of Lewis’s leaves are a collector and an electrolyzer (lines 55–59).

C because, while the passage does indicate that commercial solar cells contain silicon crystals (lines 79–80), and that electrolyzers contain platinum (lines 80–81), it does not indicate that these are the principal elements of Lewis’s artificial leaves. Rather, the passage explains that the principal elements of Lewis’s leaves are a collector and an electrolyzer (lines 55–59).

Question 40. The best answer is J because the passage states that “the exhaust from burning the hydrogen later in a fuel cell is water” (lines 77–78).

The best answer is NOT:

F because the passage does not claim that burning hydrogen in a fuel cell creates electron energy that splits silicon crystals. Instead, the passage states that “the exhaust from burning the hydrogen later in a fuel cell is water” (lines 77–78).

G because the passage does not claim that burning hydrogen in a fuel cell causes the hydrogen to bond with oxygen. Instead, the passage states that “the exhaust from burning the hydrogen later in a fuel cell is water” (lines 77–78).

H because the passage does not claim that burning hydrogen in a fuel cell causes the fuel cell’s lining to deteriorate. Instead, the passage states that “the exhaust from burning the hydrogen later in a fuel cell is water” (lines 77–78).

SCIENCE • PRACTICE TEST 1 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is B. According to Table 1, at 273 K, the molar volume of H₂ at 5.00 atm is 4.496 L, and the molar volume of H₂ at 10.0 atm is 2.256 L. The absolute value of the difference between the two molar volumes is 2.240 L. A, C, and D are incorrect; the difference is closest to 2.2 L. B is correct.

Question 2. The best answer is G. According to Table 2, at 323 K, the molar volume of Ar was the smallest at 26.486 L, followed by N₂ with a molar volume of 26.492 L, then He with a molar volume of 26.504 L, and finally H₂ with the largest molar volume of 26.521 L. F is incorrect; the molar volume of He is greater than the molar volume of N₂. G is correct. H and J are incorrect; Ar has the smallest molar volume, and H₂ has the greatest molar volume.

Question 3. The best answer is B. In both Table 1 and Table 2, at any given temperature and pressure, the greatest difference between the molar volume of O₂ and the molar volume of Ar is 0.002 L. This is the smallest difference observed and makes the molar volume of O₂ most similar to the molar volume of Ar. A is incorrect; the molar volumes of O₂ and He differ by approximately 0.05 L. B is correct. C is incorrect; the molar volumes of O₂ and H₂ differ by a minimum of 0.012 L. D is incorrect; the molar volumes of O₂ and N₂ differ by a minimum of 0.006 L.

Question 4. The best answer is F. According to Table 2, at 1.00 atm and 773 K, the molar volumes of the gases range from 63.440 L to 63.453 L; none of these values are smaller than the molar volume of an ideal gas. F is correct. G, H, and J are incorrect; none of the gases listed in Table 2 have a molar volume less than the molar volume of an ideal gas.

Question 5. The best answer is D. Because the mean free time decreases as a sample’s volume decreases, the mean free time would be least for a 1 mol sample of the gas with the smallest molar volume. According to Table 1, O₂ at 100.0 atm has a molar volume of 0.198 L. This is the smallest molar volume listed in Table 1. A is incorrect; He at 0.500 atm has a molar volume of 44.825 L, which is not the smallest of the gases listed. B is incorrect; O₂ at 0.500 atm has a molar volume of 44.773 L, which is not the smallest of the gases listed. C is incorrect; He at 100.0 atm has a molar volume of 0.247 L, which is not the smallest of the gases listed. D is correct; O₂ at 100.0 atm has the smallest molar volume of the gases listed and will therefore have the least mean free time.

Question 6. The best answer is J. In order to answer this item, the examinee must know that the average kinetic energy of the molecules in a sample of O₂ increases as the temperature increases. Based on Table 2, a 1 mol sample of O₂ with a volume of 18 L has a temperature of approximately 223 K, and a 1 mol sample of O₂ with a volume of 63 L has a temperature of approximately 773 K. The sample with the volume of 63 L has a higher temperature, and therefore the average kinetic energy of the molecules in this sample is greater. F and G are incorrect; the molecules in the sample with a volume of 63 L are more likely to have a greater average kinetic energy. H is incorrect; the average kinetic energy of the molecules in the 63 L sample is more likely greater because it is at the higher temperature not the lower temperature. J is correct.

Passage II

Question 7. The best answer is B. According to Figure 3, as cleaning time increased from 0 minutes to 30 minutes and then to 60 minutes, the corresponding average number of colonies per dish went from 79 to 29 and then to 12. A is incorrect; the trend consistently decreases not increases with increasing cleaning time. B is correct. C and D are incorrect; the average number of colonies trend did not start in one direction and then change to the opposite direction.

Question 8. The best answer is J. The description of Experiment 3 states that 3 groups of 10 S. carnaria flies were used. F, G, and H are incorrect; 5, 10, and 24 flies are less than the actual number of flies used in Experiment 3. J is correct; there were a total of 30 flies used in Experiment 3.

Question 9. The best answer is A. The first paragraph states that the experiments were conducted to study the transfer of bacteria from one surface to another by flies. It is true that the bacteria being transferred could be disease-causing and be spread by the flies after walking in the enclosure containing E. coli. A is correct; Figure 1 shows that after the flies walked in an enclosure containing E. coli and were then placed on the sterile nutrient agar, bacteria were cultured from the nutrient agar plates. B is incorrect; the 2 species of flies were examined in separate procedures. There was no interaction between the 2 species in the experiments, and Figure 1 does not show the results of such an interaction. C is incorrect; Figure 1 shows that both species of flies transferred E. coli from the enclosure to the nutrient agar. D is incorrect; the experiments did not mix flies of the 2 species and did not study whether one species of fly transferred bacteria to the other species, and Figure 1 does not show the results of such an interaction.

Question 10. The best answer is G. The experiments were done to determine if flies transferred bacteria from one surface to another. To ensure the flies were the only source of the bacteria colonies that grew on the nutrient agar, the agar had to be sterilized before the flies and any bacteria they carried were placed on the agar. F is incorrect; the agar was sterilized to be sure all bacteria on the agar were killed before the flies were placed in the dishes. G is correct. H is incorrect; the agar was not a food source for the flies, and sterilizing the agar would have done nothing to ensure that it had nutrients even if it were a food source. J is incorrect; the nutrient agar already contained the necessary nutrients for bacteria growth. The sterilization process kills any bacteria on the agar; it does not affect the bacteria nutrients that were already there.

Question 11. The best answer is A. To see if the new species (Species X) transferred more bacteria than either of the 2 species in the experiments, Species X flies would have to be subjected to the same procedures as the other 2 species. A is correct; only Experiment 1 used both original species of flies. Adding a group of Species X flies to that experiment would allow a comparison of the number of colonies transferred by each of the 3 species. These data would allow the student’s claim to be evaluated. B is incorrect; just changing the kind of bacteria in Experiment 1 would still include only the original 2 species of flies; no Species X flies would be included. There would be no data for Species X that could be used to evaluate the claim. C is incorrect; Experiment 2 included only 1 of the 2 original species of flies. To evaluate the claim, data for all 3 species would need to be collected. The design of Experiment 2 would not provide those data. D is incorrect; just changing the kind of bacteria in Experiment 2 would still include only 1 of the original 2 species of flies; in addition, no Species X flies would be included. Data for all 3 species would need to be collected to evaluate the claim.

Question 12. The best answer is F. In Experiment 3, S. carnaria flies were allowed to walk in an enclosure containing E. coli and then allowed various lengths of time to clean themselves before being placed on nutrient agar. Figure 3 shows that the longer the time to clean, the fewer bacteria colonies were produced on the agar. F is correct; this experiment tested whether cleaning time affected the average number of colonies per dish, and the results indicate that the flies removed bacteria as they cleaned themselves. G is incorrect; Experiment 3 used the procedures from Experiment 1, where the flies were allowed to walk in the E. coli enclosure for exactly 5 minutes. Since exposure time was held constant, this experiment would not be able to test a hypothesis about the effect of varying exposure time. H and J are incorrect; Experiment 3 used only S. carnaria flies. Without the second species of fly included, Experiment 3 cannot test whether one species transferred more bacteria or removed bacteria better than the other species.

Question 13. The best answer is B. Figure 1 shows that the average number of colonies per dish for S. carnaria that had walked in the enclosure for 5 min was about 90. Figure 2 shows that the average number of colonies per dish for S. carnaria that had walked in the enclosure for 5 minutes, the same length of time as in Experiment 1, was about 82. Even though the conditions were the same (same species, same walking time), it would be common for the results to be different by chance. A is incorrect; the question asks why the results for S. carnaria were different in Experiment 1 and Experiment 2 even though the species of fly and the walk time were the same. The number of E. coli colonies transferred by the other species of fly would not explain the difference between the S. carnaria results since the M. domestica flies were tested separately. B is correct. C is incorrect; the question asks why the results for S. carnaria were different in Experiment 1 and Experiment 2 even though the species of fly and the walk time were the same. The number of E. coli colonies transferred by the other species of fly would not explain the difference between the S. carnaria results since the M. domestica flies were tested separately. D is incorrect; the S. carnaria data from Experiment 1 and the specified S. carnaria data from Experiment 2 were both for a walk time of 5 min. Since the walk times were the same, that could not be an explanation for the difference in the number of colonies.

Passage III

Question 14. The best answer is F. Figure 1 displays a plot line representing the %O₂ in Earth’s atmosphere from 250 mya to 64 mya. The single data point along that line that is closest to 21% is at the x-axis value of 250 mya (a value of approximately 20.5%). F is correct. G is incorrect. The %O₂ value at 200 mya is approximately 14.5%, much less than 21%. H is incorrect. The %O₂ value at 150 mya is approximately 13.9%, much less than 21%. J is incorrect. The %O₂ value at 100 mya is approximately 19.1%, less than 21% and not as close to 21% as the data point at 250 mya.

Question 15. The best answer is C. Figure 2 shows that at an initial %O₂ of 17%, the flame duration for dry paper is approximately 8 sec and the flame duration for pine wood is approximately 2 sec. The difference is closest to 6 sec. A and B are incorrect. The values 2 sec and 4 sec are less than the actual difference of 6 sec. C is correct. D is incorrect. The value of 8 sec is greater than the actual difference of approximately 6 sec.

Question 16. The best answer is G. In Figure 1, there are 7 time periods, covering 200 mya–140 mya, in which paleowildfires occurred, but the %O₂ values were all less than 15%. Any interval within that range would have data that are inconsistent with the claim. F is incorrect. 250 mya–230 mya had paleowildfires, but the %O₂ was greater than 15%. Those data are consistent, not inconsistent, with the claim. G is correct. H and J are incorrect. Both 120 mya–100 mya and 90 mya–70 mya had paleowildfires, but the %O₂ was greater than 15%. Those data are consistent, not inconsistent, with the claim.

Question 17. The best answer is C. Figure 2 shows that the lowest initial %O₂ values at which each of the materials ignited are 13% for the match, 14% for the dry paper, 15% for the candle, and 16% for the pine wood. The order of the materials from highest initial %O₂ to ignite to lowest initial %O₂ to ignite is pine wood, candle, dry paper, and match. A and B are incorrect. Match would be last in the order, as it had the lowest initial %O₂ to ignite. C is correct. D is incorrect. Candle should come before dry paper in the order since the candle had a higher initial %O₂ to ignite than did the dry paper.

Question 18. The best answer is F. Figure 1 shows bars representing the number of paleowildfires for each of a number of time periods, each covering a 10 million year interval, starting 5 million years before the labeled year and ending 5 million years after the labeled year (e.g., the bar labeled 140 mya represents the period 145 mya–135 mya). The question asks about the data for 95 mya–85 mya, which corresponds to the bar labeled 90 mya. That bar shows there were 4 paleowildfires over that time interval. F is correct. G, H, and J are incorrect. The values 9, 14, and 19 are too high.

Question 19. The best answer is B. Figure 2 shows that at an initial %O₂ of 16%, the pine wood had a flame duration of approximately 0.1 sec, the match had a flame duration of approximately 2.2 sec, the candle had a flame duration of approximately 3 sec, and the dry paper had a flame duration of approximately 6 sec. A is incorrect. The dry paper had the longest flame duration. B is correct. C and D are incorrect. The dry paper had the longest flame duration.

Passage IV

Question 20. The best answer is G. In order to answer this item, the examinee must know that plants take up nutrients from the soil. Student 2 claimed that the amount of phosphorous (a nutrient) that a plant receives determines its stem color. It follows that Student 2 would be the most likely to agree that the soil in which a Population A plant is grown will influence its stem color. F is incorrect; Student 1 did not indicate that the stem color depended on the amount of nutrients that a plant receives. G is correct. H and J are incorrect; both Student 3 and Student 4 stated that the amount of nutrients received by a plant does not affect stem color.

Question 21. The best answer is A. Student 1 claimed that plants receiving 8 hr or more of sunlight each day had purple stems, which is consistent with the finding that the presence of the purple pigment in plant tissues protects the tissues from being damaged by sunlight. Student 2 claimed that the amount of sunlight a plant receives does not affect the stem color; this is not consistent with the finding. A is correct. B is incorrect; Student 1 indicated that plants receiving the most sunlight will have purple stems, not green stems. C and D are incorrect; the finding better supports the explanation of Student 1.

Question 22. The best answer is F. In order to answer this item, the examinee must know that the green pigment, chlorophyll, can be used for photosynthesis. All 4 of the students stated that all plants in Population A produce the green pigment chlorophyll. The explanations of all 4 students are therefore consistent with the statement that both green-stemmed and purple-stemmed plants produce a pigment that can be used for photosynthesis. F is correct. G, H, and J are incorrect; all 4 students stated that all the plants in Population A produce a pigment that can be used for photosynthesis.

Question 23. The best answer is D. Only Student 1 claimed that sunlight affects the plants’ stem color; however, Student 1 stated that if a plant receives 8 hr or more of sunlight each day, then it produces the purple pigment and its stem will be purple. Student 1 would therefore not agree that providing a purple-stemmed plant with additional sunlight will change the stem color to green. Students 2, 3, and 4 would not be likely to agree that sunlight would affect the stems’ color in any way. A, B, and C are incorrect; none of the students would be likely to agree that providing a purple-stemmed plant with additional sunlight will cause its stem to become green. D is correct.

Question 24. The best answer is H. In order to answer this item, the examinee must know how to work a genetic cross. According to Student 3’s explanation, a plant with either the Gene Q genotype Qq or the Gene Q genotype QQ will produce the purple pigment, and therefore will have a purple stem. A plant with the Gene Q genotype qq will produce the green pigment, and therefore will have a green stem. If the 2 purple-stemmed plants that were crossed had the Qq genotype, then their offspring would be approximately 25% green-stemmed with the qq genotype, and approximately 75% purple-stemmed with either the QQ genotype or the Qq genotype. F is incorrect; based on Student 1’s explanation, because the stem color depends on exposure to sunlight, plants grown under the same conditions would have the same stem color. G is incorrect; based on Student 2’s explanation, because the stem color depends on the amount of phosphorous received by the plants, plants grown under the same conditions would have the same stem color. H is correct. J is incorrect; Student 4 claimed that purple-stemmed plants have the Gene Q genotype qq, and therefore all the offspring of 2 purple-stemmed plants would have purple stems.

Question 25. The best answer is D. In order to answer this item, the examinee must know how to work a genetic cross. Student 4 claimed that purple-stemmed plants have the Gene Q genotype qq and green-stemmed plants have either the Gene Q genotype Qq or QQ. A cross between a plant with the qq genotype (a purple-stemmed plant) and the Qq genotype (a green-stemmed plant) would produce some green-stemmed offspring with the Qq genotype and some purple-stemmed offspring with the qq genotype. A and B are incorrect; based on Student 4’s explanation, the Gene Q genotype of the purple-stemmed parent must be qq. C is incorrect; a cross between a purple-stemmed plant with the qq genotype and a green-stemmed plant with the QQ genotype would produce only green-stemmed offspring with the Qq genotype. D is correct.

Question 26. The best answer is J. Student 1 claimed that plants that receive sunlight for 8 hr or more each day have a purple stem. All plants that receive 9 hr of sunlight per day would therefore have a purple stem, and none would have a green stem. Student 2, Student 3, and Student 4 all agreed that the amount of sunlight received by a plant does not affect the stem color, and therefore a plant receiving 9 hr of sunlight could have either a purple stem or a green stem. F is incorrect; Student 1 would not agree with the statement. G is incorrect; while Student 2 likely would agree, Students 3 and 4 would also agree with the statement. H is incorrect; while Students 3 and 4 likely would agree, Student 2 would also agree with the statement. J is correct; Students 2, 3, and 4 would all agree that a plant receiving 9 hr of sunlight each day could have either a purple stem or a green stem.

Passage V

Question 27. The best answer is B. According to Figure 2, March was the month in which a total of 70 L of H₂ was produced. According to Table 1, the average solar irradiance in the month of March was 153.8 W/m². A is incorrect; 77.8 W/m² was the average solar irradiance in January, not March. B is correct; in the month of March, when 70 L of H₂ was produced, the solar irradiance was 153.88 W/m². C is incorrect; 197.5 W/m² was the average solar irradiance in May, not March. D is incorrect; 206.4 W/m² was the average solar irradiance in July, not March.

Question 28. The best answer is H. According to Figure 1, O₂ is produced at the anode and H₂ is produced at the cathode during electrolysis. According to Step 3 of the experiment, electrolysis was initiated at 8:00 a.m. Then, eight hours later (at 4:00 p.m.), in Step 4, the amount of H₂ that had been produced was measured. F is incorrect; H₂ was not produced at the anode. G is incorrect; the amount of O₂ gas was not measured each day. H is correct; at 4:00 p.m. each day, the amount of H₂ gas was measured at the cathode. J is incorrect; O₂ gas was not produced at the cathode and was not measured each day.

Question 29. The best answer is B. According to the passage, a 25% by mass aqueous solution of NaOH was added to the tank in Step 2 of the experiment. In 200 g of this solution, 25% of the mass would be NaOH: 25% × 200 g = 50 g. A is incorrect; 25 g is 12.5% of 200 g. B is correct; 200 g of the solution would contain 50 g of NaOH. C is incorrect; 200 g of an aqueous solution of NaOH cannot contain 200 g of NaOH because that would not be a solution, it would be pure NaOH. D is incorrect; the mass of NaOH in the 200 g of solution cannot exceed the total mass of the solution.

Question 30. The best answer is F. In order to answer this item, the examinee must know that, for balanced chemical equations involving gases, the coefficients may be interpreted in terms of gas volumes. The balanced equation for the electrolysis reaction is 2H₂O → 2H₂ + O₂. So, for every 2 L of H₂ gas produced, 1 L of O₂ gas will be produced. According to Figure 2, 40 L of H₂ gas was produced in February. Therefore, the number of liters of O₂ produced was (40 L)/2 = 20 L. F is correct. G is incorrect; 40 L of H₂ were produced in February, and only half that amount of O₂ would have been produced. H is incorrect; this is twice the amount of H₂ that was produced, and according to the chemical equation only half as much O₂ would be produced. J is incorrect; the largest volume of H₂ produced in a month during the experiment was less than 90 L, so 100 L of O₂ could not have been produced in February since only half as much O₂ as H₂ could be produced each month.

Question 31. The best answer is C. According to the description of the experiment, Steps 1-5 were performed daily. Step 2 states that 4.0 L of NaOH solution were added to the tank. There are 30 days in June, so 30 days × 4.0 = 120 L of NaOH solution were added in June. A, B, and D are incorrect; Step 2 was performed once daily for 30 days in June.

Question 32. The best answer is J. Table 1 gives the value of the average solar irradiance for each month, with no data provided for May 11 or any other individual day. F, G, and H are incorrect; 197.5 W/m² was the average solar irradiance for May, but without any data for May 11, there is no way to know whether the solar irradiance was less than, equal to, or greater than the average value. J is correct; with data given in Table 1 only for the average solar irradiance for May, the solar irradiance for May 11 cannot be determined from the given information.

Question 33. The best answer is D. In order to answer this item, the examinee must know that an aqueous NaOH solution has more ions than pure liquid H₂O, and that solutions with more ions have higher electrical conductivity. Since the H₂ gas is produced by the electrolysis of H₂O, the higher the conductivity the more H₂ produced. A is incorrect; pure liquid H₂O does not contain more ions than aqueous NaOH solution and does not have higher conductivity. B is incorrect; while pure liquid H₂O does have fewer ions and thus lower electrical conductivity than aqueous NaOH, that would result in less H₂, not more. C is incorrect; pure liquid H₂O would produce less H₂ because it has fewer ions, not more ions, than aqueous NaOH and thus has a lower electrical conductivity. D is correct; pure liquid H₂O has fewer ions and lower conductivity than aqueous NaOH and would produce less H₂ during electrolysis.

Passage VI

Question 34. The best answer is H. Figure 1 shows a vibrating string with 2 nodes, which matches the sketch in Table 1 for the 3rd harmonic. F is incorrect; the sketch in Table 1 for the 1st harmonic shows 0 nodes, and Figure 1 shows a string with 2 nodes. G is incorrect; the sketch in Table 1 for the 2nd harmonic shows 1 node, and Figure 1 shows a string with 2 nodes. H is correct; Figure 1 and the sketch in Table 1 for the 3rd harmonic both show a string with 2 nodes. J is incorrect; the sketch in Table 1 for the 4th harmonic shows 3 nodes, and Figure 1 shows a string with 2 nodes.

Question 35. The best answer is C. The sketch made in the new trial shows the vibrating string with 5 nodes. Based on the sketches shown in Table 1, the number of nodes on a vibrating string is always one more than the number of the harmonic. There are 4 nodes shown for the 5th harmonic, so a string having 5 nodes must correspond to the 6th harmonic. According to the results of Experiment 1 for String Z, as the number of the harmonic increases, the frequency increases by about 4 Hz. So, the frequency of the 6th harmonic should be greater than 19.8 Hz, or approximately 19.8 Hz + 4 Hz = 23.8 Hz. According to the results of Experiment 2, as the number of the harmonic increases, the tension, T, decreases. For String Z, the tension required for the 5th harmonic was 0.16 N, so the tension for the 6th harmonic should be less. A is incorrect; f should be greater than 19.8 Hz. B is incorrect; f should be greater than 19.8 Hz, and T should be less than 0.16 N. C is correct; 25.0 Hz is greater than 19.8 Hz, and 0.11 N is less than 0.16 N. D is incorrect; T should be less than 0.16 N.

Question 36. The best answer is G. For String Y, µ = 0.08 g/cm. The mass of a piece of string is equal to its length multiplied by µ, so a piece of String Y that is 1 cm in length will have a mass of 1 cm × 0.08 For String X, µ = 0.02 g/cm, and for String Z, µ = 0.16 g/cm. So, for a piece of String X to have the same mass as the piece of String Y, it would have to be 4 times as long, and for a piece of String Z to have the same mass it would have to be half the length. F and H are incorrect; String X and String Z have different values of µ than String Y, so 1 cm lengths of those strings would not have the same mass as a 1 cm length of String Y. G is correct; since String X has a value of µ that is ¼ the value of µ for String Y, a piece of String X that is 4 times as long (4 cm) will have the same mass as a 1 cm piece of String Y. J is incorrect; String Z has a greater value of µ than String Y, so a length greater than 1 cm would not have the same mass.

Question 37. The best answer is D. The rules for counting significant digits are as follows: 1) All non-zero digits are significant. 2) All zeros between non-zero digits are significant. 3) Zeros that appear after the decimal point are significant if they follow a non-zero digit. The number 1,250 contains 3 significant digits (1, 2, and 5; the zero is not significant), the number 125.0 contains 4 significant digits (1, 2, 5, and the 0 following the decimal point which occurs after 3 non-zero digits), the number 12.5 has 3 significant figures (1, 2, and 5 are all significant digits), and the number 0.00125 contains 3 significant digits (the 3 zeros that occur before the non-zero digits are not significant, but 1, 2, and 5 are significant). A, B, and C are all incorrect; the data in Table 1 were all reported with 3 significant digits. D is correct.

Question 38. The best answer is H. For String X, Table 1 lists 11.2 Hz as the frequency for the 1st harmonic (f₁). For String X, the frequency for the 2nd harmonic (n = 2) was 22.4 Hz (exactly twice f₁), and for the 3rd harmonic (n = 3) was 33.5 (approximately 3 times f₁). The rest of the data for String X follows the same pattern, indicating that the equation fn = n × f₁ is most consistent with the results of Experiment 1 for String X. F is incorrect; for the 2nd harmonic, the equation fn = n + f₁ yields fn = 2 + 11.2 = 13.2 Hz, which does not match the 2nd harmonic frequency (22.4 Hz) given in Table 1. G is incorrect; for the 2nd harmonic, the equation fn = n − f₁ yields fn = 2 − 11.2 = −9.2 Hz, and negative frequencies do not exist. This also does not match the 2nd harmonic frequency (22.4 Hz) given in Table 1. H is correct. J is incorrect; for the 2nd harmonic, the equation fn = n ÷ f₁ yields fn = 2 ÷ 11.2 = 0.179 Hz, which does not match the 2nd harmonic frequency (22.4 Hz) given in Table 1.

Question 39. The best answer is D. According to the description of the experiments, for String X, µ = 0.02 g/cm; for String Y, µ = 0.08 g/cm; and for String Z, µ = 0.16 g/cm. Table 2 shows that as µ increased from string to string, the tension increased, with String Z requiring a tension of 0.25 N for the 4th harmonic. A string with a mass per unit length, µ, of 0.32 g/cm would require a tension greater than 0.25 N. A, B, and C are incorrect; the indicated tensions are lower than 0.25 N, so they would not be great enough. D is correct; the tension required for the 4th harmonic of the new string would be greater than 0.25 N.

Question 40. The best answer is H. According to the description of the experiments, µ increased from String X to String Y, to String Z. Considering the results of Experiment 1 for the 3rd harmonic, f decreased from string to string, going from 33.5 Hz for String X, to 16.8 Hz for String Y, to 11.9 Hz for String Z. The results of Experiment 2 show that the tension, T, for the 3rd harmonic increased from string to string, going from 0.06 N for String X to 0.22 N for String Y, and 0.44 N for String Z. F is incorrect; f decreased as µ increased. G is incorrect; f decreased, and T increased as µ increased. H is correct. J is incorrect; T increased as µ increased.

Chapter 4:
Identifying Areas for Improvement

Your practice test scores alone provide very little insight into what you need to do to improve your score. For example, you may have missed a certain math question because you haven’t yet taken trigonometry or because you misread the question or the answer choices or because you were anxious about finishing the test on time.

When evaluating your performance on any of the practice tests in this book or elsewhere, examine not only whether you answered a question correctly or incorrectly but also why you answered it correctly or incorrectly. Recognizing why you chose the correct or incorrect answer sheds light on what you need to do to improve your score on future practice tests and on the ACT. Perhaps you need to review certain subjects, take a particular course, develop a better sense of how much time to spend on each question, or read questions and answer choices more carefully.

In this chapter, we offer guidance on how to evaluate your performance on ACT Practice Test 1 in order to identify subject areas and test-taking strategies and skills that you may need to work on. Take a similar approach to evaluate your performance on subsequent practice tests.

Reviewing Your Overall Performance

After you have determined your scores, consider the following questions as you evaluate how you did on the practice tests. Keep in mind that many of these questions require you to make judgment calls based on what you were thinking or the steps you took to decide on the answer choice you selected. The answer explanations in chapter 4 may help you make these determinations, but ultimately you are the only one who can determine why or how you chose the correct or incorrect answer.

Did you run out of time before you completed a test?

If so, read the sections in this book on pacing yourself. See chapter 2 for general advice that applies to all tests, and see chapters 5 through 9 for advice specific to each test. Perhaps you need to adjust the way you use your time in responding to the questions. Remember, there is no penalty for guessing, so try to answer all questions, even if you have to make an educated guess.

Did you spend too much time trying to understand the directions to the tests?

Make sure you understand them now, so you won’t have to spend too much time reading them when you take the test.

Did you rush through the test and make mistakes?

People tend to make mistakes when they are in a hurry. If you had plenty of time remaining at the end of the test but made mistakes, you probably hurried through the test and made errors such as these:

Misreading a passage

Misreading a question

Not reading or considering all answer choices

Selecting a response that was an incomplete answer

Selecting an answer that did not directly respond to the question

Did a particular type of question confuse you?

Use the explanatory answers following each practice test to help you identify any mistakes you may have made regarding certain question types or answer choices. The explanatory answers can help you understand why you may have chosen the incorrect answer and avoid making that same mistake again.

After taking a practice test on the online platform, you can go to the Metrics tab, click on the bar graph of any assessment, and then navigate to a list of right and wrong answers. This can help you find the right explanations and determine areas to focus on. If you flagged questions that you found difficult or confusing, you can also see them listed here.

Highlighting Strengths and Areas for Improvement on the English Test

The process of scoring your English practice test and reviewing the answer explanations should reveal the reason you chose the correct or incorrect answer for each question. If you struggled to answer questions on the test because you have not yet acquired certain English language knowledge and skills, review the questions and your answers closely to determine more specifically what you need to work on.

The English test requires knowledge and skills in several areas. The best way to raise your score is to improve your English language skills, which you can accomplish in the following ways:

Take an English composition course. Such a course will help you write more clearly, logically, and concisely while developing a better understanding of English punctuation, grammar, and usage conventions.

Practice your writing skills in other courses. In most courses, including English literature, social science, speech, and perhaps even science, you have opportunities to practice your writing skills and receive feedback.

Read well-written publications in the form of books, magazine articles, and online content from reputable sources—material that has been professionally edited. As you read, pay attention to punctuation, grammar, usage, sentence structure, writing strategy, organization, and style to see how a variety of writers express themselves while adhering to the same conventions.

Practice writing and having your writing edited by an English teacher or someone else who is qualified to provide feedback.

Test-Taking Errors

A low test score does not necessarily mean that you lack the English language knowledge and skills required to do well on the test. It may indicate that you rushed through the test and made mistakes, spent too much time on certain questions that you didn’t finish, or committed some other test-taking error(s). As you evaluate your answers to determine why you missed certain questions, consider your test-taking strategies and skills. Place a checkmark next to each of the following common test-taking errors you think you need to work on eliminating:

Worked too slowly: You may need to improve your reading speed and comprehension or try answering the easy questions first and then returning to the harder questions if time remains.

Rushed through the test: If you finished with plenty of time remaining but made mistakes, you may need to spend more time reading and understanding the passages, reading the questions, or carefully considering all of the answer choices.

Misread passages: If you missed questions because of misreading or misinterpreting passages, work on your reading comprehension. Try reading more carefully and rereading when you do not fully understand a passage.

Misread questions: Every question points to the correct answer, so read questions carefully and make sure you understand what a question is asking before you choose your answer.

Did not consider all answer choices: If you tend to select the first answer choice that seems to be correct, try considering all answer choices before making your final selection. A good way to double-check an answer is to find reasons to eliminate the other three choices.

Did not consider the writing style: The entire passage conveys the author’s overall writing style, which you may need to consider when answering certain style-related questions.

Did not consider a question’s context: Writing strategy and organization questions often require consideration of surrounding text. You may need to skim the passage first before answering these questions or read one or two sentences before or after the sentence in question.

Did not account for a word’s connotations: Many words have a denotation (a literal meaning or dictionary definition) and a connotation (a thought or emotion that the word evokes from the reader or listener). To answer some usage questions, you must consider what the word means in the context in which it is used.

Did not connect an underlined portion of text with its corresponding question: The underlined portion of the text and the corresponding question work together to point to the correct answer choice, so be sure to consider them both when selecting your answer.

Overlooked differences in the answer choices: Answer choices may differ so subtly that you overlook the differences, so be sure to recognize what’s different about each choice before selecting your answer.

Chose an answer that introduced a new error: Some answer choices correct the error in the underlined text but introduce a new error. Do not choose an answer that creates a new error.

Did not choose the best answer: Two or more answers may be correct, but the English test requires that you choose the best answer. Again, consider all answer choices before selecting an answer.

Did not reread the sentence using the selected answer: A great way to double-check an answer is to insert it in place of the underlined text and then reread the sentence to make sure it makes sense.

Missed a two-part question: With a two-part question, each of the answer choices typically starts with “yes” or “no” followed by a reason, so you must determine first whether the answer is yes or no and then why. Carefully compare and consider the reasons before making your selection.

Did not consider interrelated questions: A question may be easier to answer after you have answered the next question, so consider skipping back to a question if you feel that answering the current question has given you new insight.

See chapter 5 for in-depth coverage of test-taking strategies and skills that may help to raise your English test score.

Highlighting Strengths and Areas for Improvement on the Mathematics Test

The process of scoring your mathematics practice test and reviewing the answer explanations should reveal your strengths and any areas for improvement. You may discover that you are a whiz at algebra and geometry but are in dire need of a refresher course in trigonometry. Or, you may find that your math knowledge and skills are sound in all areas but you need to work on test-taking strategies to ensure that your test results accurately reflect your knowledge and skills.

Use the checklists in the following sections to flag subject areas and test-taking skills you may need to focus on.

Math Subject Areas

If you struggled to answer questions on the test because you have not yet acquired the requisite math language knowledge and skills, review the questions and your answers closely to determine more specifically what you need to work on.

Your performance on the ACT mathematics test may be affected by your ability to handle certain types of questions. For example, you may breeze through straightforward, basic math questions but get tripped up by word problems. As you evaluate your performance on mathematics in Practice Test 1, try to identify the types of questions you struggle with most:

Basic math: These questions are straightforward with very little text. You just need to do the math.

Basic math in settings: These are word problems that challenge your ability to translate the problem into one or more mathematical equations and then solve those equations.

Very challenging math problems: These can be basic math or basic math in settings questions that challenge your ability to reason mathematically and perhaps draw from your knowledge of more than one math subject area to solve them. In addition to the differences in how math problems are presented, you may encounter question sets—two or more sequential math problems related to the same information.

Test-Taking Errors

Incorrect or unanswered questions on the practice test may be less of a reflection of your math knowledge and skills and more a reflection of your test-taking strategies and skills. As you review your scores and answers, try to determine whether you committed any of the following common test-taking errors:

Worked too slowly: If you answered questions correctly but your score suffered from unanswered questions because you ran out of time, you may simply need more practice to improve your speed.

Rushed through the test: If you finished with plenty of time remaining but made mistakes, you may need to spend more time reading and understanding the questions and doing the math before selecting an answer.

Got stuck on a very challenging question: Answering the easy questions first and then returning to the harder questions later may help you address this issue.

Misread the question: The question contains all information you need to answer it. Misreading the question may cause you to extract and use the wrong information in your calculations or calculate an answer for something other than what the question directed.

Overlooked information in the answer choices: Answer choices often provide clues as to what form the answer is in. A glance at the answer choices can often clarify what the question is asking for.

Overlooked or misinterpreted information in an image: Many math questions include an image, table, or graph that provides key information. Misreading an image will lead you to select the wrong answer choice.

Did not use logic to solve a problem: Math questions, especially the very challenging ones, often test your ability to reason through problems.

Not doing the math: Although you are not required to show your work on the test, consider writing out your calculations to double-check your reasoning and avoid mental errors. Also, when a question includes an image, consider writing any dimensions provided in the question on to the image so that the image contains all of the measurements you have to work with.

Not double-checking your answers: For many questions, you can insert the answer you think is correct into the equation provided and do the math to double-check the answer choice. Take the opportunity to double-check answers when given the opportunity.

For math test strategies and tips, turn to chapter 6.

Highlighting Strengths and Areas for Improvement on the Reading Test

The process of scoring the reading practice test and reviewing the answer explanations should reveal the reason you chose the correct or incorrect answer for each question. Reasons for choosing wrong answers or struggling with certain questions can be classified in three categories:

Subject matter

The type of passage—literary narrative or informational—may affect your ability to read and comprehend the passage and answer questions about it. For example, you may have no trouble answering questions about fact-based passages in social science and natural science but struggle reading and understanding literary narratives.

Reading skills

The reading test is designed to evaluate numerous skills, including the ability to identify details in the text, draw generalizations about those details, and understand the meaning of a word or phrase based on how it is used in a sentence. In addition, each passage challenges you to read quickly and with understanding.

Test-taking strategies and skills

Not reading the entire passage, misreading the question or answer choices, and not verifying an answer choice with the passage can all lead to careless mistakes.

Use the checklists in the following sections to flag the types of reading passages, reading skills, and test-taking strategies and skills you may need to focus on.

Types of Reading Passages

Your ability to comprehend reading passages and answer questions about them may vary based on the type of passage. For example, if you are accustomed to reading science books and articles, you are probably familiar with many of the concepts and vocabulary in the science passages on the test; therefore, you might expect to have no trouble reading, comprehending, and answering questions about such passages. However, if you have read very little fiction, you may find it challenging to identify the plot (sequence of events), draw conclusions about characters, or sense the mood that a passage is intended to evoke. In short, you may struggle more with certain types of reading passages than with others.

As you score your reading test and review the answer explanations, use the following checklist to flag any types of reading passages you found particularly challenging:

Literary narrative: Passages from short stories, novels, and memoirs

Social science: Informational passages that cover topics such as anthropology, archaeology, biography, business, economics, education, geography, history, political science, psychology, and sociology

Humanities: Informational passages about topics including architecture, art, dance, ethics, film, language, literary criticism, music, philosophy, radio, television, and theater

Natural science: Informational passages related to subjects such as anatomy, astronomy, biology, botany, chemistry, ecology, geology, medicine, meteorology, microbiology, natural history, physiology, physics, technology, and zoology

Reading Skills Tested

The ability to read, comprehend, and answer questions about passages involves numerous skills. Questions on the test are written specifically to evaluate these skills. As you review the answer explanations, place a checkmark next to any of the following skills you think you need to develop more fully:

Identify and interpret details: Nearly all questions require an ability to identify and interpret details from the passage that support whichever answer choice you select. Many questions specifically state, “According to the passage …” This skill is essential for performing well on the reading test.

Determine the main idea of a paragraph(s) or passage: A few questions may require an ability to recognize the general meaning or point of one or more paragraphs.

Understand comparative relationships (comparison and contrast): Questions may ask about comparisons and contrasts made in the passage.

Understand cause-effect relationships: Some reading passages explore cause-effect relationships. Others are accompanied by questions that more subtly test your ability to identify cause-effect relationships.

Make generalizations: To answer many reading questions, you must be able to draw conclusions from or make generalizations about details provided in the passage.

Determine the meaning of words or phrases from context: You are likely to encounter several questions on the ACT reading test that challenge you to determine the meaning of a word or phrase based on the context in which it is used.

Understand sequences of events: A few reading test questions may require an ability to read and comprehend a series of events.

Draw conclusions about the author’s purpose and method: You may be asked to get into the mind of the author and figure out what their attitude, purpose, or method is.

Understand arguments: Some items may ask you to identify an argument being made in a passage or to examine support for an argument.

For more about reading skills tested, including examples of the types of questions used to evaluate these skills, turn to chapter 7.

Test-Taking Errors

Even if your reading speed and comprehension are solid, you may miss questions by committing one or more of the following common test-taking errors. Place a checkmark next to each error you think you may be susceptible to making:

Read too slowly or too quickly: By reading too slowly, you may not have sufficient time to read all passages and answer all questions. However, reading too quickly may result in errors or having to return to a passage several times to locate the evidence needed to decide which answer choice is correct.

Did not read the entire passage: Skim-reading a passage is useful for understanding what a passage is about, but it often results in overlooking the details required to answer specific questions. Read the entire passage word for word.

Misread the question: Questions, especially those that contain the word NOT, can be tricky. Make sure you understand what a question is asking as you evaluate the various answer choices.

Misread or overlooked an answer choice: Misreading an answer choice or not considering all answer choices can result in mistakes. Consider all answer choices and read them carefully.

Did not verify an answer choice with the passage: If time allows, try to verify every answer choice by locating details in the passage that support it. Use the same technique to rule out other answer choices when necessary.

For additional reading test strategies and tips, turn to chapter 7.

Highlighting Strengths and Areas for Improvement on the Science Test

The process of scoring the science practice test and reviewing the answer explanations should reveal the reason you chose the correct or incorrect answer for each question. Reasons for choosing wrong answers or struggling with certain questions can be classified into three categories:

Subject matter

The science test does not require in-depth knowledge of biology, chemistry, earth science, space science, or physics. Nor does it require you to memorize formulas or solve complex math problems. However, questions are presented in the context of these subject areas, and you may need some knowledge of scientific terms or concepts to answer some of the questions.

Passage type

Science passages are presented in three different formats: Data Representation (graphs, tables, illustrations); Research Summaries (from experiments); and Conflicting Viewpoints (alternative theories and hypotheses). You may struggle more with the items presented in one type of passage than in the others.

Test-taking strategies and skills

The science test evaluates your ability to extract and use information presented in a variety of formats to solve problems and answer questions. Even if you are highly skilled and knowledgeable in all science subject areas, your score will suffer if you make careless mistakes or are so careful that you run out of time before answering all of the questions.

Use the checklists in the following sections to flag the subject areas, passage types, and test-taking strategies and skills you may need to focus on.

Science Subject Areas

You may benefit from identifying subject areas in which you struggle. Use the following checklist to flag subject matter you may need to review:

Biology: Cell biology, botany, zoology, microbiology, ecology, biochemistry, genetics, and evolution

Chemistry: Properties of matter, acids and bases, kinetics and equilibria, thermo-chemistry, organic chemistry, and nuclear chemistry

Earth and Space sciences: Geology, meteorology, oceanography, environmental science, stars, planets, galaxies, and the universe.

Physics: Mechanics, gravitation, thermodynamics, electromagnetism, fluids, solids, and optics

Types of Science Passages

As you review answer explanations and evaluate your performance on the science test, check to see whether you had more trouble with items in certain types of science passages than others. Place a checkmark next to any passage types that you found particularly challenging:

Data Representation passages focus primarily on assessing your ability to understand, evaluate, and interpret information presented in graphs, tables, and illustrations.

Research Summary passages focus primarily on assessing your ability to understand, analyze, and evaluate the design, execution, and results of one or more experiments.

Conflicting Viewpoints passages focus primarily on assessing your ability to compare and evaluate alternative theories, hypotheses, or viewpoints on a specific observable phenomenon.

For more about these different passage types and guidance on how to approach the items in them effectively, turn to chapter 8.

Test-Taking Errors

As mentioned previously, the science test does not require in-depth scientific knowledge. It relies more on your ability to understand and identify detailed information presented in a variety of formats—text, graphs, tables, and diagrams. If your science test score is lower than you had hoped, you may have committed one or more test-taking errors. Place a checkmark next to each of the following test-taking errors that you think you need to work on avoiding:

Worked too slowly: If time expired before you had a chance to answer all 40 questions, you need to pick up the pace.

Worked too quickly: If you finished with plenty of time remaining but made mistakes, you need to practice slowing down and reading the science passages, questions, and answer choices more carefully.

Misread or misinterpreted text: If you missed questions because you misread a passage, question, or answer choice, check this box.

Misread or misinterpreted a graph or table: Graphs, tables, and images contain much of the information required to answer the science test questions.

Misread or misinterpreted a research summary: You may need to develop a better understanding of the scientific method for designing and conducting experiments.

Did not use reason effectively to find the answer: Most of the questions on the science test challenge your ability to think and reason. If you struggled to understand questions, check this box. You may be able to improve your score by adopting a problem-solving strategy that steps you through the question, as discussed in chapter 8.

For science test-taking strategies that will help you avoid these common mistakes and others, turn to chapter 8.

Highlighting Strengths and Areas for Improvement on the Writing Test

The optional writing test is designed to evaluate your ability to write at a level expected of students entering first-year college English composition courses. A solid essay demonstrates your ability to clearly state your perspective on a complex issue and analyze the relationship between your perspective and at least one other perspective, develop and support your ideas with reasoning and examples, organize your ideas clearly and logically, and communicate your ideas effectively in standard written English.

As noted in chapter 3, we strongly recommend consulting others to help you evaluate your writing practice test. Self-assessment is an invaluable skill, but others often see what we cannot. If you must work independently, read your essay with the most critical eye you can, asking yourself whether a reader who came to it with no knowledge of the prompt or what you meant to say would understand your argument. After scoring your writing practice test, use the checklists in the following sections (organized by domain) to highlight writing skills you may need to develop more fully and to avoid errors related to writing strategy and process.

Writing Skills Tested

As you evaluate your writing practice test, consider which skills contributed to your scores. In chapter 9, a full set of sample essays is included. Though the prompt there is different than the one in chapter 3, the quality of writing in each of the essays is similar to that of essays for any topic. Comparing your own work to those samples will help you evaluate the skill displayed in your practice test. You may be able to improve your scores significantly by more fully developing only one or two of the following skills. Place a checkmark next to each skill you think you need to work on:

Clearly state your own perspective on a complex issue and analyze the relationship between your perspective and at least one other perspective: If another reader cannot easily identify a clear perspective, practice formulating thesis statements. Whenever you write an essay, practice stating your thesis in the first few sentences of the essay. By presenting your perspective in the introduction, you not only state your main idea clearly but also give your essay a focal point.

If you had trouble analyzing the relationship between your perspective and at least one other perspective, practice writing counterarguments. Pick a debatable issue and choose a stance. Now, imagine what someone who disagrees with you might say, and practice writing paragraphs that first present the other person’s side of the issue. Then offer your response. Next, imagine a perspective that is in general agreement with yours but differs in some important ways. How do you respond to this perspective? As you think and write, ask yourself: What accounts for the similarities and differences among your perspective and others you can imagine? Where are the strengths and weaknesses in these other perspectives, and where are the strengths and weaknesses in your own? Most importantly, ask yourself how engaging with another view—whether it generally agrees or disagrees with your own—can help you advance an argument. Considering these questions as you practice can help you learn to analyze and engage with different perspectives.

Develop and support your ideas with reasoning and examples: Failure to support your assertions can result in a lower score. Remember that every claim you make should be backed up with good supporting evidence. Ask yourself whether the reasoning or evidence you provided sufficiently explains your thinking, or whether another sentence or two would help clarify your meaning. As you explain the reasoning behind your argument, remember that logical fallacies, including overgeneralization and moral equivalence (associating minor offenses with moral atrocities), can weaken your ideas. Additionally, the assumption that a reader shares or inherently understands your viewpoint can lead to underdevelopment of ideas.

Organize your ideas clearly and logically: An essay should flow directly from point A to point B and not repeat itself or wander off track. Consider the extent to which the ideas in the body paragraphs are focused on arguing the thesis: are there ideas present that are not obviously connected to your main point? Are the ideas clearly related to one another? How might transitions be improved? Similarly, think about the order in which your ideas are presented: does the arrangement add meaning (e.g., opening with a metaphor that describes the issue in the prompt, refuting counterarguments before building your own, or concluding with an example that illustrates the argument) or are the ideas essentially listed? Do the ideas build upon one another or do they function in isolation? Thinking about questions such as these can help you learn to write a more cohesive essay. (Prewriting, discussed in the next section, can help ensure that your essay is well organized.)

Communicate your ideas effectively in standard written English: If your essay contains several errors in grammar, usage, and mechanics, it would be beneficial to review rules and practice a variety of exercises associated with those. Equally important, however, are word choice, sentence structure, and style. If your essay does not include much variety of either vocabulary or sentence type, you might practice constructing the same sentences in different ways, experimenting with synonyms and fluctuating between simple and complex sentences. Pay close attention to the voice and tone: how might a reader interpret your attitude about the issue? How much personality belongs in the argument, and how can it be conveyed through word choice? Answering these sorts of questions can help you with evaluating your writing and improving your use of language to reach an audience.

You can develop all of these skills in high school English classes and other classes that require you to write essays and where you receive feedback that targets these skills. For more about improving your writing test score, along with sample essays that demonstrate the differences between high-scoring and lower-scoring essays, turn to chapter 9.

Writing Strategy or Process Errors

When scoring an essay, the focus is on the product, but the score may be a reflection of the process used to produce that essay. For example, prewriting (planning) can help you think of good ideas, ensure that your ideas are presented logically, and remind you to provide evidence to support your ideas. After scoring your practice essay, think back on your process, including planning, and how it impacted your essay and place a checkmark next to any of these writing strategy or process errors you may have committed:

Poor pacing: Composing too quickly may result in careless errors, whereas working too slowly may result in an incomplete essay or insufficient time to review and correct errors.

Insufficient prewriting (planning): It is difficult to write an effective essay, especially in timed conditions, if you have not spent time thinking about how to approach the task, considering what you might want to say and how to say it most constructively. If you had trouble generating and developing ideas or engaging with multiple perspectives, consider using the guided prewriting section found in the test booklet. The questions presented in this section are intended to help you produce a perspective and analyze its relationships with other points of view. They are also useful as you think about how you will support your ideas. Because it can be difficult to organize your ideas as you write, you may want to consider using the prewriting space to write an outline or draw a diagram. You do not need a detailed outline, but starting with a thesis and mapping a structure to support it can help you define the logic of your argument before you begin to write it. This can be particularly helpful when writing in timed conditions.

Not reviewing or editing: If you completed your essay with time to spare, did not review or edit it, and your essay has errors related to grammar, usage, sentence structure, or style, check this box. Practice with reading and editing while you write, even just with sentences and paragraphs, will help you get better at this.

Insufficient practice: Producing well-written essays requires practice and feedback, which you often receive only in a formal English composition course. The practice writing tests in this book provide additional opportunities, but we strongly recommend that you have your practice writing tests evaluated by a qualified third party—perhaps an English teacher or a fellow student who is a strong writer.

For additional tips on improving your writing test score, turn to chapter 9.

Part Three:
Improving Your Score

In This Part

This part features various ways to improve your scores on the English, mathematics, reading, science, and optional writing tests. Here, you get a preview of the types of questions you can expect on each test, along with test-taking strategies and skills that apply specifically to each test:

English: Find out more about test content, look at sample questions, and develop strategies for choosing the best answer.

Mathematics: Learn about the subject areas covered on the test, the types of math problems you will encounter, and strategies for improving your speed and accuracy in answering questions.

Reading: Discover the types of reading passages you will encounter on the test, the types of questions you will need to answer, and strategies for improving your reading speed and comprehension.

Science: Identify the areas of science covered on the test, the types of questions you will encounter, and test-taking strategies and skills for extracting information from passages and using it to reason your way to the correct answers.

Writing: Check out a sample writing prompt, find out what the people scoring your essay will be looking for, read sample scored essays from poor to excellent, and pick up a few strategies that may help to raise your writing score.

Chapter 5:
Improving Your English Score

On the ACT English test, you have 45 minutes to read five passages, or essays, and answer 75 multiple-choice questions about them—an average of 15 questions per essay. The essays on the English test cover a variety of subjects; the sample passages that follow this discussion range from a personal essay about the different ways of figuring one’s age to an informative essay about the legal history of school dress codes.

Content of the ACT English Test

The ACT English test is designed to measure your ability to make the wide variety of decisions involved in revising and editing a given piece of writing. The test measures your understanding of the Conventions of Standard English (punctuation, usage, and sentence structure); Production of Writing (topic development, organization, unity, and cohesion); and Knowledge of Language (word choice, style, and tone). Although you may use more informal or conversational language in your own writing, the test emphasizes the standard written English that is taught in schools around the country.

Different passage types are used to provide a variety of rhetorical situations. Passages are chosen not only for their appropriateness in assessing writing skills but also to reflect students’ interests and experiences.

Questions on the English test fall into three categories:

Production of Writing (topic development, organization, unity, and cohesion)

Knowledge of Language (precision and concision in word choice, consistency in style and tone)

Conventions of Standard English (sentence structure and formation, punctuation, and usage)

You will receive four scores for the ACT English test: a total test score based on all 75 questions and three reporting category scores based on specific knowledge and skills in the categories previously described. If you choose to take the writing test, you will also receive an English Language Arts (ELA) score based on an average of your English, reading, and writing test scores.

You will not be tested on spelling, vocabulary, or rote recall of the rules of grammar. Grammar and usage are tested only within the context of the essay, not by questions such as “Must an appositive always be set off by commas?” Likewise, you won’t be tested directly on your vocabulary, although the better your vocabulary is, the better equipped you’ll be to comprehend the reading passages and answer questions that involve choosing the most appropriate word.

The English test doesn’t require you to memorize what you read. The questions and essays are side-by-side for easy reference. This is not a memorization test.

The questions discussed on the following pages are taken from the sample passages and questions that follow on pages 217–223. If you prefer, you can work through the sample passages and questions before you read the rest of this discussion. However, to better understand the English test, you may want to first read the discussion, then work through the sample passages and questions.

Types of Questions on the ACT English Test

Many questions refer to an underlined portion of the essay. (As noted in Chapter 1, items taken online will be marked by highlighting instead of underlining. In the examples that follow, which show items as they would appear on paper, we’ll stick to underlining.) You must decide on the best alternative for that underlined portion. Usually, your options include NO CHANGE, which means that the essay is best as it’s written. Sometimes, you’ll also have the option of deleting the underlined portion. For example, the following question (from Sample Passage II on pages 219–221) offers you the option of removing the word to from the sentence.

In this example, the best answer is not to delete the underlined portion but to leave it as it is (F).

Other questions on the English test may ask about a section of the essay or an aspect of the essay as a whole. For example, in the following question (from Sample Passage I on pages 217–219), you’re given a sentence to be added to the essay, and then you’re asked to decide the most logical place in the essay to add that sentence.

In this example, the best answer is C, because Paragraph 3 focuses on the European musical influences on the O’odham people of Arizona, and the last sentence of the paragraph specifically refers to the musical influences of German immigrants.

Let’s look at some additional examples of the kinds of questions you’re likely to find on the ACT English test. If you want to know what an individual question looks like in the context of the passage in which it appears, turn to the pages indicated. You can also use those sample passages and questions for practice, either before or after reading this discussion.

Conventions of Standard English

Conventions of Standard English questions focus on the conventions of punctuation, grammar and usage, and sentence structure and formation.

Punctuation questions involve identifying and correcting the following misplaced, missing, or unnecessary punctuation marks:

Commas

Apostrophes

Colons, semicolons, and dashes

Periods, question marks, and exclamation points

These questions address not only the rules of punctuation but also the use of punctuation to express ideas clearly. For example, you should be prepared to show how punctuation can be used to indicate possession or to set off a parenthetical element.

In many punctuation questions, the words in every choice will be identical, but the commas or other punctuation marks will vary. It’s important to read the choices carefully in order to notice the presence or absence of commas, semicolons, colons, periods, and other punctuation. The following example of a punctuation question comes from Sample Passage I on pages 217–219.

It may help you to read through this sentence without paying attention to the punctuation so you can identify its grammatical construction. The subject of this sentence is “the polka music and button accordion.” What follows that subject might seem like the predicate verb of the sentence, but it’s not. The phrase “played by German immigrant railroad workers” is a participial phrase (a phrase formed with the past participle “played”). This participial phrase functions as an adjective because it modifies the nouns it follows (“the polka music and button accordion”).

After the participial phrase is the predicate verb of the main clause, “left.” Then comes a phrase that explains what was left (the direct object “their mark”) and a prepositional phrase that explains where it was left (“on waila”).

Now we can deal with the question about what kind of punctuation should follow that participial phrase. Sometimes, these phrases are set off from the main clause with commas to indicate that the phrase is parenthetical or provides information not essential to the meaning of the sentence. That’s not the case here for two reasons. First, there’s no comma at the beginning of the participial phrase. Second, the phrase is essential to the sentence; the sentence is not referring to just any polka music and button accordion but to the music and accordion played by those German immigrant railroad workers (presumably, not while they were working on the railroad).

Ignoring the participial phrase for a minute, we need to ask ourselves what kind of punctuation we would usually place between the subject “the polka music and button accordion” and the verb “left.” Our answer should be no punctuation at all, making G the best answer. Of course, you could answer this question without this rather tedious analysis of the parts of the sentence. You might simply decide that because the sentence contains no other punctuation, you would never insert a single punctuation mark between the subject and the predicate of the main clause. Or you might just plug in each of the four punctuation choices—semicolon, no punctuation, colon, comma—and choose the one that looks or sounds best to you.

Grammar and usage questions involve choosing the best word or words in a sentence based on grammar and usage conventions. Some examples of poor and better phrases are given in the following.

Grammatical agreement

(Subject and verb)

“The owner of the bicycles are going to sell them.”

should be:

“The owner of the bicycles is going to sell them.”

* * *

(Pronoun and antecedent)

“Susan and Mary left her briefcases in the office.”

should be:

“Susan and Mary left their briefcases in the office.”

* * *

Pronoun forms and cases

“Seymour and Svetlana annoyed there parents all the time.”

should be:

“Seymour and Svetlana annoyed their parents all the time.”

* * *

Idioms

“The definition of a word can be looked down in the dictionary.”

should be:

“The definition of a word can be looked up in the dictionary.”

Questions dealing with pronouns often have to do with using the proper form and case of the pronoun. Sometimes they address a pronoun’s agreement with its antecedent, or referent. In such cases, consider the entire sentence, and sometimes the preceding sentence, to make sure you know what the antecedent is. Consider the following question (from Sample Passage I on pages 217–219).

Here, the possessive pronoun in question refers back to the subject of the main clause (“they”), which in turn refers back to the subject of the introductory subordinate clause (“the dancers”). Thus, the best answer is the third-person plural possessive pronoun (“their,” A). Choice B might seem like a possibility because they’re sounds like their (that is, they’re homonyms). However, they’re is a contraction for they are. We can rule out C and D because of the pronoun-antecedent agreement problem and also because it’s is not a possessive pronoun but a contraction for it is, and its’ is not even a word.

Sentence structure questions involve the effective formation of sentences, including dealing with relationships between and among clauses, placement of modifiers, and shifts in construction. Following are some examples:

Subordinate or dependent clauses and participial phrases

“These hamsters are excellent pets because providing hours of cheap entertainment.”

This sentence could be rewritten as:

“These hamsters are excellent pets, providing hours of cheap entertainment.” (participial phrase)

It could also be revised as:

“These hamsters are excellent pets because they provide hours of cheap entertainment.” (subordinate/dependent clause)

Run-on or fused sentences

“We discovered that all of our friends had already seen the movie they thought it was terrible.

This sentence should actually be two:

“We discovered that all of our friends had already seen the movie. They thought it was terrible.

Comma splices

“The anteaters had terrible manners, they just ate and ran.”

This sentence could be rewritten as:

“The anteaters had terrible manners. They just ate and ran.”

Because a semicolon can serve as a “soft” period, the sentence could also be rewritten as:

“The anteaters had terrible manners; they just ate and ran.”

Sentence fragments

“When he burned his lunch.”

This needs a subject to let us know who “he” is and what he did:

“Julio didn’t lose his temper when he burned his lunch.”

Misplaced modifiers

“Snarling and snapping, Juanita attempted to control her pet turtle.”

Unless Juanita was doing the snarling and snapping, the sentence should be rewritten:

“Snarling and snapping, the pet turtle resisted Juanita’s attempt to control it.” It could also be rewritten this way:

“Juanita attempted to control her pet turtle, which snarled and snapped.”

Shifts in pronoun person or number

“Hamsters should work at the most efficient pace that one can.”

This should be rewritten as:

“Hamsters should work at the most efficient pace that they can.”

Many questions about sentence structure and formation will ask you about how clauses and phrases are linked. This means that you may have to consider punctuation or the lack of punctuation, which can create problems such as comma splices, run-on sentences, or sentence fragments. You also may have to consider various words that can be used to link clauses and phrases: conjunctions such as and, but, because, and when, and pronouns such as who, whose, which, and that. The following question (from Sample Passage I on pages 217–219) is a good example of a sentence structure question.

What would be the best way to link the clause “It is a social music” and the phrase “performed [or performing] at weddings, birthday parties, and feasts”? Relative pronouns such as that and which stand in for the noun that the relative clause modifies. (They relate the clause to the noun.) One way to try out choices such as F and G is to replace the relative pronoun with the noun and then decide if the resulting statement makes sense:

Social music performed at weddings, birthday parties, and feasts. (F)

This does not make sense. Musicians perform, but the music itself does not. Music is performed.

In social music it is performed at weddings, birthday parties, and feasts. (G)

This also seems nonsensical. What does it refer to—social music?

The other two choices offer a different approach to connecting information in a sentence. The phrases “performing at weddings, birthday parties, and feasts” (H) and “performed at weddings, birthday parties, and feasts” (J) are participial phrases. Similar to adjective clauses, these phrases modify a noun. We can rule out H for the same reason that we rejected F: it doesn’t make sense to think of “social music” as “performing.” However, it sounds fine to refer to “social music” as “performed” (J).

Production of Writing

Production of Writing questions focus on writing strategy and organization.

Topic development questions focus on the choices made and strategies used by a writer in the act of composing or revising an essay. These questions may ask you to make decisions concerning the appropriateness of a sentence or essay in relation to purpose, audience, unity, or focus, or the effect of adding, revising, or deleting supporting material.

The following question (from Sample Passage I on pages 217–219) is a fairly typical example of the kinds of writing decisions that strategy questions ask you to make.

It’s important to read these questions carefully and, sometimes, to reread the essay or parts of the essay. This question is fairly clear-cut, but it does suggest that you need a pretty good sense of what Paragraph 3 is about. A quick review of the paragraph indicates that it is focused on how the O’odham and their music were influenced by other musical styles and instrumentation they encountered.

Which of these parenthetical statements is most relevant to that focus? Choice D, which states that woodwind instruments are frequently found in jazz bands, is not. Likewise, choice C, which indicates that woodwind instruments are now often constructed of metal, strays from the paragraph’s topic. Choice B, which points out that fiddles were once widely used in waila bands, is getting closer, but this too seems a diversion, unconnected to the other information in this paragraph. Guitars, woodwinds, and button accordions are mentioned but not fiddles or violins.

Choice A, however, provides an appropriate and relevant elaboration. It draws the connection between the O’odhams’ introduction to marching bands and woodwinds in the early 1900s and the eventual inclusion of saxophones in a typical waila band.

Organization questions deal with the order and coherence of ideas in an essay and the effective choice of opening, transitional, and closing statements. For example, you may be asked about the organization of ideas (the most logical order for sentences within a paragraph or paragraphs within an essay) or about the most logical transitional phrase or statement.

The following question (from Sample Passage II on pages 219–221) is a good example of the kind of organization question you might encounter.

The choices in this question are sometimes referred to as conjunctive adverbs or transitional words or phrases because their main job is to connect or link the statement in one sentence with the statement in a preceding sentence. These are often little words—so, thus, soon, yet, also—that do a lot of work to make an essay logical.

In order to answer such questions correctly, it helps to think about the logical relationship between the sentences, as well as the logical relationships expressed by the choices. The main statement of the opening sentence of this paragraph is “I now find meaningful the difference [in computing one’s age] I once found confusing.” The second sentence states, “This difference points to significant underlying cultural values.” The writer then goes on to explain those cultural values.

Which of these four choices enables readers to move most easily from the opening sentence into the rest of this paragraph? Choice A suggests that the second statement contrasts with the first statement. A typical dictionary definition for otherwise is “in different circumstances.” Similarly, choice B, though, suggests that the statement to follow is contrary to or in opposition to the preceding statement. Neither of those adverbs works well here. Nor does then (choice D), which usually expresses a time relationship—meaning “next” or “soon after in time.”

The best choice here is C. The phrase in fact is often used to introduce a statement that builds on the preceding statement. We can pare down these opening sentences to their bare essentials to show that the phrase works well here: “I now find the difference in computing one’s age meaningful. In fact, the difference points to important cultural values about life experience and longevity.”

Knowledge of Language

These questions involve effective word choices in terms of writing style, tone, clarity, and economy. Sometimes, a phrase or sentence that isn’t technically ungrammatical is nevertheless confusing because it’s poorly written. Sometimes, a word or phrase clashes with the tone of the essay. Good writing also involves eliminating excessively wordy or redundant material and vague or awkward expressions.

Similar to most writing strategy and organization questions, style questions require a general understanding of the essay as a whole. The following style question (from Sample Passage III on pages 221–223) focuses on the issues of economy and consistency of tone.

You will be better able to recognize the appropriateness of choice J if you know that lax means “lacking necessary strictness, severity, or precision” and indifferent means “lacking interest, enthusiasm, or concern.” These terms touch on two related but distinct concerns—academic laziness and apathy. One could imagine school board members using these very words in their meetings. And the words are consistent with the overall style and tone of this straightforward, informative essay about a legal case.

Choices G and H are fairly easy to rule out if you think about the generally formal tone of the essay. It’s not that one should never use slang phrases such as “bored to tears” or “blow off” in one’s writing; it’s just that this particular essay is not the place to use them. When we consider that this statement is describing the school board members’ belief, these phrases are even more inappropriate.

It seems more in character for school board members to be concerned about student inefficiency, but F is a weak choice because the phrase “inefficient toward their school work” sounds odd or awkward. Perhaps it’s the preposition that trips us up. The word toward works fine in J when describing attitudes (“lax,” “indifferent”) toward school work, but the word inefficient is describing an ability or skill.

* * *

The questions provided here are a small sample of the kinds of questions that might be on the test. The previous question, for example, is only one kind of style question; it doesn’t cover all the elements of style that might be addressed on the test. The sample passages and questions at the end of this section have all the examples referred to in this chapter as they would appear in a test. These sample passages and questions and the later practice tests will provide you with a thorough understanding of the ACT English test.

Strategies for Taking the ACT English Test

Pace Yourself

The ACT English test contains 75 questions to be completed in 45 minutes, which works out to exactly 36 seconds per question. Spending 1 minutes skimming through each essay leaves you about 30 seconds to respond to each question. If you spend less time than that on each question, you can use the remaining time allowed for this test to review your work and to return to the questions that were most difficult for you. Another way to think of it is that you have 45 minutes to read and answer the questions for five essays, giving you a maximum of 9 minutes for each essay and its questions.

Be Aware of the Writing Style Used in the Essay

The five essays cover a variety of topics and are written in a variety of styles. It’s important that you take into account the writing style used in each essay as you respond to the questions.

Some of the essays will be anecdotes or narratives written from an informal, first-person point of view. Others will be more formal essays, scholarly or informative in nature, often written in the third person. Some questions will ask you to choose the best answer based not on its grammatical correctness but on its consistency with the style and tone of the essay as a whole. For example, an expression that’s too breezy for an essay on the life of President Herbert Hoover might be just right for a personal narrative about a writer’s attempt at learning to skateboard.

Consider a Question’s Context before Choosing an Answer

Some people find it helpful to skim an essay before trying to answer the associated questions. Having a general sense of the essay in mind before you begin to answer questions involving writing strategy or style can help. If you encounter questions about the order of sentences within a paragraph, or the order of paragraphs within an essay, or where to add a sentence in an essay, you may want to answer those questions first to make sure that the major elements of the essay are arranged logically. Understanding the order of the passage may make it easier for you to answer some of the other questions.

As you’re answering each question, be sure to read at least a sentence or two beyond the sentence containing the portion being questioned. You may need to read even more than that to understand what the writer is trying to say.

Be Aware of the Connotations of Words

Vocabulary isn’t tested in an isolated way on the ACT English test. Nevertheless, a good vocabulary and an awareness of not only the dictionary definitions of words but also the connotations (feelings and associations) suggested by those words will help you do well on the test.

The following question (from Sample Passage II on pages 219–221) asks you to think about how certain words and their connotations can function in terms of the rest of the essay.

Which word best captures or summarizes what has been described in the preceding paragraph? The word contest (F) doesn’t seem right because it suggests a competition between opposing sides or teams. In a similar vein, the word dispute (H) doesn’t fit here because it generally refers to a verbal debate or argument. The word change (G) is a little off because it expresses the idea of transformation, making something or someone different, which doesn’t accurately summarize that opening paragraph. The word difference (J), however, seems just right. It echoes the verb in the first sentence of the preceding paragraph, but more importantly, it accurately reflects the writer’s perspective up to this point in the essay that the American way and the Korean way of computing a person’s age are not competing or arguing with each other. They are simply unlike each other (and because of that mismatch, a bit confusing).

In questions such as this one, you have to focus on what the words mean and what associations the words have for the typical reader.

Look for a Stated Question

Before responding to a question identified by an underlined portion, check for a stated question preceding the options. If there is one, it will provide you with some guidelines for deciding on the best choice. Some questions will ask you to choose the alternative to the underlined portion that is NOT or LEAST acceptable. Here’s an example from Sample Passage I on pages 217–219.

For these types of questions, look closely at the underlined portion, because the question has told you that it is acceptable. Likewise, three of the alternative choices are acceptable. The best answer, in this case, is the one that is not acceptable. In the underlined portion, a dash is used between two independent clauses: “The music is mainly instrumental” and “the bands generally consist of guitar, bass guitar, saxophones, accordion, and drums.” The dash is sometimes thought of as a less formal type of punctuation, but it can work quite well to provide emphasis or to signal that an explanation will follow.

Placing a period (C) or a semicolon (D) between these two independent clauses would also be acceptable. Likewise, choice A is acceptable because it too places a semicolon between the two clauses, using the phrase “in general” rather than the adverb “generally.” Choice B is not acceptable and is, therefore, the best answer. A comma is not usually a strong enough punctuation mark between two independent clauses not joined by a conjunction. Notice that this sentence has other commas, used to distinguish nouns in a series. How would a reader know that the comma between the clauses is a much stronger break than those other commas?

Whether a stated question is presented or not, you should carefully examine what is underlined in the essay. Consider the features of writing that are included in the underlined portion. The options for each question will contain changes in one or more aspects of writing.

Note the Differences in the Answer Choices

Many of the questions that refer to underlined portions will involve more than one aspect of writing. Examine each choice and note how it differs from the others. Consider all the features of writing that are included in each option.

Avoid Making New Mistakes

Beware of correcting mistakes in the essay and, in your haste, picking a response that creates a new mistake. Be observant, especially in questions where the responses have similar wording. One comma or apostrophe can make all the difference, as the following question (from Sample Passage III on pages 221–223) illustrates.

Perhaps you took only a moment to reject choice A because of the unnecessary comma between the noun review and the prepositional phrase “of students’ rights.” And if you were able to make that call, you may have ruled out choice B for the same reason. It is probably more difficult to recognize that the comma between the noun rights and the conjunction and (D) is unnecessary and misleading. Because you were thinking about how the underlined portion should be punctuated, you may also have wondered about the plural apostrophe in the word students’ but then realize that the apostrophe is in the same place in all four choices. (The best answer is C.)

Determine the Best Answer

There are at least two approaches you can take to determine the best answer to a question about an underlined portion. One approach is to reread the sentence or sentences containing this portion, substitute each of the answer choices in turn, and decide which is best. Another approach is to decide how the underlined portion might best be phrased and then look for your phrasing among the choices offered. If the underlined portion is correct as it is, select the NO CHANGE option.

If you can’t decide which option is best, you may want to mark the question in your test booklet so you can return to it later. Remember: you’re not penalized for guessing, so after you’ve eliminated as many options as you can, take your best guess.

Reread the Sentence Using Your Selected Answer

After you have selected the answer you feel is best, reread the corresponding sentence or sentences in the essay, substituting the answer you’ve selected for the underlined portion or for the boxed numeral. Sometimes an answer that sounds fine out of context doesn’t fit within the sentence or essay. Be sure to keep in mind both the punctuation marks and words in each possible response; sometimes just the omission of a comma can make an important difference.

Watch for Questions about the Entire Essay or a Section of the Essay

Some questions ask about a section of the essay. They are identified by a question number in a box at the appropriate point in the essay, rather than by an underlined portion. (If you’re taking the test online, you will see highlighted asterisks in brackets instead of numbers in boxes.) Here’s an example from Sample Passage II on pages 219–221.

This question asks you to think about the role this sentence plays in terms of the paragraph as a whole. If the sentence were deleted, the paragraph would lose the elaboration on the point that Korean tradition indicates that everyone becomes a year older on New Year’s Day, regardless of when they were actually born. Without the sentence, the point about the “added significance of the Korean New Year celebration” (F) would have been unstated.

Some other questions ask about an aspect of the essay as a whole. If you are taking the test on paper, these questions are placed at the end of the essay, following boxed instructions like these:

If you are testing online, similar instructions will appear above the individual items at the end of the item set. You may want to read any questions that ask about the essay as a whole first so you can keep them in mind while you’re reading through the essay. For questions about a section of the essay or the essay as a whole, you must decide the best answer on the basis of the particular writing or revision problem presented in the question.

Be Careful with Two-Part Questions

Some questions require extra thought because you must decide not only which option is best but also which supporting reason for an option is most appropriate or convincing. The following question occurs at the end of Sample Passage III on pages 221–223. Each option begins with either a yes or no response, followed by a supporting reason for that response.

Once you decide whether the essay would or would not fulfill the writer’s goal, as described in the question, you need to decide which reason or explanation provides the most appropriate support for the answer and is most accurate in terms of the essay. Sometimes, the supporting reason does not accurately reflect the essay (the explanations in B and C, for example). Sometimes, the reason accurately reflects the essay but doesn’t logically support the answer to the question. And sometimes, the reason might logically support the question (that is, the writer’s goal) but that reason overstates the focus of the essay. It may be fair to say that Kevin Bannister’s case led to a review of student rights, but this essay does not at any point describe Kevin encouraging other students to exercise their rights, as A states. The best answer is D; this essay is more an objective reporting on a legal case about student rights (and that case’s historical significance) than it is a persuasive argument or call to students to exercise those rights.

Watch for Interrelated Questions

As pointed out previously, you’ll sometimes find that the best way to answer questions about a passage is not necessarily in their numbered order. Occasionally, answering a question after you’ve answered the one that follows it is easier. Or you might find two questions about different elements of the same sentence, in which case considering them both together may be helpful.

In the following example (from Sample Passage III on pages 221–223), considering questions 40 and 41 together may be helpful, because they’re contained in the same sentence. First, answer the question that seems easier to you. Once you’ve solved that problem in the sentence, turn to the other question.

Questions 40 and 41 deal with different kinds of writing problems. Question 40 is about choosing the most logical transitional word, and question 41 is about the correct use in this sentence of the gerund (a verb form with an -ing ending that’s used as a noun). You might find that answering question 41 helps you to figure out the answer to question 40. The best answer to question 41 is C—the noun phrase “wearing jeans” works as the subject of the dependent clause “that wearing jeans would actually impair the learning process of Kevin or of his fellow classmates.” Try penciling in your answer choice for 41 (that is, edit the essay) so that you can more easily read the sentence while responding to question 40. Does this approach make it easier for you to decide that the most logical answer to question 40 is J (“however”)?

* * *

Remember that this section is only an overview of the English test. Directly or indirectly, a question may test you in more than one of the areas mentioned, so do not become overly concerned with categorizing a question before you answer it. And, although awareness of the types of questions can help you be a more critical and strategic test-taker, just remember: the type of question you’re answering isn’t important. Most importantly, focus on what the question asks and do your best to pick the best answer based on evidence provided in the passage.

SAMPLE PASSAGE I

SAMPLE PASSAGE II

SAMPLE PASSAGE III

Answer Key for English Test Sample Questions

1. D

2. F

3. B

4. J

5. A

6. G

7. A

8. G

9. A

10. J

11. C

12. J

13. A

14. G

15. C

16. J

17. B

18. J

19. A

20. F

21. C

22. F

23. A

24. J

25. B

26. F

27. A

28. H

29. D

30. G

31. C

32. J

33. A

34. H

35. C

36. G

37. D

38. H

39. A

40. J

41. C

42. F

43. C

44. F

45. D

Prep Online!

Want even more ways to prep? Go to act.wiley.com to access our online platform or use our companion app. Take online practice tests and track your progress, create your own question sets, and use flash cards to practice. Flag difficult or confusing questions for review. To get started, go to act.wiley.com, and register with the PIN on the back of the front cover of this book. Once registered, you can also use our companion app if you prefer to study from your mobile device.

Chapter 6:
Improving Your Math Score

The ACT mathematics test asks you to answer 60 multiple-choice questions in 60 minutes. The questions are designed to measure your mathematical achievement—the knowledge, skills, and reasoning techniques that are taught in mathematics courses through the beginning of grade 12 and that are prerequisites for college mathematics courses. Therefore, the questions cover a wide variety of concepts, techniques, and procedures. Naturally, some questions will require computation, but you are allowed to use a calculator on the mathematics test. You’ll need to understand basic mathematical terminology and to recall some basic mathematical principles and formulas. However, the questions on the test are designed to emphasize your ability to reason mathematically, not to focus on your computation ability or your ability to recall definitions, theorems, or formulas.

Content of the ACT Mathematics Test

The ACT mathematics test emphasizes the major content areas that are prerequisites to successful performance in entry-level courses in college mathematics.

Nine scores are reported for the ACT mathematics test: a total test score based on all 60 questions and eight reporting category scores based on specific mathematical knowledge and skills. The reporting categories are Preparing for Higher Mathematics (which includes separate scores for Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability); Integrating Essential Skills; and Modeling. Descriptions follow.

Preparing for Higher Math

This category captures the more recent mathematics that students are learning, starting when they begin using algebra as a general way of expressing and solving equations. This category is divided into the following five subcategories:

Number and Quantity: Demonstrate knowledge of real and complex number systems. You will understand and reason with numerical quantities in many forms, including integer and rational exponents, and vectors and matrices.

Algebra: Solve, graph, and model multiple types of expressions. You will employ many different kinds of equations, including but not limited to linear, polynomial, radical, and exponential relationships. You will find solutions to systems of equations, even when represented by simple matrices, and apply your knowledge to applications.

Functions: The questions in this category test knowledge of function definition, notation, representation, and application. Questions may include, but are not limited to, linear, radical, piecewise, polynomial, and logarithmic functions. You will manipulate and translate functions, as well as find and apply important features of graphs.

Geometry: Define and apply knowledge of shapes and solids, such as congruence and similarity relationships or surface area and volume measurements. Understand composition of objects and solve for missing values in triangles, circles, and other figures, including using trigonometric ratios and equations of conic sections.

Statistics and Probability: Describe center and spread of distributions, apply and analyze data collection methods, understand and model relationships in bivariate data, and calculate probabilities, including the related sample spaces.

Integrating Essential Skills

These questions address concepts typically learned before grade 8, such as rates and percentages; proportional relationships; area, surface area, and volume; average and median; and expressing numbers in different ways. You will solve problems of increasing complexity, combine skills in longer chains of steps, apply skills in more varied contexts, understand more connections, and become more fluent.

Modeling

This category represents all questions that involve producing, interpreting, understanding, evaluating, and improving models. Each question is also counted in the other previously identified appropriate reporting categories. This category is an overall measure of how well you use modeling skills across mathematical topics.

Types of Questions on the ACT Mathematics Test

The questions on the ACT mathematics test differ in terms of content and complexity. The rest of this section gives you examples of questions—of various types and complexities from all content areas. All of the questions used in the examples are from actual ACT mathematics tests that have been taken by students from across the country. A solution strategy is given for each question. As you read and work through each example, please keep in mind that the strategy given is just one way to solve the problem. Other strategies may work even better for you.

Basic Math Problems

The type of question you’re probably the most familiar with (and probably find the easiest) is the stripped-down, bare-bones, basic math problem. Problems of this type are simple and straightforward. They test readily identifiable skills in the content areas, usually have very few words and no extra information, ask the very question you’d expect them to ask, and usually have a numeric answer.

Question 1 is a good example of a basic math problem.

This problem has very few words, asks a direct question, and has a numeric answer. The solution is simple: Convert 4% to a decimal and multiply by 1,100 to get (0.04)(1,100) = 44, choice D. You probably wouldn’t need your calculator on this problem, but remember that you may use it if you wish. If you chose answer B or E, you may have used rules about moving decimal points and moved the wrong number of places.

Question 2 is a basic algebra problem.

You should know what to do to answer the question the instant you read the problem—use the distributive property (FOIL—first, outside, inside, last) and get x(x – 5) + 4(x – 5) = x² – 5x + 4x + 4(–5) = x² – x – 20, choice G. On this problem, you probably wouldn’t use your calculator. If you chose F, you probably just multiplied the first terms and the last terms. Check your answer by substituting a number (try 6) into the original expression and into your answer. If the results are not equal, then the expressions cannot be equivalent.

Question 3 is an example of a basic problem from algebra.

This problem gives you a system of linear equations with unknowns x and y and asks for the value of y. You might be able to solve this problem intuitively—the only number that can be added to and subtracted from another number and give the same result for the problem (x + y and x – y both give 1) is 0, so y must be 0, choice B. Or, you could use algebra and reason that, because x + y and x – y both equal 1, they equal each other, and x + y = x – y gives 2y = 0, so y = 0. Although some calculators have graphing or matrix functions for solving problems of this type, using a calculator on this problem would probably take most students longer than solving it with one of the strategies given here. If you chose answer D, you probably found the value of x rather than the value of y.

Question 4 is an example of a basic problem in geometry.

This problem has a few more words than some of the other examples of basic problems you’ve seen so far, but the most important word is slope. Seeing that you are given two points, you would probably think of the formula that defines the slope of a line through two points:

.

Applying the formula gives = = –2, choice K. If you chose answer J, you probably got the expression for slope upside down. The change in y goes on top.

Here is another basic geometry problem from the ACT mathematics test.

Similar to many geometry problems, this problem has a figure. The figure tells you what you are given (an angle of 37°) and what you’re asked to find (its supplement, marked by “?”). You need not mark anything on the figure, because all the important information is already there. If you know that the sum of the measure of an angle and the measure of its supplement equals 180°, a simple subtraction gives the correct answer (180° – 37° = 142°), choice D. If you chose A, you found the complement, not the supplement.

A word of caution is in order here. You probably noticed that “Cannot be determined from the given information” is one of the options for question 5. Statistics gathered over the years for the ACT mathematics test show that many students choose “Cannot be determined from the given information” even when the answer can be determined. You should not think that whenever “Cannot be determined from the given information” is an option, it is automatically the correct answer. It isn’t, as question 5 demonstrates. Later in this section is a question for which the correct answer is “Cannot be determined from the given information.” Be sure to think carefully about problems with this answer choice.

You’ll also find basic geometry problems, such as question 6, on the ACT mathematics test.

This question asks you to find the sine of ∠A in the triangle shown in the figure. If you have studied trigonometry, you’ve seen questions similar to this before. The lengths of all three sides of the triangle are given on the figure, even though only two are actually needed for finding sin ∠A. The extra information is there not to confuse you but rather to test your ability to sort out the information you need from the information you are given. Picking 6 (the length of the side opposite ∠A) and 10 (the length of the hypotenuse) and forming the ratio gives the correct answer, 0.60, choice H. The cosine and the tangent of ∠A are also present in the answer choices. In order to do well on problems such as this one, you need to be able to tell which trigonometric function is which.

Basic Math Problems in Settings

Basic math problems in settings are what people often call word problems or story problems. They typically describe situations from everyday life in which you need to apply mathematics in order to answer a real-life question. The major difference between this type of problem and the basic math problems that you’ve seen in the examples so far is that the problem isn’t set up for you—you have to set it up yourself. Most people find this to be the most difficult part of word problems. The key steps are reading the problem carefully, deciding what you’re trying to find, sorting out what you really need from what’s given, and then devising a strategy for finding the answer. Once the problem is set up, finding the answer is not much different from solving a basic math problem.

You can find basic math problems in settings in all of the content areas. Question 7 is an example.

Here, you’re asked to find the total cost of some bananas and tomatoes. The important information is that the total cost includes 2.5 pounds of bananas at $0.34 per pound and 2.5 pounds of tomatoes at $0.66 per pound. A straightforward solution strategy would be to multiply to find the cost of the bananas and the cost of the tomatoes and then add to find the total cost. Now, the problem you’re left with is very basic—calculating 2.5(0.34) + 2.5(0.66). Using your calculator might save time and avoid computation errors, but if you see that 2.5(0.34) + 2.5(0.66) = 2.5(0.34 + 0.66) = 2.5(1.00) = 2.50, answer C, you might be able to do the computation more quickly in your head.

Basic algebra problems also can be in settings. Question 8 is an example.

In this problem, you’re given a relationship (in the form of an equation) between temperatures expressed in degrees Fahrenheit (F) and degrees Celsius (C). You’re also given a temperature of 14 degrees Fahrenheit and asked what the corresponding temperature would be in degrees Celsius. Your strategy would probably be to substitute 14 into the equation in place of the variable F. This leaves you with a basic algebra problem—solving the equation 14 = C + 32 for C. Before going on to the next problem, checking your answer would probably be a good idea. If you chose –10° (answer choice F), substitute –10 for C, multiply by , and add 32 to see if the result is 14°F and confirm that your answer choice was indeed correct. Checking doesn’t take long, and you might catch an error.

Question 9 is an example of an algebra problem in a setting.

After reading the problem, you know that it is about travel and that the basic formula “distance equals the rate multiplied by the time” (D = rt) or one of its variations will probably be useful. For travel problems, a table is often an efficient way to organize the information. Because the problem asks for Amy’s usual speed (rate), it would probably be wise to let the variable r represent her usual speed in miles per hour (mph). You might organize your table like this:

Distance (miles)

Rate (mph)

Time (hours)

Usual trip

200

r

This trip

200

r + 10

Then, because the time for this trip is 1 hour less than the time for the usual trip , solving –1 will give the answer. Solving this equation is a matter of using routine algebra skills and procedures. The solution, r = 40, choice C, answers the question, “What is her usual driving speed?” A quick check shows that driving 200 miles at 40 mph takes 5 hours and that driving 200 miles at 50 mph (which is 10 mph faster) takes 4 hours (which is 1 hour less). This quick check should convince you that your answer is correct.

Geometry problems can be in settings, too. Question 10 is an example.

In this problem, you’re told that you will be working with the standard (x,y) coordinate plane and that you will need to find a distance. The distance formula should immediately come to mind. All you need is two points, and those are given. The problem now becomes a basic math problem—applying the distance formula:

Your calculator might be useful in finding (20 – 5)² + (14 – 10)², but you should not press the square root key because most of the answer choices are in radical form.

A geometry problem in a setting is illustrated by question 11.

Question 11 has no figure, which is sometimes the case with geometry problems. It might be wise to draw your own figure and label it with the appropriate numbers from the problem. “A person 2 meters tall casts a shadow 3 meters long” is a pretty good clue that you should draw a right triangle with the vertical leg labeled 2 and the horizontal leg labeled 3. And, “a telephone pole casts a shadow 12 meters long” suggests that you should draw another right triangle with the horizontal leg labeled 12. Finding the height of the pole amounts to finding the length of the other leg of your second triangle, which you would label with a variable, say h. Your figure would be similar to this:

The triangles are similar (they’re both right triangles and the angle that the sun’s rays make with the ground is the same for both because the shadows were measured at the same time), so finding the height of the pole amounts to setting up and solving a proportion between corresponding sides of the triangles—a basic math problem. Your proportion might be . Cross multiply—that is, multiply the numerator of each (or one) side by the denominator of the other side—to get 3(h) = 12(2), or 3h = 24, and solve to get h = 8, choice C. Because the numbers are quite simple to work with, you probably wouldn’t use your calculator on this problem.

Last (but not least) of the basic math questions, question 12 shows an example of a trigonometry problem in a setting.

This problem has a figure, and the figure is labeled with all the necessary information, including a question mark to tell you what you need to find. To set up the problem, you need to decide which of the trigonometric ratios involves the hypotenuse and the side opposite the given angle of a right triangle. Once you decide that the sine ratio is appropriate, you have only a basic trigonometry problem to solve: sin 20° = , or 500 sin 20° = h. Then, using the approximation for sin 20° given in the note, calculate h ≈ 500(0.34) = 170, choice G. You may want to use your calculator to avoid computation errors. If you chose K, then you probably used the value for cosine rather than sine. Answer H comes from using tangent rather than sine.

Very Challenging Problems

The ACT mathematics test emphasizes reasoning ability, so it naturally has problems that can be very challenging. Because these problems are designed to test your understanding of mathematical concepts and your ability to pull together what you have learned in your math classes, they will probably be unlike problems you usually see. Some will be in settings, and some won’t. Some will have figures, and some won’t. Some will have extra information that you should ignore, and some won’t have enough information, so the correct answer will be “Cannot be determined from the given information.” Some will have numeric answers, some will have answers that are expressions or equations that you have to set up, and some will have answers that are statements for you to interpret and judge. On some questions your calculator will be helpful, and on others it will be better not to use it. All of the questions will share one important characteristic, however—they will challenge you to think hard and plan a strategy before you start to solve them.

Question 13 is a challenging problem.

You certainly wouldn’t want to calculate 537¹⁰² by hand, and your calculator doesn’t display enough digits for you to be able to read off the ones digit for this very large number, so you have to figure out another way to see the ones digit. A good place to start might be to look at the ones digit for powers of 7 because 7 is the ones digit of 537. Maybe there will be a pattern: 7⁰ = 1, 7¹ = 7, 7² = 49, 7³ = 343, 7⁴ = 2,401, 7⁵ = 16,807, 7⁶ = 117,649, 7⁷ = 823,543. It looks like the pattern of the ones digits is 1, 7, 9, 3, 1, 7, 9, 3, . . ., with the sequence of these 4 digits repeating over and over. Now, if you can decide where in this pattern the ones digit of 537¹⁰² falls, you’ll have the problem solved. You might organize a chart like this:

Ones digit

1

7

9

3

Power of 7

0

4

1

5

2

6

3

7

The next row would read “8 9 10 11” to show that the ones digits of 7⁸, 7⁹, 7¹⁰, and 7¹¹, respectively, are 1, 7, 9, and 3. You could continue the chart row after row until you got up to 102, but that would take a lot of time. Instead, think about where 102 would fall. The numbers in the first column are the multiples of 4, so 100 would fall there because it is a multiple of 4. Then 101 would be in the second column, and 102 would fall in the third column. Therefore, the ones digit of 537¹⁰² is 9, choice E.

Question 14 is an algebra problem designed to challenge your ability to think mathematically and use what you’ve learned.

Here you are told that a < –1. Then you are asked for the relationship between a³ and a². By stopping to think for a moment before trying to manipulate the given inequality or experimenting with numbers plugged into the answer choices, you might realize that if a < –1, then a is a negative number, so its cube is a negative number. Squaring a negative number, however, gives a positive number. Every negative number is less than every positive number, so the correct relationship between a³ and a² is a³ < a², choice G. Of course, there are other ways to approach the problem.

For another very challenging algebra problem, look at question 15.

In this problem, you’re asked to find the value of a variable, but the variable is in the exponent. After some thought you might decide to try to rewrite so that it is raised to a power. You should remember that the square root is the same as the power, so, after using some properties of exponents, . Now at least the left side and the right side of the equation have the same form, but the bases of the two expressions aren’t the same—they’re reciprocals. In thinking about the connection between reciprocals and exponents, it is good to realize that taking the opposite of the exponent (that is, making it have the opposite sign) will flip the base, because a–k = . That means . So now, with , n = , choice A.

Geometry problems can also be very challenging. Question 16 is an example.

This problem might seem confusing at first because it contains two different variables and no figure to clarify. You’re told that m is a constant but k changes. So, to get started, you could pick a value for m, say m = 1. Then, at least you can start sketching a figure. The point (0,k) is on the y-axis and k increases starting with 2, so you could start by drawing a figure similar to this:

You can see the triangle that the problem mentions. If you think of the line segment from (0,0) to (0,k) as the base and the line segment from (2,1) to (0,1) as the height, you can see that as k increases, the base of the triangle gets longer but the height remains the same. From geometry, you know that the area of a triangle is given by (base)(height). Therefore, the area will increase as the base gets longer. So, the area will increase as k increases, choice F. You should be able to reason that for any value of m, the result would have been the same, and you can feel confident that the correct answer is the first answer choice.

Question 17 is an example of a very challenging geometry problem.

This problem has a figure, but none of the information given is marked on the figure. A wise move is to mark the figure yourself to indicate which sides are congruent and which side is 10 units long. You need to find the area of ΔABC, and you know that the base BC is 10 units long. You need the measure of the height AD before you can apply the formula for the area of a triangle. You might ask yourself, “Is there any way to get the height?” If you were given the measure of one of the angles or the measure of one of the congruent sides, you might be able to find the height, but no other information is given. With a little more thought, you should realize that the height can be any positive number because there are infinitely many isosceles triangles with bases 10 units long. You conclude that not enough information is given to solve this problem, and the correct answer choice is E: “Cannot be determined from the given information.”

This is the example that was mentioned earlier when “Cannot be determined from the given information” is the correct answer. Remember not to jump to a hasty conclusion when “Cannot be determined from the given information” is an answer choice. Sometimes it is the right answer, but sometimes it isn’t.

Very challenging problems can be in settings, too. Question 18 is an example.

In this problem, whenever the pennies in the bag (which contains an unknown number of pennies) are divided evenly among 6 children, 7 children, or 8 children, 1 penny is always left over. This means that if you take the extra penny out of the bag, then the number of pennies left in the bag will be divisible (with no remainder) by 6, 7, and 8. You should ask yourself, “What is the smallest number that is divisible by 6, 7, and 8?” In mathematical terminology, you’re looking for the least common multiple of 6, 7, and 8. One way to find the least common multiple is to use the prime factorizations of the three numbers and to find the product of the highest power of each prime that occurs in one or more of the three numbers. This process will yield 2³ · 3 · 7 = 168. (As a check: 168 ÷ 6 = 28, 168 ÷ 7 = 24, and 168 ÷ 8 = 21.) But wait! You’re not quite finished. Remember to add back in the penny that you took out of the bag originally to make the divisions come out even. Thus, your answer is 169, choice J.

Question 19 is an example of an algebra word problem that is very challenging.

This is an example of a problem that has a mathematical expression as its answer. Finding an expression to answer a question usually makes you think more than finding a numerical answer because the variables require you to think abstractly. In this problem, you are told that out of a class of n students, p% play 1 or more musical instruments. Finding the percent of students who play no musical instrument is simple: (100 – p)%. To find the number of students who play no musical instrument, you’d probably want to convert (100 – p)% to a decimal and multiply by n. If 100 – p were a number you’d automatically move the decimal point two places to the left. But, because there’s no decimal point to move in 100 – p, you have to think about what you need to do to convert (100 – p)% to a decimal. Moving the decimal point two places to the left is the same as dividing by 100, so (100 – p)% as a decimal is , and the number of students who play no musical instrument is , choice C.

Question 20 is an example of a very challenging geometry problem in a setting.

This problem is different from any of the problems you’ve seen so far because its answer is a graph. And, instead of giving you an equation and asking you to identify the equation’s graph, this problem describes a situation and asks you to decide which graph represents the situation. You need to think about what the description of each of Ramona’s activities says in terms of distance as a function of time and what each activity would translate into graphically. For example, at first, Ramona walked at a constant rate down the sidewalk. Therefore, she moved farther away from her doorstep as time elapsed, and her distance from her doorstep increased at a constant rate as time increased. So, the first part of the graph should be a line segment with a positive slope. Unfortunately, all five graphs start out this way, so none of the options can be eliminated at this point. The next thing Ramona did was stop for 4 seconds. If she stood still, her distance from her doorstep would not change even though time was still elapsing. This part of the graph should then reflect a constant value for d as time increases. It should be a horizontal line segment. This information allows you to eliminate options F, G, and K, because they do not have a horizontal line segment. Ramona’s next activity helps you decide between H and J. Ramona walked back home at the same rate along the same route as before. On her way back home, her distance from her doorstep decreased at a constant rate as elapsed time increased. This would be graphed as a line segment with a negative slope, and therefore J is the correct graph.

Another word problem that challenges you to think mathematically is question 21.

This problem is about computing a distance, but it’s a distance in three-dimensional space without a picture to help you. For this problem, drawing a sketch of the situation might help. Your sketch might be a “box” such as this:

You need to find the length of the diagonal from the lower left corner of the front of the box to the top right corner of the back of the box. This is the hypotenuse of a right triangle (ΔOBT on the following redrawn figure) that has its right angle at B. One leg of this triangle has length 1, but the other leg is BT, and you don’t know the length of BT.

A closer look shows that BT is the hypotenuse of ΔTAB, which has its right angle at A and legs that measure 5 and 4. Using the Pythagorean theorem gives BT =.

Now you can use the Pythagorean theorem again to get which is about 6.5, choice A.

Question Sets

The mathematics test often contains sets of questions that all relate to the same information. Questions 22–24 illustrate a question set that relates to information from a paragraph and a graph. The mathematics test sometimes contains two question sets with two to four questions per set.

Once you’ve looked at the information given for a group of questions, you can use the same sorts of strategies to answer the questions that you would use on any question on the ACT mathematics test. Question 22 requires you to read the graph and compare the costs of renting a car from the two companies, assuming that the car is going to be driven 50 miles. From the graph, the cost for Speedy Car Rental appears to be about $40, and the cost of Quick Car Rental appears to be about $35. These points are marked on the graph that is redrawn below.

So Robert will incur the least cost if he rents from Quick Car Rental because that cost is $5 less, choice F.

Question 23 requires you to determine how much more Robert would pay if he rented a car from Quick Car Rental and drove 78 miles than if he drove 77 miles. Using mathematical concepts might be a better approach than trying to read the graph, because you might not be able to read the graph accurately enough. You know from coordinate geometry that, in the standard (x,y) coordinate plane, the slope of a line gives the rate of change in y per unit change in x, which is exactly what you want to find in this problem—how much the cost at Quick Car Rental changes when the car is driven 1 more mile.

The formula to determine the slope of a line is m = , where m is the slope, (x₁,y₁) are the coordinates of one point, and (x₂,y₂) are the coordinates of the other. Two points that are easy to read accurately off the graph are (0,15) and (50,35), labeled on the following redrawn graph. Plug the coordinates into the equation to get . So, the difference for driving 78 miles instead of 77 miles (that is, for driving 1 more mile) is $0.40, choice D.

In question 24, you are asked for the cost of renting a car from Speedy Car Rental and driving it 150 miles. You can’t simply read the cost off the graph, because 150 isn’t on the graph, but you can find an equation of the line for Speedy Car Rental and then plug 150 into the equation. Recall that a line is determined by any two points on the line—call them (x₁,y₁) and (x₂,y₂)—and that one way of finding an equation of the line is by first finding slope with m = and then using the two-point form of the equation of a line, (y − y₁) = m(x − x₁). Here, you can use two points that are easy to read off the graph for Speedy Car Rental, such as (0,30) and (100,50), shown on the redrawn graph on the next page. The slope through any two points on this line is m = = 0.2, and the equation (y − 30) = 0.2(x − 0) fits all of the points on the line. This equation can be rewritten as (y − 30) = 0.2x. So, when x = 150, that means (y − 30) = 0.2(150) and then y − 30 = 30 and then y = 60. The cost is $60, choice F.

As you have seen in the sample questions in this section, the mathematics test includes many types of questions. Some will be easy for you, and some will be hard. They all will require you to demonstrate as much as possible about what you know and can do in mathematics.

Answer Key for Mathematics Test Sample Questions

1. D

2. G

3. B

4. K

5. D

6. H

7. C

8. F

9. C

10. G

11. C

12. G

13. E

14. G

15. A

16. F

17. E

18. J

19. C

20. J

21. A

22. F

23. D

24. F

Strategies for Taking the ACT Mathematics Test

Pace Yourself

You have 60 minutes to answer 60 questions, which gives you an average of 1 minute per problem. Some problems will take you less than 1 minute, and some will take you more. Don’t spend too much time on any one question. You should keep a close eye on your watch to make sure you work at a pace that will enable you to finish the test in the 60 minutes allotted. When determining your pace, be aware that the questions are arranged approximately in order of difficulty: easier questions first and hardest last.

Answer All Questions

Answer all questions even if you have no idea how to solve some of them. If you’re stumped and have time, eliminate as many of the options as you can and then guess from among the remaining choices. If time is running out and you don’t have time to eliminate any of the options, guess anyway. Even a wild guess has a 20% chance of being correct, but a blank has no chance of being correct. Remember, your score is based solely on the number of questions you answer correctly—there is no penalty for guessing and no penalty for wrong answers. Scores are most comparable if everyone answers every question.

Answer All the Easy Questions First, Then Go Back to Answer the Hard Ones

Easy and hard are relative terms. What might be easy for one student might be hard for another. You know which math topics are easy for you and which are hard. Answer all the questions that are easy for you and then go back to the hard ones. Remember that you don’t get more points for answering hard questions. All questions, no matter how easy or hard, count equally toward your mathematics total score. If you don’t see a way to solve a problem, or if the method you’re using seems to be taking a lot of time, take your best guess (as explained in the previous section) or skip the question and move on to questions that you can answer more easily. If you skip the question, don’t forget to mark in the test booklet (never on the answer document) all those questions that you skip so that you can easily return to them later.

Note: In some circumstances you are not permitted to write in your test booklet. In those circumstances, you’ll be given scratch paper, and you can use it to jot down the numbers of the questions you skip.

Read Each Problem Carefully

Read carefully enough so you know what you’re trying to find before you start looking for it and so you know what you have to work with to help you find it. Remember that questions may contain extraneous details you will need to ignore or insufficient information to solve the problem. Think twice before choosing “Cannot be determined from the given information,” because test-takers often choose this option when the answer, in fact, can be determined from the information given. Make sure you are not overlooking a key piece of information provided or an alternate strategy for solving the problem.

Look for Information in the Answer Choices

Sometimes looking at the answer choices provides valuable information about the form of the answer. For example, you might be able to judge whether your answer should be left in radical form or converted to a decimal approximation, whether your polynomial answer should be left in factored form or multiplied out, or whether you should spend time reducing a probability to lowest terms. For some problems, you have to analyze the options as part of your solution strategy. For example, when a question asks, “Which of the following statements is true?” and the statements are the five options, you probably need to examine each option in turn. Sometimes, using the options gives you an alternate way to solve a problem. For example, suppose you’re trying to solve a quadratic equation and you can’t get the quadratic expression to factor and can’t remember the quadratic formula. You might be able to get the correct answer by substituting the options, in turn, into the equation until one works. This strategy should be used very sparingly, however, because it can be more time-consuming than other strategies.

Use Illustrations Wisely and Whenever You Can

The old saying “A picture is worth a thousand words” holds true on the mathematics test:

Refer to illustrations whenever they are provided.

If no illustration is provided and one might be useful, draw your own illustration in the test booklet. This can be especially helpful in solving word problems.

Transfer information from the question to the illustration, if you think it might be helpful. For example, you might write dimensions on the figure that are given in the question but aren’t shown on the figure or that you calculate in the process of solving the problem, or you might add marks to show congruences or draw auxiliary lines such as perpendiculars and diagonals.

Note: In some circumstances you are not permitted to write in your test booklet. In those circumstances, you’ll be given scratch paper to use.

Use Your Calculator Wisely

Each problem on the mathematics test can be solved in a reasonable amount of time without a calculator. A calculator is most helpful if you are very familiar with the one you bring to the test and you use it wisely during the test. Experimenting with the capabilities of a new calculator during the testing session or using a calculator in situations when a non-calculator approach would be better can cost you precious time. Bring the calculator that you are most familiar with—the one you use in your math classes or at home—but make sure it is an ACT-permitted calculator (visit www.actstudent.org for details). Don’t worry that other students have more sophisticated calculators than yours; the type of calculator that students use should not make a difference in their scores. Use your calculator wisely; remember that a non-calculator strategy is often better than a calculator strategy. And don’t believe everything your calculator tells you. Make sure the numbers it gives you are reasonable and make sense.

Think!

Your head is by far a more powerful and efficient problem-solving tool than a pencil or a calculator. Think before you plunge in and begin working on a problem. Don’t panic if you suddenly can’t remember a formula or all of the steps of a procedure you’ve been taught. You can often find another way to do a problem that will work just as well. For example, you don’t have to write and solve an equation for every algebra word problem. You might be able to reason through such a problem and get the correct answer without an equation. Sometimes the best option is to let your common sense about numbers take over.

Show Your Work

You have certainly heard this before—probably in every math class you’ve ever taken. Of course, you’re not going to have time during the test to write down every step for every problem the way you might on a homework assignment, but writing down at least some of what you are thinking and doing as you solve a problem will be worth the time it takes. If you’re using a calculator, you can write down the numbers that you plug into it and the intermediate results it gives you, to keep a running record of what you did. If you don’t write anything down and your answer for a problem doesn’t match any of the answer choices, your only alternative is to start over. But, if you have at least something written down, you may be able to go back over your work and find your mistake. Also, if you have time at the end of the test to go back and check your answers, having something written down will enable you to check your work more quickly.

Check Your Answers

Before you leave a question, make sure your answer makes sense. Don’t believe everything your calculator tells you; make sure that the answer your calculator displays makes sense to you and that your answer actually answers the question. For example, if a problem about oranges and apples asks for the number of apples, make sure your answer doesn’t give the number of oranges, or if a problem asks for the altitude of a triangle, make sure your answer isn’t the hypotenuse. Remember, if you have time remaining after answering all of the questions, use it wisely and go back and check your work. That’s a skill that will help you in college and career, too.

Prep Online!

Want even more ways to prep? Go to act.wiley.com to access our online platform or use our companion app. Take online practice tests and track your progress, create your own question sets, and use flash cards to practice. Flag difficult or confusing questions for review. To get started, go to act.wiley.com, and register with the PIN on the back of the front cover of this book. Once registered, you can also use our companion app if you prefer to study from your mobile device.

Chapter 7:
Improving Your Reading Score

Designed to measure your reading comprehension, the ACT reading test comprises four sections, three of which contain one long prose passage and one that contains two shorter prose passages. One of the sections may include a mixed-information format—visual and quantitative elements (like graphs, diagrams, and tables) that accompany the passage and contain information relevant to the passage topic. Each passage or passage set is followed by 9–11 multiple-choice questions, for a total of 40 questions. You are given 35 minutes to complete the test. The passages on the reading test come from published materials, such as books and magazines, written at a level that a first-year college student can expect to read for a class.

Content of the ACT Reading Test

The ACT reading test contains a mix of passages from the following categories:

Literary narrative (literary passages from short stories, novels, and memoirs)

Humanities (informational passages on architecture, art, dance, ethics, film, language, literary criticism, music, philosophy, radio, television, and theater)

Social science (informational passages on anthropology, archaeology, biography, business, economics, education, environmentalism, geography, history, political science, psychology, and sociology)

Natural science (informational passages on anatomy, astronomy, biology, botany, chemistry, ecology, geology, medicine, meteorology, microbiology, natural history, physiology, physics, technology, and zoology)

Each passage is preceded by a heading that identifies what type of passage it is (“Informational” or “Literary Narrative”), names the author, and may include a brief note that helps in understanding the passage. Each section contains a set of multiple-choice test questions. These questions do not test the rote recall of facts from outside the passage, isolated vocabulary terms, or rules of formal logic. In sections that contain two short passages, some of the questions involve both of the passages in the section. In sections that contain an element like a graph, figure, or table, some of the questions will involve the graphic or quantitative element.

You will receive four scores for the ACT reading test: a total test score based on all 40 questions and three reporting category scores based on the following specific knowledge and skills. You will also see an Understanding Complex Texts indicator, which is meant to indicate your level of proficiency in understanding the central meaning in complex texts.

Key Ideas and Details

Read texts closely to determine central ideas and themes. Summarize information and ideas accurately. Read closely to understand relationships and draw logical inferences and conclusions including understanding sequential, comparative, and cause-effect relationships.

Craft and Structure

Determine word and phrase meanings, analyze an author’s word choice, analyze text structure, understand authorial purpose and perspective, and analyze characters’ points of view. You will interpret authorial decisions and differentiate between various perspectives and sources of information.

Integration of Knowledge and Ideas

Understand authors’ claims, differentiate between facts and opinions, and make connections between different texts. Some questions will require you to analyze how authors construct arguments, evaluating reasoning and evidence from various sources; others will require you to piece together information from multiple texts or from different formats (e.g., graphs, diagrams, or tables).

If you choose to take the writing test, you will also receive an English Language Arts (ELA) score based on an average of your English, reading, and writing test scores.

Types of Questions on the ACT Reading Test

On the reading test, the questions fall into one of the three reporting categories previously described. You shouldn’t worry about these categories while you’re taking the reading test. It’s most important that you focus on the questions themselves and on what they ask you about a given passage. Because each passage is different, the kinds of questions will vary from passage to passage. Still, there are some general types of questions you’re likely to encounter. Most questions will ask you to do one of the following:

Identify and interpret details.

Determine the main idea of a paragraph, paragraphs, or a passage.

Understand comparative relationships (comparisons and contrasts).

Understand cause-effect relationships.

Make generalizations.

Determine the meaning of words from context.

Understand sequences of events.

Analyze the author’s purpose and method.

Understand and analyze arguments.

Understand information across multiple texts.

Sometimes the reading test contains other types of questions, but don’t worry. Just make sure you read each passage and its questions carefully. You’ll find that the information you need to determine the best answer for a question is always available in the passage. Questions that illustrate some common types of questions on the reading test follow.

Representative ACT Reading Test Questions

Details. Some test questions ask you to locate or understand a key detail from a passage. A detail can be something as seemingly simple as a characteristic of a person, place, or thing, or a particular date. Other questions of this type require you to do a bit more interpreting of minor or subtly stated details. The question below was taken from a literary narrative about a violin lesson, which is found on page 265.

You’ll have to look around the passage for the information you need—not unusual for this kind of question. Choice A is the best answer. In the fifth paragraph (lines 17–27), Allegra is getting ready to play for Mr. Kaplan. She notes that “he was going to know the instant I got to the top of the second page that I hadn’t been practicing the Mozart. At that spot there’s a fast shift from first finger to fourth finger on the G string, and you have to get ready for it. You can’t let a shift like that take you by surprise” (lines 22–27). It is clear from these lines that Allegra thinks Mr. Kaplan will know she hasn’t practiced if she isn’t ready for this shift. Mr. Kaplan mentions the dynamics of Allegra’s playing, but this is after she has played the piece for him (B). Likewise, the cadenza and Allegra’s tape are mentioned in the passage, but neither is mentioned in relation to Mr. Kaplan knowing that Allegra hasn’t practiced. In the sixth paragraph (lines 28–33), Allegra notes that there are three cadenzas in the concerto, but she doesn’t state that she’s worried about playing the first movement’s fast enough (C). In lines 59–62, it’s clear that the tape was made before this particular lesson (D).

Main Ideas. To answer this kind of question, you need to be able to determine the focus of a passage or of a paragraph or paragraphs in a passage. You shouldn’t count on finding this information summed up in the first paragraph of a passage or in the first sentence of a paragraph. You may have been advised to make the first sentence of each paragraph the topic sentence in your own writing, but not every writer does that. You’ll need to figure out what the author’s main point is in one or more paragraphs or in an entire passage by reading the paragraph(s) or passage carefully.

Main idea questions can be fairly straightforward. The following question, based on a social science passage about the development of perceptual abilities (page 268), is pretty direct:

The idea that the interaction between nature and experience shapes the development of perceptual abilities (H) is the clear focus of the entire passage. In the first paragraph, the author states that “the ancient central question of psychology” is “how much is due to nature and how much to nurture (or, in developmental terms, to maturation and to learning)” (lines 5–8). The second through eighth paragraphs (lines 9–85) describe research designed to help answer this question as it relates to the development of perceptual abilities in children. The last paragraph sums up the passage by saying that this research helps us “catch the first glimpse of how mind is constructed out of matter by experience” (lines 88–89). Though in lines 50–53 the author describes the rapid development of infants between four and seven months old, this is only a minor part of the passage, so F is incorrect. The seventh paragraph (lines 61–73) does mention that organisms can be permanently harmed if they miss critical life experiences, but this, also, isn’t the main point of the passage, making G incorrect. Choice J is just plain wrong: the whole passage deals with how research on physical skills and abilities has added to our knowledge of the growth of the mind.

As that example shows, you may have to rule out answer choices that either are supporting (rather than main) ideas or simply misstate what the passage says. Both types of wrong answers appear in this next example, based on the natural science passage about lightning and fire (page 270):

Choice B is the best answer here. Tree mortality rates “describe only direct injury” to trees (line 56), but lightning can also kill trees indirectly by making them vulnerable to insects, wind, and mistletoe and by causing fires. Although A is true, according to lines 54–56, the fact that Arizona researchers record tree mortality by volume is a minor point. The paragraph never claims that ponderosa pine trees are resistant to secondary diseases or that pine tree forests draw fewer lightning strikes than do many other habitat types in Arizona, so both C and D are incorrect.

Some questions for literary narrative passages will use phrases such as main conflict or main theme instead of main idea, but you should approach the questions in the same way as you would other main idea questions. Here’s an example based on a literary narrative passage about a young woman, Cally Roy (page 266):

You have to read the whole passage carefully to sort out what the main conflict is because there’s at least some truth to all of the answer choices. Choice J turns out to be the best of the four choices because the main conflict is within the narrator herself. She journeys away from home and “into the city’s bloody heart” (lines 18–19), she wonders “about the meaning of [her] spirit name” (line 22), she feels out of place in her “Frankenstein body” (line 76), and she ends the passage torn between her “city corner” and her life “back home” (lines 82–83). The narrator says her mother loves Frank “too much to live with” him (lines 36–37) and also that Frank “can’t drag himself away from the magnetic field of mother’s voice” (lines 68–69), but the tension between the narrator’s mother and Frank isn’t the main conflict of the passage, making F wrong. There could be some hostility between the narrator and her mother because the narrator doesn’t seem to want to go to the tribal college like her mother wants her to (see lines 79–82), but the narrator also wants to “curl next to her and be a small girl again” (lines 74–75), so mother-daughter hostility isn’t the main conflict, either, ruling out G. Choice H misses the mark because although the narrator has left her home and her mother, her grandmothers are only briefly talked about in the passage (see lines 24–33), so the main conflict can’t revolve around them.

Comparative Relationships. You’re likely to find questions asking you to make comparisons and contrasts in passages that contain a lot of information or that feature multiple characters or points of view. This kind of test question can make you process a lot of information—you may be asked to weigh one concept against another and identify a significant difference between the two. But comparison and contrast questions aren’t always overly complicated. In the following example, based on a humanities passage about the artist Pieter Saenredam (page 269), the comparison is directly made in a few lines in the passage:

Lines 16–17 state, “Like Vermeer, Saenredam was a perfectionist and his output was fairly small.” Thus, D is the best answer. It speaks to both parts of the similarity—their output being fairly small and the idea that they were both perfectionists. The passage states that Saenredam was an “outstanding draftsman” (lines 17–18), so A cannot be true. The passage does not give us information about Vermeer’s principles of design and spatial dimension (B), nor does it indicate that Vermeer used shadows and religious subjects in a way similar to Saenredam (C).

Cause-Effect Relationships. Cause-effect questions can arise in passages when it is important to understand the cause or result of specific actions, events, or ideas. In a literary narrative passage, perhaps one character’s actions caused another character to act a certain way. In an informational passage, it might be important to understand the consequences of a specific decision or policy. Sometimes the answer to a cause-effect question is stated in the passage; sometimes you have to piece together the information you’ve read and work out the answer on your own.

Here’s an example of a fairly direct cause-effect question, based on the literary narrative passage about Cally Roy (page 266):

The information needed to answer this question is in the first paragraph: once the narrator lost her indis, she says, she “began to wander from home, first in my thoughts, then my feet took after” (lines 11–13). Choice G is therefore the best answer. Choice F is pretty much the opposite of the truth, in the sense that the narrator decided to leave home. Although the narrator claims she “remember[s] every detail” of her indis (line 5), this isn’t because she lost it but because “the turtle hung near my crib, then off my belt, and was my very first play toy” (lines 5–7). So H can’t be the best answer. Choice J is incorrect because the narrator never really implies that losing her indis has caused her to fight with her family. Although her mother was “in a panic” (line 27) over the narrator’s decision to leave, this seems more out of concern for the narrator than the result of a fight.

Following is an example of a somewhat more complex cause-effect question, this time based on the natural science passage on lightning and fire (page 270):

Although the question lets you know to look in the third paragraph, the wording of that paragraph is subtle and requires close reading. The relevant information is in lines 45–46: “Lightning helps to fix atmospheric nitrogen into a form that rain can bring to Earth.” This matches nicely with B, which says that less nitrogen would be found on Earth. Although nitrogen would remain in the atmosphere if lightning didn’t fix it, the paragraph never suggests that rain wouldn’t fall to Earth, making A tempting but wrong. The paragraph doesn’t suggest that if lightning didn’t fix atmospheric nitrogen, electrical current couldn’t be conducted by air or that lightning bolts would strike the earth with less frequency, making C and D incorrect.

Generalizations. This type of question usually asks you to take a lot of information—sometimes the whole passage—and boil it down into a more concise form. A generalization question may involve interpreting mood, tone, or character, or it may ask you to make some kind of general observation or draw a conclusion about the nature of an argument the author is making. The following example, based on the literary narrative about Allegra’s violin lesson (page 265), focuses on personality or character:

This question requires you to sum up Allegra’s attitude toward Mr. Kaplan based on the passage as a whole. The best answer is G. Though there is no one specific moment that establishes this good-natured respect, their interactions and conversation most strongly suggest Allegra’s attitude toward her teacher. Allegra clearly wants to perform well for Mr. Kaplan, which shows her respect for him. We can see this in the way Allegra practices the shift without making any noise (lines 46–47) and in the fact that she had worked so hard on her tape for the Bloch Competition. And there are lighthearted moments throughout that speak to this respect being good-natured. Allegra loves her lessons (“In the summer I get to have morning lessons twice a week, and I love it” [lines 14–15]); she notes with affection the way Mr. Kaplan looks (lines 41–42); and she and Mr. Kaplan smile or laugh at moments during practice (lines 76, 88, 90). There is no indication in the passage that Allegra views Mr. Kaplan with an attitude of ridicule (F). There are moments that could be misread as ridicule, like when Allegra notes that Mr. Kaplan’s “ears stick out in a funny way” (line 41), but it’s important to read those moments in the larger context of the passage. Allegra goes on to say, “I love the way he looks” (lines 41–42), which speaks to her fondness for Mr. Kaplan. There’s also nothing in the passage to point to a general attitude of resentful obedience (H). Allegra takes direction from Mr. Kaplan, but she doesn’t display any resentment. And while Allegra and Mr. Kaplan are comfortable with each other, it goes too far to say that Allegra’s attitude toward Mr. Kaplan is one of close friendship (J). They have a good working relationship, but there’s nothing in the passage to suggest that Allegra considers Mr. Kaplan a close friend. At one point Allegra compares Mr. Kaplan to her softball coach when she says, “My softball coach and my violin teacher were overlapping each other” (5–6). This suggests that Allegra views Mr. Kaplan as another adult in a role of authority rather than a close friend.

Meanings of Words. Questions about meanings of words ask you to determine from context what a particular word, phrase, or statement most nearly means. In some cases, the word or words will probably be unfamiliar to you, but even when familiar words are tested, you’ll have to look at the context in which they appear to determine the closest synonym or paraphrase. Sometimes looking at a single sentence of the passage is enough to figure this out, but other times you’ll have to look at sentences before or after the given word, phrase, or statement in order to determine the closest meaning.

Many meanings-of-words questions will focus on a single word or a short phrase. The answer choices will include synonyms for the word or phrase that you might find in a dictionary or thesaurus, but only one of the choices will truly reflect how the word or phrase is used in this particular case. Look at the following example, based on the humanities passage about Pieter Saenredam (page 269):

All of the answer choices could be synonyms for fixes depending on context. Only Choice A, though, makes sense here. The passage tells us that certain drawings contain such detailed information that we can place the artist at a specific time and place. Thus, the ink-wash shadow in this drawing establishes (fixes) a time. It would not make sense to say that the shadow corrects (B), repairs (C), or hardens (D) the time.

Sequence of Events. In some passages, the order, or sequence, in which events happen is important. Sequence-of-events questions may ask you to determine when, for example, a character in a literary narrative passage did something or to figure out the order in which the researchers described in an informational passage performed certain steps in a biology experiment.

Sequence questions will often require you to take in information from the whole passage or from large sections of the passage in order to determine a correct order of events. This is true of the question below, based on a natural science passage about the small-comet theory (page 271):

The passage details how Frank and Sigwarth came up with the small-comet theory, the scientific community’s reaction to the theory, and new developments since the theory was first presented. Because the timeline skips around in the passage, it’s important to read carefully to understand the sequence of events. The best answer is H. In the sixth paragraph (lines 41–50), we’re told that the small-comet theory first started to take shape when Sigwarth was Frank’s graduate student. As they analyzed photos, they noticed dark specks appearing in images from a NASA satellite. Lines 59–62 state: “Based on their images, the Iowa scientists estimated 20 comets an hour . . . were bombarding the Earth.” Thus, the analysis of the images eventually led to the small-comet theory. Choice F cannot be correct because this new evidence was presented after the small-comet theory had been put forth (lines 15–19). This choice may be tempting because it appears in the passage before Choice H. The same is true of Choice G. But since the photo analysis eventually led to the small-comet theory, it would be incorrect to state that the theory was put forth first (G). The passage also makes clear that Frank and Sigwarth’s theory was not well received by the scientific community when it was first put forth, so Choice J has to come after Choices G and H.

Author’s Purpose and Method. Questions about the author’s purpose or method focus on the craft of writing—the main purpose of a passage, what role parts of a passage (such as a paragraph) play in the whole work, and so on.

An example should help clear up what this category is about. Taken from a social science passage on the Erie Canal (page 267), this question asks you to consider the function of a paragraph in the passage:

In the fifth paragraph, we’re told that the idea of a canal connecting the Hudson with the Great Lakes “had been around for many years but always dismissed as hopelessly impracticable” (lines 28–29). The sixth paragraph builds on this by describing the major issues involved in the construction of the Erie Canal. Therefore, the best answer is Choice D. The first sentence of this paragraph states, “One can understand the reluctance, for the project was huge by the standards of the day” (lines 39–40). The paragraph then details what made the project so daunting: the canal would be the longest in the world, it would require moving 11.4 million cubic yards of earth and rock, and its expense was equal to 1 percent of the entire country’s gross domestic product. Choice A is incorrect because these are not obstacles Clinton himself had to face to gain public support; in fact, the passage notes only that Clinton built public support (line 37) and doesn’t indicate that there were obstacles to this at all. Choice B is incorrect because there’s no information in the paragraph about how the plan won over the reluctant state legislature. Choice C is incorrect because although the paragraph notes that the Erie Canal “put the Empire in the Empire State” (lines 51–52), it doesn’t detail how; this is explored in the rest of the passage.

Arguments. Some questions deal with the arguments and claims made in passages. These questions may ask you to identify an argument or to examine support for a statement made in the passage. They may also ask you to identify the difference between fact and opinion, or to understand how an author might try to persuade readers. The examples below will help you understand what kinds of questions you might see in this category. The first is taken from the humanities passage about Pieter Saenredam (page 269) and asks you to identify a main claim from the passage:

Choice F is the correct answer because it identifies one of the passage’s central claims. In the second paragraph of the passage, we’re told that many of Saenredam’s drawings survive, and that “they offer intimate insights into his art and life” (line 20). The passage author then spends a significant portion of the passage exploring what those insights are. We can see this in lines 39–80, which detail the different aspects of Saenredam’s life and art that can be gleaned from his drawings. Since so much of the passage is spent exploring this idea, we can call this a central claim of the passage. Choice G might be tempting because we’re told that Saenredam was an outstanding draftsman and that “his output was fairly small” (line 17). But Choice G goes a step beyond this in asserting that Saenredam produced little of importance. While we know that he doesn’t enjoy the same level of fame as Vermeer or Rembrandt, the passage does not assert that his work is of little importance; rather, the author notes that many connoisseurs consider Saenredam an equal of these more famous artists and that Saenredam produced works “among the supreme masterpieces of Dutch art” (lines 51–52). Choice H is incorrect because it is a detail in the last paragraph of the passage (lines 81–89) rather than a central claim. Choice J is incorrect because this is not a statement made in the passage. In the first line of the passage we’re told that “thanks to Vermeer and Rembrandt, art of the 17th-century Dutch Golden Age is box-office magic” (lines 1–2), but this is not further explored or explained in the passage.

The next example is from the social science passage about the Erie Canal (page 267). It focuses on a specific statement in the passage and asks you to determine how the author supports that statement:

The answer to this question can be found in the ninth paragraph (lines 70–78), right after the claim in lines 70–72. Questions that ask for supporting evidence will not always be this straightforward and will often require that you look at the wider passage to find the answer, but in this case the answer can be found in the same paragraph as the claim. The best answer is C because this paragraph follows up the claim by providing statistics to show how the population of New York increased after the Erie Canal opened. Earlier in the passage we’re told that the Erie Canal was finished in 1825. According to population statistics provided in the ninth paragraph, the population of New York had been increasing at a rate of roughly 30,000 every decade before the Erie Canal opened. After the canal’s opening, the population increased at a much faster pace: by more than 100,000 from 1830 to 1840, more than 200,000 from 1840 to 1850, and almost 300,000 from 1850 to 1860. Choice A is incorrect because the quotation from Holmes in lines 66–67 mainly helps show how much produce flowed eastward after the canal opened; it points to prosperity but doesn’t provide specific support for the claim. Choice B is incorrect because the canal had not been finished in 1800. The 9 percent of American exports passing through New York in 1800 is low; in 1860, after the canal had been open for several decades, that percentage was much higher. Choice D is incorrect because the passage doesn’t describe other projects undertaken in New York after the canal was completed. “Megaprojects” are mentioned in lines 90–92, but they are not specific to New York, and they are provided as examples to show how the success of the Erie Canal encouraged big thinking.

Answer Key for Reading Test Sample Questions

1. A

2. H

3. B

4. J

5. D

6. G

7. B

8. G

9. A

10. H

11. D

12. F

13. C

Strategies for Taking the ACT Reading Test

Performance on the ACT reading test relies not only on reading speed and comprehension but also on test-taking strategies and skills. The following sections describe strategies and skills specifically for improving your ACT reading test score.

Pace Yourself

Before you read the first passage of the reading test, you may want to take a quick look through the entire reading test. If you choose to do this, flip through the pages and look at each of the passages and their questions. (Note that the passages begin on the pages to your left, and the questions follow.) You don’t need to memorize anything—you can look at any of the reading test passages and questions during the time allotted for that test.

Some readers find that looking quickly at the questions first gives them a better idea of what to look for as they’re reading the passage. It you’re a slow reader, though, this may not be a good strategy. If you do decide to preview the questions, don’t spend too much time on them—just scan for a few key words or ideas that you can watch for when you read the passage. To see what approach works best for you, you might want to try alternating between previewing the questions and not previewing the questions as you work through the practice tests in this book. Remember that when you take the ACT for real, a clock will be running. Plan your approach for the reading test before you take the actual ACT.

Use the Time Allotted

You have 35 minutes to read four passages and answer 40 questions. You’ll want to pace yourself so you don’t spend too much time on any one passage or question. If you take 2 to 3 minutes to read each passage, you’ll have about 35 seconds to answer each question associated with the passage. Some of the questions will take less time, which will allow you more time for the more challenging ones.

Because time is limited, you should be very careful in deciding whether to skip more difficult questions. If you skip the difficult questions from the first passage until you work through the entire reading test, for example, you may find that you’ve forgotten so much of the first passage that you have to reread it before you can answer the questions that puzzled you the first time through. It may work better for you to think of the test as four separate units, giving yourself time to finish every passage and item set (approximately 8 minutes and 30 seconds each). Then you can try to complete all the questions for a passage within its allotted time. Answer all the questions; you’re not penalized for guessing.

Think of an Overall Strategy That Works for You

Are you the kind of person who likes to get the big picture first, then carefully go over your work? Do you like to answer the questions you’re sure of right away and then go back and puzzle out the tougher ones? Or are you something of a perfectionist? (Do you find it hard to concentrate on a question until you know you got the one before it right?) There isn’t any right way or wrong way to approach the reading test—just make sure the way you choose is the way that works best for you.

Keep the Passage as a Whole in Mind

Your initial look at the whole reading test should give you some ideas about how to approach each passage. Notice the subject heading and short paragraph before each passage. These “advance organizers” tell you whether the passage is literary narrative or informational, where the passage comes from, who wrote it, and sometimes a little information about the passage. Occasionally an advance organizer will define a difficult word, explain a concept, or provide background information. Reading the advance organizers carefully should help you be more prepared as you approach each passage.

Always remember that the reading test asks you to refer to and reason on the basis of the passage. You may know a lot about the subject of some of the passages you read, but try not to let what you already know influence the way you answer the questions, because the author’s perspective may differ from yours. There’s a reason why many questions begin with “According to the passage” or “It can reasonably be inferred from the passage.” If you read and understand the passage well, your reasoning ability will help you to figure out the correct answer. During the reading test, you can refer back to the passages as often as you like.

Find a Strategy for Approaching Each Question

First, read each question carefully so you know what it asks. Look for the best answer, but read and consider all the options, even though you may feel you’ve identified the best one. Ask yourself whether you can justify your choice as the best answer.

Some people find it useful to answer the easy questions first and skip the difficult ones (being careful, of course, to mark the answer document correctly and to mark in the test booklet the questions they skipped). Then they go back and consider the difficult questions. When you’re working on a test question and aren’t certain about the answer, try to eliminate choices you’re sure are incorrect. If you can rule out a couple of choices, you’ll improve your chances of selecting the correct answer. Keep referring back to the passage for information.

Reading Strategies Summary

The sample passages used as examples in this section can be found on the following pages. They come from ACT tests that thousands of students have already taken. Remember, the passages and items in this section don’t represent every type you’re likely to see, but they should give you a good idea of some of the kinds of questions you’ll encounter when you take the ACT reading test. For a more complete picture of what the ACT reading test will look like, six complete reading tests are included in the six practice ACT tests in chapters 3 and 10. And remember that the best way to do well on the ACT reading test is to have a solid understanding of each passage—so read quickly but carefully.

Prep Online!

Want even more ways to prep? Go to act.wiley.com to access our online platform or use our companion app. Create your own question sets to practice. Use highlighting and notes to analyze each passage. To get started, go to act.wiley.com, and register with the PIN on the back of the front cover of this book.

Chapter 8:
Improving Your Science Score

The ACT science test asks you to answer 40 multiple-choice questions in 35 minutes. The questions measure the interpretation, analysis, evaluation, and problem-solving skills associated with science. The science test is made up of several passages, each of which is followed by multiple-choice questions.

Content of the ACT Science Test

The content areas of the ACT science test parallel the content of courses commonly taught in grades 7 through 12 and in entry-level college courses. Passages on the test represent the following content areas (examples of subjects included in each content area are given in parentheses):

Biology (cell biology, botany, zoology, microbiology, ecology, biochemistry, genetics, and evolution)

Chemistry (properties of matter, acids and bases, kinetics and equilibria, thermo-chemistry, organic chemistry, and nuclear chemistry)

Earth and Space sciences (geology, meteorology, oceanography, environmental science, stars, planets, galaxies, and the universe)

Physics (mechanics, gravitation, thermodynamics, electromagnetism, fluids, solids, and optics)

Advanced knowledge in these areas is not required, but background knowledge acquired in general, introductory science courses may be needed to correctly respond to some of the items.

The science test stresses science skills and practices over recall of scientific content, complex mathematics skills, and reading ability. The science skills and practices fall into three reporting categories. A brief description of each reporting category is as follows.

Interpretation of Data: Manipulate and analyze scientific data presented in tables, graphs, and diagrams (e.g., recognize trends in data, translate tabular data into graphs, interpolate and extrapolate, and reason mathematically).

Scientific Investigation: Understand experimental tools, procedures, and design (e.g., identify variables and controls) and compare, extend, and modify experiments (e.g., predict the results of additional trials).

Evaluation of Models, Inferences, and Experimental Results: Judge the validity of scientific information and formulate conclusions and predictions based on that information (e.g., determine which explanation for a scientific phenomenon is supported by new findings).

The use of calculators is not permitted on the science test but should also not be needed.

Format of the ACT Science Test

The scientific information presented in each passage of the ACT science test is conveyed in one of three different formats:

The Data Representation format requires you to understand, evaluate, and interpret information presented in graphic or tabular form.

The Research Summaries format requires you to understand, evaluate, analyze, and interpret the design, execution, and results of one or more experiments.

The Conflicting Viewpoints format requires you to evaluate several alternative theories, hypotheses, or viewpoints on a specific observable phenomenon.

You’ll find examples of the kinds of passages that you’re likely to find in each of the formats in the pages that follow.

The sample ACT science test passages and questions in this section are representative of those you’ll encounter in the actual ACT. The following chart illustrates the content area, format, and topic covered by each sample passage given in the remainder of this section:

Passage

Content area

Format

Topic of passage

I

Chemistry

Data Representation

Calorimetry

II

Physics

Research Summaries

Illuminance

III

Biology

Conflicting Viewpoints

Conjugation

Data Representation Format

This type of passage presents scientific information in charts, tables, graphs, and diagrams similar to those found in science journals and texts. Examples of tables used in an actual Data Representation passage administered to students are found in Sample Passage I that follows.

The questions you’ll find in the Data Representation format ask you to interpret charts and tables, read graphs, evaluate scatterplots, and analyze information presented in diagrams. There are five sample questions presented with the sample Data Representation passage.

Discussion of Sample Passage I (Data Representation)

According to this Data Representation passage, the amount of heat generated when a material is burned in oxygen can be determined using a bomb calorimeter. The bomb calorimeter has an outer shell made of an insulating material. Inside this shell is a bomb (steel casing) immersed in a fixed amount of water. When a material is burned inside the bomb, the water absorbs heat generated by the combustion, causing the temperature of the water to increase. The amount of the increase in water temperature depends on the amount of heat absorbed by the water. So, if we measure the increase in water temperature, we can calculate the amount of heat released when a material is burned inside the bomb.

Note that the passage contains three tables. Table 1 lists the temperature change of the water and the amount of heat generated when 1 g of each of four foods is burned in the calorimeter. Table 2 lists the amounts of heat released when various quantities of the sugar sucrose are burned. Table 3 lists several chemical compounds and their chemical formulas, as well as the amount of heat released for each compound when 0.5 g of the compound is burned in the calorimeter.

Question 1 asks you to determine how the change in water temperature varied as the amount of sucrose burned increased, based on the data in Tables 1 and 2. Notice that the change in water temperature and the amount of heat released are listed in Table 1 for each material burned. In Table 2, the amount of sucrose burned and the amount of heat released are listed, but the change in water temperature is not listed. Let us assume that the relationship between the amount of heat released and the change in water temperature for sucrose is the same as the relationship between the amount of heat released and the change in water temperature for the materials listed in Table 1. According to Table 2, as the amount of sucrose burned increased, the amount of heat released steadily increased. According to Table 1, as the amount of heat released increased, the magnitude of the change in water temperature steadily increased. Therefore, as the amount of sucrose burned increased, the magnitude of the change in the water temperature steadily increased. The best answer is A.

Question 2 asks you to choose a graph that best illustrates the relationship between the amount of heat released and the change in water temperature for the four substances listed in Table 1. According to the data in Table 1, as the change in water temperature increased, the amount of heat released steadily increased. No data in Table 1 supports the conclusion that as the change in water temperature increased the amount of heat released decreased or remained constant. Therefore, G is the best answer.

Question 3 asks you to predict, based on the data in Table 2, the fractional change in the amount of heat released by sucrose when the amount of sucrose burned is decreased by half. An examination of the data in Table 2 shows that when the amount of sucrose burned was decreased by half, the amount of heat released decreased by half. For example, when the amount of sucrose burned was decreased from 4.0 g to 2.0 g, the amount of heat released decreased from 64.0 kJ to 32.1 kJ; that is, the amount of heat released also decreased by half. (The amount of heat released actually decreased by 31.9 kJ, which is not exactly half of 64.0 kJ, but the 0.1 kJ difference between 31.9 kJ and 32.0 kJ can be attributed to limitations in the precision of the measurements [the amount of heat released is rounded off to the nearest 0.1 kJ] and can be ignored.) The amount of heat released was also decreased by half when the amount of sucrose burned was decreased from 2.0 g to 1.0 g and again when the amount of sucrose burned was decreased from 1.0 g to 0.5 g. Therefore, one can conclude that when the amount of sucrose burned is decreased by half, the amount of heat released during the burning of sucrose is decreased by half, so B is the best answer.

Question 4 asks you to list the foods from Tables 1 and 2 in increasing order, from the food that releases the least amount of heat per gram of food to the food that releases the greatest amount of heat per gram of food. According to Table 1, the amount of heat released was determined for 1 g samples of each of the foods listed. Therefore, the amount of heat listed in Table 1 for each food item is the amount of heat released per gram of food. In Table 2, the amount of heat released is given for various masses of sucrose. To get the amount of heat released per gram of sucrose we can divide the amount of heat released by the mass of sucrose that was burned. However, an easier method is to notice that a trial was conducted using 1.0 g of sucrose, and during that trial, the amount of heat released was 16.0 kJ. Therefore, the amount of heat released per g of sucrose was 16.0 kJ/g. An inspection of the heat released by the combustion of the foods in Table 1 shows that the potato sample released the least amount of heat (3.2 kJ/g), followed by the egg sample (6.7 kJ/g), the bread sample (10.0 kJ/g), and the cheese sample (17.0 kJ/g). The amount of heat per g released by sucrose, 16.0 kJ/g, places sucrose between the cheese sample and the bread sample. Therefore, the correct order is potato, egg, bread, sucrose, cheese. The best answer is F.

Question 5 asks you to use Tables 1 and 2 to estimate the amount of heat released when 5.0 g of potato is burned. Notice that Table 1 provides you with the amount of heat released (3.2 kJ) when 1.0 g of potato is burned. You might guess that burning 5.0 g of potato in the calorimeter would cause the release of five times the amount of heat released when 1.0 g of potato is burned. Do you have any evidence to support this guess? Table 1 only lists the amount of heat released when 1.0 g of potato is burned. Table 2 provides the amount of heat released from various amounts of sucrose, but not potatoes. In the absence of information to the contrary, you can assume that the relationship between the amount of potato burned and the amount of heat released is similar to the relationship between the amount of sucrose burned and the amount of heat released. According to Table 2, the heat released in kJ equals 16 times the mass of sucrose burned in grams. Note that this relationship holds whether 0.1 g of sucrose is burned or 4.0 g of sucrose is burned. For example, if 0.1 g of sucrose is burned, 0.1 g × 16 kJ released per g of sucrose = 1.6 kJ of heat released. If 4.0 g of sucrose is burned, 4.0 g × 16 kJ released per g of sucrose = 64 kJ of heat released. This relationship is a linear relationship. If the relationship between the amount of potato burned and the amount of heat released is also linear, then burning five times the amount of potato will release five times the amount of heat. Because 3.2 kJ of heat was released when 1.0 g of potato was burned, 5 × 3.2 kJ = 16 kJ will be released when 5.0 g of potato is burned. The answer closest to 16 kJ is 15 kJ, choice C.

Research Summaries Format

This type of passage provides descriptions of one or more related experiments or studies similar to those conducted by researchers or science students. The descriptions typically include the design, procedures, and results of the experiments or studies. The results are often depicted in graphs or tables. Sample Passage II provides an example of the Research Summaries format that shows the results of two different experiments with light bulbs. The questions you’ll find in the Research Summaries format ask you to understand, evaluate, and interpret the design and procedures of the experiments or studies and to analyze the results. There are five sample questions presented with this sample Research Summaries passage.

Discussion of Sample Passage II (Research Summaries)

This Research Summaries passage describes two experiments in which a student uses two identical paraffin blocks to compare the brightness of the light from one source (Fixture 1) with the brightness of the light from another source (Fixture 2). Fixture 1 contains five light bulbs, Bulbs A through E, and Fixture 2 contains only one light bulb, Bulb F (see Figure 1 in the passage). The two paraffin blocks are set between the fixtures. The two blocks are separated by a sheet of aluminum foil, so that the block on the left is illuminated only by bulbs in Fixture 1, and the block on the right is illuminated only by Bulb F in Fixture 2. The distance, L, between Fixture 1 and the aluminum foil can be varied, but the distance between Fixture 2 and the foil, 0.200 m, is fixed.

In Experiment 1, one bulb at a time is lit in Fixture 1, and Bulb F is lit in Fixture 2. For each combination of lit bulbs, L is varied until the two blocks glow equally brightly. This value of L is recorded in Table 1 along with the combination of lit bulbs used to obtain this value of L. In Experiment 2, two or more bulbs at a time are lit in Fixture 1, and Bulb F is lit in Fixture 2. For each combination of lit bulbs, L is varied until the two blocks glow equally brightly. This value of L is recorded in Table 2 along with the combination of lit bulbs.

Question 6 asks you why the student turned off the room lights before measuring L. Recall that the student was to compare the brightness of the light produced by Fixture 1 to the brightness of the light produced by Fixture 2 under a variety of conditions. The presence of light sources other than Fixtures 1 and 2 could have introduced error into the measurements of L by making one fixture or the other seem brighter than it really was. The overhead lights were turned off so that all of the light on the blocks came from the light bulbs in Fixtures 1 and 2. Thus, F is the best answer.

Question 7 proposes that Fixture 1 be replaced by a different fixture holding six light bulbs instead of five. Each of the light bulbs in the new fixture is identical to Bulb F. The question asks you to estimate L for the case that all six light bulbs in the new fixture, as well as Bulb F, are lit. According to Table 2, as the number of lit bulbs in Fixture 1 increased from two to five, L increased. So if the new fixture is used, increasing the number of lit bulbs from five to six, one would expect L to be greater than the value of L given in Table 2 for five lit bulbs in Fixture 1, 0.446 m. Only D contains a value for L exceeding 0.446 m, so D is the best answer.

Question 8 asks you to determine the main purpose of Experiment 1. In Experiment 1, one bulb at a time was lit in Fixture 1, but the location of the lit bulb in Fixture 1 was varied. Thus, the main purpose of Experiment 1 must have been to determine the effect, if any, that the location of the lit bulb had on the value of L. Only H states that the purpose of Experiment 1 was to determine if the position of the lit bulb within Fixture 1 affected L, so H must be the best answer.

Question 9 proposes that the five light bulbs in Fixture 1 be replaced with a single light bulb, and that when the new bulb and Bulb F are lit, for the two blocks to glow equally brightly, L must equal 0.446 m. You are asked to compare the brightness of the new bulb to the brightness of one of the original bulbs in Fixture 1. According to Table 2, the two paraffin blocks glowed equally brightly when all five bulbs in Fixture 1 were lit and L was 0.446 m, the same as the L obtained with the new bulb. Thus, the brightness of the new bulb would have to equal the sum of the brightness of the five original bulbs. Because each of the five original bulbs had the same brightness, the new bulb would have to be five times as bright as one of the original bulbs. Only C is consistent with this conclusion, so the best answer is C.

Question 10 proposes that in Experiment 2, Bulb F be replaced by a much brighter bulb, Bulb G. For each combination of lit bulbs in Fixture 1 and Bulb G lit in Fixture 2, when the two paraffin blocks are equally bright, how would the value of L compare to that obtained when Bulb F was used in Fixture 2? Because Bulb G is brighter than Bulb F and would be the same distance (0.200 m) away from the aluminum foil as Bulb F, the paraffin block closer to Bulb G would glow more brightly than it glowed when Bulb F was used. Thus, for each combination of lit bulbs in Fixture 1, to make the two blocks glow with equal brightness, Fixture 1 would have to be closer to the blocks than when Bulb F was used. That is, when Bulb G was used, L for each combination of lit bulbs in Fixture 1 would have to be less than when Bulb F was used for the two blocks to glow with equal brightness. Only choice G is consistent with this conclusion. The best answer is G.

Conflicting Viewpoints Format

This type of passage provides several alternative theories, hypotheses, or viewpoints on a specific observable phenomenon. These conflicting viewpoints are based on differing premises or on incomplete data and are inconsistent with one another. Sample Passage III, a biology passage on gene replication, is an example of the Conflicting Viewpoints format. Notice that this passage presents the theories of four different students.

The questions you’ll find in Conflicting Viewpoints passages ask you to understand, analyze, evaluate, and compare several competing theories, hypotheses, or viewpoints. Five sample questions are presented with this sample Conflicting Viewpoints passage.

Discussion of Sample Passage III (Conflicting Viewpoints)

According to this Conflicting Viewpoints passage, plasmids (small DNA molecules, each molecule consisting of genes arranged in a circle) are found in bacteria. While a plasmid is replicating (producing an identical copy of itself) in one bacterium, the gene copies are being transferred to a second bacterium, the recipient bacterium, eventually forming a complete copy of the plasmid in the recipient bacterium.

Notice the diagram of a plasmid in the passage. The plasmid in the diagram contains six genes. The passage tells us that when the plasmid replicates, it produces a linear copy of itself; that is, the six genes in the copy are arranged in the same order as in the original plasmid, but the genes in the copy are first arranged in a row rather than in a circle. The plasmid copies one gene at a time, and, according to the passage, the gene copies are transferred to the recipient bacterium one at a time in the order in which the copies are produced. For example, if the plasmid copies Gene F, followed by Gene X, Gene F will be transferred to the recipient bacterium first, followed by Gene X. Once all of the genes of the original plasmid have been copied and transferred to a recipient bacterium, the two ends of the linear plasmid copy connect to each other, forming a circle just like the one in the passage.

Four students agree that the rate of gene transfer between bacteria is constant and occurs at the rate of one gene every 15 minutes, so a complete plasmid is transferred between the bacteria in 6 × 15 = 90 minutes. However, the identity of the first gene to be replicated and the direction (clockwise or counterclockwise around the circle) in which replication proceeds are subjects of disagreement among the four students.

According to Student 1, Gene X is always replicated and transferred first, and Gene F is always replicated and transferred last. That is, replication always starts with Gene X and proceeds in a clockwise direction around the plasmid.

According to Student 2, replication always begins with either Gene F or Gene X. If Gene F is first, then Gene X is last; that is, if replication begins with Gene F, then replication proceeds in a counterclockwise direction around the plasmid. If Gene X is first, then Gene F is last; that is, if replication begins with Gene X, then replication proceeds in a clockwise direction around the plasmid.

According to Student 3, replication can start with any gene but always proceeds in a clockwise direction around the plasmid.

According to Student 4, replication can start with any gene and can proceed in either direction around the plasmid.

Question 11 asks you to predict how many complete genes would have been transferred to the recipient bacterium if gene transfer had been interrupted 50 minutes after transfer had begun. According to the passage, one gene was transferred every 15 minutes. Therefore, three genes would have been transferred in 3 × 15 = 45 minutes. A partial gene transfer would have occurred in the remaining 5 minutes, but the question asks about complete gene transfers, so you can ignore the partial gene transfer. The answer is three genes. Therefore, the best choice is B.

Question 12 asks you to suppose that all six genes in a plasmid are replicated and that Gene G is the first gene replicated. You are asked to predict the third gene replicated, assuming that Student 3’s model is correct. According to Student 3’s model, replication can start with any gene but always proceeds around the plasmid in a clockwise direction. Therefore, starting with Gene G and proceeding in a clockwise direction, Gene F would be the second gene replicated and Gene X would be the third gene replicated. The best answer is J.

Question 13 asks which students believe that any of the six genes on the plasmid can be the first gene transferred to a recipient bacterium. According to the passage, the order in which genes are transferred is the same as the order in which genes are replicated. Student 1 asserts that replication always begins with Gene X, so Student 1 would disagree with the statement that any of the six genes on the plasmid can be the first gene transferred. Student 2 asserts that replication always begins with either Gene X or Gene F, so Student 2 would disagree with the statement that any of the six genes on the plasmid can be the first gene transferred.

According to Students 3 and 4, replication can begin between any two genes on the plasmid, so they agree that any of the six genes on the plasmid can be the first gene transferred to a recipient bacterium. Because only Students 3 and 4 agree that any gene on the plasmid can be the first gene transferred, the best answer is C.

Question 14 asks you to suppose that the transfer of genes between two bacteria was interrupted 30 minutes after the transfer began. You are asked to select from among a list of genes (A, R, G, and X) the gene that could NOT have been transferred to the recipient bacterium within the allotted 30 minutes, assuming that Student 2’s model is correct. According to the passage, one complete gene transfer occurs every 15 minutes. Therefore, two complete gene transfers would have occurred after 2 × 15 = 30 minutes. Based on Student 2’s model, gene transfer can start with Gene X and proceed around the plasmid in a clockwise direction, or transfer can start with Gene F and proceed around the plasmid in a counterclockwise direction. If transfer had started with Gene X, Gene R would have been the second gene transferred. If transfer had started with Gene F, Gene G would have been the second gene transferred. Therefore, we conclude Genes X, R, F, and G could have been transferred. The only gene in the list that could not have been transferred is Gene A. Based on Student 2’s model, if Gene X had been the first gene transferred, then 4 × 15 = 60 minutes would have been required for Gene A to be transferred, because Gene A is the fourth gene in the clockwise direction from Gene X. If Gene F had been the first gene transferred, 3 × 15 = 45 minutes would have been required for Gene A to be transferred, because Gene A is the third gene in the counterclockwise direction from Gene F. The best answer is F.

Question 15 asks you to suppose that the transfer of genes between two bacteria was interrupted after the transfer of Gene A had been completed, and that no incomplete transfer of a gene occurred after the transfer of Gene A. You are asked to determine the number of minutes between the time that gene transfer began and the time at which gene transfer was interrupted, assuming that Student l’s model is correct. According to Student 1, Gene X is always transferred first, and Gene F is always transferred last. That is, transfer always starts with Gene X and proceeds in a clockwise direction around the plasmid. If we count genes in the clockwise direction, starting with Gene X, we find that Gene A is the fourth gene, so Gene A would have been the fourth gene transferred. According to the passage, each complete transfer of a gene requires 15 minutes. Thus, the number of minutes between the time at which the transfer of Gene X began and the time at which the transfer of Gene A was completed would have been 4 × 15 = 60 minutes. The best answer is D.

Strategies for Taking the ACT Science Test

Performance on the ACT science test relies mainly on the ability to understand and process scientific information presented in various formats but can also be affected by problem-solving strategies and skills. The following sections describe strategies and skills specifically for improving your ACT science score.

Develop a Problem-Solving Method

Because you have only a limited time in which to take the science test, you may find it helpful to work out a general problem-solving method that you can use for all or most of the questions. The method described here is certainly not the only way to solve the problems, but it is one that works for most science problems. Whether you see a way to adapt this method, or you work out your own approach, use the method that works best for you.

One approach to solving problems is to break the process into a series of smaller steps, such as these:

Restate the problem in your own words.

Decide what information is needed to solve the problem.

Extract the needed information from the passage. Information may include data, concepts, or even conclusions you’ve been able to draw from the information provided.

Consider any additional scientific knowledge (terms or concepts) you may have.

Organize the information and use reason to arrive at the answer.

Compare your answer to the answer choices and choose the option you think is correct.

Take Notes

As you read a question, take notes in the test booklet or on scratch paper to record what the question is asking and what information you have at your disposal to answer the question. (In some circumstances you are not permitted to write in your test booklet. In those circumstances, you’ll be given scratch paper to use.) Sometimes, the process of writing down or reviewing notes reveals the answer or helps you develop an effective approach to finding the answer.

Pace Yourself

Remember, you have 35 minutes to read several passages and their accompanying questions (40 questions altogether). That’s about 5 minutes for each passage and the accompanying questions. You can think of it as 40 questions in 35 minutes, or a little less than a minute per question. If you’re like most people, you’ll find some of the passages more familiar and probably easier than some of the others, so it’s a good idea to try to work fast enough to allow yourself time to come back to any questions you have trouble answering the first time.

Practice Interpreting Graphs, Tables, and Diagrams

Much of the information you need to answer the science test questions is presented graphically in the form of graphs, tables, and diagrams. Practice interpreting tables and different types of graphs, including pie charts, line charts, bar or column charts, and scatter charts, especially those included in science articles. Examine graphs and tables closely until you understand the data and can pick out specific pieces of data.

Tip: Pay attention to any and all text in graphs, tables, or diagrams, because any of this text is likely present to serve as instruction for how to interpret the data:

Graphs

Read the axis labels and the labels for any lines (curves) present. Typically, the y-axis indicates what is being measured (the dependent variable) and the x-axis most often indicates what is being manipulated (the independent variable). Some graphs may have a legend (labeled Key) that identifies line styles and the quantities they represent. Graphs may also have notes at the bottom of the graph to supply additional information.

Tables

Look at the column and row headings, which will identify quantities and their units of measure. Often (but not always) manipulated variables (independent variables) will be on the left side of the graph and the measured quantity (the dependent variable) will be to the right of the graph. Some tables will have notes at the bottom that provide vital information for interpreting the data.

Diagrams

Diagrams often contain labeled parts and could represent everything from a food web to a laboratory setup or show the cross-section of an object, such as the layers of Earth or of Earth’s atmosphere. Diagrams generally contain more text than numbers. Look for a title (above the diagram) or a caption (below the diagram) and for labels on the diagram itself. The diagram may not have a title, but parts of it may be labeled, as in a diagram of a laboratory setup that sheds light on how an experiment works.

Give yourself some time to figure out what the graph, table, or diagram is showing you in general. You can always look at these graphic representations more closely when answering questions, but having a general idea of what they show may shed light on what the questions are asking.

Make the Most of the Information in Graphs

Graphs illustrate data in ways that can be very useful if you follow a few rules. First, it’s important to identify what is being displayed in the graph (e.g., mass, volume, velocity). What unit or units of measurement is (are) used (e.g., grams, liters, kilometers per hour)? Graphs usually have axis labels that provide this information and some will have a key or legend or other short explanation of the information presented. Many graphs consist of two axes (horizontal and vertical), both of which will be labeled, and some may have dual axes with more than one curve. Remember, the first thing to find out about any graph is exactly what the numbers represent.

Once you’ve identified what is being presented in a graph, you can begin to look for trends in the data. The main reason for using a graph is to show how one characteristic of the data tends to influence other characteristics.

For a coordinate graph, notice how a change on the horizontal axis (or x-axis) relates to the position of the variable on the vertical axis (or y-axis). If the curve shows angles upward from lower left to upper right (as in Figure 1a), then, as the variable shown on the x-axis increases, so does the variable on the y-axis (a direct relationship). An example of a direct relationship is that a person’s weight increases as his or her height increases. If the curve goes from the upper left to the lower right (as in Figure 1b), then, as the variable on the x-axis increases, the variable on the y-axis decreases (an inverse relationship). An example of an inverse relationship is that the more players there are on a soccer team, the less time each of them gets to play (assuming everyone gets equal playing time). If the graph shows a vertical or horizontal line (as in Figure 1c), the variables are probably unrelated.

Figure 1

Sometimes, a question will ask you to estimate a value for one characteristic based on a given value of another characteristic that is beyond the limits of the curve shown on the graph. In this case, the solution will require you to extrapolate, or extend, the graph. If the curve is a relatively straight line, just use your pencil to extend that line far enough for the value called for to be included. If the graphed line is a curve, use your best judgment to extend the line to follow the apparent pattern. Figure 2 shows how to extend both types of graphs.

Figure 2

Another type of graph problem asks you to estimate a value that falls between two known values on a curve. This process is called interpolation. If the curve is shown, it amounts to finding a point on the curve that corresponds to a given value for one characteristic and reading the value for the other characteristic. (For example, “For a given x, find y.”) If only scattered points are shown on the graph, draw a “best-fit line,” a line that comes close to all of the points. Use this line to estimate the middle value. Figure 3 shows a best-fit line.

Figure 3

One very useful kind of graph shows more than one curve on the same pair of axes. Such a graph might be used when the results of a number of experiments are compared or when an experiment involves more than two variables. Analysis of this sort of graph requires that you determine the relationship shown by each curve and then determine how the curves are related to one another. Figure 4 shows a graph with multiple curves.

Figure 4

Make the Most of the Information in Tables

To understand what a table is showing you, you need to identify the information or data presented. You need to know two things about the information or data: the purpose it serves in the experiment and the unit (or units) of measurement used to quantify it. Generally, experiments intentionally vary one characteristic (the independent variable) to see how it affects another (the dependent variable). Tables may report results for either or both.

Once you have identified the variables, it might be helpful to sketch a graph to illustrate the relationship between them. You might sketch an x-axis and a y-axis next to the table and decide which variable to represent on each axis. Mark off the axes with evenly spaced intervals that enable all of the numbers for a category to fit along each axis. Plot some points. Again, draw a best-fit line and characterize the relationship shown.

As with graphs and diagrams, you may be asked to look for trends in the data. For example, do the numbers representing the dependent variable increase or decrease as the numbers representing the independent variable increase or decrease? If no pattern is clear, you may want to sketch a rough graph as discussed above. You may also need to make predictions about values of quantities between the data points shown (interpolation) or beyond the limits of those shown on the table (extrapolation). Another type of problem may require you to compare data from multiple columns of a table or between two or more graphs or tables. A simple examination of the numbers may be enough to see a relationship, but you may find it helpful to sketch a graph containing a curve for each category. The curves may be compared as described previously in “Make the Most of the Information in Graphs.”

Develop an Understanding of Scientific Investigations

When working with a Research Summaries passage, you should be able to understand scientific processes. This includes identifying the designs of experiments, identifying assumptions and hypotheses underlying the experiments, identifying controls and variables, determining the effects of altering the experiments, identifying similarities and differences between the experiments, identifying the strengths and weaknesses of the experiments, developing other experiments that will test the same hypothesis, making hypotheses or predictions from research results, and creating models from research results.

Carefully Analyze Conflicting Viewpoints

When reading a Conflicting Viewpoints passage, first read the introductory information. This describes the phenomena about which the viewpoints will differ. It may also present a graph, table, or diagram, as well as discuss aspects that all of the viewpoints share. Then, read each viewpoint closely and note what is the same and different in each. Note each viewpoint’s strengths and weaknesses. Use your own scientific knowledge and common sense to draw conclusions about each viewpoint. Which viewpoint sounds most credible? Which has the most evidence to back it up? With an understanding of and opinion about each viewpoint, you are better equipped to understand and answer questions about them.

Prep Online!

Want even more ways to prep? Go to act.wiley.com to access our online platform or use our companion app. Take online practice tests and track your progress, create your own question sets, and use flash cards to practice. Flag difficult or confusing questions for review. To get started, go to act.wiley.com, and register with the PIN on the back of the front cover of this book. Once registered, you can also use our companion app if you prefer to study from your mobile device.

Chapter 9:
Improving Your Score on the Optional Writing Test

On the ACT writing test, you have 40 minutes to read a prompt and to plan and write an essay in response to it. The prompts on the writing test cover a variety of subjects intended to reflect engaging conversations about contemporary issues, and they are designed to be appropriate for response in a 40-minute timed test.

The writing test is an optional test on the ACT. Should you decide to take the writing test, it will be administered after the multiple-choice tests. Taking the writing test will not affect your scores on any of the multiple-choice tests or the Composite score. Rather, in addition to your scores from the multiple-choice tests and your Composite score, you will receive a writing score and may receive an English Language Arts (ELA) score.

You will have a short break between the end of the last multiple-choice test and the beginning of the writing test.

Content of the ACT Writing Test

The test consists of one writing prompt that describes a complex issue and provides three different perspectives on the issue. You are asked to read the prompt and write an essay in which you develop your own perspective on the issue. Your essay must analyze the relationship between your perspective and one or more perspectives. You may adopt one of the perspectives given in the prompt as your own, or you may introduce one that is completely different from those given. The test offers guidance and structure for planning and prewriting, but planning and prewriting are optional and do not count toward the score. Your score will also not be affected by the perspective you take on the issue. Your essay will be evaluated based on the evidence that it provides of your ability to do the following:

Clearly state your own perspective on a complex issue and analyze the relationship between your perspective and at least one other perspective.

Develop and support your ideas with reasoning and examples.

Organize your ideas clearly and logically.

Communicate your ideas effectively in standard written English.

How Your Essay Will Be Scored

Your essay will be scored analytically using a rubric with four domains that correspond to different writing skills (turn to chapter 3 for a copy of the actual analytic rubric for the ACT writing test). Two trained readers will separately score your essay, giving it a rating from 1 (low) to 6 (high) in each of the following four domains: Ideas and Analysis, Development and Support, Organization, and Language Use and Conventions. Each domain score represents the sum of the two readers’ scores using the ACT Writing Test Analytic Rubric in chapter 3. If the readers’ ratings differ by more than one point, a third reader will evaluate the essay and resolve the discrepancy. Your writing score is calculated from your domain scores and is reported on a scale of 2 to 12.

The readers take into account that you had merely 40 minutes to compose and write your essay. Within that time limit, polish your essay as best as you can. Make sure that all words are legible; handwriting is not scored, but readers must be able to decipher the essay. With careful planning, you should have time to briefly review and edit your essay after you have finished writing it. Keep in mind that you probably will not have time to rewrite or even recopy your essay. Instead, you should take a few minutes to think through your essay and jot preliminary notes on the planning pages in the scoring booklet before you begin to write. Prewriting (planning) helps you organize your ideas, manage your time, and keep you on track as you compose your essay.

Sample Prompt and Essays

In preparation for the ACT writing test, examine the sample writing prompt, essays, and scoring explanations in the following sections. The sample prompt shows what you can expect to encounter on test day; the sample essays serve as models of low-, medium-, and high-scoring essays; and the scoring explanations provide insight into the criteria the readers will use to score your essay.

Sample ACT Writing Test Prompt

Writing test prompts are similar to the following example. The standard directions in the Essay Task section are a part of all prompts used in the writing test. You might want to practice by planning for and writing in response to this prompt for 40 minutes before you look ahead to the sample responses from other writers. If you took the practice test in chapter 3 and choose not to respond to this sample prompt, you may want to compare your essay to the sample essays that follow. Although the topics are different, evaluating the quality of the writing is a similar process.

Planning Your Essay

Your work on these prewriting pages will not be scored.

Use the space below and on the back cover to generate ideas and plan your essay. You may wish to consider the following as you think critically about the task:

Strengths and weaknesses of different perspectives on the issue

What insights do they offer, and what do they fail to consider?

Why might they be persuasive to others, or why might they fail to persuade?

Your own knowledge, experience, and values

What is your perspective on this issue, and what are its strengths and weaknesses?

How will you support your perspective in your essay?

Sample Essay Responses

The essays that follow are sample essays produced in response to the given writing prompt. The essays and the accompanying scoring explanations illustrate how writing at different levels is evaluated and scored for the ACT writing test. The essays in no way represent a full range of ideas, approaches, or styles that could be used. Although we all can learn from reading other people’s writing, you are encouraged to bring your own distinct voice and writing skills to the test. You want to produce your own best essay for the writing test—not an imitation of someone else’s essay writing.

The following essays have been evaluated using the analytic rubric for the ACT writing test (see chapter 3). This same rubric will be used to score the response that you write for the ACT writing test. Each essay is followed by a scoring explanation that comments on the essay.

Sample Essay 1 (Score: 1111)

Score Explanation

The writer’s attempt to rearrange the prompt does not demonstrate skill in writing an argumentative essay.

Ideas and Analysis (1): The writer’s intentions are hard to discern. Although the first sentence suggests that the essay will argue in favor of Perspective Three, there is no analysis to help shape or clarify the main idea of this essay. Instead, there is a confusing attempt to piece together ideas from the prompt. It is difficult to determine what this writer is trying to convey, and thus it is difficult to identify an intelligible argument.

Development and Support (1): Reasoning and illustration are unclear. Instead of elaborating on the idea that Perspective Three is favorable (“I say three”), the writer simply repeats the perspective (“because with so many sources the people are listening more an more music and […] discovering more with new musicians than they ever before”). Attempts to develop this point further are incoherent, because subsequent explanations do not clearly relate to a main idea (“And they said a matter of simple economics; cheap is good, but free is better,” “Free music is to online music and radio stations and choosing instead to release new music”).

Organization (1): This response does not exhibit an organizational structure. Although the piece does assume the appearance of a paragraph, the presentation of ideas within this paragraph is disorderly. Because these ideas do not clearly relate to one another, they cannot be logically grouped. Although the writer uses transitional language (“because,” “And they said”), the transitions fail to logically connect ideas.

Language Use and Conventions (1): This essay is unsuccessful in communicating a larger idea, and many of its shortcomings can be attributed to poor language control. Even though this response is heavily dependent on language drawn from the prompt, usage errors are abundant (“people are listening more an more music and it is discovering more with new musicians than they ever before”) and sentences are poorly formed (“And they said a matter of simple economics; cheap is good, but free is better”). As a result, the writer fails to demonstrate skill in using language to convey an argument.

Sample Essay 2 (Score: 2222)

Score Explanation

The writer generates an argument in response to the task, but the argument is imprecise in its focus and inconsistent in its execution.

Ideas and Analysis (2): The writer generates an argument that weakly responds to multiple perspectives on the issue. Although something of a thesis is evident—“free music is awesome” because of the benefits to music lovers—it is only loosely related to the prompt’s question of whether the value of music in our lives is changing. Analysis of the issue and its perspectives is incomplete and, in some respects, irrelevant. For example, it is unclear how the writer’s point that “there are so many ways you can get music […] you see students listen to music in school and at college” is related to the thesis or even to the concept of free music. The writer’s critique of the idea that free music causes the value we place on music to decline is similarly imprecise (“Some people believe [free music] make music value go way down. People go to concerts and buy tickets and memorbila that it make them atists money”).

Development and Support (2): Development and support fail to fully clarify the argument and contribute to the inconsistent sense of purpose exhibited by this response. In many cases, reasoning and illustration are circular (“There are so many ways you can get music. Such as computers, phones, radios and CD’s. There are so many sources to get music from that almost anyone can listen to it”) and redundant (“Who can beat free? No one; that’s the best it can get free! Music is so wide spread that people don’t have to pay for music anymore. You can get it free anywhere except from name brand online music store”).

Organization (2): This response does exhibit an organizational structure. The writer offers an introduction and conclusion, and the body paragraphs in between are each seemingly dedicated to a main idea. A closer examination of this structure, however, reveals a number of inconsistencies. Grouping of ideas, for example, is somewhat unclear—the final body paragraph includes a counterargument that doesn’t seem to address the main point of the paragraph. Furthermore, the absence of transitions within paragraphs contributes to the repetitive quality of the development.

Language Use and Conventions (2): Imprecise word choices, repetitive phrasing, unclear sentence structures, and grammatical errors: these are the markers of inconsistent skill in using language, and these markers are prevalent in this essay. A number of phrases appear multiple times throughout the essay (“their/there are so many,” in particular), reflecting imprecision in vocabulary and word choice; a number of fragments and run-on sentences reveal weak mechanical control. Although the writer’s exuberant voice (“that’s the best it can get free!”) is generally appropriate for the rhetorical purpose—after all, the argument is that free music is awesome—this relative strength does not outweigh the essay’s many weaknesses in the use of language.

Sample Essay 3 (Score: 3333)

Score Explanation

The writer generates an analytical argument that considers other perspectives, but the essay exhibits lapses in clarity that keep it from achieving a higher score.

Ideas and Analysis (3): The writer generates the thesis that, despite the trend toward free music, the value of music is rising. Although this idea reflects a clear focus on the issue, its execution reveals lapses in thought and purpose. In analyzing the issue and its perspectives, the writer discusses the positive and negative effects of free music. This contextual framework proves to be limited, because it results in simplistic analysis of the perspectives (see, for example, the writer’s rebuttal of Perspective One and the writer’s affirmation of Perspective Two). Furthermore, the negative effects the writer articulates occasionally contradict the positive effects: in the second paragraph, the writer claims that people still pay for music, but the third paragraph states that “[i]nstead of spending money on music people have began to spend it on other things.” Finally, it is not always clear how the positive and negative effects the writer outlines are intended to relate to the question of the value we place on music and thus to the thesis. Though the writer attempts to make these connections (“Although there have been negative effects of free music the value of music has not gone down”), the juxtaposition of positive and negative effects, as an analytical technique, is only somewhat clear in this argument.

Development and Support (3): The argument’s thesis takes shape through reasoning and illustration, which offer clarifying explanations of the positive and negative effects the writer perceives. However, this development, although relevant, is overly general (“People are still willing to pay to see music, but now they have more money, so they are able to spend it on other things as well. As more music continues to be free, more people will continue to listen to it. Without music becoming free its value would have gone down because it was too expensive”), and key ideas go unsupported (“Overall the positive effects are much higher than the negative ones”).

Organization (3): The positive-negative framework provides a basic organizational structure, allowing the ideas in this response to cohere as an argument. Transitions, particularly in the topic sentences of the body paragraphs, signal shifts in the discussion and are somewhat successful in connecting ideas across the essay. Despite these strengths, however, the piece falls short of adequacy in the Organization domain. The thesis is intended to control the argument but is unable to do so; the question of the value we place on music falls in and out of focus. Furthermore, the arrangement of the discussions on positive and negative effects is a bit haphazard; the writer jumps back and forth between these discussions without an evident purpose in doing so.

Language Use and Conventions (3): The use of language exhibits basic clarity. Sentence structures are clear; errors, although distracting, rarely impede understanding; and the writer’s voice and tone are appropriate for the purpose. However, as in the other three domains, language use demonstrates only developing skill. Though the writer makes reasonable word choices, vocabulary and phrasing are often overly general (“The lowered price of music has caused music to be available to more people and has not caused the value to go down,” “Throughout time music has become more inexpensive than ever”), leading to imprecision in expression.

Sample Essay 4 (Score: 4444)

Score Explanation

This argument engages with multiple perspectives on the issue in the prompt, building its case around the implications of two conflicting views.

Ideas and Analysis (4): This argument recognizes a complexity inherent to the issue and its perspectives: it may be possible that the availability of free music allows us to build a greater appreciation for music and causes music to lose some of its value. The writer makes this argument by analyzing Perspectives One and Three, touching on implications of both (“When music wasn’t free, people treasured the music they did have and when they aquired more, they tended to treasure and understand the value of their music […] Now, it is available to anyone and for no price, making it not as special,” “Since music is now more often free, people from all areas in the economic status can listen and expand their realm of experiences. People are more likely to try out new music styles or artists because it is there and there is nothing stopping them from listening”). Had the writer pursued this apparent contradiction further, the argument would have become more complex, perhaps receiving a higher score. Even so, ideas and analysis in this response exhibit a degree of clarity and sophistication that are absent in the previous responses, earning the essay a score of 4 in this domain.

Development and Support (4): Lines of clear reasoning and illustration clarify meaning and purpose as the writer develops the thesis. The second paragraph, for example, provides clear reasoning to support the idea that free music builds our appreciation for music; similarly, the third paragraph rationalizes the idea that we don’t value music as much as we used to. Although the writer is able to provide support for the argument, anticipating and addressing questions from the reader—How can it be that the value of music is both appreciating and depreciating? Is it possible that we’re talking about more than one type of value?—would have brought these lines of reasoning together and strengthened the argument by considering factors that may complicate it.

Organization (4): The shape of this argument reflects its controlling idea, which is first presented in the introduction. Ideas are grouped and sequenced: within paragraphs, ideas unfold logically, and the two premises of the argument are connected clearly, with a transition to move the reader from the first premise into the second (“However, free music does dilute the value of it”). The sequence of ideas does not conclude logically; the final paragraph seems to summarize a discussion that was never carried out. Perhaps this was an attempt to leave the reader with an interesting idea to consider, but the relevance of this idea (music offers experiences other forms of entertainment cannot match) to the larger argument is entirely unclear.

Language Use and Conventions (4): Some precise word choices (“dilute,” “sacredness,” “treasure,” “limitation,” “realm of experiences”) underscore the meaning of the argument. However, this precision is counterbalanced by awkward phrasing (“However, recently it has been becoming more available for no price at all”) and many vague and ambiguous pronouns (“By having it be available to everyone whenever they want, it does decrease the sacredness of it”). Although these issues and errors don’t always impede understanding, they negatively affect the overall quality of expression.

Sample Essay 5 (Score: 5555)

Score Explanation

The writer uses an extended example to analyze and evaluate multiple perspectives on the issue, addressing implications and critiquing underlying values.

Ideas and Analysis (5): The argument productively engages with multiple perspectives. For example, the writer uses Perspective Three as a basis for analyzing and evaluating Perspective One. In doing so, the writer addresses Perspective One’s assumption that “a decrease in monetary value of individual songs” also means that “we now view music with less appreciation.” This analysis serves to refine and advance a precise thesis: the value of music in our society is not decreasing; instead, by making music more accessible, we are only growing in our appreciation of music, and artists are benefitting as a result. Subsequent analysis is not quite as critical—the second point, that many other kinds of entertainment include music, is of a lower order, and the personal example does not meaningfully contribute to the discussion that precedes it. Even so, this thoughtful argument is worthy of a 5 in the Ideas and Analysis domain.

Development and Support (5): Development and support deepen understanding. Although some of the details in this example are probably unnecessary, the treatment as a whole is channeled toward conveying and bolstering the significance of the idea that free music affords musicians greater exposure, which is an important piece of the thesis. Other ideas are not developed quite so thoroughly, and the argument as a whole would be considerably stronger were it to consider complicating factors, such as objections that might be raised by someone with an opposing viewpoint on the issue. On balance, however, this is a well-developed essay.

Organization (5): Although this response does not achieve the unity and coherence required of a 6, it does exhibit the markers of a productive organizational strategy. The introduction presents the controlling idea, and the argument takes its shape around this idea, with all the writer’s points working to advance and support the larger argument. A logical sequence of ideas contributes to the effectiveness of the argument; the discussion on our appreciation of music (paragraph two) is followed with a discussion on the role of music in other forms of entertainment (paragraph three), and these discussions work together to build and refine the idea that free music is not causing us to lose appreciation for music. Unfortunately, the momentum of the argument is halted by the fourth paragraph, which introduces a personal example that does not differ meaningfully from the discussion carried out in paragraph two.

Language Use and Conventions (5): Advanced sentence structures convey ideas with precision (“No movie today is produced without a soundtrack, possibly consisting of the work of several artists”), and word choice is precise (“this free platform,” “caused music to be more prevalent in our society,” “financial barrier”). Although the response does exhibit some clunky syntax (“After the release of his videos, the videos went viral”) and a few minor usage errors (“the vast majority of these kinds of entertainment also includes music”), the overall use of language works in service of the argument.

Sample Essay 6 (Score: 6666)

Score Explanation

This argument earns the highest scores because of a sustained, critical examination of the implications of the issue and its perspectives.

Ideas and Analysis (6): This argument is driven by a nuanced, precise thesis: shifting economic circumstances may have changed our purchasing habits when it comes to music, but these changes in consumption do not reflect a change in the value our culture places on music. By viewing the issue and its perspectives through the lens of culture and economics, the writer has employed an insightful context for analysis. Within this context, the writer is able to examine the implications of Perspective Two (the discussion on surplus) while critiquing Perspective One’s assumption that this economic phenomenon is also a cultural matter. In doing so, the writer has generated an argument that critically engages with multiple perspectives on the issue.

Development and Support (6): In developing and supporting the argument, the writer keeps the thesis in full focus and thus produces an integrated line of reasoning and illustration. A concise explanation of the concept of surplus deepens the argument’s insights, and the importance of this concept to the larger argument is made clear by way of an important qualification—this is an economic issue, but it is also a cultural matter—that enriches and bolsters the thesis (“If we only consider economics, we might conclude that our preference for free music suggests that we place less value on music than we did in the past; however, a look at the role music plays in our culture suggests that we value it as much as ever”). In supporting the idea that our culture has not devalued music, the writer makes skillful use of a list of examples that, in their accumulation, fortify the claim that “[t]he prevelance of music has not diminished; if anything it has increased.” In these ways, reasoning and illustration are effective in conveying the meaning and importance of this argument.

Organization (6): The precise thesis brings unity and cohesion to this argument. The thesis guides a logical progression of ideas: the piece begins by introducing the main idea before discussing its central premises in turn. An effective conclusion reinforces the thesis and even manages to advance the discussion further by making efficient use of a historical context (“People have shared experiences with each other through song for thousands of years, and for much of this time, free music has been readily available. Though its monetary value may shift across time, the cultural value of music is consistent”). Transitions, both within paragraphs (“Then, of course, there are our more direct experiences with music”) and between them (“however, a look at the role music plays in our culture suggests that we value it as much as ever/Think of how often we encounter music in our daily lives”), form strong connections between ideas and make for smooth movement across the argument’s premises.

Language Use and Conventions (6): The use of language enhances this argument. Precise word choices communicate the conceptual understanding on which this argument depends (“surplus,” “commodity”) and the fine distinctions on which it rests (“Such an emotional connection is much deeper than a monetary connection”). Stylistic choices are strategic and effective, as the writer shifts from a more formal register when discussing economic considerations (“A surplus of any commodity will necessarily drive down the price of that commodity”) to a more informal register when discussing culture (“We carry music with us, in our pockets, wherever we go. Music plays at the grocery store, at the coffee shop, at the mall”). Errors in grammar, usage, and mechanics are virtually nonexistent.

Strategies for Taking the ACT Writing Test

Although your writing score reflects the quality of the product (the essay) you write, the writing process you follow can have a major impact on your score. For example, if you do not spend a few minutes prewriting (planning) before you start writing, you could “paint yourself into a corner” by following a line of logic that leads to an illogical conclusion and have no time left to start over.

The following sections present a few writing, prewriting, and postwriting strategies to improve the process you follow when writing your essay. Of course, no writing process can make up for a lack of knowledge and skill, which take years of study and practice to develop. If you need to sharpen your writing skills, we recommend that you take a course in English composition and practice writing and studying others’ writing frequently.

Prewrite

Some writers like to plunge right in, but this is seldom a good way to do well on a timed essay. Prewriting gets you acquainted with the issue, suggests patterns for presenting your thoughts, and gives you a little breathing room to come up with interesting ideas for introducing and concluding your essay. Before writing, then, carefully consider the prompt and make sure you understand it—reread it if you aren’t sure. Decide how you want to answer the question in the prompt. Then jot down your ideas on the topic: identify your own position and list reasons and/or examples that you will use to explain your point of view on the issue. Write down what you think someone might say in opposition to your point of view, and think about how you would refute their argument. Consider the broader context: what economic, social, historical, cultural, political, etc. circumstances surround it, and how do the specifics of your argument connect to that bigger picture? Try creating an outline or drawing a diagram to help you determine how best to organize the ideas in your essay. You should do your prewriting on the pages provided in your writing test booklet. You can refer back to these notes as you write the essay itself on the lined pages in your answer document.

Write

When you’re ready to write your essay, proceed with the confidence that you have prepared well and that you will have attentive and receptive readers who are interested in your ideas. At the beginning of your essay, make sure readers will see that you understand the issue. Explain your point of view in a clear and logical way. If possible, discuss the issue in a broader context and evaluate the implications or complications of the issue. Address other perspectives presented in the prompt. Also consider what others might say to refute your point of view and present a counterargument to those potential objections. Employ logical reasoning and use specific examples to explain and illustrate what you’re saying. Vary the structure of your sentences, and choose varied and precise words. Make logical relationships clear by using transitional words and phrases. Don’t wander off the topic. End with a strong conclusion that summarizes or reinforces your position.

Is it advisable to organize the essay by using a formula, such as the five-paragraph essay? Points are neither awarded nor deducted for following familiar formulas, so feel free to use one or not as best suits your preference. Some writers find formulas stifling, other writers find them a solid basis on which to build a strong argument, and still other writers just keep them handy to use when needed. The exact numbers of words and paragraphs in your essay are less important than the clarity and development of your ideas. Writers who have something to say usually find that their ideas have a way of sorting themselves out at reasonable length and in an appropriate number of paragraphs.

Review Your Essay

Aim to allow for a few minutes at the end of the testing session to read over your essay. Correct any mistakes in grammar, usage, punctuation, and spelling. If you find any words that are hard to read, recopy them so your readers can read them easily. Make any corrections and revisions neatly, between the lines (but not in the margins). Your readers take into account that you had merely 40 minutes to compose and write your essay. Within that time limit, try to make your essay as polished as you can.

Practice

There are many ways to prepare for the ACT writing test. You may be surprised that these include reading newspapers and magazines, listening to news analysis on television or radio, and participating in discussions and debates about issues and problems. These activities help you become more familiar with current issues, with different perspectives on those issues, and with strategies that skilled writers and speakers use to present their points of view and respond to a range of viewpoints.

Of course, one of the best ways to prepare for the ACT writing test is to practice writing. Practice writing different kinds of texts, for different purposes, with different audiences in mind. The writing you do in your English classes will help you, as will independent practice in writing essays, stories, poems, plays, editorials, reports, letters to the editor, a personal journal, or other kinds of writing that you do on your own. Strive to consider the quality of your writing from someone else’s perspective: would a reader see it as well developed and well organized, and having precise, clear, and concise language? Because the ACT writing test asks you to explain your perspective on an issue in a convincing way, engaging in exercises related to persuasive and argumentative writing (such as editorials or essays discussing controversial issues) is especially helpful. However, since many writing skills are transferable from one genre to another, practicing a variety of different kinds of writing will help make you a versatile writer able to adjust to different writing occasions and assignments. Additionally, analyzing others’ writing will help you strengthen and evaluate your own. Practice writing critiques of arguments in which you assess clarity of thought, logical reasoning and evidence used to support the thesis, organization of ideas, and the effects of language choices.

Share your writing with others and get feedback. Feedback helps you anticipate how readers might interpret your writing and what types of questions they might have. It will also help you identify your strengths and weaknesses as a writer. Also, keep in mind what the ACT readers will be looking for as they score your essay by examining the analytic rubric for the ACT writing test (in chapter 3). Consult with others (teachers, peers, etc.) to make sure your writing meets the criteria described for the high-scoring essays.

You should also get some practice writing within a time limit. This will help build skills that are important in college and career. Taking the practice ACT writing tests in this book will give you a good idea of what timed writing is like and how much additional practice you may need.

NOTES

Part Four:
Taking Additional Practice Tests

In This Part

This part features five additional practice tests. Here, you take and score the tests and look at your scores from a number of different perspectives, so you can use the results more effectively in your educational and career planning. Specifically, this part gives you the opportunity to do the following:

Take five additional practice tests.

Score your practice tests to determine your raw score, scaled scores (similar to the scores the ACT reports), and your estimated percentage rank (how well you did compared to other students who took the tests).

Evaluate your ACT scores from different perspectives to gain insight into what your scores mean in terms of college and career planning.

Chapter 10:
Taking Additional Practice Tests

In this chapter, you’ll find five additional practice ACT tests, copies of real answer documents for recording your answers, and explanatory answers for the questions on all of the multiple-choice tests.

Each practice test features the contents of the tests in the same order as they will be on the ACT: the English test, the mathematics test, the reading test, the science test, and the optional writing test. Following each complete practice test, you will find the explanatory answers for the multiple-choice questions on that test in the same pattern as the individual tests (English, mathematics, reading, and science).

Prep Online!

Want even more ways to prep? Go to act.wiley.com to access our online platform or use our companion app. Access all practice tests and track your progress.

Two copies of the answer documents that you can tear out and use to record your answers for the multiple-choice tests precede each practice test. (Two copies of these answer documents have been provided in case you make errors or if you would like to retake a practice test. When you take the actual ACT test, however, only one answer document will be provided.) One copy of the writing test answer document, which you can tear out (or photocopy) and use to write your essay, is provided for each practice writing test.

Simulating Testing Conditions

We recommend that you take all practice tests under conditions similar to those you will experience on test day. See chapter 3 for instructions.

Planning Your Essay

Use this page to continue planning your essay. Your work on this page will not be scored.

ENGLISH • PRACTICE TEST 2 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is B because it uses a simple present tense singular verb that agrees with the singular noun building. It also creates a complete sentence.

The best answer is NOT:

A because it attaches the main verb is to the relative pronoun that, creating a clause that interrupts the sentence and creates a sentence fragment (an incomplete sentence).

C because the contraction it’s (meaning “it is”) creates a faulty conjunction resulting in a fragment connected to an independent clause.

D because it removes the main verb from the sentence, resulting in a sentence fragment.

Question 2. The best answer is F because it mentions the “legacy of the Chinese community,” which refers to the cultural significance of the building, and “the nineteenth-century American West,” which refers to the building’s historical significance.

The best answer is NOT:

G because it names specific features of the building. The features themselves do not introduce the building’s historical and cultural significance.

H because it identifies the groups responsible for preserving and operating the building today but does not introduce the historical and cultural significance of the building.

J because it mentions some of the contents of the building’s kitchen. The contents of the kitchen do not introduce the historical and cultural significance of the building.

Question 3. The best answer is C because it correctly uses the past tense verb were attracted, which is consistent with served.

The best answer is NOT:

A because it uses the present tense in a sentence that requires the past tense. Also, it creates an illogical thought regarding what travelers might have been attracted to the land.

B because it uses the future tense in a sentence that requires the past tense.

D because it uses the present tense in a sentence that requires the past tense.

Question 4. The best answer is G because it provides a link to the information that follows by providing the names of the two young Chinese men who are referred to in the next sentence and the rest of the essay.

The best answer is NOT:

F because the preceding sentence does not make a claim about Hay and On.

H because the introduction of the men’s names is necessary. Knowing that Hay and On are the men who bought the building is necessary for understanding the essay at this point.

J because it incorrectly suggests that this part of the essay focuses on Hay and On’s partnership rather than on introducing Hay and On as the men who bought the building.

Question 5. The best answer is D because it uses a plural past tense verb remained. The essay’s content calls for the past tense, and the sentence’s verb must agree with its subject, men.

The best answer is NOT:

A because it uses a present tense verb remains, which does not agree with the sentence’s subject. Also, it is not parallel with the other verbs in the sentence (combined and organized).

B because it uses the auxiliary verb has, which does not agree in number with the sentence’s subject and is not parallel with the other verbs in the sentence.

C because it combines the correct auxiliary verb have with the incorrect verb remain, resulting in an improperly formed verb. Also, it is not parallel with the other verbs in the sentence.

Question 6. The best answer is G because it creates a parallel structure in which making and curing (used later in the sentence) are in the same form. The preposition for correctly applies to both verbs.

The best answer is NOT:

F because it inserts a dependent clause, creating a sentence in which the verbs are not parallel.

H because it inserts a dependent clause that isn’t parallel with the verb curing.

J because it makes the latter half of the sentence into a compound predicate, which creates a problem with parallelism with the verb curing.

Question 7. The best answer is A because it uses the possessive pronoun whose, which clearly explains that the treatments were those of the patients.

The best answer is NOT:

B because it is unnecessarily wordy and redundant; the idea of previous treatments explains that the treatments were already experienced.

C because it illogically indicates that the patients were the previous treatments.

D because the phrase “of whom” creates an illogical sentence with an unclear meaning.

Question 8. The best answer is F because the preceding sentence discusses Hay’s medical expertise as the reason for his fame and noteworthiness.

The best answer is NOT:

G because the sentence does not mention any specific examples of Hay’s diagnoses.

H because the resulting paragraph would be unevenly weighted toward On when the essay describes the two men as partners. The information about Hay is important regardless of On’s involvement with the medical clinic.

J because the paragraph is about both Hay and On, not On only.

Question 9. The best answer is A because the preceding sentence lists six services that the building eventually provided. If the sentence were deleted, the paragraph would lose the details that indicate the scope of services.

The best answer is NOT:

B because the sentence provides no claims about which aspect of Kam Wah Chung & Co. was most important to visitors.

C because the sentence does not provide a summary of one visitor’s experiences at Kam Wah Chung & Co.

D because the sentence provides no indication of how long Kam Wah Chung & Co. was prosperous.

Question 10. The best answer is J because the word into is grammatical and clearly indicates a transition from the Great Depression to the 1940s.

The best answer is NOT:

F because beginning is a present participle, not a preposition. The sentence has a series of prepositional phrases (“through the turn of the century” and “during the Great Depression”). This final phrase needs to match the structure of the two preceding phrases.

G because the pronoun it is singular and cannot refer to the plural businesses. This it has no clear referent. The resulting sentence does not make clear what entered the 1940s.

H because it creates an illogical statement; businesses cannot become the 1940s.

Question 11. The best answer is C because the past tense is called for in the sentence, and the verb form became aligns with was restored, a past tense verb used previously in the sentence.

The best answer is NOT:

A because has became is an incorrect verb form.

B because the auxiliary verb have does not agree in number with the singular subject of the sentence, building.

D because become is a present tense verb form; the context and structure of the sentence call for a past tense verb.

Question 12. The best answer is J because it is the only option that does not introduce a redundancy into the sentence.

The best answer is NOT:

F because it is unnecessarily wordy and redundant. The word designated already conveys the idea that the museum was called a National Historic Landmark.

G because it is redundant; designated already conveys the idea of having the appropriation of.

H because it is redundant; designated already conveys the idea of being identified as.

Question 13. The best answer is D because no transitional word or phrase is needed in the sentence.

The best answer is NOT:

A because the word besides indicates that a previous idea is being added onto, which isn’t the case.

B because the phrase “in conclusion” does not offer a logical transition from the idea of the museum being designated a national landmark to the idea that the museum encapsulates an era.

C because the sentence gives an exact year when the building became a National Historic Landmark (2005), so “in time” is illogical here.

Question 14. The best answer is J because sentence 2 explains why the artifacts left inside the building were preserved. It is logical to infer that they wouldn’t need to be preserved unless the building had been closed for a long time, which is exactly what sentence 5 states. Placing sentence 2 after sentence 5 makes the paragraph logical by putting the events in chronological order.

The best answer is NOT:

F because as it is now, sentence 2 interrupts the historical discussion of how Kam Wah Chung & Co. prospered and shifted in leadership over the years.

G because placing sentence 2 before sentence 1 illogically presents the information about the preservation of artifacts prior to mentioning the closing of Kam Wah Chung & Co.

H because placing sentence 2 after sentence 3 interrupts the historical discussion of how Kam Wah Chung & Co. shifted in leadership.

Question 15. The best answer is C because the focus of the essay is on the historical role of the Kam Wah Chung & Co. building. The essay details how the building was founded, who used it, and for what purposes. The essay does not outline the steps the state of Oregon took to restore the building.

The best answer is NOT:

A because although the essay mentions the restoration of the building, it primarily offers an overview of the building’s historical role rather than explaining the steps the state of Oregon took to restore the building.

B because although the essay mentions how the artifacts were preserved, it primarily offers an overview of the building’s historical role rather than explaining the steps the state of Oregon took to restore the building.

D because the essay does not critique On’s business philosophies or Hay’s medical diagnoses and treatments.

Passage II

Question 16. The best answer is H because it correctly inserts a comma only after the prepositional phrase that begins the sentence.

The best answer is NOT:

F because it incorrectly inserts a comma between the subject (fair) and the verb (looks).

G because it incorrectly inserts a comma between the subject (fair) and the verb (looks) and sets off the subject (“a Renaissance fair”) as nonessential information.

J because it incorrectly adds a semicolon after fair. A semicolon must separate two independent clauses. In this case, it separates two fragments (incomplete sentences).

Question 17. The best answer is D because it correctly uses the possessive pronoun their and the preposition past to explain the direction of movement; the people are passing by costumed characters and colorful booths.

The best answer is NOT:

A because it uses the contraction they’re (they are) in place of their (possessive).

B because it uses the contraction they’re (they are) in place of their (possessive) and the past tense verb passed in place of the preposition past.

C because it uses the past tense verb passed in place of the preposition past.

Question 18. The best answer is G because it creates a logical sentence that contrasts theme parks and Renaissance fairs. This comparison makes sense in the paragraph, which has been describing how theme parks and Renaissance fairs are similar up to this point.

The best answer is NOT:

F because it illogically suggests that roller coasters and Ferris wheels are the reason why Renaissance fair attractions are inspired by sixteenth-century England.

H because it creates an illogical cause-effect relationship between the roller coasters and Ferris wheels of theme parks and the sixteenth-century inspirations of Renaissance fairs.

J because it creates an illogical cause-effect relationship. Roller coasters and Ferris wheels are not the reason why Renaissance fair attractions are inspired by sixteenth-century England.

Question 19. The best answer is A because no punctuation is needed here. The absence of punctuation creates the clearest indication that the sentence is referring to the horses that are carrying knights.

The best answer is NOT:

B because it makes “carrying knights” appear as nonessential information and results in a clause that lacks a verb: Horses to a jousting match.

C because it incorrectly places a comma between the subject (“horses carrying knights”) and the prepositional phrase that explains where they are going (“to a jousting match”).

D because it offers the beginning of a nonessential phrase (“carrying knights to . . .”) that has no second comma later in the sentence to close it. This creates an ungrammatical sentence.

Question 20. The best answer is G because the verb clip-clop provides the sound the horses’ hooves make on the streets, which is a sensory detail about the horses’ movement.

The best answer is NOT:

F because the verb walk does not provide a sensory detail that clearly conveys the horses’ movement.

H because the verb move only conveys the vague idea of movement without providing any sensory details.

J because the verb travel only conveys the vague idea of movement from one place to another without providing any sensory details.

Question 21. The best answer is D because it correctly positions the phrase “ranging from king-sized turkey legs to suits of armor” so that it modifies wares. The wares are the things that vary in this way.

The best answer is NOT:

A because it incorrectly suggests that the vendors are what range from turkey legs to suits of armor.

B because it offers the action (“peddling wares”) before the subject (vendors) and separates the two with the modifier about the types of wares. The result is an unclear sentence.

C because it incorrectly modifies vendors, suggesting that the vendors range from turkey legs to suits of armor.

Question 22. The best answer is G because it effectively introduces the subject that is developed in the paragraph and in the rest of the essay: the hard work that goes into re-creating the past at the Renaissance fair.

The best answer is NOT:

F because it misleads the reader into thinking that what follows will be about how interesting Renaissance fairs are instead of about the challenges of working at a Renaissance fair.

H because it suggests that what follows will focus on the fun of working at the Renaissance fair instead of on the challenges of working there.

J because it suggests that the paragraph and essay will focus on a specific day when the narrator attended a Renaissance fair whereas the paragraph and essay explain the challenges of working at a Renaissance fair.

Question 23. The best answer is C because it results in a complete sentence with a comma separating the main clause from the participial phrase that begins with substituting.

The best answer is NOT:

A because it improperly has substituting as the beginning of a sentence, which results in a sentence fragment.

B because it creates a comma splice (two or more complete sentences separated by only a comma). The two complete sentences joined by the comma both begin with the subject we.

D because it incorrectly places a semicolon between a main clause and a participial phrase. A semicolon must separate two independent clauses.

Question 24. The best answer is F because it uses the past tense verb introduced, which is parallel with the verb served (the other verb in the sentence’s compound predicate). The past tense is used in most of the essay.

The best answer is NOT:

G because it incorrectly uses the infinitive to introduce when the past tense is needed. Also, it is not parallel with the verb served.

H because it incorrectly uses the participle introducing when the past tense is called for. Like G, it isn’t parallel with served.

J because it shifts the tense from the past to the present and, similar to G and H, isn’t parallel with served.

Question 25. The best answer is D because it correctly uses the pronoun who to introduce the clause that describes the person the narrator was pretending to be. In this sentence, who is required because it functions as the subject of the clause.

The best answer is NOT:

A because it uses the object pronoun whom instead of the subject pronoun who.

B because by using the verb were in this sentence, the writer is incorrectly describing a past event as if it were a hypothetical future one.

C because it, like A, uses the object pronoun whom instead of the subject pronoun who.

Question 26. The best answer is J because no punctuation is needed here. The absence of punctuation creates the clearest and most understandable sentence that links the subject costumes to the verb consisted.

The best answer is NOT:

F because it creates the nonessential clause “they consisted of confining corsets.” The resulting sentence lacks a necessary verb between costumes and the attributes of the costumes (confining corsets, several scratchy petticoats, and heavy velvet gowns).

G because it creates a comma splice (two or more complete sentences separated by only a comma). The word they becomes the subject of the second complete sentence.

H because it inserts the preposition of, which creates the ungrammatical phrase “because of our costumes consisted.”

Question 27. The best answer is C because the sentence about the costumes theme park characters wear isn’t very relevant in an essay about working at a Renaissance fair, especially given that the first paragraph makes a distinction between Renaissance fairs and theme parks.

The best answer is NOT:

A because although Renaissance fairs and theme parks are compared earlier in the essay, this sentence doesn’t pertain to this paragraph’s discussion of the costumes the narrator wore at the Renaissance fair.

B because although the preceding sentence does discuss uncomfortable costumes, it relates to the narrator’s experience at a Renaissance fair, not at a theme park.

D because the information about costumes worn by characters at theme parks is not found elsewhere in the essay.

Question 28. The best answer is H because it most clearly and concisely refers to all manner of inventions. It does not repeat the same idea, and it does not add unnecessary words to the sentence.

The best answer is NOT:

F because it is redundant and wordy. The phrase “after the sixteenth century” already conveys the idea of things that had come into existence more recently.

G because it adds wordiness and redundancy. The phrase “any kind of object or type of item” is redundant, as is the phrase “created and introduced for use.”

J because it creates a notable shift in tone. “Stuff from” is more informal than the tone in the rest of the essay.

Question 29. The best answer is B because the phrase “for example” serves as a transition from the preceding sentence, which discusses describing things in Renaissance terms, to this sentence, which has the narrator describing a photograph as a small painting in a tiny box.

The best answer is NOT:

A because the adverbial conjunction however implies that the ideas in this sentence contrast with the ideas in the preceding sentence, which isn’t the case.

C because the phrase “one time” suggests that the incident with the camera happened only once, an idea that is contradicted by the sentence’s use of the auxiliary verb would, which suggests that the event happened more than once.

D because instead suggests that this event happened in place of what was described in the previous sentence. This isn’t the case since the sentence offers an idea that is in line with the preceding sentence.

Question 30. The best answer is J because it removes unnecessary and redundant phrases from the sentence.

The best answer is NOT:

F because it is redundant. The essay makes clear that the narrator worked at the Renaissance fair during summer and that the fair closed once the three months were over.

G because it needlessly repeats the idea that the narrator’s work ended when the fair closed.

H because it is redundant; the essay has already made clear that the fair took place during the summer.

Passage III

Question 31. The best answer is A because no punctuation is needed here. The absence of punctuation creates the clearest and most understandable sentence explaining that the blast of water was caused by a breach in the reservoir.

The best answer is NOT:

B because it adds an unnecessary and confusing comma between by and a breach.

C because it adds an unnecessary and confusing comma between caused and by.

D because it adds an unnecessary and confusing comma between water and caused. This comma sets up the information about the cause as nonessential, but it leaves the first part of the sentence as a fragment.

Question 32. The best answer is J because it begins the sentence with the pronoun it, which agrees in number with the singular noun blast, to which it refers.

The best answer is NOT:

F because it begins the sentence with the plural pronoun they, which does not agree in number with the noun blast, which is singular.

G because it begins the sentence with the subordinating conjunction that, which results in a sentence fragment (an incomplete sentence).

H because it begins the sentence with a subordinating conjunction which and therefore results in a sentence fragment.

Question 33. The best answer is B because the singular possessive form park’s is the correct punctuation here. In addition, a comma is required after the word time in order to set off the dependent clause that begins the sentence from the main clause of the sentence.

The best answer is NOT:

A because it uses the plural parks rather than the possessive park’s, which would correctly show possession.

C because it incorrectly uses the plural possessive parks’. The phrase “one of Missouri’s most popular state parks” clearly identifies Johnson’s Shut-Ins as one state park.

D because it fails to include a comma after time, which is required to set off the dependent clause that begins the sentence from the main clause of the sentence.

Question 34. The best answer is G because the word ultimately is logical and indicates chronology. Despite the marred beauty, over a billion years’ worth of history was revealed in the end (or, ultimately).

The best answer is NOT:

F because the word specifically calls for one or more precise examples. The sentence instead mentions a large swath of history without specific examples.

H because the word instead signals a change from what was expected, which doesn’t make sense in the context of the sentence.

J because the word thus indicates a cause-effect relationship between the marred beauty and the revealing of over a billion years’ worth of Earth’s geologic history. No such cause-effect relationship exists.

Question 35. The best answer is C because it uses the verb began, which is the appropriate tense and verb form in this sentence.

The best answer is NOT:

A because had began is an incorrect verb form.

B because the verb begun needs an auxiliary verb, such as had, in order to be correct.

D because it uses the verb begun without an accompanying auxiliary verb.

Question 36. The best answer is H because no punctuation is needed here. The dependent clause that begins with when should follow immediately after the main clause.

The best answer is NOT:

F because adding a period after ago results in a sentence fragment (incomplete sentence) beginning with the word when.

G because it incorrectly adds a semicolon after ago, separating a dependent clause from an independent clause. A semicolon must separate two independent clauses.

J because it removes the subordinating conjunction when, resulting in a run-on, or fused, sentence.

Question 37. The best answer is D because it is the only concise and clear option that presents the idea of cooling without being redundant.

The best answer is NOT:

A because it is unnecessarily wordy; cooling already encapsulates the idea of temperature.

B because “cooled down” means to come to a lower temperature; the phrase is redundant.

C because “lowered its temperature” means to cool; the phrase is redundant.

Question 38. The best answer is F because no punctuation is needed here. The absence of punctuation creates the clearest and most understandable sentence about the substance that was formed, rhyolite.

The best answer is NOT:

G because the punctuation suggests that the word rhyolite provides a definition or clarification about silica-rich. As a noun (rather than an adjective), rhyolite cannot serve this function.

H because it suggests that rock (all rock) is silica-rich rhyolite formed by the cooling and crystallizing of slow-moving magma, which is illogical.

J because it adds an unnecessary and confusing comma between the verb form and the noun indicating what was formed, silica-rich rhyolite rock.

Question 39. The best answer is B because it provides information that helps explain the park’s name (Johnson’s Shut-Ins), which otherwise might confuse readers.

The best answer is NOT:

A because the essay provides no evidence that people feel shut in when visiting the park.

C because the phrase does not depart from the overall tone of the essay, which is neither formal or informal. Rather, the phrase has a direct relationship to the park’s name and should be included.

D because the phrase contributes to, rather than interrupts, the description of the Black River.

Question 40. The best answer is H because it places a comma between the main clause and the explanatory participial phrase that follows it.

The best answer is NOT:

F because it inserts the conjunction and before the word creating. This creates a compound predicate wherein the two verbs must be parallel. In this case, creating is not parallel with confined.

G because it incorrectly places a semicolon between a main clause and a participial phrase. A semicolon must separate two independent clauses.

J because it places a comma between the two verbs in a compound predicate. A conjunction is needed to make this construction grammatical.

Question 41. The best answer is A because it uses the singular possessive pronoun its, which agrees with the singular noun surge, and it uses the preposition in to clearly describe the water cutting a path through the region.

The best answer is NOT:

B because it uses the preposition on, which suggests that the surge of water followed a path that was already there. It also uses the plural possessive pronoun their, which does not agree in number with the singular noun surge.

C because it uses the plural possessive pronoun their, which does not agree in number with the singular noun surge.

D because it uses the preposition on, which suggests that the path was already there. In more clearly indicates that the surge of water created the path.

Question 42. The best answer is J because it uses the singular verb contains, which agrees in number with the subject of the sentence, channel, which is also singular.

The best answer is NOT:

F because it uses the plural verb contain, which does not agree in number with subject of the sentence, channel.

G because it uses the verb have, which does not agree in number with the sentence’s subject, channel.

H because are does not agree in number with the sentence’s subject, channel.

Question 43. The best answer is C because it is clearest about who is returning to the park (swimmers, hikers, and campers), and its tone is consistent with the rest of the essay.

The best answer is NOT:

A because it uses the vague pronoun some, which does not clearly explain who or what has returned to the park.

B because it features an informal tone that departs from the tone of the rest of the essay.

D because it features an informal tone that doesn’t fit in the essay.

Question 44. The best answer is J because it is the only option that does not introduce a redundancy into the sentence.

The best answer is NOT:

F because it is redundant; the idea contained in the word back is already conveyed by returned.

G because it is redundant; the idea of coming back to the park is already conveyed by returned.

H because it is redundant; to revisit the park is already conveyed by returned.

Passage IV

Question 45. The best answer is A because no punctuation is needed here. The absence of punctuation creates the clearest and most understandable sentence explaining that the narrator was peering through light-polluted skies.

The best answer is NOT:

B because it incorrectly sets off “peering through” as nonessential information and leaves the main clause incomplete: “inexperienced astronomer light-polluted skies.”

C because it incorrectly places a colon after astronomer, suggesting that the phrase “peering through light-polluted skies” defines the term “inexperienced astronomer.”

D because it incorrectly uses a comma to separate the preposition through from the noun light-polluted skies.

Question 46. The best answer is H because it correctly creates an independent clause, which is necessary following a comma plus and construction.

The best answer is NOT:

F because it has the participle being, which cannot function as a main verb. The result is that the second part of the sentence is not an independent clause.

G because it includes the pronoun them, which does not clearly refer to a noun previously mentioned in the paragraph. Also, “by them” interrupts the verb phrase “is said to be.”

J because it uses the participle having in place of a main verb, which means that the second part of the sentence is not an independent clause.

Question 47. The best answer is A because it correctly uses commas to set off the phrase “in some mythologies.” In this sentence, the phrase is nonessential information, so using commas around the phrase is appropriate.

The best answer is NOT:

B because it sets off the phrase “who in some mythologies” from the rest of the sentence and results in a confusing sentence that suggests Orion and the hunter are separate figures and that Orion only appears when a hunter fights Taurus the Bull: “Orion appears as a hunter is fighting Taurus the Bull, another constellation.”

C because it indicates that the phrase “in some mythologies is fighting Taurus the Bull” is nonessential information. Setting off the phrase in this way results in an ungrammatical sentence: “Orion appears as a hunter who another constellation.”

D because it sets off the phrase “some mythologies” as nonessential and results in an ungrammatical sentence: “Orion appears as a hunter who in is fighting Taurus the Bull, another constellation.”

Question 48. The best answer is H because it uses the plural verb are, which agrees in number with the plural subject of the sentence, stars. In addition, the verb form are is in the present tense, as are the verbs in the preceding sentence.

The best answer is NOT:

F because it uses the singular verb has, which does not agree in number with the sentence’s subject, stars.

G because it uses the past progressive were being when the context of this sentence and the preceding sentence call for the present tense.

J because it uses the singular verb is, which does not agree in number with the sentence’s subject, stars.

Question 49. The best answer is C because it is the only option that contains a main clause and, therefore, is the only one that is a complete sentence.

The best answer is NOT:

A because it does not contain a main clause. The dependent clause “when gravity causes gas and dust to collapse” is followed by a participial phrase that lacks a subject, “forming stars.”

B because it lacks a main clause. This option is one long dependent clause.

D because it lacks a main clause, consisting instead of one dependent clause.

Question 50. The best answer is J because it correctly punctuates the appositive phrase “home to thousands of young stars” by putting commas around it. This phrase adds nonessential information that helps define nebula.

The best answer is NOT:

F because it offers two phrases that begin with the verb is and connects those phrases only with a comma; this sentence structure would require the linking word and in place of the comma.

G because it incorrectly connects the two phrases beginning with is with a comma and the linking word and (rather than with the linking word alone).

H because it correctly sets off “home to thousands of young stars” as nonessential but incorrectly adds the conjunction and, which results in an ungrammatical sentence: “The nebula and is often called a ‘galactic nursery.’”

Question 51. The best answer is D because the Great Orion Nebula is introduced in the sentence preceding Point D. The added sentence expands on the discussion of that nebula.

The best answer is NOT:

A because the nebula has not yet been mentioned at this point in the paragraph, so placing the sentence here is illogical and confusing.

B because the nebula has not yet been mentioned at this point in the paragraph.

C because the nebula has not yet been mentioned at this point in the paragraph.

Question 52. The best answer is J because the word so serves as a logical transition from the preceding sentence, which discusses the narrator’s struggle to get the nebula in focus, to this sentence, which explains that the narrator switches to a higher-powered eyepiece. The word so conveys the idea of intent or purpose; the narrator switches the eyepiece in an attempt to bring the nebula into focus.

The best answer is NOT:

F because the narrator purposely switches to a higher-powered eyepiece to bring the nebula into focus. The switch is not coincidental.

G because the word similarly indicates a comparison; no comparison is stated or implied in the paragraph.

H because the word besides indicates that a previous idea is being added onto, which isn’t the case.

Question 53. The best answer is A because it correctly uses the past tense verbs tried and had (I’d). At this point in the essay, the narrator is describing a past event, so the past tense is called for.

The best answer is NOT:

B because the contraction “I’d have” suggests the conditional “I would have.” This shifts the meaning to a hypothetical situation in the past that is not supported by the essay.

C because it uses the present tense try rather than the past tense tried.

D because it uses the present tense try rather than the past tense tried.

Question 54. The best answer is G because it correctly uses the word them to refer to the distant objects, whereas the phrase “one side of them” clearly explains that the viewer is looking to one side of the distant objects.

The best answer is NOT:

F because it is unclear and illogically suggests that objects have only one side.

H because it incorrectly substitutes the contraction they’re for the possessive pronoun their.

J because one’s is ambiguous in meaning. This could mean a distant object’s side or a viewer’s side.

Question 55. The best answer is B because the sentence explains how averted vision works. Deleting the sentence would result in an essay that is less clear.

The best answer is NOT:

A because it does not elaborate on why the narrator was capable of using averted vision. Rather, the sentence explains how averted vision works.

C because the level of technical detail is not out of place in this essay, which describes details about using a telescope to view a nebula.

D because the main point of the paragraph is to explain how the narrator was able to view the nebula. Using the principle of averted vision was the key strategy for the narrator. Rather than digressing from the main point, it helps explain the main point.

Question 56. The best answer is H because it correctly establishes the comparison the narrator is making. The view with averted vision is far better than the view when looking directly at the nebula.

The best answer is NOT:

F because it indicates the wrong comparison. This phrase suggests that both averted and direct vision resulted in a better view, but averted vision permitted more of that same better view. The essay does not support this comparison.

G because it suggests that averted vision resulted in a farther view and incorrectly adds a comma between the modifier (farther) and the object it modifies (view). This is confusing in meaning and is not supported by the essay.

J because it indicates that far and better are coordinate adjectives (adjectives that can be switched without affecting the meaning of the sentence). The idea of a better, far view is unclear and unsupported by the essay.

Question 57. The best answer is A because the word illuminated makes sense in this context. The four bright stars help reveal the Trapezium star cluster.

The best answer is NOT:

B because the word emanated suggests that the cluster was spread out by or flowed from the bright stars. The bright stars are part of the cluster; the cluster does not emanate from them and is not emanated by them.

C because the word emulated suggests the idea of copying; the four bright stars are not copying the star cluster.

D because the word eliminated suggests that the bright stars are destroying the cluster. This is not supported by the essay.

Question 58. The best answer is F because the plural possessive birds’ and the plural eggs correctly convey that the stars look like eggs laid by birds in a nest.

The best answer is NOT:

G because it uses the singular possessive bird’s instead of the plural possessive. To be correct, the pronoun would need to be preceded by an article such as a, but no such article is present.

H because the noun birds lacks the apostrophe that is necessary to convey the idea of possession.

J because it lacks an apostrophe with birds and uses an erroneous apostrophe after eggs, suggesting that the eggs possess something. No such possession is supported by the essay.

Question 59. The best answer is A because it concludes the essay by referring back to an idea presented in the first paragraph of the essay, as required by the stem. The sentence refers to the narrator’s trek outside during the winter, which is mentioned in the first paragraph of the essay.

The best answer is not:

B because it introduces additional tips for using telescopes rather than referring back to the first paragraph of the essay.

C because it suggests that the narrator’s goal was to view Orion’s belt and sword and explains that Orion is useful in locating other constellations. Orion’s sword and belt and any relationship between Orion and other constellations are not mentioned in the first paragraph of the essay.

D because it introduces more information about the Trapezium star cluster and the narrator’s reading. These ideas do not have any connection to the first paragraph of the essay.

Question 60. The best answer is G because the essay focuses on one particular experience of viewing the constellation Orion, from setting up the telescope to focusing on one specific part of the constellation, the nebula.

The best answer is NOT:

F because it states that the essay recounts several past events, yet only one experience is discussed in the essay.

H because it indicates that the essay focuses on the Orion Nebula and its process of star formation are the focus of the essay. Although the Orion Nebula is a significant part of the essay, the essay does not discuss the process of star formation in the nebula. Rather, it focuses on the narrator’s experience.

J because it implies that averted vision is the main subject of the essay, which isn’t the case. Additionally, the fact that the narrator describes the averted vision technique in brief does not demonstrate that the essay is about a personal experience with astronomy.

Passage V

Question 61. The best answer is D because it results in a complete sentence with a comma separating the main clause from the appositive phrase “metaphors for Little’s feelings about social issues and historical events.”

The best answer is NOT:

A because it creates a comma splice (two or more complete sentences separated by only a comma). The word they becomes the subject of the second complete sentence. The sentence requires a conjunction after the comma in order to be grammatical. The phrase “in other words” cannot function as a conjunction.

B because it creates a comma splice with the second sentence beginning with they.

C because it creates a run-on, or fused, sentence (two complete sentences with no punctuation between them).

Question 62. The best answer is G because it meets both criteria of the question. It is punctuated correctly with dashes that set off the phrase “mostly triangles and rectangles.” This punctuation also indicates that all Little’s shapes, not just his triangles and rectangles, are painted in vibrant and contrasting hues.

The best answer is NOT:

F because although the punctuation is acceptable, the resulting sentence suggests that only the triangles and rectangles are painted in vibrant and contrasting hues.

H because it is not correctly punctuated. The phrase “and narrow rectangles” should be included in the dashes along with “mostly triangles.” Also, it is unclear whether all the shapes (or only the rectangles) are painted in vibrant and contrasting hues.

J because although the punctuation is acceptable, the resulting sentence suggests that only the triangles and rectangles are painted in vibrant and contrasting hues.

Question 63. The best answer is B because it correctly sets off the nonessential phrase “he says” using commas.

The best answer is NOT:

A because it fails to use punctuation to set off the phrase “he says” from the rest of the sentence.

C because it incorrectly sets off his subject as nonessential information, creating an ungrammatical sentence: “But he says is color.”

D because it lacks the necessary comma after says that closes the nonessential phrase “he says.”

Question 64. The best answer is H because the sentence, although informative, is not strongly related to the paragraph’s general discussion of Little’s art. Adding information about Syracuse University would blur the focus of the first paragraph.

The best answer is NOT:

F because the sentence does not contain the kind of biographical information that would clearly connect to the paragraph that follows and therefore would not make for a smooth transition.

G because the sentence does not state that Little first became focused on color at Syracuse University.

J because the sentence does not create confusion about Little’s work with geometric figures; it simply offers a detail about the school where Little earned his MFA, Syracuse University.

Question 65. The best answer is D because it is the only option that does not introduce a redundancy into the sentence.

The best answer is NOT:

A because it repeats the idea that Little blends his own paint, which is mentioned in the previous sentence.

B because it repeats the idea from the previous sentence that Little blends his own paint. Also, the idea that Little does so is already conveyed in the action word applies.

C because it repeats the idea that Little makes his own blends of paint. This is mentioned in the previous sentence. Also, the phrase “his own blends that he made” is redundant; it is unnecessary to state that his own blends are those that he made.

Question 66. The best answer is J because it most clearly and logically conveys the idea that Little’s paintings are big, as the measurements (6 feet by 8 feet) make clear.

The best answer is NOT:

F because voluminous would convey an idea about how much something can hold or about a three-dimensional aspect; this is an illogical descriptor for a painting and is not supported by the two-dimensional measurements that follow in the sentence.

G because it contradicts other information in the sentence. The measurements of the paintings are provided in the sentence, so it clearly cannot be immeasurable.

H because mountainous suggests a three-dimensional shape that is neither conveyed nor supported by the two-dimensional measurements that follow in the sentence.

Question 67. The best answer is B because the phrase “for example” serves as a transition from the preceding sentence, which discusses Little’s use of color and lines, to this paragraph, which provides a specific description of one of Little’s paintings that uses lines.

The best answer is NOT:

A because the phrase “by all means” doesn’t make sense in this context. This idiomatic expression has no connection to the sentence in which it is placed. On a literal level, the lines do not bisect the painting in all directions or by all methods.

C because the phrase “in contrast” suggests that Bittersweet Victory differs from Little’s other work. Yet the essay explains that Little often uses lines and then focuses on the lines in Bittersweet Victory as a specific example.

D because the word thereafter doesn’t make sense in this context, especially because Bittersweet Victory was painted before the work discussed in the preceding paragraph.

Question 68. The best answer is G because it is the only unacceptable alternative to the underlined phrase. The phrase “vertically beige” offers a misplaced modifier; something cannot be beige in a vertical way.

The best answer is NOT:

F because it conveys the same idea as the underlined phrase. The canvas is bisected in a vertical direction by a beige line.

H because it conveys the same idea as the underlined phrase, that the canvas is bisected by a vertical, beige line.

J because it conveys the same idea as the underlined phrase, that the canvas is bisected by a vertical, beige line.

Question 69. The best answer is C because the participle stretching creates a grammatical sentence that also makes sense.

The best answer is NOT:

A because it inserts the subordinating which into this clause, which was already subordinated from the main clause. This creates a confusing sentence structure. This option also shifts verb tense from the present to the past.

B because it inserts the subordinating which, creating multiple and confusing levels of subordinating clauses.

D because it creates an independent clause (“each one stretches from the bottom to the top of the canvas”) in the middle of another independent clause (“three orange triangles angle slightly to the right”). The result is an unclear sentence created from a series of phrases that are spliced together.

Question 70. The best answer is J because it is the only option that does not introduce a redundancy into the sentence.

The best answer is NOT:

F because it mentions that the orange triangles are on the canvas’s left half, which is a detail that appears previously in the sentence.

G because it repeats the idea that the triangles are on the left half of the canvas.

H because it repeats the idea, stated previously in the sentence, that the triangles appear on the left half of the canvas.

Question 71. The best answer is C because it uses the plural verb cut, which agrees in number with the plural subject of the sentence, bands. It also uses the preposition through, which makes sense in the sentence.

The best answer is NOT:

A because it uses the singular verb cuts, which does not agree in number with the plural subject of the sentence, bands.

B because it uses the singular verb cuts, which does not agree in number with the plural bands. It also uses the past tense verb crossed as if it were a preposition, which is incorrect.

D because it uses the past tense verb crossed as if it were a preposition, which is incorrect.

Question 72. The best answer is F because it attaches the preposition to to the verb lends, which creates a correct idiomatic expression.

The best answer is NOT:

G because it uses the preposition on with lends, which isn’t a correct idiomatic expression. It also doesn’t make sense logically.

H because it uses the preposition into with lends, which creates an incorrect idiomatic expression. Also, this phrase doesn’t make logical sense.

J because it uses the preposition with with lends, which creates an incorrect idiomatic expression.

Question 73. The best answer is C because it conveys the comparison between the effect of Little’s work and a jazz collaboration in the most clear and concise way. It does not repeat the same idea, and it does not add unnecessary words to the sentence.

The best answer is NOT:

A because the idea that something is like something else already conveys the idea that it might remind you of something else.

B because reminiscent of and echoes are redundant, making the phrase itself unnecessarily wordy.

D because it appears to be more concise, but the meaning is unclear. It could suggest that the effect of Little’s work is like a jazz collaboration, that Little’s work makes the viewer feel like he or she is in a jazz collaboration, or that Little’s work makes it seem like he is part of a jazz collaboration.

Question 74. The best answer is F because it builds on the paragraph’s previous reference to rhythm and unity by mentioning a perfect jazz collaboration and offers a comparison between Little and this jazz collaboration.

The best answer is NOT:

G because the comparison to jazz does not indicate anything about the popularity of Little’s paintings.

H because the following paragraph mentions one person’s assessment of Little’s work, not several people’s.

J because the essay does not suggest that Little had any unique goals for Bittersweet Victory. Rather, the paragraph about Bittersweet Victory provides a specific example of the ideas the essay presents about Little’s work in general.

Question 75. The best answer is B because the essay discusses how Little uses bright colors and shapes to convey energy and the essence of people’s experiences as human beings.

The best answer is NOT:

A because the essay does not focus on one viewer’s conclusion that the lines in Bittersweet Victory communicate optimism.

C because the essay does not focus on what Little hoped to create with Bittersweet Victory, and it does explain what the painting looks like.

D because the essay does in fact suggest some of the effects Little’s work achieves.

MATHEMATICS • PRACTICE TEST 2 • EXPLANATORY ANSWERS

Question 1. The correct answer is C. The restaurant is rotating 180° in 45 minutes. That is 60° every 15 minutes. That is 240° every 60 minutes. You might want to sketch something similar to the following drawing:

If you like an algebraic solution, you can set up a proportion and solve it: .

Most people who do not get this right choose D, which is a reasonable approximation.

Question 2. The correct answer is H. After subtracting the onetime fee from the amount on Brendan’s check ($500 − $140), the remaining $360 goes toward the amount spent on monthly fees. You can find the number of months of membership covered by the check by dividing the remaining $360 by the monthly fee of $40 per month, giving 9 months as the result.

You could also solve this problem by setting up and solving the equation 140 + 40m = 500, where the expression 140 + 40m represents the cost of a gym membership for m months.

Question 3. The correct answer is D. The group of 27 people paid a total of $249.75 (27 × $9.25 per person) in advance. Because the group consisted of more than 25 people, the actual cost was $229.50 ($27 × $8.50 per person). The refund is the difference between the amount paid and the actual cost, which is $249.75 − $229.50 = $20.25. If you chose C, you could have failed to read the problem carefully and figured the refund for a group of 25 people.

Question 4. The correct answer is H. The number of possible outcomes (that is, the total number of members eligible to be chosen as representative) is 13 − 3 = 10, and the number of favorable outcomes (choosing Samara only) is 1. The probability of the favorable outcomes is equal to . So, the probability of Samara being chosen as representative would be . Careful reading is essential; if you chose G, you may have overlooked the words CANNOT and NOT.

Question 5. The correct answer is D. Let s represent the score on the sixth test. Then the average score on the 6 tests is equal to , or equivalently . Be sure to read carefully: the average is 85 points, not percent. Interpreting the average as a percent leads to E (the most common incorrect answer), rather than the correct answer of .

Question 6. The correct answer is F. The sum of the measures of all four interior angles in any quadrilateral is always 360°. The given three angle measures add up to 65° + 100° + 75° = 240°, so the missing angle measure is 360° − 240° = 120°.

If was parallel to , then the measure of ∠B and the measure of ∠C would add up to 180° and the answer would be G. But the problem does not say that those sides are parallel, and it turns out that they are not parallel.

If you chose K, you may have calculated the average of the three given angle measures.

Question 7. The correct answer is C. The shorter two sides are the same length in ΔABC, so the same thing has to happen in any triangle similar to it. That means that is the same length as , which is 3 meters. Then, the perimeter of ΔDEF is 3 + 3 + 5 = 11 meters.

The most common incorrect answer is A, correctly finding the length of and stopping there.

Question 8. The correct answer is G. Follow the correct order of operations to simplify the expression. |3(−2) + 4| = |−6 + 4| = |−2| = 2. Keep in mind that absolute value of a rational number is its distance from 0 on the number line.

You may have chosen F if you did not take the absolute value of −2. You may have chosen H if you did |3 − 2 + 4|. You may have chosen J if you did |3 + 2 + 4|. You may have chosen K if you did |3(2) + 4|.

Question 9. The correct answer is A. This problem is asking you to figure out when two quantities multiplied together can be zero. The only way two quantities can be multiplied together to get an answer of zero is if at least one of the quantities is zero. So, either (x + a) = 0 or (x + b) = 0. The first of these equations is true when x = –a and the second when x = –b. These are the two solution values for x.

As a check, substitute –a in for x. The original equation becomes (–a + a)(–a + b), which simplifies to (0)(–a + b), and zero times anything is zero, so the original equation holds when x = –a. You could check x = –b in the same manner.

If you chose E, you may have solved the two equations incorrectly, or you may have just looked at the quantities and chosen the +a and +b that appeared in the problem.

If you missed this problem, you might try substituting a value of x from your answer into the original equation to see what happens.

Question 10. The correct answer is F. Because and , m∠JMG, m∠LHK, m∠MJL are all less than or equal to 90°, has the greatest degree measure.

We know that m∠JMG = 90° (H is NOT correct) because the tangent to a circle is always perpendicular to the radius drawn to the point of tangency. Because ΔMGJ is a right triangle with right angle ∠JMG, the other angles in the triangle, ∠MJG and ∠MGJ, are acute. This means that m∠MJL < 90° (K is NOT correct) and m∠MGJ < 90°. Because the degree measure of an arc of a circle is equal to the measure of the central angle that intercepts that arc, m∠MGJ = m. Therefore, (G is NOT correct). Because and form a semicircle, and because , . Because ∠LHK is inscribed in semicircle , m∠LHK = 90° (J is NOT correct).

Question 11. The correct answer is B. To find BC when AD is 30 units, AC is 16 units, BD is 20 units, and the points are along as shown in the following, you must notice that is the intersection of and .

So the sum of the lengths of and would be the same as the sum of the lengths of and , because AC = AB + BC, BD = BC + CD, and AD = AB + BC + CD. By substitution, AC + BD = AB + BC + BC + CD = AB + BC + CD + BC = AD + BC.

By substituting lengths AD + BC = AC + BD, or 30 + BC = 16 + 20, or 30 + BC = 36. Subtracting 30 from both sides yields BC = 6.

If you chose A, you probably subtracted 16 from 20. If you chose E, you probably thought you needed more information to solve the problem.

Question 12. The correct answer is K. There are many ways to solve this equation. One solution is the following:

start with

12x

= –8(10 − x)

divide both sides by –8

= 10 − x

add x to both sides

= 10

multiply both sides by –2

x

= –20

Another solution method would be to graph y = 12x and y = –8(10 − x) and see where the two graphs intersect. A calculator would produce these graphs, and you could find an approximate solution. That is good enough for this problem because the answer choices are spread apart.

This is a problem in which checking your answer is easy and can pay off. When x = –20, the left side of the original equation is 12(–20), which is –240. The right side is –8(10 − (–20)), which simplifies to –8(10 + 20), then to –8(30), and then to –240. This solution checks. No other answer choice would satisfy the equation.

If you chose H or J, you may have multiplied out –8(10 − x) to get –80 + x or –80 − x and done the rest of the steps correctly. You could have caught this by checking your answer. If you made an error with minus signs, you may have chosen one of the other answer choices.

Question 13. The correct answer is E. Because the cardboard extends 2 inches beyond the cake on all sides, the cardboard forms a rectangle whose length and width are each 4 inches longer than the length and width of the rectangular cake, as shown in the following figure. The area of aluminum foil that is exposed (the shaded region in the figure) equals the area of the foil covering the entire cardboard surface (or area of the cardboard) minus the area of the foil covered by the cake. So the area, in square inches, of aluminum foil exposed equals 20(16) − 16(12) = 320 − 192 = 128.

Question 14. The correct answer is J. The following figure shows the cake after it has been cut. The length of the cut cake is (16 inches) ÷ (2 inches per piece) = 8 pieces. The width of the cut cake is (12 inches) ÷ (2 inches per piece) = 6 pieces. Because the cake has 6 rows each containing 8 pieces, the cake was cut into 6(8) = 48 pieces.

Question 15. The correct answer is D. The following table lists all expenses for Ken’s cake that were given in the problem.

The total amount the Math Club will pay Ken is the sum of the costs shown in the table, $5.00 + $1.73 + $2.67 + $0.22 = $9.62.

Question 16. The correct answer is H. Sketching a picture can be helpful.

These points are on opposite sides of the y-axis, and an equal distance away from the y-axis, because the x-coordinates are 3 and –3. So, the midpoint will be the y-intercept of the line. The y-coordinate of the midpoint is , which is 4.

If the points were not so nicely spaced with the y-axis, you could find the equation of the line through the two points and use it to identify the y-intercept. The slope of the line would be the change in y divided by the change in x, . The point-slope form of the equation is then y − 2 = . Next, put this into slope-intercept form , and the 4 is the y-intercept.

From the picture alone, you could deduce that the line had to cross the y-axis between 2 and 6. This observation eliminates all the answer choices except the correct one.

Question 17. The correct answer is D. Let x (shown in the following figure) represent the distance between the centers of the 2 holes. Because the 3 segments with lengths inches, x inches, and inches are collinear, the sum of their lengths must be . Therefore, inches.

Question 18. The correct answer is H. Each week, both ponds get shallower. The following table shows what happens for the first few weeks.

Now

1 week

2 weeks

3 weeks

4 weeks

First pond

180 cm

179 cm

178 cm

177 cm

176 cm

Second pond

160 cm

159.5 cm

159 cm

158.5 cm

158 cm

Difference

20 cm

19.5 cm

19 cm

18.5 cm

18 cm

The ponds are getting closer and closer to the same depth, at the rate of 0.5 cm per week. Because the ponds started out 20 cm different, it will take 20 ÷ 0.5 = 40 weeks to bring them to the same depth.

You could also check the answer choices. Answer F is not correct because, after 10 weeks, the first pond would be 180 − 10 = 170 cm deep, and the second pond would be 160 − 5 = 155 cm deep. The other incorrect answers can be eliminated in the same way.

The most common incorrect answer was G. If you chose that answer, you may have reasoned that it would take 20 weeks for the first pond to get down to the level of the second pond. And that is correct, except that the second pond has become shallower during those 20 weeks, so the ponds are not the same depth.

Question 19. The correct answer is E. A line will always have an equation of the form x = a or y = mx + b, for suitable constants a, m, and b. And, if a graph has an equation that can be put into one of these forms, the graph is a line.

Equation A is already in the first form, where a = 4.

Starting with Equation B, divide both sides by 3 and you will get y = 2. This is the second form, with m = 0 and b = 2.

Equation C can be manipulated into the second form as follows: x − y = 1 ⇒ –y = 1 − x ⇒ + y = −1 + x ⇒ y = x − 1, which has m = 1 and b = –1.

Equation D is already in the second form, with m = and b = –2.

Equation E can be written as y = –x² + 5. This is the equation of a parabola, shown below. It is the only one of the equations that is not a line.

Question 20. The correct answer is G. All the answer choices are in terms of ∠A. Many people remember the trigonometric functions in the context of a right triangle, in terms of the lengths of the side opposite the angle, the side adjacent to the angle, and the hypotenuse. For the triangle given in the problem, the side opposite ∠A has length 12 cm, the side adjacent to ∠A has length 5 cm, and the hypotenuse has length 13 cm. The values of the trig functions are , , and .

The only answer choice that gives one of these is G.

If you chose F, you may have been expecting the angle to be at one end of the horizontal base of the triangle. The value of cos B is . Triangles can be rotated to any position. The terms opposite, adjacent, and hypotenuse are chosen to apply when the triangle is in an arbitrary position.

Question 21. The correct answer is D. To find the location of the water fountain located halfway between points B and D, it makes sense to give coordinates to the points relative to point A (see the following diagram). The first coordinate is the number of blocks east, and the second coordinate is the number of blocks north.

The water fountain is at the midpoint of , and so the midpoint formula applies. For points with coordinates (x₁,y₁) and (x₂,y₂), the midpoint has coordinates . For B (10,0) and D (7,9), the midpoint is .

B is halfway between A and C. Choice C is halfway between B and F. If you chose E, you may have found the wrong coordinates for C, D, or E.

Once you put coordinates on the picture, you can see that only one answer choice is reasonable.

Question 22. The correct answer is H. Although it may not be worth your time to sketch a graph during the ACT, you should at least have a general idea of the situation in your mind. This is the equation of a parabola. Common sense will tell you that if the car is going faster, it will take a longer distance to brake to a stop. So the parabola is opening upward.

The horizontal dashed line on the graph is where the braking distance is 150 feet. Only half of the parabola is shown. There are two points where the parabola intersects this line. One would be to the left of the y-axis, which represents a negative speed for the car. If you solve an equation to find the intersection points, you will have to discard the intersection point with a negative speed.

If you took the time to create a graph, perhaps even on a graphing calculator, you might be able to estimate closely enough to choose among the answer choices. The desired speed is the x-coordinate of the intersection point.

To get this speed algebraically, the desired braking distance is 150 feet, and the equation gives the relation between speed (x) and braking distance (y). So you can solve the equation . One solution path starts by multiplying both sides by 40 and continues as follows: or x = 40. You must discard the first solution. The only remaining solution is x = 40, which represents a speed of 40 miles per hour.

If you chose J, you may have done everything correctly except that when you solved (x + 50)(x − 40) = 0, you thought x = 50 was a solution. If you substitute 50 for x in the equation (x + 50)(x − 40) = 0, you will see that it is not a solution.

If you chose F, you may have made a numerical mistake when you substituted x = 10 into the breaking-distance equation. The value is . It might be tempting to reduce to 50 and then get 3(50) = 150, which is what you are looking for. But is 5, not 50.

Substituting the answer choices into the equation is a reasonable strategy for this problem. You can use the results from one of the answer choices to help you choose the next one to substitute, because you probably know that it takes longer to stop if you are going faster. The results of these substitutions are given in the following:

Speed (mph)

Calculations

Braking distance (ft)

F

10

15

G

30

90

H

40

150

J

50

225

K

60

315

Question 23. The correct answer is A. Substitution gives and f (1) = 1² + 1 + 5 = 7. Then .

If you chose C, you may have started substituting 4 in function g and then continued substituting 4 into function f. The value of is .

Question 24. The correct answer is K. There are 125 juniors who could be chosen. For each of those 125 juniors, there are 100 seniors who could be chosen. That makes 125 · 100 = 12,500 different pairs of students who could be chosen.

If you chose J, you probably added 125 and 100. If you chose G, perhaps you were figuring that once 100 pairs were formed, there would be no seniors left to put into another pair. Only one pair will be chosen, but there are many more than 100 pairs that are possible choices.

Question 25. The correct answer is B. The line on the graph has a negative linear correlation because as x increases y decreases. The line Mia drew goes through the points (0,10) and (3,1). To find the slope, , we use m = and we get . The y-intercept, where the line crosses the y-axis, is at positive 10. Inserted into , where b is the y-intercept, we get the equation . If you thought A, you did not determine the correct y-intercept. If you thought C or D, you did not determine the correct slope. If you thought E, you did not determine the correct y-intercept or slope.

Question 26. The correct answer is F. You could certainly test all of the answer choices to solve this problem. The first choice, –10, leaves the left side of the relation as |–10 − 24|, which simplifies to |–34|, which is 34. And 34 ≤ 30 is false, so this is the correct answer.

Another way to solve this problem is to think about the interpretation of absolute value as a distance: |t − 24| ≤ 30 means that the distance on the number line between t and 24 is at most 30 units. This distance would be greater than 30 only when t was more than 30 above 24 or more than 30 below 24. That is when t is more than 54, or t is less than –6. Answer choices G–K are all closer to 24 than this.

The most common wrong answer is 54 (K), which is right at the limit of how far away it can get from 24. Still, –10 is farther away from 24 than 54 is.

Question 27. The correct answer is D. The phrase “5 times a number n” can be represented as 5n. If this is subtracted from 15, the expression 15 − 5n represents the result. Saying that this result is negative can be represented as 15 − 5n < 0. Subtracting 15 from both sides gives –5n < –15, and then dividing both sides by –5 gives n > 3 (remember to reverse the direction of the inequality).

Most people who missed this chose E. This could come from not reversing the inequality in the last step of the solution, or it could come from subtracting 15 from 5n rather than subtracting 5n from 15.

Answer choice B is the result of solving 15 − 5n = 0. This would give the boundary where the expression changes from positive to negative, so it’s closely related to the problem you were asked to solve. If you chose this, you would still need to find the values of n where the expression is negative, knowing that n = 3 is the only place the expression is zero.

Question 28. The correct answer is F. Because (x² + 8x + 7) = (x + 7)(x + 1), you can factor the numerator further into the product (x + 1)(x + 7)(x − 3). Similarly, because (x² + 4x − 21) = (x + 7)(x − 3), you can factor the denominator further into the product (x + 7)(x − 3)(x + 1). Then, as long as the denominator is not zero (that is, as long as x is not equal to –7, 3, or –1, which is guaranteed by the requirement that x > 21), you can write the given rational function as . Using the commutative property for multiplication, the factors in the numerator can be reordered, producing the equivalent expression . Because the numerator and denominator are equal, this rational expression is equal to 1.

Question 29. The correct answer is B. Imagine the original 9 data items in order from smallest to largest. You might sketch a picture something like that shown in the following. The median is the fifth item in this list, because it is the middle value in the set.

When the additional 4 data items are put into the list, there are 9 + 4 = 13 items on the list. Because 2 of these items are greater than the original median and 2 of these items are less than the original median, the original median is the middle value in the new set. That makes the original median the new median.

Question 30. The correct answer is K. The shaded area is the area of the larger circle minus the area of the smaller circle. The area of the larger circle is πr² = π (10)² = 100π square centimeters. The area of the smaller circle is π(5)² = 25π square centimeters. The difference is 75π square centimeters.

If you chose J, you probably found the difference in the perimeters of the two circles. You may have used the perimeter formula rather than the area formula. Another possibility is that you calculated 10² as 2 · 10 and 5² as 2 · 5. But 10² is 10 · 10, and 5² is 5 · 5.

Question 31. The correct answer is E. The mean of a and b is . Because a is positive and b is negative If | a | > | b |, then the mean is positive. If | a | < | b |, then the mean is negative. If | a | = | b |, then the mean is 0. Because we only know the sign of a and b and NOT their magnitudes, we cannot determine if the mean is positive, negative, or 0.

If you chose A, you might not have realized that if a = 3 and b = –4, the mean of a and b is a negative number: If you chose B, you might not have realized that if a = 4 and b = –4, the mean of a and b is 0: . If you chose C, you might not have realized that every number is positive (greater than 0), negative (less than 0), or neither (equal to 0). If you chose D, you might not have realized that the mean could be a positive number or a negative number: if a = 4 and b = –2, ; if a = 3 and b = –4,

Question 32. The correct answer is G. If the x-coordinate is 20, then the y-coordinate can be found by substituting 20 for x.

0.005(20)² − 2(20) + 200 = 0.005(400) − 40 + 200 = 0.5(4) + 160 = 2 + 160.

In theory, you could read the value off the graph, but you would not be able to read it accurately enough.

Many incorrect answers are caused by mistakes with the first term, 0.005x². If you chose F, you may have made a decimal error calculating 0.005(20)² and gotten 0.2 rather than 2.0. Other errors in calculating this term lead to H, J, and K.

Question 33. The correct answer is D. The distance formula (or the Pythagorean theorem) gives this distance directly. It is 200(1.414) = 282.8

Another way to solve this is to notice that the length of is 200 units, and is longer. Also, the path from F to O to G is 400 units long, and the direct path along is shorter than this path. So D is the only reasonable answer among those given.

Question 34. The correct answer is F. The shaded region is entirely contained in the given triangle because the curve is below the hypotenuse of the triangle, . The area of the triangle is made up of the shaded area plus the unshaded area above the curve and inside the triangle. So the shaded area is less than the area of the triangle.

Question 35. The correct answer is B. With a = 4.2, b = 5.0, and a 5° measure for ∠C, then the law of cosines gives the length of the third side of the triangle (the distance between the cargo ship and the fishing boat) as

If you chose C, you probably missed the minus sign in the middle of the expression. About half the students who do not get the correct answer choose C.

The 85° angle in answer choices D and E would be the angle measure by the fishing boat, but only if the angle by the cargo ship was a right angle. It turns out that it isn’t a right angle.

Question 36. The correct answer is F. Because a³ = b, then b² = (a³)². Substituting this into the equation c = b² gives c = (a³)². Because (a³)² = a⁶, the result is c = a⁶.

The most common incorrect answer is G. If you chose that answer, you probably wrote (a³)² as a⁵. If you write (a³)² out as (a³)(a³) and then (a · a · a)(a · a · a), you can see that it is a⁶.

If you chose H, you probably wrote (a³)² as 2(a³).

Question 37. The correct answer is B. The cost of renting a car from Sea Horse for 2 days is 2(50) + 0.25m where m is the number of miles driven. Because Francisco has $255 to spend, the maximum number of miles he can drive if he rents from Sea Horse is the solution to the equation 100 + 0.25m = 255, or m = 160.

Similarly, the maximum number of miles Francisco can drive if he rents from Ocean Blue is the solution to 2(60) + 0.20m = 255, or m = 675, because 675 − 620 = 55. If Francisco rents from Ocean Blue, he can travel 55 miles more than if he rents from Sea Horse. If you chose A, you may have made an error when solving 100 + 0.25m = 255 and 2(60) + 0.20m = 255. If you chose C, you may have divided cost per day by the cost per mile for each company, and then subtracted those quotients; Ocean Blue Car Rental has the greater quotient. If you chose D, you may have subtracted the daily cost of rental from Ocean Blue Car Rental from the total allotted amount. If you chose E, you may have found that each car rental would give Francisco the same number of miles.

Question 38. The correct answer is G. The area of a parallelogram is given by bh, where b is the length of the base and h is the height (here, the distance between the bottom and the top). It sometimes helps to picture this formula geometrically.

If you cut off the right triangle from the right side, it fits exactly onto the left side to form a rectangle. The rectangle has the same area as the parallelogram. The rectangle’s area is bh, where b is the length of the base and h is the height. This is even the same formula as for the parallelogram. The difference is that h is the length of a side of the rectangle, but it is not the length of a side of the parallelogram.

And so, for either the rectangle or the parallelogram, b = 10 coordinate units and h = 6 coordinate units, making the area bh = 10 · 6 = 60 square coordinate units.

The distance from (0,0) to (3,6) is coordinate units. If you chose J, you probably multiplied this side length by the length of the base, 10 coordinate units. This is the stereotypical mistake when figuring the area of a parallelogram. The picture shows why the height is the right thing to use, not the length of the side.

If you chose H, you may have calculated the length from (0,0) to (3,6) as and multiplied by the length of the base.

Question 39. The correct answer is E. Because n and m are both natural numbers, the sum of n and m is another natural number, n + m. Natural numbers are a subset of integers, integers are a subset of rational numbers, rational numbers are a subset of real numbers, and real numbers are a subset of complex numbers. Therefore, n + m belongs to the sets found in I, II, III, IV, and V. If you chose A, you might not have realized that rational numbers are a subset of real numbers and therefore a subset of complex numbers. If you chose B, you might not have realized that the sum of two natural numbers is another natural number, and that real numbers are a subset of complex numbers. If you chose C, you might not have realized that the sum of two natural numbers is another natural number, which is also an integer. If you chose D, you might not have realized that sum of two natural numbers is another natural number.

Question 40. The correct answer is G. If you don’t see a way to approach this problem right off, a useful general technique is to look for some concrete numbers that illustrate the conditions. One thought is to start checking numbers from 1,000 on up to find a perfect square. A calculator would be a good idea. , , , oh, this will take a while. A perfect square between 1,000 and 9,999 would have to have its square root between and because the square root function is an increasing function. This will help you find examples more quickly: 25² = 625 is too low; 35² = 1,225 is in the interval. The smallest perfect square in this interval is 32² = 1,024. Because 100² = 10,000, the largest perfect square in this interval has to be 99² = 9,801. The square roots of all these perfect squares are the integers from 32 up to 99. All these square roots have 2 digits.

A quicker way is to find and , which is a range that contains all possible square roots of the perfect squares. Any integer in this range has 2 digits.

The most common incorrect answer is K. If you chose this answer, perhaps you made a calculation error that led you to believe you’d found a perfect square between 1,000 and 9,999 whose square root had 3 digits. And then you correctly found one whose square root had 2 digits. Your logic was correct. Some students probably choose K because they do not know how to solve the problem. Maybe that’s as good a guess as any, but looking for concrete numbers would be a good strategy if you have time.

Question 41. The correct answer is C. The expected occupancy rate is the sum of the products of each occupancy rate and its corresponding probability: 0.6(0.2) + 0.7(0.4) + 0.8(0.3) + 0.9(0.1) = 0.73. To calculate the expected number of rooms that will be occupied during the coming summer season, multiply the expected occupancy rate by the total number of rooms: 0.73(80) ≈ 58.

If you chose A, you might have calculated the average of the probabilities and multiplied that by the total number of rooms: . If you chose B, you might have converted the probabilities in the table to percentages and then found the average percentage: . If you chose D, you might have calculated the average of the complement probabilities and multiplied that by the total number of rooms: . If you chose E, you might have calculated the complement of the probabilities, converted those complement probabilities to percentages, and then found the average complemented probability:

Question 42. The correct answer is F. To calculate a matrix product, you go across each row in the first matrix and down each column in the second matrix. You multiply the terms from a row by the corresponding terms from the column, and you add all those terms together for the row-column combination and put the sum in that row-column of the result matrix. You do this for each row-column combination.

That explanation is correct but pretty abstract. Your math text might have some examples that you can look over to make things more concrete.

In this case, there is only 1 element in each row of the first matrix, and 1 element in each column in the second matrix. The matrix product is:

The computations in G are basically correct, but the terms were put in the wrong places.

If you chose K, you may have reasoned that whatever role the 1 played in the second matrix, the –1 would cancel it out, and the 0 would not change that. If all the terms were combined, that would be the case. But a matrix can keep the terms separate.

Question 43. The correct answer is D. Because the base is a straight line, these two angle measures add up to 180°. In the language of algebra, this can be represented as (4x + 6) + (2x) = 180. Solving this for x gives 6x + 6 = 180, then x + 1 = 30, then x = 29. This makes one angle measure 4(29) + 6 = 122 degrees and the other angle measure 2(29) = 58 degrees. (Check: Is 122° + 58° equal to 180°? Yes.)

The problem asks for the measure of the smallest of these two angles. That is 58°.

If you chose C, you probably just stopped as soon as you found the value of x. The problem asks for something different. The other popular incorrect answer is E.

Question 44. The correct answer is F. The new value of b is (b − 1), and the new value of c is (c + 2). Substituting into the expression for a gives 2(b − 1) + 3(c + 2) − 5, which simplifies to 2b − 2 + 3c + 6 − 5. Because you are looking for the change in a, try to write this expression in terms of the original expression for a. You can do this as (2b + 3c − 5) − 2 + 6, which simplifies to (2b + 3c − 5) + 4. And that is the old value of a increased by 4.

If you chose H, you may have expanded 2(b − 1) + 3(c + 2) to 2b − 1 + 3c + 2.

Question 45. The correct answer is C. We want to find the number of gallons of fertilizer, x, for which the rate is equal to We do this by solving for x: and then multiplying by the conversion factor given in the item. We want to eliminate all units besides gallons to get the answer: gallons.

You may have gotten A if your conversion setup did not eliminate acres in the numerator and had gallon in the denominator, so you got acre per gallon.

You may have gotten B if your conversions were inverted and you found per gallon. You may have gotten D if you divided by 0.5 acre instead of multiplying by 0.5 acre and therefore got gallon per acre. You may have gotten E if your conversion did not eliminate square feet in the numerator and fluid ounces in the denominator and got square feet times gallon per fluid ounce.

Question 46. The correct answer is J.

Because no booths can be empty, imagine 1 person sitting in each booth. That leaves 10 people standing around waiting for you to tell them where to sit. How many booths can you fill up with another 3 people each? Well, you can get 3 groups of 3 people from the 10 who are still standing, with 1 person left over. That means that you can fill at most 3 booths with 4 people. There will be 1 booth with 2 people, and the other 6 booths will have 1 person. (Check: Are there 20 people? 3(4) + 0(3) + 1(2) + 6(1) = 12 + 2 + 6 = 20. Yes. Are there 10 booths? 3 + 0 + 1 + 6 = 10. Yes.)

If you chose K, you filled up 5 booths with 4 people each. But, you left the other 5 booths with no one sitting there. The problem specified that NO booths are empty. (This is the most common wrong answer.)

If you chose G, you may have just miscounted. Make sure you check your work. You might want to draw a diagram for problems like this so that you can check your work more easily.

Question 47. The correct answer is D. You can calculate the chances of Events A and B both occurring by multiplying the probability of each event occurring. That means that the correct expression is P(A ∩ B) = P(A) · P(B).

If you chose A, you might have thought the probability of Event A occurring is the same as the probability of Event B occurring. If you chose B, you might have thought the probability of Event A occurring is the complement of the probability of Event B occurring. If you chose C, you might have thought that the probability of Event A occurring and the probability of Event B occurring should be added together rather than multiplied. If you chose E, you might have confused the formula for the probability of A and B both occurring with the formula for the probability of A or B occurring, P(A ∪ B) = P(A) + P(B) − (P(A) · P(B)).

Question 48. The correct answer is J. The following figure shows the 3-4-5 right triangle with sides formed by the x-axis, the vertical line through (4,–3), and the terminal side of θ. The angle, α, formed by the terminal side and the x-axis is called the reference angle of θ. The relationship between θ and α is cos α = |cos θ|. From the figure, you can see that cos α = = = |cos θ|. Because the terminal side of θ lies in Quadrant IV, cos θ is positive. Therefore, cos θ = .

Question 49. The correct answer is A. If x is a negative number, then let y = –x, where y is a positive number. Then is just y. In terms of x, this says . For example, let x be –5. The left side is , which simplifies to , and then to 5. The right side is –(–5), which is also 5.

For any number x, its square and the square of its opposite are equal: (x)² = (–x)². For example, (5)² = (–5)². This shows that . When x is a positive number, or zero, then . Putting these last two statements together, whenever x is a positive number or zero. For example, when x = 5, .

Summarizing, you now know that whenever x is a negative number, and whenever x is positive or zero. Another way of saying this is .

Because |x| = |–x| for all values of x, the paragraphs above show that I and II are saying the same thing—they’re equivalent.

However, II is always positive or zero, and III is always negative or zero, so the only time they are equal is when x is zero. For example, when x = 1, |–1| = 1 but –|1| = –1. So II and III are not equivalent.

The most common incorrect answer is C. Even though statements II and III look a lot alike—they have the exact same symbols in almost the same order—they are not equivalent. One is never negative and one is never positive.

If you answered E, you probably saw that II and III are not equivalent. Expression I looks so much different than either of the others that it is tempting to just say it can’t be the same. One approach would be to test a few numbers in the expressions. Be sure that one is positive and one is negative. If you substitute these into I and into II correctly, you will find they match. Then, you should suspect that I and II could be equivalent and look for a way to convince yourself of this.

Question 50. The correct answer is K. Statement F, that and are parallel, is true because both are perpendicular to the same other line, .

Because ∠DEB is marked with a right angle, is perpendicular to , and so G is true.

The two angles, ∠ACB and ∠FCE, are vertical angles, so H is true.

Statement J is true because the angles in ΔBAC are congruent to the angles in ΔEFC. First, ∠A is congruent to ∠F because they are both right angles. Next, ∠ACB and ∠FCE are vertical angles. And third, the remaining angles must have the same measure because the sum of the interior angle measures in any triangle is 180°.

Because all of the other statements are true, you would expect statement K to be false. The following diagram shows such a case. Only if ∠ECF is congruent to ∠EDF can be congruent to .

Question 51. The correct answer is D. This geometric figure has six sides, but you are only given the length of four of those sides. One of the slickest ways to find the perimeter is to move two of the sides to form a rectangle with the same perimeter. The following drawing shows the new rectangle:

The bottom of this rectangle is 4 inches long, and the right side is 3 inches long. So, the perimeter is 4 + 3 + 4 + 3 = 14 inches.

An alternate method is to deduce that the left side is 3 inches long because it is the same length as the vertical sides on the right. And the last unknown side is 1 inch long because it is the difference between the horizontal 4-inch side on the bottom and the horizontal 3-inch side on the top. Then the perimeter (going clockwise) is 4 + 3 + 3 + 2 + 1 + 1 = 14 inches.

If you chose C, you may have forgotten to add in the horizontal side that connects the vertical 2-inch side and the vertical 1-inch side.

If you chose A, you may have added just the numbers given directly on the figure. Or you may have calculated the area instead of the perimeter.

Question 52. The correct answer is F. Because points A and B are stationary, the side of ΔABC will not change in length or direction. The altitude of ΔABC with respect to side is the segment having one endpoint at point C that is perpendicular to . The area of ΔABC, in square coordinate units, can be found using the following formula:

area = (AB)(the length of the altitude from C to )

Because the length AB must remain constant, the altitude from C of any new triangle whose area is equal to that of the original ΔABC must have the same length. Three of these new triangles (and their altitudes from C) are shown in the following figures:

In order that all altitudes from the moving point C have equal lengths, C must lie on the line l (shown in each figure), where line l is parallel to . Because line l is parallel to , the lines must have equal slopes. Therefore, the slope of line l = the slope of = .

Question 53. The correct answer is D. Marshall made 24 calls on the first day. He makes 5 more calls each day than he had the day before. That means he made 29 calls on the second day. The following table shows the number of calls he made on each of the 20 days:

Day

1

2

3

4

5

6

7

8

9

10

No. calls

24

29

34

39

44

49

54

59

64

69

Day

11

12

13

14

15

16

17

18

19

20

No. calls

74

79

84

89

94

99

104

109

114

119

You could try to add all of these up. You might make a mistake, even with a calculator but that method is straightforward and would work.

Another approach is to notice that the number of calls for the first day and the last day add up to 143, as do the number of calls for Day 2 and Day 19, as do the number for Day 3 and Day 18, as do all the other pairs of days, working forward from the beginning and backward from the end. There are 10 pairs of days, each with 143 calls. That is 1,430 calls for the 20 days.

A third approach is to notice that this is an arithmetic series, where each term is 24 + 5k, where k represents the numbers from 0 to 19. When k is 0, then it is Day 1,and there are 24 + 0 calls. With sigma notation, the sum of all the calls on the 20 days can be represented as . This is equivalent to , which is equivalent to . The first summation is saying to add 24 + 24 + . . . 24, where thereare 20 of the 24s added together. That is just 24 · 20 = 480. The second summation is a common one and simplifies to . That makes the series sum to 480 + 5(190) = 480 + 950 = 1,430 calls.

A fourth approach relies on accurately remembering the following formula for the sum of an arithmetic series: , where the first term in the series is a, the common difference between terms is d, there are n terms in the series, and the sum is Sn. Substituting the quantities you know gives calls.

If you used the summation approach and got C, you may have simplified to , leaving out the multiplier of 24.

If you chose B, you may have simplified the summation to , leaving out the factor of 5. Or, you may have calculated the number of calls for Day 10 and multiplied this by 10.

Question 54. The correct answer is K. This is called a piecewise-defined function because it is pieces of different functions put together to form a single function. When x ≤ 1, the equation is f (x) = x² − 2, so f (1) = 1² − 2 = –1 and f (0) = 0² − 2 = –2. (Actually, this information is enough to eliminate all the graphs except the correct one. But you might want to read the rest of this explanation anyhow.)

The graph of y = x² − 2 is a parabola, opening upward. Its graph is shown on page 589. The only part of the graph that applies for this piecewise-defined function is the part where x ≤ 1. The rest of the graph is represented with dashes.

When 1 < x < 5, then f (x) = x − 7, so f (2) = 2 − 7 = –5 and f (4) = 4 − 7 = –3. This is a straight line. A graph is shown in the following, with the parts outside 1 < x < 5 shown with dashes.

When x ≥ 5, the equation is f (x) = 4 − x, so f (5) = 4 − 5 = –1 and f (6) = 4 − 6 = –2. This is also a straight line. Its graph is shown in the following, with the part outside x ≥ 5 shown with dashes.

K puts all these pieces together.

Question 55. The correct answer is D. The formula for calculating the number of permutations of objects taken at a time is Therefore, the correct expression is If you chose A, B, C, or E, you may have used the incorrect formula. The expression in A gives 5 times the number of objects. The expression in B gives the total permutations for 10 objects. The expression in C gives the number of permutations for 15 objects taken 10 at a time. The expression in E gives the number of combinations of 15 objects taken 5 at a time.

Question 56. The correct answer is K. To find an equivalent expression, you could simplify the expression by multiplying the numerator and denominator by the complex conjugate of the denominator, .

. If you chose F, you might have incorrectly thought that you could eliminate the x’s and the 1’s in the expression If you chose G, you might have incorrectly thought that you could eliminate the i’s in the expression . If you chose H, you might have incorrectly multiplied the expression by its complex conjugate. If you chose J, you might have incorrectly thought that .

Question 57. The correct answer is E. You can use the fact that Point A has coordinates (–6,–2) and Point B has coordinates (3,4), so the component form of is . Point C has coordinates (4,–2) and Point D has coordinates (4,3), so the component form of is . Writing and in terms of the unit vectors, i = and j = results in = 9i + 6j and = 0i + 5j. Therefore, vector + = (9 + 0)i + (6 + 5)j = 9i + 11j.

If you chose A, you may have incorrectly thought that = . If you chose B, you may have incorrectly thought that = and = . If you chose C, you may have incorrectly thought that = . If you chose D, you may have incorrectly thought that = .

Question 58. The correct answer is J. Let L₁ feet be the length of Pendulum 1 and t₁ seconds be the time for a complete swing of Pendulum 1. Let L₂ and t₂ describe Pendulum 2 in the same way. The time for a complete swing of Pendulum 1 is triple the time required for a complete swing of Pendulum 2. This means that t₁ = 3t₂.

The most common approaches to solving problems like this involve finding an equation that contains the two variables the question asks about, here L₁ and L₂, and solving for one variable or solving for the ratio of the variables.

By the equation that relates L to t, the equation t₁ = 3t₂ becomes (which is an equation that contains both L₁ and L₂). Dividing both sides by 2π gives the equation . Squaring both sides gives . Multiplying both sides by 32 gives L₁ = 9L₂. So, Pendulum 1’s string is 9 times the length of Pendulum 2’s string.

The most common incorrect answer is G. If you chose that, you might have reasoned that if one variable triples, then any other variable must also triple. This happens for some functions, notably linear functions, but the function in this problem is not linear. The value of L must go up by a factor of 9 so that the square root will go up by a factor of 3.

If you chose H, you may have reasoned that, in order for the square root to go up by a factor of 3, the quantity under the square root must go up by a factor of 6. That would mean that L would go up by a factor of 6. This turns out not to be enough, because if L goes up by a factor of 6, the square root will only go up by a factor of , which is less than 3.

Question 59. The correct answer is A. By properties of logarithms, loga(xy)² = 2 loga(xy) = 2(logax + logay) = 2(s + t).

If you chose D, you may have done all of the previous steps correctly, except for thinking that loga(xy) = logax · logay (using multiplication rather than addition on the right side).

Answer C could come from thinking that loga(xy)² = loga(x²y²) = logax² · logay² = 2 logax · 2 logay. The first and last steps are correct, but not the middle one.

Question 60. The correct answer is F. Let d be her distance in 1990. Her distance in 1991 would be 1.1 · d. And her distance in 1992 would be 1.2(1.1 · d), which simplifies to 1.32 · d. This represents an increase of 32% from 1990 to 1992.

The most common incorrect answer is G. If you chose this, you probably added the 10% and the 20% to get 30%. This would work fine if the percents were percents of the same thing. But the first increase is a percent of the 1990 distance, while the second is a percent of the 1991 distance.

One good strategy for investigating problems like this is to choose a specific number to represent the initial distance. Say you choose 10 feet for her 1990 distance. The 1991 distance would be the original 10 feet plus a 10% increase, which is 1 more foot, for a total of 11 feet. To find the 1992 distance, take the 11 feet and add 20% of this amount, which is 2.2 feet. Then, the 1992 distance is 11 + 2.2 = 13.2 feet. The percent increase from the original 10 feet is . These are the same operations done in the first method, but the calculations are done with concrete numbers rather than abstract variables.

READING • PRACTICE TEST 2 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is A because throughout the passage Crown is explicitly characterized as industrious and fastidious; his life and business are described as being ruled by the three tenets of order, accuracy, and modernity, all of which are grounded in his reverence for hard work. This description and characterization firmly reinforce the stereotype that Germans are tidy, meticulous, and industrious.

The best answer is NOT:

B because Crown is characterized consistently throughout the passage as adhering to the principles of order and industry in all aspects of his life and work; there is no evidence in the passage that he weakens the German stereotype.

C because Crown is explicitly described as accepting and even revering the principle of hard work. His personal philosophy that “without industry there was no reward” (lines 86–87) is described as being ingrained in him “deeper than the marrow of his bones” (lines 90–91). This clearly does not weaken the industrious aspect of the German stereotype.

D because there is no evidence in the passage that Crown expects others to do the tidying up for him.

Question 2. The best answer is H because it can most reasonably be inferred that the “appointment at twelve” referred to in line 17 would occur that day, whereas the “emergency meeting” referred to in lines 4–5 is scheduled to take place “this Friday” (line 5), indicating that the meeting would happen in the near future.

The best answer is NOT:

F because “this Friday” in line 5 indicates that the meeting will happen on a day in the near future, whereas the appointment is indicated as being scheduled for that day. If the meeting and the appointment were meant to happen on the same day, the narrator likely would have said “today” instead of “this Friday.”

G because the passage makes it clear that the meeting “this Friday” has not yet occurred, especially considering it is described as an immediate concern of Crown’s.

J because the passage makes it clear that the meeting is an immediate concern of Crown’s, and that the meeting will happen “this Friday,” indicating the near future, not years in the future.

Question 3. The best answer is B because lines 47–57 describe the principle of modernity to which Crown unwaveringly subscribes, giving examples of how quickly he embraces new technology. Zwick, however, is reluctant to move from using an old-fashioned quill pen to a modern typewriter (lines 62–64), learning to typewrite only when he is compelled to.

The best answer is NOT:

A because there is no clear evidence in the passage that Zwick adheres to a certain level of fastidiousness regarding the meeting of deadlines.

C because the passage characterizes Zwick as being clearly unafraid to state his preferences to his superior (Crown), but there is no evidence in the passage that Crown is afraid to state his preferences to his superiors. Indeed, there is no suggestion in the passage that Crown has superiors.

D because there is no evidence in the passage that Zwick holds concern about the company’s public image; Crown, however, is clearly concerned with the company’s image, as evidenced in lines 66–67, when he says that using quill pens instead of typewriters “makes Crown’s look old-fashioned.”

Question 4. The best answer is F because when Zwick is said to have “blanched” in line 72, it is in response to Crown’s proposal that a woman be hired as a typewriter if Zwick refuses to learn typewriting. Zwick’s indignation is expressed in the rest of line 72: “A woman? In my office?”

The best answer is NOT:

G because the passage makes clear that the woman is a theoretical employee, not an actual visitor in the office.

H because the passage makes clear from context that Zwick is not excited about the prospect of a female employee; the passage also makes clear that the female employee being discussed is theoretical.

J because the passage makes clear that Crown will hire a female employee only if Zwick continues to refuse to learn to typewrite; Crown has not actually hired anyone.

Question 5. The best answer is D because lines 2–5 clearly state that Crown’s “most immediate” worry was a “civic responsibility” that he would soon be discussing at a meeting.

The best answer is NOT:

A because there is no evidence in the passage that Crown is preoccupied with whether he will be on time for his weekly trim; the appointment for the trim is only mentioned as a passing matter of fact.

B because the passage makes clear in lines 52–54 that Crown had no hesitation in installing expensive pasteurization equipment in his brewery; the passage also makes clear that this is not a preoccupation of his at the time described in the passage’s opening.

C because the passage does not indicate that Crown is at all preoccupied with Zwick’s behavior, and the passage also indicates that Crown’s exchange with Zwick in lines 62–74 took place before the time described in the passage’s opening.

Question 6. The best answer is G because the passage states that Crown was “a mediocre student in most school subjects” but that “at ciphering he was a prodigy” (lines 33–34).

The best answer is NOT:

F because the passage states that Crown was a “mediocre student in most school subjects” (lines 33–34); he was exceptionally gifted only at ciphering.

H because there is no evidence in the passage that Crown was a successful student whether he applied himself or not; he is simply described as being a mediocre student outside of his talent at ciphering.

J because there is no evidence in the passage that Crown’s success as a student increased as he mastered counting aids.

Question 7. The best answer is C because the passage characterizes Crown in lines 42–46 as prone to asking questions of his employees that would elicit a specific answer, likely one that involved numbers. The question about sales figures in C best fits these characteristics.

The best answer is NOT:

A because there is no evidence in the passage supporting the idea that Crown is likely to ask an open-ended, personal question of his employees.

B because the passage most strongly suggests in lines 42–46 that Crown’s questions to his employees most likely involve numbers, and a question about repairing old equipment does not involve numbers.

D because there is no evidence in the passage supporting the idea that Crown is concerned about team dynamics among his employees to the point where he would ask such a question of them. Lines 42–46 also most strongly suggest that Crown’s questions to his employees involve numbers, and the question about team-building does not involve numbers.

Question 8. The best answer is H because the passage describes Crown as subscribing to the principle of modernity, and his exchange with Zwick in lines 62–74 most nearly suggests that quill pens were the status quo in offices in the United States at the time the passage was set, though more advanced technology was beginning to become available. To Crown, who wanted his business to use the “newest methods” (line 51) of technology, such as typewriters and mechanical adding machines, these quill pens seemed “old-fashioned” (line 67).

The best answer is NOT:

F because the passage indicates that the typewriter is among the “modern machines” (line 56) that Crown insists be used in his office.

G because the passage indicates in lines 56–58 that the mechanical adding machine is one of the “modern machines” (line 56) that Crown insists be used in his office.

J because the passage gives no clear evidence that abacuses are widely used in US offices at the time the passage is set. The abacus mentioned in the passage is described as an ancient counting device (line 39) that Crown keeps in his office, “within reach” (line 40). Presumably such an ancient counting device is not widely used in US offices at the time the passage is set, but Crown does not necessarily seem to see the abacus as becoming increasingly obsolete.

Question 9. The best answer is A because the metaphor used in the passage to describe Crown’s three principles primarily includes language about building, which is a fundamental part of architecture as a discipline. Line 26 describes Crown’s second principle of accuracy as a “keystone,” and lines 76–78 compare Crown’s three principles to a “solid house or building” that is “supported by a strong foundation”: Crown’s attitude toward hard work.

The best answer is NOT:

B because business is only mentioned in the passage in the very literal sense of Crown’s brewery business and its operations.

C because astronomy is not mentioned in the passage.

D because education is mentioned in the passage only in the literal sense of Crown’s education as a student.

Question 10. The best answer is H because the passage describes the photographs of annual brewery picnics decorating Crown’s office as “fading” and “brown” (line 81), indicating that they have hung on the wall of his office (and thus that Crown has been in the brewery business) for a length of time.

The best answer is NOT:

F because the passage makes no mention of outdated refrigerators; it only mentions that Crown invested in “refrigerated freight cars” (lines 55–56), which represented a new technology at the time.

G because the passage makes no mention of how long the cross-stitch made by Crown’s wife has been hanging on his office wall.

J because there is no mention of such a bell in the passage; it only mentions the “pinging bell on the black iron typewriter” (lines 59–60).

Passage II

Question 11. The best answer is D because there is no mention in the passage of William’s response to Caroline’s discovery, thus there is no clear indication of how he felt about her discovery.

The best answer is NOT:

A because there is no evidence in the passage that William either applauded Caroline’s discovery or was disappointed that she wasn’t looking for nebulae.

B because there is no evidence in the passage that William either supported Caroline’s discovery or verified it himself.

C because there is no evidence in the passage that William resented how quickly Caroline’s discovery was verified.

Question 12. The best answer is J because the passage states that “the forty-foot [octagon tube] would be higher than a house” (line 14). This is a direct comparison used to emphasize the enormous size of the “octagon tube 40 foot long” (line 6).

The best answer is NOT:

F because the series of ladders mentioned in line 16 is a description of part of the telescope itself; the telescope is not being compared to the ladders.

G because the wooden gantry mentioned in line 10 is described as something the telescope would have to be mounted in; the telescope itself isn’t compared to the gantry.

H because the haylofts mentioned in line 34 are described as part of the stables that could be converted into an apartment; the telescope is not compared to the haylofts.

Question 13. The best answer is B because the first four paragraphs in the passage focus on William Herschel and his telescope project, but the remainder of the passage focuses primarily on his sister Caroline and her astronomical work; the fifth paragraph serves as a transition, moving the passage’s discussion from details about William’s telescope project to details about Caroline’s work.

The best answer is NOT:

A because the passage does not explain any specific methods Caroline used to perform her comet sweeps.

C because the passage does not say that Caroline herself made renovations to the stables, nor does it specify that the renovations would be done to accommodate William’s telescope.

D because the passage does not compare Caroline’s observation techniques with William’s; at this point, the passage shifts to a discussion of Caroline’s astronomical work.

Question 14. The best answer is H because the passage says in lines 79–80 that “The account written into [Caroline’s] ‘Book of Work Done’ catches something of her growing excitement.” This statement is then supported and illustrated by the excerpt from Caroline’s “Book of Work Done” that immediately follows. Her writing “IS A COMET” in capital letters (line 85), and the statement that she “did not go to rest” until she had written to the Royal Society about the comet (lines 85–88), also reveal her enthusiasm about her discovery.

The best answer is NOT:

F because though the excerpt in the passage indicates that it took Caroline a bit of time to verify that her finding was a comet, the passage contains no clear outline of the process by which Caroline determined her finding was a comet.

G because the passage indicates that the excerpt contains notes from Caroline’s own work, not that the notes were made for William in particular.

J because though the passage implies that Dr. Blagden and Mr. Aubert were points of authority regarding astronomical discovery at the time, it does not explain the role they may have had in verifying Caroline’s discovery.

Question 15. The best answer is A because in the context of lines 9–13, it is clear that the word finest is being used in juxtaposition with the description of the enormous telescope and its workings. The telescope was so massive that it would have to be mounted in an enormous gantry and turned by two workmen, but it would be so intricate and precise that it could be adjusted in “fine,” or “slight,” ways by the astronomer.

The best answer is NOT:

B because the word fairest generally denotes either lightness in complexion or appearance, or it pertains to justice and equity. However, the word finest in the context of lines 9–13 is meant to indicate precision, not any of the concepts associated with fairness.

C because the context of lines 9–13 indicates that the word finest is being used in the sense of precision, and it would be inaccurate to describe precise or exact fingertip adjustments as thin.

D because the word greatest denotes either size or level of excellence. The word finest in the context of lines 9–13 is clearly meant to indicate the precision involved in the adjustments, not any of the concepts associated with greatness.

Question 16. The best answer is J because the sentence in lines 17–21 states that Caroline would have to be in the special booth below William “to avoid light pollution, where she would have her desk and lamp, celestial clocks, and observation journals,” meaning that the light from her lamp (which she needed to record her observations) would have affected William’s ability to observe the night sky though the telescope.

The best answer is NOT:

F because the passage states that both Caroline and William would be “shouting commands and replies” (lines 22–23); there is no evidence that Caroline would be relaying William’s instructions to workmen.

G because there is no evidence in the passage that Caroline preferred seclusion when working on calculations; the passage states that she would work in the booth “to avoid light pollution” (line 19), not because she wanted to be alone.

H because the passage does not indicate the size of the viewing platform or the number of people it could hold, so there is no evidence in the passage to support the idea that the platform wouldn’t be large enough to hold both William and Caroline.

Question 17. The best answer is B because lines 25–27 directly answer the question of why William and Caroline moved to “The Grove”: “William had decided that his grand project required a new house with larger grounds for constructing and erecting the telescope.” They moved to “The Grove,” which is described as meeting these requirements.

The best answer is NOT:

A because the passage makes no mention of what motivated William to embark on his project; it only mentions when he was inspired to begin the project (“in the summer of 1785” (line 1)).

C because the passage mentions that Caroline was “unable to calculate the mathematical coordinates” of the comet she discovered, but it does not give any reason as to why she was unable to do so.

D because the passage does say that “the verification of Caroline’s comet was achieved much more rapidly than William’s discovery of the planet Uranus” (lines 89–91), but it does not directly specify how long it took the Royal Society to verify that Caroline’s discovery was a comet.

Question 18. The best answer is F because the passage states that because of the reflector’s “large aperture, its tube appeared much fatter, heavier and stubbier than normal reflectors of this type” (lines 42–44). Thus it can most reasonably be inferred that the reflector’s aperture was larger than those of typical telescopes of that type at the time.

The best answer is NOT:

G because there is no mention in the passage of the size of the reflector’s box-frame.

H because the passage states that the reflector’s magnification was “comparatively low at twenty-four times” (lines 51–52), meaning that it had less magnifying power compared to similar telescopes at the time.

J because the passage states that the reflector was “designed specifically for its huge light-gathering power” (lines 49–50), indicating that, if anything, it likely had more light-gathering power than similar telescopes at that time, not less.

Question 19. The best answer is C because the passage states in lines 62–66 that “Caroline thought she had spotted an unknown stellar object moving through Ursa Major” which “appeared to be descending, but barely perceptibly, towards a triangulation of stars in the beautifully named constellation Coma Berenices.”

The best answer is NOT:

A because lines 62–66 clearly state that the comet was moving “towards” the stars in Coma Berenices, not through Coma Berenices or toward the Pole Star.

B because lines 62–66 clearly state that the comet was moving “towards” the stars in Coma Berenices, not through Coma Berenices or toward the Big Dipper.

D because lines 62–66 clearly state that the comet was moving “through” Ursa Major and “towards” the triangulation of stars in Coma Berenices, not through them.

Question 20. The best answer is F because the passage states in lines 67–70 that “to find something so quickly, and in such a familiar place (the Great Bear or Big Dipper being the first stop of every amateur stargazer wanting to locate the Pole Star), seemed wildly unlikely.” Thus the passage indicates that Caroline’s find was unlikely because she found the comet quickly in a part of the sky that was very familiar to stargazers.

The best answer is NOT:

G because there is no evidence in the passage that Caroline had more knowledge of nebulae than she did of comets.

H because the passage mentions in lines 90–91 “William’s discovery of the planet Uranus,” but there is no mention of Caroline being involved in that discovery.

J because the passage indicates that Caroline had plenty of experience with mathematical calculations in astronomy, and though line 73 does state that she was “unable to calculate the mathematical coordinates” of her comet, the passage gives no indication that her discovery was unlikely because she had little experience with such calculations.

Passage III

Question 21. The best answer is B because the first paragraph of passage A reveals Gornick’s belief that her mother and the character of her mother in her memoir are not exactly the same; the second paragraph reveals Gornick’s belief that, similarly, the narrator of the memoir and her actual self are not quite the same. Together, in the context of the passage as a whole, these paragraphs serve to introduce the idea that the characters in Gornick’s memoir differ from the people they are based on.

The best answer is NOT:

A because though the paragraphs provide a few details implying a measure of popularity for Gornick’s book, the main purpose of these two paragraphs, especially in the context of the passage as a whole, is to establish the idea in B, not to establish her book’s popularity.

C because there is no indication in the passage that Gornick is overly frustrated with her readers’ questions and comments.

D because Gornick argues in line 42 that “memoirs belong to the category of literature,” but she is not suggesting that memoirs are fiction and should be classified as such. Her argument is that “emotional truth” is more important in memoirs than are completely literal and accurate details.

Question 22. The best answer is F because lines 8–16 explain that the party guest was disappointed because she felt Gornick was “nothing like the woman who wrote Fierce Attachments!” The quotation “We ourselves were just a rough draft of the written characters” (lines 20–21) exemplifies the discrepancy between an actual person and a character depicted in a memoir that led to the guest’s disappointment.

The best answer is NOT:

G because the party guest’s disappointment had nothing to do with Gornick’s perceived similarity to Gornick’s mother. The guest’s disappointment stemmed from the fact that the narrator of the book and Gornick herself were “not exactly the same” (line 16).

H because the quotation in question refers to the idea that Gornick had hoped to express in her memoir, whereas the party guest’s disappointment had to do with the unexpected difference between the narrator in the book and Gornick herself.

J because the quotation in question refers to the insight that Gornick had hoped to express in her memoir, whereas the party guest’s disappointment had to do with the unexpected difference between the narrator in the book and Gornick herself.

Question 23. The best answer is B because Gornick identifies the heart of her memoir in lines 31–32: the revelation that “I could not leave my mother because I had become my mother.”

The best answer is NOT:

A because the author indicates that the walks she took with her mother in Manhattan in the 1980s are part of “the context in which the book is set” (lines 34–35), but the passage does not indicate that Gornick believes them to be the heart of her memoir.

C because the author indicates that her childhood experiences in the Bronx in the 1950s are part of “the context in which the book was set” (lines 34–35), but the passage does not indicate that Gornick believes them to be the heart of her memoir.

D because the author states in lines 31–32 that she believes the heart of her memoir is the revelation she had about having become her mother, not just that they had a shared history.

Question 24. The best answer is J because the author claims in lines 42–43 that “memoirs belong to the category of literature, not of journalism.”

The best answer is NOT:

F because the author explicitly states in lines 42–43 that memoirs do not belong to the category of journalism.

G because the author explicitly claims in line 42 that “memoirs belong to the category of literature”; personal diaries are not mentioned in the passage.

H because the author explicitly claims in line 42 that “memoirs belong to the category of literature”; she also goes on to say that memoirs need not be as literally accurate as historical narrative (lines 43–46).

Question 25. The best answer is C because the first paragraph asserts that Hemingway’s fiction contained autobiographical elements and his “protagonists are often conscious projections and explorations of the self” (lines 55–56).

The best answer is NOT:

A because the passage states in lines 53–56 that Hemingway’s fictional protagonists are often projections of the self; there is no mention in the passage of Hemingway basing his protagonists on composites of his friends.

B because the passage states in lines 53–56 that Hemingway’s fictional protagonists are often projections of the self; there is no mention in the passage of Hemingway basing his protagonists on family members.

D because the passage states in lines 53–56 that Hemingway’s fictional protagonists are often projections of the self; there is no mention in the passage of Hemingway’s protagonists being completely made-up characters.

Question 26. The best answer is F because the passage explains in lines 61–73 that “A Moveable Feast is particularly complex because Hemingway was clearly conscious that it would be his literary testament” and that he thus used the book to portray himself and his contemporaries in a certain light. Lines 73–76 state that “A Moveable Feast could hardly be an objective portrayal of its author and his contemporaries, and the accuracy of the anecdotes becomes an issue that can never be entirely resolved.”

The best answer is NOT:

G because though the passage mentions that Hemingway “felt that he had been unfairly portrayed by some of his contemporaries” (lines 67–68), the passage indicates that the question of accuracy has to do with Hemingway’s own writing, not with the writings of others.

H because the passage makes no mention of Hemingway being unable to produce documents to support his stories.

J because the passage makes no mention of Hemingway claiming the excellence of his memory or of others doubting such a claim.

Question 27. The best answer is B because the author of passage B states that “A Moveable Feast is particularly complex” (line 61) and that it “appears as a fascinating composite of relative factual accuracy and clear dishonesty of intent” (lines 87–88). These statements, in addition to details the author provides throughout the passage about Hemingway’s purposeful blurring of fact and fiction, support the idea that the passage author believes A Moveable Feast to be a complex example of a book that combines fact and fiction.

The best answer is NOT:

A because the passage author makes no particular claim about the quality of any of Hemingway’s other works, nor does she compare A Moveable Feast to any of Hemingway’s other works.

C because the passage author makes clear that she believes the accuracy of A Moveable Feast is in question and “an issue that can never be entirely resolved” (lines 75–76).

D because the passage author does not suggest anywhere in the passage that A Moveable Feast should be read alongside other books from the time period; her argument pertains primarily only to A Moveable Feast.

Question 28. The best answer is J because in passage A, Gornick’s point is that her memoir was not necessarily literally true; what mattered to her was portraying “not the literalness of the situation, but the emotional truth of the story” (lines 38–39). She explains that the characters in her memoir differed from the actual people they were based on in that “these characters could not live independent of the story which had called them into life, as they existed for the sole purpose of serving that story” (lines 21–24). Similarly, throughout passage B, Hemingway is described as selectively using material from his life and blurring fact and fiction in order to best serve the story he wanted to tell: “He clearly overlooked a great deal of material, distorted some, and generally selected the episodes so that they would show him as innocent, honest, dedicated, and thoroughly enjoying life” (lines 83–86).

The best answer is NOT:

F because the passages indicate that both Gornick and Hemingway may not have been completely literally accurate in their memoirs, but their stories were based on a foundation of real-life situations—not wholly fictional ones.

G because though passage B states that Hemingway wanted “to leave to the world a flattering self-portrait” (lines 72–73), nowhere in passage A does Gornick indicate that she was concerned with portraying herself in a flattering way in her memoir.

H because though passage B states that Hemingway wanted to “present his own version of personal relationships” (lines 68–69) and “get back at people against whom he held a grudge” (lines 70–71), nowhere in passage A does Gornick indicate that she was motivated to write her memoir to “settle old scores.”

Question 29. The best answer is C because in passage A, Gornick explains her belief that, in memoir, complete literal accuracy is not necessary but that the point is to convey the “emotional truth of the story” (line 39), “trying, as honestly as possible, to get at the bottom of the tale at hand” (lines 48–49). She states that “what actually happened is only raw material; what matters is what the memoirist makes of what happened” (lines 39–41). Similarly, in passage B, Hemingway is portrayed as focusing on the particular stories he wanted to portray rather than focusing on factual accuracy: “He invented and lied relatively seldom about pure facts. When he did so, it was usually in order to reinforce the pattern he had created . . .” (lines 79–81). Thus it seems that both Gornick and Hemingway would agree that creating a cohesive, meaningful, and artistic whole is more important than detailing plain facts in a memoir.

The best answer is NOT:

A because there is no evidence in either passage that Gornick or Hemingway would believe that a writer has as much license to create when writing memoir as he or she does when writing fiction.

B because both passages indicate that the exact details of events are less important than the story the memoirist wants to tell that is based on memories of events. There is no evidence in either passage that Gornick or Hemingway would believe a writer should exclude an event entirely from a memoir if he or she cannot remember the exact details of the event.

D because there is no evidence in either passage that either Gornick or Hemingway would believe memoirists should write only about incidents that have documented evidence supporting their stories; neither author is concerned with evidence as fact.

Question 30. The best answer is G because the main idea expressed in passage A is that Gornick believes that “what actually happened is only raw material; what matters is what the memoirist makes of what happened” (lines 39–41). This idea echoes the quotation, which indicates that there is necessarily a difference between a memoir, which is a story, and the details and facts of real life.

The best answer is NOT:

F because though there is an anecdote about Gornick not meeting a particular reader’s expectation, that story is simply supporting Gornick’s point that characters in memoirs differ from real people; the anecdote does not relate to the quotation’s claim that a memoir is a story and not a history.

H because the statement in passage B about Hemingway viewing A Moveable Feast as his literary testament explains only his motivation for writing the story the way he did; it doesn’t relate to the quotation’s claim that a memoir is a story and not a history.

J because the statement in passage B claiming that Hemingway seldom lied about pure facts focuses on the factual accuracy of his memoir or how much it reflected history, and this idea stands in contrast to the quotation’s claim that memoir is in fact a story and not a history.

Passage IV

Question 31. The best answer is D because the passage focuses on Suarez’s research on colonizing ants and his conclusions about what enables some species to survive over others.

The best answer is NOT:

A because the passage makes clear that Argentine ants living in the United States had already been discovered; in order to examine why some colonizing organisms fail and some succeed, Suarez hoped to examine “early samples of Argentine ants collected in the United States” (lines 7–8).

B because the passage primarily focuses on ant species and does not compare the physical characteristics of ants to other insects. The passage also focuses more exclusively on the behavior of ants rather than their physical characteristics.

C because the passage makes no mention of the technology scientists use to determine the size of supercolonies.

Question 32. The best answer is G because peppered throughout this passage are certain colloquial phrases not often seen in scientific tracts, including that a scientist did it “the hard way” (lines 3–4), that one scientist was the “guru of ant gurus” (line 27), that Argentine ants were “wimps” (line 52), and that certain species always “made bank” (line 73). The use of such relaxed language helps create a casual tone for the reader.

The best answer is NOT:

F because the passage includes no personal anecdotes, never even mentioning the author’s life or incorporating the use of the word I.

H because the passage author uses informal language at times but includes no quotations that are humorous.

J because the passage includes no “self-critical” asides, as again the author does not place himself in the passage in any way other than through his use of colloquial language.

Question 33. The best answer is C because the first paragraph tells readers that Suarez “found some brown jars” at the Smithsonian in 1999, meaning this event occurred before the turn of the century, well before the other choices.

The best answer is NOT:

A because lines 63–66 state that “Case joined forces with Holway and Suarez” to study ant aggression but that happened only after Suarez and Holway had been classifying the ants (lines 28–29), which happened only after Suarez found the jars.

B because line 86 states that those ants were brought together “in 2009,” a full decade after Suarez first found the brown jars.

D because lines 25–28 state that Holway and Ward were “solicited” to help Suarez with classifying the jars Suarez had previously found in the Smithsonian, which couldn’t have happened until Suarez found the jars.

Question 34. The best answer is G because the opening sentence of the fifth paragraph states the focus of the paragraph: that when a group moves to a new area, “possible futures diverge” (line 42). What follows in the paragraph are examples of these possible futures and the indication that it’s unlikely for a species to survive, let alone thrive in a new area.

The best answer is NOT:

F because the paragraph is not focused specifically on Argentine ants but discusses pioneering species in general and the likelihood that they will survive.

H because the paragraph does not provide a definition of invasive species, nor does the paragraph specifically mention ants.

J because the paragraph does not mention or focus on Argentine ants specifically, nor does it compare their survival rates with those of other species.

Question 35. The best answer is D because lines 56–58 state that if Argentine ants from different colonies are placed together, “they accept each other.” This is noted directly after line 55 describes this as “strange” behavior, so it can be assumed that in most similar situations ants would fight one another, not accept one another.

The best answer is NOT:

A because the lines in question have nothing to do with the prevalence of supercolonies among ant species but with the trait of Argentine ants to accept each other.

B because the passage does not differentiate in these lines between California’s Argentine ants and the same ants in other places.

C because the lines in question don’t discuss California’s ecosystem in any way.

Question 36. The best answer is F because lines 1–3 state that Suarez was “like many biologists” who “struggled for years with the question of which colonizing organisms fail and which succeed.”

The best answer is NOT:

G because lines 1–3 make it clear that Suarez was one of many; no dates are attached to the work done by the others.

H because lines 1–3 make it clear that many biologists struggled with this question. Moreover, there is no indication in the passage that Suarez was affiliated with the Smithsonian, and he worked alongside others—Holway and Ward—who were affiliated with different universities.

J because lines 1–3 state that Suarez was “like many biologists.”

Question 37. The best answer is D because lines 15–18 state that what Suarez found in the brown jars other than Argentine ants was “far more interesting: some of the ethanol-filled jars were jammed with vials of ants collected at ports of entry in the eastern U.S. from 1927 to 1985.” Those ants provided the basis for Suarez’s research.

The best answer is NOT:

A because lines 14–15 state that “Suarez ultimately found relatively few samples of Argentine ants,” meaning they were not “most of the samples” at all.

B because lines 25–28 state that Suarez recruited Ward and Holway to help him, not that they had accrued all these samples.

C because line 24 states that the brown jars revealed “394 separate samples” which line 29 explains were “232 distinct species,” but the passage otherwise does not say how many of those ants might have been previously “undiscovered.”

Question 38. The best answer is F because line 52 clearly states Argentine ants are “squishy, small, stingless wimps.”

The best answer is NOT:

G because lines 51–53 describe those ants as “ecologically dominant,” yet small and not physically dominant.

H because the passage makes clear Suarez found samples of the ants in the Smithsonian, not that he discovered the species himself.

J because lines 84–88 state that “one conglomeration of Argentine ants stretched the length of California, another from Italy to Portugal . . . until, in 2009, workers from those two “colonies” (along with a third from Japan) were put together . . .” Thus, the passage makes clear that Argentine ants existed in Japan to such a degree that they could form with other colonies to create a supercolony. There is no indication in the passage that the species did not thrive in Japan.

Question 39. The best answer is B because lines 69–71 say that studies show that “aggressive ants wasted energy fighting (and dying), and so gathered less food and fared poorly.”

The best answer is NOT:

A because the passage does not indicate that aggressive ants live in larger colonies than do peaceful ants.

C because the passage does not indicate that aggressive ants are more likely than peaceful ants to live in a colony.

D because the passage does not indicate that aggressive ants are more likely than peaceful ants to be a “survivor species.” In fact, lines 69–71 state that aggressive ants spend more time “dying” because they fight so much.

Question 40. The best answer is G because this fact is stated clearly in lines 78–79: “Ants flash chemical badges identifying their home nest.”

The best answer is NOT:

F because this idea is not supported by the passage, as lines 79–80 indicate that without those chemical markers, “no one knows who is friend or foe,” with the end result of that being that peace breaks out. When peace breaks out, the term colony gets muddied and supercolonies form, with nests exchanging workers and queens.

H because the passage makes clear that supercolonies form only when chemical markers are absent and that swapping ants between colonies is not normal.

J because the passage discusses conglomerations of Argentine ants in supercolonies that go “the length of California, another from Italy to Portugal” (lines 85–86), but the passage doesn’t indicate which of those is bigger or if one of those is the “largest” supercolony in the world.

Passage I

The best answer is B. The figure shows the first generation (Individuals 1 and 2), the second generation (Individuals 4, 6, and 7), the third generation (Individuals 10, 11, 12, 13, 15, 16, and 17), and the fourth generation (Individuals 18–23). A, C, and D are incorrect; the figure shows four generations. B is correct.

The best answer is G. In order to answer this item, the examinee must know that the more closely related two individuals are to each other, the greater the genetic similarity is likely to be. According to the figure, Individuals 12 and 13 are sisters and would likely have the greatest genetic similarity. F is incorrect; individuals 3 and 4 are mates, not siblings. G is correct; Individuals 12 and 13 are sisters and would have the greatest genetic similarity. H is incorrect; Individuals 16 and 24 are not blood relatives. J is incorrect; Individuals 18 and 21 are second cousins.

The best answer is D. In order to answer this item, the examinee must know how to work a genetic cross. According to the figure, both Individuals 23 and 24 have Trait G. According to the passage, Trait G is recessive. It follows that Individuals 23 and 24 both have the gg genotype and that all their children will also have the gg genotype. All their children will therefore have Trait G. A, B, and C are incorrect; all four of the children will have Trait G. D is correct.

The best answer is H. According to the figure, the grandchildren of Individuals 1 and 2 are Individuals 10, 11, 12, 13, 15, 16, and 17. According to the key for the figure, a black circle and black square represent individuals with Trait G. Of the grandchildren, only Individuals 10 and 16 have Trait G. F, G, and J are incorrect; two of the grandchildren have Trait G. H is correct.

The best answer is D. In order to answer this item, the examinee should know that with a sex-linked trait, an affected female passes the trait to all her sons. According to the figure, Individuals 4 and 10 were the only females with Trait G who had a son. Individual 4’s son, Individual 11, did not have Trait G. It follows that Trait G is not a sex-linked trait. A and B are incorrect; Trait G is not a sex-linked trait. C is incorrect; Individual 4 did not pass Trait G to her son. D is correct.

The best answer is J. According to the passage, Individual 21 has the Gene G genotype Gg. According to the figure, Individual 21 does not have Trait G. The passage states that Trait G is the recessive trait. An individual with the Gg genotype will have the dominant trait. F and G are incorrect; an individual with the Gg genotype will not have Trait G. C is incorrect; Trait G is a recessive trait. J is correct; the individual will not have Trait G, the recessive trait.

Passage II

The best answer is A. In order to answer this item, the examinee must know that a balance is used to determine mass. Figure 2 gives the average mass per seed for each group. In order to determine the average mass per seed, the scientists would have to measure the mass of the seeds using a balance. A is correct. B is incorrect; the pH was not measured in this experiment. C is incorrect; a telescope is typically used for viewing distant objects and would not have been needed for this experiment. D is incorrect; a thermometer is used to measure temperature.

The best answer is G. According to the passage, the experiment was conducted to investigate the effects of different pollination treatments on fruit production and seed mass. F is incorrect; the location of the plants was not a variable in the experiment. G is correct; the experiment investigated different types of pollination. H is incorrect; the experiment did not measure the amount of time until fruit ripened. J is incorrect; the scientists did not question whether or not the flowers were typically pollinated by hummingbirds.

The best answer is A. According to Table 1, the flowers in Group 1 were self-pollinated whereas the flowers in Group 2 were cross-pollinated, using pollen from a single donor. A is correct. B is incorrect; the pollen used for Group 1 was from the same plant as the flowers in Group 1. C is incorrect; the pollen received by each Group 2 flower was collected from a single donor. D is incorrect; the pollen used for Group 1 was from a single plant.

The best answer is H. Figure 1 shows the percent of flowers that produced fruit. In order to calculate this percentage, the examinee must divide the number of flowers that produced fruit by the total number of flowers. F and G are incorrect; the number and mass of seeds is not relevant. H is correct. J is incorrect; the number of flowers producing fruit should be in the numerator, and the total number of flowers should be in the denominator.

The best answer is B. According to the passage, the anthers are the pollen-producing structures in the flower. By removing the anthers, the flower would not be able to spontaneously self-pollinate. A is incorrect; without the anthers present, the flowers would not be able to spontaneously self-pollinate. B is correct. C and D are incorrect; the presence or absence of anthers would not affect the ability of the flowers to be pollinated by hummingbirds.

The best answer is G. According to Figure 1, 0% of the flowers in Group 4 produced fruit. This suggests that the nylon bags successfully prevented the normal pollinators from pollinating the flowers, because none of the flowers in Group 4 were pollinated. F is incorrect; 20% of the flowers receiving self-pollination treatments produced fruit. G is correct; 0% of the flowers in Group 4 produced fruit, indicating that the nylon bags prevented normal pollinators from pollinating the flowers. H and J are incorrect; the data suggest that the bags did prevent the normal pollinators from pollinating the flowers.

The best answer is D. The results given indicate the average mass per seed but not the number of seeds. Without knowing the number of seeds, one cannot figure out the total mass of the seeds. A, B, and C are incorrect; there is not enough information to determine the total mass of the seeds produced by the flowers. D is correct.

Passage III

The best answer is H. F and G are incorrect; both CH₄ and CO₂ were produced indicating that the organic matter was being broken down by both aerobic and anaerobic bacteria. H is correct; the organic material was most likely broken down more rapidly during the warmer summer months. J is incorrect; the organic material was most likely broken down less rapidly in the winter.

The best answer is A. According to Figures 1 and 2, for both bog soil and fen soil, as the water table levels decreased from +1 cm to −20 cm, the total CO₂ emissions increased. The figures also show that for both bog soil and fen soil, as the water table levels decreased, the total CH₄ emissions also decreased. A is correct. B is incorrect; the total CO₂ emissions increased. C is incorrect; the total CH₄ emissions decreased. D is incorrect; the total CO₂ emissions increased.

The best answer is F. According to the passage, gas emissions for each soil section were measured. By keeping a lid on each tank, the scientists would have been able to collect and measure all the gases emitted by each section. F is correct; the scientists would get a better measurement if none of the emitted gases were lost from the tank. G is incorrect; the scientists’ results would be incorrect if atmospheric gases entered the tank. H is incorrect; the bacteria were in the soil and were not likely to leave the tanks. J is incorrect; the tanks were made of glass allowing sunlight to enter the tanks.

The best answer is D. According to Figures 1 and 2, the amount of CO₂ emitted from the fen soil at each WT level was greater than the amount emitted from the bog soil. The amount of CH₄ emitted from the fen soil at each WT level was also greater than the amount emitted from the bog soil. One may conclude that the levels of nutrients that sustain both types of bacteria are greater in the fen soil than in the bog soil. A is incorrect; the data suggest that the fen soil contains higher levels of nutrients for both aerobic and anaerobic bacteria. B is incorrect; the data suggest that there are higher levels of nutrients for aerobic bacteria in fen soil. C is incorrect; the data suggest that there are higher levels of nutrients for anaerobic bacteria in fen soil. D is correct.

The best answer is F. According to the passage, aerobic bacteria generate CO₂. The results illustrated in Figures 1 and 2 show that CO₂ was produced in both types of soil at all WT levels, indicating that aerobic bacteria were present in the soil sections that were completely submerged in water. F is correct. G is incorrect; CO₂ was also emitted from those sections. H and J are incorrect; the results indicate that aerobic bacteria were present in all the sections.

The best answer is C. According to Figure 2, the fen soil section with a WT of −10 cm had a total CO₂ emission of 48 mol C/m² over the 3-month period. The average CO₂ emission per month is 48/3 = 16 mol C/m². A is incorrect; an average CO₂ emission of 10 mol C/m² would result in a total emission of 30 mol C/m². B is incorrect; an average CO₂ emission of 13 mol C/m² would result in a total emission of 39 mol C/m². C is correct; an average CO₂ emission of 16 mol C/m² would result in a total emission of 48 mol C/m². D is incorrect; an average CO₂ emission of 19 mol C/m² would result in a total emission of 57 mol C/m².

The best answer is J. F is incorrect; because the tanks were covered, no precipitation would fall on the samples. G is incorrect; all live plants were removed from the sections. H is incorrect; the volume of each sample was much less than the wetlands. J is correct; because the tanks were made of glass, the samples would be exposed to the same amount of daylight as the wetlands.

Passage IV

The best answer is B. Because the weight of an object is related to its mass, the door with the greatest mass is the door with the greatest weight. According to the passage, the door with the greatest weight had a weight of 76 lb and was used in Study 2. A is incorrect; the door used in Study 1 had a weight of 61 lb. B is correct; doors with weights of 51 lb, 61 lb, and 76 lb were used in Study 2. C is incorrect; the doors used in Study 3 each had a weight of 61 lb. D is incorrect; the doors tested in Study 2 had different masses.

The best answer is F. According to the passage, in Study 2, D was held constant, and W and S were varied. In Study 3, W was held constant, and D and S were varied. F is correct. G is incorrect; W was varied in Study 2. H is incorrect; W was varied in Study 2 only. J is incorrect; W was held constant in Study 3 only.

The best answer is D. According to the results of Study 2, when D = 30 in and S = 50 in, Fn,av increases as W increases. When W = 76 lb, Fn,av = 46 lb. If an additional door with W = 90 lb had been tested, Fn,av would most likely have been greater than 46 lb. A, B, and C are incorrect; Fn,av would have been greater than 45 lb. D is correct.

The best answer is H. Figure 1 shows that Fv,av remained constant at all values of S. Figure 1 also shows that Fh,av was greater than Fv,av for all S < 30 in, equal to Fv,av for S = 30 in, and less than Fv,av for all S > 30 in. F and G are incorrect; Fh,av was greater than Fv,av for all S < 30 in. H is correct; Fh,av was greater than Fv,av for all S < 30 in, and less than Fv,av for all S > 30 in. J is incorrect; Fh,av was less than Fv,av for all S > 30 in.

The best answer is B. According to Figure 2, in Study 2, the lowest Fn,av was 27 lb. According to Figure 3, in Study 3, the lowest Fn,av was 33 lb. The lowest value for Fn,av of 27 lb was measured when W = 51 lb, D = 30 in, and S = 70 in. A is incorrect; under these conditions, Fn,av = 45 lb. B is correct; under these conditions, Fn,av = 27 lb. C is incorrect; under these conditions, Fn,av = 48 lb. D is incorrect; under these conditions, Fn,av = 33 lb.

The best answer is J. Figure 1 shows that as S was varied, there was no change in Fv,av, while Fh,av decreased as S increased. Fv,av was independent of S.F is incorrect; this shows that Fh,av was dependent on S.G is incorrect; Fh,av did not remain constant as S increased. H is incorrect; Fv,av did not decrease as S increased. J is correct; Fv,av remained constant as S increased.

The best answer is C. A is incorrect; according to Figure 3, under these conditions, the net force on each hinge was 55 lb and the hinge would not break. B is incorrect; under these conditions, the net force on each hinge was 35 lb and the hinge would not break. C is correct; under these conditions, the net force on each hinge was 62 lb and the hinge would break. D is incorrect; under these conditions, the net force on each hinge was 37 lb and the hinge would not break.

Passage V

The best answer is J. According to the passage, none of the students mentioned argon. All four students referred to “almost all the gas remaining . . .,” which suggests that other gases, such as argon, could be present. The fact that air contains less than 1% argon by volume does not weaken the explanation given by any of the students. F, G, and H are incorrect; the information does not weaken any of the explanations. J is correct.

The best answer is A. Because the quartz tube was heated with a Bunsen burner, it was important that the silicone hoses had a strong resistance to heat. Because a chemical reaction was taking place when the steel wool was heated, it was important that the silicone hoses have a low chemical reactivity. No water was used in the experiment, nor was water generated, and therefore the solubility of the silicone hoses in water would not be important. A is correct; it is most important that the silicone hoses be resistant to heat and have a low chemical reactivity. B is incorrect; the hoses should also have low chemical reactivity, and the water solubility of the hoses is not relevant. C is incorrect; the hoses should also have strong resistance to heat, and the water solubility of the hoses is not relevant. D is incorrect; the water solubility of the hoses is not relevant.

The best answer is J. According to Student 4, the Fe reacted with CO₂ in the air, and after the reaction, almost all the remaining gas was O₂. Because the CO₂ was used up, the percent CO₂ by volume decreased. Because the remaining gas was nearly all O₂, the percent O₂ by volume increased as the CO₂ reacted. F is incorrect; the percent CO₂ decreased as the CO₂ reacted with the Fe. G is incorrect; the percent CO₂ decreased and the percent O₂ increased. H is incorrect; the percent O₂ increased as the amount of CO₂ decreased. J is correct.

The best answer is C. According to Student 1, air contains 20% N₂ by volume, and after the N₂ reacted with the Fe, almost all the gas remaining was O₂. It follows that Student 1 believes air is approximately 80% O₂. Student 2 states that air contains about 80% O₂. Student 3 states that air contains 20% O₂ by volume, and after the O₂ reacted with the Fe, almost all the gas remaining was N₂. It follows that Student 3 believes air is approximately 80% N₂. According to Student 4, air contains about 20% CO₂ by volume, and after the CO₂ reacted with the Fe, almost all the gas remaining was O₂. It follows that Student 4 believes air is approximately 80% O₂. Students 1, 2, and 4 all believe that air contains approximately 80% O₂ by volume and therefore would agree that, by volume, air contains more O₂ than N₂. A, B, and D are incorrect; Students 1, 2, and 4 would agree that, by volume, air contains more O₂ than N₂. Student 3 states that air is approximately 80% N₂. C is correct.

The best answer is H. In order to answer this item, the examinee needs to understand how reactants and products are placed in chemical equations. According to Student 3, the Fe reacted with the O₂ to form Fe₂O₃. Fe and O₂ are reactants and will appear on the left side of the equation. Fe₂O₃ is the product and will appear on the right side of the equation. F is incorrect; the reactants and product are on the wrong sides of this equation. G is incorrect; N₂ and FeN are not involved in the reaction. H is correct. J is incorrect; N₂ and FeN are not involved in the reaction.

The best answer is B. According to the passage, Students 1 and 4 claim that almost all the gas remaining is O₂. Student 2 claims that almost all the remaining gas is a mixture of about 75% O₂ and 25% N₂. Student 3 claims that almost all the remaining gas is N₂. Students 2 and 3 would agree that the gas remaining was at least 20% N₂ by volume. A is incorrect; Student 3 would also agree. B is correct. C is incorrect; Students 1 and 4 would not agree. D is incorrect; Students 2 and 3 would agree.

The best answer is G. According to Student 1, the Fe reacted with all the N₂, indicating that N₂ is the limiting reagent, and Fe is present in excess. Student 2 stated that the Fe reacted with some of the O₂, indicating the Fe is the limiting reagent and O₂ is present in excess. Student 3 stated that the Fe reacted with all the O₂, indicating that O₂ is the limiting reagent and Fe is present in excess. Student 4 stated that the steel wool reacted with all the CO₂, indicating that CO₂ was the limiting reagent and Fe was present in excess. Only Student 2 would likely agree that Fe was the limiting reagent. F, H, and J are incorrect; only Student 2 would agree that Fe was the limiting reagent. G is correct.

Passage VI

The best answer is C. According to Table 2, the baryon contains 2 spin-up quarks and 1 spin-down quark. The sum of those spins is therefore ℏ. The baryon contains 3 spin-up quarks. The sum of those spins is therefore ℏ. A, B, and D are incorrect; the spin of the baryon is ℏ, and the spin of the baryon is ℏ. C is correct.

The best answer is G. In order to answer this item, the examinee needs to know that an “electrically neutral” particle has an electric charge of 0. The quark charges are given in Table 1. F is incorrect; u, c, and t quarks each have a charge of so the net charge is +2. G is correct; a u quark has a charge of and the d and s quarks each have a charge of , so the net charge is 0. H is incorrect; this baryon has 3 spin-down quarks. J is incorrect; this baryon has 3 spin-up quarks.

The best answer is D. In order to answer this item, the examinee needs to know that the charge on a proton is +1. According to Table 2, the quark content of a proton is uud. According to Table 1, a u quark has a charge of and each d quark has a charge of , so the net charge is +1, which is consistent with the known charge of a proton. A, B, and C are incorrect. D is correct.

The best answer is F. According to Table 2, the quark content of a baryon is sss. According to Table 1, each s quark has a charge of and, therefore, the net charge of a baryon is −1. F is correct; the d, s, and b quarks each have a charge of , so the net charge is −1. G is incorrect; each s quark has a charge of and the c quark has a charge of , so the net charge is 0. H is incorrect; each s quark has a charge of and the t quark has a charge of , so the net charge is 0. J is incorrect; the u and c quarks each have a charge of and the s quark has a charge of , so the net charge is +1.

The best answer is A. In order to answer this item, the examinee must know that nucleons are limited to protons and neutrons. According to Table 2, the quark content of a proton is uud, and the quark content of a neutron is udd. Based on this information, one can conclude that nuclei are made up of u and d quarks. A is correct. B, C, and D are incorrect; there are only u and d quarks in protons and neutrons.

The best answer is F. The masses and charges for the quarks are given in Table 1. F is correct; the d quark has a mass of 5 MeV and a negative charge. The u quark has a mass of 3 MeV and a positive charge. The quark with a positive charge is not more massive than the quark with the negative charge. G is incorrect; the s quark has a mass of 104 MeV and a negative charge. The c quark has a mass of 1,270 MeV and a positive charge. The positively charged quark is more massive than the negatively charged quark. H is incorrect; the b quark has a mass of 4,200 MeV and a negative charge. The t quark has a mass of 171,200 MeV and a positive charge. The positively charged quark is more massive than the negatively charged quark. J is incorrect; the statement is not true for Generation 1.

Planning Your Essay

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ENGLISH • PRACTICE TEST 3 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is A because it clearly and succinctly indicates that the young woman arrived at the same location where the narrator was waiting.

The best answer is NOT:

B because it unnecessarily repeats the first part of the sentence, explaining again that the narrator is waiting in a veterinarian’s office.

C because it unnecessarily repeats that the narrator is waiting in the office. This information has already been established in the first part of the sentence, “I was waiting in the veterinarian’s office.”

D because it unnecessarily repeats that the narrator is there in the office. This information is already established in the first part of the sentence, “I was waiting in the veterinarian’s office.”

Question 2. The best answer is G because the verb scuttling provides a vivid description of the iguana’s movement. This choice also provides a description of the iguana’s rain forest environment, “dank undergrowth.”

The best answer is NOT:

F because “walking on the ground” does not satisfy the requirement in the question that the choice be a vivid description. “Walking on the ground” indicates what the iguana does but is not a vivid description of the iguana’s action or environment.

H because “living underneath the treetops” states an obvious point about iguanas and nearly restates the next part of the sentence, “resting high in the trees.” No vivid modifiers or verbs are used.

J because the words “down low” are repetitive and the expression “moving about down low” is vague and imprecise.

Question 3. The best answer is C because the comma after trees indicates that the iguanas, not the canopy itself, are hidden in the trees.

The best answer is NOT:

A because it is nonsensical given the context of the sentence. The comma after trees followed by “which are hidden in the canopy” indicates that the trees themselves are hidden in the canopy.

B because it is a comma splice. “They’re . . . trees” is an independent clause. “They are hidden in the canopy” is another independent clause. Two independent clauses cannot be joined using only a comma.

D because the semicolon is incorrectly placed between an independent clause and an explanatory phrase in a simple sentence. Semicolons are used to join two independent clauses.

Question 4. The best answer is G because the contrast between the narrator’s desire to be polite and the narrator’s reluctance emphasizes the narrator’s feelings toward the iguana. If the phrase were removed, the following sentence would suggest the narrator is ambivalent about the iguana’s presence, which contrasts with the beginning of the third paragraph when the narrator “guardedly” examines the iguana. The phrase is critical to establishing the narrator’s negative feelings toward the iguana.

The best answer is NOT:

F because “wishing to be polite, but with reluctance in my voice” describes an action taking place at the time the woman asked permission to take the iguana out of its carrier. This does not offer any suggestion that the narrator had a previous experience with iguanas out of their carriers at veterinary offices.

H because the narrator’s overall attitude toward the iguana is negative. She “guardedly” examines the iguana. She is amazed that the woman “tenderly caresses” the animal and initially feels pity for the woman who gives love to an animal the narrator initially feels can’t love the woman back. The phrase “with reluctance in my voice” is consistent with this negative attitude.

J because the purpose of the paragraph is not to provide background information on iguanas in general; it is a continuation of the narrative about the narrator’s encounter with an iguana at the veterinarian’s office.

Question 5. The best answer is D because the rows specified in the response indicate the pattern of spikes that appear on the reptile. The word lined also indicates the position and pattern of the spikes.

The best answer is NOT:

A because “it had a spine with tiny spikes” indicates the size of the spikes but not the pattern of the spikes.

B because the spikes “just beginning to develop again” indicates the potential size of the spikes and their development but not the arrangement or pattern of the spikes as stipulated in the stem.

C because “there were small spikes on its armored back” indicates the size of the spikes and provides a visual description of the appearance and texture of the reptile’s back but does not indicate the pattern of the spikes.

Question 6. The best answer is G because it creates a clear, logical, and parallel sentence (the verbs caressed and watched are parallel in form). The pronoun it later in the sentence also has a clear and logical antecedent, pet.

The best answer is NOT:

F because it is overly wordy and does not fit with the rest of the sentence. The underlined text is not parallel with the phrase “and watched it” later in the sentence, and the pronoun it has no clear antecedent.

H because the verb caressing is in the ongoing present tense, which is inconsistent with the past tense watched later in the sentence. This creates a confusing sequence of time when part of the action is an ongoing present action, caressing, and part of the action occurred in the past, watched.

J because it results in an illogical and ungrammatical transition to the rest of the sentence. The pronoun it in the remaining sentence also has no clear antecedent.

Question 7. The best answer is B because the word woman clarifies the meaning of the sentence by indicating who is lavishing attention on the iguana and serves as a clear antecedent to the pronoun her used later in the sentence.

The best answer is NOT:

A because there is an incorrect shift in pronouns from us to her in the same sentence. There is also no antecedent for the word us in this sentence or the preceding sentence (the narrator does not join the young woman in lavishing affection on the iguana).

C because the plural noun people is not a logical antecedent for the singular pronoun her. There is no mention in the sentence or in the rest of the essay of a wider audience lavishing attention on the iguana.

D because the pronoun you is an incorrect pronoun shift. The essay is a narrative written in the first person, and there aren’t any logical or stylistic reasons for the narrator to shift to the second person you at this point. You does not serve as a logical antecedent for the pronoun her used later in the sentence.

Question 8. The best answer is J because no comma is needed to separate the modifiers describing the iguana’s eyes and how they shone and the prepositional phrase.

The best answer is NOT:

F because there is an unnecessary comma between a modifier and a prepositional phrase. No comma is needed to set off the prepositional phrase “from its scaly face.”

G because there is an unnecessary comma between a preposition (from) and its object (“its scaly face”).

H because there is an unnecessary comma between modifiers joined by the conjunction and. No comma is needed here because and is joining two adjectives, not two independent clauses.

Question 9. The best answer is B because the word supposed means to assume. This word does not match the context of the iguana staring steadily and fixedly like a judge, nor is it a reasonable alternative for the word regarded. Supposed also does not track with the object, me, and creates the nonsensical idea that the iguana is assessing the narrator like a judge.

The best answer is NOT:

A because the word scrutinized means to study closely. This word matches the context of the rest of the sentence, which compares the iguana to a judge delivering a verdict.

C because the word appraised means to survey and evaluate. This word matches the context of the rest of the sentence, which compares the iguana to a judge delivering a verdict.

D because the word considered means to look attentively at someone or something. This word matches the context of the rest of the sentence, which states the iguana stares “steadily and fixedly” at the narrator.

Question 10. The best answer is F because it clearly indicates that the narrator is comparing the iguana’s actions to a judge delivering (or giving) the verdict.

The best answer is NOT:

G because the phrase “having a delivery of a verdict” is awkward and wordy, and it does not make sense in the given context. Without an explanation, it’s hard to imagine how an iguana’s actions could be like a judge having a delivery of a verdict.

H because the phrase “in deliverance with a verdict” does not make sense in this context (a judge delivers a verdict; she does not deliver the verdict with the verdict). The intended meaning of this action is unclear, especially when likened to the actions of the iguana.

J because the plural verb form deliver does not agree with the singular noun judge.

Question 11. The best answer is D because the sentence is complex (containing an independent and a dependent clause), so commas aren’t needed to separate two independent clauses. There also isn’t any nonessential information in the portion that needs to be set apart by punctuation.

The best answer is NOT:

A because there is an unnecessary comma between cat and the conjunction and. The phrase “cat and me” functions as a compound object in this sentence and should not be interrupted by a comma.

B because there are unnecessary commas around words that are essential to the meaning of the sentence (“and me from the hallway”). Setting these words apart with commas indicates that they are not crucial to understanding the sentence, but without them the sentence would state that the cat, not the hallway, leads to the examination room.

C because there is an unnecessary comma between the independent clause ending with hallway and the dependent clause beginning with that.

Question 12. The best answer is F because the word looking offers a concise and effective choice to indicate the comparison between the appearance of the iguana and the appearance of a kitten.

The best answer is NOT:

G because the phrase “like as if it was” offers a wordy and repetitive description of the iguana. This repetition is distracting and unnecessary. It is also overly informal given the style and tone of the rest of the essay.

H because the phrase “appearing something like” is wordy and vague. The phrase also does a poor job of setting up the comparison in the sentence “appearing something like as content as a kitten, and close its eyes again.” The meaning here is unclear.

J because the phrase “sort of like it was” is wordy and vague, which makes the comparison in the sentence less clear. The phrase is also overly informal for the style and tone of the essay.

Question 13. The best answer is B because placing the sentence at Point B further explains the young woman’s statement that the iguana liked being held. The sentence is a logical extension of the preceding sentence.

The best answer is NOT:

A because neither the woman nor her pet iguana have entered the office yet, so placing the sentence at Point A is incorrect. The pronoun she in the added sentence would have no antecedent, so it would be unclear who is speaking.

C because placing the sentence at Point C interrupts the logical flow between the narrator’s statement that she dislikes iguanas and her reasons for disliking the creatures.

D because placing the sentence at Point D interrupts the narrative flow between the iguana opening its eyes and it staring at the narrator.

Question 14. The best answer is F because the essay focuses on the narrator’s surprise that the iguana is pampered and loved by its owner. The iguana is lovingly caressed by its owner, which the narrator finds both amazing and unsettling.

The best answer is NOT:

G because there is no indication in the essay that the narrator believes the woman is impolite. The woman politely asks the narrator if she can let the reptile out of its carrier, and the narrator gives her approval. The narrator’s guarded response comes from her awe at the relationship between owner and pet, not from annoyance.

H because the essay makes it clear that the narrator does not like iguanas, but it does not tell the story of why the narrator dislikes the creatures. The essay is primarily about the narrator’s observation of a bond between the iguana and its owner on a particular day at the veterinary clinic.

J because the essay focuses on the narrator’s observations of one iguana in a veterinary clinic. Only a brief mention is given to where iguanas live. Any physical descriptions in the essay focus on one pet iguana, not iguanas in general or as a species.

Passage II

Question 15. The best answer is A because the conjunction but contrasts the achievement of qualifying for the Olympics with the fact that Mills was not expected to do well. This choice also correctly coordinates two independent clauses by joining them with a comma and a coordinating conjunction.

The best answer is NOT:

B because the conjunctive adverb nonetheless introduces a second independent clause. Using a comma and no coordinating conjunction between the independent clause ending with Olympics and nevertheless creates a comma splice. A semicolon after the word Olympics would be one option for making this construction correct.

C because it introduces an illogical transition. The fact that Mills qualified but was a long shot establishes a contrast, not an intensification of the first action as “in fact” implies. Furthermore, this option introduces a comma splice by joining two independent clauses with a comma. A semicolon is needed after the word Olympics to make this construction correct.

D because it creates a comma splice by joining two independent clauses with a comma. This choice also provides no transitional word indicating a contrast between the ideas that Mills qualified and that he was a long shot.

Question 16. The best answer is F because no comma is needed between the object, medal, and the prepositional phrase “for the United States in the event.”

The best answer is NOT:

G because no comma is needed between the object, medal, and the prepositional phrase that follows.

H because gold and medal are not coordinating adjectives that require a comma between them. Placing a comma between them indicates that the order of the adjectives can be reversed, but logically, gold must come before medal. Also, no comma is needed between the object, medal, and the prepositional phrase that follows.

J because Olympic and gold are not coordinating adjectives that require a comma between them.

Question 17. The best answer is C because the verb lagged earlier in the sentence indicates that the qualifying time was slower than that of Ron Clarke. The word behind is the only choice that is idiomatic in this context (“lagged behind”), and it also creates the most logical sentence.

The best answer is NOT:

A because the verb lagged earlier in the sentence indicates that the qualifying time was slower than that of Ron Clarke. The word above does not fit logically with lagging (describing Mills’s time as both “falling behind” and above is confusing). The phrase “lag above” is also not idiomatic.

B because the adverb around does not fit logically with the verb lagged earlier in the sentence. It is not clear what “lagged around” would mean in this context. “Lagged around” is also not idiomatic.

D because the preposition from does not pair logically with the verb lagged. The phrase “lagged from” is also not idiomatic.

Question 18. The best answer is G because placing Sentence 3 before Sentence 2 presents events in a logical, chronological order. For example, Sentence 3, which describes Mills as having a qualifying time that was one minute slower than the world record holder’s, explains Sentence 2’s assertion that Mills was a “long shot.”

The best answer is NOT:

F because the information about the qualifying times of the runners is interrupted by the result of the Olympic race itself. The sentences create an unnecessary shift in time and are out of chronological order.

H because placing Sentence 2 before Sentence 1 presents a statement that purposefully contrasts with the information that Mills was a “long shot” before the essay has even established that Mills was unlikely to win. The transition word however would be unexplained if Sentence 2 were to start the paragraph.

J because this order places the information about Mills winning the gold medal before information about Mills qualifying for the race. Also, this order does not clearly establish up front who Mills is and what race is being discussed.

Question 19. The best answer is A because it correctly places commas around the appositive “an Oglala Lakota,” which further identifies Mills.

The best answer is NOT:

B because commas are needed to separate the subject of the sentence, Mills, from the appositive, which further identifies the subject (“an Oglala Lakota”).

C because it does not correctly set off the appositive “an Oglala Lakota” from the rest of the sentence.

D because it does not correctly set off the appositive “an Oglala Lakota” from the rest of the sentence.

Question 20. The best answer is H because it follows logically from the information given about Mills’s desire to be a boxer and transitions to information that follows about Mills pursuing running.

The best answer is NOT:

F because despite extending the idea from the previous sentence, it does not transition to the next paragraph in the essay, which describes Mills’s accomplishments as a runner.

G because despite extending the idea from the previous sentence, it does not transition to the next paragraph in the essay, which describes Mills’s accomplishments as a runner. This choice also says that Mills did not make it as a boxer but leaves the reader wondering why.

J because it gives the reader more information about the various sports Mills tried, which doesn’t connect with the information about boxing and running in the paragraph. It also doesn’t connect well with the information in the next paragraph about Mills as a runner.

Question 21. The best answer is C because it clearly establishes that while in the Marines, Mills, rather than his talent, began racing again.

The best answer is NOT:

A because the phrase “races became part of his life again” is a misplaced modifier. This construction indicates that it’s the races that are in the Marines, not Mills.

B because the phrase “his talent raced back to him” is a misplaced modifier. In this construction, it’s Mills’s talent that is in the Marines, which is illogical. Also, the idea that Mill’s talent raced back to him is an awkward use of personification that’s inconsistent with the tone of the rest of the essay.

D because the phrase “racing was in his life again” is a misplaced modifier. In this construction, it’s racing that is in the Marines, which is illogical.

Question 22. The best answer is H because it refers directly to the 1964 Olympics, the time and place that were established in the first paragraph. It also refers to Mills’s training before the Olympics, which effectively introduces the paragraph’s focus on Mills’s preparations.

The best answer is NOT:

F because it is vague and therefore a weak introduction to the paragraph. It also doesn’t reference the topic of the first paragraph.

G because although it hints at Mills’s success after the Olympics, it does not effectively introduce the paragraph, which focuses on Mills’s preparations and the fact that Mills was a long shot.

J because it is vague and therefore a weak introduction. It also doesn’t reference the topic of the first paragraph.

Question 23. The best answer is A because in the phrase “rather unknown,” rather indicates that at least some people knew of Mills’s talent before the 1964 Olympics.

The best answer is NOT:

B because the word rather in the sentence qualifies unknown by indicating that at least some people knew Mills was talented. Removing rather indicates Mills was completely unknown, but it does not lose a description of the approach Mills used to motivate himself.

C because removing the word rather in the sentence and stating that Mills was entirely unknown does not explain why Mills decided to run in the Olympics. The sentence merely states that Mills was determined to win after qualifying.

D because there is no indication in the sentence that Mills required more training because he was unknown or “rather unknown.”

Question 24. The best answer is H because the word undeterred indicates that Mills did not allow the fact that the Olympic shoe sponsor did not send him shoes to prevent him from racing. Mills borrowed shoes so he can compete.

The best answer is NOT:

F because the word luckily implies that it was simple chance that Mills was able to borrow a pair of shoes, not that it was the result of Mills’s commitment to winning.

G because the word eventually implies that at a later time Mills was able to borrow a pair of shoes. No indication of the role of commitment is indicated here. The word eventually is an indication of when, not how.

J because the word concentrating here is vague. The reader doesn’t know if Mills is concentrating on the race or on borrowing the shoes. There is no suggestion of commitment on Mills’s part to borrowing the shoes, merely the suggestion that he is concentrating on an unknown objective.

Question 25. The best answer is D because adding the sentence would interrupt the transition between Mills being ready to hit the starting line and the description of the actual race in the following paragraph.

The best answer is NOT:

A because the sentence adds information about only one gold medalist in the 1964 Olympics. Also, this statement is only tangentially related to the topic of the essay and interrupts the transition between Mills being ready to hit the starting line and the description of the actual race in the following paragraph.

B because the sentence is only tangentially related to the topic of the essay and interrupts the transition between Mills being ready to hit the starting line and the actual race described in the following paragraph.

C because it implies that the essay is focused on the US track team. The essay is focused only on one member of the US track team, Mills. Furthermore, only two US runners’ shoes are mentioned, not the shoes of all the members as implied in this choice.

Question 26. The best answer is J because it is clear from the context of the essay that the people mentioned in the sentence are in first place and second place at the start of the last lap. Referring to Gammoudi and Clarke as leaders is the most logical, idiomatic choice given the sentence.

The best answer is NOT:

F because an overseer is one who has authority over others. It is clear from the context of the essay that the people mentioned in the sentence are on their last lap of a race. Therefore, they are runners in the race and not overseers who have authority over the other racers.

G because a ruler is one who has authority over others. It is clear from the context of the essay that the people mentioned in the sentence are on their last lap of a race. Therefore, they are runners in the race and not rulers who have authority over the other racers.

H because it is clear from the context of the essay that the people mentioned in the sentence are on their last lap of a race. Therefore, they are runners in the race rather than authorities who may be outside of the race itself.

Question 27. The best answer is A because “who had been in third place” is a clause that adds nonessential information to the main idea of the sentence. Interrupters or nonessential clauses are set off with commas.

The best answer is NOT:

B because two commas are needed to set off a nonessential clause from the rest of the sentence.

C because two commas are needed to set off a nonessential clause from the main sentence. Using one comma creates confusion here because it looks as if Mills is being directly addressed, and there is no antecedent for the pronoun who.

D because “who had been in third place” is nonessential information. It is a nonessential clause that needs to be set apart from the main idea of the sentence.

Question 28. The best answer is F because the use of the auxiliary verb had requires the use of the participle run.

The best answer is NOT:

G because the use of the auxiliary verb has requires the use of the participle run, not the past tense ran. The present has also is not appropriate here in the context. The race was completed.

H because the race is completed, requiring the use of the past tense. Using present tense here shifts the verb tense in the paragraph from past to present and creates an illogical sequence of time.

J because the use of the auxiliary verb had requires the use of the participle run, not the past tense ran.

Question 29. The best answer is C because it has already been stated that Mills won the race, beating Gammoudi and Clarke, in the same paragraph as the underlined portion. The information is not needed for emphasis and is therefore unnecessarily repetitious.

The best answer is NOT:

A because who Mills finished ahead of is not mentioned in the opening paragraph of the essay. Therefore, the underlined portion does not connect in a meaningful way to the opening paragraph of the essay.

B because it has already been stated that Mills won (and therefore beat the former leaders in the race). It merely repeats the fact unnecessarily, without adding additional details.

D because the information is repetitious and not needed, not because it strays from the main point.

Passage III

Question 30. The best answer is H because placing a period after the word unfolds separates the two independent clauses into two complete sentences.

The best answer is NOT:

F because placing a comma after the word unfolds creates a comma splice between two independent clauses.

G because placing a comma after the word boy indicates that the movie scene unfolds a boy, which doesn’t make sense. It also could be read that the scene, not the boy, is out exploring.

J because a semicolon or a period is needed to separate the independent clauses. Without punctuation, the sentence becomes a run-on, and the logic of the sentence is hard to follow.

Question 31. The best answer is D because the sentence clearly introduces information about what draws an audience into a movie scene, which sets up the examples in the next sentence and introduces the topic of the essay.

The best answer is NOT:

A because the pronoun that has no clear antecedent, and the expression does not work logically with the rest of the sentence.

B because the expression “for the time being” provides a vague sense of how long the audience might be drawn into a scene by sound, but this information is irrelevant to the rest of the sentence and the essay.

C because nevertheless indicates that the information provided in this sentence contrasts with information provided earlier in the essay. This sentence does not, however, provide a contrast; it introduces new information about what draws audience members into scenes like this.

Question 32. The best answer is F because the verb swept implies that the action was swift and dramatic.

The best answer is NOT:

G because it suggests that silent movies had a gradual exit. Talkies “invited the beginning of what would one day . . .” implies that the transition from silent movies occurred over time, not swiftly or dramatically.

H because it does not mention silent movies or the role that talkies played in their demise.

J because it does not mention silent movies or the role that talkies played in their demise.

Question 33. The best answer is C because the pronoun who correctly functions as the subject of the verb figured (who refers to the predicate noun Foley).

The best answer is NOT:

A because whom functions as the object of a verb or a preposition (the person or thing that receives the action of the verb). Because the action “figured out” in this sentence is done by Foley, not to Foley, the subject pronoun who is required, not the objective pronoun whom.

B because whom functions as the object of a verb or a preposition (the person or thing that receives the action of the verb). Because the action “figured out” in this sentence is done by Foley, not to Foley, the subject pronoun who is required, not the objective pronoun whom. The reflexive pronoun himself becomes part of the noun that who refers to (Foley himself).

D because the pronoun he creates a run-on sentence (two independent clauses are joined without punctuation).

Question 34. The best answer is H because it completes the sentence by clearly and grammatically connecting the act of squeezing a sock of cornstarch with its result (“produces a sound like that of footsteps in the snow”).

The best answer is NOT:

F because the phrase “a sound like that of . . .” dangles in the sentence, seeming to describe cornstarch as the sound of footsteps in the snow. The sentence is also incomplete; it doesn’t state what Foley figured out about squeezing a bag full of cornstarch.

G because the comma after cornstarch and the pronoun which indicates that “which makes a sound like that of footsteps in the snow” is an appositive that describes cornstarch itself, not the act of squeezing a sock full of cornstarch. This results in an incomplete sentence.

J because although “to get” connects the phrase “a sound like that of footsteps in the snow” to the act of squeezing a sock full of cornstarch, the sentence as constructed does not represent a complete thought. (What did Foley figure out about squeezing a sock full of cornstarch to get a sound like walking in the snow?)

Question 35. The best answer is C because an illusion is perceiving something in a way that misinterprets the thing’s true nature. Foley is misleading the audience into perceiving the sound of the cane as many people walking.

The best answer is NOT:

A because an allusion is a reference to a historical event in literature or a reference to something in passing. Foley is not creating a reference to history here or a reference to something in passing. The context of the sentence indicates that Foley wants to create the impression that people are walking on foot.

B because elude means to evade. Foley is using a cane to create the impression that people are walking on foot, not to avoid people on foot.

D because an allusion is a reference to a historical event in literature or a reference to something in passing. Foley is not creating a reference to history here or a reference to something in passing. The context of the sentence indicates that Foley wants to create the impression that people are walking on foot.

Question 36. The best answer is J because it results in a clear, logical sentence. Eventually functions as an adverb modifying the verb earned. This indicates when Foley earned the status of Hollywood legend.

The best answer is NOT:

F because the use of the word that in the underlined portion creates an incomplete sentence that lacks a clear subject and verb.

G because it creates an incoherent sentence that lacks a clear subject and verb. It is also unnecessarily wordy.

H because it creates an incoherent sentence that lacks a clear subject and a clear connection between the subject and verb. The phrase “that eventually even so” is also vague and unnecessarily wordy.

Question 37. The best answer is D because ending the sentence with information about Foley’s status as a “Hollywood legend” creates a logical transition to the next paragraph, which further explains the process Foley pioneered.

The best answer is NOT:

A because this information is not directly related to the discussion of Foley’s contributions, and it unnecessarily states a fact that has already been clearly established (movies with sound had not been around for long).

B because it unnecessarily repeats information provided earlier about how Foley used a cane as a prop.

C because the fact that sound editing takes place after the action has been filmed has already been explained in the first sentence of the paragraph, “sounds are recorded after the cameras have stopped rolling.”

Question 38. The best answer is F because “arises from” means to originate from a source or to begin to occur or exist. The Foley process was created in response to the need for absolute quiet when capturing dialogue. (Foley artists add in the “sound clutter of real life” later.)

The best answer is NOT:

G because “aroused from” means to evoke or awaken. “The need for ‘Foley’” was not evoked or awakened by the sound clutter of real life; the need didn’t even exist until sound was introduced in movies.

H because without the preposition from, the sentence suggests that Foley was the source of the “sound clutter of real life,” which is illogical.

J because the singular subject “The need for ‘Foley’” requires the singular verb arises. The form arise is used with plural words. The sentence is also lacking the preposition from between arise and “the sound.”

Question 39. The best answer is D because the underlined portion draws a distinction between a Foley artist and a sound artist. This reduces the chance that a reader will assume that the terms “sound technician” and “Foley artist” refer to the same role.

The best answer is NOT:

A because the underlined portion indicates that there is a distinction between a Foley artist and a sound artist without explaining the role of either occupation.

B because the underlined portion indicates that there is a distinction between a Foley artist and a sound artist without explaining the origin of the term “Foley artist.” The origin of the term is explained in the first sentence of the second paragraph of the essay.

C because the underlined portion indicates that there is a distinction between a Foley artist and a sound artist without indicating the degree to which a sound technician is influenced by the work of John Foley.

Question 40. The best answer is J because it continues the subject-verb pattern established in the paragraph: “An airplane flying, a phone ringing, a door slamming.”

The best answer is NOT:

F because it breaks the subject-verb pattern established in the paragraph. Only a subject is provided: “An airplane flying, a phone ringing, a door ___________?”

G because the clause, “which is not part of the scene,” is wordy and unnecessary. This choice also breaks the subject-verb pattern by using the word slamming as an adjective, not a verb.

H because it breaks the subject-verb pattern established in the paragraph. Only a subject is provided: “An airplane flying, a phone ringing, a sound of a door.”

Question 41. The best answer is B because it uses two dashes to correctly set off a nonessential phrase.

The best answer is NOT:

A because it incorrectly sets off a nonessential phrase with a colon and a dash.

C because it incorrectly sets off a nonessential phrase with a comma and a dash.

D because the phrase “a small room with a screen, a microphone, and countless props” interrupts the main clause in the sentence and must be set off with a pair of commas or dashes.

Question 42. The best answer is F because untold means too many to count or measure. Here, the amount of money being saved is emphasized. It is so much that the actual amount is unknown.

The best answer is NOT:

G because the sentence implies that the movie’s budget was cut drastically, which was positive. The word unspeakable suggests that the cut was something negative, which is illogical given the context of the essay.

H because it adds an illogical personification to the essay. To describe the money itself as speechless implies that at other times the money spoke.

J because the movie’s budget was cut by thousands of dollars, a limited sum. Endless implies that the amount that was cut from the movie was infinite.

Question 43. The best answer is C because “an army’s worth” is nonessential and therefore needs to be set off with commas. The commas clarify that “an army’s worth” refers to the actors and horses.

The best answer is NOT:

A because “an army’s worth” is nonessential and needs to be set off with punctuation. Without punctuation, it’s difficult to determine who would be headed overseas.

B because it results in a comma splice between two independent clauses.

D because “an army’s worth” is nonessential and needs to be set off with punctuation. Without punctuation, the sentence is ungrammatical and illogical.

Question 44. The best answer is G because the sentence emphasizes how Foley’s work impacted on both the filmmakers and the audience. It reveals that the actors and horses were able to stay home rather than embark on an expensive journey and that the audience didn’t know the difference between the actual sounds of a battlefield and the sounds created using Foley’s techniques.

The best answer is NOT:

F because the sentence does not indicate that the audience ever learned about Foley’s work.

H because the sentence does not mention the movie’s director; therefore, there’s no shift in focus from Foley to the director.

J because the sentence does not argue that his work was insignificant to the public; it just states the audience wasn’t aware that the sounds were not the actual sounds of a battlefield.

Passage IV

Question 45. The best answer is C because the comma after the word University correctly separates the introductory clause “in her lab at Princeton University” from the sentence’s main clause.

The best answer is NOT:

A because if the description “molecular biologist” is treated as nonessential and set aside by commas, it is unclear whether it describes Princeton University or Bonnie Bassler.

B because it incorrectly separates with a comma the subject “Bonnie Bassler” from the verb leans.

D because a comma is needed after the word University in order to separate the introductory clause “in her lab at Princeton University” from the sentence’s main clause.

Question 46. The best answer is J because it correctly uses a comma to separate the main idea of the sentence from an aside that provides additional details.

The best answer is NOT:

F because a semicolon is used to combine two independent clauses. “Her face illuminated by an aquamarine glow” is not an independent clause.

G because the coordinating conjunction and must be preceded by a comma in order to correctly join the two independent clauses.

H because the comma between dishes and “her face” must be followed by a coordinating conjunction such as and in order to avoid a comma splice.

Question 47. The best answer is C because the comma after bacteria paired with the comma after glow accurately signals that the nonessential phrase “caused by a particular species of bacteria” describes “the glow.”

The best answer is NOT:

A because the prepositional phrase “of bacteria” modifies the word species. Prepositional phrases cannot be separated from what they modify by a comma.

B because the prepositional phrase “of bacteria” is essential to the meaning of the sentence and should not be set aside with commas, nor should “of bacteria” be separated from the noun it modifies, species.

D because a comma is needed after bacteria in order to enclose the entire nonessential phrase “caused by a particular species of bacteria” in commas, signaling that this phrase describes “the glow.”

Question 48. The best answer is H because it correctly uses the plural possessive form of researcher, resulting in a sentence that is both understandable and grammatical.

The best answer is NOT:

F because the text “and their discoveries” requires the noun researchers to be nonpossessive. As worded, this sentence describes Bassler as being intrigued not only with the researchers’ inventions but also with the researchers themselves.

G because the wording in this option requires researcher to be nonpossessive. Also, the singular possessive form researcher’s does not agree in number with the plural pronoun their.

J because as worded, the sentence requires a possessive form of researcher. Note that the words “and their,” found in two of the other choices, have been removed. The sentence now states that Bassler was intrigued only by the researchers’ discoveries, not by the researchers themselves. Only a possessive form of researcher in this context would be grammatical.

Question 49. The best answer is C because the phrase “a luminescent marine bacteria” is an appositive renaming Vibrio fischeri. This phrase is nonessential and must be set off with a comma.

The best answer is NOT:

A because it incorrectly uses a semicolon to separate the main part of an independent clause from an appositive phrase. A semicolon is used to join independent clauses.

B because the phrase that follows “a luminescent marine bacteria” is nonessential to the sentence and must be set off with a comma. The words “which is” are also unnecessarily wordy.

D because the phrase “a luminescent marine bacteria” is an appositive renaming Vibrio fischeri. This phrase is nonessential and must be set off with a comma.

Question 50. The best answer is J because the present tense allows is consistent with the use of the present tense in this paragraph.

The best answer is NOT:

F because it shifts the established verb tense in the paragraph from present to past. The sentence uses present tense verbs to describe the actions of the bacteria: they assemble, begin, and release. The use of the past tense allowed here would create an illogical pattern, with one step in the process of glowing inexplicably happening in the past.

G because the use of the past conditional tense in this series of present tense descriptions suggests an essential step in the glowing may or may not have occurred in the past. The bacteria must, however, hear the message to release a high concentration of autoinducer.

H because the shift from the present to the present perfect tense results in an ambiguous, confusing sequence of events.

Question 51. The best answer is A because a comma is needed to separate the dependent clause from the independent clause in the sentence.

The best answer is NOT:

B because dashes are used to indicate an abrupt break in thought. There is not an abrupt change in thought between the dependent clause and the independent clause in this sentence; the clauses express a sequence of events that are closely related.

C because it creates a sentence fragment. The words “once the bacteria have released a high enough concentration of autoinducer” create a dependent clause that must be attached to an independent clause to make a complete sentence.

D because it creates a run-on sentence by not using a comma between the dependent clause that begins the sentence and the independent clause that follows.

Question 52. The best answer is G because it logically indicates that after some time, Bassler discovered a similar process of glowing occurring in a related species of bacteria.

The best answer is NOT:

F because “On the contrary” signals a contrast. There is no contrast between the discovery of the process of glowing in one species of bacteria and the discovery of a similar process in another species of bacteria.

H because the fact that Bassler made an important scientific discovery suggests that this is a significant event. Ordinarily suggests that the discovery was common and ongoing. This ongoing discovery does not work with the simple past tense verb found, which indicates that the discovery was a one-time event.

J because the word namely is used to introduce a specific example of or specific, detailed information about something that has already been discussed. Bassler’s discovery of the process of glowing in another species of bacteria has not yet been mentioned in the essay; therefore, the use of this transition word is not logical.

Question 53. The best answer is A because the words “related bacterial species” in the underlined portion are essential to the meaning of the sentence and should not be set off by commas.

The best answer is NOT:

B because the words related and bacterial are not coordinating adjectives. A comma between the words indicates they are coordinating and can be reversed without affecting the meaning, but if these two words were reversed the sentence would not make sense. Also, the words “bacterial species” are essential to the sentence and should not be set off by commas.

C because the words related and bacterial are not coordinating adjectives. The order of the words cannot be reversed, and a comma between the words would incorrectly indicate that they can be.

D because no comma is needed between the word called and Vibrio harveyi. In this case, there is no need for a comma between a verb and its object.

Question 54. The best answer is J because it conveys that bacteria can communicate with other bacteria nearby. This choice is not repetitive and does not create an odd or informal image of bacteria within the paragraph.

The best answer is NOT:

F because it is overly informal for the academic tone of the essay.

G because it is unnecessarily repetitive. Both neighboring and proximity mean “nearby.”

H because it is unnecessarily repetitive. Locale means “in the area.” To say “surrounding locale” is to repeat the concept of “in the area.”

Question 55. The best answer is D because them is an object pronoun, a pronoun that refers to a person or thing that receives the action of a verb. A demonstrative pronoun, a pronoun that points to a specific thing, is needed in this part of the sentence to refer back to the word species.

The best answer is NOT:

A because “the kinds” refers back to the bacteria that live in humans.

B because species clearly refers to a type of bacteria that live in humans.

C because those has a clear antecedent in the sentence: species.

Question 56. The best answer is F because the verb form communicate correctly agrees with the plural subject “virulent strains” in the sentence.

The best answer is NOT:

G because has is a singular verb, which does not agree with the plural subject “virulent strains.”

H because in this sentence is is a singular verb, which does not agree with the plural subject “virulent strains.”

J because in this sentence communicates is a singular verb, which does not agree with the plural subject “virulent strains.”

Question 57. The best answer is D because the words “these bacteria” help the reader understand that the bacteria in the preceding sentence are the bacteria being discussed in this sentence. “These bacteria” also establishes the subject without being redundant.

The best answer is NOT:

A because it unnecessarily repeats the idea that the bacteria are “disease spreading.” The reader has already been told that the bacteria are virulent, and this idea is further established later in this sentence with “spreading disease.”

B because it has already been established in the paragraph and in the essay that Bassler has studied the bacteria. To repeat the idea here is unnecessary and redundant.

C because it has already been established at the end of the preceding sentence that the bacteria are found in humans. To repeat the idea here is unnecessary and redundant.

Question 58. The best answer is G because it correctly uses the object pronoun her as the object of the verb enable. The words “her team” also clearly refer to the other scientists with whom Bassler is working.

The best answer is NOT:

F because an object pronoun is required to receive the action of the verb enable. The pronoun she functions as a subject, not an object.

H because herself is a reflexive pronoun, which is ungrammatical in this sentence. The context calls for an object pronoun (her). Also, the pronoun them has no clear antecedent.

J because the pronoun them has no clear antecedent.

Question 59. The best answer is B because the information would clearly communicate why Bassler and her team study bacteria and what they hope the result of disrupting quorum sensing will be for humans.

The best answer is NOT:

A because the paragraph has already clearly established that Bassler is working to understand “bacteria found in humans.” The proposed information would not serve this function.

C because it is not important to the meaning of the sentence for the reader to know which particular strains of the bacteria attack humans’ immune systems.

D because the focus of the essay was on Bassler’s discovery of the fact that bacteria in humans use quorum processing, not on how Bassler and her team plan to disrupt that processing. This information would be an inappropriate conclusion because it would require more explanation.

Passage V

Question 60. The best answer is G because subterranean refers to something below the surface of the earth, and routes refers to different lines the subway system runs. This is a logical and precise choice of words given the context.

The best answer is NOT:

F because it suggests the subway is creeping beneath the ground, which doesn’t make sense on either a literal or a metaphorical level. The word vicinity, meaning “nearby,” is also an odd word choice; the system doesn’t exist nearby but within the city limits.

H because the word submerged typically refers to something pushed below the surface of water. The London subway is not located entirely beneath water, nor does the passage suggest that it is. This description introduces an inaccuracy.

J because the subway is described in the essay as being below the city streets, rather than in alleys that are “low down,” which is a vague and confusing description.

Question 61. The best answer is D because the essay begins by establishing that a system of mapping was needed after the subway system was built. It follows logically that the next sentence would be about the early mapping system, so no transition word is needed.

The best answer is NOT:

A because the words “as a result” are not logical here. Building the subway did not require the early maps to “superimpose the subway lines over standard maps of London.” This is just the technique these maps happened to use.

B because the information that this word introduces is not one example of many different types of early maps that were developed; it is the only type that the passage discusses. Therefore, “to provide an example” is incorrect.

C because secondly indicates that what follows is the second event, idea, or step in a process or series. However, the information provided in the paragraph is not framed as a series (there is no firstly). The transition word secondly creates a logical inconsistency.

Question 62. The best answer is H because indecipherable indicates that the maps were not able to be read at all, suggesting the highest degree of failure for a map—it was unusable.

The best answer is NOT:

F because obscured suggests that the routes were difficult, but not impossible, to read. It does not eliminate the possibility that the map could be read and used by subway riders.

G because disappointing does not suggest the “highest degree of failure.” It indicates that the maps did not live up to expectations but does not say they were not able to serve their function.

J because “didn’t fully capture” the subway indicates that the maps at least partially captured the routes.

Question 63. The best answer is C because this information is only tangentially related to the information in the paragraph. The focus of the first paragraph is on the method of mapping the subway that was devised in the 1800s. Details about the modern subway system distract from the focus on these early maps.

The best answer is NOT:

A because providing details about the modern subway is not essential information in a paragraph that focuses on early subway mapping systems. Adding the sentence would also interrupt the transition from a discussion of the first attempts to map the subway to the discussion of a later (more effective) method of mapping.

B because the modern name of the subway does not suggest the need for a clear, accurate map. Such a map already exists, according to the essay (thanks to Beck).

D because the first paragraph does not focus on recent maps of the London Underground; it is about the mapping of the Underground in the 1800s.

Question 64. The best answer is G because the stylistic outline is being compared to the sketch. The construction “more . . . than” works syntactically and creates a clear, precise comparison.

The best answer is NOT:

F because besides means “other than” or “in addition to,” neither of which makes sense within the sentence. The “more a” at the beginning of the sentence does not connect logically with besides.

H because instead creates a sentence with faulty syntax. The construction “more . . . instead” does suggest a comparison, but the preposition of would be needed after instead to avoid faulty sentence structure. A “more . . . than” construction captures the main idea more precisely.

J because into here suggests a transformation from one thing to another. The words “more . . . than” at the beginning of the sentence signal that the sentence will make a comparison, not describe a transformation.

Question 65. The best answer is C because the beginning of the sentence contains an introductory phrase that requires a comma between it and the main part of the sentence.

The best answer is NOT:

A because the phrase before the semicolon lacks a verb and therefore is not an independent clause. Semicolons are used to separate independent clauses; a semicolon is not needed and is incorrect.

B because the conjunction and suggests that two ideas are being coordinated. Here, there is no coordination between two independent clauses. The beginning of the sentence is an introductory phrase that sets up a comparison to follow.

D because it creates a fragment by placing a period after the introductory phrase that begins the sentence. This phrase lacks a verb and cannot be an independent clause.

Question 66. The best answer is J because it correctly combines the two adjective phrases “grid-like structure” and “color-coded routes” with the conjunction and, making it clear that these were both features of Beck’s map.

The best answer is NOT:

F because it creates an ambiguity that makes the meaning of the sentence unclear: Did the map have a color-coded route, or was it the grid-like structures that had a color-coded route? In the context of the sentence, the phrase “having also” creates a faulty construction.

G because it creates an ambiguity that makes the meaning of the sentence unclear: Did the map have a color-coded route, or was it the grid-like structures that had a color-coded route? It also creates a structurally faulty sentence.

H because it creates an ambiguity that makes the meaning of the sentence unclear: Did the map have a color-coded route, or was it the grid-like structures that had a color-coded route? It also creates a structurally faulty sentence.

Question 67. The best answer is A because “to show” makes the first clause in this sentence a dependent introductory clause, which creates a sentence with grammatically appropriate subordination.

The best answer is NOT:

B because “would show” creates a comma splice by making the introductory phrase at the beginning of the sentence an independent clause.

C because “had shown” creates a comma splice by transforming an introductory phrase into an independent clause.

D because showed creates a comma splice by making the introductory phrase at the beginning of the sentence an independent clause.

Question 68. The best answer is F because it provides a specific example of how Beck simplified the map by deleting the references to the city streets that had obscured some of the Underground routes.

The best answer is NOT:

G because it merely indicates Beck’s annoyance at the curving lines on the map. It does not provide an example of how Beck simplified the existing maps for subway passengers.

H because it indicates that Beck knew the maps had to be simple, but it does not give an example of how Beck created his “simplest possible schema.”

J because it indicates the map’s iconic status, but it does not provide an example of the map’s simple schema.

Question 69. The best answer is B because to increase means to become larger or greater in size, amount, or number. This is the correct word given the context, because it’s the number of riders (ridership) the Transport Board hoped to increase.

The best answer is NOT:

A because rise is an intransitive verb that means to move upward. The subway ridership itself would not literally move upward; rather, the number of riders would increase.

C because enlarge means to increase in size rather than number. The subway ridership would not increase in physical size; rather, the number of riders would increase.

D because upend means to cause something to be upside down or to fall down. The number of subway riders is increasing; the group is not being turned upside down or caused to fall down.

Question 70. The best answer is G because “the board” makes it clear that it was the Transport Board that was desperate to increase subway ridership and revenues.

The best answer is NOT:

F because as written, the sentence indicates it was the limited number of copies that were “willing to try anything to increase subway ridership and therefore revenues.” The sentence fails to name “the board” as the group that is printing the copies, which makes this misreading possible.

H because as written, the sentence indicates it was the copies that were “willing to try anything to increase subway ridership and therefore revenues.” The sentence fails to name “the board” as the group that is printing the copies, which makes this misreading possible.

J because as written, the sentence indicates it was the copies that were “willing to try anything to increase subway ridership and therefore revenues.” The sentence fails to name “the board” as the group that is printing the copies, which makes this misreading possible. In addition, the lack of a verb in this phrase creates a sentence fragment.

Question 71. The best answer is B because Sentence 1 discusses the fact that the Transport Board initially resisted the map, and Sentence 5 explains why the board resisted the map. This is a logical way to present this information and provides a smooth transition to the rest of the paragraph.

The best answer is NOT:

A because Sentence 5, which explains why the Transport Board resisted Beck’s map, is out of place in the middle of a discussion about the map’s success.

C because placing Sentence 5 after Sentence 2 breaks the logical progression from the board’s resistance to the map to the reasons for the resistance. This placement is also not logical because it mentions the creation of copies of the map before mention of the board’s initial resistance to the idea.

D because placing Sentence 5 after Sentence 3 breaks the logical progression from the board’s resistance to the map to the reasons for the resistance. This placement is also not logical because it explains the board’s resistance to the map after mentioning the later copying of the map and the map’s success.

Question 72. The best answer is H because its is a singular possessive pronoun referring to the word map. Because map is singular, the pronoun and antecedent agree in number. Also, a possessive is needed because the sentence is referring to the basic elements that are features of the map.

The best answer is NOT:

F because it’s is a contraction for “it is.” Saying that “he retained it is basic elements” creates a nonsensical, ungrammatical sentence. At this point, the sentence also requires a possessive pronoun to refer back to the map. The contraction it’s is not possessive.

G because their is a plural possessive pronoun. The antecedent of the pronoun in the sentence is map, which is singular. A pronoun and its antecedent must agree in number.

J because its’ is not the correct possessive form of it. The correct possessive for it is its, without an apostrophe.

Question 73. The best answer is C because a comma should not separate any of the elements in the noun phrase “approach to mapping,” nor should there be a comma between the noun phrase and the verb remains.

The best answer is NOT:

A because a comma should not separate the noun phrase “approach to mapping” from the verb remains.

B because a comma should not separate the adjective diagrammatic from the noun phrase “approach to mapping.” The comma separating this phrase from the verb remains is also incorrect.

D because the comma separates the prepositional phrase “to mapping” from the noun approach, which incorrectly breaks up the noun phrase that serves as the subject of the sentence: “[Beck’s] approach to mapping.”

Question 74. The best answer is J because it clearly and concisely identifies Beck’s mapping method as what other urban transit maps model. This also works as a suitable conclusion for the sentence and the essay because it is a fitting description of Beck’s approach as described in the essay.

The best answer is NOT:

F because the use of the pronoun this creates an ambiguous pronoun reference. This could refer to the approach, to the field of information, to the map’s basic elements, to the world, and so on, which makes the meaning of the sentence unclear.

G because “this means” creates an ambiguous pronoun reference. This option is also redundant because it has already been stated that Beck’s approach is “standard in the field.”

H because this option is redundant; it has already been stated that Beck’s approach is “deceptively simple.”

Question 75. The best answer is B because it places the added sentence, which explains why Beck left out the actual distances between points, immediately after the sentence that reveals Beck left out the distances. This creates a logical progression from Beck’s decision to the reasoning behind his decision.

The best answer is NOT:

A because Point A occurs during a discussion of early versions of subway maps. The added sentence refers to Beck’s maps, which have not been introduced yet. The sentence does not make sense without the information about Beck and his mapping that are provided in Paragraph 2.

C because the sentence immediately before Point C refers to the refinements that Beck made to his map after it had already become a success. The essay makes it clear that even Beck’s first maps left out actual distances; therefore, leaving out the distances was not a refinement but part of the original diagram. The added sentence does not logically fit at Point C because this placement suggests Beck’s reasons for not including the distances are related to later refinements to the map.

D because the sentence immediately before Point D discusses how Beck’s approach to mapping has been widely adopted. The added sentence, however, explains a specific statement made about the map’s features in Paragraph 2. This placement for the added sentence not only puts the sentence too far away from the point it is meant to explain but also it interferes with the last paragraph’s attempt to describe the broader impact Beck’s map has had on the world.

MATHEMATICS • PRACTICE TEST 3 • EXPLANATORY ANSWERS

Question 1. The correct answer is C. The area of a rectangle is equal to the product of its width and length, A = WL. Because the top surface of the rectangular table has an area of 100 square feet and a width of 5 feet, 100 = 5 L and 20 = L. If you chose E, you may have set up the equation incorrectly and calculated the area for a length of 100 feet and a width of 5 feet.

Question 2. The correct answer is J. The number of possible outcomes (that is, the total number of bills in the wallet) is 2 + 9 + 5 = 16, and the number of favorable outcomes (choosing a twenty-dollar bill) is 5. The probability of a favorable outcome is equal to . So, the probability of a twenty-dollar bill being randomly selected from the wallet is . If you chose F, you could have overlooked how many possible favorable outcomes there are.

Question 3. The correct answer is E. In order to determine how many combinations of clown costumes Elmo can make, multiply the number of items in each category that makes up a complete costume (noses, pairs of lips, and wigs), 4 · 3 · 2 = 24. If you chose B, you may have added the number of items Elmo has in each category to find the total number of items rather than the number of combinations of items that make a complete costume.

Question 4. The correct answer is F. The remaining materials for care packages are 30 pens (3 boxes with 10 pens each, 3 · 10 = 30), which can fill 6 care packages at 5 pens each (); 20 notebooks (4 boxes with 5 notebooks each, 4 · 5 = 20), which can fill 10 care packages at 2 notebooks each (); 24 envelopes (2 boxes with 12 envelopes each, 2 · 12 = 24), which can fill 8 care packages at 3 envelopes each (); 84 cookies, which can fill 7 care packages at 12 cookies each (); and 45 bars of candy (4.5 boxes with 10 candy bars each, 4.5 · 10 = 45), which can fill 9 care packages at 5 candy bars each (). Because the remaining pens can create the least number of care packages, 6, that is the additional number of complete care packages Esteban and his family can make with the remaining materials. If you chose J, you may have failed to realize that every care package must be complete.

Question 5. The correct answer is C. A right circular cone with a height of 28 inches and a radius of 6 inches would have an approximate volume of 1,056 cubic inches: .

Question 6. The correct answer is G. Because is perpendicular to , the measure of is . The measure of is because the sum of the measures of the angles in a triangle is , and . Because and create a straight line, the measure of is because .

Question 7. The correct answer is B. The sum of the two expressions can be found algebraically by combining like terms, (0.1x² + 3x + 80) + (0.5x² – 2x + 60) = (0.1x² + 0.5x²) + (3x – 2x) + (80 + 60) = 0.6x² + x + 140. If you chose A, you may have calculated the difference of the expressions.

Question 8. The correct answer is H. The slope-intercept form, y = mx + b where m is the slope and b is the y-intercept, can be used to write the equation of a line that represents the relationship between y and x. The slope of the line that represents the relationship between d and t is the rate at which the cart is rolling, which is . When you substitute the value of the slope into the slope-intercept form and use d and t in place of y and x, you get d = 3t + b. To determine b, the d-intercept of the line, substitute a given ordered pair in the table for d and t in the equation and solve for b. . Therefore the equation that represents the relationship between d and t is d = 3t + 15. If you chose J, you could have mixed up the values of the slope and d-intercept in the equation.

Question 9. The correct answer is C. The original price of the pants was $40 but Dmitry bought them at the discounted price of $30 which is $10 less than the original price because $40 – $30 = $10. The percent of the discount is of the original price. If you chose E, you could have calculated the percent the discounted price is of the original price.

Question 10. The correct answer is G. The absolute value of a number is its magnitude. The magnitude of –6 is 6 and the magnitude of (7 – 41) is 34. Therefore, |–6| – |7 – 41| = 6 – 34 = –28. If you chose J, you may have added 6 and 34.

Question 11. The correct answer is C. The total number of shares of stock owned by Samantha, Nyla, and Jerry is . The value of each single share of stock is per share. Therefore, the value of the shares of stock that Samantha owns is . If you chose A, you may have divided the combined value of the shares of stock by the number of shares of stock owned by Samantha only and rounded to the nearest dollar: . If you chose B, you may have erroneously computed . If you chose D, you may have thought the value of the shares of stock that Samantha owns is of the combined value of the shares of stock or . If you chose E, you may divided the combined value of the shares of stock by the number of shares of stock owned by Nyla and Jerry and then multiplied by the value of the shares of stock that Samantha owns: .

Question 12. The correct answer is G. Customers who are at least 18 years of age are represented on the number line by a closed dot on 18 to indicate 18 is part of the solution and shading of the number line to the right of 18. Customers who are less than 30 years of age are represented on the number line by an open dot on 30 to indicate 30 is NOT part of the solution and shading of the number line to the left of 30. As a result, the number line that illustrates the required age range of at least 18 but less than 30 years of age has a line segment with a closed dot on18, shading between 18 and 30, and an open dot on 30. If you chose F, you chose the number line that represents customers who were between 18 and 30 years of age, inclusive. If you chose H, you chose the number line that represents customers who were 30 years of age or younger. If you chose J, you chose the number line that represents customers who were younger than 30 years of age. If you chose K, you chose the number line that represents customers who were younger than 18 years of age or older than 30 years of age.

Question 13. The correct answer is D. The Triangle Proportionality Theorem states that if a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally. Therefore, because , then . Similarly, because , then . Thus, . If you chose B, you may have found the sum of EG and GC only: . If you chose A, you may have multiplied the sum of EG and GC by : . If you chose E, you may have multiplied the sum of EG and GC by : . If you chose C, you may have added AE, DF and FB: .

Question 14. The correct answer is G. First, set up an inequality with the closest perfect square integer values below and above the integer 50: Next, take the square root of all three parts: . Finally, divide all three parts by 2: . Now, is greater than 3.5 and less than 4, which makes 4 the closest integer to . If you chose F, you may have used 36 as the closest perfect square integer value below 50 and neglected to find the closest perfect square integer value above 50: . Similarly, if you chose H, you may have used 100 as the closest perfect square integer value above 50 and neglected to find the closest perfect square integer value below 50: . If you chose K, you may have found that and then doubled the value on the left.

Question 15. The correct answer is D. Let x represent a factor of the sum of Jane’s age and her daughter’s age. Then, we have . Therefore, Jane’s age is . If you chose A, you may have multiplied 4 by the average of the 9 and . If you chose B, you may have subtracted 9 and 2 from the sum of their ages: . If you chose C, you may have subtracted 9 from the sum of their ages: . If you chose E, you may have subtracted 4 from the sum of their ages:.

Question 16. The correct answer is H. First, we compute the fraction of the operating budget that is allocated to library books and scholarships. This is the sum of the fractions for each allocation: . To compute the fraction of the operating budget that remains for other uses, we subtract the previous sum from the whole of the operating budget: . If you chose F, you may have subtracted the fraction of the operating budget that is allocated to library books from the fraction of the operating budget that is allocated to scholarships. If you chose G, you selected the fraction of the operating budget that is allocated to library books and scholarships only. If you chose K, you selected the fraction of the operating budget that is NOT allocated to library books.

Question 17. The correct answer is A. The second fraction in the proportion may be simplified to , so that we have . We may use the multiplication property of equality to solve the proportion. We multiply both sides of the equation by the product

Next, we solve the resulting linear equation for .

If you chose B, you may have subtracted the numerator of the second fraction from the denominator of the second fraction. If you chose C, you selected the value of , which is . If you chose D, you may have subtracted the numerator of the second fraction from the denominator of the second fraction and then added . If you chose E, you selected the value of x for which the denominator of the first fraction will be equal to the denominator of the second fraction. However, .

Question 18. The correct answer is J. The total area of the 2 shaded triangles can be found by subtracting the area of the unshaded triangle from the area of the rectangle. The area of the rectangle is square inches. The area of the unshaded triangle is square inches. Thus, the total area of the 2 shaded triangles is square inches. If you chose F, you may have thought that the total area of the 2 shaded triangles is the area of the unshaded triangle. If you chose H, you may have subtracted 2 times the area of the larger shaded triangle from the area of the rectangle: . If you chose K, you may have found the area of the rectangle only.

Question 19. The correct answer is C. We need to find the ordered pair that satisfies all three of the inequalities in the given system. Therefore, the x-coordinate of the ordered pair must be greater than 2, the y-coordinate of the ordered pair must be greater than 0, and the sum of the x-coordinate and the y-coordinate of the ordered pair must be less than 5. The only ordered pair that satisfies all three of the inequalities is (3,1). If you chose A, you may have chosen (1,3) because it satisfies the second and third inequalities; however, it does not satisfy the first inequality. Similarly, if you chose B, you may have chosen (2,2) because it satisfies the second and third inequalities; however, it does not satisfy the first inequality. If you chose D, you may have chosen (3,2) because it satisfies the first and second inequalities; however, it does not satisfy the third inequality. If you chose E, you may have chosen (4,0) because it satisfies the first and third inequalities; however, it does not satisfy the second inequality.

Question 20. The correct answer is H. For real numbers b and c, the range of any sine function of the form is . Thus, the range of the function is . It follows that will have y-values such that . Thus, the range of is . If you chose F, you may have ignored the 3 in the given function and instead found the range of the function . If you chose G, you may have computed the range as . If you chose J, you may have thought was the range of the function and then found the range of the function to be .

Question 21. The correct answer is D. In the composition first replace each x found in , the inside function, with the input −3. Next, replace each x found in with the value . First of all, , so . Accordingly, , so . If you chose A, you may have thought and attempted to compute : , and so . If you chose B, you may have thought , so that , and If you chose C, you may have attempted to compute . However, you may have dropped the constant from the function , so that . In addition, you may have thought , so that . Then . If you chose E, you may have found , and so .

Question 22. The correct answer is G. We may set up a system of two equations in two variables to model the dollar amounts that Joan and Chris each paid for the fabrics. Let x be the price, in dollars, of 1 yard of flannel fabric. Let y be the price, in dollars, of 1 yard of calico fabric. Then we have . To solve this system, multiply the second equation by −3, and add it to the first equation. .

Then, solve for y: . The price, in dollars, of 1 yard of calico fabric is $4. If you chose F, you may have solved the system for x, the price, in dollars, of 1 yard of flannel fabric. If you chose H, you may have divided the total number of yards of fabric bought by Joan and Chris in half: . If you chose J, you may have divided the sum of the dollar amounts that Joan and Chris each paid by the total number of yards of calico fabric bought: . If you chose K, you may have found how much more Joan paid and then divided it by how much more calico fabric she bought: .

Question 23. The correct answer is C. To find the median of a data set, arrange the data values in order from least to greatest. The median is the value separating the upper half of the data from the lower half. When a data set has an odd number of values, the median is the exact middle value. When a data set has an even number of values, there are two middlemost values. Average them to find the median. In order from least to greatest, the scores in this data set are . The two middlemost scores are 86 and 88, which makes the key . If you chose A, you may have found the mean of the ten scores: . If you chose B, you selected the average of the mean and the median: . If you chose D, you may have chosen the least of the two middlemost scores of the unordered ten scores: . If you chose E, you may have found the mean of the two middlemost scores of the unordered ten scores: .

Question 24. The correct answer is H. Opposite sides of a parallelogram are congruent. Thus, the side of the parallelogram that measures 16 inches has a side opposite to it that also measures 16 inches. It follows that the sum of the measures of the parallelogram’s remaining two sides is equal to inches. Therefore, each of the two sides must measure inches. If you chose F, you may have subtracted the given side from the perimeter and then selected three side lengths whose sum was the value of that difference: and . However, sides of length and 36 inches do not form a parallelogram. If you chose G, you have selected a parallelogram with a perimeter of inches. If you chose J, you may have subtracted the given side from the perimeter before dividing by 2: . However, the perimeter of the parallelogram would then be inches.

Question 25. The correct answer is E. First, note that the shaded region is also a rectangle and that each of its dimensions is a fraction of the corresponding dimension of rectangle ABCD. Now, let the area of rectangle ABCD be given by , where L is the length and W is the width. Each row in rectangle ABCD has 6 squares, and each row in the shaded region has 5 squares. Thus, the length of the shaded region is . Each column in rectangle ABCD has 4 squares, and each column in the shaded region has 3 squares. Thus, the width of the shaded region is . It follows that the area, in square units, of the shaded region is . If you chose A, you may have computed the area of a single small square only, neglecting the fact that there are 5 small squares in a row and 3 small squares in a column. If you chose B, you may have first computed the area of a single small square and also noticed that there are 3 small squares in a column, but you neglected the fact that there are 5 small squares in a row. If you chose C, you may have found that the length of the shaded rectangle is the length of rectangle ABCD. As a result, you may have multiplied this fraction by the length of a single small square. If you chose D, you may have first computed the area of a single small square and also noticed that there are 5 small squares in a row, but you neglected the fact that there are 3 small squares in a column.

Question 26. The correct answer is G. We can set up a proportion where each side represents the probability of randomly drawing a red marble; that is, . Let x be the number of additional red marbles added to the 42 marbles. It follows that . We can use the multiplication property of equality to solve the proportion. We multiply both sides of the equation by the product . Next, we solve the resulting linear equation for x: . If you chose F, you may have computed and rounded up. If you chose K, you may have solved the proportion , rounded the solution up to the nearest integer, and added to 42.

Question 27. The correct answer is E. Negative exponents signify multiplicative inverses and thus are the reciprocal of positive exponents. This means that a base raised to a negative exponent is equivalent to 1 divided by the base raised to the positive of the exponent. Therefore, . If you chose A, you may have multiplied the exponent by the base. If you chose D, you may have used the reciprocal of the positive of the exponent in the denominator: .

Question 28. The correct answer is F. Jamie’s claim is a conditional statement in the form of a hypothesis followed by a conclusion. The hypothesis of Jamie’s claim is “a triangle is in set A,” and the conclusion of the claim is “it is not isosceles.” Now, the only way for a conditional statement to be false is for the hypothesis to be true and the conclusion to be false. Because is a counterexample that proves Jamie’s claim is false, it must be true that is a triangle in set A and that is isosceles. If you chose G, you selected the statement for which the hypothesis is true and the conclusion is true. If you chose H, you neglected the fact that obtuse triangles may be isosceles or scalene, so you selected the statement for which the hypothesis is false and the conclusion may be true or false. If you chose J, you selected the statement for which the hypothesis is false and the conclusion is true. If you chose K, you selected the statement for which the hypothesis is false and the conclusion is false.

Question 29. The correct answer is D. The area of a parallelogram is given by the formula where b is the base and h is the height of the parallelogram. Side is a base of parallelogram ABCD, and the height of parallelogram ABCD is equal to the distance between and . Therefore, the area, in square coordinate units, of parallelogram ABCD is given by . If you chose B, you may have used the formula for the area of a triangle: . If you chose E, you may have used the formula for the perimeter of a square: .

Question 30. The correct answer is H. To find the distance between two points and , we can use the distance formula, . It follows that the distance between B(0,4) and D(4,1) is given y coordinate units. If you chose F, you may have switched the plus and minus signs in the distance formula: . If you chose J, you may have incorrectly computed the distance as .

Question 31. The correct answer is A. To find the slope of a line containing two points and , use the slope formula . Line contains the points B(0,4) and C(5,4). It follows that the slope of is given by . If you chose B, you may have computed the difference in the x-coordinate and y-coordinate of point C(5,4): . If you chose D, you may have computed the difference in the x-coordinates of B(0,4) and C(5,4): . If you chose E, you may have computed the slope as .

Question 32. The correct answer is J. When we reflect a point over the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (its sign is changed). Therefore, the coordinates of the image of A(−1,1) after reflection over the y-axis are (1,1). If you chose F, you selected the image of point D(4,1) after reflection over the y-axis. If you chose G, you selected the image of point A(−1,1) after reflection over the x-axis, where the x-coordinate remains the same, but the y-coordinate is transformed into its opposite. If you chose H, you selected the image of point A(−1,1) after reflection over the origin (0,0), where both the x- and y-coordinates are transformed into their opposites. If you chose K, you selected the image of point D(4,1) after reflection over the x-axis.

Question 33. The correct answer is A. First, rewrite the product so that each factor has the same base: . Next, apply the power rule for exponents, , to each factor. Therefore, we have . Finally, apply the product rule for exponents, , to combine the 2 factors. Thus, we have . If you chose B, you may have rewritten the base of the first factor as and then incorrectly applied the power rule for exponents: . If you chose C, you may have used the greater of the bases together with the sum of the exponents: . If you chose D, you may have simplified the second factor and then multiplied it by the base of the first factor: . If you chose E, you may have multiplied the bases and multiplied the exponents: .

Question 34. The correct answer is K. The school admissions office accepts 2 of every 7 applicants. That means that 5 of every 7 applicants are NOT accepted. Let x be the number of applicants that were not accepted. We may set up a proportion where each side represents the ratio . It follows that . We may use the multiplication property of equality to solve the proportion. We multiply both sides of the equation by the product : . Then, we solve the linear equation for x: . If you chose F, you may have divided the total number of applicants into parts and then computed . If you chose G, you may have solved the proportion . If you chose H, you may have divided the total number of applicants into 9 parts and then computed . If you chose J, you may have doubled the number of applicants that were accepted: .

Question 35. The correct answer is B. First, note that by the properties of exponents, . Next, note that because the functions and are inverse functions, then . It follows that . If you chose A, you may have simplified the radical but then incorrectly applied the product property of logarithms:. If you chose C, you may have simplified the radical but then incorrectly applied the inverse property,, and thought that . If you chose E, you may have dropped the square root when simplifying: .

Question 36. The correct answer is F. In a circle graph, each different sector represents a proportion of a total. Moreover, the measure of each central angle of a circle graph is proportional to the quantity it represents. Because there are 360° in a circle, Jie must represent each part of the data as a proportion of 360. First, we note that apples, bananas, and strawberries were each chosen as favorites by an equal number of the remaining students. Thus, bananas were chosen as the favorite fruit of students out of the 90 students in the survey. It follows that Jie will represent bananas on the circle graph as a sector with a central angle that measures . If you chose G, you may have thought the central angle in the circle for the 15 students who chose peaches represented 15% and computed . If you chose H, you may have thought the central angle in the circle for the 15 students who chose peaches was and computed . If you chose J, you may have thought the central angle in the circle for the 15 students who chose peaches was and computed . If you chose K, you may have thought the central angle in the circle for the 15 students who chose peaches measured 15° and computed .

Question 37. The correct answer is E. The denominators of the two fractions are unlike. We may rewrite each fraction with a new denominator that is equal to the least common multiple of their denominators: 5x. We do this by multiplying each of the two fractions by additional fractions that are equivalent to 1. Then we may finally add the numerators of the rewritten fractions. Thus, we have . If you chose A, you may have placed the sum of the numerators over the product of the denominators: . If you chose B, you may have placed the product of the numerators over the product of the denominators: . If you chose C, you may have added the numerators and added the denominators: . If you chose D, you may have multiplied the numerator and denominator of each fraction and put the sum over the sum of the denominators: .

Question 38. The correct answer is K. The total number of nonstudent residents who replied to the survey was . The number of nonstudent residents who replied that they disapproved of the change in hours was 353. Thus, of the nonstudent residents replied that they disapproved of the change in hours. If you chose F, you selected the fraction of college students who replied that they disapproved: . If you chose G, you selected the fraction of high school students who replied that they disapproved: . If you chose H, you selected the fraction of high school and college students who replied that they disapproved: . If you chose J, you selected the fraction for which the denominator is the total number of residents who replied with disapproval, including high school and college students, and not the total number of nonstudent residents: .

Question 39. The correct answer is D. The total number of college student and nonstudent residents who replied either approve or disapprove is residents. This is the total number of residents who were NOT high school students and did NOT reply with no opinion. It follows that the probability that the person chosen will NOT be a high school student and will NOT have replied with no opinion is . If you chose A, you may have computed the probability that the person chosen will be a high school student who replied either approve or disapprove: . If you chose B, you may have computed the probability that the person chosen will be a college student or a nonstudent who replied with no opinion: . If you chose C, you may have attempted to compute the probability that the person chosen will be a nonstudent who replied approve. However, you may have divided by the total number of residents who replied either approve or with no opinion: . If you chose E, you may have computed the probability that the person chosen will NOT be a high school student who replied with no opinion: .

Question 40. The correct answer is H. Of the 15 incorrectly classified residents, some are college students who approved, and some are high school students who approved. We may first set up a linear equation involving the 60% of the college students who approved. Let x be the number of incorrectly classified college students who approved. We know that there are 14 correctly classified college students who approved. Thus, , or . Now we solve for x. We distribute on the right-hand side to get . Next we subtract the constant term 14 from both sides: . Then we subtract the variable term 0.60x from both sides: . After dividing, we have college students. This means that the remaining 5 incorrectly classified residents are high school students. Finally, the percent of high school students who replied that they approved is , or 70%. If you chose F, you may have used the table values to find 60% of the total number of college students: . Next, you may have computed , or 60%. If you chose G, you may have used the table values to find the percentage of high school students who replied that they approved: , or 67%. If you chose J, you may have used the table values and added 15 to the total number of high school students who replied that they approved: , or 75%. If you chose K, you may have used the table values to find the percentage of high school students who replied that they approved and then added 15%. Thus, , and so .

Question 41. The correct answer is A. Let Set A be the set of where . Set B is then where . The mean of Set A is , and the mean of Set B is . Because , . Thus, the mean of Set B is greater than the mean of Set A. The median of both Set A and Set B is c; thus B, D, and E are not correct answers. Set A and Set B each consists of 5 distinct numbers, so there is no mode for either set. This means that C and E are not correct answers.

Question 42. The correct answer is G. Because the function is an odd function, . For example, , and . Thus, , so G is the correct answer. It is true that , so F is not the correct answer. By the cofunction identity, , so H is not the correct answer. If you picked J, you might not have remembered . Because the function is even, . This means that Thus, J is not the correct answer. If you chose K, you might have forgotten the identity, Solving for gives . Because , . Thus, , so K is not the correct answer.

Question 43. The correct answer is D. The smallest square that will fit a circle with a diameter of 8 inches is a square with side lengths 8 inches. The box will thus have a base that is a square with side length 8 inches. Because the height of the box is 3 inches, the volume is 3(8²), or 192 cubic inches. If you selected A, you might have multiplied the side length of the base by the height of the box, 3(8), instead of multiplying the area of the base by the height of the box. If you selected B, you might have found the area of the base, instead of the volume of the box. If you selected C, you might have confused the height of the box with the side length of the base and found 8(3²) instead of 3(8²). If you selected E, you might have found the volume of a cube with side length 8.

Question 44. The correct answer is G. Draw diagonal . Triangle is a right triangle with and , so . Because , , and is a right triangle with right angle D. The tangent of an angle in a right triangle, is the ratio of the lengths of the side opposite the angle and the side adjacent to the angle. Thus,

tan A is . If you chose F, you might have found . If you chose H, you might have found . If you chose J, you might have found . If you chose K, you might have found .

Question 45. The correct answer is D. There are 7 days in a week. Because , 196 days ago it was Tuesday. This means that 197 days ago was a Monday, 198 days ago was a Sunday, 199 days ago was a Saturday, and 200 days ago was a Friday. If you picked an answer other than D, you might have not realized that the remainder when 200 is divided by 7 is equal to 4, or you might not have known to count back 4 days from Tuesday.

Question 46. The correct answer is G. Because and are vertical angles, they are congruent. This means that . Substituting back into the equation tells us . Because line m is perpendicular to line n, . Because , . If you selected F, you might have thought that and were supplementary and found the value of x in the equation . If you selected H, you might have estimated from the diagram that was slightly less than but didn’t know how to calculate the value exactly. If you selected J, you might have thought that line q bisected the angle, making and congruent. If you selected K, you might have found the value of x in the equation . You might have thought that and then found the angle complementary to 36°: .

Question 47. The correct answer is E. Because and , the greatest common factor (GCF) of 30 and 40 is 2(5) = 10, and the least common multiple (LCM) is . If you selected A, you may not have realized that the GCF of 6 and 20 is 2 and the LCM is 60. If you selected B, you may not have realized that the GCF of 10 and 12 is 2 and the LCM is 60. If you selected C, you may not have realized that the LCM of 10 and 20 is 20. If you selected D, you may not have realized that the GCF of 20 and 60 is 20 and the LCM is 60.

Question 48. The correct answer is H. Because all the sides are different lengths, the triangle is scalene. Because the length of the longest side squared is greater than the sum of the squares of the lengths of the other two sides (), the triangle is obtuse. If you selected F, you may not have known that in an acute triangle, the length of the longest side squared is less than the sum of the squares of the lengths of the other two sides: . If you selected G, you may not have known that in a right triangle, the length of the hypotenuse squared is equal to the sum of the squares of the lengths of the other two sides: . If you selected J or K, you may not have known that an isosceles triangle has at least two congruent sides.

Question 49. The correct answer is D. Because the team has a 60% chance of winning on Saturday, the probability that they will lose on Saturday is . Because the team has a 35% chance of winning on Sunday, the probability that they will lose on Sunday is . The probability of them losing both games is thus or 26%. If you selected A, you may have found the probability that they will lose on Saturday but win on Sunday: . If you selected B, you may have found the probability that they will win both games: . If you selected C, you may have found the difference between the given probabilities: . If you selected E, you may have found the probability that they will win on Saturday but lose on Sunday: .

Question 50. The correct answer is J. The domain of a rational function, like f, excludes any x-values that make the denominator 0. This includes both removable points of discontinuity (holes) and nonremovable points of discontinuity (vertical asymptotes). Solving gives us solutions and . The domain of f is thus . If you selected F, you might not have known that removable points of discontinuity (like 3 for f) are also domain restrictions. If you selected G, you might have incorrectly factored and then found only the nonremovable points of discontinuity for the incorrect function: . If you selected H, you might not have known that nonremovable points of discontinuity (like −1 for f) are also domain restrictions. If you selected K, you might have incorrectly simplified f by canceling the 3s: . You might have then found the domain restrictions of the incorrect function.

Question 51. The correct answer is E. The first three numbers are set and do NOT affect the number of possible phone numbers. The choices for possible phone numbers have the form 555-XXXX. We note that each X in a phone number may be any of the 10 digits allowed (0 through 9). Therefore, we have possible phone numbers. If you chose C, you selected the case where each of the first three digits of a phone number has 5 choices:. If you chose D, you may not have included 0 in the number of digits allowed:. If you chose A, you selected the case where only 1 of the first 3 digits of a phone number has 5 choices, or or , and each of the last 4 digits of the phone number has 9 choices, . Thus, .

Question 52. The correct answer is F. A circle is the set of all points whose distance from the center is equal to the radius. Therefore, the measure of the radius of the given circle is equal to the distance between the center, (1,3) and the given point on the circle,(4,7). The distance between any two points and is given by . It follows that the radius of the given circle has a measure of coordinate units. Thus, the given circle is the set of all points that are 5 coordinate units from the center (1,3). If you chose G, you selected the intersection of circles with radii of 5 coordinate units centered at (1,3) and (4,7). If you chose H, you selected the parallel line segments above and below the line segment from (1,3) to (4,7). If you chose J, you selected the perpendicular bisector of the line segment with endpoints (1,3) and (4,7). If you chose K, you selected the closed region composed of a rectangle whose endpoints are capped off with semicircles. The length of the rectangle is formed by two parallel line segments above and below the line segment from (1,3) to (4,7), and the two semicircles are centered at each of the endpoints (1,3) and (4,7).

Question 53. The correct answer is B. To find the x-coordinate of the point of intersection of the two graphs, we set the right-hand side of the two equations equal to each other and solve for x. First, we have . Next, we subtract 3 from both sides to get . Now, we note that the exponent property of logarithms states that . It follows from this property that if we have , then we will have . Thus, . If you chose A, you may have dropped the ln and solved the equation . If you chose C, you may have moved the exponent down from the expression and to the front as multiplication:. If you chose D, you may have incorrectly thought and attempted to solve using this erroneous property: .

Question 54. The correct answer is F. The three machines copy at the same rate. Thus, as long as they are running together, the number of copies will increase at the same rate, r. When a machine breaks down the rate is reduced by . A rate will correspond to the slope of a line segment on the graph of n versus t. There will be 5 connected line segments on the graph due to the machine break downs. From 8:00 a.m. to 10:00 a.m., the first line segment has slope r. From 10:00 a.m. to 12:00 p.m., the breakdown of Machine A makes the second line segment have slope . From 12:00 p.m. to 1:00 p.m., the intersection of the breakdowns of Machines A and B makes the third line segment have slope . From 1:00 p.m. to 3:00 p.m., the breakdown of Machine B makes the fourthline segment have slope . Finally, from 3:00 p.m. to 5:00 p.m., the slope of the fifth line segment is r. The graph that matches these conditions has the first and fifth line segments with equal and greatest incline, followed by the second and fourth line segments with equal slope, and last, by the third line segment with the least incline. If you chose G, you selected the graph for which the number of copies will increase at the greatest rate between 12:00 p.m. and 1:00 p.m.; however, the breakdowns of Machines A and B during this time frame make this impossible. If you chose H, you selected the graph for which there are only three connected line segments, which does not match the scenario. If you chose K, you selected the graph for which the number of copies will increase at the same rate.

Question 55. The correct answer is E. Let p be the number of $1 decreases in the price of the caps. If , there are 40 caps sold per week. For each $1 decrease in p, 4 more caps are sold. It follows that the number of caps sold for 1 week will be . Moreover, the price per cap for 1 week will be . Now, from the given note we know that the revenue, R, for 1 week is . After multiplying the two binomials, we have , which is a quadratic function in terms of p. Therefore, the maximum value of R will occur at the vertex. For a given quadratic function , the vertex is found by computing and then evaluating y at to find the maximum value. It follows that for , . Then, evaluating at , we find that . If you chose A, you may have thought the maximum revenue equals the given number of caps sold times the given price per cap: . If you chose C, you may have thought the maximum revenue equals 4 more than the given number of caps sold times $1 less than the given price per cap: . If you chose D, you may have thought the maximum revenue equals 8 more than the given number of caps sold times $2 less than the given price per cap: .

Question 56. The correct answer is K. First, we may write the linear inequality in slope-intercept form . From the condition , we know that the boundary line has a negative slope,. Moreover, we know that the boundary line has a y-intercept,, located on the positive y-axis. Finally, indicates that all the (x,y) coordinates on the boundary line and in the half-pane below the boundary line satisfy the inequality. If you chose F, you have selected a graph that has a boundary line with a positive slope. If you chose G, you have selected a graph that has (x,y) coordinates in the half-plane above the boundary line for which the inequality is NOT true. If you chose H or J, you have selected a graph that has a boundary line with a y-intercept located on the negative y-axis.

Question 57. The correct answer is A. First, we note that to make the 500 banners, the club needed to purchase a minimum of yards of blue material and a minimum of yards of white material. Next, we note that each 10-yard bolt of blue material can be used to make banners, and each 12-yard bolt of white material can be used to make banners. Moreover, is the closest multiple of 10 that is greater than 125, and is the closest multiple of 12 that is greater than . It follows that the club purchased 130 yards of blue material and 192 yards of white material. The 130 yards of blue material could make banners, and the 192 yards of white material could make banners. Therefore, the club was able to make a total of banners, which included 12 extra banners. If you chose B, you may have divided the 130 yards of blue material by the number of yards in a bolt of blue material:. If you chose C, you may have divided the total number of yards of each material that was purchased by the sum of the yards of material needed to make each banner:. If you chose D, you may have divided the 192 yards of white material by the number of yards in a bolt of white material:. If you chose E, you may have calculated the overage from the blue material only: banners with 20 extra banners possible.

Question 58. The correct answer is F. We note that to find the expanded form of , we may use the cube of a binomial formula:. There are four terms in the result. The exponents of a decrease in each term, while the exponents of b increase in each term. The middle terms contain a factor of 3, and the second and fourth terms are negative. For the case of , we have . Now, for the imaginary number . It follows that . If you chose G, you may have computed for the last term:. If you chose J, you have selected the expression where the middle terms do NOT contain a factor of 3. If you chose K, you have selected the expression where the two middle terms are missing.

Question 59. The correct answer is D. First, we note that the graph rises to the left and rises to the right, or , and . Thus, the degree of the function is even, and the leading coefficient is positive. The graph of the function has zeros located at ,, and . These correspond to the polynomial factors x, and . Next, we find the multiplicity of each zero, that is, how many times a particular number is a zero for a given polynomial function. We note that the sign of does NOT change from one side of to the other side because the graph touches the x-axis at 0 and turns around. This means that a zero of even multiplicity occurs at . We also note that the sign of changes from one side of to the other side and the sign of changes from one side of to the other side. That is, the graph crosses the x-axis at −4 and 6. This means that the zero at and the zero at are of odd multiplicity. Therefore, the only function that satisfies all the above conditions is . If you chose A, you have selected a function with an odd degree. If you chose B or C, you have selected a function that has zeros located at ,, and . If you chose E, you have selected a function that has a zero of odd multiplicity at and a zero of even multiplicity at .

Question 60. The correct answer is K. We can only multiply two matrices if the number of columns in the first matrix is the same as the number of rows in the second matrix. Matrix A has n columns, and Matrix C has k rows. Therefore, the matrix product AC is NOT possible. If you chose F, Matrix E has m columns, and Matrix D has m rows, so the matrix product ED is possible. If you chose G, Matrix D has k columns, and Matrix C has k rows, so the matrix product DC is possible. If you chose H, Matrix C has n columns, and Matrix E has n rows, so the matrix product CE is possible. If you chose J, Matrix A has n columns, and Matrix E has n rows, so the matrix product AE is possible.

READING • PRACTICE TEST 3 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is B because lines 21–22 clearly state why the blond woman is traveling to Palm Beach: “she’s taking the bus to see” a man who “left for a construction job” there.

The best answer is NOT:

A because the passage does not address why the character “you” is leaving Memphis.

C because the blond woman turns away from the character “you” at the end of the passage, so there is no indication of what she is thinking.

D because the passage does not address where the blond woman is from originally.

Question 2. The best answer is H because lines 22–25 state that the man in Palm Beach thinks the blond woman’s eyes are “as blue as” the Atlantic Ocean, and he cannot bear to look at “the thing” (the Atlantic Ocean) one more time if the blond woman isn’t there with him.

The best answer is NOT:

F because the man in Palm Beach works in a construction job; it is not the thing he cannot bear to look at.

G because the blond woman’s blue eyes are mentioned as a point of comparison with the Atlantic Ocean; they are not the thing the man in Palm Beach cannot bear to look at.

J because a bus is the setting where the scene in the passage takes place; it is not the thing the man in Palm Beach cannot bear to look at.

Question 3. The best answer is D because the word occasional is modifying home, not porch lights or fireflies. The “you” character is watching homes as the bus moves along, and those homes are not close together.

The best answer is NOT:

A because Lines 34–35 state that the porch lights are “perched, fat and throbbing” outside every home.

B because Lines 34–35 state that the porch lights are “perched, fat and throbbing” outside every home.

C because firefly porch lights are described; actual fireflies are not mentioned.

Question 4. The best answer is F because the girl does not acknowledge the narrator in any way.

The best answer is NOT:

G because the girl never speaks.

H because the passage provides no indication of how the girl perceives the narrator or whether she even notices his presence on the train.

J because the girl does not express any reaction to the narrator’s presence.

Question 5. The best answer is B because lines 88–89 reveal that the narrator had been in a dark frame of mind before he watched the girl toss the oranges to her brothers, so when he wants her to fail at opening the window, he is feeling “unspeakable fatigue” with his “tedious life.”

The best answer is NOT:

A because the passage never suggests that the girl is helpless or has an uncertain future; she struggles with the window but eventually opens it.

C because the narrator doesn’t notice the boys until after the window is open.

D because the train conductor is not around when the girl attempts to open the window.

Question 6. The best answer is F because lines 84–85 indicate that the girl needed to open the window to toss oranges “to her younger brothers as a token of gratitude.”

The best answer is NOT:

G because there is no evidence in the passage that suggests the girl had to prove anything.

H because the girl never acknowledges the narrator, so there is no support for her needing to create space between the two of them.

J because there is no evidence in the passage that suggests the girl feels a need to freshen the air in the train.

Question 7. The best answer is C because lines 44–46 state that the narrator heard the conductor cursing and the “clattering of dry-weather clogs” coming from the ticket gate. These sounds and the direction from which they emanate provide strong cues that someone is about to board the train at the last minute.

The best answer is NOT:

A because the passage does not reference the screech of the train’s brakes.

B because the passage does not reference the rustle of paper parcels.

D because the young girl in the passage does not shout.

Question 8. The best answer is J because the situation described in both passages involves an encounter between two characters traveling in close quarters. In both passages, the encounter has a strong impact on the main character, whose state of mind is shifted by the second character’s words or actions.

The best answer is NOT:

F because only Passage A uses the second person point of view.

G because the time period in which these passages are set is never clearly indicated.

H because there is no dialogue in Passage B.

Question 9. The best answer is D because the only character in either passage who shows interest in having a conversation is the blond woman in Passage A. The first paragraph in Passage A clearly shows that the “you” character does not want to talk, and neither character in Passage B shows any interest in conversing.

The best answer is NOT:

A because the “you” character’s actions in lines 5–11 (pulling lips tight, staring at the floor, motioning to an open novel) are all clear indications that this character has no interest in communicating with the blond woman.

B because the girl is intent on opening the window and shows no interest in communicating with the narrator.

C because lines 52–59 reveal that the narrator is repelled by the girl and even attempts to “blot her existence.”

Question 10. The best answer is F because in Passage A, the “you” character describes the blond woman as having teased hair and “sad, neglected teeth” (lines 13–14). In Passage B, the narrator describes the girl as having “lusterless hair”; chapped, red cheeks; and “a grimy woolen scarf” (lines 52–56).

The best answer is NOT:

G because Passage A does not suggest that the blond woman delayed the bus’s departure.

H because when the “you” character in Passage A and the narrator of Passage B first see the blond woman and the young girl, respectively, neither knows the reason the other character is traveling.

J because both the “you” character in Passage A and the narrator of Passage B use disparaging language to describe the blond woman and the young girl, respectively. There is no evidence in either passage to support the idea that the blond woman and the young girl are envied or that life seems easy to them.

Passage II

Question 11. The best answer is D because lines 3–5 make it clear that Stevenson “turned his back on the Victorian idol, progress,” and instead steered toward the “rougher fringes.” The phrase “skirts of civilization” in lines 69–70 conveys the same idea: Stevenson preferred the gas lamp over any “technological miracle of the future” (line 62).

The best answer is NOT:

A because the phrase “fire of adventure” describes the theme of Stevenson’s novels, which is not directly related to his reluctance to embrace progress.

B because the phrase “an epic ocean voyage” refers to a literal sea journey; it is not synonymous with the “rougher fringes” of civilization.

C because the phrase “a glittering hieroglyph” refers to electric lights, which represent progress, something Stevenson objects to.

Question 12. The best answer is F because lines 48–60 describe the places the author visited in order to gather information about Stevenson.

The best answer is NOT:

G because there is no evidence in the passage to suggest that Stevenson’s novels contain biographical information about Stevenson.

H because the passage contains no evidence to support the idea that the author worked for D. & T. Stevenson, Engineers.

J because where the author “comes from” is not addressed in the passage.

Question 13. The best answer is D because the paragraph’s focus is on Stevenson’s family; lines 14–15 state that Stevenson was “born into a Scottish family of civil engineers, esteemed for its technological genius.”

The best answer is NOT:

A because the paragraph never mentions that Stevenson’s grandfather insisted on anything.

B because Stevenson’s desire to be a writer is not mentioned in the second paragraph.

C because the paragraph does not include a comparison between Stevenson’s grandfather’s lighthouses and his father’s screens.

Question 14. The best answer is G because lines 60–64 capture the main idea of the fifth paragraph with the author’s description of Stevenson imagining a future London flashing with electric lights.

The best answer is NOT:

F because the paragraph does not mention the plot of any of Stevenson’s books.

H because the opposite is true: Stevenson preferred the gas lamps, which is evidenced by the statement “Not for him improvements in optics” (line 68).

J because the main focus of the paragraph is Stevenson’s prediction and not his father’s engineering feats.

Question 15. The best answer is C because line 50 (“he tried his hand at being an apprentice engineer”), lines 87–88 (“Stevenson . . . became a mariner himself”), and lines 6–8 (“his most popular novels . . .”) provide evidence that Stevenson was an engineer, a mariner, and a writer.

The best answer is NOT:

A because the passage provides evidence that Stevenson had also been an engineer and a mariner.

B because the passage provides no evidence that Stevenson was a lamplighter.

D because the passage provides no evidence that Stevenson was a builder.

Question 16. The best answer is H because the image of telephone wires in line 11 suggests progress, which Stevenson was not interested in; he preferred “the sound of clashing swords” (line 10), which, in the context of the paragraph, represents the opposite of progress.

The best answer is NOT:

F because lines 15–22 provide evidence that technological progress did, in fact, occur in Stevenson’s lifetime.

G because lines 1–3 provide evidence that, in fact, Stevenson preferred to avoid civilization’s “increasing reliance on contraptions.”

J because the passage provides no evidence that Stevenson was a sword fighter.

Question 17. The best answer is A because lines 23–25 state that Stevenson had been expected to join the family business. The phrase “a great wringing of hands” is used to describe the family’s implied dismay at Stevenson’s announcement that he would not, in fact, be following their expectations.

The best answer is NOT:

B because the passage provides no evidence that the family criticized Stevenson’s diet.

C because the passage provides no evidence that the family was humiliated; rather, they were greatly disappointed.

D because the family’s consternation in line 28 is presented as a possible result of the pleas Stevenson makes in his letters for his family to accept him as he is; it happens later, after the wringing of hands over Stevenson’s announcement about not joining the family business.

Question 18. The best answer is J because lines 35–36 provide a quote from Stevenson revealing that he preferred to travel without a set itinerary: “I travel not to go anywhere, but to go.” Lines 37–38 suggest that Stevenson found happiness in open-ended travel: “I travel for travel’s sake. The great affair is to move.”

The best answer is NOT:

F because Stevenson’s own words in lines 35–38 indicate that the destination was not important to him.

G because lines 34–35 indicate that Stevenson provided “the template for generations of college-educated adventurers”; they do not say that traveling should replace education.

H because the only mention of the character David Balfour is in line 52, and there is no indication that Stevenson’s travels were a model for Balfour.

Question 19. The best answer is A because the meaning of the idiomatic phrase “stumbled across” is “found by accident,” and this is the only option that logically fits the context of the sentence. The narrator found Abernethy House by accident.

The best answer is NOT:

B because the passage provides no evidence that the author staggered.

C because the passage provides no evidence that the author “unearthed” a building.

D because the passage provides no evidence that the author “tripped over” a building.

Question 20. The best answer is J because lines 83–85 directly state that “Thomas Stevenson’s name may not have been widely known,” but “his lights were in every part of the world.”

The best answer is NOT:

F because the passage provides no evidence that Robert Louis Stevenson and his father, Thomas, were estranged.

G because lines 15–20 explain how Thomas Stevenson’s father was “Britain’s greatest builder of lighthouses” and how Thomas “followed him into the profession.” Clearly, Thomas Stevenson would not have been unaware that his name would become associated with lighthouses.

H because the passage provides no evidence that Thomas was more famous than his son, Robert.

Passage III

Question 21. The best answer is B because lines 71–85 suggest that the author’s cultural intuition, which she acquired on her reservation, gives her the knowledge to know that “kivas are safe places” and not the “frightening places” described in Gerald McDermott’s book. In lines 71–72, the author directly states that she draws upon her cultural intuition when reading a book about Pueblo Indians.

The best answer is NOT:

A because the reference to Bruchac is about storytelling, not about the author’s cultural intuition.

C because the passage does not mention where the author has presented her research.

D because the passage provides no evidence that the author and Silko discussed anything.

Question 22. The best answer is G because lines 1–13 explain the value and functions of traditional stories: to pass “religious beliefs, customs, history, lifestyle, language, [and] values” from one generation to another and to transmit “an entire culture, a worldview complete with strategies for survival.”

The best answer is NOT:

F because there is no mention of stories changing as they are passed from one generation to the next.

H because the paragraph states that traditional stories include folktales, myths, and legends; these are not compared or contrasted.

J because there is no mention of a culture’s worldview changing over time.

Question 23. The best answer is D because lines 41–44 directly state that “in order for it to be acceptable . . . [the story] should remain true to the spirit and content of the original.”

The best answer is NOT:

A because lines 33–41 make it clear that it is acceptable for storytellers to add and change details in the stories they are telling.

B because lines 39–40 state that “a storyteller may revise a story according to his or her own interpretation.”

C because lines 35–38 suggest that it is acceptable for audience members to offer new details.

Question 24. The best answer is G because the author’s statement that her home pueblo is different from other pueblos (lines 67–69) precedes her discussion of McDermott’s book and provides support for her critique that his book fails to show the differences among the many pueblos in New Mexico (lines 74–78).

The best answer is NOT:

F because the culture and traditions of her home pueblo are not specifically described in the passage; rather, the author discusses the traditions of the Pueblo people as a whole.

H because the author never compares her tribe’s stories with the stories of other tribal nations.

J because the passage does not contain a list of criteria the author uses when evaluating books marketed as “Native American folktales.”

Question 25. The best answer is C because lines 86–88 clearly state that “depictions that are culturally acceptable at one Pueblo are not necessarily acceptable at a different Pueblo.” Elders take the cultural values of their specific community (or audience, line 92) into account when determining whether books are culturally acceptable for children of that community.

The best answer is NOT:

A because the passage does not address the entertainment value of books, comparatively or otherwise.

B because the passage does not address the popularity of books among tribal members.

D because elders are concerned with the appropriateness of books for their specific communities (lines 86–92); there is no mention of elders being concerned with the way books represent the worldviews of many groups.

Question 26. The best answer is H because lines 16–17 state that the hunting stories contain information “about the behavior and migration patterns of mule deer.”

The best answer is NOT:

F because Silko never mentions rescuing hunters from other tribes.

G because there is no mention of documenting the number of successful hunts.

J because Silko mentions locations of fresh water and lost piñon-nut gatherers, but she does not state that hunting stories help people find caches of food.

Question 27. The best answer is A because lines 65–67 directly state this: “As a scholar in American Indian studies, I know there are great distinctions between and across American Indian tribal nations.”

The best answer is NOT:

B because there is no evidence to suggest that the author and McDermott were friends.

C because there is no evidence to suggest that the author is an editor for picture books.

D because there is no evidence to suggest that the author is an elder.

Question 28. The best answer is G because in lines 66–67 the author is making the point that there are “great distinctions” between and across American Indian tribal nations. In this context, great is synonymous with significant.

The best answer is NOT:

F because excessive does not logically fit the context of the paragraph.

H because exuberant does not logically fit the context of the paragraph.

J because splendid does not logically fit the context of the paragraph.

Question 29. The best answer is D because lines 67–70 directly state that one of the differences among the pueblos in New Mexico is that “there are several different language groups.”

The best answer is NOT:

A because the Pueblo communities mentioned are all in New Mexico, so the geographic differences cannot be vast.

B because a disparity of resources is never discussed.

C because approaches to parenting are not discussed.

Question 30. The best answer is J because lines 84–85 directly state that the author knows kivas as “safe places of worship and instruction.”

The best answer is NOT:

F because the author says that for her, kivas are “safe places,” not places of fear and trial.

G because kivas are never described by the author as mysterious or exciting.

H because kivas are not mentioned in relation to rest or healing.

Passage IV

Question 31. The best answer is B because the passage begins with a discussion of “the spontaneous vegetation that dominates the neglected interstices” (lines 3–5), goes on to define weeds (lines 24–25), and then discusses how weeds “survive in derelict urban wastelands” and are “famous (or infamous) for their ability to grow under extremely harsh conditions” (lines 49–51).

The best answer is NOT:

A because the passage never presents an argument for eradicating weeds.

C because the passage is not a report, and it does not mention a need for more vegetation in urban environments.

D because the passage does not mention the work or opinions of environmentalists.

Question 32. The best answer is H because the author’s perspective throughout the passage best fits the biological one described in the second paragraph: “weeds are opportunistic plants that are adapted to disturbance” (lines 26–27). Support for this perspective is found in a number of places in the passage: “The plants that grow and survive in derelict urban wastelands are famous . . . for their ability to grow under extremely harsh conditions” (lines 49–51); a successful urban plant is “opportunistic in its ability to take advantage of locally abundant resources” (lines 73–75); urban plants are “tolerant of the stressful growing conditions” (line 76).

The best answer is NOT:

F because the idea that weeds grow in places where people don’t want them is only summarized; it is not developed enough to represent the author’s own perspective.

G because the problem of weeds in agriculture is only summarized; it is not developed enough to represent the author’s own perspective.

J because the city dweller’s notion that weeds are “perceived as ugly” or a potential security hazard is only summarized; it is not developed enough to represent the author’s own perspective.

Question 33. The best answer is B because based on lines 31–33, economic crops are agricultural plants, which compete with “spontaneous vegetation,” or weeds.

The best answer is NOT:

A because ragweed is a type of “spontaneous vegetation,” or weed.

C because urban plants are described as spontaneous plants in the first paragraph.

D because calcium-loving grasses are described as an example of urban weeds (lines 63–70).

Question 34. The best answer is G because lines 28–31 state that weed “pervasiveness in the urban environment is simply a reflection of the continual disruption that characterizes that habitat—they are not its cause.”

The best answer is NOT:

F because the process of removing weeds is not discussed in the passage.

H because there is no evidence in the passage to suggest that there is a pervasive acceptance of weeds in urban areas.

J because the passage does not provide a comparison of the life cycle of weeds with the life cycle of other plants.

Question 35. The best answer is C because the word greenery refers to the “spontaneous vegetation,” or weeds, introduced in lines 4–5 and further defined and discussed throughout the first paragraph.

The best answer is NOT:

A because in the context of the paragraph, greenery refers to “spontaneous vegetation,” not to cultivated plants.

B because in the context of the paragraph, greenery refers to “spontaneous vegetation,” not to landscapes that are protected.

D because in the context of the paragraph, greenery refers to “spontaneous vegetation,” not to crops.

Question 36. The best answer is F because both sources cite specific examples that support the passage author’s statement that weeds, “through a quirk of evolutionary fate, . . . developed traits in their native habitats that . . . ‘preadapted’ them to flourish in cities” (lines 51–54). The transitional word similarly (line 63) further establishes the complementary relationship between the study and the book.

The best answer is NOT:

G because the conclusions are similar, so they could not be contrasting.

H because the passage provides no evidence to suggest that Lundholm used Gilbert’s book.

J because the paragraph clearly establishes that Lundholm and Marlin’s study and Gilbert’s book are not irrelevant to each other: both sources drew similar conclusions about weeds that originated in limestone-rich habitats.

Question 37. The best answer is D because lines 78–80 state that so-called weeds “managed to survive the transition from one land use to another as cities developed.” This statement, and especially the author’s use of the word managed, makes it clear that the author is appreciative and respectful of urban plants’ adaptability and resilience.

The best answer is NOT:

A because the paragraph provides no suggestion of alarm.

B because the paragraph provides no indication that the author fears for weeds’ survival; rather, he is impressed by their ability to survive.

C because the paragraph provides no evidence to suggest that the author is ever annoyed about anything.

Question 38. The best answer is F because lines 11–13 directly state that Norway maple was among the plants “brought in intentionally or unintentionally by people.”

The best answer is NOT:

G because the passage does not indicate that the Norway maple was brought by wind.

H because the passage does not indicate that the Norway maple was brought by water.

J because the passage does not indicate that the Norway maple was brought by birds.

Question 39. The best answer is B because lines 15–16 make it clear that “on their own” refers to “dispersed by wind, water, or wild animals,” which indicates people were not involved.

The best answer is NOT:

A because the passage provides no evidence that any of the plants being discussed were brought to urban environments one at a time.

C because the passage directly states that the plants were brought by “wind, water, or wild animals”; they were, therefore, not self-propelled.

D because the word voluntarily suggests that the plants had a choice, which would be impossible given that plants do not have the ability to choose whether they are relocated or not.

Question 40. The best answer is J because lines 20–21 directly state that “if left undisturbed long enough,” weeds “may even develop into mature woodlands.”

The best answer is NOT:

F because the passage provides no evidence to suggest that weeds would eventually compete for space and die out.

G because the passage provides no evidence to suggest that weeds might eventually enhance landscaped gardens.

H because the passage provides no evidence to suggest that weeds might eventually dry out the soil.

Passage I

The best answer is A. According to Student 4, the atoms from smallest to largest are F, Cl, Br, and I. The table shows that the atoms from smallest to largest atomic mass are F, Cl, Br, and I. As atomic mass increases, atomic radius also increases. A is correct. B, C, and D are incorrect: as atomic mass increases, atomic radius increases.

The best answer is H. According to the passage, only Student 2 states that As does not have a lone pair. Students 1, 3, and 4 all state that As has a lone pair. F, G, and J are incorrect: Students 1, 3, and 4 state that As has a lone pair. H is correct.

The best answer is C. Students 1 and 2 both propose planar structures for AsF₃ in which all the atoms lie in the same plane. Students 3 and 4 both propose pyramidal structures in which the As lies above the plane of the three F. Only Students 1 and 2 would agree with the statement. A, B, and D are incorrect: Students 3 and 4 propose structures for AsF₃ that are not planar, and therefore they are not likely to agree with the statement. C is correct.

The best answer is J. Student 1 claims that there are 2 unique angles in the AsF₃ molecule, and Students 2, 3, and 4 claim that there is only 1 unique angle in the AsF₃ molecule. None of the students would agree that there are 3 unique bond angles in the molecule. F, G, and H are incorrect: none of the students would agree with the claim. J is correct.

The best answer is A. According to the passage, the sum of the angles in Student 1’s model is 180 + 90 + 90 = 360. The sum of the angles in Student 2’s model is 120 + 120 + 120 = 360. The sum of the angles in Student 3’s model is 109 + 109 + 109 = 327. The sum of the angles in Student 4’s model ranges from 100 + 100 + 100 = 300 to 111 + 111 + 111 = 333. Only Students 1 and 2 are likely to agree that the sum of the bond angles is equal to 360°. A is correct. B, C, and D are incorrect: only Students 1 and 2 would agree that the sum of the bond angles is 360°.

The best answer is J. According to the passage, Student 2 claims that As has no lone pair and the molecule is trigonal planar. Student 3 claims that As has a lone pair and, because of this, the molecule is trigonal pyramidal. Because N has a lone pair, it is more likely that it will adopt the trigonal pyramid conformation. F and G are incorrect: because of the lone pair, it is not likely that the ammonia molecule will adopt a trigonal planar conformation. H is incorrect: the bond angle is more consistent with Student 3’s description. J is correct.

The best answer is D. According to Table 1, the bond angles vary depending on the type of atom bonded to As. Only Student 4 claimed that the bond angles would vary, and therefore the data is most consistent with Student 4’s description. A, B, and C are incorrect: Students 1, 2, and 3 all claimed that the bond angles would be the same for the different molecules. D is correct.

Passage II

The best answer is F. According to Table 2, all the offspring from Cross 1 had a black coat. If both of the parents were BBEE, then all the offspring would have also been BBEE. According to Table 1, the genotype BBEE corresponds to a black coat. The hypothesis is consistent with the results of Cross 1. F is correct. G is incorrect: the offspring of Cross 1 had black coats. H and J are incorrect: the hypothesis is consistent with the results of Cross 1.

The best answer is D. According to Table 2, the genotypes bbEE and bbEe resulted in brown coats. The offspring from Cross 2 with a brown coat must have been either bbEE or bbEe.A is incorrect: bbee would have a yellow coat. B is incorrect: BBEE would have a black coat. C is incorrect: BbEE or BbEe would have a black coat. D is correct: both bbEE and bbEe would have a brown coat.

The best answer is H. According to Table 1, offspring with one or more copies of the E allele of Gene E would have a black coat or a brown coat. Table 2 shows that 2 of the Cross 3 offspring had a black coat, and 2 of the offspring had a brown coat. There were 6 offspring total. Four out of 6, or 2/3, of the offspring had one or more copies of the E allele of Gene E. F, G, and J are incorrect: 2/3 of the offspring had one or more copies of the E allele of Gene E. H is correct.

The best answer is B. To answer this item, the examinee must be familiar with dominant-recessive gene nomenclature. Capital letter for dominant and lowercase letter for recessive. According to Table 1, the genotype bbee with all recessive alleles corresponds to a yellow coat. According to Table 2, only Crosses 2 and 3 had offspring with a yellow coat, and therefore only Crosses 2 and 3 could have had only recessive alleles of Gene B and Gene E. A is incorrect: Cross 1 had no offspring with yellow coats. B is correct. C is incorrect: Cross 1 had no offspring with yellow coats. D is incorrect: Crosses 2 and 3 both had offspring with yellow coats that could have had the genotype bbee.

The best answer is J. According to Table 1, the EE genotype results in a black or brown coat color, and the ee genotype results in a yellow coat color. The observation that the ee genotype always corresponds to a yellow coat color indicates that the Gene E phenotypic expression is not affected by Gene B. F and G are incorrect: the data are not consistent with the hypothesis. H is incorrect: EE does not always result in a black coat. J is correct.

The best answer is C. To answer this item, the examinee must understand the segregation of chromosomes into gametes. For a dog with the genotype BbEE, half of the gametes will contain the B allele and the other half will contain the b allele. A, B, and D are incorrect: 50% will contain the B allele. C is correct.

Passage III

The best answer is J. According to Figure 2, the highest %, corresponding to the greatest average wet strength, was observed for the PTs submerged in water for 10 min and heated in the 140°C oven with a . F is incorrect: the PTs heated in the 110°C oven had a value less than 25%. G is incorrect: the PTs heated in the 120°C oven had a value less than 35%. H is incorrect: the PTs heated in the 130°C oven had a value of 40%. J is correct.

The best answer is A. According to Figure 2, as the oven temperature increased from 110°C to 140°C, the value for PTs submerged in water for 2 hr increased from approximately 23% to 48%. A is correct. B, C, and D are incorrect: the value increased steadily as the temperature increased.

The best answer is F. According to the passage, in Step 1 the control PTs were submerged in water, and in Step 3 the control PTs were heated in an oven at 25°C. F is correct. G is incorrect: the oven temperature was 25°C. H and J are incorrect: the PTs were submerged in water.

The best answer is D. According to the passage, the PTs in both Experiments 1 and 2 were soaked in water for 10 min, 2 hr, or 24 hr. None of the PTs was soaked in water for 18 hr. A, B, and C are incorrect: PTs were not soaked for 18 hr in either experiment. D is correct.

The best answer is G. According to Figure 1, the PTs submerged in water for 10 min had a higher value at all oven temperatures than did the PTs submerged in water for 2 hr. F is incorrect: the value at 2 hr was less than the value at 10 min. G is correct. H is incorrect: the values were not the same. J is incorrect: the value at 10 min was always greater than the value at 2 hr.

The best answer is C. The results of Experiment 2 show that wet strength of PTs treated with both GLA and zinc nitrate was greater than the wet strength of PTs treated with water. Because the results show that treatment with GLA and zinc nitrate did increase the wet strength of the PTS, the results of Experiment 2 refute the prediction. A and B are incorrect: Experiment 1 did not investigate the effect of treating the PTs with GLA and zinc nitrate. C is correct. D is incorrect: Experiment 2 does not support the prediction.

The best answer is G. In both experiments, the wet strength of the PTs is expressed as a percentage of the dry strength. Because this percentage is less than 100%, the dry strength is greater than the wet strength. F is incorrect: the wet strength was less than 100% of the dry strength. G is correct. H and J are incorrect: the dry strength was greater than the wet strength.

Passage IV

The best answer is B. To answer this item, the examinee must be familiar with basic scientific instruments and know that an electronic balance is used to measure mass. Tables 2 and 3 list the average final mass of the adult frogs that would have been measured with an electronic balance. A is incorrect: a graduated cylinder is used to measure volume. C is incorrect: a metric ruler is used to measure length. D is incorrect: a calorimeter is used to measure changes in heat during a chemical reaction or process. B is correct: an electronic balance is used to measure mass.

The best answer is F. According to Table 1, the percent by mass of protein increased in Diets 1–5. Table 2 shows that the average final mass of the frogs also increased for the frogs fed Diets 1–5. F is correct. G, H, and J are incorrect: as the percent by mass of protein increased, the average final mass of the frogs also increased.

The best answer is B. According to the passage, the frogs were placed in outdoor tanks. It is most likely that the wire mesh was used to keep the frogs in the tanks and to keep predators out of the tanks. The tanks were covered after the frogs were placed in the tanks, so the mesh was not used to place the frogs in the tanks. A, C, and D are incorrect: the mesh was used to prevent predators from entering the tanks and keep the frogs from leaving the tanks. B is correct.

The best answer is H. According to Table 1, the number of calories per gram increased in Diets 6–10. Table 3 shows that the average final mass of the frogs increased as the frogs were fed Diets 6–8, but then decreased for the frogs fed Diets 8–10. F, G, and J are incorrect: the average final mass of the frogs increased and then decreased. H is correct.

The best answer is C. To answer this item, the examinee must know that organisms that belong to the same species also belong to the same genus. According to the passage, the species Rana rugulosa was studied. All the frogs were the same species and genus. A, B, and D are incorrect: the frogs belonged to the same genus and the same species. C is correct.

The best answer is G. According to the passage, in Experiment 1 the starting mass of the frogs was 3.3 g, and each frog was fed 1,000 mg of food twice a day for a total of 2,000 mg. In Experiment 2, the starting mass of the frogs was 7.9 g, and each frog was fed 2,000 mg of food once a day. F is incorrect: the initial mass of each frog was less in Experiment 1 than in Experiment 2. G is correct: the initial mass of each frog in Experiment 2 was 7.9 g, and the initial mass of each frog in Experiment 1 was 3.3 g. H and J are incorrect: the frogs in both experiments were fed 2,000 mg of food per day.

The best answer is D. According to Table 1, Diets 1–5 all contained the same number of calories per gram, and the number of calories per gram was varied in Diets 6–10. To determine whether the number of calories per gram in the diet affected the growth, the farmer should have compared the results of Diets 6–10. A and B are incorrect: the percent by mass of protein was varied in Diets 1–5, and this would give no information about the effect of the number of calories per gram in the diet. C is incorrect: Diets 6–10 varied in the number of calories per gram. The percent by mass of protein was held constant. D is correct.

Passage V

The best answer is F. According to Figure 3, the average water content of soil values for the 4 dates were closest to one another, differing by less than 5%, at a depth of 30 cm. F is correct. G is incorrect: the values were slightly more spread out at a depth of 60 cm. H is incorrect: the values had a range that was greater than 10% at a depth of 100 cm. J is incorrect: the values had a range of approximately 15% at a depth of 140 cm.

The best answer is A. According to the passage, the slots near the end of the steel pipe allowed only soil gas to enter the pipe. A is correct. B, C, and D are incorrect: only soil gas entered the pipe.

The best answer is J. According to the passage, CO₂ is produced through 2 processes, but the experimental procedure does not provide any way of determining how much of the gas is produced by either process. F, G, and H are incorrect. J is correct: there is no way of knowing what percentage of the gas is produced by respiration in plant roots and how much is produced through decomposition of organic matter in this experiment.

The best answer is B. According to Figure 2, the percentage recorded is the average CO₂ content of soil gas by volume. To calculate this amount, one would divide the volume of CO₂ by the total volume of the gas sample. A is incorrect: to determine the percentage of CO₂ in the gas, one would have to divide by the volume of the gas sample. B is correct. C is incorrect: the percentage of CO₂ in the gas sample is being calculated, not the percentage of CO₂ in the water sample. D is incorrect: not all the gas collected in the steel pipe was analyzed for its CO₂ content, and therefore only the volume of the gas removed from the steel pipe via the syringe should be used in the percentage calculation.

The best answer is J. According to Figure 3, the average water content of the soil increased for the samples collected on November 23 and December 7, and the average water content decreased for the samples collected on October 26 and November 9. F is incorrect: the average water content increased only on November 23 and December 7. G is incorrect: the average water content decreased only on October 26 and November 9. H is incorrect: the average water content increased on November 23 and December 7 and decreased on October 26 and November 9. J is correct.

The best answer is D. According to Figure 2, for the samples collected on November 23, as the depth increased, the average CO₂ content also increased. At a depth of 140 cm, the average CO₂ content was approximately 0.41% by volume. If another diffusion well was positioned at a depth of 145 cm, then the average CO₂ content of the soil gas would have been greater than 0.40% by volume. A, B, and C are incorrect: the CO₂ content would have been greater than 0.40%. D is correct.

The best answer is G. According to Figure 3, on November 23 at a depth of 60 cm, the soil had an average water content of 20% by mass. A 10 g sample of soil would have contained 2 g of water (20% of 10 g = 2 g). F is incorrect: the mass of water would be 1 g if the average water content was 10% by mass. G is correct. H is incorrect: the mass of water would be 5 g if the average water content was 50% by mass. J is incorrect: if 10 g of water was in the sample, then the sample was 100% water and contained no soil.

Passage VI

The best answer is D. According to Figure 3, as time increased, the depth in motor oil also increased. At a time of 45 msec, the depth of the steel ball in motor oil was approximately 1.9 mm. The depth at time = 50 msec would most likely have been slightly greater than 1.9 mm. A, B, and C are incorrect: the depth would have been greater than 1.9 mm. D is correct.

The best answer is G. To answer this item, the examinee must know that buoyant forces are always directed upward and the gravitational force is directed downward. According to the passage, drag is a force that opposes motion. Because the ball is moving downward, drag is an upward force. F is incorrect: D should be an upward force. G is correct. H and J are incorrect: G is a downward force and B is an upward force.

The best answer is C. According to Figure 1, the steel ball in motor oil reaches terminal speed, where the speed remains constant, after approximately 25 msec. Figure 2 shows that the steel ball in glycerin reaches terminal speed after approximately 10 msec. It required less time for the steel ball to reach terminal speed in glycerin. A and B are incorrect: it took more time to reach terminal speed in motor oil. C is correct. D is incorrect: it took approximately 25 msec in motor oil and only 10 msec in glycerin.

The best answer is F. According to Figure 1, the terminal speed of the steel ball in motor oil was approximately 48 mm/sec. Figure 2 shows that the terminal speed of the steel ball in glycerin was approximately 10 mm/sec. The terminal speed was greater in motor oil. F is correct. G is incorrect: the terminal speed was approximately 48 mm/sec in motor oil and 10 mm/sec in glycerin. H and J are incorrect: the steel ball’s terminal speed was greater in motor oil.

The best answer is C. According to Figure 3, in both motor oil and glycerin, the depth of the steel ball increased over time. According to Figures 2 and 3, over time the draw increased and then leveled off. The drag on the steel ball was not proportional to the depth of the ball because as the depth increased, the drag increased and then remained roughly constant. A and B are incorrect: it is not reasonable to conclude that the drag on the steel ball was directly proportional to the depth of the ball. C is correct. D is incorrect: the drag increased and then remained roughly constant.

The best answer is H. According to Figure 3, the steel ball reached a depth of 0.50 mm in motor oil after approximately 16 msec. Figure 1 shows that, after 16 msec in motor oil, the drag on the steel ball was approximately 270 μN. F is incorrect: the drag reached 230 μN after approximately 9 msec, and at this time the steel ball was at a depth of only about 0.20 mm. G is incorrect: the drag reached 250 μN after approximately 11 msec, and at this time the steel ball was at a depth of only about 0.25 mm. H is correct: the drag reached 270 μN after approximately 14 msec, and the steel ball at this time was at a depth of about 0.50 mm. J is incorrect: the drag reached 290 μN after approximately 30 msec, and the steel ball at this time was at a depth of about 1.20 mm.

Planning Your Essay

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ENGLISH • PRACTICE TEST 4 • EXPLANATORY ANSWERS

Question 1. The best answer is B because it correctly identifies the rhetorical impact of losing the phrase “and my idol.” An idol is greatly admired, so it is logical to conclude that if the narrator idolized her sister—“a guitar buff”—she would want to learn to play the guitar, too.

The best answer is NOT:

A because it fails to correctly identify the rhetorical impact of the phrase “and my idol.” This phrase indicates nothing about the narrator’s age when she learned to play the guitar.

C because it fails to correctly identify the rhetorical impact of the phrase “and my idol.” This phrase suggests nothing about the age difference between the narrator and her sister.

D because it fails to correctly identify the rhetorical impact of the phrase “and my idol.” This phrase suggests nothing about degree of musical talent.

Question 2. The best answer is F because it provides the appropriate punctuation (a colon) to precede a list (the places the narrator took her guitar).

The best answer is NOT:

G because it introduces unnecessary punctuation that makes the narrator’s point less clear and creates an ungrammatical sentence. Placing the period after the word around creates a vague statement that loses the emphatic point that the narrator carried the guitar around everywhere (not just around). In addition, the unnecessary punctuation creates an ungrammatical sentence (a fragment in this case) beginning with the word Everywhere.

H because it uses grammatically incorrect punctuation (a semicolon) to introduce a list.

J because it fails to provide any punctuation to precede the list. The statement ending with the word everywhere is a complete sentence that requires punctuation to precede the list.

Question 3. The best answer is C because it correctly distinguishes between possessives and plurals by using an apostrophe to form the plural possessive friends’ and no apostrophe in the plural noun houses.

The best answer is NOT:

A because it incorrectly provides the plural noun friends where the plural possessive friends’ is needed.

B because it incorrectly provides the singular possessive friend’s where a plural is needed and incorrectly provides the singular possessive house’s where the plural noun houses is needed.

D because it incorrectly provides the singular possessive friend’s.

Question 4. The best answer is F because it provides the appropriate punctuation and capitalization for the two complete sentences and supplies the necessary comma after the introductory clause “No matter where I was” to avoid ambiguity in terms of whether the writer is saying “No matter where I was” or “No matter where I was playing.”

The best answer is NOT:

G because it lacks a comma after the word and, creating a run-on sentence.

H because it lacks a comma after the word was, creating ambiguity in terms of whether the writer is saying “No matter where I was” or “No matter where I was playing.”

J because it incorrectly uses commas to join two complete statements without any connector words.

Question 5. The best answer is A because it provides the most precise expression of the idea described in the stem. The word assailed best illustrates “the fervor with which the narrator communicated with the airport personnel” because it figuratively conveys the narrator’s energy in the interaction.

The best answer is NOT:

B because it provides a word choice that fails to precisely describe the idea identified in the stem; the neutral word approached does not adequately illustrate fervor.

C because it provides a word choice that fails to precisely describe the idea identified in the stem; the neutral word questioned does not adequately illustrate fervor.

D because it provides a word choice that fails to precisely describe the idea identified in the stem; the neutral word contacted does not adequately illustrate fervor.

Question 6. The best answer is J because it provides the appropriate pronouns for this sentence. The subjective pronoun case who is needed here because the word who serves as the subject of the dependent clause, and the pronoun me is the object.

The best answer is NOT:

F because it inappropriately uses a reflexive pronoun. The object is not the same person as the subject, so the reflexive pronoun myself is grammatically incorrect.

G because it incorrectly provides the objective pronoun case whom where the subjective pronoun case is needed. In addition, the object is not the same person as the subject, so the reflexive pronoun myself is grammatically incorrect.

H because it incorrectly provides the objective pronoun case whom where the subjective pronoun case is needed.

Question 7. The best answer is D because it eliminates redundancy and unnecessary wordiness.

The best answer is NOT:

A because it fails to eliminate redundancy at the paragraph level; the idea that this is an extended trip is mentioned earlier in the paragraph.

B because it fails to eliminate wordiness and redundancy at the paragraph level; the phrase “due to the fact that I was on an extended trip” contains a redundant reference to the extended trip and lacks concision.

C because it fails to eliminate redundancy at the paragraph level; the idea that the narrator is in Hawaii is mentioned earlier in the paragraph.

Question 8. The best answer is H because it provides the most logical transition based on the surrounding context. The word though logically conveys the shift from the narrator feeling upset in the preceding paragraph to the narrator’s worries dissipating.

The best answer is NOT:

F because it provides an illogical transition word; the word otherwise provides no logical meaning in this context.

G because it provides an illogical transition word; the word therefore suggests a cause-effect relationship between ideas that does not exist here.

J because it provides an illogical transition word; the word instead means “alternatively,” which makes no sense in this context.

Question 9. The best answer is D because it provides the idiomatically correct preposition in context. The phrase “into the . . . air” is consistent with standard English usage.

The best answer is NOT:

A because it provides the preposition upon, which creates an idiomatically nonstandard expression.

B because it provides the preposition amid, which creates an idiomatically nonstandard expression.

C because it provides the preposition onto, which creates an idiomatically nonstandard expression.

Question 10. The best answer is J because it is the most precise word for the context. The word issued correctly and logically conveys the idea that the tones came from an instrument.

The best answer is NOT:

F because it supplies an imprecise word choice for the context; the word accrued conveys the idea of accumulating, which does not make sense for describing musical tones.

G because it supplies an imprecise word choice for the context; the word distributed conveys the idea of something being passed out or delivered, which does not make sense for describing musical tones.

H because it supplies an imprecise word choice for the context; the word appeared conveys the idea of something becoming visible, which does not make sense for describing musical tones.

Question 11. The best answer is A because it is a complete statement, preventing the introduction of a rhetorically ineffective fragment.

The best answer is NOT:

B because it creates a sentence fragment.

C because it creates a sentence fragment.

D because it creates a sentence fragment.

Question 12. The best answer is G because it uses the appropriate conjunction for indicating a comparison (the word than), and the phrase “that of a guitar” clearly indicates that the comparison is between the guitar and the ukulele.

The best answer is NOT:

F because it uses the adverb then instead of the conjunction than.

H because it contains the pronoun it, which has no clear antecedent here, making the sentence unclear in terms of what is being compared.

J because it incorrectly supplies the adverb then where the conjunction than is needed. In addition, it contains the pronoun it, which has no clear antecedent here, making the sentence unclear in terms of what is being compared.

Question 13. The best answer is B because it provides the most specific description of the music the narrator played, as defined in the stem.

The best answer is NOT:

A because it uses the general word music, which lacks the specificity of the term “Hawaiian classics.”

C because it uses the general term “tropical tunes,” which lacks the specificity of the term “Hawaiian classics.”

D because it uses the general word things, which is too vague to have any specific meaning.

Question 14. The best answer is H because it provides the idiomatically correct preposition in context. The phrase “playing . . . with the locals” is clear and consistent with standard English usage.

The best answer is NOT:

F because it creates the phrase “playing . . . as the locals,” which is unclear in meaning and is inconsistent with standard English usage.

G because it creates the phrase “playing . . . through the locals,” which creates an illogical meaning and is inconsistent with standard English usage.

J because it creates the phrase “playing . . . along the locals,” which is unclear in meaning and is inconsistent with standard English usage.

Question 15. The best answer is C because it best expresses the idea specified in the stem by referring to the narrator’s closeness to her sister and love of playing the guitar. These are key points in the first two paragraphs.

The best answer is NOT:

A because it fails to fulfill the goal specified in the stem; neither the ukulele nor Hawaii is mentioned in the first two paragraphs.

B because it fails to fulfill the goal specified in the stem; the narrator’s time in Hawaii is not discussed in the first two paragraphs.

D because it fails to fulfill the goal specified in the stem; the narrator’s business trip is not the central focus of the first two paragraphs.

Question 16. The best answer is J because it eliminates redundancy and unnecessary wordiness.

The best answer is NOT:

F because it fails to eliminate redundancy at the sentence level; the sentence already mentions that she had ideas.

G because it fails to eliminate redundancy at the sentence level; the sentence already mentions that she had ideas.

H because it fails to eliminate redundancy at the sentence level; the sentence already mentions that she had ideas, so we know the ideas were her own.

Question 17. The best answer is B because it provides the most accurate description of how the paragraph break would create two separate but cohesive paragraphs. The information that precedes this point focuses on why and how Lamarr came up with the idea for “a sophisticated radio-controlled guidance system.” But the information that follows this point has a different focus; it explains how Lamarr’s invention would work.

The best answer is NOT:

A because it provides an inaccurate description of the two paragraphs that would be created; it suggests that two inventions are discussed here when only one is mentioned.

C because it provides an inaccurate description of the essay’s focus here; the section preceding this point in the essay does not provide an overview of Lamarr’s film career.

D because it provides an inaccurate description of the two paragraphs that would be created; except for mentioning where she grew up, the section preceding this point in the essay does not include details about Lamarr’s childhood, and the section that follows focuses on Lamarr’s work in particular rather than on general information about radio signals.

Question 18. The best answer is H because it ensures correct subject-verb agreement. The plural verb form are jammed agrees with the plural subject radio signals.

The best answer is NOT:

F because it lacks subject-verb agreement; the singular verb form is does not agree with the plural subject radio signals.

G because it lacks subject-verb agreement; the singular verb form has been does not agree with the plural subject radio signals.

J because it lacks subject-verb agreement; the singular verb form is jammed does not agree with the plural subject radio signals.

Question 19. The best answer is A because it correctly separates two distinct statements into two sentences with correct punctuation.

The best answer is NOT:

B because it incorrectly places a period after the word envisioned, creating a sentence fragment beginning with the word A.

C because it incorrectly uses a comma to join two independent clauses.

D because it incorrectly places a semicolon after the word envisioned. A semicolon must be followed by an independent clause rather than a fragment.

Question 20. The best answer is J because it eliminates redundancy and unnecessary wordiness.

The best answer is NOT:

F because it fails to eliminate redundancy at the sentence level; the phrase “like that” is redundant because the word such is used earlier in the sentence.

G because it fails to eliminate redundancy at the sentence level; the phrase “similar to that” is redundant because the word such is used earlier in the sentence.

H because it fails to eliminate redundancy at the sentence level; the word difficult is redundant because the word hard is used later in the sentence.

Question 21. The best answer is B because it provides the most precise wording for the context; the word implement suggests putting something into action, which precisely describes what Lamarr was trying to do.

The best answer is NOT:

A because it is illogical in this context; the word instigate suggests provoking or inciting, which is not something one does to an idea.

C because it is illogical in this context; the word discharge suggests the idea of unloading something, which makes no sense in this context.

D because it is illogical in this context; the word uphold suggests supporting or defending something. Lamarr wanted to put her idea into practice; she did not need to defend it.

Question 22. The best answer is F because it provides appropriate and consistent punctuation (commas) to set off the nonessential element (the word however).

The best answer is NOT:

G because it fails to provide appropriate and consistent punctuation to set off the nonessential element by substituting a semicolon for the comma after the word war.

H because it fails to provide appropriate and consistent punctuation to set off the nonessential element by omitting the comma after the word however.

J because it lacks any punctuation to set off the nonessential element.

Question 23. The best answer is C because it is the most effective placement of the statement in terms of logic and cohesion. Placing Sentence 3 after Sentence 4 ensures that the paragraph discusses the events in chronological order.

The best answer is NOT:

A because it creates a sequence of events that is not chronological; the event in Sentence 3 occurs after the event in Sentence 4.

B because it creates a sequence of events that is not chronological; the event in Sentence 3 occurs after the event in Sentence 1.

D because it creates a sequence of events that is not chronological; the event in Sentence 3 occurs before the event in Sentence 5.

Question 24. The best answer is G because it best expresses the idea specified in the stem by strongly and specifically emphasizing that the declassification of spread spectrum was a turning point in the history of communication. The word transformed indicates a dramatic change in communications, and the phrase “communications landscape” indicates that the change affected many facets of communication.

The best answer is NOT:

F because it is a less effective choice based on the goal specified in the stem; the phrase “made a difference” is too general to suggest a turning point.

H because it is a less effective choice based on the goal specified in the stem; even though the phrase “had an impact on communications” suggests that the declassification of spread spectrum had a strong effect on communications, the phrase fails to clearly indicate a turning point in the history of communication technology.

J because it is a less effective choice based on the goal specified in the stem; the phrase “revolutionized things” is imprecise and unclear.

Question 25. The best answer is B because it provides the appropriate punctuation (an em dash) to set off the nonessential element (the phrase “cellular phones, wireless Internet networks, the Global Positioning System”). The em dash that precedes the nonessential element is consistent with the em dash that follows the nonessential element.

The best answer is NOT:

A because it fails to use appropriate and consistent punctuation to set off the nonessential element; a comma rather than an em dash precedes the nonessential element.

C because it fails to use appropriate and consistent punctuation to set off the nonessential element; a colon rather than an em dash precedes the nonessential element.

D because it fails to use appropriate and consistent punctuation to set off the nonessential element; a comma rather than an em dash precedes the nonessential element. In addition, it fails to include the comma after the word phones to appropriately separate items in a list.

Question 26. The best answer is H because it corrects the introduction of a rhetorically ineffective fragment by providing the appropriate verb form function to make this a complete sentence.

The best answer is NOT:

F because it creates a sentence fragment; it lacks a predicate.

G because it creates a sentence fragment; it lacks a predicate.

J because it creates a sentence fragment; it lacks a predicate.

Question 27.The best answer is A because it creates an expression consistent with standard English usage. The idiom “It wasn’t until” is used to emphasize that a relatively lengthy period passed before Lamarr and Antheil were given credit for spread spectrum.

The best answer is NOT:

B because it is an idiomatically nonstandard and vague expression; the word Such has no clear antecedent.

C because it introduces a vague pronoun; the pronoun This has no clear antecedent.

D because it introduces a vague pronoun; the pronoun That has no clear antecedent.

Question 28. The best answer is J because it corrects the introduction of an error in coordination and subordination.

The best answer is NOT:

F because it contains an error in coordination created by adding a comma and the word they after the name Antheil, making the relationship between what comes before and after the comma unclear.

G because it contains an error in coordination created by adding an em dash and the word both after the name Antheil; the em dash serves no clear purpose here and therefore makes the relationship between what comes before and after the em dash unclear.

H because it contains an error in coordination. The compound subject Lamarr and Antheil is incorrectly followed by the infinitive verb form to receive, failing to provide a predicate for the sentence.

Question 29. The best answer is D because it eliminates the illogical and confusing transition word. The link between this sentence and the preceding one is obvious; no other transition is needed.

The best answer is NOT:

A because it provides an illogical transition word for the context; the word However suggests two opposing ideas, which is not the case here.

B because it provides an illogical transition word for the context; the word Conversely suggests two opposing ideas, which is not the case here.

C because it provides an unnecessary transition word for the context; there is no clear rhetorical purpose for the word Anyway in this context.

Question 30. The best answer is F because it offers a clear and convincing reason the essay accomplishes the purpose identified in the stem. This essay gives an overview of the history of Lamarr’s invention. The essay begins with Lamarr’s idea and then goes on to explain how the invention was developed and why it was important.

The best answer is NOT:

G because it identifies an incorrect reason the essay has accomplished the specified purpose; Lamarr and Antheil could not have changed the course of World War II with spread spectrum because, according to the essay, spread spectrum was not fully developed until after World War II.

H because it indicates that the essay hasn’t accomplished the specified primary purpose when it has; the second half of the essay explains the importance of spread spectrum.

J because it indicates that the essay hasn’t accomplished the specified primary purpose when it has and identifies a reason that does not accurately describe the essay; the essay gives very little attention to the film industry.

Question 31. The best answer is B because it properly distinguishes among pronouns, contractions, and possessives by providing the phrase “There are” to correctly set up the independent clause and agree with plural noun turbines.

The best answer is NOT:

A because it incorrectly provides the contraction They’re, which means “They are.” This phrase creates an ungrammatical sentence.

C because it incorrectly substitutes the possessive Their, creating an ungrammatical sentence.

D because it incorrectly substitutes the contraction There’s, which means “There is.” This phrase creates an ungrammatical sentence and fails to agree with the plural noun turbines.

Question 32. The best answer is H because it ensures correct subject-verb agreement. The subject of this part of the sentence is the singular word task. The singular verb form represents agrees with the singular subject task.

The best answer is NOT:

F because it lacks subject-verb agreement; the plural verb form have represented does not agree with the singular subject task.

G because it lacks subject-verb agreement; the plural verb form are representing does not agree with the singular subject task.

J because it lacks subject-verb agreement; the plural verb form represent does not agree with the singular subject task.

Question 33. The best answer is A because it correctly signals a contrast between this sentence and the preceding sentence. The idea that servicing the turbine blades “that slice through the air is a serious challenge” contrasts with the preceding idea that “ladders inside the tower simplify access to the generators and controllers.”

The best answer is NOT:

B because it signals a similarity rather than a contrast between the ideas in these two sentences.

C because it signals a time marker that is illogical; there is nothing in the essay to suggest servicing the turbine blades happens instantly.

D because it incorrectly signals a transition to an order of steps.

Question 34. The best answer is G because it provides appropriate and consistent punctuation (em dashes) before and after the nonessential element (“those long fiberglass vanes that slice through the air”).

The best answer is NOT:

F because it lacks appropriate punctuation after the word blades to correctly set off the nonessential element.

H because it uses inconsistent punctuation (an em dash after the word blades and a comma after the word air) to set off the nonessential element.

J because it lacks appropriate punctuation after the word air to correctly set off the nonessential element.

Question 35. The best answer is A because it prevents the introduction of redundant or unnecessary wording.

The best answer is NOT:

B because it introduces redundancy at the sentence level; the phrase “something they’re able to do” is redundant because the sentence already says “Rock climbers are . . . capable.”

C because it contains an internal redundancy; ascending and climbing indicate the same action.

D because it introduces redundancy at the sentence level; the phrase “using rope” is redundant because the use of rope has already been mentioned in the sentence.

Question 36. The best answer is F because it prevents the introduction of a squinting modifier. It correctly places the subject (“rock climbers”) after the comma so that the introductory clause “After completing specialized training” correctly modifies “rock climbers.”

The best answer is NOT:

G because it creates a squinting modifier; it incorrectly makes “old skills and new knowledge” the subject, which suggests that “old skills and new knowledge” have completed specialized training.

H because it creates a squinting modifier; it incorrectly makes “new careers” the subject, which suggests that “new careers” have completed specialized training.

J because it shifts to the passive voice, making it unclear who has completed specialized training.

Question 37. The best answer is D because it correctly provides the appropriate preposition for the standard English phrase “arrive at.”

The best answer is NOT:

A because it incorrectly provides the preposition across, which creates a nonstandard and illogical phrase; technicians could not arrive by being across the turbine.

B because it incorrectly substitutes the preposition with, which creates a nonstandard and illogical phrase; the word with suggests that the technicians already had the turbine with them when they arrived.

C because it incorrectly substitutes the preposition via, which creates a nonstandard and illogical phrase; the word via suggests that the technicians reached a new location by using a turbine.

Question 38. The best answer is J because it provides the most effective introduction to the paragraph. “Whatever the job, safety is the first priority” correctly introduces the main topic of the paragraph: safety.

The best answer is NOT:

F because it provides a detail (the length of the blades) that is not clearly connected to the main topic of the paragraph: safety.

G because it provides a detail (the rise in the number of turbine-related jobs) that is not clearly connected to the main topic of the paragraph: safety.

H because it provides a detail (the number of parts) that is not clearly connected to the main topic of the paragraph: safety.

Question 39. The best answer is B because it correctly punctuates two independent clauses with a comma and the word and.

The best answer is NOT:

A because it incorrectly uses a semicolon to separate an independent clause and a dependent clause.

C because it incorrectly uses a comma to join two independent clauses, which creates a run-on sentence.

D because it fails to provide any punctuation between two independent clauses.

Question 40. The best answer is J because it uses the most logical subordinate conjunction for the context. The word If correctly introduces a conditional clause that explains when technicians stay on the ground.

The best answer is NOT:

F because it provides an imprecise word choice; the word Whether incorrectly indicates that the sentence will present two options, which it does not do.

G because it provides an imprecise word choice; the phrase “So that” illogically suggests the intention of creating lightning.

H because it provides an imprecise word choice; the word Unless illogically suggests that the technicians do not stay on the ground when there’s lightning, which contradicts the idea that the technicians take safety precautions.

Question 41. The best answer is C because it ensures appropriate and consistent punctuation (commas) before and after the nonessential element (“along with rigorous procedures and training”).

The best answer is NOT:

A because it uses punctuation (an em dash) that is inconsistent with the punctuation used later in the sentence (a comma after the word training) to set off the nonessential element.

B because it substitutes punctuation (a semicolon) that is inconsistent with the punctuation used later in the sentence (a comma after the word training) to set off the nonessential element.

D because it lacks appropriate punctuation after the word these to correctly set off the nonessential element.

Question 42. The best answer is F because it ensures correct subject-verb agreement. The subject of the sentence is the plural word Precautions. The plural verb form make agrees with the plural subject Precautions.

The best answer is NOT:

G because it lacks subject-verb agreement; the singular verb form is making does not agree with the plural subject Precautions.

H because it lacks subject-verb agreement; the singular verb form has made does not agree with the plural subject Precautions.

J because it lacks subject-verb agreement; the singular verb form makes does not agree with the plural subject Precautions.

Question 43. The best answer is D because it corrects the introduction of an error in parallelism regarding the noun phrases. The noun phrase “plenty of climbing practice” correctly parallels the structure of the other noun phrases in the sentence (“fresh air,” “great vistas,” and “ample time off”).

The best answer is NOT:

A because it disrupts the parallel structure by interrupting the series of noun phrases with the infinitive phrase “to practice climbing daily.”

B because it disrupts the parallel structure by interrupting the series of noun phrases with the independent clause “they practice climbing regularly.”

C because it disrupts the parallel structure by interrupting the series of noun phrases with the conditional phrase “while often practicing climbing.”

Question 44. The best answer is H because it best expresses the idea specified in the stem that “rock climbers in particular may find being a rope technician an appealing occupation.” The question “what more could a climber want?” suggests that the elements identified earlier in the sentence would appeal to rock climbers; rock climbers could want nothing more.

The best answer is NOT:

F because it is an ineffective choice based on the goal specified in the stem; it poses a question about the job of a rope technician in general rather than expressing the idea specified in the stem.

G because it is an ineffective choice based on the goal specified in the stem; it poses a question about rock climbers in general rather than expressing the idea specified in the stem.

J because it is an ineffective choice based on the goal specified in the stem; it poses a question directly to the reader (who may or may not be a rock climber) rather than expressing the idea specified in the stem.

Question 45. The best answer is A because the statement “Enter rock climbers” introduces rock climbers, the main subject of the essay. Point A correctly places this sentence where it would introduce rock climbers prior to any other reference to rock climbers in the essay.

The best answer is NOT:

B because it would interrupt the paragraph by reintroducing rock climbers. At this point in the essay, it is already clear that rope technicians are often rock climbers.

C because it would interrupt the paragraph by reintroducing rock climbers. At this point in the essay, it is already clear that rope technicians are often rock climbers.

D because it would interrupt the paragraph by reintroducing rock climbers. At this point in the essay, it is already clear that rope technicians are often rock climbers.

Question 46. The best answer is J because it ensures correct subject-verb agreement. The singular verb form blends agrees with the singular subject Scene at the Signing of the Constitution of the United States (the title of the painting).

The best answer is NOT:

F because it lacks subject-verb agreement; the plural verb form blend does not agree with the singular subject.

G because it lacks subject-verb agreement; the plural verb form have blended does not agree with the singular subject.

H because it lacks subject-verb agreement; the plural verb form are blending does not agree with the singular subject.

Question 47. The best answer is C because it provides the clearest and most specific information asked for in the stem by indicating where the painting is on display (Washington, DC).

The best answer is NOT:

A because it fails to indicate what the stem asks for; it gives the location of the event characterized in the painting rather than where the painting is on display.

B because it fails to indicate what the stem asks for; it mentions the experience of those who see the painting on display but gives no indication of the location.

D because it fails to indicate what the stem asks for; it mentions that the painting has been on display but gives no indication of the location.

Question 48. The best answer is H because it eliminates the unnecessary punctuation between the verb and the preposition.

The best answer is NOT:

F because it provides unnecessary punctuation; the em dash after the word presided creates an unclear sentence with an illogical interruption of the phrase “presided over.”

G because it introduces unnecessary punctuation; the comma after the word presided creates an unclear sentence with an illogical interruption of the phrase “presided over.”

J because it introduces unnecessary punctuation; the semicolon after the word presided creates an unclear sentence with an illogical interruption of the phrase “presided over.” In addition, the phrase following the semicolon forms an incomplete statement.

Question 49. The best answer is D because it eliminates redundancy by providing the most precise and concise wording. In addition, it maintains a tone that is consistent with the rest of the essay.

The best answer is NOT:

A because it contains an internal redundancy; the phrase “final role” and the word ending mean the same thing.

B because it contains an internal redundancy; the word ended and the phrase “in the conclusion of” mean the same thing.

C because it provides a phrase that is imprecise in meaning and creates a tone that is too informal for the essay.

Question 50. The best answer is J because it eliminates redundancy by providing the most precise and concise wording.

The best answer is NOT:

F because it contains an internal redundancy; the word prior and the phrase “in advance of” mean the same thing.

G because it contains an internal redundancy; the word preparation and the phrase “leading up to” mean the same thing.

H because it contains an internal redundancy; the words advance and preceding mean the same thing.

Question 51. The best answer is A because it prevents the introduction of an error in subordination in the sentence structure. The phrase “into which” most clearly and correctly establishes that the quills would have been dipped into the inkwells.

The best answer is NOT:

B because it introduces an error in subordination; it inaccurately reads as though the inkwells are being dipped into something rather than the quills being dipped into the inkwells.

C because it introduces an error in subordination; it creates a sentence with unclear meaning in terms of the relationship between or actions with the inkwells and quills.

D because it introduces an error in subordination; it creates a sentence with unclear meaning in terms of the relationship between or actions with the inkwells and quills.

Question 52. The best answer is F because it prevents the introduction of an error in subordination in sentence structure. The sentence clearly and correctly establishes that Christy was “noting color, texture, design” while scouring countless drawings.

The best answer is NOT:

G because it introduces an error in subordination; it creates a sentence with unclear meaning in terms of what was noted and by whom.

H because it introduces an error in subordination; it creates a sentence with unclear meaning in terms of what was noted.

J because it introduces an error in subordination; it creates a sentence with unclear meaning in terms of the nature of the drawings Christy scoured.

Question 53. The best answer is D because it corrects the introduction of a rhetorically ineffective fragment. The phrase “He hunted” provides both the subject and verb for the sentence.

The best answer is NOT:

A because it creates a rhetorically ineffective sentence fragment.

B because it introduces a rhetorically ineffective sentence fragment.

C because it introduces a rhetorically ineffective sentence fragment.

Question 54. The best answer is G because it is the most effective placement of the sentence in terms of logic and cohesion. Sentence 2 informs the reader about Christy’s trip “to Philadelphia to study how the light falls through the windows.” The added sentence provides more information about the reason for the trip, logically following Sentence 2. Sentences 3 and 4 should follow the added sentence because Sentences 3 and 4 focus on more specific aspects of Christy’s preparations for creating the painting.

The best answer is NOT:

F because it is an illogical placement of the sentence within the paragraph. The added sentence expands on why and when Christy traveled to Philadelphia, so it would be illogical to place it after Sentence 1, which gives information about where and when the painting was installed and precedes any reference to Christy’s trip to Philadelphia. The references to “He” and “his trip” in the added sentence would have no clear meaning.

H because it is an illogical placement of the sentence within the paragraph. The added sentence expands on why and when Christy traveled to Philadelphia, so it would be illogical to place it after Sentence 3, which focuses more specifically on the inkwells and quills.

J because it is an illogical placement of the sentence within the paragraph. The added sentence expands on why and when Christy traveled to Philadelphia, so it would be illogical to place it after Sentence 4, which focuses more specifically on Christy’s research involving drawings of period furniture and fabrics.

Question 55. The best answer is B because it correctly eliminates the punctuation separating the word boat from the description that tells us about that boat (one that “experts now agree could not have been the vessel that carried the revolutionary leader across the river”).

The best answer is NOT:

A because it provides unnecessary punctuation; it incorrectly provides a period separating the word boat from the description that tells us about that boat and creates a rhetorically ineffective fragment starting with the word Experts.

C because it introduces unnecessary punctuation; it incorrectly provides a semicolon separating the word boat from the description that tells us about that boat. In addition, it incorrectly creates a fragment following the semicolon.

D because it introduces unnecessary punctuation; it incorrectly provides a comma separating the word boat from the description that tells us about that boat.

Question 56. The best answer is H because it correctly eliminates unnecessary punctuation in the phrase “another painting of the signing.”

The best answer is NOT:

F because it provides unnecessary punctuation; the comma after the word another incorrectly sets off the phrase “painting of the signing of the US Constitution” as a nonessential element.

G because it provides unnecessary punctuation; the comma after the word signing incorrectly sets off the phrase “of the US Constitution” as a nonessential element.

J because it provides unnecessary punctuation; the comma after the word painting incorrectly sets off the phrase “of the signing of the US Constitution” as a nonessential element.

Question 57. The best answer is B because it best expresses the idea specified in the stem by supporting the claim about the grandeur of the moment and emphasizing that Christy gave Washington a special status. The phrase “a hero among heroes” emphasizes the grandeur by characterizing all the signers as heroic and singling out Washington’s special status as the most heroic of the group.

The best answer is NOT:

A because it fails to express the idea specified in the stem; it references the fame of Christy’s painting but says nothing about Washington’s special status.

C because it fails to express the idea specified in the stem; it mentions that Christy used visual techniques to single Washington out, but it does nothing to support the claim about the grandeur of the moment.

D because it fails to express the idea specified in the stem; it mentions that Christy did single Washington out, but does nothing to support the claim about the grandeur of the moment.

Question 58. The best answer is G because it eliminates an error in subordination in the sentence structure. The correct sentence structure makes clear that Franklin and Madison are examples of the many luminaries depicted in the painting.

The best answer is NOT:

F because it contains an error in subordination; the faulty sentence structure makes it unclear whether Franklin and Madison are in the painting or are absent but are being compared to the figures who are in the painting.

H because it introduces an error in subordination; the faulty sentence structure illogically suggests that only Franklin and Madison are being referred to by the phrase “many of the assembled men.”

J because it introduces an error in subordination; the faulty sentence structure illogically suggests that only Franklin and Madison are being referred to by the phrase “many of the assembled men.”

Question 59. The best answer is A because it creates the most logical ordering of paragraphs within the essay. Paragraph 2 describes the measures Christy took to prepare for the work on his famous painting. Paragraph 3 then logically begins with the phrase “Such measures may seem standard,” which directly refers to the measures described in Paragraph 2.

The best answer is NOT:

B because it creates an illogical ordering of the paragraphs within the essay; Paragraph 3 begins with “Such measures may seem standard,” which would make no sense as the first paragraph of the essay. The reader would not know to whom or what the essay is referring.

C because it creates an illogical ordering of the paragraphs within the essay; Paragraph 3 begins with “Such measures may seem standard,” which has no clear connection to Paragraph 1. Paragraph 1 introduces the painting rather than the measures Christy took to produce it.

D because it creates an illogical ordering of the paragraphs within the essay; Paragraph 3 begins with “Such measures may seem standard,” which has no clear connection to Paragraph 4. Rather, Paragraph 4 logically follows Paragraph 3 because Paragraph 3 refers to a painting that is not historically accurate, and Paragraph 4 begins with the statement “Christy’s painting also plays with the truth.”

Question 60. The best answer is H because it offers a clear and convincing reason the essay does not accomplish the purpose identified in the stem. Rather than explaining how Christy’s painting changes the direction of his career, the essay focuses on Christy’s approach to creating Scene at the Signing of the Constitution of the United States.

The best answer is NOT:

F because it indicates that the essay has accomplished the primary purpose identified in the stem when it hasn’t and gives an inaccurate description of the essay. The essay does not indicate that Christy’s painting led a trend in historical art.

G because it indicates that the essay has accomplished the primary purpose identified in the stem when it hasn’t and gives an inaccurate description of the essay. The essay does not discuss the impact of Scene at the Signing of the Constitution of the United States on Christy’s career.

J because it fails to offer a clear and convincing reason the essay does not accomplish the purpose identified in the stem. The essay does not indicate or address Christy’s subject matter throughout his career; it focuses on only one painting.

Question 61. The best answer is A because it best maintains the stylistic pattern established earlier in the sentence. The phrase “dizzying mazes of lines” contains a detailed image that most closely matches the pattern of detailed images created by the adjectives and nouns in the phrases “layers of petals, intricate spirals and rosettes, teardrops bending within circles.”

The best answer is NOT:

B because it fails to maintain the stylistic pattern; the phrase “something with a dizzying effect” is too vague to match the level of detail established in the preceding phrases in the series.

C because it fails to maintain the stylistic pattern; the phrase “mazes that she creates” disrupts the pattern because it has significantly less detail and specificity and reintroduces the subject.

D because it fails to maintain the stylistic pattern; the phrase “so many lines” disrupts the pattern because it has significantly less detail and specificity than preceding phrases in the series.

Question 62. The best answer is G because it correctly distinguishes between plurals and possessives. The term centuries-old is correctly written as a compound adjective (to convey that paj ntaub has been practiced for many centuries) rather than a possessive noun.

The best answer is NOT:

F because it inaccurately substitutes the singular possessive century’s for the plural noun centuries. In addition, it substitutes the superlative oldest for the word old when there is no clear context to indicate a comparison with other forms of Hmong needlework.

H because it inaccurately substitutes the plural possessive centuries’ for the plural noun centuries.

J because it inaccurately substitutes the singular possessive century’s for the plural noun centuries.

Question 63. The best answer is D because it deletes irrelevant information. The first paragraph is mainly about Pang Xiong as a master of paj ntaub, but the sentence in question describes recent trends in paj ntaub in general. Details about recent trends in paj ntaub are irrelevant at this point in the essay.

The best answer is NOT:

A because it retains irrelevant information and inaccurately describes the relationship between the sentence in question and the surrounding text. The sentence in question offers no connection to Pang Xiong’s embroidery style.

B because it retains irrelevant information and inaccurately describes the relationship between the sentence in question and the surrounding text. Pang Xiong’s work with paj ntaub is the main subject of the essay. The sentence in question offers no connection to Pang Xiong, so its reference to recent trends fails to place the subject of the essay in a modern context.

C because it offers an incorrect reason to delete information and inaccurately describes the relationship between the sentence in question and the surrounding text. The paragraph focuses on Pang Xiong as a master of a single style of Hmong needlework: paj ntaub. The paragraph does not describe the various styles of ancient Hmong needlework arts.

Question 64. The best answer is G because it eliminates an error in coordination in sentence structure. The participial phrase “living in northern Laos” modifies the word woman and accurately explains that Pang Xiong lived in northern Laos when she was a young woman.

The best answer is NOT:

F because it creates an error in coordination; the comma after the word woman separates two coordinate elements, creating an ungrammatical sentence that is unclear in terms of the relationship between the details about when Pang Xiong was a young woman and when she lived in northern Laos.

H because it introduces an error in coordination; it creates an ungrammatical shift in verb tense that makes the meaning of the sentence unclear.

J because it introduces an error in coordination; it creates an ungrammatical sentence that is unclear in terms of the relationship between the detail about living in northern Laos and how long Pang Xiong has been creating stitched textiles.

Question 65. The best answer is C because it corrects the introduction of a misplaced modifier. The parenthetical phrase offers examples of types of clothing, so it would most logically be placed after the word clothing to modify it and offer clarification about how flower cloth is “worn as clothing.”

The best answer is NOT:

A because it creates a misplaced modifier; the placement of the parenthetical phrase after the term “flower cloth” suggests that flower cloth is defined by the phrase “commonly as a shirt, dress, coat, or collar,” which is inaccurate based on the information given in the essay.

B because it introduces a misplaced modifier; the placement of the parenthetical phrase after the word made suggests that the parenthetical phrase explains or defines how flower cloth is made, which it does not.

D because it introduces a misplaced modifier; the placement of the parenthetical phrase after the word needlework suggests that the parenthetical phrase explains or defines something about needlework, which it does not.

Question 66. The best answer is F because it ensures subject-verb agreement; the singular verb form is designed agrees with the singular subject Flower cloth.

The best answer is NOT:

G because it lacks subject-verb agreement; the plural verb form have been designed does not agree with the singular subject Flower cloth.

H because it lacks subject-verb agreement; the plural verb form are designed does not agree with the singular subject Flower cloth.

J because it lacks subject-verb agreement; the plural verb form design does not agree with the singular subject Flower cloth.

Question 67. The best answer is D because it best expresses the idea specified in the stem by building on the information provided earlier in the sentence about a common theme in paj ntaub patterns and images. The sentence refers to animals, which leads to a common theme of celebrating the natural world.

The best answer is NOT:

A because it fails to express the idea specified in the stem; the idea of versatile patterns is too vague and broad to build on the theme of animals or the natural word.

B because it fails to express the idea specified in the stem; the detail about master artists creating paj ntaub clothing for special occasions has no clear connection to the common animal patterns referred to earlier in the sentence.

C because it fails to express the idea specified in the stem; the idea that paj ntaub patterns are colorful has no clear connection to the common animal patterns referred to earlier in the sentence.

Question 68. The best answer is H because it correctly separates two coordinate adjectives (tiny and tight) with a comma while omitting unnecessary punctuation after the words tight (between the adjective and the noun) and stitches (clearly indicating that the artist makes use of two key features: “tiny, tight stitches” and “several complex techniques”).

The best answer is NOT:

F because it contains unnecessary punctuation; the comma after the word stitches inappropriately separates the two features the artist makes use of: “tiny, tight stitches” and “several complex techniques.”

G because it contains unnecessary punctuation; it inaccurately separates the adjective tight from the noun it needs to modify: stitches.

J because it both fails to include necessary punctuation and contains unnecessary punctuation; it fails to separate the two coordinate adjectives (tight and tiny) with a comma, and it places a comma after the word stitches, which inappropriately separates the two features the artist makes use of: “tiny, tight stitches” and “several complex techniques.”

Question 69. The best answer is A because it prevents the introduction of an error in coordination and subordination in the sentence structure. The preposition in is needed before the relative pronoun which to indicate that what follows in the sentence describes “reverse appliqué.”

The best answer is NOT:

B because it introduces an error in subordination; it creates an ungrammatical sentence with an unclear meaning in terms of the relationship between the term “reverse appliqué” and the information that follows.

C because it introduces an error in coordination; it creates both a run-on sentence and an unclear statement in terms of the relationship between the term “reverse appliqué” and the information about the shapes being cut out.

D because it introduces an error in coordination; the comma after the word appliqué inappropriately creates two complete statements joined by a comma. This introduces an ungrammatical and unclear statement in terms of the relationship between the term “reverse appliqué” and the information about the shapes being cut out.

Question 70. The best answer is J because it eliminates an error in parallelism in the sentence structure. It provides the appropriate passive voice form added to parallel the passive voice form are cut, which is used earlier in the sentence.

The best answer is NOT:

F because it contains an error in parallelism; it incorrectly uses the present participle adding rather than the passive voice form added.

G because it introduces an error in parallelism; it incorrectly uses the phrase “as an addition” rather than the passive voice form added.

H because it introduces an error in parallelism; it incorrectly uses the phrase “to add them” rather than the passive voice form added.

Question 71. The best answer is B because it corrects the use of a vague pronoun. The phrase “the surface of the fabric” clearly identifies where the stitches are layered: on the fabric.

The best answer is NOT:

A because it uses a vague pronoun; the possessive pronoun its has no clear antecedent, making it unclear which object’s surface is being referred to.

C because it introduces a vague pronoun; the pronoun it has no clear antecedent, making it unclear which object’s surface is being referred to.

D because it introduces a vague pronoun; the pronoun their has no clear antecedent, making it unclear which object’s surface is being referred to.

Question 72. The best answer is F because it correctly identifies that the writer should make the revision and accurately states the rhetorical impact of doing so. The adjective regular is vague; the more specific adjective mass-produced creates a clearer contrast between the homogeneous styles of clothing that are popular today and handcrafted paj ntaub.

The best answer is NOT:

G because it inaccurately states the rhetorical impact of making the revision. Although the adjective mass-produced describes the clothing that Pang Xiong is not fond of, it does nothing to indicate how or where Pang Xiong wants her work sold.

H because it incorrectly indicates that the writer should not make the revision. In addition, it inaccurately states the rhetorical impact of the original word. The word regular applies to clothing most people wear today; it does not refer to paj ntaub clothing at all.

J because it incorrectly indicates that the writer should not make the revision. In addition, it inaccurately states the rhetorical impact of the original word. The adjective mass-produced is more specific than the vague adjective regular.

Question 73. The best answer is D because it accurately eliminates the use of unnecessary transition words. No transition word or phrase is needed to clarify the connection between the ideas in this sentence and the preceding one.

The best answer is NOT:

A because it provides a transition word that is illogical for the context; the word However suggests that this sentence will present a contrast to what came before, which is not the case here.

B because it introduces a transition word that is illogical for the context; the transition phrase “For example” suggests that the sentence will provide an example, which is not the case here.

C because it introduces a transition word that is illogical for the context; the word Besides fails to provide a logical transition from the discussion of Pang Xiong’s clothing when she was young to the discussion of Pang Xiong’s clothing today and how she would like to inspire others. It is unclear what the word Besides would mean in this context.

Question 74. The best answer is F because it provides the clearest and most precise wording based on the stem. The phrase “to do so” clearly refers to wearing flower cloth, which is precisely what Pang Xiong wants to inspire others to do. This wording best indicates that Pang Xiong wants others to share her appreciation of paj ntaub by wearing it.

The best answer is NOT:

G because it is unnecessarily wordy and imprecise. The phrase “attempt that approach” is less precise because it does not clearly refer to the specific action of wearing flower cloth.

H because it does not offer precise wording to indicate that Pang Xiong wants others to share her appreciation of paj ntaub by wearing it. It vaguely states that Pang Xiong wants to inspire people she knows, but it doesn’t indicate what she wants to inspire them to do.

J because it does not offer precise wording to indicate that Pang Xiong wants others to share her appreciation of paj ntaub by wearing it. Instead, it vaguely indicates that she wants to inspire others in general.

Question 75. The best answer is C because it is the most effective sentence to connect the ideas in the paragraph based on the criteria in the stem. By explaining that Pang Xiong has recently worked with nine young Hmong women in a formal apprenticeship, the sentence builds on the ideas mentioned earlier in the paragraph: that Pang Xiong wants to inspire an appreciation of paj ntaub in others and teaches the skill. The sentence also connects to the final sentence of the essay because it refers to nine young Hmong apprentices who are examples of the “new generation” mentioned in the final sentence.

The best answer is NOT:

A because it offers little connection to ideas presented earlier in the paragraph and fails to connect to the final sentence in the essay; this sentence mentions Pang Xiong’s appreciation of others wearing traditional clothing in general (not only paj ntaub) but offers no connection to her “showing a new generation the joys of paj ntaub.”

B because it builds on one idea presented earlier in the paragraph (teaching) but fails to connect to the final sentence in the essay; this sentence focuses on Hmong adults who are Pang Xiong’s age rather than on the “new generation” referred to in the final sentence.

D because it offers no connection to the ideas presented earlier in the paragraph or to the final sentence of the essay; this sentence refers to Pang Xiong’s family’s story, but her family is not discussed elsewhere in the paragraph.

MATHEMATICS • PRACTICE TEST 4 • EXPLANATORY ANSWERS

Question 1. The correct answer is B. The probability of selecting either a red marble or a blue marble is calculated by adding the probability of selecting a red marble and the probability of selecting a blue marble: . If you chose A, you may have thought the probability is the positive difference between the probability of selecting a red marble and the probability of selecting a blue marble. If you chose C, you may have added the values in the numerator and the values in the denominator. If you chose D, you may have multiplied the numerators and added the denominators. If you chose E, you may have multiplied the probabilities.

Question 2. The correct answer is G. The graph shows that, of the students who were present on Thursday, 8 were in Group 1, 12 were in Group 2, 6 were in Group 3, 2 were in Group 4, and 0 were in Group 5. The probability that a student from Group 4 is selected at random from the class on Thursday can be calculated by taking the number of students present on Thursday who were in Group 4 and dividing it by the total number of students present on Thursday in the class: . If you chose F, you may have incorrectly identified the number of students present on Thursday who were in Group 4 as 1 instead of 2. If you chose H, you may have found the probability of selecting Group 4 from the 5 groups. If you chose J, you may have found the probability of selecting Group 4 from the 4 nonempty groups. If you chose K, you may have found the probability of selecting 1 student from Group 4.

Question 3. The correct answer is A. To solve for the value of j given a value of k, substitute the value of k into the equation to get ; subtract 54 from both sides of the equation, , to get and multiply both sides of the equation by , , to get . If you chose B, you may have multiplied by instead of its reciprocal: . If you chose C, you may have multiplied 40 by and then subtracted from 54: . If you chose D, you may have forgotten the 54 and solved : . If you chose E, you may have forgotten the 54 and attempted to solve but multiplied by instead of its reciprocal: .

Question 4. The correct answer is H. First, substitute the value of x into the expression: . Next, subtract 8 from 3: . Finally, because the absolute value of a number is its distance from 0, and because distance is positive, the absolute value of –5 is 5. If you chose F, you may have thought the absolute value bars change the – sign to +, calculated 3 + 8, and then changed the sign of 11 to −11. If you chose G, you may have subtracted 8 from 3 but neglected to calculate the absolute value. If you chose J, you may have simply chosen the value of x. If you chose K, you may have thought the absolute value bars change the – sign to + and calculated 3 + 8.

Question 5. The correct answer is A. The change in temperature can be determined by subtracting the starting temperature from the ending temperature: . If you chose B, you may have added instead of subtracting, , and made the result negative because the temperature dropped. If you chose D, you may have added instead of subtracting: . If you chose E, you may have subtracted in the wrong order or considered the starting temperature to be F and the ending temperature to be F: .

Question 6. The correct answer is G. The amount of money Ming paid for the car after the $1,000 down payment and 28 payments of $200 each is . Because the car had a purchase price of $5,400, the total she paid was $1,200 more than the purchase price: . If you chose F, you may have subtracted the purchase price of the car from only the total Ming paid in the 28 payments: . If you chose H, you may have subtracted the down payment from the purchase price of the car: . If you chose J, you may have calculated the total Ming paid in the 28 payments: . If you chose K, you may calculated the total Ming paid for the car and neglected to calculate how much more that was than the purchase price: .

Question 7. The correct answer is E. When a regular hexagon is inscribed in a circle, the radius of the circle is the same value as each side length of the hexagon because the diagonals of a hexagon form 6 congruent equilateral triangles. Because all the side lengths of a regular hexagon are the same and there are 6 sides in a hexagon, multiply the side length by 6 to find the perimeter: . If you chose A, you may have calculated the circumference of the circle: . If you chose B, you may have thought that diagonals of the hexagon form 6 congruent 30-60-90 triangles and used as a side length: . If you chose C, you may have thought that the side lengths of the hexagon were each 1 less than the radius of the circle: . If you chose D, you may have correctly determined that the side lengths were 4 but multiplied by 5 sides instead of 6: .

Question 8. The correct answer is J. The L-shaped floor plan is a composite shape. Find the missing horizontal length by subtracting the given horizontal lengths: 50 – 22 = 28. Find the missing vertical length by subtracting the given vertical lengths: 40 – 22 = 18. One possible method to find the area of the composite shape is to find the area that remains when a 28-by-18 rectangle is subtracted from a 50-by-40 rectangle: . If you chose F, you may have thought both missing lengths were 28 and found the perimeter of the floor plan instead of the area: . If you chose G, you may have calculated the area of the 28-by-18 rectangle that is not included in the floor plan: . If you chose H, you may have found a missing length to be 28 and thought the floor plan could be decomposed into two rectangles that are 22 by 28: . If you chose K, you may have calculated the sum of the area of a 22-by-50 rectangle and a 22-by-40 rectangle, which represents an overlap: .

Question 9. The correct answer is C. To classify the type of quadrilateral determined by the vertices, calculate the slopes of the sides to figure out which, if any, sides are parallel. The slope of is . The slope of is . The slope of is . The slope of is . There are two sides with a slope of , and . Because and have the same slope, they are parallel. The other sides are not parallel to each other. A trapezoid has exactly one pair of parallel sides. Therefore, Quadrilateral is a trapezoid. If you chose A, you may have thought the diagonals were perpendicular. If you chose B, D, or E, which are all parallelograms, you may have thought one pair of parallel sides was enough, or you may have miscalculated the slopes of the sides.

Question 10. The correct answer is H. Given that and , . For , . If you chose F, you may have calculated : . If you chose G, you may have calculated : . If you chose J, you may have calculated the product of and : . If you chose K, you may have calculated : .

Question 11. The correct answer is E. Julie's profit is the product of the number of hot dogs she sells and the price she sells them for minus the cost of her supplies: . In order for her to make a profit, that value must be greater than 0: . If you chose A, you selected the inequality that models making a profit if each hot dog sells for $1 each. If you chose B, you selected the inequality that models making no profit if each hot dog sells for $1 each. If you chose C, you may have thought that the purchase of supplies increased the profit and selected the inequality that models a profit if each hot dog sells for $1 each. If you chose D, you selected the inequality that models the number of hot dogs Julie can sell that keeps her from making a profit.

Question 12. The correct answer is G. To determine the slope of the line , rewrite the equation of the line to its slope-intercept form, , where is the slope of the line and is the -intercept. Subtract from both sides of the equation to get , and then divide both sides of the equation by 8 to get . Therefore, the slope is . If you chose F, you may have thought the slope was the coefficient of the x term when the equation was in this form: . If you chose H, you may have thought the slope was the coefficient of the x term when you divided by 5: , . If you chose J, you may have thought the slope was the coefficient of the x term in the given form of the equation: . If you chose K, you may have thought the slope was the constant in the given form of the equation: .

Question 13. The correct answer is A. The solution to the system of equations is the (x, y) pair that satisfies both equations in the system. One way to solve this system is by substitution. Begin by solving one of the equations for one of its variables. Then, substitute the solution from this first step into the other equation. If you solve the first equation for x, you have , . Next, substitute this expression for into the second equation to get . Now, solve this new equation for y: . You can substitute this y-value into either equation to solve for the value: . Thus, the solution to the system is (). If you chose B, you may have selected a value for and used it to solve the first equation for y: . If you chose C, you may have selected a value for and used it to solve the first equation for : . If you chose D, you may have selected a value for y and used it to solve the first equation for x: . If you chose E, you may have selected a value for y and used it to solve the first equation for x:.

Question 14. The correct answer is K. Convert the 2 inches on the map to the number of miles apart the towns are by multiplying 2 inches (2 = ) by 16 miles per of an inch. The inches cancel out, leaving the number of miles apart the towns are: in × = 176 miles. If you chose F, you may have calculated = 11. If you chose G, you selected the number of miles that are represented by inch, not 2 inches. If you chose H, you may have calculated (16) = 44. If you chose J, you may have calculated = 64, which is how many miles are represented by 1 inch.

Question 15. The correct answer is E. To multiply a matrix by a scalar, you multiply each term in the matrix by the scalar: . If you chose A, you may have been thinking of matrix multiplication and multiplied each term in the matrix by the scalar and then added the terms of each column: . If you chose B, you may have multiplied each term in the matrix by the scalar and then added the terms of each row: . If you chose C, you may have added the scalar to each term in the matrix: . If you chose D, you may have divided each term in the matrix by the scalar: .

Question 16. The correct answer is J. The tangent of an angle in a right triangle is equal to the ratio of the length of the leg opposite that angle to the length of the leg adjacent to that angle: . If you chose F, you might have found . If you chose G, you may have found cotA. If you chose H, you may have found sinA. If you chose K, you may have found the reciprocal of cosA, secA.

Question 17. The correct answer is D. Observe that 8 miles per hour is equal to miles per minute. Because distance is equal to the product of rate and time, it will take12 minutes for Tina to run miles. If you chose A, you may have divided the rate in minutes per mile by the time in minutes: . Notice that this is the reciprocal of the key. If you chose B, you may have divided the rate, in miles per hour, by the time, in minutes: . If you chose C, you may have divided the time, in minutes, by the rate, in miles per hour: .

Question 18. The correct answer is G. . If you chose F, you may have multiplied the 6 by before squaring it: . If you chose H, you may have squared 3 instead of : . If you chose J, you may have squared 6 instead of : . If you chose K, you may have multiplied the by before squaring it: .

Question 19. The correct answer is B. Because is perpendicular to both and , is parallel to . Because and are two parallel lines cut by transversal , alternate interior angles are congruent. Thus, . Angles and form a straight line; thus they are supplementary: . Because and are the acute angles of right triangle , they are complementary: . If you chose A, you may have computed . If you chose C, you may have thought was isosceles and computed . If you chose D, you may have found instead of . If you chose E, you may have computed .

Question 20. The correct answer is F. Because the function value at 5 is 2, and the function value at 15 is 6, the rate of change of the function is Because the function is linear, you can use the point-slope formula where m is the rate of change, is a specific input of the function, and is the respective output. Substituting If you chose B, you may have switched the input and output values: If you chose C, you may have selected an expression that was true for an input of 5 only: n − 3 → 5 – 3 = 2. If you chose D, you may have selected the expression that was true for an input of 15 only: n – 9 → 15 – 9. If you chose E, you may have selected an expression that was true for an input of 5 only: (n − 5) + 2 → (5 − 5) + 2 = 2.

Question 21. The correct answer is C. The first table lists the temperatures at each hour between 8:00 a.m. and noon. The second table lists the temperatures at each hour between noon and 4:00 p.m. Because the temperature fell at a constant rate, it first fell below 49°F sometime between 2:00 p.m. and 3:00 pm.

Temperature rose °F each hour

Temperature fell 1°F each hour

Time

Temperature in °F

Time

Temperature in °F

8:00 a.m.

49°F

Noon

51°F

9:00 a.m.

49°F

1:00 p.m.

50°F

10:00 a.m.

50°F

2:00 p.m.

49°F

11:00 a.m.

50°F

3:00 p.m.

48°F

Noon

51°F

4:00 p.m.

47°F

If you chose A, you may have thought the temperature at noon was 49°F. If you chose B, you picked the option that would be true if the temperature had fallen at 2°F each hour. If you chose D, you did not consider non-integer degree values between 49°F and 48°F. If you chose E, you picked the option that would be true if the temperature had fallen at °F each hour.

Question 22. The correct answer is K. The 4 unit exams and the final exam were worth a total of 600 points. The lowest number of points that earned a grade of B was 600(0.80) = 480 points. The lowest number of points that earned a grade of A was 600(0.90) = 540 points. Therefore, students with scores ranging from 480 points to 539 points earned a grade of B. On the 4 unit exams, Hugo earned a total of 82 + 88 + 91 + 83 = 344 points. Thus, his final exam score was between 480 – 344 = 136 points and 539 – 344 = 195 points. If you chose F, G, H, or J, you picked a score on the final exam that is in the range 136–195 and, thus, results in a grade of B.

Question 23. The correct answer is A. The base of each of the 10 bowling pins shown in the figure is represented by a circle. The area of a circle with radius r is πr². Therefore, when all of the pins are set up, the total area, in square inches, that is covered by the bases of the 10 pins is 10∙π ≈ 39.8 or 40 square inches. If you chose B, you may have chosen the value closest to 10 times the circumference (πd) of a single bowling pin: 10∙π(2.25) ≈ 71. If you chose C, you may have chosen the value closest to the sum of the area of 10 pins and 10 times the circumference of a single bowling pin: 40 + 71 = 111. If you chose D, you may have squared the number of pins and dropped the pi, 10²∙ ≈ 127, which is closest to 125. If you chose E, you may have used the diameter instead of the radius: 10∙π(2.25)² ≈ 159.

Question 24. The correct answer is G. In the figure, the bowling area and the pin deck are each in the shape of a rectangle. The area of a rectangle with length L and width W is LW. Therefore, the total area of the bowling lane is 65(3.5) = 227.5 square feet. Similarly, the area of the pin deck is 5(3.5) = 17.5 square feet. Therefore, the ratio of the total area of the bowling lane to the area of the pin deck is = ⇒ 13:1. If you chose F, you may have chosen the ratio of the area of the non-pin deck bowling lane to the area of the pin deck: ⇒ ⇒ 12:1. If you chose H, you may have chosen the ratio of the total area of the bowling lane to the area of the non-pin deck bowling lane: ⇒ ⇒ 13:12. If you chose J, you may have chosen the ratio of the perimeter of the non-pin deck bowling lane to the perimeter of the pin deck: ⇒ ⇒ 127:17. If you chose K, you may have chosen the ratio of the total perimeter of the bowling lane to the perimeter of the pin deck: ⇒ ⇒ 137:17.

Question 25. The correct answer is D. Let x represent the score Halle needs to earn in her 3rd game. Then, to find this unknown score, solve the equation = 172. First, add the numbers in the numerator of the fraction on the left side of the equation: = 172. Next, multiply by 3 on both sides of the equation: 3 = 3(172) ⇔ 324 + x = 516. Therefore, x = 516 – 324 = 192. So, Halle needs to earn 192 points in her 3rd game to have an average score of 172 points. If you chose A, you may have computed ≈ 165. If you chose B, you may have thought the unknown score was equal to the given average. If you chose C, you may have computed 2(172) – = 182. If you chose E, you picked the option that would earn Halle an average greater than 172, because ≈ 175.

Question 26. The correct answer is F. The area of a rectangle is equal to the product of its width and length: A = WL. You can call the unknown width x and the unknown length 3x because the length is 3 times the width. Then, 300 = x(3x). To solve for x, you divide both sides by 3 and then take the square root. 300 divided by 3 is 100. The positive square root of 100 is 10. So the width, x, is 10. If you chose G, you found the length instead of the width; you should have chosen the shorter of 10 and 30. If you chose H, you may have divided 300 by 3 to get 100 but then took half of 100 instead of taking the square root. If you chose J, you may have divided 300 by 3 and then stopped. If you chose K, you may have divided 300 by 3 to get 100, but then you took half of 100 to get 50 and then multiplied by 3 to get the length.

Question 27. The correct answer is C. Every parallelogram has 2 pairs of congruent sides. So if 1 of its sides measures 16, then another side must measure 16, and there must be 2 more sides of unknown length. Call that unknown length x. The perimeter is the sum of all the side lengths; we have 96 = 16 + 16 + x + x, or 96 = 32 + 2x. Subtract 32 and divide by 2, and you get x = 32. If you chose A, you may have solved 96 = 16 + 16 + 16 + x, using 16 as 3 side lengths. If you chose B, you may have solved the equation 96 = 16 + 2(x + 16) for x. If you chose D, you may have solved the equation 96 = 16 + x + x for x.

Question 28. The correct answer is H. Each of two directions has three lanes. You can add the widths of the lanes, 12 + 6 + 8, and then multiply by 2 to account for both directions: 2(12 + 6 + 8) = 52. If you chose F, you may have forgotten to multiply by 2. If you chose G, you may have doubled the 12 but not the 6 or 8: (12 + 12 + 6 + 8).

Question 29. The correct answer is A. If there are 2,500 students and 4 out of every 10 students ride the bus, then the number of students who ride the bus, x, can be found by solving . The number of students who ride the bus is 1,000. If 3 out of every 8 who ride the bus are freshman, then the number of students who are freshman and ride the bus, y, can be found by solving Alternatively, you can find of of 2,500 by multiplying

Question 30. The correct answer is H. Using the Pythagorean identity, sin²θ + cos²θ = 1, we have + cos²θ = 1, which is equivalent to cos²θ = , which is equivalent to cosθ = Because 90 degrees < cosθ < 180 degrees, cosθ must be negative. If you chose F, you may have found cosecant instead of cosine. If you chose G, you may have found tangent instead of cosine and forgot to consider the quadrant. If you chose J, you may have found secant instead of cosine. If you chose K, you may have found cosecant instead of cosine and changed the sign to negative.

Question 31. The correct answer is C. To find , solve the equation by multiplying both sides by (t + 1). This gives you . Because the function is undefined only when both and 1 are values for which . If you chose A, you may have found the value for which is undefined. If you chose B or D, you may have factored incorrectly: . If you chose E, you may have incorrectly factored to be .

Question 32. The correct answer is J. To find the distance between the 2 radar stations, you have to find AB in the given figure. Using the Pythagorean Theorem, ; thus, . Alternatively, you could recognize that this triangle is similar to the triangle that represents the Pythagorean triple: 5-12-13. Because and , . If you chose F, you may have found BD instead of AB. If you chose G, you may have thought BD = 13,000 – 12,000 and then added 1,000 + 9,000. If you chose K, you may have thought triangle was isosceles.

Question 33. The correct answer is C. Because the airplane is flying due west and point A is due west of point D, the airplane is flying on a path parallel to . In the standard (x,y) coordinate plane, both A and D are on the x-axis, so the airplane is flying on a line parallel to the x-axis. Because the airplane is 12,000 feet above D(9,000, 0), the airplane is currently at (9,000, 12,000). The line that is parallel to the x-axis and goes through (9,000, 12,000) is y = 12,000. If you chose A, you may have chosen the vertical line that goes through (9,000, 12,000) instead of the horizontal line. If you chose D, you may have used the straight-line distance the plane was from B instead of the distance the plane was from . If you chose E, you may have used the straight-line distance the plane was from A instead of the distance the plane was from .

Question 34. The correct answer is G. Because the airplane is currently directly above D and flying on a path parallel to to get to a point directly above A, it will travel this distance: AD = 9,000 feet. Because the airplane is traveling at a rate of 300 feet per second, the time it will take the airplane is 30 seconds. If you chose F, you may have confused Station B and Station A and divided 5,000 (the distance from D to B) by 300. If you chose H, you may have divided 12,000 by 300. If you chose J, you may have divided 13,000 by 300. If you chose K, you may have divided 15,000 by 300.

Question 35. The correct answer is A. When the airplane is directly above point A, it forms the right triangle shown in Figure 1. From question 32, you know that AB = 14,000. You also know that is 90°, and you can estimate that and are both between 40° and 50°. Figure 2 shows the new triangle at a certain point in time after the plane has flown due west. Notice that in Figure 2 is larger than in Figure 1 and and are smaller than in Figure 1. You can estimate to be greater than 90° and both and to be less than 40°. This shows that is increasing, and and are decreasing. Therefore, “I only” is the correct answer.

Question 36. The correct answer is G. The area of the original poster is 4(2) = 8 square feet. The area of the new poster will be 0.5(8) = 4 square feet. The length of the new poster will be (4) = 3 feet. Therefore, the width of the new poster will be = = 1 feet. If you chose F, you may have chosen the given fraction or you may have found the reciprocal of the width of the new poster: . If you chose H, you selected the value that is of the width of the original poster: (2). If you chose J, you selected the value that is of the area of the new poster: (4). If you chose K, you selected the value that is of the area of the original poster: (8).

Question 37. The correct answer is E. To find the solution set, simplify the right side of the equation. Multiply the 2 and the binomial (x + 3) to get x + 6 = 2x + 6 − x. Next, combine like terms to get x + 6 = x + 6. Observe that the resulting equation will be true for any real number x. If you chose A, you may have multiplied the 2 by the first term in the binomial only and then solved: x + 6 = 2x + 3 − x ⇒ x + 6 = x + 3 ⇒ 6 = 3. If you chose B, C, or D, you may have verified that the given equation was satisfied with the value in the set.

Question 38. The correct answer is J. Let L be the length of the region. Let W be the width of the region. The perimeter, in feet, of the region will be 2L + 2W = 28. To express the width W in terms of the length L, rewrite the equation as 2W = 28 − 2L or W = 14 − L. The area, in square feet, of the region is A = LW. Use the fact that W = 14 − L to rewrite the area as A = L(14 − L) or A = 14L − L². This quadratic equation represents a function of L where the maximum value occurs at the vertex. Thus, the maximum value occurs for L = = 7, and the maximum value is A = 7(14 − 7) = 49. So, the area of the largest rectangular region Steve can enclose is 49 square feet. If you chose F, you may have thought the dimensions 4 and 10 yield the greatest area. If you chose G, you may have thought the dimensions 5 and 9 yield the greatest area. If you chose H, you may have thought 6 and 8 yield the greatest area and didn’t consider that a square is a rectangle. If you chose K, you may have mistaken the width as 28 − L and the area as A = L(28 − L), which yields L = 14 and W = 14.

Question 39. The correct answer is C. The addition of the professional athlete’s annual income will not change the median significantly. The median is calculated using the middle 1 or 2 values in a data set, written in numeric order, so it will not be influenced by an extreme outlier. The median annual income of the original group of 5 people is between $30,000 and $35,000 and so is the median annual income of the new group of 6 people. If you chose A, you picked a measure that is not resistant to outliers. Because the range is based on the minimum and maximum values in a data set, it will be influenced by the extreme outlier. The range of the annual income of the original group of 5 people is roughly $35,000 − $30,000 = $5,000, but the range of the annual income of the new group of 6 people is roughly $1,000,000 − $30,000 = $970,000. If you chose B, you picked a measure that is not resistant to outliers. The mean is calculated using every value in the data set. Thus, it will be influenced by the extreme outlier. If you chose D, you picked a measure that is not resistant to outliers. The standard deviation is roughly the typical distance that the values in a data set fall from the mean. In the original group of 5 people, all of the values are reasonably close to the mean, so the standard deviation is small. But because there is an outlier of $1,000,000 in the new group of 6 people, the typical distance of the values from the mean is much higher, so the standard deviation is much higher.

Question 40. The correct answer is K. Ana and Amy completed + = = of the job. Ruben finished the remaining 1 − = of the job in 2 hours. Because all 3 worked at the same rate, each person completed = of the job per hour. It follows that it would have taken 1 person, working alone, = = 7.5 hours to complete the entire job. If you chose F, you may have solved x + x + x = 1. If you chose G, you may have computed 2 − − . If you chose H, you may have computed + + 2. If you chose J, you may have thought Ana worked 2 hours so you computed = ⇒ ⇒ .

Question 41. The correct answer is C. Applying the exponent of 4 to all factors in the numerator gives . Rewriting this expression gives , which is equivalent to . If you chose B, you may have multiplied the coefficient 2 by the exponent 4 and combined the exponents −1 and 4 to get . If you chose D, you may have mistaken the square root symbol for a 4th root. If you chose E, you may have ignored the square root symbol and thought equals and also thought equals .

Question 42. The correct answer is G. The contestant knows the oldest, so the probability of getting the oldest correct is 1. The contestant guesses the 2nd oldest from the other 3 rock stars, so the probability of getting the 2nd oldest correct is . Assuming the first 2 are correct, the probability of guessing the 3rd oldest is , which leaves only 1 person for the 4th oldest. Multiplying these probabilities, , you get . If you chose F, you may have thought the contestant guessed all 4 and multiplied . If you chose H, you may have chosen the denominator 4 because there were 4 rock stars. If you chose J, you may have chosen the denominator 3 because there were 3 positions the contestant didn’t know. If you chose K, you may have thought the contestant could be either correct or incorrect with equal probability.

Question 43. The correct answer is D. Here is one course of simplification.

Rewrite the given expression with two pairs of common denominators:

Combine fractions with like denominators:

Rewrite, using multiplication of the reciprocal:

Reduce the 12 and 6 to 2 and 1:

Multiply numerators, using distribution, and multiply denominators:

If you chose A, you may have neglected to get common denominators and added numerators and denominators to get . If you chose B, you may have neglected to distribute the factor 2 to the 2x in the last step. If you chose C, you may have neglected to distribute the factor 2 to the 3 in the last step. If you chose E, you may have thought that in the first step was .

Question 44. The correct answer is K. The fundamental counting principle allows us to multiply the number of ways to fill each position to get the total number of unique strings of characters. There are 10 digits that could fill each of the first 3 positions and 26 letters that could fill each of the last 6 positions, so the number of license plates is . If you chose F, you may have added 10 and 26. If you chose G, you may have thought there were only 6 possible characters for each of the 6 positions. If you chose H, you may have thought that no letters and only digits were being used. If you chose J, you may have thought there were only 9 digits instead of 10.

Question 45. The correct answer is A. The function is equivalent to . To turn into , we’d have to add 1 to x and add 3 to y. So the graph of will be shifted 1 unit to the right and 3 units up. For example, the point (0,0) satisfies , and the point (1,3) satisfies . If you chose B, you may have thought was equivalent to . If you chose C, you may have confused the directions right and up. If you chose D, you may have thought the positive 3 and negative 1 meant there must be some shift in a positive direction (right) and some shift in a negative direction (down). If you chose E, you may have thought was equivalent to but then mixed up the x and y axes and didn’t realize the shift on each axis should be in the positive direction.

Question 46. The correct answer is K. The logarithmic equation is equivalent to the exponential equation . Because , it follows that . If you chose F, you might have thought the logarithmic equation was equivalent to the exponential equation . If you chose G, you might have thought the logarithmic equation was equivalent to the exponential equation . If you chose H, you might have thought the logarithmic equation was equivalent to the equation . If you chose J, you might have thought .

Question 47. The correct answer is D. The fraction and . Because , it follows that is between and for . If you chose A, you might have ignored the 2 in . If you chose B, you might have ignored the 2 in and included the denominators of the given fractions as well as . If you chose C, you might have known was between and and converted to but didn’t consider other values for D. If you chose E, you might have added the denominators of and .

Question 48. The correct answer is F. Whenever you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. The inequality is equivalent to . If you chose G or H, then you might not have realized that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. Notice that the inequality is true, but both inequalities and are false. If you chose J, you might not have remembered the additive property of inequality that says if , then . Thus, it is false that . Adding or subtracting a negative number from both sides of the inequality does not require reversing the inequality symbol. If you chose K, you might not have realized that this inequality is not true for all values of a, b, and c. Notice that the inequality , but is not true.

Question 49. The correct answer is B. Subtracting from both sides of the equation gives . Dividing that equation by and then taking the inverse cosine of both sides gives . Let be the largest angle in the triangle. Because the largest angle, C, is opposite the longest side, define . Plugging in the values , , and gives the equation . If you chose A, you might have thought the largest angle was opposite the shortest side. If you chose C, D, or E, you might have added 2ab instead of dividing by 2ab.

Question 50. The correct answer is K. If Pete’s average score on 4 tests is x points, then the sum of his scores on those 4 tests is 4x points. Let y be Pete’s score on the 5th test. His average score on all 5 tests is . Multiplying both sides of this equation by 5 gives . Subtracting 4x from both sides gives . His average score on the 5th test must be 10 greater than x. If you chose F, you might have thought the question asked how many points higher than x is x + 2. If you chose G, you might have thought that x + 2 was the average of 2 scores (old test and new test) instead of 5 scores. If you chose H, you might have chosen a number equal to the total number of tests. If you chose J, you might have multiplied the change in average, 2, by the number of tests already taken, 4.

Question 51. The correct answer is D. Two intersecting lines form pairs of adjacent angles, called linear pairs, which are supplementary. Also, two intersecting lines form pairs of congruent angles, called vertical angles. Because the measure of ∠B is 3 times the measure of ∠A, the angles are not congruent angles. Therefore, ∠B and ∠A must be adjacent angles that form a linear pair, and so they are supplementary. Let x be the measure of ∠A in degrees. Then, x + 3.5x = 180 and so 4.5x = 180 ⇔ x = 40. Hence, the measure of ∠A is 40°. If you chose A, you may have thought the angles were complementary, x + 3.5x = 90. If you chose B, you may have computed ≈ 26. If you chose E, you may have computed ≈ .

Question 52. The correct answer is J. The sequence is defined recursively, so begin with the given initial value of s₁ = 3 and compute the values of s₂, s₃, and s₄. Each calculation is shown in the table.

n

sn = 2s(n − 1) + n + 1

1

s₁ = 3

2

s₂ = 2s(2 − 1) + 2 + 1 = 2s₁ + 2 + 1 = 2(3) + 2 + 1 = 9

3

s₃ = 2s(3 − 1) + 3 + 1 = 2s₂ + 3 + 1 = 2(9) + 3 + 1 = 22

4

s₄ = 2s(4 − 1) + 4 + 1 = 2s₃ + 4 + 1 = 2(22) + 4 + 1 = 49

If you chose F, you may have stopped at s₂. If you chose G, you may have multiplied 2 times the value of s₂. If you chose H, you may have stopped at s₃.

Question 53. The correct answer is E. If a is an integer less than −1, then |a| is greater than 1. Also, if a is an integer less than −1, then a² is an integer greater than 1, and thus, −a² is an integer less than −1. Finally, if a is an integer less than −1, then is a negative number greater than −1, and thus, − is a positive number less than 1. So −a² < −1 < − < 1 < |a|. Therefore, the expressions ordered from least to greatest are −a² < − < |a|. If you chose A or B, you may not have noticed that − is a positive number and −a² is a negative number. If you chose C, you may have ordered the expressions from greatest to least. If you chose D, you may not have noticed that − is less than 1 and |a| is greater than 1.

Question 54. The correct answer is J. First create the probability distribution for the random variable X. There are 10 equally likely outcomes in the sample space: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4. Each value of X and its associated probability, P(X), is listed in the table. The expected value of X, E(X), is calculated by adding all X·P(X) products. Thus, E(X) = ∑XP(X) = 1(0.1) + 2(0.2) + 3(0.3) + 4(0.4) = 3. If you chose F, you may have divided the number of distinct cards by the total number of cards: = 0.4. If you chose G, you may have chosen the sum of all the probabilities, ∑P(X) = 1. If you chose H, you may have found the mean of 1, 2, 3, and 4. If you chose K, you may have thought “expected value” meant the value of X that is associated with the greatest probability.

X

P(X)

1

= 0.1

2

= 0.2

3

= 0.3

4

= 0.4

Question 55. The correct answer is B. Define 3 consecutive odd integers x, y, and z such that x < y < z with the expressions x = 2n + 1, y = 2n + 3, and z = 2n + 5 where n is an integer. The sum of x, y, and z is, therefore, 2n + 1 + 2n + 3 + 2n + 5 = 6n + 9 = 3(2n + 3) = 3y. If you chose A or C, you may have chosen an expression that represents the sum if x, y, and z are the same number. If you chose D, you may have rewritten x + y + z as x + x + 2 + x + 2 + 2 and then incorrectly simplified to 3x + 2. If you chose E, you may have chosen the expression that represents the average of the 3 consecutive odd integers rather than the sum.

Question 56. The correct answer is G. Because the mean of the 5 numbers is 24, the sum of the 5 numbers must be 5(24). Solving gives x = 37. Because the median of the 4 numbers is 38, the arithmetic mean of the middle 2 numbers (2nd and 3rd greatest numbers) must be 38. One of the middle numbers must be 29 because 8 is less and 53 is greater. Solving gives y = 47. Therefore,. If you chose F, you may have taken the additive inverse of the given median. If you chose H, you may have calculated . If you chose J, you may have chosen the given median. If you chose K, you may have thought the value of y couldn’t be determined because the order of the 4 numbers wasn’t given.

Question 57. The correct answer is A. Let the length and width of such a rectangle be l inches and w inches. It is given that the area is 144 square inches, so lw = 144. If we assume A is true, the perimeter is 48 inches, and l + w = 24 inches. Solving the system , we get only one solution: l = w = 12. But this doesn’t meet the condition that the rectangle’s length is greater than the width. Therefore, 48 inches cannot be the perimeter for such a rectangle. Alternatively, you can write all lw factor pairs of 144 (where ) and double each l + w sum to get possible 2(l + w) perimeters. If you chose B, you didn’t realize that l = 24 and w = 6 satisfy the conditions. If you chose C, you didn’t realize that l = 36 and w = 4 satisfy the conditions. If you chose D, you didn’t realize that l = 48 and w = 3 satisfy the conditions. If you chose E, you didn’t realize that l = 72 and w = 2 satisfy the conditions.

Question 58. The correct answer is J. The y-coordinate of the center of the circle is 8. One endpoint of a diameter has a y-coordinate of 11, which is 3 greater than 8. So the other endpoint must have a y-coordinate that is 3 less than 8. If you chose F, you may have subtracted 11 − 10. If you chose G, you may have used the x-coordinate of the center, 7, and subtracted the difference of 11 and 7 from 7; or you may have subtracted the y-coordinate of the center from 11. If you chose H, you may have subtracted the x-coordinate of the center from 11. If you chose K, you may have chosen the y-coordinate of the center.

Question 59. The correct answer is D. For any values of length, width, and depth, the volume reflecting the increase in length and width can be represented by (1.1l)(1.1w)(d), which is equivalent to 1.21(lwd). The value 1.21 represents a 21% increase. If you chose A, you may have thought the percent increase in volume would equal the percent increase in length and width. If you chose B, you may have rounded the result of to the nearest 1%. If you chose C, you may have added 10% + 10%. If you chose E, you may have thought all three dimensions were increased by 10%.

Question 60. The correct answer is K. Because x = −1 is a solution, x +1 is a linear factor. Dividing by x + 1 gives . The discriminant of the quadratic formula is , which for is equal to . If you chose F, you may have thought a negative discriminant meant the solutions are both negative.

READING • PRACTICE TEST 4 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is A because the narrator makes clear that he does not know or remember all the details of the story he relates about Jantzen. The narrator states, “I’m not acquainted with the details, having been in high school at the time. But I can imagine” (lines 31–32). Later, the narrator points out that his memory “grows shaky” (line 46) because he had graduated from high school and moved out of town. When the narrator returned, “the steam-car operation was spoken of with scorn by the people who had been against it” (lines 50–52), which suggests hearsay.

The best answer is NOT:

B because the passage does not mention the narrator ever having spoken with Jantzen. Instead, the narrator states that he was “not acquainted with the details” (line 31).

C because the passage does not indicate that the entire story is fabricated. The narrator frames the story as if it actually happened, providing details about Jantzen and enough information about the events to strongly suggest that the story did happen.

D because the passage makes clear that the narrator was not a participant in the events. “I’m not acquainted with the details. . . . But I can imagine” (lines 31–32).

Question 2. The best answer is H because the phrase “though maybe not as quick as he should have been to smell a rat” (lines 23–24) suggests that Jantzen was not sensitive to the possibility that someone might try to take advantage of him. For the narrator to bring up Jantzen’s not being quick to “smell a rat” hints that Jantzen, ultimately, was tricked in some way.

The best answer is NOT:

F because, as it is presented in the passage, the fact that Jantzen ran the bank does not in itself foreshadow his downfall more strongly than response H does. This detail is used to help establish Jantzen’s position.

G because the passage does not make a clear connection between people coming up with ideas in the Thirties and Jantzen’s downfall. This detail provides context for the story rather than strongly foreshadowing Jantzen’s downfall.

J because, though the passage mentions that Jantzen might have had a steam-driven car, and that he may have had a fondness for them, the detail does not provide foreshadowing. It suggests one reason Jantzen might have been interested in the idea to resurrect the steam-driven car.

Question 3. The best answer is D because the passage suggests that people in town didn’t know who convinced Jantzen to invest in steam-driven cars. Lines 19–21: “Who knows if it was a single person or a cohort. Maybe a stranger or some friends of friends.”

The best answer is NOT:

A because the passage does not indicate that the townspeople knew who was involved in the investment scheme. Instead, lines 19–21 suggest that they could only speculate about this.

B because although strangers and friends of friends are mentioned as people who hypothetically could have convinced Jantzen to invest (lines 20–21), their involvement is portrayed as speculation only. The suggestion is that the townspeople didn’t know, not that some people believed it was strangers and others believed it was friends of friends.

C because although an undescribed cohort is mentioned as possibly convincing Jantzen to invest (line 20), any involvement is portrayed as speculation only.

Question 4. The best answer is H because the passage presents options I, III, and IV as being true of the townspeople’s behavior, as conveyed in lines 50–54. “By the time I got back home the steam-car operation was spoken of with scorn by the people who had been against it and not at all by those who had promoted it. The visitors to town who promoted it had disappeared.”

The best answer is NOT:

F because it includes option II, “People in town blamed the loss of money on Jantzen having cheated.” This contradicts the point made in lines 55–56: “There was talk not of cheating but of mismanagement.”

G because it does not include option I, “Visitors who promoted steam cars had left town,” which is made clear in lines 53–54.

J because it includes option II, “People in town blamed the loss of money on Jantzen having cheated.” This contradicts information provided in lines 55–56: “There was talk not of cheating but of mismanagement.”

Question 5. The best answer is B because lines 14–16 state that times were hard in the Thirties and that people were coming up with ideas to make money. “In the hard times of the Thirties people were still coming up with ideas. You can be sure, men were nursing a notion bound to make them a million dollars.” “In the hard times of the Thirties” indicates that times were hard. “Men were nursing a notion bound to make them a million dollars” indicates that people were trying to come up with money-making schemes.

The best answer is NOT:

A because lines 14–16 refer to the 1930s, not to people in their thirties. This is supported by the reference to “those days” in line 17.

C because the lines suggest that men wanted to make a million dollars (“nursing a notion bound to make them a million dollars”), not that they were actually making as much as a million dollars a year.

D because the lines do not indicate or suggest that people felt that they should take their money-making plans to Jantzen. The lines instead capture a general trend in the 1930s, according to the narrator.

Question 6. The best answer is J because fostering, a synonym for nursing, makes sense in the context of people coming up with new money-making schemes (lines 14–17). In this context, fostering means “to promote the growth and development of,” which is similar to the meaning of nursing as the word is used in the sentence.

The best answer is NOT:

F because rearing is not a contextually appropriate synonym for nursing as the word is used in the sentence. “To rear” means to support until maturity, usually in the context of people or animals, or to erect by building, which does not make sense in context.

G because educating is not a contextually appropriate synonym for nursing as the word is used in the sentence. Educating usually refers to teaching or informing, which does not make sense in context.

H because healing is not a contextually appropriate synonym for nursing as the word is used in the sentence. Healing typically means curing, which does not make sense in context.

Question 7. The best answer is A because as the narrator speculates about who might have convinced Jantzen to invest, he notes Jantzen’s admiration of appearances. Lines 21–22: “Well dressed and plausible looking, you may be sure. Horace set store by appearances.”

The best answer is NOT:

B because the narrator does not suggest that Jantzen would not have loaned money to someone who wasn’t wealthy. The passage implies that the person would have been “well dressed and plausible looking,” but the focus is on appearances, not wealth or risk.

C because the narrator does not mention age as a factor Jantzen would have considered, nor does the passage indicate that Jantzen would have trusted someone who had once owned a steam-driven car.

D because the narrator does not indicate the person who convinced Jantzen to invest needed to be intelligent. Instead, the narrator suggests Jantzen would have relied on appearances. “Well dressed and plausible looking, you may be sure. Horace set store by appearances” (lines 21–22). Jantzen himself may not have been “as quick as he should have been to smell a rat” (lines 23–24), which implies he may have been fooled rather easily.

Question 8. The best answer is F because the passage makes clear that the new version of the steam-driven car would be an improved version of earlier models. The passage states that the new model would be less expensive and quiet, which suggests that the earlier cars were expensive and noisy. “This new model would be an improved version, of course, and have the advantages of being economical and not making a racket” (lines 28–30).

The best answer is NOT:

G because there is no indication in the passage that the original steam-driven cars were reliable or fast.

H because the passage does not indicate that the original steam-driven cars were unattractive and impractical. Impracticality may be implied since economy is mentioned as a benefit of the new model, but attractiveness is never mentioned.

J because the passage does not indicate that the original steam-driven cars were luxurious or durable.

Question 9. The best answer is C because the passage makes clear in lines 38–39 that “the bank had put up the loan.” It goes on: “It was Jantzen’s decision and there was some confusion that he had put in his own money. He may have done so, but he had also dipped improperly into bank funds, thinking no doubt that he could pay it back with nobody the wiser” (lines 39–43).

The best answer is NOT:

A because the passage does not mention any involvement of “some of Jantzen’s wealthy friends.”

B because the passage states in lines 40–41 that Jantzen may have invested his own money but does not indicate that this definitely occurred or that it was his entire life savings. The passage bluntly states, however, that he did use bank funds. “But he had also dipped improperly into bank funds, thinking no doubt that he could pay it back with nobody the wiser” (lines 41–43).

D because the passage does not make clear that the entrepreneurs from Toronto, Windsor, or Kitchener referred to in lines 34–35 invested any money. The passage states that “others would ask if they [the entrepreneurs] had backing,” and goes on to say that “they did indeed, because the bank had put up the loan” (lines 36–39).

Question 10. The best answer is G because lines 65–68 state that it was pride that led Jantzen to agree to take the job at the Hawksburg bank. “Surely he could have refused, but pride, as it was thought, chose otherwise. Pride chose that he be driven every morning those six miles to sit behind a partial wall of cheap varnished boards, no proper office at all.”

The best answer is NOT:

F because pride is not presented as a possible reason for Jantzen’s decision to invest in steam-driven cars. The narrator speculates that Jantzen may have been swayed by someone plausible looking and also suggests that Jantzen may have had a steam-driven car himself and may have “had a fondness for them” (lines 27–28).

H because the narrator makes it clear that Jantzen did not look unhappy when Oneida drove him to work. Lines 77–80: “I don’t see Oneida looking downtrodden or unhappy at the arrangement, nor her father looking actually unhappy. Dignity was what he had, and plenty of it.”

J because although the passage notes that Jantzen had to sit in an office made out of varnished boards, the passage does not indicate that Jantzen himself created the office.

Passage II

Question 11. The best answer is C because the paragraph in which the description of the fountain pen appears is about the ways in which plastic allowed designers to embrace “the spirit of modernity” (lines 3–4). In addition, the lines before the mention of the fountain pen suggest that everyday objects, when created out of plastic, could seem exciting. Lines 12–16: “. . . a lingo of curves and dashes and teardrop shapes that created a feeling of speed and motion in everyday objects. Streamline a fountain pen and even that stolid item declared: we’re hurtling toward the future here!”

The best answer is NOT:

A because the passage does not mention plastic items looking identical as a result of being streamlined.

B because the passage does not indicate that designers were critiqued for creating items that were beautiful rather than functional.

D because it contradicts the suggestion in the passage that fountain pens were in fact changed by new design trends. Lines 15–16: “Streamline a fountain pen and even that stolid item declared: we’re hurtling toward the future here!”

Question 12. The best answer is F because the paragraph notes that plastics allowed designers to create quality designs at lower prices. “There was another reason designers embraced plastics. From the mid-twentieth century on, modern design has been guided by an egalitarian gospel, a belief that good design needn’t cost a lot of money” (lines 17–20).

The best answer is NOT:

G because the paragraph mentions only one slogan that was associated with plastics, and the slogan supports the main idea that plastics could be used to create appealing products at low prices.

H because the paragraph does not mention that plastics were challenging to work with.

J because the paragraph does not indicate that designers who embraced plastics prized the mundane over the beautiful. Rather, the idea was that mundane things could be made beautiful.

Question 13. The best answer is A because a number of points in the passage suggest that designers felt that plastics encouraged inventiveness. Lines 2–4: “They loved the design freedom that synthetics offered and the spirit of modernity the materials embodied.” Lines 5–10: “Bakelite, the world’s first synthetic plastic, spoke ‘in the vernacular of the twentieth century . . . the language of invention, of synthesis,’ and he [Frankl] urged his fellow designers to use their full imaginative powers to explore the new materials’ frank artificiality.”

The best answer is NOT:

B because the passage does not mention that consumers demanded attractively designed items.

C because the passage does not indicate that people who created items out of plastics were seen as risk takers.

D because the passage does not suggest or indicate that Bakelite was difficult to work with.

Question 14. The best answer is G because the passage lists a number of examples of items made from plastics that didn’t work for the purposes for which they were made. The passage also states that during the 1950s, plastic technology improved, in turn improving the objects that were made from plastics. Lines 37–43: “There were plastic plates that melted in hot water, plastic toys that cracked on Christmas morning, plastic raincoats that grew clammy and fell apart in the rain. Polymer technology improved during the 1950s as manufacturers figured out how to make better plastics and, even more important, how to match the right polymer with the right application.”

The best answer is NOT:

F because the passage notes that even in the 1930s and 1940s, plastics could be made to appear streamlined. Lines 10–12: “As interpreted by Frankl and other designers working with Bakelite in the ’30s and ’40s, that was the language of streamlining.”

H because there is no indication that manufacturers had not figured out whether consumers would buy plastics. In fact, the examples listed in the last paragraph (plastic plates, plastic toys, plastic raincoats) suggest that consumers did buy everyday items made of plastics.

J because the first paragraph of the passage notes that designers loved to work with plastics. Lines 1–4: “Designers were enthralled by the universe of possibility from plastics’ earliest days. They loved the design freedom that synthetics offered and the spirit of modernity the materials embodied.”

Question 15. The best answer is D because the lines that come before this statement make it clear that plastics had become part of people’s everyday routines. “As House Beautiful observed in 1955, ‘The news is not that plastics exist, but [that] they have already been so assimilated into our lives.’ The average person was ‘conditioned to plastics’” (lines 78–82).

The best answer is NOT:

A because the passage does not mention that the production and use of plastics represented increased consumerism.

B because the passage does not indicate that people preferred to buy things made out of plastics over things made out of other materials. The passages stresses that consumers didn’t really have a choice because plastic “surrounded everyone” (line 48). “Once plastic products filled the stores, people had no choice but to consume what they were offered” (lines 56–58). “The average person was ‘conditioned to plastics’” (lines 81–82).

C because the passage does not indicate that people found plastics to be a threat to traditional ways of life.

Question 16. The best answer is G because the passage asserts that “a sleepy householder had to watch only once in disbelief as a polyethylene juice pitcher bounced off the kitchen floor to begin accepting plastic in a practical way no matter how strong the conceptual disdain for it” (lines 66–70). The juice pitcher provides a specific example of plastic’s durability, which was enough to overcome “disdain” for the material.

The best answer is NOT:

F because the passage does not indicate that the juice pitcher was part of an advertisement.

H because the paragraph in which the quoted lines appear is not about how plastics improved, but rather about the effects of improvements. As noted in response G, the lines serve as an example of plastic’s durability.

J because the lines show how plastic could win people over, not bias people against it. “A sleepy householder had to watch only once in disbelief as a polyethylene juice pitcher bounced off the kitchen floor to begin accepting plastic in a practical way no matter how strong the conceptual disdain for it” (lines 66–70).

Question 17. The best answer is C because the passage specifically describes toys that were made out of plastic as being both less durable and less destructive. Lines 70–74: “Even plastic toys, despite the brittle polystyrene items that broke on Christmas morning, proved superior in many ways. A toy soldier of molded polyethylene could not scratch the furniture as readily as an old-fashioned lead soldier.”

The best answer is NOT:

A because the passage does not mention that plastic toys were more flexible and detailed.

B because the passage does not indicate that plastic toys were less costly, and, as noted in response C, they were often less sturdy than nonplastic toys. Lines 70–71: “Even plastic toys, despite the brittle polystyrene items that broke on Christmas morning.”

D because the passage does not discuss the relative popularity of plastic toys among kids and parents.

Question 18. The best answer is F because both passages include quotations about plastics, either from designers who used plastics or from publications writing about plastics. Passage A: “To furniture designer Paul T. Frankl, a material like Bakelite, the world’s first synthetic plastic, spoke ‘in the vernacular of the twentieth century . . . the language of invention, of synthesis’” (lines 4–8). “Plastics’ adaptability and glibness undermined their capacity to achieve ‘dignity’ as legitimate materials worthy of being taken seriously, one critic wrote” (lines 32–34). Passage B: “Sidney Gross, who joined Modern Plastics in 1952 and became editor in 1968, recalled that he had ‘agitated a lot’ over the years to get SPI, the trade association for the plastics industry, to quit trying to convince people ‘that plastic is not bad’” (lines 49–53). “As House Beautiful observed in 1955, ‘The news is not that plastics exist, but [that] they have already been so assimilated into our lives.’ The average person was ‘conditioned to plastics’” (lines 78–82).

The best answer is NOT:

G because although Passage B refers to Modern Plastics and House Beautiful, it does not analyze these publications or assert that they promoted plastics. Passage A does not mention publications that promoted plastics.

H because neither passage defines the key concepts that were used to market plastics.

J because neither passage personifies artwork or objects that were made of plastics.

Question 19. The best answer is D because both passages indicate that the public believed plastic was interior. Passage A, lines 30–31: “The growing reputation of plastic as an inferior material.” Lines 35–40: “This impression was exacerbated by people’s unfortunate experiences with plastics in the immediate postwar years. There were plastic plates that melted in hot water, plastic toys that cracked on Christmas morning, plastic raincoats that grew clammy and fell apart in the rain.” In Passage B, lines 58–64 indicate that after the plastics industry solved postwar quality problems and plastics worked better, people still held on to the idea that plastic was inferior. “Things made of plastic were better designed and lasted longer. People intuitively recognized that fact even if they retained an intellectual notion that plastic was bad or shoddy.”

The best answer is NOT:

A because there is no indication in either passage that people found plastics unattractive in design. In fact, Passage A suggests that items made from plastics could be beautiful. Lines 18–21: “From the mid-twentieth century on, modern design has been guided by an egalitarian gospel, a belief that good design needn’t cost a lot of money, that even the most mundane items could be things of beauty.” Passage B does not discuss plastics’ aesthetic qualities.

B because although plastics’ artificiality is mentioned in Passage A, it is not suggested that this is unnerving, but rather that it is something to be embraced. Lines 8–10: “He urged his fellow designers to use their full imaginative powers to explore the new materials’ frank artificiality.” Passage B does not discuss plastics’ artificiality.

C because Passage A notes that plastics were relatively inexpensive. Lines 24–26: “Plastics were the ideal medium for that mission: malleable, relatively inexpensive, and made for mass manufacture.” Passage B does not discuss the cost of plastics. Moreover, neither passage indicates that the public believed items made of plastics were “novelties.”

Question 20. The best answer is J because both passages use toys as an example of problems with the quality of plastics. In Passage A, the example follows a paragraph that asserts plastic’s reputation as an inferior material. Lines 35–40: “This impression [that plastics were inferior] was exacerbated by people’s unfortunate experiences with plastics in the immediate postwar years. There were plastic plates that melted in hot water, plastic toys that cracked on Christmas morning, plastic raincoats that grew clammy and fell apart in the rain.” The passage goes on to assert that technology improved during the 1950s, but “the damage to plastic’s reputation had been done” (lines 43–44). In Passage B, toys also provide an example of a flaw. Lines 70–72: “Even plastic toys, despite the brittle polystyrene items that broke on Christmas morning, proved superior in many ways.” In this case, despite the problem with quality (“brittle polystyrene items that broke on Christmas morning”), plastic could be superior in other ways (“not scratch the furniture”).

The best answer is NOT:

F because although Passage B notes that plastic items could be superior to what they replaced (“Even plastic toys, despite the brittle polystyrene items that broke on Christmas morning, proved superior in many ways”), Passage A uses toys as an example of bad design, not good design. Lines 35–40: “This impression was exacerbated by people’s unfortunate experiences with plastics in the immediate postwar years. There were plastic plates that melted in hot water, plastic toys that cracked on Christmas morning, plastic raincoats that grew clammy and fell apart in the rain.”

G because Passage A does not mention that plastic toys were particularly popular, and the example of toys in Passage B is used to demonstrate both quality problems and plastics’ superiority.

H because, in both passages, the example of toys is provided to show problems with plastics, not the variety of plastic items that were produced. Passage A: “This impression was exacerbated by people’s unfortunate experiences with plastics in the immediate postwar years. There were . . . plastic toys that cracked on Christmas morning” (lines 35–39). Passage B: “. . . plastic toys, despite the brittle polyethylene items that broke on Christmas morning” (lines 70–71).

Passage III

Question 21. The best answer is C because the paragraph tells a story that is narrated in a biography of García Márquez. The author of the passage specifically notes this at the beginning of the second paragraph. “When Gerald Martin, around the middle of his rich and resourceful biography of García Márquez, starts to tell this story” (lines 9–11).

The best answer is NOT:

A because as noted in response C, the paragraph tells the story of García Márquez’s writing the novel. The paragraph does not mention misconceptions about how long it took to write One Hundred Years of Solitude.

B because the paragraph describes only the circumstances surrounding García Márquez’s writing one particular novel, not novels in general.

D because the paragraph does not discuss García Márquez’s childhood at all.

Question 22. The best answer is F because the author of the passage specifically states that he believes García Márquez to be a gifted writer. Lines 44–46: “When he got into the car to set out for Acapulco, he was a gifted and hardworking writer, certainly.”

The best answer is NOT:

G because although the passage mentions García Márquez’s journalism, there is no mention in the passage that the author preferred his journalism to his novels.

H because although the author of the passage notes that García Márquez’s novels borrow from local facts and legends, there is no indication that he thinks García Márquez does so too much. Lines 61–66: “It takes pieces of already thoroughly mythified reality—there is scarcely an extravagant incident in his novels and stories that doesn’t have some sort of basis in specific, local fact or legend—and finds the perfect, unforgettable literary home for them.”

J because the author of the passage refers to Martin’s insistence on excessive melancholy, not García Márquez’s. Lines 83–87: “There is perhaps a slight imbalance in Martin’s insistence on the writer’s sadness, an excess of melancholy; but it’s a good corrective to García Márquez’s own joking cheerfulness and elaborate ironies.”

Question 23. The best answer is A because in the first paragraph of the passage, it is made clear that the “illumination” is referring to García Márquez’s writing of the novel. “Many years later, and many times over, the writer Gabriel García Márquez was to remember the day he discovered how to set about writing his great novel. He was driving from Mexico City to Acapulco when the illumination hit him” (lines 1–5). When the word is used again in line 37, it is in reference to the story that is first told in the first paragraph.

The best answer is NOT:

B because the passage notes that García Márquez directly stated that he modeled an aspect of his writing after Kafka’s, not that Martin discovered this. Lines 31–34: “What García Márquez found was a way of telling it. He would combine, as he frequently said, the narrative tone of his grandmother with that of the author Franz Kafka.”

C because the reference to “illumination” occurs well before the passage author notes that García Márquez based his stories on local facts and legends, and also because the use of “illumination,” as noted in response A, is in reference to García Márquez, not the passage’s author.

D because there is no indication in the passage that García Márquez considered his completion of One Hundred Years of Solitude miraculous. As noted in response A, the use of “illumination” refers to García Márquez’s discovery of “how to set about writing his great novel” (line 3).

Question 24. The best answer is H because Martin interrupts the story about García Márquez to claim that it is not true. Lines 9–12: “When Gerald Martin, around the middle of his rich and resourceful biography of García Márquez, starts to tell this story, the reader may be a little surprised, even disappointed.” Lines 22–26: “After ‘and then,’ Martin writes in mock apology, ‘It seems a pity to intervene in the story at this point but the biographer feels constrained to point out that there have been many versions of this story . . . and that the one just related cannot be true.’”

The best answer is NOT:

F because there is no indication in the passage that García Márquez preferred to write in seclusion.

G because the passage does not indicate that Martin’s biography of García Márquez focuses on analyzing his novels rather than on discussing the author’s development as a writer.

J because, as noted in response H, the disappointment the reader might feel is in reference to the story not being true, not to the lack of information about why García Márquez drove back to Mexico City. In addition, later in the passage Martin notes that García Márquez probably did not drive back to Mexico City. Lines 27–28: “The writer probably continued to Acapulco.”

Question 25. The best answer is B because compelled means “urged forcefully or irresistibly,” which makes it a contextually appropriate synonym of constrained here. Martin feels as if he must point out that the story cannot be true.

The best answer is NOT:

A because restrain means to hold back from, and the author is not holding back from pointing out that “there have been many versions of this story . . . and that the one just related cannot be true” (lines 25–26).

C because coerced implies being persuaded by outside forces, and there is no indication in the passage that Martin had to be persuaded by someone else to share the truth about García Márquez’s story.

D because limited means confined or restricted, and there is no indication in the passage that Martin felt that his options were restricted.

Question 26. The best answer is G because the passage specifically notes that García Márquez’s grandmother believed the stories she told were true. Lines 32–35: “He would combine, as he frequently said, the narrative tone of his grandmother with that of the author Franz Kafka. She told fantastic stories as if they were true, because for her, they were true.”

The best answer is NOT:

F because the passage notes that García Márquez imitated Kafka, not that his grandmother did. Lines 32–34: “He would combine, as he frequently said, the narrative tone of his grandmother with that of the author Franz Kafka.”

H because there is no indication in the passage that García Márquez’s grandmother hoped to become a successful author.

J because the passage states that García Márquez learned from his grandmother, not that his grandmother learned from him. Lines 32–34: “He would combine, as he frequently said, the narrative tone of his grandmother with that of the author Franz Kafka.”

Question 27. The best answer is C because the passage notes that García Márquez made jokes that indicated his gratitude for his life. “García Márquez made many jokes about his fame over the years. These jokes are witty and complicated acts of gratitude for a destiny the writer was sure could have been quite different” (lines 49–52).

The best answer is NOT:

A because there is no mention in the passage that García Márquez ever hoped that his best work had yet to be written.

B because there is no mention in the passage that García Márquez was ever concerned that his accomplishments had been distorted by others.

D because there is no mention in the passage that García Márquez ever believed that he deserved more credit for his wit and the complexity of his writing.

Question 28. The best answer is J because the passage cites a quotation by García Márquez that suggests he believed he might have been a better person if he had stayed in Aracataca. “One of his finest sentences, written in an article in 1983, concerns a dream of the life he might have led if he had stayed in his isolated birthplace of Aracataca, Colombia. ‘I would not perhaps be the same person I am now but maybe I would have been something better: just a character in one of the novels I would never have written’” (lines 52–58).

The best answer is NOT:

F because there is no indication in the passage that García Márquez ever stated that he should have written One Hundred Years of Solitude sooner.

G because there is no indication in the passage that García Márquez ever stated that he wished he had completed his journey to Acapulco. In addition, the passage suggests that García Márquez did complete his journey. Lines 27–28: “The writer probably continued to Acapulco.”

H because there is no indication in the passage that García Márquez ever wished he had taken his fame less seriously.

Question 29. The best answer is B because the passage author directly states that the biography helps balance García Márquez’s joking cheerfulness and elaborate ironies. Lines 83–88: “There is perhaps a slight imbalance in Martin’s insistence on the writer’s sadness, an excess of melancholy; but it’s a good corrective to García Márquez’s own joking cheerfulness and elaborate ironies, and we can return to the master if we get too depressed.”

The best answer is NOT:

A because, as noted in response B, the author directly states that the biography helps balance García Márquez’s joking cheerfulness and elaborate ironies.

C because, as noted in response B, the author directly states that the biography helps balance García Márquez’s joking cheerfulness and elaborate ironies.

D because, as noted in response B, the author directly states that the biography helps balance García Márquez’s joking cheerfulness and elaborate ironies.

Question 30. The best answer is J because in this context, master refers to García Márquez, who is referenced earlier in the sentence. Lines 83–88: “There is perhaps a slight imbalance in Martin’s insistence on the writer’s sadness, an excess of melancholy; but it’s a good corrective to García Márquez’s own joking cheerfulness and elaborate ironies, and we can return to the master if we get too depressed.” The passage author is asserting that we can return to the master himself, García Márquez, when Martin’s biography seems too dark.

The best answer is NOT:

F because, as noted in response J, in this context, master refers to García Márquez, who is referenced earlier in the sentence. Lines 83–88: “There is perhaps a slight imbalance in Martin’s insistence on the writer’s sadness, an excess of melancholy; but it’s a good corrective to García Márquez’s own joking cheerfulness and elaborate ironies, and we can return to the master if we get too depressed.” If the passage author were referring to himself here, it would not make sense in context.

G because, as noted in response J, in this context, master refers to García Márquez, who is referenced earlier in the sentence. Lines 83–88: “There is perhaps a slight imbalance in Martin’s insistence on the writer’s sadness, an excess of melancholy; but it’s a good corrective to García Márquez’s own joking cheerfulness and elaborate ironies, and we can return to the master if we get too depressed.” García Márquez’s joking cheerfulness is in contrast to Martin’s melancholy.

H because, as noted in response J, in this context, master refers to García Márquez, who is referenced earlier in the sentence. Lines 83–88: “There is perhaps a slight imbalance in Martin’s insistence on the writer’s sadness, an excess of melancholy; but it’s a good corrective to García Márquez’s own joking cheerfulness and elaborate ironies, and we can return to the master if we get too depressed.” The reference to Kafka comes much earlier in the passage, and therefore does not make sense in this context.

Passage IV

Question 31. The best answer is B because the passage explains how increasingly large distances were measured throughout history. The first sentence of the passage helps establish the overall organization: “One measure of the progress of human civilization is the increasing scale of our maps.” What follows is a series of historical examples to illustrate this idea. The first paragraph describes a map from the twenty-fifth century B.C. showing a thirty-acre plot of land; the second paragraph describes Eratosthenes’s process for measuring the circumference of Earth in the third century B.C.; the third paragraph describes Richer’s measurement of the distance between Earth and Mars in 1672; the fourth paragraph describes Newton’s measurement of the distance between Earth and the nearest stars. Each example is of an increasingly large distance.

The best answer is NOT:

A because the passage is about more than just attempts to determine the distance of stars from Earth. As noted in response B, the passage describes attempts to measure distance on Earth as well as distances from Earth to other objects in the universe.

C because although the passage does include an explanation of the calculations used by Eratosthenes to measure Earth’s circumference, this is limited to one paragraph. It does not describe the passage as a whole.

D because “collection of anecdotes” doesn’t capture how the passage moves through historical examples of increasingly large distances. Response B more accurately captures the passage’s overall organization.

Question 32. The best answer is H because the paragraph presents examples of the ways in which humans’ understanding of their surroundings expanded over time. The first sentence of the paragraph, “One measure of the progress of human civilization is the increasing scale of our maps” (lines 1–2), suggests that the paragraph will discuss this expansion. The paragraph begins with an example of a relatively small scale and proceeds with examples that show how this scale broadened.

The best answer is NOT:

F because the paragraph does not discuss Eratosthenes or the time period in which he made his calculations.

G because there is no discussion in the paragraph of early geographers concluding that Earth was curved.

J because although the paragraph acknowledges the ancient Greeks, it does not summarize all of their contributions to astronomy. Instead, the information is included to show how humans’ understanding of their surroundings expanded over time, as noted in response H.

Question 33. The best answer is B because the passage notes that these models of the universe did not include size or scale of objects. Lines 6–10: “In the earliest recorded cosmologies, such as the Babylonian Enuma Elish, from around 1500 B.C., the oceans, the continents, and the heavens were considered finite, but there were no scientific estimates of their dimensions.” Lines 10–13: “The early Greeks, including Homer, viewed Earth as a circular plane with the ocean enveloping it and Greece at the center, but there was no understanding of scale.” Lines 13–18: “In the early sixth century B.C., the Greek philosopher Anaximander, whom historians consider the first mapmaker, and his student Anaximenes proposed that the stars were attached to a giant crystalline sphere. But again there was no estimate of its size.”

The best answer is NOT:

A because the passage notes that in at least one of the models, the universe was considered finite. “In the earliest recorded cosmologies, such as the Babylonian Enuma Elish, from around 1500 B.C., the oceans, the continents, and the heavens were considered finite, but there were no scientific estimates of their dimensions” (lines 6–10).

C because there is no mention in these lines of any similarities between ancient models of the universe and modern maps.

D because only one of the examples of the ancient models of the universe is noted to have positioned the citizens’ homelands at the center of the universe. “The early Greeks, including Homer, viewed Earth as a circular plane with the ocean enveloping it and Greece at the center, but there was no understanding of scale” (lines 10–13).

Question 34. The best answer is F because the passage notes that we do not have sufficient experience to relate to the distance from Earth to the nearest stars. “Newton’s estimate of the distance to nearby stars was larger than any distance imagined before in human history. Even today, nothing in our experience allows us to relate to it” (lines 77–80). The examples that follow in the paragraph help illustrate this point.

The best answer is NOT:

G because it contradicts the paragraph’s point that even advancements in space travel would not make the distance from Earth to the nearest stars seem small. In fact, the passage notes that “if we traveled in the fastest rocket ship ever manufactured on Earth, the trip would last 100,000 years, at least a thousand human life spans” (lines 84–86).

H because the last paragraph is not about when the distance was calculated. Rather, the paragraph is about how far this distance is—so far that nothing in our experience allows us to relate to it.

J because the paragraph does not indicate that Newton’s estimate of the distance between Earth and the nearest stars was incorrect.

Question 35. The best answer is A according to lines 10–13: “The early Greeks, including Homer, viewed Earth as a circular plane with the ocean enveloping it and Greece at the center, but there was no understanding of scale.”

The best answer is NOT:

B because it was Anaximander and Anaximenes who described Earth as a giant crystalline sphere with stars attached. “In the early sixth century B.C., the Greek philosopher Anaximander, whom historians consider the first mapmaker, and his student Anaximenes proposed that the stars were attached to a giant crystalline sphere” (lines 13–17).

C because the passage mentions 7.2 degrees in relation to Eratosthenes’s work to calculate the circumference of Earth. “Eratosthenes knew that the sun was not overhead at noon in Alexandria. In fact, it was tipped 7.2 degrees from the vertical, or about one fiftieth of a circle” (lines 30–32).

D because the measurement of a plot of land 354 iku in size was recorded well before the time of the ancient Greeks. “A clay tablet dating from about the twenty-fifth century B.C. found near what is now the Iraqi city of Kirkuk depicts a river valley with a plot of land labeled as being 354 iku (about thirty acres) in size” (lines 2–6).

Question 36. The best answer is J because the passage states, “Eratosthenes reasoned that if he knew the distance from Alexandria to Syene, the full circumference of the planet must be about fifty times that distance. Traders passing through Alexandria told him that camels could make the trip to Syene in about fifty days, and it was known that a camel could cover one hundred stadia (almost eleven and a half miles) in a day” (lines 36–43). This information suggests that Eratosthenes needed to know the time it took camels to travel between the cities and how far they could travel in a day.

The best answer is NOT:

F because the passage notes that Eratosthenes used information about the curvature of Earth and the angle of the sun to calculate the circumference of Earth, not the distance between Syene and Alexandria.

G because the passage notes that Eratosthenes used his knowledge of the distance between Syene and Alexandria to calculate the circumference of Earth. Lines 36–39: “Eratosthenes reasoned that if he knew the distance from Alexandria to Syene, the full circumference of the planet must be about fifty times that distance.” He could not know Earth’s circumference until he knew the distance between these cities.

H because, as noted in response F, Eratosthenes used information about the height of the sun at noon in each city and the length of shadows cast on the ground to calculate the circumference of Earth, not to calculate the distance between Syene and Alexandria.

Question 37. The best answer is C because the passage suggests that the distance from Earth to other points in the solar system could not be calculated until the telescope was invented. “As ingenious as they were, the ancient Greeks were not able to calculate the size of our solar system. That discovery had to wait for the invention of the telescope, nearly two thousand years later” (lines 50–53).

The best answer is NOT:

A because there is no mention in the passage that astronomers needed to find proper observation points before they could determine the distance between Earth and other points in the solar system.

B because there is no mention in the passage of astronomers using ancient Greek calculations to determine the distance between Earth and other objects in the solar system.

D because there is no mention in the passage that Earth and Mars had to align for astronomers to calculate the distance from Earth to other points in the solar system.

Question 38. The best answer is J because the passage indicates that Newton’s calculation of the distance to the nearest stars was less acknowledged than his other work. “Only someone as accomplished as Newton could have been the first to perform such a calculation and have it go almost unnoticed among his other achievements” (lines 63–66). “Almost unnoticed among his other achievements” suggests that this calculation was less acknowledged than other achievements.

The best answer is NOT:

F because the passage indicates that Newton’s calculation was “almost unnoticed among his other achievements” (lines 65–66). This suggests that his other achievements were considered more important.

G because there’s no indication in the passage that this work was speculative or that it was more speculative than Newton’s other work.

H because there’s no indication in the passage that this work was not complete or that it was less complete than Newton’s other work.

Question 39. The best answer is A because the language used to describe how Newton wrote his calculation emphasizes the time period in which he worked and how old-fashioned his tools seemed, particularly in the context of describing an advanced, complicated calculation: “Writing his computations in a spidery script, with a quill dipped in the ink of oak galls” (lines 70–71). Newton was calculating the distance of stars ten trillion miles away while using a rudimentary writing tool.

The best answer is NOT:

B because there is no indication in the passage of how long Newton’s calculation took, much less that it took a long time to decipher.

C because there is no description in the passage of the artistic flourishes in the section of Newton’s Principia in which the calculation appears.

D because there is no mention in the passage of the mistakes Newton made when calculating the distance between Earth and the nearest stars.

Question 40. The best answer is H because the paragraph is about travel and distance. The lines before set out help make this clear. “The fastest most of us have traveled is about 500 miles per hour, the cruising speed of a jet. If we set out for the nearest star beyond our solar system at that speed, it would take us about 5 million years to reach our destination” (lines 80–84).

The best answer is NOT:

F because the sentence is about travel, not about a vision. “Described a vision” doesn’t make sense in this context.

G because the sentence is about travel, not about stating a purpose. “Stated a purpose” doesn’t make sense in this context.

J because the sentence is about travel, not about creating an arrangement. “Created an arrangement” doesn’t make sense in this context.

Passage I

The best answer is C. According to Table 1, at 45°C after a 75 min resting time, a 1.0% aqueous mixture of Gum W has a viscosity of 6,825 cP, an aqueous mixture of Gum X has a viscosity of 3,462 cP, an aqueous mixture of Gum Y has a viscosity of 1,639 cP, and an aqueous mixture of Gum Z has a viscosity of 1,562 cP. The viscosity decreases from Gum W to X to Y to Z. A, B, and D are incorrect; these graphs do not show the correct trend of decreasing viscosity. C is correct.

The best answer is H. According to Table 1, for a given temperature, the viscosity of a gum mixture increased as the rest time increased. A 1.0% mixture of Gum Y at 65°C had a viscosity of 802 cP after a resting time of 75 min and a viscosity of 1,075 cP after a resting time of 102 min. One would predict that after a resting time of 100 min, the viscosity would most likely be between 802 cP and 1,075 cP. F and G are incorrect; the viscosity would be greater than 800 cP. H is correct. J is incorrect; the viscosity would be less than 1,100 cP.

The best answer is C. According to Figure 1, for a gum concentration of 2.0%, Gum Z had the lowest viscosity, followed by Gum X, then Gum W. Gum Y had the highest viscosity. A and B are incorrect; the 2.0% mixture of Gum Z had the lowest viscosity. C is correct. D is incorrect; the 2.0% mixture of Gum Y had the highest viscosity.

The best answer is F. According to Figure 1, a 1.3% aqueous mixture of Gum W had the highest viscosity, greater than 10,000 cP. F is correct. G is incorrect; the viscosity of a 1.3% aqueous mixture of Gum X was less than 10,000 cP. H is incorrect; the viscosity of a 1.3% aqueous mixture of Gum Y was less than 10,000 cP. J is incorrect; the viscosity of a 1.3% aqueous mixture of Gum Z was less than 10,000 cP.

The best answer is B. According to Table 1, the viscosity of the aqueous gum mixtures decreased as the temperature increased. A 1.0% aqueous mixture of Gum Z at 25°C and a resting time of 75 min had a viscosity of 1,879 cP, and a similar solution at 45°C had a viscosity of 1,562 cP. One would predict that a 1.0% aqueous mixture of Gum Z at 30°C and a resting time of 75 min would have a viscosity between 1,562 cP and 1,879 cP. A is incorrect; the viscosity would be greater than 1,562 cP. B is correct. C and D are incorrect; the viscosity would be less than 1,879 cP.

The best answer is H. According to Figure 1, Gum Y had a viscosity of 100,000 cP at a gum concentration of approximately 2.2%. Gums X and Y did not have a viscosity of 100,000 cP until their concentrations were greater than 2.5%. The viscosity of Gum Z did not reach 100,000 cP even at a gum concentration of 3.0%. Gum Y had a viscosity of 100,000 cP at a lower concentration than any of the other 3 gums. F is incorrect; Gum W had a viscosity of 100,000 cP at a concentration greater than 2.5%. G is incorrect; Gum X had a viscosity of 100,000 cP at a concentration greater than 2.5%. H is correct; Gum Y had a viscosity of 100,000 cP at a concentration of approximately 2.25%. J is incorrect; Gum Z did not have a viscosity of 100,000 cP at any concentration.

Passage II

The best answer is C. According to Figure 1, a 60% BD by volume sample would have an A of approximately 0.6 at 1,746 cm⁻¹. A and B are incorrect; A would be greater than 0.55. C is correct. D is incorrect; A would be less than 0.65.

The best answer is F. According to Figure 2, as the percent by volume of BD increased, A at 1,746 cm⁻¹ also increased. F is correct. G, H, and J are incorrect; A increased only.

The best answer is A. According to Figure 2, as the percent BD by volume decreased, A at 1,746 cm⁻¹ also decreased. The fuel sample in Study 3 with the smallest A would be that with the lowest percent BD by volume. Sample W had the lowest percent BD by volume. A is correct; the percent BD by volume for Sample W was 4.0%. B is incorrect; the percent BD by volume for Sample X was 6.0%. C is incorrect; the percent BD by volume for Sample Y was 4.8%. D is incorrect; the percent BD by volume for Sample Z was 4.7%.

The best answer is H. In order to answer this item, the examinee must know that a catalyst is not a reactant or a product and how to write a chemical equation. According to the passage, soybean oil and methanol react in the presence of a catalyst to form FAMEs. Soybean oil and methanol are the reactants, and FAMEs are the products. F, G, and J are incorrect; FAMEs should appear on the product side of the equation. H is correct.

The best answer is B. In order to gain useful information from the absorbance data for Study 2, the students had to measure the absorbance at a wavenumber at which either BD or PD, but not both, absorbed strongly. According to Figure 1, BD absorbed strongly at 1,172 cm⁻¹ and PD did not, while both BD and PD absorbed at 1,464 cm⁻¹. The students would most likely have measured the absorbance in Study 2 at 1,172 cm⁻¹. A is incorrect; BD absorbed strongly at 1,172 cm⁻¹, and PD did not. B is correct. C and D are incorrect; a wavenumber of 1,172 cm⁻¹ would have been a better choice.

The best answer is J. According to the passage, BD contained FAMEs and PD did not. Figure 1 shows that BD did not strongly absorb light at a wavenumber of 900 cm⁻¹ but did absorb at 1,250 cm⁻¹. A sample that contained only FAMEs would show the same absorbance behavior. F and G are incorrect; the sample would more strongly absorb at a wavenumber of 1,250 cm⁻¹. H is incorrect; PD does not contain FAMEs. J is correct.

The best answer is A. In order to answer this item, the examinee must know that there are 1,000 mL in 1 L. According to Table 1, Sample Y is 4.8% BD by volume. A 10 L sample would therefore contain approximately 0.05 × 10 L = 0.5 L of BD, which is equal to . A is correct. B is incorrect; 0.5 L = 500 mL. C and D are incorrect; the sample would contain 0.5 L of BD.

Passage III

The best answer is H. According to Figure 1, the inner core is approximately 1,200 km thick, the outer core is approximately 2,300 km thick, the lower mantle is approximately 2,200 km thick, and the upper mantle/crust is approximately 600 km thick. The outer core and lower mantle are most similar in thickness. F, G, and J are incorrect; the outer core and lower mantle are most similar, with thicknesses of approximately 2,300 km and 2,200 km, respectively. H is correct.

The best answer is A. Figure 2 shows that the innermost 30% of Earth’s mass is located between r = 0 km and r = 3,400 km. A is correct. B is incorrect; just under 40% of Earth’s mass is located between r = 0 km and r = 3,900 km. C is incorrect; approximately 50% of Earth’s mass is located between r = 0 km and r = 4,500 km. D is incorrect; 70% of Earth’s mass is located between r = 0 km and r = 5,300 km.

The best answer is J. According to Figure 1, the crust ends and the atmosphere begins at r = 6,400 km. Figure 2 shows that 100% of Earth’s mass is located within 6,400 km of the center of Earth. From both figures, it can be concluded that Earth’s radius is approximately 6,400 km. F is incorrect; 1,400 km is the radius of the inner core. G is incorrect; 3,500 km is the distance from the center of Earth to the edge of the outer core. H is incorrect; 5,700 km is the distance from the center of Earth to the edge of the lower mantle. J is correct; 6,400 km is the distance from the center of Earth to Earth’s surface.

The best answer is C. According to Figure 2, throughout the atmosphere and into space, as the distance from the center of Earth increases, the strength of the gravitational field decreases. At r = 13,000 km, gE = approximately 2.4 N/kg. Based on the rate at which gE was decreasing, at r = 14,000 km, gE would most likely be close to 2.0 N/kg. A and B are incorrect; gE would most likely be greater than 1.5 N/kg. C is correct. D is incorrect; gE would most likely be less than 2.5 N/kg.

The best answer is F. According to Figure 2, the outermost 400 km contains 10% of Earth’s mass. Earth’s crust, the outermost 30 km, therefore contains much less than 10% of Earth’s mass. F is correct. G is incorrect; the outermost 400 km contains 10% of Earth’s mass. H is incorrect; the outermost 4,000 km contains 90% of Earth’s mass. J is incorrect; 99% of Earth’s mass in contained in the outermost 5,400 km.

The best answer is A. In order to answer this item, the examinee must know that weight is directly proportional to gravitational field strength. According to Figure 1, at r = 2,000 km, gE = 7 N/kg, and at r = 4,000 km, gE = 10.2 N/kg. Because the strength of the gravitational field is less at r = 2,000 km, the rock will weigh less at r = 2,000 km than at r = 4,000 km. A is correct. B is incorrect; the rock located at r = 4,000 km will weigh more. C is incorrect; because the rocks have identical masses, the rock in the stronger gravitational field will weigh more. D is incorrect; the value of gE is not the same at both locations.

Passage IV

The best answer is G. According to the passage, Student 1 stated that biological aging is caused by ROS produced by cellular respiration. Student 4 stated that biological aging is caused by lipofuscin produced by cellular respiration. Neither Student 2 nor Student 3 claimed that the cause of biological aging is related to cellular respiration. F is incorrect; Student 4 also claimed that biological aging is caused by a substance produced by cellular respiration. G is correct; Students 1 and 4 claimed that biological aging is caused by a substance produced by cellular respiration. H is incorrect; Students 2 and 3 did not claim that the cause of biological aging is related to cellular respiration. J is incorrect; Students 1 and 4 made the claim about cellular respiration.

The best answer is B. Student 2 claimed that biological aging is caused by cross-links formed between proteins in the cell. Cross-links are a type of chemical bond. None of the other students’ explanations involved the formation of chemical bonds between proteins. The finding would be most consistent with the explanation given by Student 2. A is incorrect; Student 1 claimed that biological aging is caused by ROS. B is correct. C is incorrect; Student 3 claimed that biological aging is caused by DNA damage and that cross-linked proteins do not affect cell function. D is incorrect; Student 4 claimed that biological aging is caused by lipofuscin and that cross-linked proteins do not accumulate in the cell.

The best answer is F. In order to answer this item, the examinee must know that proteins are composed of amino acids. Student 2 claimed that biological aging is caused by cross-linking between proteins. F is correct. G is incorrect; fatty acids are not found in proteins. H is incorrect; monosaccharides are not found in proteins. J is incorrect; nucleotides are found in DNA, not proteins.

The best answer is B. Student 2 claimed that the accumulation of protein clumps formed by cross-linking of the proteins causes biological aging. Student 2 would most likely predict that a substance that prevents cross-linking would be present in a greater concentration in the cells of young adults where less cross-linking is found. A is incorrect; Student 1 did not address cross-linking of proteins in their explanation. B is correct. C is incorrect; Student 3 claimed that cross-linked proteins do not affect cell function. D is incorrect; Student 4 claimed that protein clumps do not accumulate in the cell.

The best answer is G. According to the passage, Student 2 claimed that biological aging is due to protein cross-linking that forms clumps of protein. Student 4 claimed that biological aging is due to lipofuscin that forms clumps. F is incorrect; Student 1 claimed that biological aging is due to ROS that damage proteins and lipids in a cell. G is correct. H and J are incorrect; Student 1 claimed that biological aging is due to ROS that damage proteins and lipids in a cell, and Student 3 claimed that biological aging is due to DNA damage.

The best answer is D. According to the passage, Student 1 claimed that biological aging is due to ROS that damage proteins and lipids in the cell. Antioxidants eliminate ROS before they cause damage; however, the cell does not produce enough antioxidants to eliminate all the ROS. A and B are incorrect; Student 1’s explanation did not involve cross-linked proteins. C is incorrect; this observation would weaken Student 1’s explanation. D is correct.

The best answer is G. In order to answer this item, the examinee must know that genetic mutations are caused by DNA damage. According to the passage, only Student 3 claimed that damage to the DNA is responsible for biological aging. The finding that a mutagen does not affect aging would weaken Student 3’s explanation. F is incorrect; Student 2 claimed that biological aging is caused by cross-linked proteins, and the finding would not weaken their explanation. G is correct. H is incorrect; Student 1 claimed that biological aging is caused by ROS, and the finding would not weaken their explanation. J is incorrect; Student 2 claimed that biological aging is caused by cross-linked proteins, and Student 4 claimed that DNA damage is not a factor in biological aging. The finding would weaken neither Student 2’s nor Student 4’s explanation.

Passage V

The best answer is D. According to Figure 1, the greatest percent of DOC adsorbed by CM1 was adsorbed from the pine leachate. According to Figure 2, the greatest percent of DOC adsorbed by CM2 was adsorbed from the magnolia leachate. Figure 3 shows that the greatest percent of DOC adsorbed by CM3 was adsorbed from the magnolia leachate. A and B are incorrect; the greatest percent of DOC from the pine leachate was adsorbed by CM1. C is incorrect; the greatest percent of DOC from the magnolia leachate was adsorbed by CM3. D is correct.

The best answer is J. According to Figure 3, the percent of leachate DOC adsorbed by CM3 varied from 32% to 56%. The average was 42%, but one can estimate that it must have been between 30% and 56%. F, G, and H are incorrect; the average was greater than 30%. J is correct.

The best answer is C. According to Figure 2, CM2 adsorbed 7% of the DOC in the maple leachate. Figure 3 shows that CM3 adsorbed 35% of the DOC in the maple leachate. The results of Studies 2 and 3 do not support the statement. A greater percentage of DOC in the maple leachate was adsorbed by CM3 than by CM2. A and B are incorrect; the results do not support the statement. C is correct. D is incorrect; CM2 adsorbed 7% and CM3 adsorbed 35% of the DOC in the maple leachate.

The best answer is G. In each study, 5 different types of leaf leachate were used. Each study used 1 type of clay mineral, but a different type of clay mineral was used in each study. F is incorrect; the type of lake water used was the same in all studies. G is correct. H is incorrect; the volume of leaf leachate was the same in all studies. J is incorrect; the volume of filtrate was not varied in each study.

The best answer is D. According to Figure 1, CM1 reduced the DOC in the oak leachate by 31%. Figure 2 shows that CM2 reduced the DOC in the oak leachate by 23%, and Figure 3 shows that CM3 reduced the DOC in the oak leachate by 50%. None of the clay minerals reduced the DOC in the oak leachate by more than 50%. A, B, and C are incorrect; all clay minerals reduced the DOC in the oak leachate by 50% or less. D is correct.

The best answer is J. In order to answer this item, the examinee must be able to distinguish between a suspension and a solution. According to the passage, in each of the studies, the leachate was prepared by mixing filtered lake water with a sample of leaves. After time was allowed for leaching, the mixture was filtered to remove all solid particles. The leachate was then mixed with the clay mineral. After 2 hours of stirring, the mixture was filtered to remove all solid particles. The presence of solid particles in the mixture indicated that the mixture was a suspension and not a solution. F and G are incorrect; the mixture was not a solution. H is incorrect; the clay mineral particles were not dissolved in the leachate. J is correct.

The best answer is A. According to the passage, the leachate was prepared by allowing the mixture of lake water and leaves to sit for 10 weeks at 4°C in the dark. Keeping the mixture in the dark ensured that none of the DOC would be broken down by electromagnetic energy in the visible wavelength range (i.e., light). A is correct. B is incorrect; the filtrate and clay mineral were not placed in the dark. C is incorrect; filtering the mixture of leaves and lake water would not prevent the breakdown of DOC by visible light. D is incorrect; filtering the leachate and clay mineral would not prevent the breakdown of DOC by visible light.

Passage VI

The best answer is H. According to the passage, all eight Petri dishes were set up in the same way. PD5 was turned 90° so that the dish was vertical. F and G are incorrect; the Petri dishes shown are both in a vertical orientation, indicating that they have been turned and are not in their original orientation. H is correct. J is incorrect; the Petri dish would have to be right side up when the experiment was set up, and at no time was the dish inverted.

The best answer is D. According to Experiment 2, PD8 contained M Arabidopsis seeds and was exposed to light from above for 70 hr. A is incorrect; PD1 contained WT Arabidopsis seeds and was placed in the dark for 70 hr. B is incorrect; PD2 contained WT Arabidopsis seeds. C is incorrect; PD3 was placed in the dark for 70 hr. D is correct; PD4 contained M Arabidopsis seeds and was exposed to light from above for 70 hr.

The best answer is F. According to Experiment 1, PD1 contained WT Arabidopsis seeds and was placed in the dark. PD3 contained M Arabidopsis seeds and was placed in the dark. Figure 1 shows that the radicles in PD1 extended straight down, and the radicles in PD3 had more random growth. The radicles did not have the same response to gravity. F is correct. G is incorrect; PD2 and PD4 were exposed to light. H and J are incorrect; the radicles did not have the same response to gravity.

The best answer is B. In order to answer this item, the examinee must know that above-ground plant growth typically exhibits positive phototropism. A is incorrect; hypocotyls typically grow toward a light stimulus. B is correct. C and D are incorrect; the hypocotyls most likely exhibited positive phototropism.

The best answer is J. In order to answer this item, the examinee must know that cotyledons are embryonic leaves. Plants having embryos with one seed leaf are monocots. Plants having embryos with two seed leaves are dicots. Figure 2 shows that each seedling had 2 leaves, and therefore Arabidopsis is a dicot. F and G are incorrect; Arabidopsis is a dicot. H is incorrect; the seedlings had 2 cotyledons. J is correct.

The best answer is B. According to the passage, the Petri dishes were set up with the agar and seeds and were turned 90° after being exposed to light for 70 hr. The orientation of the Petri dishes was changed one time, and therefore each Petri dish had 2 different orientations. A, C, and D are incorrect; the Petri dishes had 2 different orientations. B is correct.

The best answer is F. In order to determine the effect of light on the growth of WT Arabidopsis seedlings, the results for the Petri dish with WT Arabidopsis placed in the dark (PD1) and the Petri dish with WT Arabidopsis exposed to light (PD2) should be compared. F is correct. G and H are incorrect; PD3 contained M Arabidopsis seeds. J is incorrect; PD4 contained M Arabidopsis seeds.

Planning Your Essay

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ENGLISH • PRACTICE TEST 5 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is C because it ensures correct subject-verb agreement. The plural verb are agrees with the plural subject instruments.

The best answer is NOT:

A because it lacks subject-verb agreement; the singular verb is considered does not agree with the plural subject instruments.

B because it lacks subject-verb agreement; the singular verb does seem does not agree with the plural subject instruments.

D because it lacks subject-verb agreement; the singular verb is does not agree with the plural subject instruments.

Question 2. The best answer is H because it best maintains the pattern established in the sentence’s two previous examples. The first two examples follow a specific pattern of introducing the instrument and then describing what it was made from. The phrase “a flute made from a bamboo shoot” precisely follows this pattern.

The best answer is NOT:

F because it fails to maintain the pattern; the phrase “other brightly colored vegetables” does not introduce an instrument followed by what it was made from.

G because it fails to maintain the pattern; the phrase “vegetable instruments of all shapes and sizes” does not introduce an instrument followed by what it was made from.

J because it fails to maintain the pattern; the phrase “a certain type of root vegetable” does not introduce an instrument followed by what it was made from.

Question 3. The best answer is D because it eliminates unnecessary punctuation between the last item in the list that comprises the compound subject (“Gourds, daikon radishes, and other vegetables”) and the verb are used.

The best answer is NOT:

A because it provides unnecessary punctuation (a comma) that incorrectly separates the last part of the compound subject from the verb.

B because it provides unnecessary punctuation (a semicolon) that incorrectly separates the modifier (other) from the word it modifies (vegetables).

C because it provides unnecessary punctuation (a comma) that incorrectly sets off the final phrase of the sentence (“to round out the orchestra”) as a nonessential element. This phrase is essential because it explains what the vegetables are used for.

Question 4. The best answer is G because it correctly provides the main verb were to create a grammatically correct sentence that clearly conveys how the brothers learned to play instruments.

The best answer is NOT:

F because it incorrectly provides the modifying phrase “who were” where a main verb is needed. This creates a sentence fragment.

H because it incorrectly includes the word and before the main verb were, which could be used only if the sentence had set up two things the brothers did (lived on a farm and were taught, for example). That is not the case here.

J because it incorrectly omits the main verb were. This creates a sentence fragment.

Question 5. The best answer is D because it eliminates redundancy and unnecessary wordiness.

The best answer is NOT:

A because it introduces redundancy at the sentence level; the word manually (used later in the sentence) clearly conveys that the work was done by hand, making the phrase “Working by hand” redundant.

B because it introduces redundancy at the sentence level; the end of the sentence makes clear that the brothers consume discarded pieces of vegetables as they work, so the phrase “Eating unused vegetable parts” is redundant.

C because it introduces redundancy at the sentence level; the sentence later says the brothers use “metal drill bits,” so the phrase “Using metal tools” is redundant.

Question 6. The best answer is J because it correctly provides the subject he and verb makes in the second half of the sentence to clearly explain how Weiping creates a low pitch.

The best answer is NOT:

F because it omits the subject he in the second half of the sentence and uses the modifying phrase “which makes” where a main verb is needed. This creates a sentence fragment with no clear meaning.

G because it omits the subject he in the second half of the sentence and uses the phrase “having made” where a main verb is needed. This creates a sentence fragment with no clear meaning.

H because it omits the subject he in the second half of the sentence and uses the phrase “by making” where a main verb is needed. This creates a sentence fragment with no clear meaning.

Question 7. The best answer is B because it provides the most logical transition based on the surrounding context. The preceding sentence explains how Weiping creates a low pitch. What follows presents a contrast because it explains how Weiping creates a high pitch. The word Conversely most clearly and logically sets up the contrast between these two ideas.

The best answer is NOT:

A because it provides an illogical transition based on the surrounding context. The word Nonetheless suggests that what follows explains that even though one condition exists (the need to create a deep hole for a low pitch), another condition could still exist. The word Nonetheless also suggests that the coexistence of these two conditions might be surprising or unexpected. That is not the case here. Rather, it makes sense that if a deep hole makes a low sound, then a shallow hole would make a higher sound.

C because it provides an illogical transition based on the surrounding context. The word Otherwise suggests that what follows describes what will happen if the first condition (creating a deep hole) is not met. That is not the case here.

D because it provides an illogical transition based on the surrounding context. The phrase “Even so” suggests that what follows explains that even though one condition exists (the need to create a deep hole for a low pitch), another condition could still exist. This phrase also suggests that the coexistence of these two conditions might be surprising or unexpected. That is not the case here. Rather, it makes sense that if a deep hole makes a low sound, then a shallow hole would make a higher sound.

Question 8. The best answer is H because it uses punctuation consistent with what appears later in the sentence (a comma) to correctly set off a nonessential element. The comma after the word factors correctly sets off the phrase “like the diameter of the hole and changes in air temperature and humidity” as a nonessential element. This is extra information without which the sentence would still be grammatically correct and logical.

The best answer is NOT:

F because it incorrectly places commas before and after the word like, suggesting that the word like is the nonessential element. This creates an ungrammatical and unclear sentence.

G because it uses punctuation (an em dash) that is inconsistent with what appears later in the sentence (a comma) to set off the nonessential element. A nonessential element must be set off with consistent punctuation (pairs of commas, em dashes, or parentheses).

J because it incorrectly omits the punctuation necessary to set off the nonessential element.

Question 9. The best answer is C because it ensures correct subject-verb agreement; the plural verb affect agrees with the plural subject factors. In addition, it correctly distinguishes between the words affect and effect; the transitive verb affect is correct for this context because it clearly conveys that other factors cause an impact on the sound quality.

The best answer is NOT:

A because it fails to correctly distinguish between the words affect and effect; the word effects is incorrect in this context because it would illogically suggest that the factors listed produce the sound quality rather than having an impact on the sound quality. In addition, it lacks subject-verb agreement, using a singular verb where a plural verb is needed to agree with the plural subject factors.

B because it lacks subject-verb agreement; the singular verb affects does not agree with the plural subject factors.

D because it fails to correctly distinguish between the words affect and effect; the word effect is incorrect for this context because it would illogically suggest that the factors listed produce the sound quality rather than having an impact on the sound quality.

Question 10. The best answer is F because it correctly provides the participle producing to establish the second part of the sentence as a participial phrase describing how the loss of water affects the pitch.

The best answer is NOT:

G because it replaces the participle with a subject (“such vegetables”) and verb (produce), making the second part of the sentence an independent clause. This results in two independent clauses joined only by a comma, which is grammatically incorrect.

H because it replaces the participle with a subject (it) and verb (will produce), making the second part of the sentence an independent clause. This results in two independent clauses joined only by a comma, which is grammatically incorrect.

J because it replaces the participle with a subject (this) and verb (produces), making the second part of the sentence an independent clause. This results in two independent clauses joined only by a comma, which is grammatically incorrect.

Question 11. The best answer is A because it correctly uses consistent punctuation (commas) to set off the nonessential element. The phrase “Weidong says” is a clarifying detail that is not essential to the sentence and is therefore set off with commas after the words sound and says.

The best answer is NOT:

B because it omits the second comma (after the word says) and therefore fails to correctly set off the nonessential element.

C because it omits the first comma (after the word sound) and therefore fails to correctly set off the nonessential element.

D because it omits the commas after the words sound and says and therefore fails to correctly set off the nonessential element.

Question 12. The best answer is J because it puts the sentences in a sequence that makes the paragraph most logical. The word Still at the beginning of Sentence 3 creates the most logical connection to the end of the preceding paragraph by indicating that even though there are many factors that affect sound, water content is the most crucial. Sentence 1 logically follows Sentence 3 because it explains how quickly water content (the most crucial ingredient) is lost. Sentence 2 begins with the phrase “Because of this,” which indicates a causal relationship. This sentence most logically follows Sentence 1 because the fact that the vegetables lose water content quickly most logically explains why the brothers must carve fresh instruments before each performance.

The best answer is NOT:

F because it offers an illogical sequence of sentences in the paragraph. Sentence 1 offers no clear relationship to the information given at the end of the third paragraph. In addition, Sentence 3 should not follow Sentence 2 because the word Still at the beginning of Sentence 3 offers no clear relationship to Sentence 2. It is illogical to say that even though fresh instruments must be carved before each performance, water is the most crucial ingredient.

G because it offers an illogical sequence of sentences in the paragraph. Sentence 1 offers no clear relationship to the information given at the end of the third paragraph. In addition, Sentence 3 should not follow Sentence 1 because the word Still at the beginning of Sentence 3 offers no clear relationship to Sentence 1. It is illogical to say that even though picked vegetables lose water quickly, water is the most crucial ingredient.

H because it offers an illogical sequence of sentences in the paragraph. Sentence 1 explains why the brothers must carve fresh instruments before each show (discussed in Sentence 2). Placing Sentence 2 before Sentence 1 would eliminate the necessary causal relationship between these two sentences. In addition, Sentence 3 should not follow Sentence 1 because the word Still at the beginning of Sentence 3 offers no clear relationship to Sentence 1. It is illogical to say that even though picked vegetables lose water quickly, water is the most crucial ingredient.

Question 13. The best answer is D because it correctly provides the subject (“The brothers’ musical repertoire”) and the main verb is to create the main clause “The brothers’ musical repertoire is as varied as their instruments.” The second half of the sentence is correctly set up as a participial phrase describing the variation in the brothers’ repertoire.

The best answer is NOT:

A because it creates a sentence fragment by providing an introductory dependent clause (“While the brothers’ musical repertoire is as varied as their instruments”) where a main clause is needed.

B because it creates a sentence fragment by providing an introductory phrase (“With the brothers’ musical repertoire being as varied as their instruments”) where a main clause is needed.

C because it creates a sentence fragment by providing an introductory phrase (“Having the brothers’ musical repertoire be as varied as their instruments”) where a main clause is needed.

Question 14. The best answer is H because it provides a clear and convincing reason the sentence should not be added; the fact that each pitch is tested and perfected with an old tuner is not relevant to the concluding paragraph’s more general discussion of the Nan brothers’ performances and range of instruments.

The best answer is NOT:

F because it fails to provide a clear and convincing reason the sentence should be added. Even if the idea that the brothers test and perfect each pitch somewhat suggests the care and attention to detail with which the brothers craft their instruments, this point is not relevant to the concluding paragraph’s more general discussion of the Nan brothers’ performances and range of instruments.

G because it fails to provide a clear and convincing reason the sentence should be added. Even if the idea that the brothers test and perfect each pitch somewhat hints that the vegetables can be made into precise instruments, this point is not relevant to the concluding paragraph’s more general discussion of the Nan brothers’ performances and range of instruments.

J because it fails to provide a clear and convincing reason the sentence should not be added. The statement about how pitches are tested in no way conflicts with the idea that the brothers have a strong musical background. Rather, the statement should not be added because it is irrelevant to the concluding paragraph’s more general discussion of the Nan brothers’ performances and range of instruments.

Question 15. The best answer is B because it is the most effective placement of the sentence in terms of logic and cohesion. The statement about the brothers performing with a local theater company logically fits at Point B because it explains their connection to theater immediately before the paragraph references their “passion for performance.”

The best answer is NOT:

A because it would interrupt the general description of the brothers’ work using vegetables to craft instruments. The fact that they performed with a local theater company has no clear relationship to the discussion of their work at this point in the essay.

C because it would interrupt the discussion of how the brothers create their instruments. The fact that they performed with a local theater company has no clear relationship to how they make their instruments.

D because it would interrupt the discussion of the range of instruments and the repertoire. The fact that the Nan brothers performed with a local theater company has no clear relationship to the discussion at this point in the essay.

Passage II

Question 16. The best answer is J because it creates a grammatically correct and complete sentence by omitting the repetition of the subject (it) and a second main verb is. Deleting the phrase “it is” correctly allows for the second half of the sentence to work as an appositive that explains what a nurse log is.

The best answer is NOT:

F because it adds a subject (it) and verb (is), establishing the second part of the sentence as an independent clause. This creates a run-on sentence by incorrectly joining two independent clauses using a comma without a coordinating conjunction.

G because it adds a subject (“the term ‘nurse log’ ”) and verb (is defined), establishing the second part of the sentence as an independent clause. This creates a run-on sentence by incorrectly joining two independent clauses using a comma without a coordinating conjunction.

H because it adds a subject (“this type of log”) and verb (is), establishing the second part of the sentence as an independent clause. This creates a run-on sentence by incorrectly joining two independent clauses using a comma without a coordinating conjunction.

Question 17. The best answer is A because it does not introduce redundancy or unnecessary wordiness.

The best answer is NOT:

B because it introduces redundancy at the paragraph level; the phrase “in addition to acting as a home and providing nutrients for young plants” is redundant because this point is made clear in the preceding sentence.

C because it introduces redundancy at the paragraph level; the parenthetical noting the size of the log is redundant because this detail is made clear in the preceding sentence.

D because it introduces redundancy at the paragraph level; because the preceding sentence clearly describes the log as decaying, it is redundant to include that point again.

Question 18. The best answer is G because it eliminates unnecessary punctuation that incorrectly separates the park’s visitors from what they saw.

The best answer is NOT:

F because it provides unnecessary punctuation; the comma after the word park incorrectly separates the visitors (the indirect object) from what they are offered (“a glimpse into the complicated cycle of life”).

H because it provides unnecessary punctuation; the comma after the word life incorrectly separates the modifier (“unfolding in the forests outside the city”) from what it modifies (“the complicated cycle of life”).

J because it provides unnecessary punctuation. The commas after the words park and life incorrectly set off the direct object phrase that explains what visitors are offered (“a glimpse into the complicated cycle of life”). This creates an ungrammatical and illogical sentence.

Question 19. The best answer is A because it correctly distinguishes between the frequently confused words lying and laying and applies the idiomatically correct preposition in for the context. The word lying correctly indicates that the log itself is on the forest floor.

The best answer is NOT:

B because it fails to properly distinguish between the words lying and laying. The phrase “laying within” illogically suggests that the log is laying something else down inside the forest.

C because it provides the preposition with, which creates a nonstandard expression.

D because it fails to properly distinguish between the words lying and laying; the word laying illogically suggests that the log is laying something else down. In addition, it provides the preposition in, which creates a nonstandard expression.

Question 20. The best answer is H because it prevents an error in parallelism between the two parts of the sentence; the past tense transported correctly parallels the past tense found used previously in the sentence. In addition, the phrase “and transported” correctly provides the word and to indicate that Dion carried out two actions: he found the log and transported it.

The best answer is NOT:

F because it contains an error in parallelism; it uses the participle transporting where the finite verb transported is needed to parallel the previous finite verb found. In addition, it incorrectly places a comma after the word and, causing the phrase “transporting it to the city along with some of the soil” to look as if it is set off as a nonessential element.

G because it introduces an error in parallelism by using the infinitive to transport where the finite verb transported is needed to parallel the previous finite verb found. In addition, it incorrectly places a comma after the word and, causing the phrase “to transport it to the city along with some of the soil” to look as if it is set off as a nonessential element.

J because it introduces an error in coordination; omitting the conjunction and makes it look like the sentence is setting up a list indicating that Dion carried out at least three actions (found the log, transported the log, and did something else), but this is not the case.

Question 21. The best answer is A because it prevents the creation of a run-on sentence by establishing two complete sentences separated by a period.

The best answer is NOT:

B because it creates a run-on sentence by incorrectly joining two complete sentences using a comma without a coordinating conjunction.

C because it creates a run-on sentence by incorrectly joining two complete sentences without any punctuation or coordinating conjunction.

D because it creates a run-on sentence by incorrectly joining two complete sentences using a comma without a coordinating conjunction.

Question 22. The best answer is J because it ensures correct subject-verb agreement. The plural verb reveal agrees with the plural subject visits.

The best answer is NOT:

F because it lacks subject-verb agreement; the singular verb reveals does not agree with the plural subject visits.

G because it lacks subject-verb agreement; the singular verb has revealed does not agree with the plural subject visits.

H because it lacks subject-verb agreement; the singular verb is revealing does not agree with the plural subject visits.

Question 23. The best answer is C because it correctly distinguishes between the frequently confused words number and amount; the nouns energy and technology are both noncountable and therefore require the word amount. It correctly uses the plural noun amounts because there are two things needed for maintaining the nurse log: energy and technology. Finally, it correctly uses the preposition of to create an expression consistent with standard English usage.

The best answer is NOT:

A because it fails to correctly distinguish between the words number and amount, creating an expression that is inconsistent with standard English usage.

B because it uses the singular word amount where a plural is needed, and it incorrectly applies the preposition in where the word of is needed to create an expression consistent with standard English usage.

D because it fails to correctly distinguish between the words numbers and amounts, and it incorrectly applies the preposition in where the word of is needed to create an expression consistent with standard English usage.

Question 24. The best answer is F because it does not introduce redundancy or unnecessary wordiness.

The best answer is NOT:

G because it contains an internal redundancy; in this context, the word constantly and the phrase “on a regular basis” convey the same meaning.

H because it contains an internal redundancy; nutrients are healthy, so it is redundant to add the adjective healthful.

J because it contains an internal redundancy; in this context, the words constantly and regularly convey the same meaning.

Question 25. The best answer is B because it correctly identifies the rhetorical impact of losing the preceding sentence. The preceding sentence offers three examples (monitored humidity, soil replenishment, and filtered sunlight) to illustrate the level of effort required to maintain the nurse log in the city.

The best answer is NOT:

A because it incorrectly identifies the rhetorical impact of losing the preceding sentence. The preceding sentence refers to the necessity of monitoring humidity and replenishing soil, but it does not explain why this is “necessary to maintain nature-based exhibits” in general. It is solely focused on this particular nurse log.

C because it incorrectly identifies the rhetorical impact of losing the preceding sentence. Although the greenhouse houses the nurse log and allows for the maintenance of the nurse log in the city environment, the preceding sentence does not compare the importance of the greenhouse and nurse log in any way.

D because it incorrectly identifies the rhetorical impact of losing the preceding sentence. The preceding sentence describes some of the difficulties of maintaining the nurse log in a city environment, but it does not discuss anything in connection to “how difficult it was for Dion to build the greenhouse.”

Question 26. The best answer is J because it corrects a misplaced modifier. Placing the modifying phrase “in the middle of a busy city” after the word ecosystem clearly and logically explains that the ecosystem was in the middle of the city.

The best answer is NOT:

F because it contains a misplaced modifier. Placing the modifying phrase after the word work suggests an illogical causal relationship by indicating that the required work conveyed an important message because it took place in the middle of the city.

G because it introduces a misplaced modifier. Placing the modifying phrase after the word the creates an ungrammatical and illogical sentence suggesting that the required work conveyed an important message because it took place in the middle of the city.

H because it introduces a misplaced modifier. Placing the modifying phrase after the word this creates an ungrammatical sentence. The modifying phrase must follow the noun it is meant to modify.

Question 27. The best answer is D because it correctly distinguishes between the phrases “In accordance with” and “According to” to provide the phrase that is most contextually appropriate. The phrase “According to” accurately conveys that the sentence is explaining the artist’s perspective. In addition, the phrase supplies the idiomatically correct preposition to.

The best answer is NOT:

A because it provides the idiomatically incorrect preposition with where the preposition to is needed.

B because it fails to correctly distinguish between the phrases “According to” and “In accordance with.” The phrase “In accordance with” incorrectly signals a sense of agreement between two parties rather than indicating that what follows conveys the artist’s perspective.

C because it provides a phrase that does not make sense in context. The phrase “In accord with” incorrectly signals a sense of collaboration and agreement between two parties rather than indicating that what follows conveys the artist’s perspective.

Question 28. The best answer is H because it uses consistent punctuation (commas) to correctly set off a nonessential element. The phrase “once destroyed” is not essential to the sentence and is therefore set off with commas after the words nature and destroyed.

The best answer is NOT:

F because it fails to provide the necessary punctuation to set off the nonessential element (“once destroyed”).

G because although it correctly sets off the nonessential element (“once destroyed”), it incorrectly places a comma after the word virtually, which incorrectly separates the modifier (virtually) from the word it modifies (impossible).

J because it fails to provide the necessary punctuation to set off the nonessential element (“once destroyed”) and incorrectly places a comma after the word virtually, which incorrectly separates the modifier (virtually) from the word it modifies (impossible).

Question 29. The best answer is B because the parenthetical explains the origin of part of the installation’s title. Paragraph 2 begins by explaining the meaning of the word Vivarium in the installation’s title. The parenthetical explaining the other half of the title (Neukom) would most logically be placed at Point B, which appears right after the explanation of Vivarium.

The best answer is NOT:

A because the parenthetical does not describe anything specific about the installation or what a nurse log is, which is the focus of the discussion at Point A.

C because the parenthetical does not describe anything in relation to Dion’s process of finding the log or creating the installation, which is the focus of the discussion at Point C.

D because the parenthetical does not describe anything in relation to the work required to maintain the nurse log in the city, which is the focus of the discussion at Point D.

Question 30. The best answer is G because it offers a clear and convincing reason the essay accomplishes the purpose identified in the stem. The essay “describes Dion’s nature-based installation” in the first three paragraphs and then explains his purpose in conveying to others the importance of sustaining ecosystems.

The best answer is NOT:

F because it fails to provide a clear and convincing reason the essay accomplishes the purpose identified in the stem. It provides a version of how Dion’s installation came about that differs from the essay and does not address the message Dion hopes to share in order to educate others.

H because it fails to provide a clear and convincing reason the essay has not accomplished the purpose identified in the stem. It inaccurately asserts that the essay focuses on the appearance of the installation specifically in relation to Olympic Sculpture Park. The essay focuses much more on Dion’s message and how the installation conveys that message than it does on the installation’s appearance.

J because it fails to provide a clear and convincing reason the essay has not accomplished the purpose identified in the stem. The last paragraph of the essay does address what viewers learn from the installation.

Passage III

Question 31. The best answer is A because it prevents the introduction of an error in coordination between the two parts of the sentence; the use of a semicolon after the word commands demands that the first part of the sentence be an independent clause. The phrase “Internet navigation required” provides the subject (“Internet navigation”) and verb (required) needed to correctly establish the first part of the sentence as an independent clause.

The best answer is NOT:

B because it introduces an error in coordination between the two parts of the sentence; the modifying phrase “which required” replaces the main verb required. This makes the first part of the sentence a sentence fragment. A sentence fragment cannot be joined to an independent clause by a semicolon.

C because it introduces an error in coordination between the two parts of the sentence; the modifying phrase “that required” replaces the main verb required. This makes the first part of the sentence a sentence fragment. A sentence fragment cannot be joined to an independent clause by a semicolon.

D because it introduces an error in coordination between the two parts of the sentence; the modifying participle requiring replaces the main verb required. This makes the first part of the sentence a sentence fragment. A sentence fragment cannot be joined to an independent clause by a semicolon.

Question 32. The best answer is H because it offers phrasing that is both stylistically and tonally consistent with the essay as a whole.

The best answer is NOT:

F because it fails to match the established style. The phrasing of “obstructive hindrances” sounds too formal and contains an internal redundancy; hindrances are obstructive by nature, so it is unnecessary to include the adjective at all.

G because it fails to match the established style; the phrase “What with the problematic issues” is too informal for the style and tone of the essay.

J because it fails to match the established style; the phrase “Owing to the messiness” is too informal for the style and tone of the essay.

Question 33. The best answer is C because it provides the correct punctuation (a colon) to join two independent clauses such that the second clause explains or expands on the first clause. In this case, the idea that Andreessen believed everyone would want the Internet further explains what the writer means by the statement “Marc Andreessen believed the opposite.”

The best answer is NOT:

A because it incorrectly joins two independent clauses using a comma without a coordinating conjunction, which creates a run-on sentence.

B because it incorrectly uses a semicolon to join the independent clause (“Marc Andreessen believed the opposite”) and the dependent clause (“because everyone would want the Internet”). A semicolon can only be used to join two independent clauses.

D because it fails to provide any punctuation to join the two independent clauses, which creates a run-on sentence.

Question 34. The best answer is J because it provides the best transition to the discussion of Andreessen’s browser. The paragraph that follows describes what Andreessen created: a tool for using the Internet. The sentence “People just needed the right tool” would therefore provide the most effective transition from the discussion of why the Internet wasn’t user-friendly to the discussion of the tool Andreessen created to help solve that problem.

The best answer is NOT:

F because it fails to provide a logical transition to the discussion of Andreessen’s browser. The statement about Andreessen’s belief that Internet speeds would increase does not clearly connect to the development of Mosaic.

G because it fails to provide a logical transition to the discussion of Andreessen’s browser. The statement about the amount of information online does not clearly connect to the development of Mosaic.

H because it fails to provide a logical transition to the discussion of Andreessen’s browser. The statement about the limited number of people who had Internet access does not clearly connect to the development of Mosaic.

Question 35. The best answer is D because it correctly eliminates the unnecessary punctuation in the phrase “As a student worker for the National Center for Supercomputing Applications (NCSA) at the University of Illinois.” The abbreviation NCSA should be separated from the center’s full name only by parentheses, and no punctuation should separate the noun phrase “As a student worker” from the prepositional phrase explaining who or what the student worked for.

The best answer is NOT:

A because it incorrectly sets off the prepositional phrase “for the National Center for Supercomputing Applications” with commas. In addition, it incorrectly places a comma between the full name of the center and the parenthetical abbreviation for it.

B because it incorrectly sets off the prepositional phrase “for the National Center for Supercomputing Applications” with commas. In addition, the phrase incorrectly sets off the abbreviation with commas when the abbreviation is already enclosed by parentheses.

C because it incorrectly sets off the abbreviation with commas when the abbreviation is already enclosed by parentheses.

Question 36. The best answer is F because it best expresses the idea specified in the stem. The phrase “became enthralled” indicates that Andreessen was so drawn to the Internet that he was captivated by the it and therefore “most strongly conveys that Andreessen developed a strong affinity for the Internet.”

The best answer is NOT:

G because it fails to express the idea specified in the stem. Pointing out that Andreessen “first gained access to” the Internet at NCSA does not convey any sense that Andreessen developed an affinity for the Internet.

H because it is a less effective choice for expressing the idea specified in the stem. Although some sense of affinity could be suggested by the idea that Andreessen “spent many hours” on the Internet, it is unclear if this was by choice or necessity. In addition, there is no indication of Andreessen developing an affinity for the Internet.

J because it fails to express the idea specified in the stem. The fact that Andreessen “saw the utility of” the Internet does little to convey any sense of Andreessen developing an affinity for it.

Question 37. The best answer is A because it prevents the creation of a run-on sentence. The dependent clause “which became available in 1993” follows the independent clause and is properly set off as a nonessential element that describes a detail about Mosaic.

The best answer is NOT:

B because it creates a run-on sentence by incorrectly joining two independent clauses (“The two then worked with the NCSA to develop Mosaic” and “the NCSA made the program available in 1993”) using a comma without a coordinating conjunction.

C because it creates a run-on sentence by incorrectly joining two independent clauses (“The two then worked with the NCSA to develop Mosaic” and “they made Mosaic available in 1993”) using a comma without a coordinating conjunction.

D because it creates a run-on sentence by incorrectly joining two independent clauses (“The two then worked with the NCSA to develop Mosaic” and “it became available in 1993”) using a comma without a coordinating conjunction.

Question 38. The best answer is F because it does not introduce redundancy or unnecessary wordiness.

The best answer is NOT:

G because it introduces redundancy at the sentence level. The sentence specifies that the 60,000 copies were downloaded in Mosaic’s first year, so it is redundant to include the phrase “That year” at the beginning of the sentence.

H because it introduces redundancy at the paragraph level. The paragraph already clearly identifies Mosaic as the program that could be downloaded; it is unnecessary to add a parenthetical to the last sentence of the paragraph to clarify which program is being discussed.

J because it contains an internal redundancy; the word Approximately means the same thing as the phrase “but not exactly.”

Question 39. The best answer is D because it correctly places the modifying adverb soon after the word it; in this location, the adverb soon modifies the verb surpassed in the second independent clause to create a grammatically correct statement with the most logical meaning in context.

The best answer is NOT:

A because it contains a misplaced modifier. Placing the adverb soon after the word was creates a statement that illogically suggests Mosaic was the first web browser but then lost that status. This is impossible. When a new browser is invented, it does not replace others as the first browser.

B because it introduces a misplaced modifier. Placing the adverb soon after the word Mosaic creates a statement that illogically suggests Mosaic was the first web browser but then lost that status. This is impossible. When a new browser is invented, it does not replace others as the first browser.

C because it introduces a misplaced modifier. Placing the adverb soon after the word browser creates a statement that illogically suggests Mosaic was the first web browser but then lost that status. This is impossible. When a new browser is invented, it does not replace others as the first browser.

Question 40. The best answer is G because it correctly indicates that the phrase should be added and accurately identifies the rhetorical impact of making that addition. The phrase “adding much-needed visual appeal” helps emphasize the impact of displaying pictures and text on the same page: it made browsing more enjoyable.

The best answer is NOT:

F because although it correctly indicates that the phrase should be added, it fails to accurately identify the rhetorical impact of making that addition. The sentence does not need the added phrase to reveal that Mosaic was the first browser to display pictures alongside text; the sentence makes that point clear without the addition of the phrase.

H because it incorrectly indicates that the phrase should not be added and inaccurately describes the rhetorical impact of the phrase. The suggested phrase points out the visual appeal of adding pictures; this does not indicate that text-based documents therefore weren’t useful.

J because it incorrectly indicates that the phrase should not be added and inaccurately describes the rhetorical impact of the phrase. The suggested phrase points out the visual appeal of adding pictures; it does not indicate that Mosaic was like other browsers initially and later added visuals.

Question 41. The best answer is C because it creates a sentence structure wherein the correct subject (“the program”) immediately follows the modifying phrase (“featuring hyperlinks”). This structure clearly and logically indicates that the program featured hyperlinks.

The best answer is NOT:

A because it creates an illogical sentence; it establishes “the user” as the subject, which illogically suggests that the user featured hyperlinks.

B because it creates an illogical sentence; it establishes “the program’s user” as the subject, which illogically suggests that the user featured hyperlinks.

D because it creates a dangling modifier; this structure fails to establish a clear and logical relationship between the modifying phrase “featuring hyperlinks” and the rest of the sentence. What exactly featured hyperlinks remains unclear.

Question 42. The best answer is H because it correctly identifies the rhetorical impact of losing the preceding sentence. The quotation in the preceding sentence specifically credits Mosaic with making the Internet seem “interconnected” or “coherent.”

The best answer is NOT:

F because it fails to properly identify the rhetorical impact of losing the preceding sentence. The quotation in the preceding sentence makes no mention of what people did before Mosaic was invented.

G because it fails to properly identify the rhetorical impact of losing the preceding sentence. The quotation in the preceding sentence does not reference specific features that made Mosaic popular.

J because it fails to properly identify the rhetorical impact of losing the preceding sentence. The quotation in the preceding sentence does not compare Mosaic to, or even mention, the designs of later web browsers.

Question 43. The best answer is B because it provides the most logical transition based on the surrounding context. The word Moreover creates the most logical transition because the text that follows the transition word expands upon the idea in the preceding sentence about Mosaic’s effect on average users.

The best answer is NOT:

A because it provides an illogical transition based on the surrounding context. The word Comparatively suggests that what follows presents a comparison to what came before, which is not the case here.

C because it provides an illogical transition based on the surrounding context. The word Conversely suggests that what follows presents a contrast to what came before, which is not the case here.

D because it provides an illogical transition based on the surrounding context. The word Instead suggests that what follows offers information about what Mosaic could do in place of what was described in the preceding sentence, but that is not the case here.

Question 44. The best answer is H because it provides the most precise word choice for the context. The word released precisely conveys the idea that Mosaic was made available to the public.

The best answer is NOT:

F because it supplies an imprecise word choice for the context; the word discharged illogically suggests that the browser was let go from a position or duty.

G because it supplies an imprecise word choice for the context; the word relinquished illogically suggests that the browser was given up.

J because it supplies an imprecise word choice for the context; the word emitted illogically suggests that the browser was given off (like heat or light) from something.

Question 45. The best answer is A because it provides the most effective conclusion based on the criterion in the stem. The “contrast begun in the previous sentence” refers to the fact that there were 623 websites when Mosaic was released. The specific detail about the existence of more than 600,000 sites four years later provides the most direct contrast by highlighting the difference in the number of sites.

The best answer is NOT:

B because it fails to provide an effective conclusion based on the criterion in the stem. Mosaic’s point-and-click interface offers no direct relationship to the number of websites in existence when Mosaic was released.

C because it fails to provide an effective conclusion based on the criterion in the stem. The fact that Andreessen would go on to develop another browser offers no direct relationship to the number of websites in existence when Mosaic was released.

D because it fails to provide an effective conclusion based on the criterion in the stem. Although the sentence highlights the expansion of the Internet, this general assertion offers no direct contrast to the specific number of websites in existence when Mosaic was released.

Passage IV

Question 46. The best answer is G because it best expresses the idea specified in the stem. The word celebrated best expresses an “overwhelmingly positive reception.”

The best answer is NOT:

F because it is a less effective choice relative to the goal specified in the stem. In context, the idea that “poets were placed alongside champion athletes” hints at the idea that the poets were honored just as much as champion athletes. However, the word placed is much weaker than the word celebrated in expressing an “overwhelmingly positive reception.”

H because it fails to express the idea specified in the stem. The word accepted can be understood as a neutral idea, or it can even convey a sense of reticence, as if the poets were only reluctantly accepted. Neither of these meanings expresses an “overwhelmingly positive reception.”

J because it is a less effective choice relative to the goal specified in the stem. The word liked conveys that the poets were appreciated, but it is less effective than the word celebrated in conveying the sense of an “overwhelmingly positive reception.”

Question 47. The best answer is A because it most effectively connects this sentence to the information in the next sentence. The sentence that follows highlights the scandal as evoking the only public excitement for the literary competition. The phrase “is poorly remembered and rarely missed” provides the most effective connection because it establishes that there has been little appreciation for the literary competition.

The best answer is NOT:

B because it fails to provide a logical connection to the next sentence. The detail about other competitions offers no direct connection to the next sentence, which specifically highlights the scandal as evoking the only public excitement relating to the literary competition.

C because it fails to provide a logical connection to the next sentence. The fact that the literary competition is sometimes commented upon today offers no direct connection to the next sentence, which specifically highlights the scandal as evoking the only public excitement relating to the literary competition.

D because it fails to provide a logical connection to the next sentence. The fact that the literary competition was an homage to the traditions of ancient Greece offers no direct connection to the next sentence, which specifically highlights the scandal as evoking the only public excitement relating to the literary competition.

Question 48. The best answer is J because it eliminates unnecessary punctuation in the modifying phrase that describes which literary contest is being discussed: “the very first modern Olympic literary contest.”

The best answer is NOT:

F because it provides unnecessary punctuation by incorrectly placing a comma after the word modern; the word modern directly modifies “Olympic literary contest” and therefore cannot be separated from that phrase by any punctuation.

G because it provides unnecessary punctuation by incorrectly placing commas after the words very and first. The word very is an intensifier that modifies the word first, so these two words cannot be separated by any punctuation. The word first modifies the phrase “modern Olympic literary contest” and therefore cannot be separated from that phrase by any punctuation.

H because it provides unnecessary punctuation by incorrectly placing a comma after the words first and Olympic. The word first modifies the phrase “modern Olympic literary contest” and therefore cannot be separated from that phrase by any punctuation. The word Olympic modifies “literary contest” and therefore cannot be separated from that phrase by any punctuation.

Question 49. The best answer is D because it correctly omits the repetition of the subject (he) while maintaining the main verb insisted; this correctly creates a complete sentence.

The best answer is NOT:

A because it incorrectly repeats the subject; the subject (“French aristocrat Baron Pierre de Coubertin”) is already stated in the first part of the sentence, so the subject he should not be used in the second part of the sentence.

B because it omits the main verb insisted, using instead the modifying phrase “insistent in his belief.” This creates a sentence fragment that seems to have one long, modified subject but no predicate.

C because it omits the main verb insisted, using instead the modifier insisting. This creates a sentence fragment that seems to have one long, modified subject but no predicate.

Question 50. The best answer is H because it provides the appropriate pronoun for this sentence. The subjective pronoun who is needed because it is the subject of the verb felt (creating the phrase “who felt”). This construction clearly indicates that what follows helps describe the officials’ perspective on the modern Olympic Games.

The best answer is NOT:

F because it incorrectly provides the objective pronoun whom when the subjective pronoun is needed.

G because it incorrectly provides the objective pronoun whom when the subjective pronoun is needed. In addition, it unnecessarily includes the reflexive pronoun themselves, which does not contribute to the meaning of the sentence.

J because it incorrectly provides the word which; the word who is needed because the sentence refers to people.

Question 51. The best answer is B because it corrects the use of a vague pronoun. The word competitors clearly indicates who would submit the work for the contest.

The best answer is NOT:

A because it uses a vague pronoun; the antecedent for the word it would seem to be the Pentathlon of Muses, which is illogical in this context. The Pentathlon cannot submit work.

C because it introduces a vague pronoun; the pronoun those has no clear antecedent, making it unclear who would submit the work for the contest.

D because it introduces a vague pronoun; the pronoun they has no clear antecedent because the competitors or authors have not been mentioned yet. Therefore, who would submit work for the contest remains unclear.

Question 52. The best answer is J because it provides the most relevant detail about the Olympic literary contest at this point in the essay. The detail that submissions should be in the form of a poem “inspired by the idea of sport” directly connects to the paragraph’s introduction of the literary contest; it provides basic information about what kinds of writing should be submitted.

The best answer is NOT:

F because it provides a vague detail about Coubertin not having established a length requirement; this is only loosely related to the basic introduction of the literary contest. The detail about the preference for submissions to be poems inspired by sports is much more relevant to the basic introduction of the contest.

G because it provides a detail that is unrelated to the basic introduction of the literary contest. The title of the piece that won twelve years later (in 1924) is irrelevant to the discussion of the basic requirements and establishment of the literary contest in its first modern Olympics.

H because it provides a vague detail that is irrelevant to the basic introduction of the literary contest. There is little information about the “limitations placed on writers” in this paragraph, so the point about critics mocking such limitations has no direct relationship to the discussion at this point in the essay.

Question 53. The best answer is B because it correctly places a comma after the word year to separate the introductory phrase (“After a long deliberation during the literary event’s first year”) from the rest of the sentence. This creates a grammatically correct and clear statement about the judges’ actions.

The best answer is NOT:

A because it incorrectly uses a semicolon to separate the introductory phrase from the main clause, creating an ungrammatical sentence.

C because it incorrectly joins the introductory phrase to the main clause with a comma and the word then. In addition, the word then repeats the idea conveyed by the word after at the beginning of the sentence. This creates an ungrammatical and unclear sentence.

D because it incorrectly uses a period to separate the introductory phrase from the main clause. The phrase “After a long deliberation during the literary event’s first year” is a sentence fragment.

Question 54. The best answer is F because it correctly provides a subject (judges) to clearly indicate who refused to award the medals. In addition, it includes a comma after the word judges, which correctly sets off the phrase “so impressed by ‘Ode to Sport’ that they called it ‘the perfect poem’ ” as a nonessential element.

The best answer is NOT:

G because it creates an error in coordination between the nonessential element and the rest of the sentence. The word and creates an unclear and ungrammatical relationship between the main clause (“The judges refused to award either silver or bronze medals to any other literary competitors”) and the nonessential element (“so impressed by ‘Ode to Sport’ that they called it ‘the perfect poem’ ”). The word and incorrectly seems to set up the nonessential element as an addition to another nonessential element, which it is not.

H because it creates an error in coordination between the two parts of the sentence. The sentence already has the main verb refused to describe what the judges did; adding a second main verb (had been) creates an unclear and ungrammatical sentence.

J because it creates an error in coordination between the two parts of the sentence. The sentence already has the main verb refused to describe what the judges did; adding a second main verb (were) creates an unclear and ungrammatical sentence.

Question 55. The best answer is B because it omits the comma after Weeks to ensure that the phrase “after the Games had come to an end” is not set off in the sentence. The phrase “after the Games had come to an end” is essential information that modifies the word Weeks. Omitting the comma creates a grammatical sentence that clearly explains when the judges attempted to contact Hohrod and Eschbach.

The best answer is NOT:

A because it incorrectly places commas after the words Weeks and end, which incorrectly indicates that the phrase “after the Games had come to an end” is a nonessential element.

C because it incorrectly places a comma after the word Weeks, which creates an ungrammatical and unclear sentence. Setting off the word Weeks makes the sentence confusing because the word Weeks has no clear relationship to the rest of the sentence.

D because it incorrectly omits the comma that should follow the introductory phrase “Weeks after the Games had come to an end.”

Question 56. The best answer is F because it most effectively leads the reader from the preceding information about Hohrod and Eschbach to the information that follows about Coubertin. The preceding sentence explains that the judges were unsuccessful in reaching Hohrod and Eschbach, and the sentence that follows explains that Coubertin admitted to being the real author. The sentence explaining the judges’ discovery that Hohrod and Eschbach did not exist provides a clear and logical connection between these events.

The best answer is NOT:

G because it fails to provide an effective connection between the preceding information about Hohrod and Eschbach and the information that follows about Coubertin. The Swedish art academies’ claims about the competition have no relationship to the sequence of events that occurred between “Ode to Sport” winning and Coubertin admitting that he was the author.

H because it fails to provide an effective connection between the preceding information about Hohrod and Eschbach and the information that follows about Coubertin. The arrival of submissions for the following year’s competition has no relationship to the sequence of events that occurred between “Ode to Sport” winning and Coubertin admitting that he was the author.

J because it fails to provide an effective connection between the preceding information about Hohrod and Eschbach and the information that follows about Coubertin. The fact that the judges had read “Ode to Sport” aloud has no relationship to the sequence of events that occurred between “Ode to Sport” winning and Coubertin admitting that he was the author.

Question 57. The best answer is C because it accurately explains that adding the sentence would repeat information provided earlier in the essay. The sentence includes two details: Coubertin founded the modern Olympic Games and established the fine arts competition. These details are introduced in the second paragraph of the essay.

The best answer is NOT:

A because it fails to identify the fact that the sentence contains information that is already given in the essay. The idea that Coubertin did not include his real name because he was involved in establishing the competition is not a valid reason for adding redundant information.

B because it fails to identify the fact that the sentence contains information that is already given in the essay. In addition, it inaccurately describes the proposed addition; the sentence does not at all suggest that Coubertin knew his poem was well written.

D because it inaccurately describes why the sentence should not be added. Although it is true that the sentence does not make clear whether Coubertin discussed the poem with the judges, the primary reason the sentence should not be added is that it would introduce redundancy.

Question 58. The best answer is H because it eliminates redundancy and unnecessary wordiness.

The best answer is NOT:

F because it introduces redundancy at the sentence level; the causal relationship is established by the introductory phrase “once Coubertin’s ruse was uncovered,” so it is redundant to add “as a result.”

G because it introduces redundancy at the sentence level; the sentence establishes that the contest was “already unpopular,” so it is redundant to add “even though dislike of it was not new.”

J because it introduces redundancy at the sentence level; the causal relationship is established by the introductory phrase “once Coubertin’s ruse was uncovered,” so it is redundant to add “because of this unveiling.”

Question 59. The best answer is D because it is the most effective placement of the statement in terms of logic and cohesion. The sentence explains the growing distrust of the competition, even among its organizers. This point would logically follow the sentence explaining that distrust of the competition grew after Coubertin’s ruse was uncovered. In addition, it would logically precede the sentence explaining when the competition was finally dropped from the Olympic Games.

The best answer is NOT:

A because it would interrupt the paragraph by introducing information about the growing distrust of the competition in the middle of offering more general information about the competition and the surrounding scandal.

B because it would interrupt the transition between the first two paragraphs. The first paragraph ends with the introduction of the scandal surrounding the first modern Olympic literary contest, and the second paragraph begins the story of how that contest began and how the scandal erupted. It would be illogical to interrupt that transition with a point about the growing distrust of the competition.

C because it would interrupt the discussion of how the competition worked in the modern Olympic Games. The statement about the growing distrust of the competition has no clear relationship to the basic description of how the competition worked.

Question 60. The best answer is G because it offers a clear and convincing reason the essay accomplishes the purpose identified in the stem: it accurately explains that the essay is describing the Pentathlon of Muses, “an element of the modern Olympic Games that was relatively short lived and is not very well remembered.”

The best answer is NOT:

F because it fails to offer a clear and convincing reason the essay accomplishes the purpose identified in the stem. It inaccurately describes the essay; rather than outlining “Coubertin’s most important accomplishments as the founder of the modern Olympic Games,” the essay focuses on Coubertin’s role in one small piece of the modern Olympic Games—the Pentathlon of Muses.

H because it indicates the essay hasn’t accomplished the specified primary purpose when it has. In doing so, it inaccurately asserts that the essay “considers the merits of fine arts competitions being a part of popular athletic events.” The essay does not do this. Rather, it focuses specifically on the lesser-known history of the Pentathlon of Muses.

J because it indicates the essay hasn’t accomplished the specified primary purpose when it has. In doing so, it inaccurately asserts that the essay discusses Coubertin’s poem “and explains why the poem influenced Coubertin to compete in literary competitions.” The essay does not do this. Rather, it focuses specifically on the relatively unknown history of the Pentathlon of Muses.

Passage V

Question 61. The best answer is B because it omits the commas to ensure that the essential element (“Louise Arner Boyd”) is not set off in the sentence.

The best answer is NOT:

A because it incorrectly places commas before and after the name “Louise Arner Boyd,” which sets off the name as a nonessential element. In addition, the comma after the word native separates the modifying phrase “San Francisco native” from the subject it modifies, “Louise Arner Boyd.” The comma after the name Boyd separates the subject from the verb.

C because it incorrectly places a comma after the name Boyd, which separates the subject from the verb.

D because it incorrectly places a comma after the word native, which separates the modifying phrase “San Francisco native” from the subject it modifies, “Louise Arner Boyd.”

Question 62. The best answer is F because it does not introduce redundancy or unnecessary wordiness.

The best answer is NOT:

G because it introduces redundancy at the sentence level. The sentence already tells us that Boyd first saw the Arctic glaciers and fjords in 1924, so it is redundant to add the phrase “which she had never before seen.”

H because it introduces redundancy at the sentence level. The sentence already tells us that Boyd saw Arctic glaciers and fjords, so it is redundant to add the phrase “both glaciers and fjords.”

J because it introduces redundancy at the sentence level. The sentence already tells us that Boyd first saw the Arctic glaciers and fjords in 1924. The word initially simply repeats the idea that this was the first time she saw the glaciers and fjords.

Question 63. The best answer is A because it correctly distinguishes between plural and singular possessives and contractions by using the word its to indicate a singular possessive referring to the Arctic.

The best answer is NOT:

B because it incorrectly uses the plural possessive their to refer to the singular subject the Arctic.

C because it incorrectly uses the contraction it’s (meaning “it is”) where the singular possessive (its) is needed.

D because it incorrectly uses the nonword its’, which appears to be a singular possessive form of its that erroneously includes an apostrophe. The possessive its never has an apostrophe.

Question 64. The best answer is H because it correctly identifies the primary rhetorical impact of losing the phrase “packed with icebergs.” The next part of the sentence states that travel by boat was treacherous; the phrase “packed with icebergs” offers one example of a particular danger that creates this condition.

The best answer is NOT:

F because it incorrectly identifies the primary rhetorical purpose of the phrase “packed with icebergs.” This phrase offers no indication of the purpose of the 1924 expedition Boyd participated in. Rather, it describes a particular danger for boat travel in the Arctic in general.

G because it incorrectly identifies the primary rhetorical purpose of the phrase “packed with icebergs.” This phrase does not serve as an explanation of techniques for making travel safer on the seas near Spitsbergen. Rather, it describes one particular danger for boat travel in the Arctic in general.

J because it incorrectly identifies the primary rhetorical purpose of the phrase “packed with icebergs.” This phrase offers no indication of why boats were not equipped to navigate around icebergs. It simply notes one particular danger of boat travel in the Arctic in general.

Question 65. The best answer is A because it best expresses the idea specified in the stem that “Boyd conceived of and managed the seven Arctic expeditions.” The word lead most strongly conveys the leadership role Boyd took in planning and managing these expeditions.

The best answer is NOT:

B because it is an ineffective choice based on the goal specified in the stem; the phrase “be a part of” indicates that Boyd was a participant, but it fails to convey that she “conceived of and managed” the expeditions.

C because it is an ineffective choice based on the goal specified in the stem; the word experience indicates that Boyd was a participant, but it fails to convey that she “conceived of and managed” the expeditions.

D because it is an ineffective choice based on the goal specified in the stem; the phrase “embark on” indicates that Boyd went on the expeditions, but it fails to convey that she “conceived of and managed” the expeditions.

Question 66. The best answer is F because it most effectively leads the reader from the first sentence of the paragraph to the information in the next two sentences. The statement about Boyd’s expanding interest provides a smooth link that explains the shift from Boyd’s focus during her first two Arctic trips (photographing the Arctic’s glaciers) to the broader goals of her later voyages (carrying out a range of scientific studies).

The best answer is NOT:

G because it provides an illogical transition to the two sentences that follow, which describe the larger ship and the broader focus of the voyages. Boyd’s opportunity to share her early photographs with the king and queen of England is not related to the later voyages and therefore fails to lead the reader from the first sentence to the two sentences that follow.

H because it provides an illogical transition to the two sentences that follow, which describe the larger ship and the broader focus of the voyages. The fact that Boyd was “the first woman to be elected to the board of the American Geographical Society” is not related to the later voyages and therefore fails to lead the reader from the first sentence to the two sentences that follow.

J because it provides a weak transition to the two sentences that follow, which describe the larger ship and the broader focus of the voyages. The fact that the first two voyages landed “on a group of islands called Franz Josef Land” is not related to the later voyages and therefore fails to lead the reader from the first sentence to the two sentences that follow.

Question 67. The best answer is C because it correctly joins two closely related independent clauses with a semicolon.

The best answer is NOT:

A because it incorrectly uses a comma to join two independent clauses, which creates a run-on sentence.

B because it uses only the word and to join two independent clauses, which creates a run-on sentence. The coordinating conjunction and requires a comma in order to correctly join two independent clauses.

D because it incorrectly uses a comma to join two independent clauses, which creates a run-on sentence.

Question 68. The best answer is J because it creates an expression consistent with standard English usage to indicate that the location is close to, but south of, the North Pole.

The best answer is NOT:

F because it creates a nonstandard expression that is unclear in meaning. The phrase “close south” does not clearly explain the location in relation to the North Pole.

G because it creates a nonstandard expression that is unclear in meaning. The phrase “anchored nearby south of the North Pole” suggests that a place has already been mentioned, and the group anchored nearby. However, no such place is mentioned in the essay.

H because it creates a nonstandard expression that only vaguely indicates the location in relation to the North Pole.

Question 69. The best answer is B because it correctly uses commas to separate items in a series. The sentence lists three teams of scientists and what they did. The comma after the word tundra correctly separates the first item in this list (“Botanists gathered plant specimens from the tundra”) from the second item in the list (“paleogeologists studied the ancient ice fields”).

The best answer is NOT:

A because it uses inconsistent punctuation to separate items in a list. The em dash after the word tundra is inconsistent with the comma used later in the sentence and creates an unclear and ungrammatical relationship between the first and second items in the list.

C because it uses inconsistent punctuation to separate items in a list. The colon after the word tundra is inconsistent with the comma used later in the sentence and creates an unclear and ungrammatical relationship between the first and second items in the list.

D because it incorrectly omits punctuation between items in a list, creating an unclear and ungrammatical relationship between the first and second items in the list.

Question 70. The best answer is G because it provides the most precise word choice for the context. The word delivered correctly and logically conveys that the camera produced (or delivered) high-quality photos.

The best answer is NOT:

F because it supplies an imprecise word choice for the context; the word freed illogically suggests that the landscape images were trapped and then set free by the camera.

H because it supplies an imprecise word choice for the context; the word performed illogically suggests that the camera carried out images, which does not make sense in this context.

J because it supplies an imprecise word choice for the context; the word disengaged illogically suggests that the images were trapped and then separated or released from the camera.

Question 71. The best answer is D because it corrects the run-on by replacing the phrase “She knew about” with the phrase “knowledgeable about.” This creates a clear causal relationship between the two parts of the sentence, communicating that because Boyd was knowledgeable about photogrammetry, she was able to use very precise methods to set up her shots.

The best answer is NOT:

A because it creates a run-on sentence by joining two independent clauses (“She knew about photogrammetry” and the clause beginning “Boyd used precise methods”) using a comma without a coordinating conjunction.

B because it creates an ungrammatical sentence; the noun phrase (“The advanced knowledge she had of photogrammetry”) does not convey a clear relationship to the main clause about Boyd using precise methods to set up her shots.

C because it creates a run-on sentence by joining two independent clauses (“She had advanced knowledge of photogrammetry” and the clause beginning “Boyd used precise methods”) using a comma without a coordinating conjunction.

Question 72. The best answer is J because it ensures correct agreement between the singular feminine pronoun her and the singular feminine antecedent Boyd, making clear that the shots in question are Boyd’s.

The best answer is NOT:

F because it lacks agreement between the pronoun its and the antecedent Boyd. Because Boyd is the antecedent, a singular feminine pronoun is needed.

G because it lacks agreement between the pronoun phrase “his or her” and the antecedent Boyd. Because Boyd is the antecedent, a singular feminine pronoun is needed.

H because it lacks agreement between the plural pronoun their and the singular antecedent Boyd. By this point in the essay, Boyd has been identified as a woman by the use of the word she. Therefore, the singular feminine pronoun her is needed for agreement.

Question 73. The best answer is A because it does not introduce redundancy or unnecessary wordiness.

The best answer is NOT:

B because it contains an internal redundancy; a foundation provides the basis for later ideas and work, just as a springboard leads to later ideas and work. In this context, the words foundation and springboard indicate the same thing.

C because it contains an internal redundancy; giving support conveys the idea of providing assistance, so it is redundant to say that something “gave support that assisted.”

D because it introduces unnecessary wordiness. The phrase “lent themselves” creates unnecessary agency on the part of the photos; it suggests that the photos might have chosen to help create the first accurate large-scale maps of the area. In addition, the phrase “the purpose of” is unnecessary; it adds words that do not contribute to the overall meaning or clarify any particular point.

Question 74. The best answer is H because it best expresses the idea specified in the stem. When the phrase “in 1955” immediately follows the phrase “A chartered flight over the North Pole,” the sentence can then go on to explain that this particular Arctic journey was Boyd’s last.

The best answer is NOT:

F because it fails to express the idea specified in the stem. Because the phrase “in 1955” immediately follows the phrase “final Arctic journey,” it indicates that this might have been Boyd’s final Arctic journey for the year 1955. However, it remains unclear if she made any Arctic journeys in later years.

G because it fails to express the idea specified in the stem. Because the phrase “in 1955” immediately follows the phrase “final Arctic journey,” it indicates that this might have been Boyd’s final Arctic journey for the year 1955. However, it remains unclear if she made any Arctic journeys in later years.

J because it fails to express the idea specified in the stem. Because the phrase “in 1955” immediately follows the phrase “final Arctic journey,” it indicates that this might have been Boyd’s final Arctic journey for the year 1955. However, it remains unclear if she made any Arctic journeys in later years.

Question 75. The best answer is C because it offers a clear and convincing reason the essay does not accomplish the purpose identified in the stem. The essay only briefly mentions that Boyd’s photographs provided the basis for the first large-scale maps of the east coast of Greenland. The essay never expands on that point to explain how this was done.

The best answer is NOT:

A because it indicates the essay has accomplished the specified primary purpose when it hasn’t. Suggesting that the essay hints at a particular point does not describe the essay’s primary purpose. In addition, the essay never fully addresses how Boyd’s photographs provided the basis for the first large-scale maps of the east coast of Greenland.

B because it indicates the essay has accomplished the specified primary purpose when it hasn’t. Explaining that Boyd had been the first to photograph this region thoroughly does not explain how her photographs were later used to make maps of the east coast of Greenland.

D because it offers an inaccurate description of the essay and therefore fails to explain why the essay does not accomplish the purpose specified in the stem. Although the essay mentions that Boyd positioned her camera to create high-resolution images, it does not focus on this point. In addition, focusing on how Boyd positioned her camera would still fail to explain how Boyd’s photographs were used to make maps of the east coast of Greenland.

MATHEMATICS • PRACTICE TEST 5 • EXPLANATORY ANSWERS

Question 1. The correct answer is D. The average amount Xuan paid for each new book is given by = $12.60. Multiply to find the amount from the sales, subtract to find the total amount spent on the new books, and divide to find the average spent per new book. If you answered A, you may have divided by 9 instead of 4: = $5.60. If you answered B, you may have divided the leftover dollar amount by 4: = $9.45. If you answered C, you may have divided by the difference of 9 and 4: = $10.08. If you answered E, you may have forgotten to subtract before dividing: = $22.05.

Question 2. The correct answer is H. The coordinates of the point after the translation are given by (−5 + 7, 7 − 5), which is (2,2) because translating right 7 coordinate units corresponds to adding 7 to the x-coordinate, and translating down 5 coordinate units corresponds to subtracting 5 from the y-coordinate. If you answered F, you may have subtracted instead of adding and added instead of subtracting: (−5 − 7, 7 + 5). If you answered G, you may have switched the 7 and 5: (−5 + 5, 7 − 7). If you answered J, you may have added for both coordinates instead of subtracting for the downward translation: (−5 + 7, 7 + 5). If you answered K, you may have added 5 and 7 for both coordinates: (5 + 7, 7 + 5).

Question 3. The correct answer is C. Shantiel’s average speed, in miles per hour, is given by = 36. Divide the number of miles traveled by the elapsed time. To find the elapsed time, you could realize that 9 a.m. the next day would be 24 hours after the time she left, and 3 a.m. the next day is 6 hours before 9 a.m. the next day. If you answered A, you may have divided by 9 instead of 18: = 72. If you answered B, you may have thought the elapsed time was 12 instead of 18: = 54. If you answered D, you may have thought the elapsed time was 21 instead of 18: ≈ 31. If you answered E, you may have found the elapsed time only: 24 − (9 − 3) = 18.

Question 4. The correct answer is J. The total number of text messages for which Juan was charged on this bill is given by 300 + = 365. The bill was greater than $10.00, so Juan sent at least 300 text messages. To find how many more than 300, subtract $10.00 from the total charge of $16.50 to find that he was charged $6.50 more than the initial $10.00, and then divide the difference by the $0.10 charge per text message beyond the first 300. If you answered F, you may have subtracted from instead of adding to the first 300 messages: 300 – = 235. If you answered G, you may have subtracted from instead of adding to the first 300 messages, forgotten to subtract the initial $10.00 from the $16.50, and divided by $1.10 instead of $0.10: 300 – = 285. If you answered H, you may have forgotten to subtract the initial $10.00 from the $16.50 and then divided by $1.10 instead of $0.10: 300 + = 315. If you answered K, you may have forgotten to subtract the initial $10.00 from the $16.50: 300 + = 465.

Question 5. The correct answer is A. The sum of the matrices is given by . Add all pairs of corresponding entries. If you answered B, you may have disregarded the negative in the first matrix: . If you answered C, you may have disregarded both negatives: . If you answered D, you may have added elements within each matrix instead of the corresponding elements: . If you answered E, you may have multiplied the matrices instead of adding: .

Question 6. The correct answer is H. The value of f(4,3) is given by 3(4)² − 4(3) = 3(16) − 4(3) = 48 −12 = 36, which is found by substituting x and y with 4 and 3, respectively, and then squaring, multiplying, and subtracting. If you answered F, you may have mixed up the values substituted for x and y: 3(3)² − 4(4) = 3(9) − 4(4) = 27 −16 = 11. If you answered G, you may have squared the 3 instead of the 4 in the first term: 3²(4) − 4(3) = 9(4) − 4(3) = 36 − 12 = 24. If you answered J, you may have mixed up the values substituted for x and y and multiplied before squaring: (3(3))² − 4(4) = 9² −16 = 81 − 16 = 65. If you answered K, you may have multiplied before squaring: (3(4))² − 4(3) = 12² − 12 = 144 − 12 = 132.

Question 7. The correct answer is D. The mean age is given by = 8. If you answered A, you may have found the mean of the four numbers given in the first sentence after “5 children”: = 5. If you answered B, you may have mixed up the number of children at each age: = 7. If you answered C, you may have found the mean of the two unique ages: = 7.5. If you answered E, you found the mode, the most frequently occurring age: 10.

Question 8. The correct answer is H. The value DE, in feet, is 4. Because , by corresponding angles, we have . We know , and so by the angle-angle postulate, we know . Because , we know BD = BA. Therefore, DE = (8) = 4. If you answered F, you may have subtracted 8 from 10: 10 − 8 = 2. If you answered G, you may have subtracted half of 10 from 8: 8 – = 3. If you answered J, you may have taken half of 10 instead of half of 8: = 5.

Question 9. The correct answer is B. The number expected to vote in favor of the proposal is given by the solution to the proportion ; ; x = = 14,828. If you answered A, you may have rounded to and solved the proportion . If you answered C, you may have subtracted the difference of 500 and 337 from 22,000: . If you answered D, you chose the total number of registered voters. If you answered E, you may have solved a different proportion: .

Question 10. The correct answer is G. The difference between the total of all Diego’s payments and the car’s purchase price is given by . To the down payment, add the product of 48 payments and the amount per payment, and then subtract the purchase price. If you answered F, you may have forgotten to add the down payment: . If you answered H, you may have subtracted the down payment from the purchase price, disregarding the monthly payments: . If you answered J, you found the amount made in monthly payments: 48($300) = $14,400. If you answered K, you didn’t subtract the purchase price $400 + 48($300) + $14,800.

Question 11. The correct answer is A. Rearrange the given equation into slope-intercept form, y = mx + b, where m is the slope. 4x + 7y = 9 → 7y = −4x + 9 → y = . In this equation, m = . If you chose B, you may have divided the whole equation by 9 first and interpreted the coefficient of x as the slope before rearranging the rest of the equation into slope-intercept form. If you chose C, you may not have divided the rearranged equation by 7 before interpreting the coefficient of x as the slope. If you chose D, you may have interpreted the given coefficient of x as the slope without rearranging the equation. If you chose E, you may have interpreted the right side of the equation as the slope.

Question 12. The correct answer is G. Because ∠BCD is supplementary to ∠DCF, m∠BCD + m∠DCF = 180°. To find m∠DCF, use the angle sum of ΔDCF, m∠CFD + m∠FDC + m∠DCF = 180°. Notice that m∠CFD = m∠GFE = 25° because they are vertical angles. Because ∠FDC is a right angle, the angle sum is 25° + 90° + m∠DCF =180° → m∠DCF = 180° − (25° + 90°) = 65°. Substituting m∠DCF = 65° into the first equation, m∠BCD + m∠DCF = 180°, results in m∠BCD + 65° = 180° → m∠BCD = 115°. If you chose F, you may have found m∠DCF and not used its supplementary relationship with ∠BCD. If you chose H or J, you may have tried to estimate the measure from the figure. If you chose K, you may have tried to use m∠GFE = 25° as a supplementary angle to ∠BCD.

Question 13. The correct answer is C. Factoring the polynomial in the given equation results in (x + 6)(x − 5) = 0. The solutions of this equation are the values of x that make the equation true. Because the left side of the equation is a product of two factors, it is sufficient for either factor to be zero, meaning (x + 6) = 0 and (x − 5) = 0. The solutions to these two equations are –6 and 5. The sum of these two solutions is −6 + 5 = −1. If you chose A, you may have thought that the coefficient –30 was a solution to the equation. If you chose B or E, you may have tried substituting –6 or 5 and found that this made the given equation true. If you chose D, you may have thought that the right side of the given equation was the solution.

Question 14. The correct answer is F. The radius of the sphere is half the diameter, so r = 2 yards. Substituting this into the given volume formula results in cubic yards. If you chose G, you may have computed . If you chose H, you may have forgotten to include the denominator of the given formula in your answer. If you chose J, you may have multiplied the diameter by 3 and forgotten to include the denominator of the given formula. If you chose K, you may have substituted the diameter instead of the radius.

Question 15. The correct answer is C. Estimate by using the known values of perfect squares and . Because , you can conclude that , which means that 10 is the smallest integer greater than because there are no integers between 9 and 10. If you chose A, you may have thought you were looking for the smallest digit in the number 85. If you chose B, you may have found that and rounded down. If you chose D, you may have checked that 12 was larger than and may not have looked for a smaller integer. If you chose E, you may have thought that the square root meant to divide by 2.

Question 16. The correct answer is K. The relationships in the three statements can be represented as shown in this figure.

Because no elements of D are elements of B, , it must follow that no elements of A are elements of C, , because A and C are entirely contained in B and D, respectively, and . F cannot be true because no elements of A are elements of C. G cannot be true because no elements of D are elements of B. H cannot be true because B and D have no common elements, and any element of C is an element of D. J cannot be true because all elements of A are elements of B.

Question 17. The correct answer is A. The midpoint (2,1) must also be the midpoint of the x- and y-component distances of the length of . Because the x-distance from point A to (2,1) is 8 − 2 = 6, point B must be 6 units from (2,1) in the x-direction, which is 2 − 6 = −4. If you chose B, you may have found the change in the x-coordinate from (2,1) to point A. If you chose C, you may have found the y-coordinate of point B. If you chose D, you may have found half the x-distance from point A to (2,1). If you chose E, you may have found the x-coordinate of the midpoint of (2,1) and point A.

Question 18. The correct answer is K. The total number of either pitcher or outfielder cards is 8 + 7 = 15. The probability of finding one of these 15 cards in one pick is the fraction of desired outcomes over all possible outcomes, = 60%. If you chose F, you may have found the probability of each desired outcome, multiplied them, and rounded to the nearest percentage. If you chose G, you may have found the probability of picking an outfielder only. If you chose H, you may have found the probability of picking a pitcher only. If you chose J, you may have found the probability of picking an infielder or a pitcher.

Question 19. The correct answer is A. Let the change in mass of nitrogen phosphate used be y and the change in the average temperature be x. Then x and y are in a proportional relationship where y = −1.2x. For the given change of 83.0°F − 75.0°F = 8.0°F, y = −1.2(8.0) = −9.6 kg. Because this is a change from a starting mass of 40.0 kg, the required application amount is 40.0 − 9.6 = 30.4 kg. If you chose B, you may have added 1.2 and 8.0 to find the change in mass. If you chose C, you may have divided 40 by 1.2. If you chose D, you may have subtracted the change in temperature from the mass before multiplying by 1.2. If you chose E, you may have found the required application amount for a change of only 1°F.

Question 20. The correct answer is G. The area of the shaded region is xy. From the figure, create the equations 6 = y + 2 + y and 5 = x + 2 + x, which follow from the equivalent side lengths of the rectangle. Solve each of these equations: 6 = y + 2 + y → 2y = 6 − 2 → y = 2 and 5 = x + 2 + x → 2x = 5 − 2 → x = . Then the shaded area xy = 2 = 3 square units. If you chose F, you may have found the value of x and squared it. If you chose H, you may have assumed all the regions were equal in area and divided 30 by 9. If you chose J, you may have assumed all the regions were equal in area and that the whole figure was a square with a side length of 6 units. If you chose K, you may have found 2(x + y) instead of xy.

Question 21. The correct answer is D. The perimeter of the scalene triangle given is 100 inches. We also know that the perimeter of the triangle is the sum of the lengths of its sides. For this triangle, that means the triangle has a perimeter of 5x + (3x + 30) + (2x + 10) = 10x + 40. Therefore, 10x + 40 must equal 100 inches because both values are the perimeter of this triangle. Thus, 10x = 60 and x = 6. Because the sides of this triangle are 5x, 3x + 30, and 2x + 10, we know that the side lengths are 5(6) = 30, 3(6) + 30 = 48, and 2(6) + 10 = 22. Because 48 is the largest among 30, 48, and 22, we know that the longest side of this triangle is 48 inches. If you chose A, you may have thought the longest side of the triangle was the value of x. If you chose B, you may have thought the longest side was the side of length 2x + 10. If you chose C, you may have thought the longest side was the side of length 5x.

Question 22. The correct answer is J. Because each council member gets a seat, there are 6 members that could be in Seat 1. Because someone is already in Seat 1, there are 5 options for Seat 2. Because someone is already in Seats 1 and 2, there are 4 options for Seat 3. Similarly, there are 3 options for Seat 4, 2 options for Seat 5, and 1 option for Seat 6. Thus, the number of different arrangements is 6(5)(4)(3)(2)(1) = 720. If you chose F, you may have added 6 + 5 + 4 + 3 + 2 + 1 = 21 instead of multiplying. If you chose G, you may have multiplied the number of council members by the number of seats available. If you chose H, you may have taken and rounded to the nearest integer. If you chose K, you may have taken 6 council members and added a 0 in front of it for each seat available.

Question 23. The correct answer is E. 200% of 1 is 2(1) = 2. The sum of 2 and 200% of 1 is equivalent to 2 + 2 = 4. 400% of 1 is 4(1) = 4. If you chose A, you may have thought that 100% of 2, which equals 2, equals 4. If you chose B, you may have thought that 150% of 2, which equals 3, equals 4. If you chose C, you may have thought that 300% of 2, which equals 6, equals 4. If you chose D, you may have thought that 300% of 1, which equals 3, equals 4.

Question 24. The correct answer is H. Given two points of a line, and , the slope of the line is given by . For this line, the points given are (0, 2) and (3, 0). So, the slope of the line is . The y-intercept of this line is (0, 2). The slope-intercept form of a line is given by where m is the slope and b is the y-value of the y-intercept. Therefore, the slope-intercept form of this line is y = x + 2. If you chose F, you may have thought that the slope of a line is given by . If you chose G, you may have thought that the slope of a line is given by and that b is the x-value of the x-intercept. If you chose J, you may have thought that b is the x-value of the x-intercept. If you chose K, you may have thought that the slope of a line is given by .

Question 25. The correct answer is C. The area of a kite is given by multiplied by its length multiplied by its width. So, for this kite, the area is given by (40)(28) = 560. If you chose A, you may have thought the area is given by . If you chose B, you may have thought the area is given by multiplied by its length multiplied by its width. If you chose D, you may have thought the area is given by multiplied its length multiplied by its width. If you chose E, you may have thought the area was given by (40)(28).

Question 26. The correct answer is H. The surface area, including the top of the pool, is 60(25) = 1,500. The area of the surface of the pool is 15(40) = 600. Therefore, the area of the patio surrounding the pool is 1,500 − 600 = 900 square feet. If you chose F, you may have calculated the area by (60 − 40)25. If you chose G, you may have calculated the surface of the pool. If you chose J, you may have calculated the area by 25(60) − 40(5)(2). If you chose K, you may have calculated the area by 25(60) − 15.

Question 27. The correct answer is D. The cost of the materials is the cost per foot multiplied by the number of feet. Because the number of feet is the perimeter of the outer edge of the patio, the number of feet is 2(60) + 2(25) = 170. Therefore, the cost is $12(170) = $2,040. If you chose A, you may have calculated the perimeter as 60 + 25 = 85. If you chose B, you may have calculated the perimeter of the pool instead of the perimeter of the outside of the patio, 2(40) + 2(15) = 110. If you chose C, you may have calculated the perimeter as 6(25). If you chose E, you may have calculated the cost of a fence around the perimeter of the pool and the cost of a fence around the outside of the patio and added them together.

Question 28. The correct answer is J. Johann’s average speed can be calculated by dividing the total distance over the total time. The total distance is given by 5(2)(40) = 400. Therefore, the average speed is given by . If you chose F, you may have calculated the total distance by 5(60). If you chose G, you may have calculated the total distance by 5(40). If you chose H, you may have calculated the total distance by 5(60). If you chose K, you may have calculated the total distance by 5(2)(60).

Question 29. The correct answer is B. The slope can be found as rise over run. The rise can be calculated by 4-9. The run can be calculated by 40-20-12. Therefore, the slope is . If you chose A, you may have calculated . If you chose C, you may have calculated . If you chose D, you may have calculated . If you chose E, you may have calculated .

Question 30. The correct answer is K. The company will order 3(1) + 4(1) + 6(2) = 19 bathtubs, 3(0) + 4(1) + 6(1) = 10 shower stalls, and 3(1) + 4(2) + 6(4) = 35 sinks. This will cost 19($250) + 10($150) + 35($120) = $10,450. If you chose F, you may have calculated the number of bathtubs as 1 + 0 + 1, the number of shower stalls as 1 + 1 + 2, and the number of sinks as 2 + 1 + 4. If you chose G, you may have calculated the number of bathtubs as 1 + 1 + 2, the number of shower stalls as 0 + 1 + 1, and the number of sinks as 1 + 2 + 4, gotten a total of $2,140, and decided that this was close enough to $2,070. If you chose H, you may have calculated the number of bathtubs as 3(1 + 0 + 1), the number of shower stalls as 4(1 + 1 + 2), and the number of sinks as 6(2 + 1 + 4). If you chose J, you may have calculated the number of bathtubs as 3(1) + 4(0) + 6(1), the number of shower stalls as 3(1) + 4(1) + 6(2), and the number of sinks as 3(2) + 4(1) + 6(4).

Question 31. The correct answer is C. To calculate half the length, exchange 1 foot for 12 inches. Thus, 5 feet 6 inches is the same as 4 feet 18 inches. Then divide each number by 2, resulting in 2 feet 9 inches. If you answered A, you may have dropped the original 6 inches, converted 1 foot to 10 inches, and divided 4 feet 10 inches by 2. If you answered B, you may have converted 1 foot to 10 inches and divided 4 feet 16 inches by 2. If you answered D, you may have rounded up to the next foot to 6 feet and divided it by 2. If you answered E, you may have added 1 to the number of feet and subtracted 1 from the number of inches; then you may have divided the number of feet by 2 and left the number of inches as is, resulting in 3 feet 5 inches.

Question 32. The correct answer is H. The total number of feet is the sum of the first four drives: . If you answered F, you may have added . If you answered G, you may have added only the first two heights: 18 + 12. If you answered J, you may have added 18 + 12 + 18. If you answered K, you may have multiplied 18 × 3.

Question 33. The correct answer is B. To reflect a point across the y-axis, multiply its x-coordinate by –1 and do not change its y-coordinate. So (2, –3)becomes (2 × –1, 3), or (–2, 3). If you answered A, you may have interchanged the coordinates. If you answered C, you may have multiplied both coordinates by –1. If you answered D, you may have multiplied the y-coordinate by –1. If you answered E, you may have interchanged the coordinates and then multiplied them both by –1.

Question 34. The correct answer is K. The mean is the sum of the four numbers divided by 4: = mean. Adding 3 to both sides yields + 3 = mean + 3. It follows that = mean + 3 where x is the addition to the four numbers that results in the new mean. Now , so x = 12. If you answered F, you may have divided the increase in the mean by the four numbers. If you answered G, you may have subtracted the increase in the mean from the four numbers. If you answered H, you may have divided the four numbers by the increase in the mean. If you answered J, you may have added the increase in the mean and the four numbers.

Question 35. The correct answer is E. Using laws of exponents, the expression is equivalent to . If you answered A, you may have distributed the –1 to each term and then distributed the 100 as the exponent of each term: . If you answered B, you may have multiplied each term by the exponent: . If you answered C, you may have used the equivalent expression and then distributed the exponent to each term. If you answered D, you may have used the equivalent expression and then thought 3 + x = 3x.

Question 36. The correct answer is G. To find a vertical asymptote, set the denominator equal to 0, 2x – 6 = 0, and solve for x. One method for solving is to first divide both sides by 2, x – 3 = 0, so x = 3. If you answered F, you may have divided the constant term in the numerator by the constant term in the denominator. If you answered H, you may have set the numerator equal to 0, 3x – 12 = 0, and divided each side by 3, x – 4 = 0, so x = 4. If you answered J, you may have set the denominator equal to 0, 2x – 6 = 0, and then divided only the x term by 2, x – 6 = 0, so x = 6. If you answered K, you may have set the numerator equal to 0, 3x – 12 = 0, and divided only the x term by 3, x – 12 = 0, so x = 12.

Question 37. The correct answer is C. The equation xy = 0 and the zero-product rule require that either x or y is equal to 0 or that both x and y are equal to 0. The second equation requires that x is equal to 0 and y is not equal to 0. Combining the requirements of these two equations, it follows that both x = 0 and must be true. If you answered A, you may have considered only the first equation and misinterpreted the zero-product rule as stating that the value of both variables must be 0. If you answered B, you may have considered the second equation but switched the restrictions and thought and y = 0. If you answered D, you may have considered the second equation but thought both the numerator and the denominator must not be 0. If you answered E, you may have tried to list all the restrictions together and obtained y may be 0 or y may not be 0, which is not an answer choice.

Question 38. The correct answer is F. To convert to , it is necessary to multiply miles per hour. If you answered G, you may have multiplied . If you answered H, you may have calculated . If you answered J, you may have multiplied . If you answered K, you may have calculated .

Question 39. The correct answer is A. One million can be written as , so 2.5 million can be written as . If you answered B, you may have thought that because 1 million has 7 digits, the exponent is 7. If you answered C, you probably thought there are 7 digits in a million and then added 1 digit to the left in 2.5, resulting in 8 for the exponent. If you answered D, you may have dropped the decimal in 2.5 and used the exponent of 10 for 1 million. If you answered E, you may have dropped the decimal point and thought the exponent for 1 million is 7.

Question 40. The correct answer is K. Let x be the distance along the level ground between the point adjacent to the 70° angle and the center of the base of the tower. Then, by the definition of tangent, tan 70° = or = . If you answered F, you may have used the equation cos 70° = . If you answered G, you may have used the equation . If you answered H, you may have used the equation tan 70° = . If you answered J, you may have used the equation sin 70° = .

Question 41. The correct answer is E. Adding the vectors and setting that sum equal to 6i – 6j results in . Equating the coefficients on each side for i and j separately results in a – 2 = 6 or a = 8 and 3 + b = –6 or b = –9. If you answered A, you may have solved the equations correctly but set the variables equal to the other variable’s value. If you answered B, you may have solved the correct equations but used the wrong sign in the resulting values. If you answered C, you may have solved a – 2 = –6 and 3 + b = 6. If you answered D, you may have solved a + 2 = 6 and 3 – b = 6.

Question 42. The correct answer is F. Subtracting 50 from both sides results in . Dividing by 10 on both sides results in – 5 = b³. Taking the third root of both sides and swapping the two expressions results in b = . If you answered G, you may have put the 50 on the left side without changing the sign and then divided and took the third root as shown. If you answered H, you may have subtracted the 50 and divided by 10, but when taking the third root was done, the third root of the was not done. If you answered J, you may have divided only the 50 and the 10 by 10, resulting in c = b³ + 5, then added the 5 on the left side of the equation and subtracted it from the left, and then switched the exponent from b to c, resulting in c³ + 5 = b. If you answered K, you may have switched the b and c.

Question 43. The correct answer is A. Substituting x + 1 for x in f(x) results in or x² + 5x + 4. If you answered B, you may have substituted x² + 3x in g(x), resulting in (x² + 3x) + 1 or x² + 3x + 1. If you answered C, you may have substituted . If you answered D, you may have substituted + . If you answered E, you may have substituted + .

Question 44. The correct answer is J. The diameter of the second circle is found by multiplying 12 by 1.25, resulting in 15. Dividing the diameters by 2 to get the radius of each results in 6 and 7.5. Using the area of a circle with radius r formula πr² results in the areas of the two circles being 36π and 56.25π. The difference in the areas is 20.25π, or about 64. If you answered F, you may have substituted the difference between the radii into the area formula, resulting in 2.25π, or about 7. If you answered G, you may have substituted the difference in the diameters into the area formula, resulting in 9π, or about 28. If you answered H, you may have found 25% of the area of the second circle, 0.25 × π(7.5)², or about 44. If you answered K, you may have substituted the diameters in for the radii in the area formula, resulting in 144π and 225π. The difference is 81π, or about 254.

Question 45. The correct answer is D. The first six prime numbers are 2, 3, 5, 7, 11, and 13. The median is the average of the middle two numbers 5 and 7, which is 6. The mean is the sum of the numbers, 41, divided by the number of terms, 6, which is 6.83. The product of 6 and 6.83 is 41. If you answered A, you may have used the numbers 2, 3, 4, 5, 6, and 7. The median is 4.5, and you multiplied by the number of items, resulting in 27. If you answered B, you may have used the numbers 2, 3, 5, 7, 9, and 11. The median is 6 and the mean is . The product of the mean and the median is 37. If you answered C, you may have used the numbers 2, 4, 6, 7, 9, and 11. The median is the average of 6 and 7, or 6.5. Multiplying by the number of items results in 39. If you answered E, you may have used the first six even numbers 2, 4, 6, 8, 10, and 12. The median is 7 and the mean is 6. The product of 7 and 6 is 42.

Question 46. The correct answer is K. By the Pythagorean identity, is true for all real values of x. If you chose F, you determined that for all real values of x, sin(7x) + cos(7x) = 7 even though sin(7(0)) + cos(7(0)) = 0 + 1 = 1. If you chose G, you determined that for all real values of x, sin(7x) + cos(7x) = 7 even though . If you chose H, you determined that for all real values of x, 7sin(7x) + cos(7x) = 14 even though 7sin(7(0)) + 7cos(7(0)) = 7(0) + 7(1) = 7. If you chose J, you determined that for all real values of x, even though sin(7(0)) * sin(7(0)) + cos(7(0)) * cos(7(0)) = 0(0) + 1(1) = 1.

Question 47. The correct answer is A. Because is a diameter, is a right angle. Therefore, is a hypotenuse of and, by the Pythagorean theorem, has a length of meters. Because the measure of angle DAC is congruent to the measure of angle DAB, and angle ADB and angle DCA are both right angles, then triangle ACD and triangle DBC are similar triangles. Therefore, , which is equivalent to . Therefore, CD = . If you chose B, you may have computed . If you chose C, you may have computed AB. If you chose D, you may have computed . If you chose E, you may have computed (BD)(AD).

Question 48. The correct answer is K. Because a > 0, |a| = a. Because b < 0, |b| = −b. Therefore, |a| − |b| = a + b. If you chose F, you determined for all positive a and negative b that |a| − |b| = |a − b| even though |1| – |–1| = 0 ≠ 2 = |1 – (–1)|. If you chose G, you determined for all positive a and negative b that |a| − |b| = |a + b| even though |1| – |–2| = 3 ≠ 1 = |1 + (–2)|. If you chose H, you determined for all positive a and negative b that |a| − |b| = |a| + |b| even though |1| – |1| = 0 ≠ 2 = |1| + |1|. If you chose J, you determined for all positive a and negative b that |1| – |–1| = 0 ≠ 2 = 1 – (–1).

Question 49. The correct answer is D. Because x < y < 4 is the only restriction on x and y, it is possible for x = 3.4 and y = 3.6. Then x + y = 3.4 + 3.6 = 7. We also know that x + y < y + y < 4 + 4 = 8. So, the greatest possible integer value of x + y is 7. If you chose A, you may have determined that x + y could not be positive. If you chose B, you may have thought that 3 was the biggest integer that x + y could be. If you chose C, you may have thought that 4 was the biggest integer that y could be. If you chose E, you may have thought x and y could each be 4.

Question 50. The correct answer is G. Because y varies directly as the square of x, then y = kx² for some constant k. Because y = 20 when x = 2, 20 = k(2²), which means that k = 5. So, when x = 3, y = 5(3²) = 45. If you chose F, you may have calculated 3(20 + 2 + 3). If you chose H, you may have used the equation y = kx instead of the equation y = kx². If you chose J, you may have used the equation y = k + x instead of the equation y = kx². If you chose K, you may have used the equation y = k – x² instead of the equation y = kx².

Question 51. The correct answer is D. The general equation for an ellipse centered at (0, 0) is = 1 where a is the length of the semimajor (horizontal) axis and b is the length of the semiminor (vertical) axis. The values for a and b can be found by checking the intersection points of the ellipse with each circle. Because the general equation of a circle with radius r centered at (0, 0) is x² + y² = r², the larger circle has a radius of and the smaller circle has a radius of . This means that the ellipse must intersect with these circles at key points of (5, 0) and (0, 2), corresponding with semimajor and semiminor axes lengths of a = 5 and b = 2, respectively. Using these as the parameters in the general ellipse equation results in = 1. If you chose A or B, you may have used the wrong parameters for the semiminor and semimajor axes. If you chose C, you may have not squared the denominators. If you chose E, you may have thought a factor of 4 was necessary to include in the denominator.

Question 52. The correct answer is H. Let the two unknown integers be x and y. Because the median of the set is 82, conclude that and because 0 < 82 and 12 < 82. Then the set of integers is . Write an equation to represent the mean: = 52. Solve for x + y: = 52 → 94 + x + y = 260 → x + y = 166. Combine with one of the inequalities to eliminate one variable: . The same can be done for y. Now there is both a lower and upper limit on the values of x and y, meaning that both values are between 82 and 84, inclusive. The only choice that fits these limits is H. If you chose F or G, you may not have considered that these values would change the median to something other than 82. If you chose J or K, you may not have considered that these values would change either the mean or the median.

Question 53. The correct answer is B. By the given definition, the integer 6 has factors of 1, 2, and 3 with a sum of . The integer 8 has factors of 1, 2, and 4 with a sum of . The integer 10 has factors of 1, 2, and 5 with a sum of . The integer 12 has factors of 1, 2, 3, 4, and 6 with a sum of . The only one of these integers that fits the given criteria of a factor sum greater than the integer itself is 12 because .

Question 54. The correct answer is G. Vanna walked 2 miles per hour for of an hour and covered a distance of . Similarly, after her speed increased, she walked . This is a total of . Because she covered this distance in 15 minutes, her average rate over the whole distance is . If you chose F, you may have only found the average rate for the first part of Vanna’s walk. If you chose H, you may have added denominators when adding fractions. If you chose J, you may have divided by an extra factor of 60. If you chose K, you may have divided the sum of the rates by 2 instead of weighting the average rate by the time spent on each part of the walk.

Question 55. The correct answer is D. Let Alani’s height be x. Then Baahir’s height is and Connor’s height is . Dividing Alani’s height by Connor’s height to find the ratio results in . If you chose A or B, you may have subtracted or added the corresponding parts of each ratio. If you chose C or E, you may have multiplied the two given ratios.

Question 56. The correct answer is K. A square root is equivalent to a power. A cube root is equivalent to a power. Nesting a power and a power gives a power (). The base of the power is x², so we have . F, G, H, and J are all equivalent to . Clearly, K is not equivalent to ; it is equivalent to .

Question 57. The correct answer is B. Let l be the length and w be the width of the original rectangle. The area of the original rectangle is lw. Increasing something by 25% is equivalent to multiplying by 1 + 0.25. Decreasing something by 10% is equivalent to multiplying by 1 – 0.10. Therefore, 1.25l and 0.9w are the length and width, respectively, of the resulting rectangle. The area of the resulting rectangle is (1.25l)(0.9w) = 1.125lw. Multiplying by 1.125 is equivalent to increasing by 12.5%. If you answered A, you may have multiplied 25% and 10%. If you answered C, you may have subtracted 10% from 25%. If you answered D, you may have multiplied 25% and 100% – 10%. If you answered E, you may have added 25% and 10%.

Question 58. The correct answer is F. A sum of 7 can be obtained with 2 and 5, 5 and 2, 3 and 4, or 4 and 3. The probability of a 2 and a 5 is because 1 of the 5 balls is a 2, and 1 of the 4 remaining balls is a 5. Similarly, the probability of a 5 and a 2 is , the probability of a 3 and a 4 is , and the probability of a 5 and a 2 is . Adding the probabilities of each of these 4 ways to obtain a sum of 7 gives . If you answered G, you may have used 2, the number of balls selected, divided by 5, the total number of balls. If you answered H, you may have used 4, the number of balls that could be drawn first, to obtain a sum of 7 (2 or 3 or 4 or 5) divided by 5, the total number of balls. If you answered J, you may have used for the probability that the first selection could make a sum of 7 (as in H), used for the probability that the second selection would be the 1 ball out of the remaining 4 balls to complete the sum of 7, and then incorrectly added and instead of multiplying them . If you answered K, you may have thought the probability for each of the 4 ways to obtain a sum of 7 is .

Question 59. The correct answer is D. A function whose graph has no x-intercepts has either a minimum value greater than 0 or a maximum value less than 0. The function y = sin x has a minimum value of –1. In order to shift the graph vertically enough so that the minimum value is greater than 0, you’d have to add a value greater than 1: . The function y = sin x has a maximum value of 1. In order to shift the graph vertically enough so that the maximum value is less than 0, you’d have to add a value less than –1: . If you answered A, you may have simply looked for the amplitude of y = sin x. If you answered B, you may have found the correct bound values for c but got the shading wrong. If you answered C, you may have considered only shifting the graph up so the minimum value was greater than 0 but not considered shifting the graph down so the maximum value is less than 0. If you answered E, you may have thought that the minimum or maximum value could be 0.

Question 60. The correct answer is G. There are 3 feet in 1 yard, so there are 3² = 9 square feet in 1 square yard. Divide the number of square feet needed by 9 to get the number of square yards needed: 360 ÷ 9 = 40. If you answered F, you may have divided by 12(2) = 24 instead of 3² = 9. If you answered H, you may have divided by 3(2) = 6 instead of 3² = 9. If you answered J, you may have divided by 2² = 4 instead of 3² = 9. If you answered K, you may have divided by 3 instead of 9.

READING • PRACTICE TEST 5 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is B because although the narrator of the first section is never explicitly identified, it is clear that the narrator of the second section is Michael as a young boy. We know this from the first line of the second section: “What had there been before such a ship in my life?” (line 37), which makes it clear that the narrator of the second section is the same eleven-year-old boy described in the previous section. It is also correct to state that both perspectives describe “elements of Michael’s journey,” as the first section describes Michael’s first experience on the ship, and the second section describes his attitude toward the journey on the day of his departure and the days leading up to his departure, both of which can be reasonably described as elements of Michael’s “journey.”

The best answer is NOT:

A because neither section describes Michael’s first week on the Oronsay. The first section describes a portion of Michael’s first day on the Oronsay, and the second section describes Michael’s experiences leading up to his trip on the Oronsay. Also, there is no evidence to suggest that either section is being told from the perspective of Michael’s mother.

C because neither section provides information about the outcomes of Michael’s journey. Instead, both sections describe events that took place before the Oronsay left the harbor.

D because there is no evidence to suggest that either section is told from the perspective of one of Michael’s relatives. Also, there is clear evidence throughout the passage that the second section is told from Michael’s point of view, as indicated by the first line of the second section: “What had there been before such a ship in my life?” (line 37).

Question 2. The best answer is F because the description in lines 52–56 of the numerous amenities aboard the Oronsay suggests that the ship has many of the services that a city might have, which supports Michael’s comparison of the ship to a city in lines 3–4.

The best answer is NOT:

G because the description of the amenities aboard the Oronsay does not support the fact that Michael’s particular cabin was below the waves or lacked a porthole. The description of Michael’s cabin is unrelated to the number of amenities aboard the ship.

H because the description of the amenities aboard the Oronsay does not support the fact that Michael chose to stay in his cabin instead of going back up for “a last look, or to wave at his relatives” (lines 22–23), which is what this statement about solitude is referring to. Michael’s decision to choose solitude belowdecks instead of waving goodbye to his family is unrelated to the number of amenities aboard the ship.

J because the description of the amenities aboard the Oronsay does not support the fact that Michael’s relatives decided to send him to England by ship. Lines 47–48 describe why Michael is on the Oronsay, but they do not indicate the size, scale, or complexity of the ship. There is no indication that the ship’s amenities factored into the decision to send Michael to England by ship.

Question 3. The best answer is D because Michael indicates that his relatives did not provide much information to prepare him for his journey. “No mention was made that this might be an unusual experience or that it could be exciting or dangerous” (lines 49–51). “I was not forewarned that the ship would have seven levels” (lines 52–53). “The departure date was marked casually on the calendar. . . . The fact of my being at sea for twenty-one days was spoken of as having not much significance” (lines 56–61). Instead, “there had been just one attempt to introduce me to the situation of the journey” (lines 65–66). Flavia, who would be traveling on the same ship, was invited to tea by Michael’s family; she then told Michael that “she would be travelling in First Class but promised to keep an eye on me” (lines 69–70). In doing so, she is giving Michael a small amount of information about the circumstances of his trip.

The best answer is NOT:

A because there is no evidence that Flavia lists anybody that Michael might meet on the ship. Instead, she simply tells Michael that she will be keeping an eye on him (line 70).

B because Michael’s mother is never mentioned in his conversation with Flavia (lines 69–73). For this statement to be true, it would have been necessary for Flavia to explain to Michael what his mother knows about his trip, which she never does.

C because there is no evidence to suggest that Flavia or anyone else drew a map of the route for Michael.

Question 4. The best answer is J because the narrator’s relatives do not seem to approach Michael’s impending departure with any strong emotions at all: “No mention was made that this might be an unusual experience or that it could be exciting or dangerous, so I did not approach it with any joy or fear” (lines 49–51). Michael also describes his relatives as marking his departure date “casually” on the calendar (line 57) and claims that his journey “was spoken of as having not much significance” (lines 60–61). All of these details suggest that his relatives were understated and matter-of-fact about Michael’s journey.

The best answer is NOT:

F because there is no evidence to suggest that Michael’s relatives expressed fear in relation to his journey. Michael claims that “no mention was made that this might be an unusual experience or that it could be exciting or dangerous, so I did not approach it with any joy or fear” (lines 49–51). This suggests that his relatives were neither fearful nor tense about the journey.

G because there is no evidence to suggest that Michael’s relatives expressed excitement or seemed frantic prior to his departure. Michael’s departure date was marked casually on the calendar, and Michael notes that “the fact of my being at sea for twenty-one days was spoken of as having not much significance” (lines 59–61). This suggests that his relatives did not view the experience as worthy of excitement.

H because there is no evidence to suggest that Michael’s relatives’ actions were either meticulous or generous. They made little effort to prepare him for the details of his trip: “I was not forewarned that the ship would have seven levels, hold more than six hundred people including a captain, nine cooks, engineers, a veterinarian, and that it would contain a small jail and chlorinated pools that would actually sail with us over two oceans” (lines 52–56). The narrator also expresses surprise that his relatives accompanied him at all (lines 61–62). These details do not characterize the relatives as either “generous” or “meticulous.”

Question 5. The best answer is B because the passage states that once Michael is on the ship, “already it felt there was a wall between him and what took place there” (lines 12–13). This suggests that Michael feels physically separated from the city on boarding the ship.

The best answer is NOT:

A because there is no evidence to suggest that Michael sees the city as morally corrupt. In fact, there is no point in the passage where he remarks on the moral character of the city in any way.

C because there is no evidence to suggest that Michael sees the city as aesthetically beautiful. The passage states that there is a “yellow glow over the city” (lines 11–12), but there is no indication that Michael finds this glow beautiful. In fact, there is no point in the passage where Michael remarks on the beauty of the city in any way.

D because there is no evidence to suggest that Michael feels he is taking the city with him. Instead, the line “already it felt there was a wall between him and what took place there” (lines 12–13) suggests that Michael feels separated from the city after boarding the ship.

Question 6. The best answer is H because the main point of the second paragraph is for the narrator to analyze why Michael did not return to the deck to wave goodbye to his relatives. The narrator states “I do not know, even now, why he chose this solitude” (lines 26–27) and then proposes a potential reason for Michael’s behavior, asking “Had whoever brought him onto the Oronsay already left?” (lines 27–28). The narrator also compares Michael’s behavior to how people generally react to such departures in films (lines 28–31). At each of these points, the narrator is trying to understand and contextualize Michael’s decision to stay in his cabin.

The best answer is NOT:

F because the passage never states that Michael’s relatives left the harbor as soon as Michael boarded the Oronsay. The narrator instead wonders whether they had already left by the time Michael was on the ship: “Had whoever brought him onto the Oronsay already left?” (lines 27–28).

G because the narrator does not state that Michael enjoyed the singing. The narrator describes Michael listening to the singing and imagining the parting of families, but he never discusses whether or not Michael enjoyed the singing: “He could hear singing and imagined the slow and then eager parting of families taking place in the thrilling night air” (lines 24–26).

J because there is no evidence to suggest that Michael’s relatives were weeping as the Oronsay departed. In fact, the narrator wonders whether his relatives had already left (lines 27–28), and the actual whereabouts or reactions of Michael’s relatives are left ambiguous.

Question 7. The best answer is A because Flavia interacts with Michael very minimally, and she resumes her other conversation as soon as the interaction is over. “She then turned away to continue the conversation I had interrupted” (lines 72–73). It can also be inferred that Flavia does not interact with Michael again after this brief exchange, as Michael claims that he “spent most of the hour listening to a few uncles and counting how many of the trimmed sandwiches they ate” (lines 73–75), which also suggests a certain degree of indifference toward Michael on the part of Flavia.

The best answer is NOT:

B because there is no evidence that Flavia viewed Michael’s behavior as rude. Though Michael does characterize his interaction with her as an interruption (line 73), it can be inferred that Flavia was invited to tea specifically to meet with Michael: “A lady named Flavia Prins, whose husband knew my uncle, turned out to be making the same journey and was invited to tea one afternoon to meet with me” (lines 66–69). Because their meeting was the stated purpose of the tea, it is not reasonable to assume that Flavia viewed Michael’s brief interaction with her as rude, even if she expressed indifference toward him, and there is no evidence to suggest that she plans to retract her promise.

C because there is no evidence that Flavia was planning to find someone else to care for Michael. Instead, she claims that she will keep an eye on him and makes no mention of anyone else: “She would be travelling in First Class but promised to keep an eye on me” (lines 69–70).

D because although it could reasonably be inferred that Flavia intends to ignore Michael, there is no evidence to suggest that she plans to make his life difficult. Instead, she simply promises to keep an eye on him (line 70) before resuming her previous conversation, which suggests that she is indifferent to Michael and will likely do little to make his life either better or worse.

Question 8. The best answer is J because the narrator compares Michael to a “little cricket” (line 35) when imagining him in his narrow bunk.

The best answer is NOT:

F because although the narrator describes Michael as having been “smuggled away” (line 35), the narrator never refers to him as a “smuggler.” In this metaphor, Michael is the thing being smuggled, not the smuggler.

G because the narrator never describes Michael as “rings and bangles.” Instead, this is how Michael describes Flavia’s jewelry: “I shook her hand carefully, as it was covered with rings and bangles” (lines 70–71).

H because the narrator never refers to Michael as green grass. Instead, he refers to him as a “green grasshopper” (line 34).

Question 9. The best answer is D because Michael mentions that he will spend twenty-one days at sea when speaking about his journey: “The fact of my being at sea for twenty-one days was spoken of as having not much significance” (lines 59–61).

The best answer is NOT:

A because the passage never states that Michael will have to rely on the expertise of a team of captains at any point. In fact, Michael only mentions the existence of one captain when he states that the ship will hold “more than six hundred people including a captain” (lines 53–54).

B because there is no evidence to suggest that Michael will disembark midjourney. The passage states that Michael will “arrive one morning on a small pier in England” (lines 82–83), but there is no mention of this arrival coming in the middle of the ship’s journey.

C because the passage instead states that Michael’s journey will take him across the Red Sea. “After I’d crossed the Indian Ocean and the Arabian Sea and the Red Sea . . . I would arrive one morning on a small pier in England” (lines 80–83).

Question 10. The best answer is H because Michael is largely ignored by the adults after his brief interaction with Flavia, and the fact that he does not recount anything else about the adults’ conversations and busies himself with the mundane task of counting sandwiches suggests that he does not find their conversations to be interesting or relevant.

The best answer is NOT:

F because there is no evidence to suggest that Michael believes the number of sandwiches his uncles eat is in any way related to the number of sandwiches that he will receive on the trip. In fact, there is no evidence to suggest that Michael knew there would be sandwiches aboard the Oronsay, as the tea scene takes place before he boards the ship.

G because there is no evidence to suggest that Michael is concerned with whether or not his uncles are enjoying the sandwiches. Instead, he is simply listening to the uncles and counting the sandwiches (lines 73–75).

J because there is no evidence to suggest that Michael feels nervous around his uncles, nor that he believes his uncles to be loud. Instead, he simply states that he spent the hour listening to his uncles (lines 73–75).

Passage II

Question 11. The best answer is D because the author of Passage A views dark gumbo as a poor execution of gumbo and is using the biscuit and brisket to illustrate real culinary achievements. In the first paragraph of Passage A, the author laments the fact that he has heard people praising gumbo for its thickness and darkness. “This was strange to me. Gumbo was supposed to be neither thick nor dark” (lines 4–5). He goes on to note, “Even more important, ‘dark’ and ‘thick’ were being used not as adjectives, but as achievements. It was as if making a dark gumbo was a culinary accomplishment on par with making a featherlight biscuit or a perfectly barbecued beef brisket” (lines 5–10). Here the biscuit and brisket are being held up as accomplishments, examples of foods the author views as real culinary successes. The author is suggesting that dark gumbo is not actually “on par with” a featherlight biscuit or perfectly barbecued beef brisket.

The best answer is NOT:

A because the author does not discuss taste in this paragraph or in the passage as a whole. Rather, the focus is on the preparation of and ingredients in gumbo. The primary function of these examples is to point out that dark gumbo is not a culinary achievement.

B because the author does not indicate that featherlight biscuits and perfectly barbecued beef brisket are specific to New Orleans cuisine. Nor does the author suggest that these foods have been corrupted; rather, they are held up as a standard of culinary achievement.

C because neither featherlight biscuits nor perfectly barbecued beef brisket are identified as being authentic New Orleans food. Moreover, the only New Orleans food that is discussed as being appealing to tourists is gumbo. Lines 2–4: “I began to hear tourists, visitors and transplants to New Orleans praising this or that gumbo for its thickness and darkness.”

Question 12. The best answer is J because the author directly states that though Prudhomme “hails from Cajun Country” (line 14), his “Louisiana cooking” has been influenced by Louisiana more broadly. Lines 15–17: “He refers to his cooking not so much as Cajun, but as ‘Louisiana cooking,’ and thus reflective of influences beyond his home parish.”

The best answer is NOT:

F because there is no indication in the passage that Prudhomme’s Louisiana cooking demands less creativity than Cajun cuisine. The author is concerned with authenticity, not creativity.

G because there is no indication in the passage that Prudhomme’s Louisiana cooking requires more discipline than Cajun cuisine. In fact, the author claims that chefs trained under Prudhomme “lacked the loving guidance and discipline that only good home training can provide” (lines 24–26).

H because there is no indication in the passage that the author believes Prudhomme’s Louisiana cooking is much easier to master than Cajun cuisine. The author does note that a lack of discipline has contributed to Prudhomme’s influence, but that lack of discipline is relative to “good home training” in terms of what good gumbo is supposed to be. It is not a comment on the actual difficulty in mastering either of these styles.

Question 13. The best answer is D because the author directly states that he blamed Prudhomme for the ruin of the gumbo universe. Lines 17–19: “For years I blamed him [Prudhomme] for the destruction of the gumbo universe.” Because many of the chefs and cooks in New Orleans were trained by Prudhomme or his students, and many were not from Louisiana, “they had no homemade guide as to what good gumbo was supposed to be” (lines 22–23).

The best answer is NOT:

A because the influence of tourists is treated as part of the problem but not the direct cause. The author notes that he is bothered by “the tyrannical influence of the tourist trade” (line 32) and that “the whole of the French Quarter” at times seemed to cater to what tourists “expected to find” (lines 34–36). Tourists expected to find these dishes because many of the chefs and cooks in New Orleans were not actually from New Orleans and had learned under Prudhomme or his students. Moreover, Prudhomme is blamed directly in lines 17–19: “For years I blamed him [Prudhomme] for the destruction of the gumbo universe.”

B because the author directly states, “The Cajun incursion in and of itself didn’t bother me” (lines 28–29).

C because there is no indication in the passage that a sudden prevalence of chicken and andouille gumbo resulted in the ruin of the gumbo universe. Chicken and andouille gumbo is mentioned as being “on menus all over town” (lines 40–41) in 1995, after Prudhomme’s influence had taken hold.

Question 14. The best answer is H because the author of Passage B states that Syrnikov has a problem: “Russians don’t hold Russian food in particularly high esteem. When they eat out, they favor more exotic cuisines, like Italian or Japanese. The tendency to find foreign food more desirable is a prejudice that goes back centuries—to a time when the Russian aristocracy spoke French, not Russian. Russian food is pooh-poohed as unhealthy and unsophisticated” (lines 46–52).

The best answer is NOT:

F because there is no indication in the passage that Syrnikov believes Russians are embarrassed by their country’s agrarian history and want to distance themselves from it. Rather, Syrnikov believes that Russians have simply lost touch with their agrarian roots.

G because there is no indication in the passage that the prejudices held by Russia’s ruling class led to an actual ban on Russian cuisine. The passage notes only that the tendency to find foreign food more desirable is a prejudice that dates back to a time when the Russian aristocracy spoke French, not Russian.

J because although Syrnikov asserts that people need to start writing down traditional recipes from “old women” in Russia, this is presented as a way to preserve a significant part of Russian culture rather than a reason for Russians not favoring their national cuisine overall.

Question 15. The best answer is B because the paragraph begins with an assertion that Syrnikov hopes to reacquaint Russians with their agrarian roots and to convince them that their national cuisine can be just as good as other cuisines. What follows in lines 75–81 is a list of ways Syrnikov is hoping to educate people. Traveling the countryside, trying the recipes he finds, blogging, consulting, and planning a user-generated database for recipes show his dedication to helping Russians find their true culinary roots.

The best answer is NOT:

A because there is no suggestion in the passage that Syrnikov is overwhelmed by the scope and number of his projects.

C because there is no indication in the passage that Syrnikov plans to open his own authentic restaurant. He has consulted “on projects to make a restaurant authentically Russian” (lines 79–80), but the passage does not suggest a goal to open his own restaurant.

D because the passage does not suggest that Syrnikov lacks culinary training.

Question 16. The best answer is H because Syrnikov is quoted as stating the following: “In the middle of the eighteenth century, there were riots because people didn’t want to grow potatoes” (lines 60–62).

The best answer is NOT:

F because Syrnikov states that potatoes are actually an American plant. “He insists that real Russian food contained no potatoes” (lines 62–63).

G because Syrnikov states that potatoes were an American plant and not part of real Russian food. “Instead, there were lots of grains, fish, and dairy, as well as honey, cucumbers, turnips, cabbage, apples, and the produce of Russia’s vast forests.…Most of Russia ate this way until the twentieth century” (lines 64–70).

J because Syrnikov states that potatoes are an American plant, not a Ukrainian plant. “What they named was horrible: borscht, which is Ukrainian, and potatoes, which are an American plant” (lines 58–60).

Question 17. The best answer is C because in lines 85–89, Syrnikov is quoted as saying, in reference to writing down recipes held by grandmothers across Russia, “To me, it’s absolutely obvious that, if we don’t wake up and find out from these old women and set it down on paper, in twenty years we won’t have anyone to ask. Russian culture will lose a very significant part of itself.”

The best answer is NOT:

A because Syrnikov believes that if the traditional Russian cuisine is not recorded, it will be lost, and “Russian culture will lose a very significant part of itself” (lines 88–89). He does not connect that loss of identity with Russian cuisine needing to reinvent itself.

B because there is no mention in Passage B of an existing database of folk recipes. Instead, Syrnikov’s plan is to use these folk recipes to build a database.

D because Syrnikov believes the opposite will happen. If the recipes are not recorded, then future generations will not be able to learn them.

Question 18. The best answer is J because the author of Passage A clearly struggles with the public’s misperception of authentic New Orleans food, while Passage B outlines Syrnikov’s efforts to correct misconceptions about Russian cuisine. In Passage A, the author is concerned that Prudhomme’s influence and the tourist trade have resulted in inauthentic New Orleans food. “There was no regard for whether the offerings were authentic New Orleans food or culture” (lines 36–37). In Passage B, Syrnikov is presented as believing that many Russians don’t actually know what foods are traditional Russian dishes: “Among the many things that annoy Syrnikov is the fact that a good number of the despised Russian dishes aren’t even Russian” (lines 53–55). Syrnikov “hopes to help Russians reacquaint themselves with the country’s agrarian roots, and to convince them that their national cuisine can be just as flavorful as anything they might find in a sushi bar” (lines 72–75).

The best answer is NOT:

F because there is no indication in Passage A that the author and Prudhomme have actually interacted. Moreover, although Passage B does present Syrnikov as being annoyed that the Russian public is ignorant about true Russian cuisine, this is not the primary focus of the passage. Rather, the focus is on Syrnikov’s efforts to correct these misconceptions.

G because Passage B is not concerned with how communities are working together to preserve Russian cuisine. Rather, Passage B describes Syrnikov’s efforts to educate the Russian people about true Russian cuisine.

H because there is no indication in Passage A that the author is prejudiced against non-Cajun food. The author states that “the Cajun incursion in and of itself didn’t bother me. We are all enriched immeasurably when we encounter other people” (lines 28–30).

Question 19. The best answer is C because both New Orleans transplants and modern Russians are presented as being misinformed about their authentic cuisines. In Passage A, the author notes that New Orleans transplants were praising gumbo for its thickness and darkness, but real gumbo “was supposed to be neither thick nor dark” (line 5). In Passage B, lines 55–60 detail a survey Syrnikov conducted with residents of Moscow and St. Petersburg, in which they were asked to name traditional Russian dishes. “What they named was horrible: borscht, which is Ukrainian, and potatoes, which are an American plant” (lines 58–60).

The best answer is NOT:

A because there is no indication in either passage that New Orleans transplants or modern Russians are perplexed. They do not display confusion about their region’s authentic cuisine; rather, they are simply misinformed.

B because New Orleans transplants are not presented as disdainful in Passage A. Instead, they praise “this or that gumbo for its thickness and darkness” (lines 3–4). But in praising this gumbo, they are not disdainful of what the passage author regards as real gumbo; they are simply misinformed. In Passage B, modern Russians are presented as being disdainful of some dishes that they believe are traditional Russian dishes, but Syrnikov points out that many of these dishes aren’t actually authentic Russian cuisine.

D because neither passage presents New Orleans transplants or modern Russians as knowledgeable. They are presented as the opposite. In Passage A, the author notes that New Orleans transplants praise “this or that gumbo for its thickness and darkness” (lines 3–4), but gumbo “was supposed to be neither thick nor dark” (line 5). In Passage B, modern Russians are presented as being disdainful of some dishes that they believe are traditional Russian dishes, but Syrnikov points out that many of these dishes aren’t actually authentic Russian cuisine. “Among the many things that annoy Syrnikov is the fact that a good number of the despised Russian dishes aren’t even Russian” (lines 53–55).

Question 20. The best answer is F because in Passage A, the author says the following about many of the cooks in New Orleans: “Many of these cooks were not from Louisiana, and thus had no homemade guide as to what good gumbo was supposed to be. As I saw it then, these were young, impressionable cooks who lacked the loving guidance and discipline that only good home training can provide” (lines 21–26). In Passage B, Syrnikov outlines a goal to create a database of Russian folk recipes by sending out “a call across all of Russia” (line 82) to connect with the women holding these recipes. “If we don’t wake up and find out from these old women and set it down on paper, in twenty years we won’t have anyone to ask. Russian culture will lose a very significant part of itself” (lines 85–89).

The best answer is NOT:

G because neither passage supports the idea that cooking authentic food is best accomplished by studying under chefs. In Passage A, the author asserts that studying under Prudhomme contributed to the problem of inauthentic gumbo: “Many of the chefs and cooks in New Orleans restaurants learned under him or under his students. Many of these cooks were not from Louisiana, and thus had no homemade guide as to what good gumbo was supposed to be” (lines 19–23). In Passage B, no mention is made of studying under chefs in restaurants. Instead, Syrnikov indicates that authentic Russian cuisine must be preserved by gathering folk recipes from “old women” across Russia.

H because neither passage presents evidence that the best way to learn how to cook traditional or authentic food is by learning about other cultures’ foods. Instead, both assert that the best way to learn is from cooks native to the area. In Passage A, the author notes that New Orleans cooks need “the loving guidance and discipline that only good home training can provide” (lines 24–26). Although the author of Passage A also states that “we are all enriched immeasurably when we encounter other people, other languages, other traditions, other tastes” (lines 29–31), this is not said in relation to learning how to cook authentic New Orleans food. Passage B notes that Syrnikov travels the Russian countryside in search of traditional recipes, but he is doing this to learn about food specific to Russian culture.

J because neither passage discusses a need to be trained in a culinary school. Rather, both passages assert that traditional or authentic cuisine can best be learned from home cooks.

Passage III

Question 21. The best answer is D because the interviewee, Morgan, does respond to the questions of the interviewer, Fabisiak, with in-depth, involved, and somewhat philosophical answers. For example, when the interviewer asks Morgan about her focus on work and to what extent it’s related to a focus on landscape more generally, Morgan does not provide a short or simple answer. She begins by responding to the question as it relates to All the Living, insisting that the presence of work in All the Living was not a “self-conscious choice” (lines 53–54), before moving into a discussion about how this particular book was written and then ruminating on her writing process in general. She goes into detail when describing how All the Living was written: “I don’t feel I made choices in the first draft of the novel. . . . I obeyed the book” (lines 57–60). In the same level of detail, she describes her feelings about writing as a vocation, arriving at this conclusion: “Frankly, the world doesn’t need more books; it needs better books. Vocation is tied up with notions of service, and as an artist you serve people by giving them your best, the work you produce that you truly believe to be of value” (lines 80–84).

The best answer is NOT:

A because the interviewer does not offer harsh commentary that requires Morgan to defend herself. The interviewer simply asks questions about Morgan’s writing, which she responds to with in-depth, thoughtful answers.

B because at no point in the interview does Morgan urge the interviewer to ask her more relevant questions.

C because, although there is an element of dialogue to the interview, Morgan does not turn any of the questions back to the interviewer.

Question 22. The best answer is H because Morgan directly states in lines 9–15, “Landscape writing—most especially when it’s done at length and in a style that deviates from prose norms, so that its very presentation is interruptive or ‘estranging’ as the formalists might have said—encourages the reader to stop, reread, listen, imagine, reconsider, admire, appreciate with new eyes.”

The best answer is NOT:

F because Morgan makes no mention of plot when discussing how landscape writing might feel “interruptive or ‘estranging.’ ”

G because Morgan makes no mention of the skill of the writer when discussing how landscape writing might feel “interruptive or ‘estranging.’ ”

J because Morgan makes no mention of the opening pages of a novel when discussing how landscape writing might feel “interruptive or ‘estranging.’ ”

Question 23. The best answer is A because Morgan agrees that landscape writing draws attention to itself but notes that it also draws attention to the land. She states, “The reader might complain that this kind of writing draws attention to itself, but this kind of writing doesn’t merely draw attention to its own aesthetic strategies—it also draws attention to land” (lines 15–18).

The best answer is NOT:

B because Morgan does not discuss the focus of the writer in terms of landscape writing calling attention to itself.

C because Morgan asserts that landscape writing does draw attention to itself but also draws attention to land: “this kind of writing doesn’t merely draw attention to its own aesthetic strategies—it also draws attention to land” (lines 16–18).

D because Morgan never indicates that some readers are unwilling to read landscape writing.

Question 24. The best answer is F because Morgan suggests that appreciation for the land can result in action. In lines 18–20, she states, “The land is imperiled; we know that. Land is always imperiled wherever the human puts his or her foot.” She goes on to argue that attention paid to the land in a narrative can lead to an appreciation of the land, which can then lead to action: “Deep appreciation can result from an engagement with that kind of beauty, and that can manifest in action. That is how it might be seen as a political act to do this kind of writing (particularly about a region, such as this one, rural Kentucky, that is continuously being ravaged by corporations that consumers unwittingly feed)” (lines 23–29).

The best answer is NOT:

G because Morgan does not suggest that a reader’s attention to the land will lead the reader to forget that the land is in peril. She suggests the opposite, that “attention paid to landscape in a narrative is . . . attention that’s paid to land itself” and that “deep appreciation can result from an engagement with that kind of beauty, and that can manifest in action” (lines 20–25).

H because there is no indication in the passage that Morgan believes a reader’s attention to the land will lead the reader to misinterpret the writer’s purpose.

J because there is no indication in the passage that Morgan believes a reader’s attention to the land will lead the reader to research a writer’s academic background.

Question 25. The best answer is B because Morgan asserts that landscape writing doesn’t just draw attention to the words on the page (“marks”), it also draws attention to the land itself. “This kind of writing doesn’t merely draw attention to its own aesthetic strategies—it also draws attention to land” (lines 16–18). Readers will not just be focused on the physical marks on the page (“words and symbols”) but on the land being described itself.

The best answer is NOT:

A because “creases and smudges” would not capture Morgan’s intent, which is to assert that landscape writing doesn’t just draw attention to the writing (“marks on a page”) but also to the land. “Creases and smudges” would not make sense in this context.

C because “notches and ticks” would not capture Morgan’s intent, which is to assert that landscape writing doesn’t just draw attention to the writing (“marks on a page”) but also to the land. “Notches and ticks” would not make sense in this context.

D because “lines and boundaries” would not capture Morgan’s intent, which is to assert that landscape writing doesn’t just draw attention to the writing (“marks on a page”) but also to the land. “Lines and boundaries” would not make sense in this context.

Question 26. The best answer is J because at this point in the passage, Morgan is discussing attention paid to landscape in a narrative and the affect it can have on readers. She asserts that “attention paid to landscape in a narrative is . . . attention that’s paid to land itself” (lines 20–22). She goes on to claim that “deep appreciation” for the land can result from an engagement “with that kind of beauty” (lines 23–24)—the beauty of the land being described in the narrative.

The best answer is NOT:

F because Morgan is not discussing humans in her work. She is focused on landscape writing.

G because Morgan is not discussing intellect at this point. She is describing how landscape writing can lead to a deep appreciation for the land on the part of the reader.

H because at this point Morgan is commenting on the land itself, not on a political act. She is noting that appreciation for the land (a result of attention paid to the landscape in a narrative) can result from an engagement with the land’s beauty. She goes on to note that this is why landscape writing can be seen as a political act, but she is not specifically referring to a political act when she says “deep appreciation can result from an engagement with that kind of beauty” (lines 23–24). That “deep appreciation” of and “engagement with” refers to the land.

Question 27. The best answer is A because Fabisiak prefaces a question about Morgan’s focus on work with the following: “Without wanting you to interpret All the Living for readers, because you’ve told me that you hate imposing yourself into people’s encounters with the book” (lines 34–37). It is clear from this statement that Fabisiak has learned this from Morgan herself (“you’ve told me”).

The best answer is NOT:

B because there is no indication in the passage that Morgan does not like to tell her readers that she lives in Kentucky.

C because although Fabisiak notes that Morgan takes work seriously and acknowledges a “commitment to hard work” (lines 46–47), there is no indication that Fabisiak knows Morgan doesn’t like to work ten hours every day. In the interview, Morgan notes that “as an artist you serve people by giving them your best . . . not just what you’re capable of producing if you work ten hours a day every day for forty years” (lines 82–86), but there is no indication that Fabisiak and Morgan have discussed ten-hour days before this interview.

D because there is no indication in the passage that Morgan does not like to discuss which regions of the United States she plans to write about.

Question 28. The best answer is G because Morgan states that “the presence of work—agrarian or domestic—in All the Living was not a self-conscious choice” (lines 52–54). This suggests that the book depicts both agrarian and domestic work.

The best answer is NOT:

F because although corporations are mentioned in the passage, Morgan does not indicate that there is anything in her book that discusses corporate work. Corporations are mentioned by Morgan in the context of how they harm the land in rural Kentucky: “continuously being ravaged by corporations that consumers unwittingly feed” (lines 27–29).

H because creative work is not mentioned or suggested as a focus of All the Living.

J because neither creative nor corporate work are mentioned or suggested as a focus of All the Living.

Question 29. The best answer is C because in lines 74–76, Morgan states that “this idea that a writer should produce a novel every year or two years, that they should be punching a clock somehow” is something that she’s wary of. In this statement, she is comparing producing a novel every year or two to punching a clock—to “rigorous work ethic for the sake of rigorous work ethic” (lines 73–74).

The best answer is NOT:

A because Morgan does not directly compare being expected to produce a novel every one or two years to working overtime.

B because Morgan neither mentions the assembly of products in a factory nor compares it to the expectation to produce a novel every one or two years.

D because Morgan does not compare being expected to produce a novel every one or two years to selling goods on commission.

Question 30. The best answer is H because Morgan states that “as an artist you serve people by giving them your best, the work you produce that you truly believe to be of value” (lines 82–84).

The best answer is NOT:

F because Morgan does not believe that artists should continually offer new work that they know people will buy. She says, “I don’t want to produce just to produce. I don’t want to write just to write, or publish just to get a paycheck. I see no value in that” (lines 78–80).

G because Morgan does not mention that an artist is serving other people by studying others’ work and learning from it. Rather, she believes that “as an artist you serve people by giving them your best” (lines 82–83).

J because Morgan never mentions that a writer should modify the focus of their work when people lose interest.

Passage IV

Question 31. The best answer is B because the main purpose of the passage is to discuss how the scientific theory of e, which is now well accepted, had a controversial past. After introducing Millikan’s initial discovery of e, the passage states that “Millikan still had years of difficult and dirty work ahead of him” (lines 24–25). From this point, the passage primarily focuses on the feud between Millikan and Ehrenhaft, and how Millikan’s attempts to prove his theory correct would “cast a lasting shadow over his scientific integrity” (lines 32–33), as he was accused of cherry-picking data (line 49) and hiding data that he considered inconvenient (lines 35–36). The passage also states that Millikan “did not convince his peers straight away” (lines 81–82) and that the arguments between him and Ehrenhaft delayed Millikan’s Nobel Prize for three years (lines 82–84), concluding with the claim that “to get his Nobel Prize, Millikan had to play hard and fast with what we might call ‘accepted practice’” (lines 91–92). Because the focus of the passage is on the controversial past of a well-accepted theory, it is reasonable to conclude that the passage’s main purpose was to use Millikan’s theory of e as an example of a well-accepted scientific idea that has a “sullied past.”

The best answer is NOT:

A because the main focus of the passage is on the controversy surrounding the existence of e, not on the process by which theories become accepted. Although the passage states that Millikan “did not convince his peers straight away” (lines 81–82), it does not discuss how he did come to convince his peers, and although it says that his Nobel Prize was “delayed for three years” (line 84), it does not explain how he gained enough acceptance to receive the prize in 1923. If anything, the passage focuses on the ways in which Millikan’s theory was initially not accepted, despite the fact that he was correct. And the passage never suggests that the process by which Millikan’s theory was accepted is representative of the process in general.

C because although the passage does mention some challenges Millikan faced when measuring e, these challenges are discussed in the context of Millikan’s selective use of data and the way in which Millikan’s use of data “cast a lasting shadow over his scientific integrity” (lines 32–33). Also, although Millikan’s scientific work was likely quite challenging and rigorous, the passage does not focus on characterizing it as such. When describing Millikan’s process in the second paragraph, the passage begins by stating “Millikan’s idea was simple” (line 6), followed by a relatively straightforward description of Millikan’s experiment. The passage does later state that “the experiment was far from simple to carry out” (line 17), as the water droplets “tended to evaporate before any measurements could be made” (lines 18–19), but the passage then immediately describes Millikan’s solution—“trying the same trick with oil droplets” (lines 20–21)—and, in the very next sentence, describes Millikan publishing his findings (lines 22–23). After this point, the passage focuses almost entirely on the controversy surrounding Millikan’s 1913 paper and discusses any difficulties he faced only in the context of this controversy. For all of these reasons, it is not accurate to say that the main focus of the passage was to describe the difficulties scientists faced in measuring e.

D because at no point does the passage claim that Millikan received credit for work that was not his own. Although the passage states that Millikan “had to play hard and fast with what we might call ‘accepted practice’” (lines 91–92) in order to get his Nobel Prize, this is in reference to Millikan potentially cherry-picking data (line 49) and hiding data that he considered inconvenient (lines 35–36), not to Millikan receiving credit for another scientist’s work. Also, there is no evidence to suggest that any scientist other than Millikan received credit for Millikan’s work, because he was eventually awarded a Nobel Prize in 1923 (line 84).

Question 32. The best answer is F because both Ehrenhaft’s and Millikan’s reputations were at stake, and they both went to great lengths to protect their reputations. The author characterizes both scientists as highly emotionally invested in proving their theories right. After Ehrenhaft first published a refutation of Millikan’s results, the passage states that “the series of experiments the desperate Millikan then performed were to cast a lasting shadow over his scientific integrity” (lines 30–33). The characterization of Millikan as “desperate” suggests that Ehrenhaft’s refutation of Millikan’s paper inspired an emotional response in Millikan, and the fact that Millikan’s subsequent experiments “cast a lasting shadow over his scientific integrity” (lines 32–33) demonstrates that Millikan’s reputation relied heavily on the success and reliability of his findings and publications. Also, the passage states that Millikan’s admirable honesty in his initial paper gave Ehrenhaft “ammunition that he used enthusiastically in his long feud with Millikan” (lines 58–59). The use of the word enthusiastically suggests that Ehrenhaft, like Millikan, was emotionally invested in proving his own theory correct. Due to the high emotional investment on the part of both parties, coupled with the public nature of their “long feud,” it is reasonable to describe their relationship as “tense” and to claim that both of their reputations were at stake.

The best answer is NOT:

G because there is no evidence to suggest that either Millikan or Ehrenhaft sabotaged one another’s experiments in any way. Instead, each one performed their own experiments to refute the claim of the other. The passage states that “Ehrenhaft refuted Millikan’s results with a similar set of experiments” (lines 26–27), and Millikan responded by publishing a paper “refuting Ehrenhaft and showing that every measurement of electric charge gives a value of e or an integer multiple of e” (lines 40–42).

H because there is no evidence to suggest that Millikan and Ehrenhaft wanted to push each other to create a stronger theory, nor is it accurate to describe their relationship as collegial. Instead, the passage describes Millikan as wanting to “crush Ehrenhaft underfoot” (line 50) and states that Ehrenhaft used Millikan’s “admirable honesty” surrounding his selection of data points as “ammunition” in their “long feud” (lines 56–59).

J because the passage specifically states that Millikan and Ehrenhaft were working on the exact same question in the field of physics—the value and existence of e—and as a result, it is not accurate to claim that Millikan and Ehrenhaft were “primarily working in different fields.”

Question 33. The best answer is D because the debate surrounding Millikan’s experiments was centered on a discrepancy between a statement in Millikan’s paper and a statement found in Millikan’s notebooks. In his paper, Millikan wrote that his data table contained “a complete summary of the results obtained on all of the 58 different drops upon which complete series of observations were made” (lines 43–45). The use of the phrase “the results obtained on all of the 58 different drops” gives the impression that Millikan used only fifty-eight drops in his experiment and that all of these drops were included in the paper. However, the passage states that “the notebooks for the 1913 paper show that Millikan actually took data on 100 oil droplets” (lines 47–48). This suggests that Millikan did not include all the data from his experiments in the paper and that he in fact omitted data from forty-two drops, leading others to question whether or not Millikan had decided to “cherry-pick the data in order to confirm his original result” (lines 49–50).

The best answer is NOT:

A because the passage actually indicates the opposite, claiming that “few laboratories managed to replicate Ehrenhaft’s results” (lines 86–87), but “students now replicate Millikan’s results all across the world” (lines 87–88).

B because at no point does the passage suggest that Millikan’s decision to switch to oil droplets was controversial. The passage only notes that Millikan switched to oil droplets because water droplets evaporated “before any measurements could be made” (line 19).

C because at no point does the passage suggest that the apparatus Millikan used to conduct his experiments was controversial.

Question 34. The best answer is G because the author describes Millikan’s decision as honest and admirable: “This admirable honesty about the selection of data points had given Ehrenhaft ammunition that he used enthusiastically in his long feud with Millikan” (lines 56–59). This suggests that the author finds Millikan’s initial honesty to be admirable, though he acknowledges that Ehrenhaft used Millikan’s admirable honesty about his less-than-perfect data to refute Millikan’s findings and claim that Millikan’s data were inaccurate. The author believes that it was Ehrenhaft’s refutation that led Millikan to hide data in his subsequent experiment, which then led to the “lasting shadow over his scientific integrity” (lines 32–33) that would haunt Millikan for years and delay his Nobel Prize. Therefore, it is reasonable to say that the author believes that Millikan’s “admirable honesty” had unfortunate consequences.

The best answer is NOT:

F because there is no indication in the passage that the author views Millikan’s decision as a mistake that “most scientists rightfully avoid.” Though the author does note that Millikan made the “mistake of full disclosure” (line 52), this disclosure is described as “admirable honesty” (line 56), which suggests that the author views Millikan’s decision to disclose his data as an honorable decision. Because of this, it doesn’t make sense to say that the author views Millikan’s full disclosure as a practice that other scientists “rightfully avoid.” Rather, the author seems to feel that Millikan’s full disclosure in his initial experiment was an admirable decision.

H because Millikan’s decision was at no point described as strategic. Moreover, it was Millikan’s full disclosure that gave Ehrenhaft the “ammunition” (line 58) he needed to question Millikan’s results in the first place, which in turn led to Millikan concealing data in his 1913 paper, a decision that would cast a shadow over his scientific integrity (lines 32–33). Instead of characterizing Millikan’s full disclosure as a strategic decision, the author describes it as “admirable honesty” (line 56).

J because although it might be reasonable to characterize Millikan’s full disclosure as naive, at no point does the author characterize his decision as desperate. Instead, the author describes Millikan’s response to Ehrenhaft’s refutation as “desperate” (line 31) and claims that this desperation caused Millikan to conceal data in his 1913 paper. The author describes Millikan’s full disclosure in his 1910 paper as “admirable honesty” (line 56).

Question 35. The best answer is C because the passage states that Millikan used oil droplets because he had a difficult time measuring water droplets before they evaporated: “Finding that water droplets tended to evaporate before any measurements could be made, Millikan set to the task of trying the same trick with oil droplets” (lines 18–21).

The best answer is NOT:

A because at no point does the passage state that other physicists used oil droplets. Rather, the passage states that Millikan used oil droplets because he found that water droplets evaporated too quickly and were therefore difficult to measure (lines 18–21).

B because although the passage states that Millikan may have “judged some droplets to be too small or too large to yield reliable data” (lines 69–70), the passage at this point is discussing only oil droplets, and the passage never states that oil droplets form more consistently sized droplets than water droplets. Rather, the passage states that Millikan used oil droplets because he found that water droplets evaporated too quickly and were therefore difficult to measure (lines 18–21).

D because at no point does the passage mention that Millikan reused either oil or water droplets for any of his experiments. Rather, the passage states that Millikan used oil droplets because he found that water droplets evaporated too quickly and were therefore difficult to measure (lines 18–21).

Question 36. The best answer is F because the primary purpose of this paragraph is to present Goodstein’s justification for why Millikan only included data from fifty-eight of the one hundred water droplets in his paper. Goodstein argues that Millikan may have excluded certain data points that were either too large or too small to yield reliable data (lines 68–70), because droplets that were too small could not be reliably measured due to random collisions with air particles (lines 72–74), and droplets that were too big would fall too fast, making them difficult to reliably measure (lines 70–72). Goodstein then argues that Millikan could have potentially viewed the fifty-eight drops as the only samples that were “complete enough” (lines 75–76) to be included in the paper, which would justify Millikan’s claim that his data table contained “a complete summary of the results obtained on all of the 58 different drops upon which complete series of observations were made” (lines 43–45). Because the author spends the entire paragraph describing Goodstein’s defense of Millikan, it is reasonable to conclude that the main purpose of the paragraph is to present Goodstein’s defense of Millikan.

The best answer is NOT:

G because the author does not argue against Goodstein’s interpretations of Millikan’s motives at any point during this particular paragraph. Instead, he describes Goodstein’s rationale for Millikan’s exclusion of data points that were too large or too small (lines 68–74) and ends by offering Goodstein’s conclusion that Millikan could have viewed the fifty-eight drops as the only samples that were “complete enough” (lines 75–76) to be included in the paper. In the subsequent paragraph, the author describes the manner in which “Goodstein undoes his defence” (line 77) of Millikan, but the author does not mention this at any point during the ninth paragraph (lines 62–76).

H because the author does not describe Millikan’s methods in much detail during this paragraph. Instead, he describes Goodstein’s rationale for excluding data points that were too large or too small (lines 68–74) and ends by offering Goodstein’s conclusion that Millikan could have viewed the fifty-eight drops as the only samples that were “complete enough” (lines 75–76) to be included in the paper. So, although the author does mention Millikan’s methods, it is only in the context of Goodstein’s defense of Millikan’s decision to only include fifty-eight drops in his data set. The author also does not mention any perspective on Millikan’s methods aside from Goldstein’s during this paragraph.

J because the author only briefly describes how Millikan’s data are represented, and this is only in the context of Goodstein’s defense of Millikan’s decision to only include fifty-eight drops in his data set. Furthermore, the paragraph does not include Millikan’s explanation for any of his methods; it instead includes an explanation from Goldstein justifying the way in which Millikan presented his data.

Question 37. The best answer is A because according to the passage, Ehrenhaft claimed that there is no fundamental minimum unit of charge and therefore no electron: “There is no fundamental, minimum unit of charge, Ehrenhaft said; there is no ‘electron’” (lines 29–30).

The best answer is NOT:

B because at no point does the passage state that Ehrenhaft believed that Millikan’s value for e was too low. Instead, the passage states that Ehrenhaft’s experiments “seemed to show that electrical charge can be infinitely small” (lines 28–29), that “there is no fundamental, minimum unit of charge” (lines 29–30), and that “there is no ‘electron’ ” (line 30).

C because at no point does the passage state that Ehrenhaft accused Millikan of failing to take prevailing scientific theories into account. To refute Millikan, Ehrenhaft instead conducted a “similar set of experiments that seemed to show that electrical charge can be infinitely small” (lines 27–29). This led Ehrenhaft to conclude that “there is no ‘electron’ ” (line 30), and he reached this conclusion based on his own attempts to replicate Millikan’s experiments, not on prevailing scientific theories.

D because at no point does the passage state that Ehrenhaft believed that the value of e varies based on the substance one is measuring. Instead, Ehrenhaft concluded that “there is no fundamental, minimum unit of charge” and that “there is no ‘electron’ ” (lines 29–30).

Question 38. The best answer is H because although the assertion that Millikan’s experiments “cast a lasting shadow over his scientific integrity” (lines 32–33) is an inherently subjective judgment, it is fair to characterize it as a “reasoned” judgment, as the author offers a great deal of evidence to support this statement. He quotes the biologist Richard Lewontin, who accused Millikan of going “out of his way to hide the existence of inconvenient data” (lines 35–36), and then references David Goodstein, who stated that Millikan “certainly did not commit scientific fraud” (line 37). Although Goodstein disagrees with Lewontin, it is clear that Goodstein is arguing against the viewpoint that Millikan committed scientific fraud, which suggests that the belief that Millikan committed fraud is not uncommon. Furthermore, the passage claims that Millikan was unable to convince his peers straight away (lines 81–82), as evidenced by the fact that Millikan’s Nobel Prize was delayed for three years (lines 83–84). Therefore, it is accurate to describe the author’s statement as a reasoned judgment, considering the evidence he provides for the controversy surrounding Millikan’s 1913 paper.

The best answer is NOT:

F because it is not accurate to describe the author’s statement as being based on “casual assumptions about scientists working in the early 1900s.” Instead, the author provides detailed evidence to support his statement. He quotes Richard Lewontin, a scientist who believes that Millikan deliberately hid the existence of inconvenient data (lines 35–36), as well as scientist David Goodstein, who claimed that Millikan “certainly did not commit scientific fraud” (line 37). This quote suggests that Goodstein is arguing against others who do believe that Millikan committed scientific fraud, which suggests that this view is not uncommon. Furthermore, the author claims that Millikan was unable to convince his peers straight away (lines 81–82), and, as evidence, he states that Millikan’s Nobel Prize was delayed for three years as a result of his peers’ distrust (lines 82–84). Because the author provides evidence to support his assertion, including quotations from other scientists, it is not reasonable to characterize this statement as a “casual assumption.”

G because at no point does the author attempt to imagine himself in Millikan’s position. In fact, the author does not mention himself directly at any point during the passage. Therefore, it is not reasonable to conclude that the author was attempting to imagine himself in Millikan’s position.

J because the author mentions Millikan’s notebooks only briefly, claiming that Millikan’s notebooks show that he “actually took data on 100 oil droplets” (line 48), and the notebooks are not mentioned at any other point.

Question 39. The best answer is A because the paragraph describes the two prevailing arguments about Millikan’s methodologies by offering two conflicting viewpoints. The biologist Richard Lewontin accuses Millikan of going “out of his way to hide the existence of inconvenient data” (lines 35–36), which suggests that Lewontin believes that Millikan did commit a certain degree of scientific fraud. However, David Goodstein states that Millikan “certainly did not commit scientific fraud” (line 37). By offering quotations from these two scientists, the author provides two conflicting viewpoints on the same topic: one stating that Millikan did commit fraud and the other stating that he did not. By providing two contrasting quotes from two other scientists, and by ending the paragraph with the question, “So where does the truth lie?” (lines 37–38), the author introduces the reader to the two prevailing opinions surrounding the ethics of Millikan’s methodologies.

The best answer is NOT:

B because the author does not discuss the background of either Lewontin or Goodstein in great detail. Although he does state that Lewontin is a biologist and that Goodstein is a physics professor, he does not try to analyze how either individual’s scientific background may have influenced his opinions about Millikan. Instead, he simply provides quotations from both scientists demonstrating their contrasting opinions, poses the question, “So where does the truth lie?” (lines 37–38), and then moves on to his own analysis of Millikan’s methodologies without mentioning either scientist’s background again.

C because the author does not discuss any experiments that refute Millikan’s findings in this paragraph. Instead, he provides two quotations from two different scientists discussing the legitimacy of Millikan’s methodologies. In fact, at no point during the passage does the author state that current experiments refute Millikan’s results. Instead, the passage states that “students now replicate Millikan’s results all across the world” (lines 87–88), which suggests that the opposite is true: modern experiments confirm Millikan’s results.

D because the author does not discuss any attempts to replicate Millikan’s experiments in this paragraph. Instead, the author provides two quotations from two different scientists discussing the legitimacy of Millikan’s methodologies. In fact, at no point during the passage does the author state Millikan’s contemporaries had difficulties replicating his findings.

Question 40. The best answer is G because the passage states that “the debate hangs on a phrase in Millikan’s 1913 paper” (lines 39–40), meaning that the debate depends on the existence of Millikan’s claim that his data table contained “a complete summary of the results obtained on all of the 58 different drops upon which complete series of observations were made” (lines 43–45). The debate centers entirely on this phrase and the discrepancies between this phrase and Millikan’s notebooks: without the existence of this phrase, the debate surrounding Millikan’s academic integrity would not exist. Therefore, it makes sense to say that the debate “depends on” a phrase in Millikan’s 1913 paper.

The best answer is NOT:

F because it does not make sense to say that the debate “continues a phrase in Millikan’s 1913 paper.” This would suggest that the existence of the phrase is somehow being “continued” by the debate surrounding it, which is illogical.

H because it does not make sense to say that the debate “sticks with a phrase in Millikan’s 1913 paper,” because the phrase “sticks with” colloquially refers to a decision to endure an activity or to stay alongside a person, and this would suggest that the debate is somehow “enduring” or “remaining with” the phrase in Millikan’s 1913 paper, which is illogical.

J because it doesn’t make sense to say that the debate “blames on a phrase in Millikan’s 1913 paper.” Although it would make sense to say that the debate “is blamed on a phrase in Millikan’s 1913 paper,” the phrase “the debate blames on” doesn’t make sense, because it’s not clear what or who is being blamed, and what for, which makes this statement illogical.

Passage I

The best answer is B. According to Figure 1, CF₂Cl₂ has a boiling point of −30°C and a molecular mass of 130 amu. A is incorrect; CF₄, with a boiling point of −125°C, has a molecular mass of 90 amu. B is correct. C is incorrect; CCl₄, with a boiling point of 80°C, has a molecular mass of 150 amu. D is incorrect; CF₂Br₂, with a boiling point of 25°C, has a molecular mass of 210 amu.

The best answer is J. In Figure 1 BP is shown on the y-axis. The higher the position of a point on the graph relative to the y-axis, the greater the boiling point. Of the compounds listed in the answers, CCl₄ has the highest BP, approximately 75°C. F is incorrect; CF₄ has a boiling point of −125°C. G is incorrect; CF₂Cl₂ has a boiling point of −30°C. H is incorrect; CF₂Br₂ has a boiling point of 25°C. J is correct.

The best answer is A. Table 1 shows that of the three compounds listed, both the molecular mass and the BP of CHCl₃ are the lowest and those of CHI₃ are the highest. As the molecular mass increases, the BP increases. A is correct; this graph shows BP increasing as molecular mass increases. B is incorrect; this graph shows BP decreasing and then increasing as molecular mass increases. C is incorrect; this graph shows BP decreasing as molecular mass increases. D is incorrect; this graph shows BP increasing and then decreasing as molecular mass increases.

The best answer is H. According to Table 1, at 1 atmosphere of pressure, CH₂I₂ has a BP of 182°C and CH₄ has a BP of −162°C. The BP of CH₂I₂ is 344°C greater than the BP of CH₄ (182 – (−162) = 344). F, G, and J are incorrect; the difference is 344°C. H is correct.

The best answer is A. According to Figure 1, the molecular mass of CF₄ is approximately 90 amu. Of the compounds listed in the answers, the molecular mass of dichloromethane—85 amu—is closest to that of CF₄. A is correct. B is incorrect; the molecular mass of trichloromethane is 119 amu. C is incorrect; the molecular mass of iodomethane is 142 amu. D is incorrect; the molecular mass of dibromomethane is 174 amu.

The best answer is H. In order to answer this item, the examinee must understand how to interpret chemical formulas. CBr₄ contains 1 carbon atom and 4 bromine atoms. According to Figure 1, CBr₄ has a molecular mass of 330 amu. If C has a mass of 12 amu, then the mass of the 4 Br is 318 (330 – 12 = 318). The mass of 1 Br is 79.5 amu (318 ÷ 4 = 79.5). F, G, and J are incorrect; the atomic mass of Br is closest to 80 amu. H is correct.

Passage II

The best answer is D. According to the passage, the present-day CO₂ concentration was 370 ppm. Figure 3 shows that the percentage of U urushiols per plant in 2004 in the 370 ppm CO₂ plot was 90%. A, B, and C are incorrect; the percentage of U urushiols per plant was 90%. D is correct.

The best answer is J. Figure 2 shows that at the end of the study, in 2004, 40% of the original PIPs in the elevated CO₂ concentration plot survived and approximately 33% of the PIPs in the present-day CO₂ concentration plot survived. F and G are incorrect; the elevated CO₂ plot had the higher percentage of original PIPs surviving. H is incorrect; the difference was 7%. J is correct.

The best answer is C. According to the passage, the conditions in both plots were identical except for the CO₂ concentration. A, B, and D are incorrect; the CO₂ concentrations were not the same. C is correct.

The best answer is H. According to Figure 1, at all times the dry biomass per plant was greater for the elevated CO₂ concentration plot than for the present-day CO₂ concentration plot. F, G, and J are incorrect; the dry biomass per plant was always greater for the elevated CO₂ concentration plot. H is correct.

The best answer is D. According to Figure 2, in 2003, 40% of the original PIPs survived in the plot with a CO₂ concentration of 370 ppm, and therefore 60% of the original PIPs had died. A, B, and C are incorrect; 60% of the original PIPs had died. D is correct.

The best answer is F. Figure 3 shows that the present-day CO₂ concentration plot had 10% S urushiols per plant, and the elevated CO₂ concentration plot had 5% S urushiols per plant. The present-day CO₂ concentration plot had a higher percentage of S urushiols per plant. F is correct. G is incorrect; 10% of the urushiols were saturated. H and J are incorrect; a greater percentage was produced in the present-day CO₂ concentration plot.

Passage III

The best answer is B. According to Figure 1, as the concentration increases, the O₃ concentration also increases. Figure 3 shows that at both 2:30 p.m. and 4:00 p.m., the concentration at Site C was lower than that at Site B. The concentration at Site C at 2:30 p.m. was approximately 0.3 ppm, and the concentration at Site C at 4:00 p.m. was approximately 1.4 ppm. The concentration, and therefore the O₃ concentration, was lowest at Site C at 2:30 p.m. A, C, and D are incorrect; the O₃ was lowest at Site C at 2:30 p.m. B is correct.

The best answer is H. According to Figure 1, as the concentration increases, the O₃ concentration also increases. Figure 3 shows that at 2:00 p.m., Site D had the lowest concentration, and therefore O₃ concentration, followed by Site C and then Site A, and Site B had the highest concentration. F, G, and J are incorrect; the correct order from lowest O₃ concentration to highest is Site D, Site C, Site A, Site B. H is correct.

The best answer is B. According to Figure 1, as the concentration increases, the O₃ concentration also increases. Figure 3 shows that the highest concentration, and therefore the highest O₃ concentration, was measured at Site B at 1:30 p.m. A, C, and D are incorrect; the highest concentration, and therefore the highest O₃ concentration, was measured at Site B. B is correct.

The best answer is G. Figure 3 shows that at 5:00 p.m. the concentration at Site B was 2.00 μmol/L and the concentration at Site C at 2:00 p.m. was 1.00 μmol/L. According to Figure 1, this corresponds to an O₃ concentration of 80 ppb for Site B and 40 ppb for Site C. The O₃ concentration at Site B at 5:00 p.m. was two times greater than the O₃ concentration at Site C at 2:00 p.m. F, H, and J are incorrect; the O₃ concentration was two times greater at 5:00 p.m. at Site B than at 2:00 p.m. at Site C. G is correct.

The best answer is C. According to Figure 1, as the concentration increased, the O₃ concentration also increased. Figure 3 shows that the concentration was greater at 5:30 p.m. at Site A than at 4:00 p.m. Because the O₃ concentration increased as the concentration increased, the O₃ concentration was also greater at 5:30 p.m. at Site A than at 4:00 p.m. A and B are incorrect; the O₃ concentration was greater at 5:30 p.m. C is correct. D is incorrect; the higher the concentration, the higher the O₃ concentration.

The best answer is J. In order to answer this item, the examinee must understand proportional reasoning involving units of measure. According to the passage, in Step 2 the vacuum pump was turned on for 25 min. If the pump drew in air at a rate of 200 mL/min, then the volume of air drawn through the test tube each time Step 2 was performed is equal to × 25 min = 5,000 mL. F is incorrect; 200 mL would be drawn through the test tube if the pump ran for 1 minute. G is incorrect; 550 mL would be drawn through the test tube if the pump ran for 2.75 min. H is incorrect; 2,500 mL would be drawn through the test tube if the pump ran for 12.5 min. J is correct; 5,000 mL would be drawn through the test tube if the pump ran for 25 min.

The best answer is A. In order to answer this item, the examinee must know the mathematical definition of percent error. According to Figure 3, at 12:30 p.m. at Site C, the measured, or experimental, value for the concentration was 1.00 μmol/L. Figure 1 shows that an concentration of 1.00 μmol/L corresponds to an O₃ concentration of 40 ppb. The percent error can be calculated as follows: × 100% = × 100%. A is correct. B is incorrect; the divisor should be the actual value of 43 ppb. C and D are incorrect; the experimental value is 40 ppb.

Passage IV

The best answer is F. According to the results of Study 2, as the wavelength decreased, y₁ also decreased. At a wavelength of 400 nm, y₁ = 10.0 mm. A value of y₁ less than 10.0 mm would most likely be obtained at a wavelength shorter than 400 nm. F is correct. G is incorrect; when the wavelength was 500 nm, y₁ = 12.5 mm. H is incorrect; when the wavelength was 700 nm, y₁ = 17.5 mm. J is incorrect; at a wavelength of 900 mm, y₁ would most likely be greater than 17.5 mm.

The best answer is C. In Study 3, slit width and wavelength were fixed while x was varied. The results shown in Table 3 indicate that y₁ increased as x increased. A and B are incorrect; both graphs show y₁ decreasing as x increases. C is correct. D is incorrect; according to Table 3, when x = 3.00 m, y₁ = 7.5 mm. The graph shown in D does not show this data point.

The best answer is F. According to the passage, x = 6.00 m in Trial 2. Table 1 shows that for Trial 2, y₁ = 15.0 mm. The results of Study 3 in Table 3 show that as x increased, y₁ also increased. One would predict that repeating Trial 2 with x = 9.00 m would result in a value of y₁ greater than 15.0 mm. (This is confirmed by noting that Trial 11 is the same as Trial 2 with x = 9.00 m and y₁ = 22.5 mm.) F is correct. G is incorrect; y₁ increased and x increased. H and J are incorrect; y₁ would be greater than 15.0 mm.

The best answer is D. A is incorrect; the width of the slit was varied in Study 1. B is incorrect; the wavelength of the laser light was varied in Study 2. C is incorrect; the distance between the slit and the screen was varied in Study 3. D is correct; the distance between the slit and the laser was not varied in any of the studies.

The best answer is F. According to Table 2, the wavelength was shortest in Trial 5 (400 nm), and therefore the energy of the photons was greatest in Study 5. F is correct. G is incorrect; the wavelength of light used in Trial 6 was 500 nm, a longer wavelength than that used in Trial 5. H is incorrect; the wavelength of light used in Trial 7 was 600 nm, a longer wavelength than that used in Trial 5. J is incorrect; the wavelength of light used in Trial 8 was 700 nm, a longer wavelength than that used in Trial 5.

The best answer is B. According to Table 1, when the slit width was doubled from 0.12 mm to 0.24 mm, the distance between the bands (y₁) decreased from 30.0 mm to 15.0 mm. As the slit width doubled, y₁ was halved. A is incorrect; y₁ was cut in half. B is correct. C is incorrect; y₁ decreased. D is incorrect; y₁ consistently decreased by one-half. As slit width increased further, from 0.24 mm to 0.48 mm, y₁ decreased from 15.0 mm to 7.5 mm.

The best answer is G. In order to answer this item, the examinee must know that 1 m = 1,000 mm. According to Table 2, in Trial 7 y₁ = 15.0 mm. In meters this is equal to 0.015 m. F, H, and J are incorrect; 15.0 mm is equal to 0.015 m. G is correct.

Passage V

The best answer is C. According to Scientist 2, CO₂ and water vapor each account for 45% of the total gas output. CO accounts for 6%, and the remaining 4% is all other gases combined. A is incorrect; this pie chart does not include the other gases. B is incorrect; this pie chart indicates that 75% of the output is water vapor. C is correct; this pie chart correctly illustrates the percentage of each gas in the output. D is incorrect; this pie chart indicates that 75% of the output is water vapor.

The best answer is F. According to Scientist 1, ascending magma causes earthquakes. Scientist 2 states that magma rises toward Earth’s surface and sometimes causes small fractures, but Scientist 2 does not state that the rising magma causes earthquakes. F is correct. G, H, and J are incorrect; Scientist 1 states that ascending magma causes earthquakes.

The best answer is B. According to the passage, Scientist 1 claims that the iron-rich lava and mantle rocks at HSVs are abundant in olivine and pyroxenes. Because feldspar is not abundant, it is most likely that Scientist 1 would expect basalt to be found at an HSV. Scientist 2 claims that feldspar is the most abundant mineral. It is most likely that Scientist 2 would expect phonolite to be found at an HSV. A is incorrect; because phonolite is rich in feldspar, Scientist 2 would expect phonolite to be found at an HSV. B is correct. C and D are incorrect; because phonolite is rich in feldspar, Scientist 1 would not expect phonolite to be found at an HSV.

The best answer is G. According to Scientist 1, the frequency of eruptions increases over time, but Scientist 2 claims that the eruption frequency will slow down over time. The discovery that older HSVs erupt more frequently than younger HSVs would best support the viewpoint of Scientist 1. F is incorrect; Scientist 1 claims that eruption frequency increases over time. G is correct. H and J are incorrect; the discovery would best support Scientist 1.

The best answer is A. Scientist 1 claims that mantle plumes exist at depths between 200 km and 400 km. Scientist 2 refers to the magma found at depths of less than 100 km. Only Scientist 1 discusses a process that may extend beneath the lithosphere (a depth below 200 km). A is correct. B, C, and D are incorrect; only Scientist 1 discusses a process that occurs beneath the lithosphere.

The best answer is H. Scientist 1 claims that the lavas at HSVs retain a lot of water from the mantle, but Scientist 2 claims that the lavas contain much less water than most mantle rocks. Assuming that not all the water was lost as water vapor, both scientists would most likely agree that the mantle rocks contained some water. F, G, and J are incorrect; both scientists would most likely agree that the rocks contained some water. H is correct.

The best answer is D. Scientist 2 states that a high concentration of dissolved CO₂ allows mantle rocks to melt at lower temperatures than they normally would. In this case, CO₂ is acting as a flux. A is incorrect; only Scientist 2’s discussion includes flux melting. B is incorrect; CO₂ is the flux. C is incorrect; only Scientist 2’s discussion includes flux melting. D is correct.

Passage VI

The best answer is J. According to Figure 3, when the GFP reporter gene was prepared with only RS2, the GFP reporter gene was expressed in cell types D, E, and F. F, G, and H are incorrect; the GFP reporter gene was expressed in cell types D, E, and F only. J is correct.

The best answer is C. According to the passage, GFP emits a green light when viewed with a certain microscope. In Experiment 1, GFP was not expressed in cell types A, C, and D. In Experiment 2, GFP was not expressed in cell types A or C. Throughout both experiments GFP was not expressed in cell types A or C, and therefore green light was not observed for cell types A or C. A and B are incorrect; green light was not observed for cell types A and C. C is correct. D is incorrect; because GFP was expressed in cell type D when the reporter gene contained only RS2 and the coding region, green light was observed for cell type D.

The best answer is H. According to Figure 2, when GFP reporter genes containing RS1–RS3 and the coding region for GFP were prepared and transfected into cells, the GFP reporter gene was expressed in cell types B, E, and F. If the reporter gene containing RS1–RS3 and the coding region for β-galactosidase was transfected into cell types A–F, then one would predict that cell types B, E, and F would show enzymatic activity. F, G, and J are incorrect; RS1–RS3 appear to be responsible for turning on gene expression in cell types B, E, and F, and therefore one would expect cell types B, E, and F to have enzymatic activity. H is correct.

The best answer is B. According to Figure 3, the GFP reporter gene was expressed in cell type F when the gene contained RS2 and when the gene contained RS1 and RS2, but the GFP reporter gene was not expressed in cell type F when the gene contained only RS1, indicating that the expression was turned on by RS2. A is incorrect; the GFP reporter gene was not expressed when only RS1 was present. B is correct; the GFP reporter gene was expressed when only RS2 was present. C is incorrect; the GFP reporter gene was not expressed when only RS3 was present. D is incorrect; the GFP reporter gene was expressed when only RS2 was present.

The best answer is G. According to the passage, reporter genes code for easily detectable proteins. Studying the reporter genes would make it much easier to determine the influence of the RSs. F is incorrect; it is most likely that the protein product of the reporter gene was more easily observed than the protein product of Gene X. G is correct. H is incorrect; the passage states that the three RSs were thought to be associated with Gene X. J is incorrect; the studies show that the three RSs did control the expression of the reporter genes.

The best answer is C. According to Figure 3, gene expression in cell type D was turned on when RS2 was used alone. Because gene expression in cell type D was turned off when RS1 and RS2 were both used, it can be concluded that RS1 turns off gene expression in cell type D. A is incorrect; gene expression is not turned on by RS1 in any cell type studied. B is incorrect; gene expression is turned on by RS2 in cell type D, but this does not explain why gene expression was turned off in cell type D when RS1 and RS2 were combined. C is correct. D is incorrect; gene expression is not turned off by RS2.

The best answer is J. According to Figures 2 and 3, RS1 appears to turn off GFP reporter gene expression in cell type D; RS2 appears to turn on expression in cell types D, E, and F; and RS3 appears to turn on gene expression in cell type B. All three RSs appear to control the expression of GFP reporter genes in one or more cell types. If the three RSs have the same control over the expression of Gene X, then the results indicate that the expression of Gene X is controlled by each RS in at least one cell type. F and G are incorrect; all three RSs do appear to control the expression of Gene X. H is incorrect; none of the RSs appears to affect expression in all the cell types. J is correct.

Planning Your Essay

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ENGLISH • PRACTICE TEST 6 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is C because it is the only option that provides a preposition that fits the context of the sentence and creates a standard English idiom (“ways of imitating”).

The best answer is NOT:

A because the phrase “ways by imitating” is not idiomatically sound.

B because the phrase “ways with imitating” is not idiomatically sound.

D because the phrase “ways at imitating” is not idiomatically sound.

Question 2. The best answer is H because it provides the appropriate verb form and verb tense (is) for the second independent clause in this sentence.

The best answer is NOT:

F because the participle being leaves the second independent clause without a predicate.

G because the verb “was being” creates an illogical shift in verb tense. The first clause of the sentence uses present tense, so the second clause should also use present tense.

J because a deletion would leave the second independent clause without a predicate.

Question 3. The best answer is B because it maintains the style and tone of the essay.

The best answer is NOT:

A because the phrase “take a back seat” strays from the more formal style of this essay.

C because the phrase “a bigger deal” strays from the more formal style of this essay.

D because the phrase “way more vital” is too colloquial for the style and tone of this essay.

Question 4. The best answer is H because it provides the appropriate punctuation (commas) to set off the nonessential element “called vocables.”

The best answer is NOT:

F because it is missing the second comma to set off the nonessential element.

G because it is missing the first comma to set off the nonessential element.

J because the comma after called is misplaced; it should be after syllables to set off the nonessential element.

Question 5. The best answer is C because it creates a sentence that is structurally sound and has proper subordination.

The best answer is NOT:

A because the word easier is a comparative adjective, but the sentence makes no comparison. In addition, it creates an awkward, unclear sentence.

B because the word easily is an adverb, but there is no word for the adverb to modify. It also creates an awkward, unclear sentence.

D because the phrase “flow in a way to dance to” creates an awkward, unclear sentence.

Question 6. The best answer is F because the phrase “often tongue-twisting,” which describes the lyrics of puirt-abeul, suggests a sequence of words or sounds that are difficult to pronounce.

The best answer is NOT:

G because “tongue-twisting” is not related to writing lyrics; the phrase describes words or sounds that are difficult to pronounce.

H because “often” refers to the frequency with which the puirt-a-beul lyrics are “tongue-twisting,” not the frequency with which puirt-a-beul is performed.

J because there is no mention of any training exercises for puirt-a-beul.

Question 7. The best answer is A because it provides the most logical transitional word to connect this sentence with the preceding one. The word though is used to indicate a statement that contrasts with something that has been said previously. In this paragraph, the idea that the “lyrics require much practice to perfect” is contrasted with the idea that “learning when to breathe” is the “greater challenge.”

The best answer is NOT:

B because the transitional phrase “at the same time” inaccurately suggests that the “greater challenge” is happening simultaneously with the requirement for “much practice to perfect.”

C because it inaccurately suggests that the “greater challenge” of “learning when to breathe” is a one-time occurrence.

D because the word still does not link this sentence with the preceding one in a logical way.

Question 8. The best answer is G because it clarifies that it is the dancers who are relying on “the steady beat,” and it avoids using a pronoun with an unclear referent.

The best answer is NOT:

F because the pronoun it has no clear referent.

H because the pronoun they has no clear referent.

J because it leaves the pronoun their, which appears later in the sentence, with no clear referent.

Question 9. The best answer is A because it is the only option that introduces the discussion that puirt-a-beul was invented out of necessity, which is the main focus of the paragraph.

The best answer is NOT:

B because the main focus of the paragraph is why puirt-a-beul was invented, not how mouth music singers must have good rhythm.

C because the main focus of the paragraph is why puirt-a-beul was invented, not how it has influenced jazz scat singing.

D because the main focus of the paragraph is why puirt-a-beul was invented, not where another form of mouth music originated.

Question 10. The best answer is H because it is the only option that has correct sentence structure. It creates two complete sentences using a period to separate two independent clauses.

The best answer is NOT:

F because it creates a run-on sentence.

G because it creates a run-on sentence.

J because it creates a comma splice.

Question 11. The best answer is D because it uses the appropriate pronoun case. The nominative pronoun who is used to introduce a clause about a person, and in this instance, the person is anyone.

The best answer is NOT:

A because the pronoun whomever is the objective case, and the sentence requires a subjective pronoun because of the verb “didn’t read.”

B because the pronoun which is used for things, not people.

C because the pronoun whom is the objective case, and the sentence requires a nominative case.

Question 12. The best answer is G because it clarifies that “this musical form” is referring to the popularity of Celtic mouth music, and it avoids using a pronoun with an unclear referent.

The best answer is NOT:

F because the pronoun them has no referent.

H because the reflexive pronoun itself has no clear antecedent.

J because there is no referent for the word one.

Question 13. The best answer is B because it creates a logical sentence with all modifiers correctly placed.

The best answer is NOT:

A because it creates an awkward sentence structure that lacks clarity. In addition, the phrase “exposing with audiences” is not a standard English idiom.

C because it creates a sentence that is both unclear and nonsensical.

D because the word worldwide is misplaced; it should be placed after audiences.

Question 14. The best answer is J because it provides the clearest, most concise wording for this sentence and avoids redundancy.

The best answer is NOT:

F because it is redundant; the adverb continually is unnecessary because the word survives already suggests a continuation.

G because it is redundant; “still remains” and “carries on” mean the same thing.

H because it is redundant and awkward; stays and “sticking around” mean the same thing.

Question 15. The best answer is A because the phrase “traditional mouth music with modern rhythms” in the underlined portion indicates that the bands incorporate “classic Celtic music and current influences” into their music.

The best answer is NOT:

B because it lacks any reference to the bands’ incorporating classic Celtic music.

C because it lacks any reference to the bands’ incorporating classic Celtic music or current influences.

D because singing and dancing on stage is unrelated to how the bands incorporate classic Celtic music and current influences.

Passage II

Question 16. The best answer is J because it is the only option that does not add unnecessary and confusing punctuation.

The best answer is NOT:

F because the phrase “called the Garamantes” is an essential element that should not be separated from the rest of the clause.

G because the phrase beginning with the word created is essential and should not be separated from the rest of the clause.

H because the colon after the word called is incorrect as it breaks up the complete subject in this sentence.

Question 17. The best answer is C because it is the only option that provides parallel verb structure.

The best answer is NOT:

A because it shifts to passive voice; the other verbs are in active voice.

B because it shifts to passive voice; the other verbs are in active voice.

D because it does not include a verb and so is not parallel with the other elements.

Question 18. The best answer is F because the preceding sentence lists the variety of crops the Garamantes grew, which clearly implies that they were successful farmers.

The best answer is NOT:

G because the concluding statement does not summarize previous information. It provides new information about farming.

H because the concluding statement includes no information about where or even if the crops were exported.

J because the concluding statement includes no information about the Garamantes importing crops.

Question 19. The best answer is A because it is the only choice that adds new information. This is the first reference to “distant mountains,” the source of the underground water.

The best answer is NOT:

B because it is redundant; the preceding sentence notes that the civilization depended on the underground tunnels.

C because it is redundant; the preceding paragraph already established that the essay is about the Garamantes.

D because it is redundant; the preceding sentence notes that the civilization depended on the underground tunnels.

Question 20. The best answer is F because it is the only option that indicates the method for building the tunnels.

The best answer is NOT:

G because the word underground does not indicate the method for building the tunnels.

H because the phrase “dimly lit” does not indicate the method for building the tunnels.

J because the word desert does not indicate the method for building the tunnels.

Question 21. The best answer is B because the comparative adverb “more easily” appropriately modifies the adjective accessible. It also indicates a comparison between the accessibility of the water before and after the tunnels reached a town or field.

The best answer is NOT:

A because the phrase “more easy” is not a correct comparative adverbial form.

C because the comparative adjective easier illogically modifies the nouns canals and reservoirs.

D because the phrase “easy and” is an imprecise and unclear description.

Question 22. The best answer is J because it is the only option that does not create a misplaced or dangling modifier.

The best answer is NOT:

F because the introductory phrase inaccurately modifies the archaeologists as if they were the ones who “left no clues.”

G because the introductory phrase inaccurately modifies the archaeologists as though they were a “genuine puzzle.”

H because the introductory phrase inaccurately modifies the archaeologists as though they were the ones who gave “no indication.”

Question 23. The best answer is B because the word than is the correct word to use in this context; it is a conjunction used to make a comparison, which this sentence does. It also creates a standard English idiom.

The best answer is NOT:

A because the word then is not the correct word to use in this context; the phrase “rather then” is not a standard English idiom.

C because the word then is not the correct word to use in this context; the phrase “rather then” is not a standard English idiom.

D because the word by is not the correct word to use in this context; the phrase “rather by” is not a standard English idiom.

Question 24. The best answer is H because it is the only option that uses the appropriate verb form. The water from the aquifer meant that the Garamantes “could rely” on “a constant supply of water.”

The best answer is NOT:

F because it is not a proper verb form.

G because it is not a proper verb form.

J because the singular verb form relies does not agree with its plural subject Garamantes.

Question 25. The best answer is A because it provides the most logical transitional word to connect this sentence with the preceding one. The word Moreover means furthermore, and this sentence provides further information about the benefits of the underground canals.

The best answer is NOT:

B because the transitional word Nevertheless suggests contrasting ideas, but the information in this sentence does not contrast with the idea in the preceding sentence.

C because the transitional phrase “In contrast” suggests contrasting ideas, but the information in this sentence does not contrast with the idea in the preceding sentence.

D because the transitional phrase “Even so” suggests contrasting ideas, but the information in this sentence does not contrast with the idea in the preceding sentence.

Question 26. The best answer is J because deleting the underlined portion is the only option that has correct sentence structure. It creates a complete sentence with a clear subject and predicate.

The best answer is NOT:

F because it creates a sentence fragment.

G because it creates a sentence fragment.

H because it creates a sentence fragment.

Question 27. The best answer is A because it provides the most logical subordinating conjunction to introduce the dependent clause in this sentence. The conjunction As is used to indicate that something happens during the time when something else is taking place.

The best answer is NOT:

B because the phrase “As to when” is unclear and unnecessarily wordy.

C because the word Whereas indicates contrast or comparison; this sentence is making a connection, not a comparison.

D because the word Though results in an illogical statement.

Question 28. The best answer is H because it is the only option that has correct sentence structure. It creates two complete sentences using a period to separate two independent clauses.

The best answer is NOT:

F because it creates a comma splice.

G because it creates a run-on sentence.

J because it creates a run-on sentence.

Question 29. The best answer is D because deleting the underlined portion avoids redundancy with information elsewhere in the paragraph.

The best answer is NOT:

A because it is redundant; preceding information notes that the ancient shafts are visible.

B because it is redundant and wordy; preceding information notes that the ancient shafts are visible.

C because it is redundant and wordy; preceding information notes that the ancient shafts are visible.

Question 30. The best answer is G because this option clearly indicates why the essay does fulfill the writer’s primary purpose. The main focus of the essay is describing how the Garamantes were able to meet their need for water in a dry area.

The best answer is NOT:

F because trade is only mentioned briefly in the first paragraph, and it has nothing to do with overcoming a natural obstacle.

H because the fact that the foggaras were not naturally occurring does support the primary purpose of explaining how the Garamantes overcame a natural obstacle.

J because the lack of water, not the foggaras, led to the Garamantes’ downfall; in fact, the foggaras aided the Garamantes by moving the water from the mountains to their settlements.

Passage III

Question 31. The best answer is D because deleting the underlined portion avoids redundancy with information elsewhere in the paragraph.

The best answer is NOT:

A because it is redundant; down and descend provide the same information.

B because it is redundant; “down below” and descend provide the same information.

C because it is redundant; downwards and descend provide the same information.

Question 32. The best answer is G because it provides the appropriate punctuation for this sentence. A comma is needed after (DOMs) to separate the two clauses in this sentence.

The best answer is NOT:

F because the verb “are programmed” is essential and should not be set off with commas.

H because a colon should not be used to separate an independent clause from a relative clause.

J because the semicolon creates a sentence fragment.

Question 33. The best answer is B because it provides the appropriate punctuation (a dash) to set off the nonessential element and also because the element ends with a dash.

The best answer is NOT:

A because a colon is not used to introduce a nonessential element.

C because a semicolon is not used to introduce a nonessential element.

D because the lack of punctuation creates a confusing sentence. The nonessential element “a veritable shock wave of photonic energy” should be set off with dashes.

Question 34. The best answer is J because the phrase “fifty trillion neutrinos” in the underlined portion is an enormous number meant to emphasize how numerous neutrinos are.

The best answer is NOT:

F because even though the underlined portion implies that neutrinos have little weight, it does not specify why this is so.

G because the underlined portion notes that neutrinos pass through a body; it does not explain how this happens.

H because the underlined portion notes that there are “fifty trillion neutrinos,” but it does not explain why this number is so high.

Question 35. The best answer is D because it provides the most logical transition to connect this sentence with the preceding one. The phrase “In fact” is used to emphasize the assertion that “Neutrinos are rarely affected by matter or electromagnetic fields.”

The best answer is NOT:

A because the transitional phrase “For this purpose” does not logically link the idea in this sentence with the idea in the preceding one.

B because the transitional phrase “In contrast” suggests two opposing ideas, which does not characterize the ideas in these two sentences.

C because the transitional word Besides means “in addition to,” but the idea in the second sentence emphasizes what is asserted in the first sentence; it does not add another assertion.

Question 36. The best answer is G because it provides the appropriate punctuation (commas) to set off the nonessential element however.

The best answer is NOT:

F because it is missing the first comma to set off the nonessential element, and the semicolon creates a sentence fragment.

H because the semicolon creates a sentence fragment.

J because it is missing the second comma to set off the nonessential element.

Question 37. The best answer is C because it clearly explains why the new sentence should not be added. The information in the first two sentences about neutrinos colliding and the selection of the site to detect those collisions would be interrupted by irrelevant information on a completely different topic.

The best answer is NOT:

A because the suggested revision is not relevant to the discussion of colliding neutrinos.

B because the suggested revision says nothing about subzero altitude.

D because zero-gravity conditions are mentioned later in the paragraph; therefore, this is not a logical reason for not adding the sentence.

Question 38. The best answer is F because it is the only option that has correct sentence structure.

The best answer is NOT:

G because it creates an awkward sentence with faulty coordination.

H because it creates a sentence fragment.

J because it creates a sentence fragment.

Question 39. The best answer is C because it provides the appropriate singular possessive pronoun for this sentence. The singular its refers to the singular noun ice that appears earlier in the sentence.

The best answer is NOT:

A because it is a contraction, not a singular possessive pronoun.

B because it is a plural possessive pronoun, not a singular possessive pronoun.

D because it is not a correct form of possessive pronoun.

Question 40. The best answer is F because it is the only option that has appropriate subject-verb agreement. The singular verb is agrees with its singular subject origin.

The best answer is NOT:

G because it does not agree with the singular subject origin.

H because it does not agree with the singular subject origin.

J because it does not agree with the singular subject origin.

Question 41. The best answer is A because it is the only option that introduces the discussion of the origins of neutrinos, which is the main focus of the paragraph.

The best answer is NOT:

B because the main focus of the paragraph is the origins of neutrinos, not scientists learning more about gamma rays.

C because the main focus of the paragraph is the origins of neutrinos, not the discovery of the specific neutrinos Bert and Ernie.

D because the main focus of the paragraph is the origins of neutrinos, not the particle accelerator.

Question 42. The best answer is F because it is the only option that has correct sentence structure. It creates two complete sentences using a period to separate two independent clauses.

The best answer is NOT:

G because it creates a run-on sentence.

H because it creates a comma splice.

J because it creates a run-on sentence.

Question 43. The best answer is B because it provides the most precise wording for this sentence. The word invaluable means “extremely useful” and accurately describes the information that could be obtained by learning more about the origins of neutrinos.

The best answer is NOT:

A because it means “luxurious or lavish,” which is not contextually appropriate.

C because it means “high-priced or posh,” which is not contextually appropriate.

D because it means opulent, which is not contextually appropriate.

Question 44. The best answer is F because it is the only option that emphasizes how information gleaned from neutrinos could have dramatic effects on how scientists study the universe.

The best answer is NOT:

G because it does not indicate how information gained from neutrinos could impact scientists’ study of the universe.

H because it does not indicate how information gained from neutrinos could impact scientists’ study of the universe.

J because it does not indicate how information gained from neutrinos could impact scientists’ study of the universe.

Question 45. The best answer is C because this option clearly indicates why the essay does not meet the writer’s primary purpose. The main focus of the essay is on how scientists at the IceCube Neutrino Observatory detect neutrinos and how this could benefit future research; it does not outline any scientific theory.

The best answer is NOT:

A because Cherenkov radiation is mentioned only briefly in the first paragraph; it is not the main focus of the essay.

B because DOMs are mentioned only briefly in the first paragraph; they are not the main focus of the essay.

D because the essay suggests that research on neutrinos could lead to new discoveries; it does not suggest that this research might contradict any other theories.

Passage IV

Question 46. The best answer is F because it uses the appropriate pronoun case. The nominative pronoun who is used to introduce a clause about a person, and in this instance, the person is “Rafael Leonardo Black.”

The best answer is NOT:

G because “of whom” is a genitive form of the relative pronoun whom, which is the wrong pronoun case for this sentence.

H because the pronoun which is used for things, not people.

J because whom is the objective pronoun case, which is the wrong pronoun case for this sentence.

Question 47. The best answer is A because it provides the clearest, most concise wording and avoids redundancy.

The best answer is NOT:

B because it is redundant; if Black, who is 64, has been creating art “for over three decades,” he has been doing so for more than half his life.

C because it is redundant; the preceding paragraph notes that Black lives in Clinton Hill.

D because it is redundant; the preceding paragraph notes that Black had recently been discovered.

Question 48. The best answer is F because information about Naumann’s decision to display Black’s drawings is the best transition to the fact that “ten of Black’s pieces sold.”

The best answer is NOT:

G because information about how “ten of Black’s pieces sold” within days makes no sense if it is not preceded by information about where and how they sold.

H because information about how “ten of Black’s pieces sold” within days makes no sense if it is not preceded by information about where and how they sold.

J because information about how “ten of Black’s pieces sold” within days makes no sense if it is not preceded by information about where and how they sold.

Question 49. The best answer is B because it provides the most appropriate punctuation to set off the prepositional phrase in this sentence; the dash is used to emphasize the prices buyers paid for Black’s work.

The best answer is NOT:

A because the comma after the word for incorrectly interrupts the prepositional phrase.

C because a semicolon should not separate an independent clause from a prepositional phrase.

D because the colon after the word for incorrectly interrupts the prepositional phrase.

Question 50. The best answer is G because it is the only option that has correct sentence structure. It creates two complete sentences using a period to separate two independent clauses.

The best answer is NOT:

F because it creates a run-on sentence.

H because it creates a comma splice.

J because it creates a run-on sentence.

Question 51. The best answer is D because it provides the clearest, most concise wording for this sentence and avoids redundancy.

The best answer is NOT:

A because it is redundant; depictions and drawings mean the same thing.

B because it is redundant; preceding information notes that the drawings were done in pencil.

C because it is redundant: preceding information notes that the drawings are collages.

Question 52. The best answer is J because the name “Wilhelm Freddie” is an essential element and should not be set off in the sentence.

The best answer is NOT:

F because the commas are incorrect; “Wilhelm Freddie” is essential and should not be set off with commas.

G because it adds an incorrect comma after Freddie.

H because it adds an incorrect comma after painter.

Question 53. The best answer is A because it is the only option that has appropriate subject-verb agreement. The plural verb fit agrees with its plural subject drawings.

The best answer is NOT:

B because it does not agree with the plural subject drawings.

C because it does not agree with the plural subject drawings.

D because it does not agree with the plural subject drawings.

Question 54. The best answer is G because the underlined portion states that the narrator liked how much there was to puzzle over, which indicates the narrator’s appreciation as well as suggests that the narrator did not understand the overall intent of the collage.

The best answer is NOT:

F because the underlined portion does not make an argument or discuss Naumann in any way.

H because the underlined portion in no way refers to Black being discovered as an artist.

J because the underlined portion reveals the narrator’s thoughts about one collage; it does not discuss modern art in general.

Question 55. The best answer is D because the best placement for the phrase “in May” is at the end of the sentence, since Black’s work created “a stir” in May.

The best answer is NOT:

A because the phrase “this complexity in May” illogically reads as though Black’s work was complex only in May.

B because the phrase “Maybe in May this complexity helps explain” illogically reads as though the complexity in Black’s work can be explained only in May.

C because the phrase “Maybe this complexity helps explain in May” illogically reads as though the complexity in Black’s work can be explained only in May.

Question 56. The best answer is J because it is the only option that establishes that Black is unmoved by the interest in his art.

The best answer is NOT:

F because the word observes does not indicate Black was unmoved by the sudden interest in his art as clearly as J does.

G because it describes Black’s celebrity status rather than indicating his response to the sudden interest in his art.

H because it describes the financial benefits to Black rather than indicating his response to the sudden interest in his art.

Question 57. The best answer is C because it provides the most logical transition between the two sentences. Black wasn’t well known, but now that the narrator knows who Black is, he or she will be on the lookout for Black’s next show.

The best answer is NOT:

A because the narrator’s knowledge of the city has no relationship to his or her desire to go to Black’s next show.

B because information about the narrator’s knowledge of art and books is not relevant to the discussion of Black’s anonymity in the preceding sentence.

D because the narrator’s interest in news has no relationship to his or her interest in going to Black’s next art show.

Question 58. The best answer is J because it does not add irrelevant information to the sentence or essay.

The best answer is NOT:

F because information about the Urban Vintage’s décor is not relevant to the essay’s focus on Black and his work.

G because information about the narrator’s laptop is not relevant to the essay’s focus on Black and his work.

H because information about the narrator’s meeting with a friend is not relevant to the essay’s focus on Black and his work.

Question 59. The best answer is B because it is the only option that does not add unnecessary and confusing punctuation.

The best answer is NOT:

A because Black is an essential element that should not be separated from the rest of the clause.

C because the clause beginning with the word where is essential and should not be separated from the rest of the sentence.

D because the clause beginning with the word where is essential and should not be separated from the rest of the sentence.

Question 60. The best answer is H because Point C in Paragraph 3 is the only logical place to add information that refers to Black’s collage Seven Lamps. In the new sentence, the phrase “in this piece” clearly refers to the only piece specifically mentioned by name: Seven Lamps.

The best answer is NOT:

F because the proposed sentence refers to a specific work Black created, and no specific work is introduced until Paragraph 3. Therefore, this placement is illogical.

G because the proposed sentence refers to a specific work Black created, and no specific work is introduced until Paragraph 3. Therefore, this placement is illogical.

J because the proposed sentence would have no clear referent at Point D, and it would interrupt the flow of the narrative in Paragraph 4.

Passage V

Question 61. The best answer is D because it is the only option that does not add unnecessary and confusing punctuation.

The best answer is NOT:

A because the phrase beginning after the word than is essential and should not be separated from the rest of the clause.

B because there is no pause in thought after the word than, so the dash is unnecessary.

C because the semicolon after the word than is incorrect as it creates two sentence fragments.

Question 62. The best answer is F because it is the only option that has correct sentence structure. It uses a comma to set off the nonessential element that starts with the word blamed.

The best answer is NOT:

G because it creates a run-on sentence.

H because it creates a comma splice.

J because it creates a sentence fragment.

Question 63. The best answer is C because it provides the most logical transition to connect this sentence with the preceding one. The word However signals two opposing ideas, which is accurate here. Pigeons are first described as nuisances, but one species of pigeon is not a nuisance. Rather, it is a great navigator.

The best answer is NOT:

A because the transitional phrase “For example” should logically be followed by an example of a disease-spreading pigeon, but it is followed by an example of a valued pigeon.

B because the transitional word Similarly signals two ideas that are essentially the same, which does not occur in the two linked sentences.

D because the transitional word Thus signals a cause-effect relationship between ideas, which is not the case here.

Question 64. The best answer is H because it provides the appropriate punctuation (a comma) to set off the appositive (“the homing pigeon”).

The best answer is NOT:

F because it creates a sentence fragment.

G because it creates a sentence fragment.

J because the comma after pigeon is missing, resulting in an incorrectly subordinated sentence.

Question 65. The best answer is D because it provides the appropriate possessive pronoun for this sentence. The singular Its refers to the singular noun pigeon that appears later in the sentence.

The best answer is NOT:

A because it is an adverb, not a possessive pronoun.

B because it is a contraction, not a possessive pronoun.

C because it is a contraction, not a possessive pronoun.

Question 66. The best answer is G because it provides the most logical subordinating conjunction to introduce the dependent clause in this sentence. The conjunction Before means “during the period of time preceding a particular event.”

The best answer is NOT:

F because it is not a subordinating conjunction and so is imprecise in the context.

H because it is not a subordinating conjunction and so is imprecise in the context.

J because it is not a subordinating conjunction and so is imprecise in the context.

Question 67. The best answer is A because it provides the best explanation of the specific communication challenges the battlefield commanders faced.

The best answer is NOT:

B because the suggested revision does not clearly identify specific locations or distances.

C because the suggested revision is relevant to the discussion of “challenges in communication.”

D because the suggested revision says nothing about pigeons today.

Question 68. The best answer is J because it provides the clearest, most concise wording for this sentence and avoids redundancy.

The best answer is NOT:

F because it is redundant; returned and “came back” mean the same thing.

G because it is redundant; “coming home” and “to its home roost” mean the same thing.

H because it is redundant; “returned home” and “to its home roost” mean the same thing.

Question 69. The best answer is D because it correctly places the modifiers in the sentence. The introductory phrase refers to a bird that was one of six hundred used in World War I, so the noun immediately after that phrase must be Cher Ami, the bird to which the phrase refers.

The best answer is NOT:

A because the introductory phrase should modify Cher Ami, not Cher Ami’s twelve missions.

B because the introductory phrase should modify Cher Ami, not Cher Ami’s twelve missions.

C because the introductory phrase should modify Cher Ami, not Cher Ami’s twelve missions.

Question 70. The best answer is J because deleting the underlined portion avoids redundancy with information elsewhere in the paragraph.

The best answer is NOT:

F because it repeats information that is already given in the first sentence of the paragraph.

G because it repeats information that is already given in the second sentence of the paragraph.

H because it repeats information that is already given in the second sentence of the paragraph.

Question 71. The best answer is B because it provides the appropriate punctuation for this sentence. A colon is needed here because the sentence describes one link to headquarters and is followed by a phrase emphasizing what that link is. This construction calls for punctuation that shows the sharp break in the sentence.

The best answer is NOT:

A because the colon needed to separate the independent clause from the phrase that follows it is missing.

C because a semicolon should not be used to separate an independent clause from a phrase.

D because a comma is not the appropriate punctuation to separate the independent clause from the phrase that follows it. The phrase “homing pigeons” does not rename or describe the noun headquarters that it directly follows.

Question 72. The best answer is H because it is the only option that has correct sentence structure. It uses a subordinating conjunction (As) to introduce the introductory dependent clause, which prevents the sentence from being a comma splice.

The best answer is NOT:

F because it creates a comma splice.

G because it creates a dangling modifier. The notion that the situation became clear that the Americans were unaware of the 77th’s whereabouts is nonsensical.

J because it creates a comma splice.

Question 73. The best answer is A because it is the only option that has correct sentence structure. It uses a comma to separate the appositive phrase “the War Cross” from the rest of the sentence. The phrase “the War Cross” directly describes the noun preceding it (medal).

The best answer is NOT:

B because it creates a comma splice.

C because it creates a comma splice.

D because it creates a sentence fragment.

Question 74. The best answer is H because the expression “extent to which” is a standard English idiom. This expression is used to discuss how true a statement might be. In this case, the sentence poses the question: To what degree did Cher Ami understand what he was doing?

The best answer is NOT:

F because the phrase “extent in which” is not a standard English idiom and does not fit the context.

G because the phrase “extent of which” is not a standard English idiom.

J because the phrase “extent which” is not a standard English idiom.

Question 75. The best answer is B because it is the only option that clearly refers to an idea expressed in the first paragraph. The last two sentences in the first paragraph say that homing pigeons are “among the best navigators of the natural world” and have an extraordinary “navigational ability.” This option connects the idea of navigational skill with Cher Ami’s missions.

The best answer is NOT:

A because it is too vague to specifically connect to any of the information in the first paragraph.

C because the first paragraph never discusses heroism.

D because it is too vague to specifically connect to any of the information in the first paragraph.

MATHEMATICS • PRACTICE TEST 6 • EXPLANATORY ANSWERS

Question 1. The correct answer is E. A parallelogram consists of 2 pairs of parallel lines. Any 2 consecutive angles in the parallelogram are supplementary. Since the angle that measures and the angle that measures are adjacent, these 2 angles are supplementary, and therefore . Solving this equation by subtracting from each side shows us that . If you chose A, you may have multiplied by 4 to get . If you chose B, you may have thought the 2 angles were complementary and then added to each side instead of subtracting. If you chose C, you may have subtracted from twice instead of once. If you chose D, you may have added twice to to get .

Question 2. The correct answer is H. The retail associate’s commission was $30 on Monday, $30 on Tuesday, $70 on Wednesday, $70 on Thursday, and $70 on Friday. In order to find the total commission the associate made for these 5 days, we add these 5 values together to get . In order to find the average daily commission for these 5 days, we divide the total commission by the number of days, 5. Therefore, the associate’s average daily commission is . If you chose F, you may have found the average of $30 and $70. If you chose G, you may have found the average of $30 and $70 and then added $1. If you chose J, you may have found $54 and then added $1. If you chose K, you may have found $54 and then added $2.

Question 3. The correct answer is B. Since , the factors of 45 are 1, 3, 5, 9, 15, and 45. Since , the factors of 50 are 1, 2, 5, 10, 25, and 50. Since , the factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. So, 45, 50, and 84 share only the common factor 1. Therefore, the greatest common factor of 45, 50, and 84 is 1. If you chose A, you may have thought 45, 50, and 84 had no common factor. If you chose C, you may have considered the greatest common factor of only 50 and 84. If you chose D, you may have considered the greatest common factor of only 45 and 84. If you chose E, you may have considered the greatest common factor of only 45 and 50.

Question 4. The correct answer is J. To solve the equation , we must isolate . First, we use the distributive property to obtain the equivalent equation . Then we multiply 2 by 12 to obtain the equivalent equation . Then we add 24 to both sides to obtain the equivalent equation . Adding like terms together on both sides gives us the equivalent equation . Then we divide both sides by 3 to get . If you chose F, you may have subtracted 24 from one side and added 24 to the other side instead of adding 24 to both sides. If you chose G, you may have distributed the 2 only to the and then added 12 to one side and subtracted it from the other side instead of adding 12 to both sides. If you chose H, you may have distributed 2 to only the first term. If you chose K, you may have ignored the second in the original equation and solved the equation .

Question 5. The correct answer is A. There are 12 white buttons and 22 total buttons. Thus there are buttons that are not white. The probability of selecting 1 button that is not white is the fraction in which the numerator is the number of buttons that are not white and the denominator is the total number of buttons. Therefore, the probability of selecting 1 button that is not white is . If you chose B, you may have added the number of red buttons to the number of blue buttons and divided by the number of white buttons. If you chose C, you may have divided the number of non-white colors by the number of colors. If you chose D, you may have divided 1 by the total number of buttons. If you chose E, you may have divided 1 by the number of buttons that are not white.

Question 6. The correct answer is F. Since inch represents 12 miles, and 5 is times as long as , 5 inches represents 10(12) = 120 miles. If you chose G, you may have multiplied 12 by 5. If you chose H, you may have multiplied 12 by 5 by . If you chose J, you may have multiplied 12 by 2. If you chose K, you may have decided that all distances are represented by 12 miles.

Question 7. The correct answer is B. Since Caden started with 45 plants and had 42 plants at the end of day 1, he sold plants on day 1. Since Caden had 42 plants at the end of day 1 and 39 plants at the end of day 2, he sold plants on day 2. Since Caden had 39 plants at the end of day 2 and 36 plants at the end of day 3, he sold plants on day 3. At the end of day 6, Caden will have sold plants for 6 days. Since Caden sells 3 plants per day, he will have sold plants. Since he started with 45 plants, he will have plants left. If you chose A, you may have chosen the number of plants left at the end of day 4. If you chose C, you may have chosen the number of plants left at the end of day 7. If you chose D, you may have chosen the day. If you chose E, you may have chosen the number of plants sold each day.

Question 8. The correct answer is H. Since represents the monthly cost, and the monthly cost is $5 plus $2 per movie rented, the relationship can be modeled by .If you chose F, you may have switched the meanings of and . If you chose G, you may have switched the meanings of and and thought the cost was $2 per month and $5 per movie rented. If you chose J, you may have thought the cost was $2 per month and $5 per movie rented. If you chose K, you may have thought you had to pay the monthly cost every time a movie was rented instead of just once a month.

Question 9. The correct answer is C. We know that . According to the Zero Factor Theorem, this is only true if or . If we solve both of these equations, we find that the 2 solutions to the original equation are and .If you chose A, you may have taken the opposite of the constants in the original equation. If you chose B, D, or E, you may have solved the 2 equations incorrectly.

Question 10. The correct answer is J. The area of a rectangle can be found by multiplying its length and width. Therefore, the area of this rectangle is square inches. Since each triangle is half the area of the rectangle, the area of each triangle must be = 24 square inches. If you chose F, you may have taken the average of the 2 lengths. If you chose G, you may have multiplied 24 square inches by . If you chose H, you may have added the 2 lengths. If you chose K, you may have multiplied the 2 lengths.

Question 11. The correct answer is C. Each fraction represents a portion of the class that participated in band, chorus, football, or basketball. The sum of these fractions represents the portion of the entire class that participated in some extracurricular activity. No student participated in more than 1 activity, so there is no overlap; in other words, none of the students who played in the band also sang in the chorus, etc. To add these fractions, express them as equivalent fractions with common denominators: . The item asks for the fraction of the class who did NOT participate in any of the 4 activities, so subtract from 1 to get a difference of . An equivalent form of is . If you chose A, you may have interpreted “no student participated in more than 1 of the following extracurricular activities” in the first sentence to mean that 0 students participated in the activities. If you chose B, you multiplied all the numerators, multiplied all the denominators, and then simplified the fraction: . If you chose D, you added all the numerators and all the denominators , and then you subtracted that sum from 1 to get . If you chose E, you chose the total fraction of students who participated in any of the 4 activities.

Question 12. The correct answer is H. The set of integers consists of 0, the counting numbers , and the opposite of the counting numbers . The value of is , which is 1; the value of is , which is 4; and so on, as shown in the table:

Number, n

n²

Value of n²

3

3²

9

4

4²

16

5

5²

25

6

6²

36

7

7²

49

8

8²

64

9

9²

81

10

10²

100

The square root of 9, or , is 3 because ; the square root of 16, or , is 4 because ; and so on. The value 61 is between 49 (which is ) and 64 (which is ). Another way to express this is . If we take the square root of each value, the inequality remains true: . Further simplifying, we can write . The inequality shows that the next greatest integer than is 8. If you chose F, you may have used a calculator to evaluate , divided that number by 2, and then rounded to the nearest integer. If you chose G, you chose the greatest integer less than . If you chose J, you may have used a calculator to evaluate and rounded to the nearest 10. If you chose K, you may have divided 61 by 2 instead of finding the square root of 61. When 61 is divided by 2, the quotient is 30.5, which rounds to 31.

Question 13. The correct answer is E. The sine ratio of a nonright angle of a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse of the triangle, or . The length of the side opposite angle C is given (6 inches), and the length of the hypotenuse of the right triangle is unknown. The sine ratio at C is also given . Let be the length of the hypotenuse, and use the proportion to solve for . Cross multiplying gives us , or equivalently . Divide both sides of the equation by 2 to find the value of : , or . If you chose A, you found the square root of the difference of 3² and 2². If you chose B, you found the square root of the sum of 3² and 2². If you chose C, you found of 6. If you chose D, you found the difference of 3² and 2².

Question 14. The correct answer is H. In an arithmetic sequence, the difference between any two consecutive terms is constant. This is called the common difference. Here, the common difference between any two consecutive terms is 4: ; ; ; and . In the general expression, the common difference is the coefficient of , where is the term position. This is because every time increases by 1, the th term increases by 4. So, the general expression must include . To find the constant in the expression, find the th term for term position . The th term for term position 1 is 1. To find the th term for term position 0, subtract the common difference, 4, from 1: . The constant in the expression is . So, the general expression is . If you chose F, G, J, or K, you chose an expression that works only for the first pair of numbers in the table.

Question 15. The correct answer is D. The perimeter of any polygon is the sum of the lengths of the polygon’s sides. If we extend the sides measuring 14 feet and 8 feet, a square can be formed as shown in the following diagram. This is because there are right angles present at the corners and two consecutive sides are congruent.

Squares have 4 congruent sides. So, we know that in the following diagram.

Since , the unknown length is 6 feet. Note that this is the same length as the unknown vertical side of the polygon because the dotted figure in the following diagram is a rectangle (there are 4 right angles).

To find the unknown horizontal side of the polygon, we can use the same logic.

Because squares have 4 congruent sides, it is true that . Since , the unknown length is 12 feet.

This is the same length as the unknown horizontal side of the polygon.

Now we have all the lengths of the sides of the polygon. To find the perimeter, add the lengths: feet. If you chose A, you multiplied 20 feet by 3. If you chose B, you added only the measurements shown on the figure. If you chose C, you left out the unknown side length of the top horizontal side. If you chose E, you may have assumed that the unknown side lengths were 8 feet and 14 feet, making the perimeter .

Question 16. The correct answer is F. To find the number halfway between and , find the average of the two numbers. Add the numbers by expressing them as equivalent fractions with common denominators: . Then, divide the sum by 2: . If you chose G, you added the numerators of the fractions and multiplied the denominators of the fractions: . If you chose H, you may have correctly expressed the fractions as equivalent fractions with common denominators but found the sum of the numerators to be 15 instead of 17. If you chose J, you added the fractions by adding the numerators and denominators: . If you chose K, you may have multiplied the given fractions: .

Question 17. The correct answer is C. So far, Sherita has made of her free throws—the numerator is the number of successful free throws, and the denominator is the total number of attempts at free throws. This free-throw average is rounded to 76.7% in the item. We can verify this by dividing 46 by 60 and noting that the quotient which rounds to 76.7%. (Note that ). Now, Sherita is going to make more attempts at successful free throws to increase her free-throw average. Let be the minimum number of free throws Sherita must make from now on to have a free-throw average of 80%. Since is the additional number of successful free throws, is added to both the numerator (the number of successful free throws) and the denominator (the total number of attempts at free throws): . She wants a free-throw average of at least 80%, which can be expressed as , or . Since we want the minimum and not a range, we can use the equality . To solve for , first cross multiply: Use the distributive property to simplify: Use the addition property of equality as the first step to isolate : . Then combine like terms: . Use the multiplication property of equality to further isolate : . Then multiply: . If you chose A, you may have set up an equation equivalent to and then solved for x by cross multiplying: . You then subtracted 46 from 48. If you chose B, you may have found a decimal approximation for and multiplied by 100: . You then subtracted that from 80. If you chose D, you subtracted 46 from 60. If you chose E, you subtracted 60 from 80.

Question 18. The correct answer is G. Substitute the expression equal to for the in the expression for : . Then, use the distributive property to simplify: . Finally, combine like terms: . If you chose F, you added the expressions equal to and . If you chose H, you substituted the expression equal to for the in the expression for but did not subtract 1. If you chose J, you may have substituted only the from into the in and then added the constants from and : . You then multiplied and combined like terms to simplify to get . If you chose K, you found .

Question 19. The correct answer is A. The mean of a set of data is the sum of all the data points divided by the number of data points in the set. Data Set A has 8 numbers, so divide the sum of the numbers by 8 to find the mean: . Data Set B has 9 numbers: all the numbers of Data Set A and an additional number that is greater than 90. Assume the 9th number is 90. Then the mean of Data Set B would be , which is greater than the mean of Data Set A, 81.625. With a 9th number greater than 90, the mean of Data Set B would be greater than . (If the 9th number were 91, the mean would be ; if the 9th number were 92, the mean would be , etc.) Therefore, the mean of Data Set B is greater than the mean of Data Set A. When a data set has an even number of data points, the median is the average of the middle two data points after the data points are in order (ascending or descending). The median of Data Set A is . When a data set has an odd number of data points, the median is the middle number after the data points are in order (ascending or descending). Data Set B has an odd number of data points: the 8 numbers in Data Set A and an additional 9th number greater than 90. The 9th number could be in three different positions among the 8 Data Set A numbers in order. Let X represent the 9th number:

Position 1: 62, 76, 76, 80, 82, 87, X, 94, 96

Position 2: 62, 76, 76, 80, 82, 87, 94, X, 96

Position 3: 62, 76, 76, 80, 82, 87, 94, 96, X

Whatever position the 9th number is in, 82 is the median because it is the 5th (the middle) of 9 numbers in order. Since 82 is greater than 81, the median of Data Set B is greater than the median of Data Set A. If you chose B, you may have confused Data Set A for Data Set B, reversing the relationships between the means and medians of both sets. If you chose C, you may have assumed that since the 9th number was the last number added to the data set, it doesn’t change the mean or median of the set. If you chose D, you may have noticed that adding a number greater than 90 would change the median from 81 to 82, but you may have used the logic described for choice C for the mean. If you chose E, you may have noticed that adding a number greater than 90 would change the mean from 81.625 to a value greater than , but you may have used the logic described for choice C for the median.

Question 20. The correct answer is J. Since the truck is losing 4 fluid ounces of radiator fluid per minute and there are 60 minutes in 1 hour, the truck will lose fluid ounces per hour. The truck’s radiator holds 480 fluid ounces, so it will take hours for the tank to be empty. The truck is traveling at 35 miles per hour, so in 2 hours it will have traveled miles. If you chose F, you may have divided 480 by 35. If you chose G, you may have divided the speed of the truck by 2. If you chose H, you may have selected the speed of the truck. If you chose K, you may have divided 480 by 4.

Question 21. The correct answer is B. The midpoint of a line segment that has end points at and is . The midpoint of this segment is thus . If you chose A, you may have subtracted the value in the formula instead of adding, then forgotten to divide by 2: . If you chose C, you may have mixed up and in the formula: . If you chose D, you may have subtracted the and values in the formula instead of adding: . If you chose E, you may have subtracted the and values in the formula instead of adding, then forgotten to divide by 2: .

Question 22. The correct answer is H. A linear function has a constant rate of change, , for all points and . Because H is the only choice where the rate of change is constant for all the given points, it must be the linear function. Notice , so is the constant rate of change. If you chose F, you may not have realized that because , the function is not linear. If you chose G, you may not have realized that because , the function is not linear. If you chose J, you may not have realized that because , the function is not linear. If you chose K, you may not have realized that because , the function is not linear.

Question 23. The correct answer is A. The longest side of a triangle is opposite the largest angle, and the shortest side of a triangle is opposite the smallest angle. Since , . Since the side lengths of the sides opposite , , and are inches, inches, and inches, respectively, . If you chose B, you may have correctly realized that was shortest but incorrectly ordered and . If you chose C, you may have correctly realized that was longest but incorrectly ordered and . If you chose D, you may have known that but incorrectly thought that was shortest instead of longest. If you chose E, you may have ordered the side lengths from longest to shortest instead of shortest to longest.

Question 24. The correct answer is F. The slope of a line through points and is . The slope of this line is thus . If you chose G, you may have added the values in the formula instead of subtracting: . If you chose H, you may have added the values in the formula instead of subtracting and mixed up the numerator and denominator: . If you chose J, you may have mixed up the values in the formula: . If you chose K, you may have mixed up the numerator and denominator: .

Question 25. The correct answer is C. Let the length of the shorter side of the rectangle be centimeters. The longer side is then centimeters. The perimeter of the rectangle is then centimeters. Solving the equation below tells us that the length of the shorter side of the triangle is 8 centimeters and that of the longer side is centimeters.

If you chose A, you may have found the length of the shorter side instead of the longer side. If you chose B, you may have thought the rectangle was a square and thus the length of all sides was equal to centimeters. If you chose D, you may have divided the 2 numbers given in the stem: . If you chose E, you may have forgotten to divide by 4 in the equation above and thought that because , the length of the longer side was 32 centimeters.

Question 26. The correct answer is F. Let a be the number of adult tickets sold. Since 200 total tickets were sold, the number of student tickets sold is . Since the price of an adult ticket is $50 and a student ticket is $25, the total collected from adult and student tickets is dollars. Solving the equation below tells us that 40 adult tickets were sold and student tickets were sold.

If you selected G, you may have thought that 80 adult tickets were sold and found the number of student tickets based on this. If you selected H, you may have thought that the number of adult tickets and student tickets must be equal. If you selected J, you may have thought that 80 student tickets were sold and found the number of adult tickets based on this. If you selected K, you may have mixed up the number of adult tickets sold with the number of student tickets sold.

Question 27. The correct answer is E. 25 out of 200 tickets were sold to first-time skiers. Since , 1 out of the 8 members of the Herzog family is a first-time skier, and the other 7 are not first-time skiers. If you selected A, you may have found the number who were first-time skiers instead of the number who were not first-time skiers. If you selected B, C, or D, you may not have known to first set up the proportion to find the number of family members who were first-time skiers, then to find 8 – x to calculate the number who were not first-time skiers. You may have guessed a reasonable number of family members.

Question 28. The correct answer is H. Alyssa’s elevation in feet is . Since t is the number of seconds after she begins skiing, corresponds to the start of the main run. The corresponding E value is 3,000: . If you selected F, you may have divided 300,000 by 10,000 instead of 100. If you selected G, you may have divided 300,000 by 1,000 instead of 100. If you selected J, you may have divided 300,000 by 10. If you selected K, you may have divided 300,000 by 1 instead of dividing by 100.

Question 29. The correct answer is E. The area of square ABCD is square meters. Since the width of the rectangle is 6 meters and the area is 324 square meters, the length is found by solving the equation . The length is thus meters. If you selected A, you may have thought that the length of the rectangle must be equal to the length of ABCD. If you selected B, you may have added the length of the square to the width of the rectangle: . If you selected C, you may have divided the area by 2(6) instead of 6: . If you selected D, you may have confused area with perimeter and thought that the perimeter of ABCD was equal to the perimeter of the rectangle: .

Question 30. The correct answer is F. You get by performing the steps below.

Step 1. Plug the matrices into the equation:

Step 2. Multiply by the scalars:

Step 3. Subtract:

If you selected G, you may have found 3A – B for the first-column entries, then found A – 3B for the second-column entries: . If you selected H, you may not have multiplied matrix B by 3 and instead found 2A – B. If you selected J, you may have added 2 to the elements in matrix A and added 3 to the elements in matrix B instead of multiplying them by the scalars. You then subtracted the matrices: . If you selected K, you may have found 2A + 3B instead of 2A – 3B.

Question 31. The correct answer is B. First, add up the total times for each group. The total time for the experimental group is 9 min 40 sec or . The average time for the experimental group is sec per mouse. The total time for the control group is 10 min 35 sec or . The average time for the control group is sec per mouse. Next, find the difference in the two averages: sec. If you chose A, you may have found the difference in the times for the middle mouse (Mouse 3). If you chose C, you may have treated the minutes and seconds separately, subtracted those amounts, and then divided by the number of mice. The total minutes for each group would be 7 and 8. min. The total seconds for each group would be 160 and 155. sec. 1 min is 60 sec, and sec. Then you may have divided: 3 sec. If you chose D, you may have found the difference in the median times for the 2 groups. If you chose E, you may have made 10 min 35 sec into 9 min 135 sec for the control group. Then the difference between the groups would be 95 sec, and sec.

Question 32. The correct answer is K. Each of the 3 digits has 10 possible integer choices, 0 through 9. In order to find the number of combinations, multiply by the number of possible values for each digit: . If you chose F, you may have thought there were only 9 possible integers and that you should add: . If you chose G, you may have added: . If you chose H, you may have decreased the possible values for each successive digit: . If you chose J, you may have used only 9 possible integers instead of 10: .

Question 33. The correct answer is C. An x-intercept is where the graph crosses the x-axis or where . The number of x-intercepts on the interval may be found by counting them on the graph. Another method is to find them algebraically by solving . Sine functions are cyclic and are equal to zero whenever you take the sine of such that k is an integer. Solve . Recall that , so the only values of k that satisfy and the domain restriction are , , , , , , and . If you chose A, you may have counted the number of endpoints only. If you chose B, you may have calculated . If you chose D, you may have calculated . If you chose E, you may have calculated .

Question 34. The correct answer is J. First, find a least common denominator of , which is or 63. So . In order for to be an integer, must be divisible by 63, and since 37 is prime, the smallest positive integer value of x that will allow for that is . If you chose F, you may have used 3(7) as the least common multiple (LCM). If you chose G, you may have used 3(9) as the LCM. If you chose H, you may have used 4(9) as the LCM. If you chose K, you may have used 3(7)(9) as the LCM.

Question 35. The correct answer is D. In parallelograms, adjacent angles are supplementary. Therefore, , so . If you chose A, you may have computed . If you chose B, you may have thought that and were the same angle measure. If you chose C, you may have computed . If you chose E, you may have thought that and were the same angle measure.

Question 36. The correct answer is K. In parallelograms, opposite sides are equal in length. Therefore, , so . If you chose F, you may have computed . If you chose G, you may have computed . If you chose H, you may have computed . If you chose J, you may have computed .

Question 37. The correct answer is E. In parallelograms, the diagonals bisect each other, so E is the midpoint of segment . The coordinates for E are found using the midpoint formula: . If you chose A, B, C, or D you may have misremembered the midpoint formula. You may have computed , , , or for A, B, C, or D, respectively.

Question 38. The correct answer is K. In the parallelogram, because alternate interior angles of parallel lines are congruent; because opposite sides of a parallelogram are equal; and because alternate interior angles are congruent. Therefore, by angle-side-angle (ASA). Similar proofs by side-angle-side (SAS) or side-side-side (SSS) would yield the same result. If you chose F, G, H, or J, you may have mistaken which sides and angles are congruent.

Question 39. The correct answer is B. First, multiply the terms using the distributive property, which is sometimes called FOIL, for binomials: . Then combine the like terms: . Next, simplify the power and root term: . If you chose A, you may have computed . If you chose C, you may have computed . If you chose D, you may have computed . If you chose E, you may have computed .

Question 40. The correct answer is H. First, find the distance the engine will travel around both circles. The circumference of a circle is . The total distance is . Next, divide the distance by the rate: . If you chose F, you may have computed . If you chose G, you may have computed . If you chose J, you might have rounded up or estimated incorrectly. If you chose K, you may have computed .

Question 41. The correct answer is B. To simplify an expression with a negative fractional exponent, apply the positive of the exponent to the reciprocal of the base of the expression. Thus, . To simplify an expression with a fractional exponent, use the exponent rule . Therefore, . If you chose A, you picked the value equal to . If you chose C, you picked the value equal to . If you chose D, you picked the value equal to . If you chose E, you picked the value equal to .

Question 42. The correct answer is F. The logarithmic equation is equivalent to the exponential equation . Because and , it follows that . If you chose G, you may have thought , so that . If you chose H, you may have thought the logarithmic equation was equivalent to the equation . If you chose J, you may have thought the logarithmic equation was equivalent to the equation . If you chose K, you may have thought , so that .

Question 43. The correct answer is D. The line has an -intercept at and a -intercept at . The slope of the line passing through these intercepts is equal to . Thus, the equation of the line in slope-intercept form is given by . The only point in the options given that satisfies this equation is . If you chose A, you may have added to each of the coordinates of the point . If you chose B, you may have subtracted from each of the coordinates of the point . If you chose C, you may have added to each of the coordinates of the point . If you chose E, you picked the point that satisfies the equation .

Question 44. The correct answer is G. After the runners have started, the shortest length of time it will take for them to again be at their starting line at the same time is equal to the least common multiple of seconds and seconds. The prime factorizations of and are and . So, the least common multiple of and is . If you chose F, you picked the value that is times the sum of and : . If you chose H, you picked the value that is times the difference of and : . If you chose J, you picked the value that is times the sum of and : . If you chose K, you picked the value that is the product of and : .

Question 45. The correct answer is D. The profit function where is quadratic and attains its maximum value at the vertex of the function. Thus, the value of for which the weekly profit will be the largest is . If you chose A, you picked the value equivalent to . If you chose B, you picked the value equivalent to . If you chose C, you picked the value equivalent to . If you chose E, you picked the largest value of .

Question 46. The correct answer is H. Since , , , and are consecutive positive integers such that , it follows that . Now consider the inequality . Combining the fractions gives , or . Multiplying both sides of this new inequality by gives . Note that . Similarly, , and . Therefore, has the greatest value. If you chose F, G, J, or K, then a counterexample would be , , , and . So, , which disproves F; , which disproves G; , which disproves J; and , which disproves K.

Question 47. The correct answer is A. The area of the larger square is square feet, so the length, in feet, of the side of the larger square is feet. The ratio of the perimeters of the two squares is , so the ratio of the side lengths of the two squares is , where is the length, in feet, of the smaller square. It follows that . If you chose B, you picked the value that is the length of the larger square. If you chose C, you picked the value that is twice the length of the smaller square. If you chose D, you may have solved the equation . If you chose E, you may have solved the equation .

Question 48. The correct answer is G. Consider the inequality . Adding to all three parts of the inequality gives . Now, since , it follows that , or . Therefore, , or . Similarly, , or . Therefore, the set of all integers that satisfy the inequality is . If you chose F, you may have used on both ends of the inequality, replaced with on the lower bound of the inequality, and replaced with on the upper bound of the inequality: . If you chose H, you may have worked similarly to F but used on the left side of the inequality: . If you chose J, you may have used a lower bound of and an upper bound of . If you chose K, you may have replaced with in the inequality: .

Question 49. The correct answer is D. For the -mph wind, , so . It follows that for the -mph wind, . If you chose A, you may have computed the force the -mph wind exerts on a -square-foot flat surface: . If you chose B, you picked the value that is equivalent to . If you chose C, you may have computed the force the -mph wind exerts on a -square-foot flat surface: . If you chose E, you picked the value that is equivalent to .

Question 50. The correct answer is J. The area of the sidewalk will be square feet. The volume of concrete needed to make the sidewalk is cubic feet. The number of bags of concrete needed to make the sidewalk is , or 58 whole bags. If you chose F, you may have computed the volume of the sidewalk as and the number of bags as , or . If you chose G, you may have computed the volume of the sidewalk as as in F and the number of bags as , or . If you chose H, you may have computed the area of the sidewalk as square feet, the volume as cubic feet, and the number of bags as . If you chose K, you may have computed the area of the sidewalk as as in H, the volume as cubic feet, and the number of bags as , or .

Question 51. The correct answer is E. Let be the radius of the circle. Since is a right triangle, then and so given the approximation in the item. Let be the length of in centimeters. Again, since is a right triangle, we can apply the Pythagorean theorem , which we can rewrite as and solve using the quadratic equation and we get . The positive value is the only one that makes sense. If you chose A, you may have used and incorrectly thought , thus concluding . If you chose B, you may have found the length of the radius and assumed that was the length of the desired segment. If you chose C, you may have assumed and solved the equation . If you chose D, you may have correctly determined the length of the radius and then subtracted that from the given length of segment .

Question 52. The correct answer is J. The average of the scores is , and so the total sum is . Let highest score and lowest score; then . Thus , so the average of the highest and lowest score is . If you chose F, you may have correctly found the sum of the highest and lowest value but did not average the two. If you chose G, you may have found the average of the two given averages and . If you chose H, you may have incorrectly changed a sign when solving for the sum of the highest and lowest values, . If you chose K, you may have found the average of the original test scores plus the list of test scores after removing the highest and lowest scores.

Question 53. The correct answer is E. Both sides of the equation can be written as a power of , as follows . Since both sides of the equation have the same base, then their exponents must be equal. Hence, we need to solve , or . Factoring this quadratic equation gives , so our solutions are . If you chose A, you may have correctly determined equivalent exponents, but incorrectly factored the quadratic equation as . If you chose B, you may have determined the common base of 3, but rewritten the original equation as and solved the quadratic equation . If you chose C, you may have correctly determined equivalent exponents, but changed a sign in the quadratic equation required to solve, so you solved . If you chose D, you may have set the exponents equal to each other and solved the quadratic equation .

Question 54. The correct answer is G. There are possible outcomes from rolling 2 dice and recording the numbers that land face up: . Adding the 2 numbers gives the following list: {2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12}. The number of outcomes less than is . Thus, the probability is . If you chose K, you may have miscounted the number of outcomes less than 6 to be 13, but correctly determined the number of possible outcomes of 36 and got . If you chose J, you may have counted the number of outcomes less than or equal to 6, which is 15, and divided by the total number of outcomes for the 2 dice. If you chose H, you may have miscounted the total number of possible outcomes as 39 and counted the total number of outcomes less than or equal to 6 to get a probability of . If you chose F, you may have counted the number of possibilities for a single roll less than 6 and divided by the total number of outcomes for the 2 dice.

Question 55. The correct answer is D. Let be the amount of time, in hours, both drivers have been traveling. Louisa has driven miles and Antonio has driven miles. At the time they pass each other, they will have driven a combined miles, that is, . The solution for in this equation is 1., which is approximately hour minutes, since . Thus, they pass each other at approximately p.m. If you chose A, you may have used mph for both drivers, then solved . If you chose B, you may have found the average of the rates 68 mph and 57 mph, which is 62.5, and then divided 240 by 62.5, which gives 3.84 hours, which would convert to approximately 3 hours 50 minutes, and ignored the start time of 2:00 p.m. If you chose C, you may have calculated the time using 70 instead of 68—that is, you may have solved the equation or divided 240 by 68 to get approximately 3.529, which incorrectly thinks is 3 hours 53 minutes or 3:53 p.m. If you chose E, you may have used mph for both drivers, then solved .

Question 56. The correct answer is J. Selecting every possible pair of points from among points is by definition the combination of things taken at a time, . If you chose F, you may have thought points would give lines. If you chose G, you may have thought points taken at a time is . If you chose H, you may not have been sure how to count the number of lines and so you may have computed . If you chose K, you may have counted each line twice by counting choices for the 1st point and choices for the 2nd point, without accounting for the fact that switching points will give the same line.

Question 57. The correct answer is A. Using the given definition, manipulate the fraction to get an equivalent expression . If you chose B, you may have calculated and ignored . If you chose C, you may have calculated and ignored and the factorials. If you chose D, you may have ignored the factorials and simplified. If you chose E, you may have thought that multiplication and the factorial operation can switch order, that is, .

Question 58. The correct answer is G. Consider consecutive positive integers: , , , . It is not necessary that at least is prime, for example, . Thus, statement I may not be true. In any sequence of consecutive positive integers, exactly are even and thus divisible by the prime number ; thus, II must always be true. Last, III is not necessarily true. Consider again: Among , none is a factor of any other number in the list. If you chose F, you may have thought that at least 1 of the 4 integers is prime, since it is true for all . If you chose H, you may not have realized that any list of 4 consecutive positive integers must contain 2 even numbers. Also, you may have thought at least 1 is prime and that at least 1 of the integers is a factor of another since it is true for . If you chose J, you may have observed that I is not always true and II is always true, but you incorrectly interpreted III. If you chose K, you may have thought all 3 options are always true.

Question 59. The correct answer is E. The expanded form of is as follows: . The coefficient of is . If you chose A, you may have thought the expansion of is , and so there is no term. If you chose B, you may have thought the expansion of is , and so the coefficient of interest is 1. If you chose C, you may have thought the expansion of is , and so the coefficient of interest is 4. If you chose D, you may have thought the expansion of is , and so the coefficient of interest is 4.

Question 60. The correct answer is K. From the diagram, is a right triangle. So . By the property of supplementary angles, . In , two sides and the included angle are known, so the law of cosines will give the measure of the remaining side. Let length of guy wire. Thus, . Taking the square root of both sides gives the desired result. If you chose F, you may have incorrectly assumed and , then calculated the length of the guy wire using the law of sines, . If you chose G, you may have incorrectly assumed and , then calculated the length of the guy wire using the law of sines, . If you chose H, you may have correctly determined but incorrectly thought and then correctly applied the law of sines, . If you chose J, you may have incorrectly thought that , and then correctly used the law of cosines, .

READING • PRACTICE TEST 6 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is D because the narrator states that her mother “rises against the sun like a skyscraper” (lines 18–19).

The best answer is NOT:

A because although the narrator and her mother view a Picasso painting (lines 28–29), the narrator does not compare her mother to a Picasso painting.

B because when the narrator refers to shadow and witness, she is talking about herself, not her mother. Line 22: “I am her small shadow and witness.”

C because “a story developing behind her eyes” (lines 34–35) is the narrator’s description of something she sees in her mother rather than a comparison between her mother and something else.

Question 2. The best answer is J because after explaining that her mother took her all around Chicago, the narrator states that the city “was given to me by my mother” (line 27).

The best answer is NOT:

F because although the narrator describes traveling “from one end of the city to the other” (line 25), she does not mention her ability to do so without getting lost.

G because although the narrator notes that her mother talks about politics (lines 20–21), she does not indicate that her mother influenced city politics.

H because although the narrator refers to herself as a small shadow (line 22), she does so in the context of describing herself in relation to her mother, not in the context of her relationship to Chicago.

Question 3. The best answer is C because the narrator explains that the reason she doesn’t verify her mother’s ideas about Picasso is that “I like my mother’s version best” (lines 40–41).

The best answer is NOT:

A because there is no indication in the passage that the narrator doesn’t know which references to check; she indicates that the reason she doesn’t check them is that she prefers her mother’s anecdotes to others she might find (lines 40–41).

B because the narrator does not indicate that she believes her mother’s anecdotes are accurate; she simply prefers them (lines 40–41).

D because it contradicts the narrator’s statement that “I like my mother’s version best” (lines 40–41).

Question 4. The best answer is H because the narrator states that the answer to the question of where her parents were born “signifies nothing” (line 48) in regard to understanding the narrator and her family.

The best answer is NOT:

F because the narrator makes no reference to questions regarding how her mother may have been like the narrator’s other ancestors.

G because the narrator states that “the meaningful question would be to ask where my ancestors lived” (lines 48–49).

J because the answer to the question would provide significant information about the narrator’s background. She notes that her connection to water “comes from my mother” (line 58).

Question 5. The best answer is B because in the context of the passage, “blinding” (line 68) and “overwhelm” (line 69) serve to illustrate the sense of reverence the narrator’s mother feels for the power and beauty of the sea as she observes it.

The best answer is NOT:

A because there is no indication in the passage that the narrator’s mother felt fright in response to watching the sea; rather, it was an experience she sought out. Line 59: “She longs for a view more than anything else.”

C because there is no indication in the passage that the narrator’s mother felt regret in response to watching the sea; rather, she was drawn to the sea and went to great lengths to acquire a good view of it (lines 59–62).

D because there is no indication in the passage that the narrator’s mother experienced quietness in response to watching the sea; rather, the narrator’s use of “blinding” (line 68) and “overwhelm” (line 69) suggest a dramatic and thrilling experience.

Question 6. The best answer is H because the comparison of the narrator’s mother to water follows from the description of the mother as a nomad or one who, while able to keep a part of herself the same, is constantly moving and changing. According to the narrator, her mother is “forever moving, changing and going, yet always retaining some essential part of her being, recognizable and intact in spite of all the places she has been. In this, she is like water, not dead water but fearsomely alive” (lines 76–80). In this context, “dead” (line 79) refers to stagnant water, or water that doesn’t move and sustain life.

The best answer is NOT:

F because the narrator’s description of her mother, which is illustrated by the contrast between water that is dead and water that is alive, is evocative of movement and change, not color (lines 76–80).

G because the word “obsolete” does not relate to the contrast being made in the passage between movement and the lack of movement.

J because while “frozen” can suggest a lack of movement, “stagnant” creates a better contrast with water that is “alive.” In the context of water, “stagnant” suggests a lack of movement, to the point of being unhealthy and unable to sustain life, while “frozen” simply suggests a different state.

Question 7. The best answer is A because the last sentence of the passage is part of the narrator’s metaphor likening her mother to water (lines 81–90). In the sentence, the narrator depicts herself as a child collecting sea glass and driftwood, or what her mother leaves behind when she goes away.

The best answer is NOT:

B because the narrator does not make any reference to memory; the child in the sentence represents the narrator at the time she is writing, as an adult.

C because the sentence is not a literal explanation of what the narrator is doing but rather a metaphorical description of how she reacts when her mother goes away.

D because the sentence is not a literal description of what the narrator found as a child but rather a metaphorical description of how she reacts when her mother goes away.

Question 8. The best answer is F because traveling and moving are referenced in both passages. Passage A, lines 24–25: “We don’t have much money, but Mom takes me from one end of the city to the other, on foot, on buses.” Passage B, lines 75–79: “My mother could only become a nomad herself—forever moving, changing and going, yet always retaining some essential part of her being, recognizable and intact in spite of all the places she has been.”

The best answer is NOT:

G because Chicago is referenced in Passage A (line 11 and line 26) but not in Passage B.

H because speaking openly and boldly is referenced in Passage A (lines 20–21) but not in Passage B.

J because staying at a hotel is referenced in Passage B (lines 60–62) but not in Passage A.

Question 9. The best answer is D because in Passage B, the narrator uses language that evokes distance and tension to describe the conflicted feelings she has about her mother. Lines 81–87: “When I gaze out, I see her, my mother, always pulling away, returning and pulling away again. I drink from her, and she slips between my fingertips. She has borne me all this way. I cannot decide whether I want her to stay or go. When she is here, I wish she would leave. When she is gone, I wish she would return.”

The best answer is NOT:

A because there is no reference in either passage to lively conversation or joy experienced by the narrators. There are no examples of conversation in Passage B, and those referenced in Passage A are one-sided or brief. Lines 32–33: “‘Was he very sad?’ I ask. ‘Yes, I think he was.’”

B because there is no reference in either passage to fierce competition or debate between the narrator and her mother.

C because there is no reference in either passage to physical affection or warmth from the narrator’s mother.

Question 10. The best answer is F because both passages include information about the narrators’ mothers’ lives. Passage A, lines 9–15: “She had never been on a train before or used a telephone. She left Standing Rock to take a job in Chicago so she could help out the family during the War. She was so petrified of the new surroundings, she stayed in her seat all the way from McLaughlin, South Dakota, to Chicago, Illinois, and didn’t move once.” Passage B, lines 44–47: “Westerners ask me where my parents were born, as though the answer will enable them to glean some knowledge. The answer is Beijing and Luoyang.” Passage B, lines 53–54: “My mother’s father was from Inner Mongolia, land of desert and grassy plains.”

The best answer is NOT:

G because although in Passage A the narrator describes her mother’s height (lines 17–20), in Passage B, the narrator does not describe her mother’s physical appearance at all.

H because there is no mention in either passage of the narrator’s mother’s academic interests.

J because while in Passage B the narrator describes where her father was from (lines 50–53), there is no mention in Passage A of the narrator’s father at all, and there is no mention in either passage of the relationship between the narrator’s mother and father.

Passage II

Question 11. The best answer is B because the passage states that young diving enthusiasts “still emerge” with implements “of the former ice trade” (lines 68–71), which indicates that the action continues in the present day, long after the ice trade’s end.

The best answer is NOT:

A because the passage states that the “first comprehensive report on the ice industry of the United States was commissioned in 1879” (lines 1–3).

C because the passage indicates that this sale took place “in the year of the great ice census” (line 21), which was commissioned in 1879 (lines 1–3).

D because the passage indicates that this was the price of ice “in the year of the great ice census” (line 21), which was commissioned in 1879 (lines 1–3).

Question 12. The best answer is F because the passage states that the 1879 national census reported “an account of the great growth of the [ice] industry in the preceding ten years” (lines 9–10).

The best answer is NOT:

G because there is no indication in the passage that damaging publicity affected the natural-ice industry in this period.

H because although the passage mentions an estimated shipping cost of $1.50 per ton (line 28) the passage does not indicate whether this was considered a high price.

J because although the passage notes the decline of the natural-ice industry, it states that the decline began in “the early decades of the twentieth century” (lines 55–56).

Question 13. The best answer is B because the passage states that New York was “by far the biggest market” (lines 12–13), and it can reasonably be inferred that New York was the metropolis subsequently described as being supplied by imports and icehouses (lines 18–20).

The best answer is NOT:

A because although the passage states that there were 135 icehouses between New York and Albany (lines 17–18), the passage does not indicate that Albany was a large ice market.

C because although the passage mentions the city of Philadelphia, it is in reference to the city’s ice shortage after “unseasonably warm weather” (line 23).

D because the passage does not mention or generalize about average US cities of the 1870s.

Question 14. The best answer is F because the passage describes the fifteen-to-twenty-inch ice in Maine as “a top-quality crop” (line 26) and states that two thousand cargoes of this ice “were shipped south to New York, Philadelphia, and other more southern cities” (lines 31–32).

The best answer is NOT:

G because the passage indicates that the ice was shipped south to various locations rather than remaining in Maine to meet local demand.

H because the passage does not indicate that the ice “famine” negatively affected the 1879 Maine ice crop.

J because although the passage states that “the demand for ice rose annually” (line 34), it does not indicate that the size or quality of the ice changed in the subsequent year.

Question 15. The best answer is A because the paragraph states that the “natural-ice trade began to decline from the early decades of the twentieth century” (lines 55–56) and claims that much of the “evidence of its former vast scale rapidly disappeared” (lines 60–61) with the loss of the icehouses.

The best answer is NOT:

B because although the paragraph mentions that sparks from steam trains occasionally caused icehouses to burn down (lines 62–63), it does not suggest that the steam train signaled the demise of ice harvesting.

C because although the paragraph notes that icehouses easily caught fire (lines 62–65), this is a subordinate detail in the paragraph rather than the main idea.

D because although the paragraph states that the natural-ice industry survived into the late 1950s in remote areas (lines 56–59), this is not characterized as a short-lived revival of the industry.

Question 16. The best answer is H because the fifth paragraph describes the “impressive variety of odd implements” (lines 70–71) found in waters formerly utilized by the ice industry. The range of “many other specialist implements” (line 79) found in industry catalogs supports the inference that these were typical ice industry tools.

The best answer is NOT:

F because the paragraph does not refer to the natural-ice industry’s ability to respond rapidly to market changes.

G because the paragraph does not refer to the natural-ice industry’s ability to erect icehouses quickly.

J because the paragraph does not indicate that ice harvesting was simple work.

Question 17. The best answer is D because the passage indicates that artifacts of the natural-ice industry remain, stating that divers “still emerge from lakes and rivers clutching an impressive variety of odd implements—plows and chisels and scrapers that fell through the ice during the harvesting” (lines 69–73). The passage also notes that “one or two museums keep small displays of these tools” (lines 73–74) and that “collectors have preserved manufacturers’ catalogs” (lines 74–75).

The best answer is NOT:

A because the author does not contradict this statement elsewhere in the passage.

B because the author does not contradict this statement elsewhere in the passage.

C because the author does not contradict the statement elsewhere in the passage.

Question 18. The best answer is J because the passage states that “the biggest market was in New York, and none of its ice was manufactured artificially” (lines 12–14).

The best answer is NOT:

F because the passage states that “none of its ice was manufactured artificially” (lines 13–14).

G because the passage states that “none of its ice was manufactured artificially” (lines 13–14).

H because the passage states that “none of its ice was manufactured artificially” (lines 13–14).

Question 19. The best answer is C because the passage states that the ice harvested in Maine was “packed in hay and sawdust” (lines 30–31) to be shipped south.

The best answer is NOT:

A because the passage does not indicate that natural ice was shipped in refrigerated boxcars.

B because the passage does not indicate that natural ice was shipped in waterproof tarps.

D because the passage does not indicate that natural ice was shipped in paper and cloth.

Question 20. The best answer is J because the passage states that “The first real crisis in the natural-ice trade was caused not by competition from artificial manufacture, but by pollution” (lines 44–46).

The best answer is NOT:

F because the passage does not refer to the impact of the Great Depression on the natural-ice industry.

G because the passage does not state that weather pattern changes caused the first crisis in the natural-ice industry.

H because although the passage mentions artificial refrigeration (lines 35–36), it does not claim that artificial refrigeration caused the first crisis in the natural-ice industry.

Passage III

Question 21. The best answer is C because the passage explores the claim that dubbing is a hybrid form that incorporates the artistry of both the actor and dubber, beginning with Antonioni’s description of Romolo Costa as “a hybrid individual born out of a chemical combination” (lines 7–8). The hybrid identities of dubbers are indicated in Vairano’s account of how some dubbers were associated with particular actors. The passage describes that dubber Luca Ward considers himself “half Ward, half [Samuel L.] Jackson” (line 85). Ward conflates the identities of Meg Ryan and her dubber (lines 86–89), further emphasizing the idea of hybridity between the dubber and actor.

The best answer is NOT:

A because the passage does not describe how dubbers want to be regarded by actors.

B because the passage does not compare the work of these two dubbers.

D because although the passage indicates that Ward’s approach differs from other dubbers’ (lines 64–68), this is a detail from the passage, not the central claim.

Question 22. The best answer is G because the comparison to Fellini accurately reflects Variano’s point of view that dubbing can be useful. The passage describes how dubbing was part of Fellini’s creative process. Lines 19–20: “Dubbing was an extension of his shoots, a technique he would use to retouch and rewrite.” The passage describes how Vairano selects dubbers according to who would perform best in the particular role, which is similar to how Fellini used dubbing creatively.

The best answer is NOT:

F because the passage notes that Antonioni disapproved of dubbing. “This ‘half Clark, half Costa’ was unbearable to Antonioni, who considered dubbing to be a mere ‘acoustic surrogate’ of acting” (lines 8–10).

H because the passage notes that Pasolini also disapproved of dubbing. “Director Pier Paolo Pasolini, who called both dubbing and subtitles ‘evils’ ” (lines 13–14).

J because the passage notes that Renoir also disapproved of dubbing. “Director Jean Renoir called dubbing a ‘monstrosity, a challenge to human and divine laws’ ” (lines 16–17).

Question 23. The best answer is B because the second paragraph describes Fellini’s extensive use of dubbing. The first paragraph of the passage recounts the perspectives of directors critical of dubbing. Lines 18–20: “Director Frederico Fellini didn’t agree with any of them. Dubbing was an extension of his shoots, a technique he would use to retouch and rewrite.”

The best answer is NOT:

A because the paragraph does not relate the author’s perspective on dubbing.

C because although the passage notes that Renoir was critical of dubbing, his comments are about dubbing in general, not in reference to Fellini’s work. Lines 16–17: “Director Jean Renoir called dubbing a ‘monstrosity, a challenge to human and divine laws.’ ”

D because the paragraph’s focus on Fellini does not function to support an argument made in the first paragraph. The first paragraph presents perspectives of directors who were against the use of dubbing; this paragraph presents an opposing perspective. Lines 18–19: “Director Frederico Fellini didn’t agree with any of them.”

Question 24. The best answer is H because the anecdote mainly provides an example of how dubbing was an integral part of Fellini’s creative process.

The best answer is NOT:

F because although the passage mentions that Fellini favored the northern accent (lines 32–33), this is a detail from the anecdote rather than its main function.

G because the anecdote is unclear about whether Fellini followed a scripted dialogue in this instance. The passage notes that Fellini did not always follow a script. Lines 20–23: “He mercilessly dubbed over his actors, changing dialogue in postproduction, sometimes having worked without a script.”

J because the passage notes that Fellini did not always follow a script. Lines 20–23: “He mercilessly dubbed over his actors, changing dialogue in postproduction, sometimes having worked without a script.”

Question 25. The best answer is D because the passage makes clear that Cortesi disagrees with the author’s assumptions, offering his own explanation. Lines 44–46: “Dubbers are used to reciting while trying to re-create the bodily sensations of what they see on the screen before them.”

The best answer is NOT:

A because the passage indicates that Cortesi disagrees with the author (lines 37–43).

B because the passage indicates that Cortesi disagrees with the author (lines 37–43).

C because although the passage indicates that Cortesi disagrees with the author (lines 37–43), Cortesi’s response is not characterized as gruff.

Question 26. The best answer is G because the details in the passage suggest that the Metropolitan cinema was a place to watch subtitled films. “There are still few options for those seeking to watch subtitled, original-language films at a movie house in Italy. The Metropolitan cinema on Via del Corso closed recently after a long battle” (lines 51–52).

The best answer is NOT:

F because the passage does not indicate that the Metropolitan cinema was a place to watch dubbed films.

H because the details in the passage suggest that the Metropolitan cinema was a place to watch subtitled films only.

J because the details in the passage suggest that the Metropolitan cinema was a place to watch subtitled films.

Question 27. The best answer is A because the passage most strongly suggests that the Italian preference for dubbing correlates to finding dubbed films much more easily than subtitled films. The passage asserts that “Italians remain hooked on dubbing” (line 55), and the last two paragraphs of the passage describe a thriving dubbing industry. The passage describes the options for watching a subtitled film as “few” (line 49).

The best answer is NOT:

B because the passage notes there are “few options” (line 49) for watching subtitled films in Italy, but dubbed films remain popular (line 55).

C because the passage notes there are “few options” (line 49) for watching subtitled films in Italy, but dubbed films remain popular (line 55).

D because the passage notes there are “few options” (line 49) for watching subtitled films in Italy, but dubbed films remain popular (line 55).

Question 28. The best answer is F because in the passage, the film Bienvenue chez le Ch’tis is provided as an example of a film considered undubbable due to its comedic reliance on linguistic misunderstanding. Lines 60–63: “Francesco Vairano, a dubber and dubbing director known for adapting foreign films considered to be ‘undubbable,’ such as the French box office hit Bienvenue chez le Ch’tis (‘Welcome to the Sticks,’ 2008), which relies on linguistic misunderstandings for much of its comedy.”

The best answer is NOT:

G because there is no mention in the passage of dramatic action that advances the plot.

H because there is no mention in the passage of reverse chronology that provides context.

J because there is no mention in the passage of extensive monologues that provide further characterization.

Question 29. The best answer is B because the passage explains that Vairano uses different dubbers with different actors. Lines 64–67: “Vairano has been one of the few directors to break the habit of matching the same Italian dubber to a foreign actor for all his films.”

The best answer is NOT:

A because although the passage identifies one French film that Vairano dubbed (lines 60–61), it does not say that dubbing French films is Vairano’s focus.

C because the passage does not indicate that Vairano mostly worked with “prima donna” dubbers and even notes that Vairano “was hated by all the prima donna dubbers” (line 69).

D because there is no indication in the passage of whether Vairona thinks dialogue should be rewritten during dubbing.

Question 30. The best answer is F because “assault” is a synonym of “challenge.” The negative connotation of the word “assault” is consistent with the negative connotation of the word “monstrosity” (line 16) in the same sentence. “An assault on” can be substituted for the phrase “a challenge to” without changing the meaning of the sentence.

The best answer is NOT:

G because “a declaration of” has a different meaning than “a challenge to,” and it would not make sense in the context of the sentence.

H because although “question” can be a synonym for “challenge,” the phrase “a question for human and divine laws” would not be contextually appropriate in this sentence.

J because “an offer to” and “a challenge to” have different meanings, and it would not make sense in the context of the sentence.

Passage IV

Question 31. The best answer is B because the passage focuses on presenting information about various scientific aspects of the creation and behavior of steel.

The best answer is NOT:

A because although the passage discusses Bessemer’s process for improving steel, it does not discuss the various experiments Bessemer conducted to develop the process.

C because although the fifth paragraph (lines 47–58) addresses philosophical questions about metallurgy, these questions function as subordinate details that contribute to the main focus of the passage.

D because although both cast iron and pig iron are mentioned in the passage, they are not directly compared, and an illustration of their differences is not a central element of the passage.

Question 32. The best answer is F because the description of the initial response to Bessemer’s process helps the author establish its success and impact in the manufacturing industry. Lines 1–6: “During the Industrial Revolution, the high price of steel meant that many large engineering projects were carried out that used instead cast iron, which is brittle and prone to failure. This was why Henry Bessemer’s new process for making steel was greeted with jubilation.”

The best answer is NOT:

G because the author does not assert an opinion that Bessemer’s process was prone to failure.

H because although the author states that Bessemer was lauded as an engineer (lines 8–9), the description of the initial response to Bessemer’s process does not relate directly to his qualifications as an engineer.

J because the author does not provide specific examples of criticism that Bessemer’s new process received.

Question 33. The best answer is D because the author includes a number of details that help establish Bergmann’s credibility. His mentorship and sponsorship of Scheele, described as a great scientist, is one of these details. Lines 20–23: “He was a mentor and sponsor of Carl Wilhelm Scheele, the greatest Swedish chemist of the age and co-discoverer of oxygen.”

The best answer is NOT:

A because although the information suggests that Bergmann was a teacher as well as a scientist, that point alone does not have a clear function in the context of the passage.

B because no comparison of Bergmann and Scheele is made in the passage.

C because there is no support in the passage indicating that the information serves to provide an example of eighteenth-century scientific communities.

Question 34. The best answer is H because the passage directly states that adding oxygen to molten pig iron results in silicon being converted into light silica slag. Lines 24–29: “Oxygen, as a component of air, was the key to the Bessemer process. It offered a way of removing impurities from pig iron and adjusting its carbon content during conversion to steel. A blast of air through the molten metal turned impurities such as silicon into light silica slag.”

The best answer is NOT:

F because although the passage mentions light silica slag as a by-product of the Bessemer process (lines 28–29), it does not indicate that the slag is converted to carbon dioxide.

G because the passage indicates that carbon is released from pig iron in the form of volatile carbon dioxide (lines 30–31), not that carbon dioxide is converted into carbon.

J because the passage indicates that silicon is one of the impurities that are converted by the process and does not indicate that impurities are converted into silicon. Lines 27–29: “A blast of air through the molten metal turned impurities such as silicon into light silica slag.”

Question 35. The best answer is B because, in the context of the passage, the word “spice” (line 37), in conjunction with the word “dash” in the following sentence, is used to suggest something added to enhance something else, which is a main focus of the discussion of steel in the fourth paragraph (lines 36–46). Lines 36–37: “It was long known that steel can be improved with a spice of other elements. A dash of the metal manganese helps.”

The best answer is NOT:

A because there is no indication in the passage that elements need to be added to steel gradually to produce the desired effect.

C because there is no indication in the passage that manganese, chromium, and nickel are expensive.

D because the positive results of blending elements are discussed in the fourth paragraph (lines 36–46). The passage indicates that adding a specific proportion of chromium (lines 42–44) makes steel rust-resistant, which contradicts the idea that blending elements has not yet yielded positive results.

Question 36. The best answer is H because although the author indicates that there have been questions raised about whether metallurgy is a science or an art, he suggests his view that it is both. Lines 49–54: “In this respect, metallurgy has long retained the air of an artisan craft…it is because it is so difficult.” He includes a quote from a well-respected physicist to support his view. Lines 54–58: “According to Rodney Cotterill, a remarkable British physicist whose expertise stretched from the sciences of materials to that of the brain, ‘metallurgy is one of our most ancient arts, but is often referred to as one of the youngest sciences.’ ”

The best answer is NOT:

F because it contradicts the idea that metallurgy is both an art and a science, which the author puts forth in the fifth paragraph (lines 47–58).

G because although the author states that metallurgy is difficult, he does not do so to suggest that this is the reason why metallurgy is not considered a science. Lines 52–54: “But the reason for this empiricism is not that the science of metallurgy is trivial; it is because it is so difficult.”

J because it directly contradicts a statement by the author. Lines 52–54: “But the reason for this empiricism is not that the science of metallurgy is trivial; it is because it is so difficult.”

Question 37. The best answer is A because in comparing the behavior of materials to the study of the social sciences, the passage suggests that both require the study of a wide range of scales. Lines 64–69: “Science has trouble dealing with such a span of scales. One might regard this difficulty as akin to that in the social sciences, where social behaviour is governed by how individuals behave but also how we interact on the scale of families and neighborhoods, within entire cities, and at a national level.”

The best answer is NOT:

B because the passage does not suggest that the study of the social sciences is based on trial-and-error experimentation.

C because the passage explains that the study of the social sciences involves the study of people (lines 67–69). The passage does not suggest that the study of social sciences involves the examination of individual atoms.

D because the passage does not indicate that either field of study produces results that must be interpreted by both scientist and artists.

Question 38. The best answer is F because the paragraph as a whole describes the way various defects in the crystal structure of a metal influence its behavior, as introduced in the first sentence of the paragraph. Lines 72–74: “The mechanical properties of metals depend on how flaws in the crystal structure, called defects, move and interact.”

The best answer is NOT:

G because although the paragraph notes dislocations as the most common fault (line 77), this is a subordinate detail in the paragraph rather than the main idea.

H because the paragraph does not describe how increasing a metal’s grain size would modify its behavior.

J because although the paragraph mentions that grains may divide into crystallite mosaics (lines 85–86), this is a subordinate detail in the paragraph rather than the main idea.

Question 39. The best answer is C because “stretched” can mean “extended,” and this meaning is contextually appropriate in the description of the wide range of Cotterill’s expertise. Lines 54–57: “According to Rodney Cotterill, a remarkable British physicist whose expertise stretched from the sciences of materials to that of the brain.”

The best answer is NOT:

A because although “stretched” can mean “strained,” it is not contextually appropriate to say that “Cotterill’s expertise strained from the sciences of materials to that of the brain.”

B because although “stretched” can mean “exaggerated,” it is not contextually appropriate to say that “Cotterill’s expertise exaggerated from the sciences of materials to that of the brain.”

D because although “stretched” can mean “amplified,” it is not contextually appropriate to say that “Cotterill’s expertise amplified from the sciences of materials to that of the brain.”

Question 40. The best answer is J because the passage directly states that reducing the size of a metal’s grains can make the metal harder. Lines 86–89: “The arrest of dislocations at grain edges means that metals may be made harder by reducing the size of their grains, a useful trick for modifying their mechanical behaviour.”

The best answer is NOT:

F because the passage does not state that reducing the size of a metal’s grains can make the metal more rust-resistant.

G because the passage does not state that reducing the size of a metal’s grains can make the metal more brittle.

H because the passage does not state that reducing the size of a metal’s grain can make the metal finer.

SCIENCE • PRACTICE TEST 6 • EXPLANATORY ANSWERS

Passage I

Question 1. The best answer is A. According to the figure, 160 mg of 24-week-old oak mulch was consumed, 148 mg of 24-week-old pine bark mulch was consumed, 45 mg of 48-week-old oak mulch was consumed, and 60 mg of 48-week-old pine bark was consumed. The greatest mass consumed was of 24-week-old oak mulch. A is correct. B, C, and D are incorrect; 160 mg of 24-week-old oak mulch was consumed, which is more than any other combination of mulch and mulch age listed.

Question 2. The best answer is J. According to the figure, as mulch age increased, the consumption of cedar, cypress, and oak bar mulches increased. As mulch age increased, the consumption of oak and pine bark mulches increased and then decreased. F is incorrect; the mass of mulch consumed did not decrease for any of the types of mulches. G is incorrect; the mass of mulch consumed increased for only 3 types of mulches. H is incorrect; the mass of mulch consumed did not initially decrease for any of the types of mulches. J is correct.

Question 3. The best answer is D. In order to answer this item, the examinee must know that detritivores, and not autotrophs, obtain energy by consuming dead and decaying plant matter. According to the passage, the mulch was allowed to decay before consumption by the termites. The termites consumed decaying plant matter and are therefore detritivores. A and B are incorrect; the termites are not autotrophs. C is incorrect; the termites consumed decaying organic material. D is correct.

Question 4. The best answer is G. In order to answer this item, the examinee must know that cell walls are composed primarily of cellulose. Because the termites consume mulch, they are consuming a considerable amount of cellulose. F is incorrect; the termites are not consuming animal cells. G is correct. H is incorrect; the termites are not consuming animal cells. J is incorrect; the cell walls of the plant cells are composed primarily of cellulose, not cholesterol.

Question 5. The best answer is D. According to the figure, 100 mg of 1-week-old oak mulch was consumed, 160 mg of 24-week-old oak mulch was consumed, and approximately 45 mg of 48-week-old oak mulch was consumed. A is incorrect; more 24-week-old mulch was consumed than 1-week-old mulch. B is incorrect; more 24-week-old mulch was consumed than 48-week-old mulch. C is incorrect; less 1-week-old mulch was consumed than 24-week-old mulch. D is correct.

Question 6. The best answer is G. In order to answer this item, the examinee must know that 1 g = 1,000 mg. According to the figure, 140 mg of 48-week-old oak bark mulch was consumed.

F, H, and J are incorrect; 0.14 g of 48-week-old oak bar mulch was consumed. G is correct.

Passage II

Question 7. The best answer is B. According to the passage, Experiment 2 followed the same procedure as Experiment 1 except a different strain of Species C was used. A is incorrect; the same incubation temperatures were tested in both experiments. B is correct. C is incorrect; samples from both experiments were lyophilized, and none was transported on ice. D is incorrect; the incubation times were the same for both experiments.

Question 8. The best answer is G. According to Table 2, as the incubation temperature increased, the percent survival at 1 week decreased. At an incubation temperature of 20°C, Strain V2 had a 29% survival rate at 1 week, and at an incubation temperature of 30°C, Strain V2 had a 2% survival rate at 1 week. One would predict that at an incubation temperature of 25°C, Strain V2 would have a percent survival at 1 week between 2% and 29%. F is incorrect; the survival rate would be greater than 2%. G is correct. H and J are incorrect; the survival rate would be less than 29%.

Question 9. The best answer is A. According to Table 2, for Strain V2, the percent survival was less for the longer incubation time at temperatures of 4°C and 20°C. The percent survival was the same for both incubation times at temperatures of 30°C and 37°C. A is correct. B, C, and D are incorrect; the percent survival was the same for both incubation times at temperatures of 30°C and 37°C.

Question 10. The best answer is H. According to the passage, Strain E was studied in Experiment 1, and Strain V2 was studied in Experiment 2. The bacteria were lyophilized in both experiments. The incubation time and temperature were varied in both experiments, and the percent survival was determined. F is incorrect; the incubation time was varied in both experiments. G is incorrect; the temperature was varied in both experiments. H is correct. J is incorrect; two different strains were studied in the experiments.

Question 11. The best answer is D. According to Table 2, after 1 week, the sample incubated at 37°C had a 0% survival rate and therefore would not have been able to infect another organism. A is incorrect; the sample incubated at 4°C had a 59% survival rate. B is incorrect; the sample incubated at 20°C had a 29% survival rate. C is incorrect; the sample incubated at 30°C had a 2% survival rate. D is correct.

Question 12. The best answer is H. According to Table 1, the sample incubated at 20°C for 1 week had the highest percent survival (69%). F is incorrect; the sample incubated at 4°C for 1 week had a survival rate of 52%. G is incorrect; the sample incubated at 4°C for 1 month had a survival rate of 51%. H is correct. J is incorrect; the sample incubated at 20°C for 1 month had a survival rate of 42%.

Question 13. The best answer is B. According to Table 1, the two samples incubated at 30°C and the two samples incubated at 37°C all had percent survival rates less than 30%. The percent survival rates for the samples incubated at 4°C and 20°C were all greater than 30%. A, C, and D are incorrect; 4 samples had percent survival rates less than 30%. B is correct.

Passage III

Question 14. The best answer is G. According to the passage, of the fluids studied, water was the least dense and Fluid B was the most dense. Table 1 shows that the buoyant force on Stone X was greatest in Fluid B and lowest in water. The buoyant force on Stone X increased as the density of the fluid in which it was submerged increased. F is incorrect; the buoyant force increased. G is correct. H is incorrect; the buoyant force increased only. J is incorrect; there was a trend: the buoyant force increased.

Question 15. The best answer is B. According to Table 1, the buoyant force for Stone Y was 1.18 N in Fluid A and 1.41 N in Fluid B. The difference was 1.41 N – 1.18 N = 0.23 N. A, C, and D are incorrect; the difference was 0.23 N. B is correct.

Question 16. The best answer is H. In order to determine the effect of the cylinder’s volume on the submerged length of the cylinder, the students must vary the cylinder’s volume and measure the submerged length. F and G are incorrect; the students must use multiple cylinders with different volumes. H is correct. J is incorrect; the cylinders must have different volumes.

Question 17. The best answer is A. Based on Figure 1, as the length of the portion of the cylinder that was submerged increased, the amount of water that was displaced also increased. Figure 1 also shows that the submerged length was greatest when the cylinder was placed in water, and therefore the amount of fluid that was displaced was greatest in water. A is correct. B is incorrect; the submerged length was greater in water than in Fluid A. C and D are incorrect; a greater volume of water was displaced than Fluid A.

Question 18. The best answer is F. According to Study 1, as the density of the fluid increased, the submerged length of the cylinder decreased. The density of Fluid B was 1.50 g/cm³, and the submerged length of the cylinder in Fluid B was 4.9 cm. One would predict that if the cylinder had been placed in a container of fluid having a density of 1.60 g/cm³, the submerged length of the cylinder would have been less than 4.9 cm. F is correct. G, H, and J are incorrect; the submerged length would most likely have been less than 4.9 cm.

Question 19. The best answer is C. A stone with a volume larger than that of Stone Z would displace more water than did Stone Z. According to the passage, the buoyant force exerted on the submerged stone is equal in magnitude to the weight of the displaced fluid. Because more fluid would be displaced, the buoyant force on the new stone would be greater than the buoyant force on Stone Z. A is incorrect; in water, the buoyant force on Stone Z was 0.94 N. The buoyant force on the larger stone would be greater than 0.94 N. B is incorrect; in Fluid A, the buoyant force on Stone Z was 1.18 N. The buoyant force on the larger stone would be greater than 1.18 N. C is correct. D is incorrect; because water is less dense than Fluid A, the weight of the displaced water (and therefore the buoyant force in water) would be less than the weight of displaced Fluid A (and therefore the buoyant force in Fluid A).

Question 20. The best answer is F. According to the passage and Figure 1, the submerged length increased as density decreased. It follows that the iceberg would have the greatest submerged volume in the less dense Atlantic Ocean. F is correct. G is incorrect; submerged volume increased as fluid density decreased. H and J are incorrect; the iceberg would most likely have the greatest submerged volume in the Atlantic Ocean.

Passage IV

Question 21. The best answer is C. According to Table 1, the total volume of solution in each trial was 100 mL. As the volume of NaClO solution increased from 0 mL to 75 mL, Tf increased. When 50 mL of NaClO solution and 50 mL of NaI solution were used, Tf = 29.0°C, and when 70 mL of NaClO solution and 30 mL of NaI solution were used, Tf = 31.7°C. One would predict that repeating the experiment with 60 mL of NaClO solution and 40 mL of NaI solution would cause Tf to be between 29.0°C and 31.7°C. A and B are incorrect; Tf would be greater than 29.0°C. C is correct. D is incorrect; Tf would be less than 31.7°C.

Question 22. The best answer is F. According to Table 1, ∆T = 3.5°C for Trial 2, and ∆T = 8.6°C for Trial 6. ∆T was 5.1°C less for Trial 2 than Trial 6. The results do not support the student’s prediction. F is correct. G is incorrect; ∆T = 8.6°C for Trial 6, so the difference between Trials 2 and 6 was 5.1°C. H and J are incorrect; the results do not support the prediction. ∆T for Trial 2 was less than ∆T for Trial 6.

Question 23. The best answer is D. According to Table 1, for each trial, the sum of the volume of NaClO solution and the volume of NaI solution was equal to 100 mL. A, B, and C are incorrect; the total volume of solution used was 100 mL. D is correct.

Question 24. The best answer is H. According to Table 1, 80 mL of NaClO and 20 mL of NaI were used in Trial 6 (80 mL = 4 × 20 mL), and Tf = 30.6°C. F, G, and J are incorrect; Tf = 30.6°C in Trial 6 when the volume of NaClO (80 mL) was 4 times as great as the volume of NaI (20 mL). H is correct.

Question 25. The best answer is B. According to Figure 1, when 20 mL of NaClO solution was used, ∆T was just under 3°C. A, C, and D are incorrect; Figure 1 shows that ∆T is closest to 3°C. B is correct.

Question 26. The best answer is J. In order to answer this item, the examinee must understand how to read chemical equations. Table 1 shows that in Trial 8, 0 mL of NaI was added. According to the equation shown in the passage, NaI is a reactant in the chemical reaction. Without both reactants present, the reaction will not proceed and no heat will be generated, resulting in ∆T = 0°C. F and G are incorrect; 0 mL of NaI was added, and NaI is a reactant. H is incorrect; 100 mL of NaClO was used. J is correct.

Question 27. The best answer is B. In order to answer this item, the examinee must know that heat is absorbed during an endothermic reaction. If the reaction had been endothermic, then the reaction would have absorbed heat from the surroundings, and the temperature of the solution would have decreased. A is incorrect; as stated in the passage, heat is released in an exothermic reaction. B is correct. C and D are incorrect; the solution temperature increases when the reaction is exothermic, as is illustrated in the results of the experiment.

Passage V

Question 28. The best answer is H. According to Figure 2, at 300 MPa, the solubility of CO₂ in rhyolite magma is 2,000 ppmw at 800°C. F is incorrect; the solubility is approximately 2,350 ppmw at 700°C. G is incorrect; the solubility is approximately 2,200 ppmw at 750°C. H is correct. J is incorrect; the solubility is approximately 1,850 ppmw at 850°C.

Question 29. The best answer is C. According to Figure 3, at 750°C for a given solubility of CO₂ in rhyolite magma, the pressure increased as the weight percent of H₂O in the magma increased. When the solubility of CO₂ in rhyolite magma was 1,250 ppmw and the pressure was 300 MPa, the weight percent of H₂O in the magma was approximately 4.3%, and when the pressure was 400 MPa, the weight percent of H₂O in the magma was approximately 5.7%. One would predict that at 750°C and 350 MPa, rhyolite magma having a solubility of CO₂ equal to 1,250 ppmw would have a weight percent of H₂O between 4.3% and 5.7%. A and B are incorrect; the weight percent of H₂O in the magma would be greater than 4.0%. C is correct. D is incorrect; the weight percent of H₂O would be less than 6%.

Question 30. The best answer is J. According to Figure 1, at 1,150°C and 50 MPa, the solubility of CO₂ in basanite magma was 300 ppmw, and at 1,150°C and 125 MPa, the solubility was 1,000 ppmw. At 1,150°C and 200 MPa, the solubility of CO₂ in tholeiitic basalt magma was 700 ppmw, and at 1,150°C and 250 MPa, the solubility of CO₂ was 1,000 ppmw. The CO₂ solubilities were closest in value when basanite magma was at 125 MPa and tholeiitic basalt magma was at 250 MPa. F, G, and H are incorrect; the CO₂ solubilities for both types of magmas were 1,000 ppmw at 125 MPa for basanite magma and 250 MPa for tholeiitic basalt magma. J is correct.

Question 31. The best answer is B. According to Figure 1, at 1,150°C and 150 MPa, the solubility of CO₂ in leucite magma was 3,000 ppmw, and the solubility of CO₂ in rhyolite magma was 700 ppmw. The solubility in leucite magma was 2,300 ppmw greater. A is incorrect; the solubility is 2,300 ppmw greater in leucite magma. B is correct. C and D are incorrect; the solubility was greater in leucite magma than in rhyolite magma.

Question 32. The best answer is F. According to Figure 2, as the temperature increased from 650°C to 1,150°C, the solubility of CO₂ in rhyolite magma at 100 MPa decreased from 800 ppmw to 400 ppmw, and the solubility at 300 MPa decreased from 2,600 ppmw to 1,300 ppmw. Increasing the temperature had a lesser effect on the solubility of CO₂ at 100 MPa. F is correct. G is incorrect; the solubility decreased by only 400 ppmw, from 800 ppmw to 400 ppmw. H and J are incorrect; a greater effect was seen at 300 MPa.

Question 33. The best answer is A. According to Figure 2, at 750°C and 200 MPa, the solubility of CO₂ in rhyolite magma is 1,500 ppmw. Figure 3 shows that at 200 MPa and a CO₂ solubility of 1,500 ppmw, rhyolite magma contains 0% H₂O. A is correct. B is incorrect; rhyolite magma with 2% H₂O has a CO₂ solubility of 1,250 ppmw at 200 MPa. C is incorrect; rhyolite magma with 4% H₂O has a CO₂ solubility of 700 ppmw at 200 MPa. D is incorrect; CO₂ is insoluble in rhyolite magma with 6% H₂O at 200 MPa.

Passage VI

Question 34. The best answer is F. According to Hypothesis 1, Earth is the solar system’s central body, and other bodies move around Earth in looped orbits. Hypothesis 2 states that the Sun is the solar system’s central body, and the planets move around the Sun in elliptical orbits. F is correct. G is incorrect; Hypothesis 2 claims that the planets follow elliptical orbits around the Sun, not Earth. H and J are incorrect; Hypothesis 1 claims that the planets follow looped orbits.

Question 35. The best answer is C. According to Figure 2, as Mars loops, the distance between Earth and Mars varies. Figure 3 shows that as Earth and Mars orbit the Sun, the distance between them varies. This is fairly obvious, as they are relatively near one another on 10/01/2005 and 12/10/2005 and farther apart on 7/24/2005 and 2/26/2006. A, B, and D are incorrect; both Figures 2 and 3 imply that the distance between Earth and Mars varies. C is correct.

Question 36. The best answer is F. The top portion of Figure 3 is consistent with Hypothesis 2, showing that over time, Earth will move a greater percentage of its smaller orbit than will Mars. F is correct. G is incorrect; Earth is shown as having a smaller orbit. H and J are incorrect; the top portion is consistent with the reasoning presented in Hypothesis 2.

Question 37. The best answer is B. According to the passage, Mars appears to move retrograde when it is moving westward relative to the stars. Figure 1 shows that Mars is moving westward, and therefore retrograde, between 10/01/2005 and 12/10/2005, a period of 70 days. A, C, and D are incorrect; Mars is retrograde for 70 days. B is correct.

Question 38. The best answer is J. Figure 2 shows that Mars’s deferent is a counterclockwise circle around Earth, the central body of the solar system according to Hypothesis 1. Figure 3 shows that Mars moves in a counterclockwise circle around the Sun, the central body of the solar system according to Hypothesis 2. F and G are incorrect; according to the hypotheses, Mars moves in a counterclockwise direction around the central body of the solar system. H is incorrect; Hypothesis 1 states that Mars orbits Earth. J is correct.

Question 39. The best answer is B. According to Figure 1, the first position shown on Figure 3 corresponds to 7/24/2005, the second corresponds to 10/01/2005, and the third corresponds to 12/10/2005. On November 7, 2005, the positions of Earth and Mars would be between those found on 10/01/2005 and 12/10/2005. These positions are best illustrated by B. A is incorrect; this figure illustrates the positions of Mars in October and Earth in December. B is correct. C is incorrect; this figure illustrates the positions of Earth in October and Mars in December. D is incorrect; this figure illustrates the likely positions of Earth and Mars around April or May.

Question 40. The best answer is F. In order to answer this item, the examinee must know that Venus is closer to the Sun than is Earth. The second rule for apparent retrograde motion in Hypothesis 2 explains retrograde motion observed in a planet with an orbit smaller than Earth’s. F is correct. G is incorrect; Venus is closer to the Sun than is Earth. H and J are incorrect; Hypothesis 2 does explain why Venus occasionally appears to move retrograde.

Chapter 11:
Scoring the Additional Practice Tests

After taking the ACT practice tests 2, 3, 4, 5, or 6, you are ready to score the test to see how you did. In this chapter, you learn how to determine your raw score, convert raw scores to scale scores, compute your Composite score, determine your estimated percentile ranks for each of your scale scores, and score your practice writing test essay.

Did you know? Practice tests taken on the online platform are scored automatically, allowing you to review your performance and see important areas to focus on right away.

Assuming you already scored practice test 1 (see chapter 3), you should be familiar with the scoring procedures.

When scoring each practice test and reviewing your scores, remember that your scores on the practice tests are only estimates of the scores that you will obtain on the ACT. If your score isn’t as high as you expected, the cause could be related to any number of factors. Maybe you need to review important content and skills. Maybe you should work a little faster, or more slowly and carefully, when taking the test. Perhaps you simply weren’t doing your best work on the test. Or maybe you need to take more challenging courses to be better prepared. Keep in mind that a test score is just one indicator of your level of academic knowledge and skills. You know your own strengths and weaknesses better than anyone else, so keep them in mind as you evaluate your performance.

Scoring Your Practice Tests

For the multiple-choice tests (English, mathematics, reading, and science), the number of questions you answer correctly is called a raw score. To figure out your raw scores for the practice tests in this book count the number of correct answers for each test using the scoring keys provided in the following sections. Then you can convert your raw scores into scale scores. Scale scores are the scores that ACT reports to students, high schools, colleges, and scholarship agencies. Raw scores are converted to a common scale score to enhance score interpretation and allow comparability across different forms. After you’ve converted your raw scores for the practice tests to scale scores, you’ll want to convert your scale scores to percentile ranks. Percentile ranks, which are explained in the following pages, are useful for interpreting your scores relative to the scores of others who have taken the ACT.

If you took the optional practice writing test, use the analytic rubric in chapter 3 (pages 109–110) to evaluate your essay and estimate your writing test score. Being objective about one’s own work is difficult, and you have not had the extensive training provided to actual readers of the ACT writing test. However, it is to your advantage to read your own writing critically. Becoming your own editor helps you grow as a writer and as a reader, so it makes sense for you to evaluate your own practice essay. That having been said, it may also be helpful for you to give your practice essay to another reader to get another perspective: perhaps that of a classmate, a parent, or an English teacher, for example. To rate your essay, you and your reader should be familiar with the analytic rubric in chapter 3 and the sample essays and scoring explanations in chapter 9, and then assign your practice essay a score of 1 (low) through 6 (high) in each of the four writing domains (Ideas and Analysis, Development and Support, Organization, and Language Use and Conventions).

Your writing test should be based on two ratings, so you may either multiply your own rating times two, or sum your rating and another reader’s rating to calculate your domain scores (2–12 for each domain). Your writing test score is the average of your domain scores and will be in a range of 2–12.

Scoring Practice Test 2

Scoring the Multiple-Choice Tests

To score each of your multiple-choice practice tests, starting with the English test, follow these six steps:

STEP 1. Write a “1” in the blank for each question that you answered correctly. An example is provided in the following box:

Key

Your answer was

1.

A

–

Incorrect

2.

J

1

Correct

3.

B

1

Correct

4.

G

–

Incorrect

English ■ Scoring Key ■ Practice Test 2

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B

F

C

G

D

G

A

F

A

J

C

J

D

J

C

H

D

G

A

G

D

G

C

F

D

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

J

C

H

B

J

A

J

B

G

C

H

D

F

B

H

A

J

C

J

A

H

A

H

C

J

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

D

J

A

G

B

H

A

F

A

G

D

G

B

H

D

J

B

G

C

J

C

F

C

F

B

STEP 2. Add the numbers you entered in step 1 and write this total in the following shaded box. This is your raw score.

Number Correct (Raw Score) for:

English Test (75 questions)

STEP 3. Repeat steps 1 and 2 for the ACT mathematics, reading, and science tests using the scoring keys on the following pages.

Mathematics ■ Scoring Key ■ Practice Test 2

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

C

H

D

H

D

F

C

G

A

F

B

K

E

J

D

H

D

H

E

G

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

D

H

A

K

B

F

D

F

B

K

E

G

D

F

B

F

B

G

E

G

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

C

F

D

F

C

J

D

J

A

K

D

F

D

K

D

K

E

J

A

F

Number Correct (Raw Score) for:

Mathematics Test (60 questions)

Reading ■ Scoring Key ■ Practice Test 2

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

A

H

B

F

D

G

C

H

A

H

D

J

B

H

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

A

J

B

F

C

F

B

F

B

J

C

F

B

J

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

C

G

D

G

C

G

D

F

D

F

B

G

Number Correct (Raw Score) for:

Reading Test (40 questions)

Science ■ Scoring Key ■ Practice Test 2

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

B

G

D

H

D

J

A

G

A

H

B

G

D

H

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

A

F

D

F

C

J

B

F

D

H

B

J

C

J

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

A

J

C

H

B

G

C

G

D

F

A

F

Number Correct (Raw Score) for:

Science Test (40 questions)

STEP 4. On each of the four tests, the total number of correct responses yields a raw score. Use the conversion table on the following page to convert your raw scores to scale scores. For each of the four tests, locate and circle your raw score or the range of raw scores that includes it in the conversion table. Then, read across to either outside column of the table and circle the scale score that corresponds to that raw score. As you determine your scale scores, enter them in the blanks provided below. The highest possible scale score for each test is 36. The lowest possible scale score for any of the four tests is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

STEP 5. Compute your Composite score by averaging the four scale scores. To do this, add your four scale scores and divide the sum by 4. If the resulting number ends in a fraction, round it off to the nearest whole number. (Round down any fraction less than one-half; round up any fraction that is one-half or more.) Enter this number in the appropriate blank below. This is your Composite score. The highest possible Composite score is 36. The lowest possible Composite score is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

Composite Score (sum ÷ 4)

Scale Score Conversion Table: Practice Test 2

Scale Score

Raw Score

Scale Score

English

Mathematics

Reading

Science

36

74–75

58–60

39–40

39–40

36

35

72–73

56–57

38

38

35

34

71

54–55

37

37

34

33

69–70

53

36

36

33

32

68

51–52

34–35

–

32

31

67

49–50

33

35

31

30

66

47–48

32

34

30

29

65

46

–

33

29

28

63–64

43–45

31

32

28

27

61–62

41–42

30

31

27

26

59–60

39–40

29

29–30

26

25

57–58

37–38

28

27–28

25

24

55–56

35–36

26–27

25–26

24

23

52–54

33–34

25

23–24

23

22

50–51

32

23–24

21–22

22

21

47–49

30–31

22

20

21

20

44–46

28–29

20–21

18–19

20

19

42–43

26–27

19

17

19

18

40–41

24–25

17–18

15–16

18

17

37–39

21–23

16

14

17

16

34–36

18–20

15

12–13

16

15

31–33

15–17

13–14

11

15

14

28–30

12–14

12

10

14

13

26–27

11

10–11

9

13

12

24–25

9–10

8–9

8

12

11

21–23

7–8

7

7

11

10

18–20

6

6

6

10

9

15–17

5

5

5

9

8

13–14

4

4

4

8

7

11–12

3

–

3

7

6

8–10

–

3

–

6

5

7

2

–

2

5

4

5–6

–

2

–

4

3

3–4

1

1

1

3

2

2

–

–

–

2

1

0–1

0

0

0

1

STEP 6. Use the table on page 1014 to determine your estimated percentile ranks (percent at or below) for each of your scale scores. In the far left column of the table, circle your scale score for the English test (from page 1012). Then read across to the percentile rank column for that test; circle or put a checkmark beside the corresponding percentile rank. Use the same procedure for the other three tests (from page 1012). Using the right-hand column of scale scores for your science test and Composite scores may be easier. As you mark your percentile ranks, enter them in the blanks provided. You may also find it helpful to compare your performance with the national mean (average) score for each of the four tests and the Composite as shown at the bottom of the table.

National Norms for ACT Test Scores Reported During the 2020–2021 Reporting Year

Score

English

Math

Reading

Science

Composite

STEM

Score

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

100

99

96

94

92

91

89

88

86

84

82

79

75

71

65

60

55

49

45

41

37

32

25

19

15

11

7

3

2

1

1

1

1

1

1

1

100

99

99

98

97

96

94

93

91

88

84

79

74

70

65

61

58

54

49

42

33

21

11

4

1

1

1

1

1

1

1

1

1

1

1

1

100

98

96

94

91

89

86

84

82

80

77

74

71

66

61

55

50

44

39

34

29

24

19

14

10

5

3

1

1

1

1

1

1

1

1

1

100

99

98

97

96

95

93

92

90

88

85

82

77

71

64

58

51

45

39

32

26

19

14

10

7

4

3

1

1

1

1

1

1

1

1

1

100

99

99

98

96

95

93

90

88

85

82

78

74

70

64

59

53

47

41

35

28

22

16

10

5

2

1

1

1

1

1

1

1

1

1

1

100

99

99

98

97

96

94

92

90

87

84

80

75

70

65

60

54

48

41

33

26

18

11

5

2

1

1

1

1

1

1

1

1

1

1

1

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Mean:

20.1

20.4

21.2

20.6

20.7

20.7

SD:

7.1

5.6

6.9

5.8

5.9

5.5

Note: These national norms are the source of U.S. Ranks, for multiple-choice tests, displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 5,368,134, are based on 2018, 2019 and 2020 graduates.

Scoring Your Practice Writing Test 2 Essay

To score your practice writing test essay, follow these steps:

STEP 1. Use the guidelines from the writing test analytic rubric in chapter 3 (pages 109–110) to score your essay. Because many essays do not fit the exact description at each score point, read each description and try to determine which paragraph in the rubric best describes most of the characteristics of your essay.

STEP 2. Because your writing test domain scores are the sum of two readers’ ratings of your essay, multiply your own 1–6 rating from step 1 by 2. Or, have both you and someone else read and score your practice essay, add those ratings together, and record the total in the Domain Score column in step 3.

STEP 3. Enter your writing test domain scores in the following box:

Domain Score

Ideas and Analysis

x 2 =

Development and Support

x 2 =

Organization

x 2 =

Language Use and Conventions

x 2 =

STEP 4. Enter the sum of the second-column scores here _________.

STEP 5. Divide sum by 4† (range 2–12). This is your Writing Subject score.

†Round value to the nearest whole number. Round down any fraction less than one-half; round up any fraction that is one-half or more.

STEP 6. Use the table below to determine your estimated percentile rank (percent at or below) for your writing subject score.

National Norms for ACT Writing Scores Reported During the 2020–2021 Reporting Year

Score

Writing

12

11

10

9

8

7

6

5

4

3

2

1

100

99

99

96

90

66

51

28

15

5

2

Mean:

6.5

SD:

1.8

Note: These national norms are the source of the U.S. Ranks for the ACT Writing scores displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 2,370,670, are based on 2018, 2019 and 2020 graduates. Writing scores earned prior to September 2016 are not represented by this table.

Scoring Practice Test 3

Scoring the Multiple-Choice Tests

To score each of your multiple-choice practice tests, starting with the English test, follow these six steps:

STEP 1. Write a “1” in the blank for each question that you answered correctly. An example is provided in the following box:

Key

Your answer was

1.

A

–

Incorrect

2.

J

1

Correct

3.

B

1

Correct

4.

G

–

Incorrect

English ■ Scoring Key ■ Practice Test 3

Key

Key

Key

1.

A

26.

J

51.

A

2.

G

27.

A

52.

G

3.

C

28.

F

53.

A

4.

G

29.

C

54.

J

5.

D

30.

H

55.

D

6.

G

31.

D

56.

F

7.

B

32.

F

57.

D

8.

J

33.

C

58.

G

9.

B

34.

H

59.

B

10.

F

35.

C

60.

G

11.

D

36.

J

61.

D

12.

F

37.

D

62.

H

13.

B

38.

F

63.

C

14.

F

39.

D

64.

G

15.

A

40.

J

65.

C

16.

F

41.

B

66.

J

17.

C

42.

F

67.

A

18.

G

43.

C

68.

F

19.

A

44.

G

69.

B

20.

H

45.

C

70.

G

21.

C

46.

J

71.

B

22.

H

47.

C

72.

H

23.

A

48.

H

73.

C

24.

H

49.

C

74.

J

25.

D

50.

J

75.

B

STEP 2. Add the numbers you entered in step 1 and write this total in the following shaded box. This is your raw score.

Number Correct (Raw Score) for:

English Test (75 questions)

STEP 3. Repeat steps 1 and 2 for the ACT mathematics, reading, and science tests using the scoring keys on the following pages.

Mathematics ■ Scoring Key ■ Practice Test 3

Key

Key

Key

1.

C

21.

D

41.

A

2.

J

22.

G

42.

G

3.

E

23.

C

43.

D

4.

F

24.

H

44.

G

5.

C

25.

E

45.

D

6.

G

26.

G

46.

G

7.

B

27.

E

47.

E

8.

H

28.

F

48.

H

9.

C

29.

D

49.

D

10.

G

30.

H

50.

J

11.

C

31.

A

51.

E

12.

G

32.

J

52.

F

13.

D

33.

A

53.

B

14.

G

34.

K

54.

F

15.

D

35.

B

55.

E

16.

H

36.

F

56.

K

17.

A

37.

E

57.

A

18.

J

38.

K

58.

F

19.

C

39.

D

59.

D

20.

H

40.

H

60.

K

Number Correct (Raw Score) for:

Math Test (60 questions)

Reading ■ Scoring Key ■ Practice Test 3

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

B

H

D

F

B

F

C

J

D

F

D

F

D

G

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

C

H

A

J

A

J

B

G

D

G

C

H

A

G

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

D

J

B

H

B

G

C

F

D

F

B

J

Number Correct (Raw Score) for:

Reading Test (40 questions)

Science ■ Scoring Key ■ Practice Test 3

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

A

H

C

J

A

J

D

F

D

H

B

J

C

J

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

A

F

D

G

C

G

B

F

B

H

C

G

D

F

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

A

J

B

J

D

G

D

G

C

F

C

H

Number Correct (Raw Score) for:

Science Test (40 questions)

STEP 4. On each of the four tests, the total number of correct responses yields a raw score. Use the conversion table on the following page to convert your raw scores to scale scores. For each of the four tests, locate and circle your raw score or the range of raw scores that includes it in the conversion table. Then, read across to either outside column of the table and circle the scale score that corresponds to that raw score. As you determine your scale scores, enter them in the blanks provided below. The highest possible scale score for each test is 36. The lowest possible scale score for any of the four tests is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

STEP 5. Compute your Composite score by averaging the four scale scores. To do this, add your four scale scores and divide the sum by 4. If the resulting number ends in a fraction, round it off to the nearest whole number. (Round down any fraction less than one-half; round up any fraction that is one-half or more.) Enter this number in the appropriate blank below. This is your Composite score. The highest possible Composite score is 36. The lowest possible Composite score is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

Composite Score (sum ÷ 4)

Scale Score Conversion Table: Practice Test 3

Scale Score

Raw Score

Scale Score

English

Mathematics

Reading

Science

36

73–75

59–60

40

39–40

36

35

71–72

57–58

39

38

35

34

69–70

55–56

37–38

37

34

33

68

54

36

–

33

32

67

53

35

36

32

31

66

52

34

35

31

30

65

50–51

33

34

30

29

64

48–49

32

33

29

28

63

46–47

31

32

28

27

61–62

42–45

30

31

27

26

59–60

40–41

29

30

26

25

57–58

37–39

28

28–29

25

24

54–56

35–36

27

27

24

23

51–53

32–34

25–26

25–26

23

22

48–50

31

23–24

23–24

22

21

45–47

29–30

22

22

21

20

42–44

27–28

21

20–21

20

19

40–41

25–26

19–20

19

19

18

38–39

23–24

18

17–18

18

17

36–37

20–22

17

16

17

16

33–35

16–19

15–16

14–15

16

15

30–32

13–15

14

13

15

14

27–29

10–12

12–13

11–12

14

13

25–26

8–9

11

10

13

12

23–24

6–7

10

9

12

11

20–22

5

8–9

8

11

10

18–19

4

7

7

10

9

15–17

–

6

6

9

8

13–14

3

5

5

8

7

11–12

–

4

4

7

6

8–10

2

–

3

6

5

7

–

3

2

5

4

5–6

1

2

–

4

3

3–4

–

–

1

3

2

2

–

1

–

2

1

0–1

0

0

0

1

STEP 6. Use the table on page 1022 to determine your estimated percentile ranks (percent at or below) for each of your scale scores. In the far left column of the table, circle your scale score for the English test (from page 1020). Then read across to the percentile rank column for that test; circle or put a checkmark beside the corresponding percentile rank. Use the same procedure for the other three tests (from page 1020). Using the right-hand column of scale scores for your science test and Composite scores may be easier. As you mark your percentile ranks, enter them in the blanks provided. You may also find it helpful to compare your performance with the national mean (average) score for each of the four tests and the Composite as shown at the bottom of the table.

National Norms for ACT Test Scores Reported During the 2020–2021 Reporting Year

Score

English

Math

Reading

Science

Composite

STEM

Score

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

100

99

96

94

92

91

89

88

86

84

82

79

75

71

65

60

55

49

45

41

37

32

25

19

15

11

7

3

2

1

1

1

1

1

1

1

100

99

99

98

97

96

94

93

91

88

84

79

74

70

65

61

58

54

49

42

33

21

11

4

1

1

1

1

1

1

1

1

1

1

1

1

100

98

96

94

91

89

86

84

82

80

77

74

71

66

61

55

50

44

39

34

29

24

19

14

10

5

3

1

1

1

1

1

1

1

1

1

100

99

98

97

96

95

93

92

90

88

85

82

77

71

64

58

51

45

39

32

26

19

14

10

7

4

3

1

1

1

1

1

1

1

1

1

100

99

99

98

96

95

93

90

88

85

82

78

74

70

64

59

53

47

41

35

28

22

16

10

5

2

1

1

1

1

1

1

1

1

1

1

100

99

99

98

97

96

94

92

90

87

84

80

75

70

65

60

54

48

41

33

26

18

11

5

2

1

1

1

1

1

1

1

1

1

1

1

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Mean:

20.1

20.4

21.2

20.6

20.7

20.7

SD:

7.1

5.6

6.9

5.8

5.9

5.5

Note: These national norms are the source of U.S. Ranks, for multiple-choice tests, displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 5,368,134, are based on 2018, 2019 and 2020 graduates.

Scoring Your Practice Writing Test 3 Essay

To score your practice writing test essay, follow these steps:

STEP 1. Use the guidelines from the writing test analytic rubric in chapter 3 (pages 109–110) to score your essay. Because many essays do not fit the exact description at each score point, read each description and try to determine which paragraph in the rubric best describes most of the characteristics of your essay.

STEP 2. Because your writing test domain scores are the sum of two readers’ ratings of your essay, multiply your own 1–6 rating from step 1 by 2. Or, have both you and someone else read and score your practice essay, add those ratings together, and record the total in the Domain Score column in step 3.

STEP 3. Enter your writing test domain scores in the following box:

Domain Score

Ideas and Analysis

x 2 =

Development and Support

x 2 =

Organization

x 2 =

Language Use and Conventions

x 2 =

STEP 4. Enter the sum of the second-column scores here _________.

STEP 5. Divide sum by 4† (range 2–12). This is your Writing Subject score.

†Round value to the nearest whole number. Round down any fraction less than one-half; round up any fraction that is one-half or more.

STEP 6. Use the table below to determine your estimated percentile rank (percent at or below) for your writing subject score.

National Norms for ACT Writing Scores Reported During the 2020–2021 Reporting Year

Score

Writing

12

11

10

9

8

7

6

5

4

3

2

1

100

99

99

96

90

66

51

28

15

5

2

Mean:

6.5

SD:

1.8

Note: These national norms are the source of the U.S. Ranks for the ACT Writing scores displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 2,370,670, are based on 2018, 2019 and 2020 graduates. Writing scores earned prior to September 2016 are not represented by this table.

Scoring Practice Test 4

Scoring the Multiple-Choice Tests

To score your multiple-choice practice tests, starting with the English test, follow these six steps:

STEP 1. Write a “1” in the blank for each question that you answered correctly. An example is provided in the following box:

Key

Your answer was

1.

A

–

Incorrect

2.

J

1

Correct

3.

B

1

Correct

4.

G

–

Incorrect

English ■ Scoring Key ■ Practice Test 4

Key

Key

Key

1.

B

26.

H

51.

A

2.

F

27.

A

52.

F

3.

C

28.

J

53.

D

4.

F

29.

D

54.

G

5.

A

30.

F

55.

B

6.

J

31.

B

56.

H

7.

D

32.

H

57.

B

8.

H

33.

A

58.

G

9.

D

34.

G

59.

A

10.

J

35.

A

60.

H

11.

A

36.

F

61.

A

12.

G

37.

D

62.

G

13.

B

38.

J

63.

D

14.

H

39.

B

64.

G

15.

C

40.

J

65.

C

16.

J

41.

C

66.

F

17.

B

42.

F

67.

D

18.

H

43.

D

68.

H

19.

A

44.

H

69.

A

20.

J

45.

A

70.

J

21.

B

46.

J

71.

B

22.

F

47.

C

72.

F

23.

C

48.

H

73.

D

24.

G

49.

D

74.

F

25.

B

50.

J

75.

C

STEP 2. Add the numbers you entered in step 1 and write this total in the following shaded box. This is your raw score.

Number Correct (Raw Score) for:

English Test (75 questions)

STEP 3. Repeat steps 1 and 2 for the ACT mathematics, reading, and science tests using the scoring keys on the following pages.

Mathematics ■ Scoring Key ■ Practice Test 4

Key

Key

Key

1.

B

21.

C

41.

C

2.

G

22.

K

42.

G

3.

A

23.

A

43.

D

4.

H

24.

G

44.

K

5.

A

25.

D

45.

A

6.

G

26.

F

46.

K

7.

E

27.

C

47.

D

8.

J

28.

H

48.

F

9.

C

29.

A

49.

B

10.

H

30.

H

50.

K

11.

E

31.

C

51.

D

12.

G

32.

J

52.

J

13.

A

33.

C

53.

E

14.

K

34.

G

54.

J

15.

E

35.

A

55.

B

16.

J

36.

G

56.

G

17.

D

37.

E

57.

A

18.

G

38.

J

58.

J

19.

B

39.

C

59.

D

20.

F

40.

K

60.

K

Number Correct (Raw Score) for:

Mathematics Test (60 questions)

Reading ■ Scoring Key ■ Practice Test 4

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

A

H

D

H

B

J

A

F

C

G

C

F

A

G

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

D

G

C

F

D

J

C

F

A

H

B

G

C

J

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

B

J

B

H

B

F

A

J

C

J

A

H

Number Correct (Raw Score) for:

Reading Test (40 questions)

Science ■ Scoring Key ■ Practice Test 4

Key

Key

Key

1.

C

15.

A

29.

C

2.

H

16.

J

30.

G

3.

C

17.

C

31.

D

4.

F

18.

F

32.

J

5.

B

19.

A

33.

A

6.

H

20.

G

34.

H

7.

C

21.

B

35.

D

8.

F

22.

F

36.

F

9.

A

23.

B

37.

B

10.

H

24.

G

38.

J

11.

B

25.

D

39.

B

12.

J

26.

G

40.

F

13.

A

27.

D

14.

H

28.

J

Number Correct (Raw Score) for:

Science Test (40 questions)

STEP 4. On each of the four tests, the total number of correct responses yields a raw score. Use the conversion table on the following page to convert your raw scores to scale scores. For each of the four tests, locate and circle your raw score or the range of raw scores that includes it in the conversion table. Then, read across to either outside column of the table and circle the scale score that corresponds to that raw score. As you determine your scale scores, enter them in the blanks provided below. The highest possible scale score for each test is 36. The lowest possible scale score for any of the four tests is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

STEP 5. Compute your Composite score by averaging the four scale scores. To do this, add your four scale scores and divide the sum by 4. If the resulting number ends in a fraction, round it off to the nearest whole number. (Round down any fraction less than one-half; round up any fraction that is one-half or more.) Enter this number in the appropriate blank below. This is your Composite score. The highest possible Composite score is 36. The lowest possible Composite score is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

Composite Score (sum ÷ 4)

Scale Score Conversion Table: Practice Test 4

Scale Score

Raw Score

Scale Score

English

Mathematics

Reading

Science

36

73–75

59–60

39–40

39–40

36

35

71–72

56–58

38

38

35

34

70

54–55

37

37

34

33

69

53

36

36

33

32

68

52

34–35

35

32

31

67

50–51

33

34

31

30

66

49

32

–

30

29

65

47–48

31

33

29

28

64

44–46

30

32

28

27

62–63

42–43

29

31

27

26

61

39–41

28

30

26

25

58–60

37–38

27

28–29

25

24

55–57

35–36

26

27

24

23

52–54

33–34

24–25

25–26

23

22

50–51

31–32

23

24

22

21

47–49

30

21–22

22–23

21

20

44–46

28–29

20

21

20

19

42–43

26–27

19

19–20

19

18

40–41

24–25

17–18

18

18

17

38–39

20–23

16

16–17

17

16

35–37

17–19

15

15

16

15

32–34

13–16

13–14

13–14

15

14

29–31

10–12

12

12

14

13

26–28

8–9

11

10–11

13

12

24–25

6–7

9–10

9

12

11

21–23

5

8

8

11

10

17–20

4

7

7

10

9

15–16

–

6

6

9

8

13–14

3

5

5

8

7

10–12

–

4

4

7

6

8–9

2

–

3

6

5

6–7

–

3

–

5

4

5

1

2

2

4

3

3–4

–

–

1

3

2

2

–

1

–

2

1

0–1

0

0

0

1

STEP 6. Use the table on page 1030 to determine your estimated percentile ranks (percent at or below) for each of your scale scores. In the far left column of the table, circle your scale score for the English test (from page 1028). Then read across to the percentile rank column for that test; circle or put a checkmark beside the corresponding percentile rank. Use the same procedure for the other four tests (from page 1028). Using the right-hand column of scale scores for your science test and Composite scores may be easier. As you mark your percentile ranks, enter them in the blanks provided. You may also find it helpful to compare your performance with the national mean (average) score for each of the five tests and the Composite as shown at the bottom of the table.

National Norms for ACT Test Scores Reported During the 2020–2021 Reporting Year

Score

English

Math

Reading

Science

Composite

STEM

Score

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

100

99

96

94

92

91

89

88

86

84

82

79

75

71

65

60

55

49

45

41

37

32

25

19

15

11

7

3

2

1

1

1

1

1

1

1

100

99

99

98

97

96

94

93

91

88

84

79

74

70

65

61

58

54

49

42

33

21

11

4

1

1

1

1

1

1

1

1

1

1

1

1

100

98

96

94

91

89

86

84

82

80

77

74

71

66

61

55

50

44

39

34

29

24

19

14

10

5

3

1

1

1

1

1

1

1

1

1

100

99

98

97

96

95

93

92

90

88

85

82

77

71

64

58

51

45

39

32

26

19

14

10

7

4

3

1

1

1

1

1

1

1

1

1

100

99

99

98

96

95

93

90

88

85

82

78

74

70

64

59

53

47

41

35

28

22

16

10

5

2

1

1

1

1

1

1

1

1

1

1

100

99

99

98

97

96

94

92

90

87

84

80

75

70

65

60

54

48

41

33

26

18

11

5

2

1

1

1

1

1

1

1

1

1

1

1

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Mean:

20.1

20.4

21.2

20.6

20.7

20.7

SD:

7.1

5.6

6.9

5.8

5.9

5.5

Note: These national norms are the source of U.S. Ranks, for multiple-choice tests, displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 5,368,134, are based on 2018, 2019 and 2020 graduates.

Scoring Your Practice Writing Test 4 Essay

To score your practice writing test essay, follow these steps:

STEP 1. Use the guidelines from the writing test analytic rubric in chapter 3 (pages 109–110) to score your essay. Because many essays do not fit the exact description at each score point, read each description and try to determine which paragraph in the rubric best describes most of the characteristics of your essay.

STEP 2. Because your writing test domain scores are the sum of two readers’ ratings of your essay, multiply your own 1–6 rating from step 1 by 2. Or, have both you and someone else read and score your practice essay, add those ratings together, and record the total in the Domain Score column in step 3.

STEP 3. Enter your writing test domain scores in the following box:

Domain Score

Ideas and Analysis

x 2 =

Development and Support

x 2 =

Organization

x 2 =

Language Use and Convention

x 2 =

STEP 4. Enter the sum of the second-column scores here _________.

STEP 5. Divide sum by 4† (range 2–12). This is your Writing Subject score.

†Round value to the nearest whole number. Round down any fraction less than one-half; round up any fraction that is one-half or more.

STEP 6. Use the table below to determine your estimated percentile rank (percent at or below) for your writing subject score.

National Norms for ACT Writing Scores Reported During the 2020–2021 Reporting Year

Score

Writing

12

11

10

9

8

7

6

5

4

3

2

1

100

99

99

96

90

66

51

28

15

5

2

Mean:

6.5

SD:

1.8

Note: These national norms are the source of the U.S. Ranks for the ACT Writing scores displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 2,370,670, are based on 2018, 2019 and 2020 graduates. Writing scores earned prior to September 2016 are not represented by this table.

Scoring Practice Test 5

Scoring the Multiple-Choice Tests

To score each of your multiple-choice practice tests, starting with the English test, follow these steps:

STEP 1. Write a “1” in the blank for each question that you answered correctly. An example is provided in the following box:

Key

Your answer was

1.

A

Incorrect

2.

J

1

Correct

3.

B

1

Correct

4.

G

Incorrect

English ■ Scoring Key ■ Practice Test 5

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

C

H

D

G

D

J

B

H

C

F

A

J

D

H

B

J

A

G

A

H

A

J

C

F

B

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

J

D

H

B

G

A

H

C

J

D

F

A

F

D

G

C

H

B

H

A

G

A

J

D

H

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

B

J

B

F

B

F

C

H

D

G

B

F

A

H

A

F

C

J

B

G

D

J

A

H

C

STEP 2. Add the numbers you entered in step 1 and write this total in the following shaded box. This is your raw score.

Number Correct (Raw Score) for:

English test (75 questions)

STEP 3. Repeat steps 1 and 2 for the ACT mathematics, reading, and science tests using the scoring keys on the following pages.

Mathematics ■ Scoring Key ■ Practice Test 5

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

D

H

C

J

A

H

D

H

B

G

A

G

C

F

C

K

A

K

A

G

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

D

J

E

H

C

H

D

J

B

K

C

H

B

K

E

G

C

F

A

K

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

E

F

A

J

D

K

A

K

D

G

D

H

B

G

D

K

B

F

D

G

Number Correct (Raw Score) for:

Math test (60 questions)

Reading ■ Scoring Key ■ Practice Test 5

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

B

F

D

J

B

H

A

J

D

H

D

J

D

H

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

B

H

C

J

C

F

D

H

A

F

B

J

A

G

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

C

H

B

F

D

G

C

F

A

H

A

G

Number Correct (Raw Score) for:

Reading test (40 questions)

Science ■ Scoring Key ■ Practice Test 5

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

B

J

A

H

A

H

D

J

C

H

D

F

B

H

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

B

G

C

J

A

F

C

F

D

F

B

G

C

F

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

B

G

A

H

D

J

C

H

B

G

C

J

Number Correct (Raw Score) for:

Science test (40 questions)

STEP 4. On each of the four tests, the total number of correct responses yields a raw score. Use the conversion table on the following page to convert your raw scores to scale scores. For each of the four tests, locate and circle your raw score or the range of raw scores that includes it in the conversion table. Then, read across to either outside column of the table and circle the scale score that corresponds to that raw score. As you determine your scale scores, enter them in the blanks provided below. The highest possible scale score for each test is 36. The lowest possible scale score for any of the four tests is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

STEP 5. Compute your Composite score by averaging the four scale scores. To do this, add your four scale scores and divide the sum by 4. If the resulting number ends in a fraction, round it off to the nearest whole number. (Round down any fraction less than one-half; round up any fraction that is one-half or more.) Enter this number in the appropriate blank below. This is your Composite score. The highest possible Composite score is 36. The lowest possible Composite score is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

Composite Score (sum ÷ 4)

Scale Score Conversion Table: Practice Test 5

Scale Score

Raw Score

Scale Score

English

Mathematics

Reading

Science

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

73–75

71–72

69–70

68

67

66

65

64

63

61–62

60

57–59

55–56

52–54

49–51

46–48

43–45

41–42

40

37–39

34–36

30–33

27–29

25–26

23–24

20–22

17–19

14–16

12–13

10–11

8–9

6–7

5

3–4

2

0–1

59–60

57–58

56

54–55

53

52

50–51

48–49

45–47

42–44

39–41

36–38

34–35

32–33

30–31

29

27–28

24–26

22–23

19–21

15–18

12–14

9–11

7–8

6

5

4

3

–

2

–

–

1

–

–

0

40

38–39

37

36

35

34

33

32

31

30

29

28

27

26

24–25

23

21–22

20

19

17–18

16

14–15

13

11–12

9–10

8

7

6

5

4

–

3

2

–

1

0

39–40

38

37

36

35

34

33

32

31

30

29

27–28

25–26

24

22–23

20–21

19

17–18

16

14–15

13

12

10–11

9

8

7

6

5

4

–

3

2

–

1

–

0

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

STEP 6. Use the table on page 1038 to determine your estimated percentile ranks (percent at or below) for each of your scale scores. In the far left column of the table, circle your scale score for the English test (from page 1036). Then read across to the percentile rank column for that test; circle or put a checkmark beside the corresponding percentile rank. Use the same procedure for the other three tests (from page 1036). Using the right-hand column of scale scores for your science test and Composite scores may be easier. As you mark your percentile ranks, enter them in the blanks provided. You may also find it helpful to compare your performance with the national mean (average) score for each of the four tests and the Composite as shown at the bottom of the table.

National Norms for ACT Test Scores Reported During the 2020–2021 Reporting Year

Score

English

Math

Reading

Science

Composite

STEM

Score

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

100

99

96

94

92

91

89

88

86

84

82

79

75

71

65

60

55

49

45

41

37

32

25

19

15

11

7

3

2

1

1

1

1

1

1

1

100

99

99

98

97

96

94

93

91

88

84

79

74

70

65

61

58

54

49

42

33

21

11

4

1

1

1

1

1

1

1

1

1

1

1

1

100

98

96

94

91

89

86

84

82

80

77

74

71

66

61

55

50

44

39

34

29

24

19

14

10

5

3

1

1

1

1

1

1

1

1

1

100

99

98

97

96

95

93

92

90

88

85

82

77

71

64

58

51

45

39

32

26

19

14

10

7

4

3

1

1

1

1

1

1

1

1

1

100

99

99

98

96

95

93

90

88

85

82

78

74

70

64

59

53

47

41

35

28

22

16

10

5

2

1

1

1

1

1

1

1

1

1

1

100

99

99

98

97

96

94

92

90

87

84

80

75

70

65

60

54

48

41

33

26

18

11

5

2

1

1

1

1

1

1

1

1

1

1

1

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Mean:

20.1

20.4

21.2

20.6

20.7

20.7

SD:

7.1

5.6

6.9

5.8

5.9

5.5

Note: These national norms are the source of U.S. Ranks, for multiple-choice tests, displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 5,368,134, are based on 2018, 2019 and 2020 graduates.

Scoring Your Practice Writing Test 5 Essay

To score your practice writing test essay, follow these steps:

STEP 1. Use the guidelines from the writing test analytic rubric in chapter 3 (pages 109–110) to score your essay. Because many essays do not fit the exact description at each score point, read each description and try to determine which paragraph in the rubric best describes most of the characteristics of your essay.

STEP 2. Because your writing test domain scores are the sum of two readers’ ratings of your essay, multiply your own 1–6 rating from step 1 by 2. Or, have both you and someone else read and score your practice essay, add those ratings together, and record the total in the Domain Score column in step 3.

STEP 3. Enter your writing test domain scores in the following box.

Domain Score

Ideas and Analysis

× 2 =

Development and Support

× 2 =

Organization

× 2 =

Language Use and Convention

× 2 =

STEP 4. Enter the sum of the second-column scores here _________.

STEP 5. Divide sum by 4† (range 2–12). This is your Writing Subject score.

†Round value to the nearest whole number. Round down any fraction less than one-half; round up any fraction that is one-half or more.

STEP 6. Use the table below to determine your estimated percentile rank (percent at or below) for your writing subject score.

National Norms for ACT Writing Scores Reported During the 2020–2021 Reporting Year

Score

Writing

12

11

10

9

8

7

6

5

4

3

2

1

100

99

99

96

90

66

51

28

15

5

2

Mean:

6.5

SD:

1.8

Note: These national norms are the source of the U.S. Ranks for the ACT Writing scores displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 2,370,670, are based on 2018, 2019 and 2020 graduates. Writing scores earned prior to September 2016 are not represented by this table.

Scoring Practice Test 6

Scoring Your Multiple-Choice Practice Tests

To score your multiple-choice practice tests, follow these eight steps:

STEP 1. Write a “1” in the blank for each English test question that you answered correctly. An example is provided in the box below:

Key

Your answer was

1.

A

Incorrect

2.

J

1

Correct

3.

B

1

Correct

4.

G

Incorrect

English ■ Scoring Key ■ Practice Test 6

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

C

H

B

H

C

F

A

G

A

H

D

G

B

J

A

J

C

F

A

F

B

J

B

H

A

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

J

A

H

D

G

D

G

B

J

D

G

C

F

C

F

A

F

B

F

C

F

A

F

B

G

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66.

67.

68.

69.

70.

71.

72.

73.

74.

75.

D

J

A

G

D

J

C

J

B

H

D

F

C

H

D

G

A

J

D

J

B

H

A

H

B

STEP 2. Add the numbers you entered in step 1 and write this total in the following shaded box. This is your raw score.

Number Correct (Raw Score) for:

Total Number Correct for English Test (75 questions)

STEP 3. Repeat Steps 1 and 2 for the ACT mathematics, reading, and science tests using the scoring keys on the following pages.

Mathematics ■ Scoring Key ■ Practice Test 6

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

E

H

B

J

A

F

B

H

C

J

C

H

E

H

D

F

C

G

A

J

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

B

H

A

F

C

F

E

H

E

F

B

K

C

J

D

K

E

K

B

H

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

B

F

D

G

D

H

A

G

D

J

E

J

E

G

D

J

A

G

E

K

Number Correct (Raw Score) for:

Total Number Correct for Math Test (60 questions)

Reading ■ Scoring Key ■ Practice Test 6

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

D

J

C

H

B

H

A

F

D

F

B

F

B

F

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

A

H

D

J

C

J

C

G

B

H

D

G

A

F

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

B

F

B

F

D

H

B

H

A

F

C

J

Number Correct (Raw Score) for:

Total Number Correct for Reading Test (40 questions)

Science ■ Scoring Key ■ Practice Test 6

Key

Key

Key

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

A

J

D

G

D

G

B

G

A

H

D

H

B

G

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

B

H

A

F

C

F

C

F

D

H

B

J

B

H

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

C

J

B

F

A

F

C

F

B

J

B

F

Number Correct (Raw Score) for:

Total Number Correct for Science Test (40 questions)

STEP 4. On each of the four tests, the total number of correct responses yields a raw score. Use the conversion table on the following page to convert your raw scores to scale scores. For each of the four tests, locate and circle your raw score or the range of raw scores that includes it in the conversion table. Then, read across to either outside column of the table and circle the scale score that corresponds to that raw score. As you determine your scale scores, enter them in the blanks provided below. The highest possible scale score for each test is 36. The lowest possible scale score for any of the four tests is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

STEP 5. Compute your Composite score by averaging the four scale scores. To do this, add your four scale scores and divide the sum by 4. If the resulting number ends in a fraction, round it off to the nearest whole number. (Round down any fraction less than one-half; round up any fraction that is one-half or more.) Enter this number in the appropriate blank below. This is your Composite score. The highest possible Composite score is 36. The lowest possible Composite score is 1.

Your Scale Scores

English

Mathematics

Reading

Science

Sum of Scores

Composite Score (sum ÷ 4)

Scale Score Conversion Table: Practice Test 6

Scale Score

Raw Score

Scale Score

English

Mathematics

Reading

Science

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

73–75

70–72

69

68

67

66

65

64

62–63

61

59–60

57–58

54–56

51–53

49–50

46–48

43–45

41–42

40

38–39

35–37

31–34

29–30

27–28

24–26

21–23

18–20

16–17

13–15

11–12

9–10

7–8

5–6

4

2–3

0–1

58–60

56–57

54–55

52–53

51

50

48–49

46–47

44–45

41–43

38–40

36–37

34–35

32–33

30–31

29

28

26–27

24–25

21–23

18–20

14–17

11–13

9–10

7–8

6

5

4

3

–

2

–

1

–

–

0

39–40

38

37

36

35

–

34

33

32

31

30

29

28

26–27

25

24

22–23

21

20

18–19

17

15–16

14

12–13

11

9–10

8

7

6

5

4

3

–

2

1

0

39–40

38

–

37

36

–

35

34

33

32

31

29–30

27–28

25–26

23–24

21–22

19–20

18

16–17

14–15

13

12

10–11

9

8

7

6

5

4

–

3

2

–

1

–

0

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

STEP 6. Use the table on page 1046 to determine your estimated percentile ranks (percent at or below) for each of your scale scores. In the far left column of the table, circle your scale score for the English test (from page 1044). Then read across to the percentile rank column for that test; circle or put a checkmark beside the corresponding percentile rank. Use the same procedure for the other three tests (from page 1044). Using the right-hand column of scale scores for your science test and Composite scores may be easier. As you mark your percentile ranks, enter them in the blanks provided. You may also find it helpful to compare your performance with the national mean (average) score for each of the four tests and the Composite as shown at the bottom of the table.

National Norms for ACT Test Scores Reported During the 2020–2021 Reporting Year

Score

English

Math

Reading

Science

Composite

STEM

Score

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

100

99

96

94

92

91

89

88

86

84

82

79

75

71

65

60

55

49

45

41

37

32

25

19

15

11

7

3

2

1

1

1

1

1

1

1

100

99

99

98

97

96

94

93

91

88

84

79

74

70

65

61

58

54

49

42

33

21

11

4

1

1

1

1

1

1

1

1

1

1

1

1

100

98

96

94

91

89

86

84

82

80

77

74

71

66

61

55

50

44

39

34

29

24

19

14

10

5

3

1

1

1

1

1

1

1

1

1

100

99

98

97

96

95

93

92

90

88

85

82

77

71

64

58

51

45

39

32

26

19

14

10

7

4

3

1

1

1

1

1

1

1

1

1

100

99

99

98

96

95

93

90

88

85

82

78

74

70

64

59

53

47

41

35

28

22

16

10

5

2

1

1

1

1

1

1

1

1

1

1

100

99

99

98

97

96

94

92

90

87

84

80

75

70

65

60

54

48

41

33

26

18

11

5

2

1

1

1

1

1

1

1

1

1

1

1

36

35

34

33

32

31

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Mean:

20.1

20.4

21.2

20.6

20.7

20.7

SD:

7.1

5.6

6.9

5.8

5.9

5.5

Note: These national norms are the source of U.S. Ranks, for multiple-choice tests, displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 5,368,134, are based on 2018, 2019 and 2020 graduates.

Scoring Your Practice Writing Test 6 Essay

To score your practice writing test essay, follow these steps:

STEP 1. Use the guidelines from the writing test analytic rubric in chapter 3 (pages 109–110) to score your essay. Because many essays do not fit the exact description at each score point, read each description and try to determine which paragraph in the rubric best describes most of the characteristics of your essay.

STEP 2. Because your writing test domain scores are the sum of two readers’ ratings of your essay, multiply your own 1–6 rating from step 1 by 2. Or, have both you and someone else read and score your practice essay, add those ratings together, and record the total in the Domain Score column in step 3.

STEP 3. Enter your writing test domain scores in the following box.

Domain Score

Ideas and Analysis

× 2 =

Development and Support

× 2 =

Organization

× 2 =

Language Use and Convention

× 2 =

STEP 4. Enter the sum of the second-column scores here _________.

STEP 5. Divide sum by 4† (range 2–12). This is your Writing test score.

†Round value to the nearest whole number. Round down any fraction less than one-half; round up any fraction that is one-half or more.

STEP 6. Use the table below to determine your estimated percentile rank (percent at or below) for your Writing test score.

National Norms for ACT Writing Scores Reported During the 2020–2021 Reporting Year

Score

Writing

12

11

10

9

8

7

6

5

4

3

2

1

100

99

99

96

90

66

51

28

15

5

2

Mean:

6.5

SD:

1.8

Note: These national norms are the source of the U.S. Ranks for the ACT Writing scores displayed on ACT reports during the 2020–2021 reporting year.

These norms, with a sample size of 2,370,670, are based on 2018, 2019 and 2020 graduates. Writing scores earned prior to September 2016 are not represented by this table.

Chapter 12:
Interpreting Your ACT Test Scores and Ranks

After taking any test, students are eager to see how they’ve done. Assuming you took and scored ACT practice test 1 in chapter 3 or took other practice tests in chapter 10 and scored them in chapter 11, you have a great deal of information to consider when determining how well you did.

Raw scores: ACT does not provide raw scores, but you have raw scores for the practice tests in this book.

Scale scores are the scores that ACT reports to students, high schools, colleges, and scholarship agencies.

Composite score is a scale score that reflects your overall performance on all of the multiple choice tests—English, math, reading, and science.

Ranks indicate the approximate percentage of ACT-tested students who scored at or below each of your scores; for example, if your mathematics rank is 85%, then you scored as well as or better than 85% of the other students who took the mathematics test.

If you take the ACT you receive the ACT Student Report, which includes scale scores, the Composite score, and the rank for each score. You can visit www.act.org to view samples of this report as well as the High School and College reports.

In this chapter, we explain how to interpret your scores and use them as a tool to help inform your education and career decisions. We encourage you to look at your ACT test scores and ranks with additional information to help guide your future education and career planning.

Understanding Your ACT Test Results

Your scores, Composite score, and ranks provide a good indication of how well you did on the test, but you can interpret these scores on a deeper level to find out more about how well prepared you are to tackle a certain course of studies or pursue a specific career. In the following sections, we help you put your scores and ranks in perspective to make them more meaningful and relevant to your education and career planning.

How ACT Scores Your Multiple-Choice Tests

ACT scores the multiple-choice tests the same way you scored your ACT practice tests in chapters 3 and 11. The first step is to do exactly what you did for your practice tests: count the number of questions you answered correctly to determine your raw score. No points are deducted for incorrect answers.

The raw score is converted to a scale score to enhance score interpretation and allow comparability across different forms. Scale scores range from 1 (low) to 36 (high) for each of the four individual tests and for the Composite score, which is the average of the four test scores.

How ACT Scores Your Writing Test

Two trained readers score each writing test based on the analytic rubric presented on pages 109–110. Each reader scores your essay on a scale from 1 (low) to 6 (high) on each domain. If their scores differ by more than 1 point on any of the four domains, a third reader scores your essay to resolve the discrepancy. This method is designed to be as impartial as possible. The writing score is calculated from your domain scores and is reported on a 2-to-12 scale.

Recognizing That Test Scores Are Estimates of Educational Achievement

No test, including the ACT, is an exact measure of your educational achievement. We estimate the amount of imprecision using the “standard error of measurement.” On the ACT, the standard error of measurement (SEM) is 2 points for each of the multiple-choice tests, 1 point for the writing test, and 1 point for the Composite score.

Because no test score is an exact measure of your achievement, think of each of your ACT scores as a range of scores rather than as a precise number. The SEM can be used to estimate ranges for your scores. To do this, just add the SEM to, and subtract it from, each of your scores. For example, if your score on the English test is 22, your true achievement is likely in the score range of 20 to 24 (22 plus or minus 2 points). Beginning with the September 2020 national test date, students who have taken the ACT test more than once will have a Superscore calculated on their behalf by ACT. Superscoring allows students to utilize their highest individual section scores across all of their test events for ACT to calculate the best possible Composite score. Students will have the option to send an individual full battery Composite score or a Superscore to colleges or scholarship agencies.

Using Ranks to Interpret Your Scores

The US and state ranks for a score tell you how your scores compare to those earned by recent high school graduates who took the ACT. The numbers indicate the cumulative percent of students who scored at or below a given score. For example, if your rank is 63%, then 63% of recent high school graduates who took the ACT scored at or below your score.

Comparing Your Test Scores to Each Other

Another way to interpret your ACT test scores is by comparing them to each other using the ranks. You may find it interesting, for example, to compare your ranks for the science and mathematics tests to your ranks for the reading and English tests. Perhaps you felt more comfortable and successful in some subject areas than in others. Making comparisons among your ACT test ranks can be especially helpful as you make decisions about the courses you will take in high school and college. A high rank in a particular area indicates that you compare well to other ACT test-takers in that subject. A low rank may indicate that you need to develop your skills more in that area.

Keep in mind, however, that scale scores from the different individual tests can’t be directly compared to each other. Scoring 23 on the ACT English and mathematics tests, for example, doesn’t necessarily mean that your levels of skill and knowledge in English are the same as they are in mathematics. The percentile ranks corresponding to the scores—not the scores themselves—are probably best for making comparisons among subject areas.

Comparing Your Scores and Ranks to Your High School Grades

After you take the ACT and receive your student report, compare your scores and ranks to your high school grades. Are your highest grades and highest ACT test scores and ranks in the same content areas? If so, you might want to consider college majors that would draw on your areas of greatest strength or seek to improve your knowledge and skills in weaker subject areas. However, if your grades and scores differ significantly, talk with your counselor about possible reasons for the differences.

Comparing Your Scores to Those of Enrolled First-Year College Students

Another way to understand your ACT test scores and ranks is by comparing them to those of students enrolled at colleges or universities you’re interested in attending. This information can be very useful as you make decisions about applying for college. Keep in mind that admissions offices use a number of measures—including high school grades, recommendations, and extracurricular activities—to determine how students are likely to perform at their schools. Still, knowing that your ACT test scores are similar to those of students already enrolled at a college or university you’re considering may make you more confident in applying for admission there.

Using ACT College and Career Readiness Standards to Help You Understand Your ACT Scores

After you calculate your scores, you may wonder what your test scores mean regarding how well you are prepared to tackle college-level courses. In other words, what do your test scores tell you about your knowledge and skills in English, math, reading, and science? One way to understand this is to consider your scores from the perspective of what students who have that score are likely to know and be able to do. ACT developed the College and Career Readiness Standards to tell you exactly that.

What Are the ACT College and Career Readiness Standards?

The ACT College and Career Readiness Standards are sets of statements that describe what students are likely to know and be able to do in each content area based on their scores on each of the tests (English, mathematics, reading, science, and writing). The statements serve as score descriptors and reflect a progression of skills and knowledge in a particular content area. The College and Career Readiness Standards are reported in terms of score range, so that the statements describe the knowledge and skills that students typically demonstrate who score in these different ranges on the multiple-choice tests: 13–15, 16–19, 20–23, 24–27, 28–32, 33–36. A score of 1–12 indicates the student is most likely beginning to develop the knowledge and skills described in the 13–15 score range for that particular test. All the College and Career Readiness Standards are cumulative, meaning that students typically can also demonstrate the skills and knowledge described in the score ranges below the range in which they scored.

How Can the ACT College and Career Readiness Standards Help You?

The purpose of the ACT College and Career Readiness Standards is to help you and others better understand what your ACT scores indicate about the knowledge and skills you likely have and what areas might need further development for you to be better prepared for college.

Because the ACT College and Career Readiness Standards provide statements that describe what you are likely to know and be able to do, you can use that information to help zero in on what specific steps you should take to further develop your college readiness. If, for example, you scored in the 16–19 range on the English test, you might infer that you likely have the skills and knowledge described in the 13–15 and in the 16–19 range. You might choose to take a closer look at the standards in the 20–23 and higher score ranges to see what courses to take, or what instruction you might need, to develop those particular areas in order to be better prepared for college. In other words, you can use the ACT College and Career Readiness Standards to help you select courses and instruction that will focus on preparing you for college.

ACT College Readiness Benchmarks

ACT has identified the minimum score needed on each ACT test to indicate a 50% chance of obtaining a B or higher or about a 75% chance of obtaining a C or higher in the corresponding first-year college course. Your score report will have a visual representation of where you scored compared to the ACT College Readiness Benchmark.

ACT Test

ACT Benchmark Score

College Course

English

18

English Composition

Mathematics

22

Algebra

Reading

22

Social Sciences/Humanities

Science

23

Biology

To increase your college readiness, consider taking additional rigorous course work before you enter college. When you meet with your academic advisor to plan your first-year college courses, select courses that are appropriate for your academic background and reflect your planned curriculum.

Planning Your Education and Career

The ACT Student Report includes a College and Career Planning section that helps you explore college majors and occupations, consider your options, and develop plans. The information in this section is all about you. Majors and occupations you may want to explore have been listed here, because they are related to the interests you expressed or occupations you said you were considering.

Seeking Additional Information and Guidance

Your ACT Student Report will provide additional information to help you understand your ACT test results and use them to make important decisions about college and to explore possible future careers.

As you approach decisions about college and careers, be sure to take advantage of all the assistance you can find. Talk to your parents, counselors, and teachers; visit your local library; and talk directly to personnel at colleges in which you’re interested. The more you can find out about all the educational options available to you and the level of your academic skills and knowledge (using such information as your ACT test results), the better prepared you’ll be to make informed college and career choices.

ACT College and Career Readiness Standards—English

These standards describe what students who score in specific score ranges on the English test are likely to know and be able to do.

Students who score in the 1–12 range are most likely beginning to develop the knowledge and skills assessed in the other ranges.

The ACT College Readiness Benchmark for English is 18. Students who achieve this score on the ACT English test have a 50% likelihood of achieving a B or better in a first-year English composition course at a typical college. The knowledge and skills highly likely to be demonstrated by students who meet the benchmark are shaded.

ACT College and Career Readiness Standards—Mathematics

These standards describe what students who score in specific score ranges on the mathematics test are likely to know and be able to do.

Students who score in the 1–12 range are most likely beginning to develop the knowledge and skills assessed in the other ranges.

The ACT College Readiness Benchmark for mathematics is 22. Students who achieve this score on the ACT mathematics test have a 50% likelihood of achieving a B or better in a first-year college algebra course at a typical college. The knowledge and skills highly likely to be demonstrated by students who meet the benchmark are shaded.

Because algebra and functions are closely connected, some standards apply to both categories.

ACT College and Career Readiness Standards—Reading

These standards describe what students who score in specific score ranges on the reading test are likely to know and be able to do.

Students who score in the 1–12 range are most likely beginning to develop the knowledge and skills assessed in the other ranges.

The ACT College Readiness Benchmark for reading is 22. Students who achieve this score on the ACT reading test have a 50% likelihood of achieving a B or better in a first-year social science course at a typical college. The knowledge and skills highly likely to be demonstrated by students who meet the benchmark are shaded.

Text Complexity Rubric—Reading

This rubric describes reading passages for ACT® Aspire® Grade 8, ACT® Aspire® Early High School, and the ACT.

Literary Narratives: Stories and Literary Nonfiction

Somewhat Challenging Literary Narratives

More Challenging Literary Narratives

Complex Literary Narratives

Highly Complex Literary Narratives

Purpose/Levels of Meaning

Have a largely straightforward purpose (chiefly literary nonfiction)

Contain literal and inferential levels of meaning (chiefly stories)

Have a largely straightforward to somewhat complex purpose (chiefly literary nonfiction)

Contain literal, inferential, and interpretive levels of meaning (chiefly stories)

Have a somewhat complex to complex purpose; apparent purpose may differ from real purpose (chiefly literary nonfiction)

Contain literal, inferential, and interpretive levels of meaning (chiefly stories)

Have a complex purpose; apparent purpose may differ from real purpose (chiefly literary nonfiction)

Contain literal, inferential, and interpretive levels of meaning (chiefly stories)

Structure

Use a mostly straightforward structure and a wide range of transitions (chiefly literary nonfiction)

Offer insights into people, situations, and events (e.g., motives)

May contain subplots, flashbacks, and flash-forwards (chiefly stories)

Explore largely straightforward conflicts that may be internal or external (chiefly stories)

May have multiple narrators, with switches clearly signaled; main characters exhibit growth and change (chiefly stories)

Use a somewhat complex structure and a full range of transitions (chiefly literary nonfiction)

Offer deep insights into people, situations, and events (e.g., motives in conflict)

May contain numerous subplots, flashbacks, and flash-forwards as well as parallel and nonlinear plots; may lack clear resolution (chiefly stories)

Explore subtle conflicts that may be internal or external (chiefly stories)

May have multiple narrators; main characters are well rounded (chiefly stories)

Use a complex structure (chiefly literary nonfiction)

Offer sophisticated and profound insights into people, situations, and events (e.g., philosophical commentary)

May contain numerous subplots, flashbacks, and flash-forwards as well as parallel and nonlinear plots; may lack clear resolution (chiefly stories)

Explore complex conflicts that are largely internal and lack an obvious or easy resolution (e.g., moral dilemmas) (chiefly stories)

May have multiple and/or unreliable narrator(s); main characters are well rounded (chiefly stories)

Use a highly complex structure (chiefly literary nonfiction)

Offer sophisticated and profound insights into people, situations, and events (e.g., philosophical commentary)

Contain plots that are intricate, nonlinear, and/or difﬁcult to discern; may lack resolution or may not be plot driven (chiefly stories)

Explore complex conflicts that are largely internal and lack an obvious or easy resolution (e.g., moral dilemmas) (chiefly stories)

May have multiple and/or unreliable narrator(s); main characters are well rounded (chiefly stories)

Language

Use some uncommon words and phrases (e.g., general academic [tier 2] words, archaic words, dialect)

Use varied sentence structures signiﬁcantly more or less formal than in everyday language

Use some somewhat challenging nonliteral and ﬁgurative language and literary devices (e.g., symbols, irony)

Observe language conventions (e.g., standard paragraph breaks) (chiefly stories)

Use some uncommon words and phrases (e.g., general academic [tier 2] words, archaic words, dialect)

Use varied, often complex, and formal sentence structures, with texts from earlier time periods containing structures uncommon in more modern reading

Consistently use somewhat challenging nonliteral and ﬁgurative language and literary devices (e.g., symbols, irony)

Largely observe language conventions, with some unconventional elements possible (e.g., dialogue marked with dashes) (chiefly stories)

Consistently use uncommon words and phrases (e.g., general academic [tier 2] words, archaic words, dialect)

Use varied, often complex, and formal sentence structures, with texts from earlier time periods containing structures uncommon in more modern reading

Consistently use challenging nonliteral and ﬁgurative language and literary devices (e.g., extended metaphors, satire, parody)

May use unconventional language structures (e.g., stream-of- consciousness)

Extensively use uncommon words and phrases (e.g., general academic [tier 2] words, archaic words, dialect)

Use varied, often complex, and formal sentence structures, with texts from earlier time periods containing structures uncommon in more modern reading

Extensively use challenging nonliteral and ﬁgurative language and literary devices (e.g., extended metaphors, satire, parody)

Use unconventional language structures (e.g., stream-of- consciousness)

Abstractness (chiefly literary nonfiction)

Depict some abstract ideas and concepts that may be important to understanding the text

Depict several abstract ideas and concepts that are essential to understanding the text

Depict numerous abstract ideas and concepts that are essential to understanding the text

Depict numerous abstract ideas and concepts that are essential to understanding the text

Density (chiefly literary nonfiction)

Have moderate information/concept density

Have moderately high information/concept density

Have high information/concept density

Have very high information/concept density

Knowledge Demands: Textual Analysis, Life Experiences, Cultural and Literary Knowledge

Assume readers can read on literal and inferential levels

Assume readers can handle somewhat challenging themes and subject matter with some maturity and objectivity

Assume readers can relate to experiences outside of their own

Call on cultural or literary knowledge to some extent

Assume readers can read on literal, inferential, and interpretive levels

Assume readers can handle somewhat challenging themes and subject matter with some maturity and objectivity

Assume readers can relate to experiences distinctly different from their own

Assume readers can read on literal, inferential, and interpretive levels

Assume readers can handle challenging themes and subject matter with maturity and objectivity

Assume readers can relate to experiences distinctly different from their own

Call on cultural or literary knowledge to some extent

Assume readers can read on literal, inferential, and interpretive levels

Assume readers can handle complex themes and subject matter with maturity and objectivity

Assume readers can relate to experiences distinctly different from their own

Require cultural or literary knowledge for full comprehension

Have low intertextuality (i.e., make no/few or unimportant connections to other texts); drawing connections between texts at the level of theme may enhance understanding and appreciation

Call on cultural or literary knowledge to some extent

Have moderate intertextuality (i.e., make some important connections to other texts); drawing connections between texts may enhance understanding and appreciation

Have moderate intertextuality (i.e., make some important connections to other texts); drawing connections between texts may enhance understanding and appreciation

Have high intertextuality (i.e., make many important connections to other texts); drawing connections between texts is essential for full understanding and appreciation

Informational Texts: Social Science, Humanities, and Natural Science

Somewhat Challenging Informational Texts

More Challenging Informational Texts

Complex Informational Texts

Highly Complex Informational Texts

Purpose

Have a largely straightforward purpose

Have a largely straightforward to somewhat complex purpose

Have a somewhat complex to complex purpose; apparent purpose may differ from real purpose

Have a complex purpose; apparent purpose may differ from real purpose

Structure

Use a mostly straightforward structure and a wide range of transitions

Exhibit norms and conventions of a general discipline (e.g., natural science)

Use a somewhat complex structure and a full range of transitions

Exhibit norms and conventions of a general discipline (e.g., natural science

Use a complex structure

Exhibit norms and conventions of a general discipline (e.g., natural science)

Use a highly complex and possibly highly formalized structure (e.g., journal article)

Exhibit norms and conventions of a speciﬁc discipline (e.g., biology)

Language

Use some general academic [tier 2] and domain-speciﬁc [tier 3] words and phrases

Use varied and some long and complicated sentence structures

Consistently use general academic [tier 2] and domain- speciﬁc [tier 3] words and phrases

Use varied and often complex sentence structures, with consistent use of long and complicated structures

Consistently use general academic [tier 2] and domain- speciﬁc [tier 3] words and phrases

Use varied and often complex sentence structures, with consistent use of long and complicated structures

Extensively use general academic [tier 2] and domain- speciﬁc [tier 3] words and phrases

Use varied and often complex sentence structures, with consistent use of long and complicated structures

Abstractness

Depict some abstract ideas and concepts that may be important to understanding the text

Depict several abstract ideas and concepts that are essential to understanding the text

Depict numerous abstract ideas and concepts that are essential to understanding the text

Depict numerous abstract ideas and concepts that are essential to understanding the text

Density

Have moderate information/concept density

Have moderately high information/concept density

Have high information/concept density

Have very high information/concept density

Knowledge Demands: Textual Analysis, Life Experiences, Content and Discipline Knowledge

Assume readers can read on literal and inferential levels

Assume readers can handle somewhat challenging subject matter, including perspectives, values, and ideas unlike their own, with some maturity and objectivity

Assume readers have everyday knowledge and some broad content knowledge, with texts at the high end of the range assuming some content knowledge

Have low intertextuality (i.e., make no/few or unimportant connections to other texts); drawing connections between texts at the level of general concept may enhance understanding

Assume readers can read on literal, inferential, and evaluative levels

Assume readers can handle somewhat challenging subject matter, including perspectives, values, and ideas unlike their own, with some maturity and objectivity

Assume readers have some content knowledge, with texts at the high end of the range assuming some discipline-speciﬁc content knowledge

Have moderate intertextuality (i.e., make some important connections to other texts); drawing connections between texts may enhance understanding

Assume readers can read on literal, inferential, and evaluative levels

Assume readers can handle challenging subject matter, including perspectives, values, and ideas in opposition to their own, with maturity and objectivity

Assume readers have some discipline-speciﬁc content knowledge

Have moderate intertextuality (i.e., make some important connections to other texts); drawing connections between texts may enhance understanding

Assume readers can read on literal, inferential, and evaluative levels

Assume readers can handle complex subject matter, including perspectives, values, and ideas in opposition to their own, with maturity and objectivity

Assume readers have extensive discipline-speciﬁc content knowledge, often in specialized subjects or areas

Have high intertextuality (i.e., make many important connections to other texts); drawing connections between texts is essential for full understanding

ACT College and Career Readiness Standards—Science

These standards describe what students who score in specific score ranges on the science test are likely to know and be able to do.

Students who score in the 1–12 range are most likely beginning to develop the knowledge and skills assessed in the other ranges.

The ACT College Readiness Benchmark for science is 23. Students who achieve this score on the ACT science test have a 50% likelihood of achieving a B or better in a first-year biology course at a typical college. The knowledge and skills highly likely to be demonstrated by students who meet the benchmark are shaded.

ACT College and Career Readiness Standards for science are measured in rich and authentic contexts based on science content that students encounter in science courses. This content includes the following:

Life Science/Biology

Animal behavior

Animal development and growth

Body systems

Cell structure and processes

Ecology

Evolution

Genetics

Homeostasis

Life cycles

Molecular basis of heredity

Origin of life

Photosynthesis

Plant development, growth, structure

Populations

Taxonomy

Physical Science/Chemistry, Physics

Atomic structure

Chemical bonding, equations, nomenclature, reactions

Electrical circuits

Elements, compounds, mixtures

Force and motions

Gravitation

Heat and work

Kinetic and potential energy

Magnetism

Momentum

The periodic table

Properties of solutions

Sound and light

States, classes, and properties of matter

Waves

Earth and Space Science

Earthquakes and volcanoes

Earth’s atmosphere

Earth’s resources

Fossils and geological time

Geochemical cycles

Groundwater

Lakes, rivers, oceans

Mass movements

Plate tectonics

Rocks, minerals

Solar system

Stars, galaxies, and the universe

Water cycle

Weather and climate

Weathering and erosion

Part Five:
Moving Forward to Test Day

In This Part

Even when you are fully prepared, mentally and physically, to take the ACT, you may need additional guidance to handle the logistics of arriving at the test center on time and with the necessary items. This part helps you avoid any unpleasant surprises on test day that might cause confusion and anxiety, which could negatively affect your performance. Specifically, in this part, you learn how to do the following:

Register for a convenient test date and test center in plenty of time to have your scores reported to the colleges and scholarship agencies of your choice by their deadlines.

Map a route and choose a means of travel that ensure you arrive at the test center on time.

Dress for comfort to ensure that you are not too hot or too cold when taking the test.

Pack everything you need for test day, so you are admitted to the testing room and have the items you need to take the test.

Find out what to expect at the test center in terms of check-in procedures, rules, and maintaining your composure and energy.

Obtain additional information you may need, including how to void your test on test day, retake the test, and gather additional information.

Chapter 13:
Registering, Planning, and Packing for Test Day

When you feel ready to take the actual ACT, the time has come to register, plan, and pack for the upcoming day. Your goal is to avoid any unpleasant surprises on test day, such as getting lost on the way to the test center, showing up without a valid ID, or wearing the wrong clothing and being physically uncomfortable during the entire test. Such surprises distract you from what should be your sole focus on test day—doing your very best on the test.

In this chapter, we help you register for the ACT, avoid the most common pitfalls that test-takers encounter leading up to test day, offer guidance on how to dress and what to pack for test day, explain what you can expect at the test center, and give you a heads up about posttest concerns, such as voiding your test on test day, retaking the test, and reporting your scores.

National Testing Program Versus State and District Testing

ACT makes the test available via national testing centers and through certain school districts or states. Registration for and administration of the test varies accordingly. For example, if your district or state offers the test, you do not need to register for that test. Instead, your district or state registers for the test and chooses a school day on which to administer it. If you want to take the test at a national test center on a Saturday, you will need to register yourself for that test. Check with your counselor to find out whether your school offers the ACT or whether you must register individually to take the ACT at a national testing center.

Registering for the ACT

If your district or state offers the ACT for your grade level test, you can skip ahead to the section “Planning and Packing for Test Day.” Your district or state will take the first two registration steps for you:

Selects a test date (typically a school day)

Chooses whether students will take the ACT with or without the writing test

Note: If you have a diagnosed disability or are an English language learner, and have documentation of receiving an accommodation or support in school, you may be eligible to take the ACT with that accommodation or support. Work with your school counselor or accommodations coordinator to determine if they have submitted the required documentation.

If your school does not offer the ACT, you must register for it through the ACT national testing program. In the following sections, we lead you through the process of choosing a national test date and test option (ACT with or without the writing test) and registering for the test. We also address special circumstances that could affect your registration.

Selecting a National Testing Date and Location

Prior to registering for the ACT through the ACT national testing program, choose the date on which you want to take the test. When choosing a date, consider the following:

Available test dates and test centers near you

College and scholarship application deadlines

Where you stand in your high school coursework

Whether you may want to take the ACT more than once

Let’s look at each of these considerations in turn.

Checking Available Test Dates and Test Centers

The ACT is offered nationally and internationally several times a year. However, it’s not offered at every test center on each test date. If you need to take the ACT on a day other than Saturday (for religious reasons), you’ll want to be especially attentive in selecting a test date when a test center near you is open on a non-Saturday date.

One of the first things you should find out, then, is where and when the ACT is being offered in your area. A quick and easy way to access available test dates and find test centers is to visit ACT’s website at www.actstudent.org. Search for test dates and deadlines to find test dates and registration deadlines. You can also look at nearby ACT test centers by searching for ACT test centers.

Note: You may not receive scores from more than one test taken on a scheduled national or international test date and one of the alternate test dates associated with that date. For example, suppose you take the test on Saturday and then again on the non-Saturday date associated with that Saturday. We will report only the scores from the first test. The second set of scores will be cancelled without refund.

Considering College and Scholarship Application Deadlines

Colleges and scholarship agencies may require that ACT test scores be submitted sometime during your junior year of high school. Find out what these deadlines are and then make absolutely sure that you take the test early enough to ensure that the colleges and scholarship agencies you’re applying to receive your ACT test scores by those deadlines.

Score reports are usually ready about 2 to 8 weeks after the test date. To be on the safe side, consider taking your ACT at least 10 weeks prior to the earliest deadline.

You may not be certain yet which school or program you’ll decide on. That’s okay. Just be sure you’re doing everything, including taking the ACT, early enough to keep all options open.

Gauging Where You Stand in Your High School Coursework and Whether You May Want to Take the ACT More Than Once

Another consideration in deciding when to take the ACT is where you stand in your high school coursework. If you’re in a college-prep program and taking a lot of courses in English, mathematics, and science in your sophomore and junior years, taking the ACT in your junior year, while those subjects are still fresh in your memory, is probably best.

Perhaps you’ll decide to take the ACT more than once, in hopes of improving your score. In that case, it’s better to take the exam early in the spring of your junior year to allow time for a second try. If you find you’re studying a significant amount of material covered on the ACT during your senior year, you may plan on retaking the ACT in your senior year, based on the reasonable assumption that your scores will reflect your improved knowledge and skills.

Taking the ACT in your junior year has several advantages:

You probably will have completed much of the coursework corresponding to the material covered on the ACT.

You will have your ACT scores and other information in time to help make decisions about your final year of high school coursework. (For example, you may decide to take additional classes in an area in which your test score was lower than you wanted it to be.)

Colleges will know of your interest and have your scores in time to contact you during the summer before your senior year, when many of them like to send information about admissions, scholarships, advanced placement, and special programs to prospective students.

You’ll have your ACT scores and information from colleges in time to make decisions about visiting campuses or contacting schools.

You’ll have the opportunity to take the ACT again if you feel your scores don’t accurately reflect your achievement.

Selecting a Test Option

When you register, you must choose one of two test options—the ACT (which includes the four multiple-choice tests: English, mathematics, reading, and science), or the ACT with the optional writing test (which includes the four multiple-choice tests plus a 40-minute writing test). Taking the writing test does not affect your composite score.

Not all institutions require the ACT writing test. Check directly with the institutions you are considering to find out their requirements, or ask your high school counselor which test option you should take.

Registering

The fastest and easiest way to register to take the ACT through its national testing program is online at www.actstudent.org. When you register on the web, you will know immediately if your preferred test center has space for you, and you can print your admission ticket. Read all the information on your admission ticket carefully to make sure it is correct.

You are guaranteed a seat and test booklet at a test center only if you register by the deadline for a test date. If you miss the late registration deadline, you can try to test as a “standby” examinee. Testing as a standby costs more and does not guarantee you a seat or test booklet. If you decide to take your chance as a standby, be sure to follow the instructions for standby testing on the ACT website. You must bring acceptable identification to be admitted. Standby examinees will be admitted only after all registered students have been seated for their test option.

However you register, you are encouraged to create your free ACT web account. You can use your ACT web account to do several things:

View your scores and score report on the web at no charge.

Send your scores to additional colleges.

Receive email updates from ACT about changes to your registration.

Make changes to your student profile.

Print your admission ticket.

Registering under Special Circumstances

See the website or our online registration brochure for instructions if special circumstances apply to you—for example, if your religious beliefs prevent you from taking the exam on Saturday and no test centers in your area offer non-Saturday test dates or if you have a diagnosed disability or are an English language learner and require accommodations or supports.

If you have a diagnosed disability, or are an English language learner, and have documentation of receiving an accommodation or support in school, you may be eligible to take the ACT with that accommodation or support. Details about the procedures for applying to test with accommodations and supports are provided on the ACT website.

Planning and Packing for Test Day

At least one week before your scheduled test date, start planning and packing for test day. You need to know where you’re going, how you’re getting there, how much time the trip will take you, how to dress, and what to pack. In the following sections, we help you plan and pack for test day.

Getting to the Test Center

If your school is administering the ACT on a school day, you simply need to arrive at your school at the start of the school day. Testing will be the first activity of the day.

Under no circumstances will you be admitted to the test after the test booklets have been distributed, so be sure to arrive on time.

If you registered to take the test through the ACT national testing program, you’ll be asked to report to the test center by 8:00 a.m. on your test date. Under no circumstances will you be admitted after the test booklets have been distributed, so be sure to arrive on time by 8:00 a.m.

You may need to walk a few blocks to get to the test center or drive several hours, perhaps to an unfamiliar city. Whatever your situation, be certain to allow plenty of time. We recommend that you plan to arrive 15 to 30 minutes early just in case you experience an unexpected delay.

Test centers vary considerably. You may be taking the ACT in your own high school, at a local community college, or in a large building on a nearby university campus. Your surroundings may be quite familiar or they may be new. If they’re new, allow yourself a few extra minutes to get acclimated. Then try to forget about your surroundings so that you can concentrate on the test.

To ensure that you arrive on time, map your route to the test center and choose a means of travel—car, train, bus, taxi, bicycle, carpool with a friend . . . whatever works best for you.

One week prior to test day, travel to the testing center using the selected means of travel. By doing a test run on the same day and at the same time (but a week early), you gain a better sense of what traffic will be like, what your parking options will be, whether the buses are running during those times, and so on.

Dressing for Test Day

The night before the test, set out the clothes you want to wear. Dress in layers so that you can adjust to the temperature in your testing room.

Keep in mind that you’re going to be sitting in the same place for more than three hours. Wearing something you’re especially comfortable in may make you better able to relax and concentrate on the test. For many people, what they’re wearing can make a difference in how they feel about themselves. Picking something you like and feel good wearing may boost your confidence.

Packing for Test Day: What to Bring

Bring with you only what you’ll need that morning, because other materials will be in your way and may be prohibited in the test room. Be sure to bring these:

Your paper admission ticket (if you are taking the test on a national or international ACT test date). Failure to bring your admission ticket will delay your scores. If your district or state is administering the test, you will not receive (or need) an admission ticket.

Acceptable photo identification. Examples of acceptable identification include current identification issued by your city/state/federal government or school, on which both your name and current photograph appear (for example, driver’s license or passport). Without acceptable identification, you will not be allowed to take the test. (See www.actstudent.org for details on what constitutes acceptable and unacceptable identification.)

Several sharpened soft-lead No. 2 pencils with good erasers (no mechanical pencils or ink pens). Test the erasers to make sure they erase cleanly without leaving any residue.

A watch without an alarm function to pace yourself. If your watch has an alarm function and the alarm goes off, it will disturb the other students, you will be dismissed, and your answer document will not be scored. Although the test supervisor will announce when 5 minutes remain on each test, not all test rooms have wall clocks for pacing yourself in the meantime.

A permitted calculator if you wish to use one on the mathematics test only (for a list of permitted and prohibited calculators, visit www.actstudent.org). You are solely responsible for knowing whether a particular calculator is permitted.

A snack and a drink to consume outside the test room only during the break.

Obtaining Additional Test Details

On certain national test dates, if you test at a national test center, you may request and pay for a copy of the multiple-choice test questions used to determine your scores, a list of your answers, and the answer key. If you take the writing test, you will also receive a copy of the writing prompt, scoring guidelines, and the scores assigned to your essay. You’ll also get information about requesting a photocopy of your answer document for an additional fee. These services are not offered for all test dates, so if you’re interested in receiving any of these services, you’ll need to check the dates on ACT’s website (www.actstudent.org) to be sure you’re choosing a test date on which the desired service is available.

At the Test Center

Knowing ahead of time what to expect at the test center can alleviate any anxiety you may feel, ensure that you do everything ACT requires in terms of checking in and obeying the rules, and help you maintain your composure. In the following sections, we describe the check-in procedure, present the rules, encourage you to communicate with the testing staff (if necessary), and provide tips on maintaining your composure and energy level.

Checking In

The way check-in procedures are handled may vary from location to location. You may find that all students are met at a central location and directed from there to different classrooms. Signs may be posted, telling you that everyone whose last name falls between certain letters should report directly to a particular room. However this part of the check-in is handled at your location, you can anticipate that certain check-in procedures will be performed, including verification of your identity.

In the room you’ll be directed to a seat by a member of the testing staff. If you are left-handed, let the testing staff know so that an appropriate desk or table may be made available to you.

Following the Rules

The below text was pulled from the Terms and Conditions: Testing Rules and Policies for the ACT ® Test at the time of publishing.

The following behaviors are prohibited. You may be dismissed and/or your test may not be scored, at ACT’s sole discretion, if you are found:

Filling in or altering responses to any multiple-choice questions or continuing to write or alter the essay after time has been called. This means that you cannot make any changes to a test section outside of the designated time for that section, even to fix a stray mark or accidental keystroke.

Looking back at a test section on which time has already been called.

Looking ahead in the test.

Looking at another person’s test or answers.

Giving or receiving assistance by any means.

Discussing or sharing test questions, answers, or test form identification numbers at any time, including during test administration, during breaks, or after the test.

Attempting to photograph, copy, or memorize test-related information or remove test materials, including questions or answers, from the test room in any way or at any time.

Disclosing test questions or answers, in whole or in part, in any way or at any time, including through social media.

Using a prohibited calculator (www.act.org/calculator-policy.html).

Using a calculator on any test section other than mathematics.

Sharing a calculator with another person.

Wearing a watch during test administration. All watches must be removed and placed face up on the desk.

Using a watch with recording, internet, communication, or calculator capabilities (e.g., a smart watch or fitness band).

Accessing any electronic device other than an approved calculator or watch. All other electronic devices, including cell phones and other wearable devices, must be powered off and stored out of sight from the time you are admitted to your testing room until you are dismissed at the end of the test.

Using highlighter pens, colored pens or pencils, notes, dictionaries, or other aids.

Using scratch paper. **

Not following instructions or abiding by the rules of the test center.

Not following the rules of the test administration.

Exhibiting confrontational, threatening, or unruly behavior.

Violating any laws. If ACT suspects you have engaged in criminal activities in connection with a test, such activities may be reported to law enforcement agencies.

Allowing an alarm on a personal item to sound in the test room or creating any other disturbance.

** If you are taking the ACT online, some use of ACT-provided scratch paper or dry erase surface may be permitted; all such use must be in accordance with ACT policies and procedures.

ACT may restrict the items you bring into the test center. All items brought into the test center, such as hats, purses, backpacks, cell phones, calculators, watches, and other electronic devices, may be searched at the discretion of ACT and its testing staff. Searches may include the use of tools, such as handheld metal detectors, that detect prohibited devices. ACT and its testing staff may confiscate and retain for a reasonable period of time any item suspected of having been used, or capable of being used, in violation of these prohibited behaviors. ACT may also provide such items to and permit searches by third parties in connection with an investigation conducted by ACT or others. ACT and its testing staff shall not be responsible for lost, stolen, or damaged items that you bring to a test center. Your test center may also have additional procedures with which you must comply.

Dismissal for Prohibited Behavior

Examinees who are dismissed because of prohibited behavior forfeit their registration for that test date. There are no options for refunds or appeals in situations involving prohibited behavior.

Eating, drinking, and the use of tobacco are not allowed in the test room. You may bring a snack to eat or drink before the test or during the break, but any food or beverage you bring must be put away during testing and must be consumed outside the test room.

Communicating with the Testing Staff

Although you are required to work silently during the test, you may need to communicate with the testing staff under certain circumstances, such as the following:

If you have problems with the testing environment, let the testing staff know immediately. Possible problems include being seated below, over, or next to a heating or cooling vent that is making you too warm or too cold; having a defective chair or desk; poor lighting that makes reading difficult; or excessive noise.

If any aspect of the test-taking procedure is not perfectly clear to you, request clarification. Testing staff will be available throughout the exam. In fact, they’ll be moving quietly around the room while you’re working. If you have a question about the administration of the test (not about any of the test questions), raise your hand and quietly ask for information.

If you need to use the restroom, ask. Bathroom breaks are permitted during the test or between tests, but you’re not allowed to make up the lost time.

If you become ill during the test, you may turn in your test materials and leave, if necessary. Let the testing staff know that you are ill and whether you wish to have your answer document scored. One caution: Once you leave the test center, you won’t be allowed to return and continue—so be sure that leaving is what you want to do. You might try closing your eyes or putting your head on the desk for a minute first; then if you feel better, you’ll be able to continue.

Maintaining Your Composure and Energy

While you’re waiting for the test to begin, you may find yourself getting anxious or jittery. That’s perfectly normal. Most of us get nervous in new situations. People handle this nervousness in different ways.

Some people find it helpful to practice mental and physical relaxation techniques. If this appeals to you, try alternately flexing and relaxing your muscles, beginning at your toes and moving up through your shoulders, neck, and arms. Meanwhile, imagine yourself in a quiet, peaceful place: at the beach, in the mountains, or just in your favorite lounge chair. Breathe deeply and evenly.

Other people like to redirect that nervous energy and turn it to their advantage. For them, concentrating on the task at hand and shutting everything else out of their minds is the most helpful strategy. If this is your style, you may even want to close your eyes and imagine yourself already working on the exam, thinking about how it will feel to move confidently and smoothly through the tests.

If you have the chance, try out the two approaches on some classroom tests and see which one works better for you. The important thing is to keep the ACT in perspective. Try not to let it become larger than life. Remember, it’s just one part of a long academic and professional career. If you begin to feel tired during the test, check your posture to make sure you’re sitting up straight. Getting enough air in your lungs is difficult when you’re slouching. You’ll stay more alert and confident if your brain receives a steady supply of oxygen.

You might want to practice those relaxation techniques again, too, because tension contributes to fatigue. As you start a new test, you might find it helpful to stretch your neck and shoulder muscles, rotate your shoulders, stretch back in your chair and take some long, deep breaths.

You can expect a short break (approximately 10 to 15 minutes) after the second test. During this break, it’s a good idea to stand up, walk around a little, stretch, and relax. You may wish to get a drink, have a snack, or use the restroom. Keep in mind, though, that you still have work ahead of you that requires concentrated effort. Eat lightly and return to the room quickly. The third test will start promptly, and you’ll need to be back at your desk and ready to go on time.

Voiding Your Answer Documents on Test Day

If you have to leave before completing all tests, you must decide whether you want your answer document scored and then inform your supervisor if you do not want your answer document scored; otherwise, your answer document will be scored.

Once you break the seal on your multiple-choice test booklet, you cannot request a test date change. If you do not complete all your tests and want to test again, you will have to pay the full fee for your test option again. If you want to take the ACT again, see www.actstudent.org for your options. Once you begin filling out your answer document, you cannot change from one test option to another.

Testing More Than Once

If you think you can improve your scores, you can retake the ACT. ACT may limit the number of times you take the ACT. The current retest limit can be found at www.actstudent.org. Many students take the test twice, once as a junior and again as a senior. Of the students who took the ACT more than once:

56% increased their Composite score

20% had no change in their Composite score

24% decreased their Composite score

You determine which set of scores are sent to colleges or scholarship programs. ACT will release only the scores from the test date (month and year) and test location (e.g., national or state) you designate. This protects you and ensures that you direct the reporting of your scores.

Our mission is helping people achieve education and workplace success. Thank you for allowing ACT to be a part of your journey and good luck on test day.

Notes

Notes

Notes

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