# The Official SAT Study Guide 2nd Edition - PDF Free Download (2022)

UOllegeBOard

The Official

Second Edition

Study Guide-

College Board, New York

This publication was written and edited by the College Board, with archival material from Educational Testing Service. Cover Design: Beth Olh·er. Assistant Director: Arthur Sprogis. Assessment Managers: James Daubs, Ed Hardin, Joel Harris. Senior Director, Mathematics: Robin O'Caliaghan. Senior Assessment Specialists: Elizabeth Daniel, Beth Hart, Colleen McDermott. Special thanks to Jim Gwyn, Senior Project Manager, and Suel\en Leavy, Book Compositor/Desktop Publisher. The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the College Board is composed of more than 5,600 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college readiness, college admissions, guidance, assessment, financial aid, enrollment, and teaching and learning. Among its best-known programs are the SA'r, the PSAT/NMSQr and the Advanced Placement Program· (Ap·). The College Board is committed to the principles of excellence and equity and that commitment is embodied in all of its programs, services, activities and concerns. Copies of this book (item # 008525) are available from your bookseller or may be ordered from Colleg.e Board Publications, P.O. Box 869010, Plano, TX 75074-0998 (teL 800-323-7155). The price is $21.95 per copy. Purchase orders above$25 are accepted. Editorial inquiries concerning this book should be addressed to the College Board, 45 Columbus Avenue, New York, NY 10023-6992. Cl 2009 The College Board and Educational Testing Service. All rights reserved. College Board, Advanced Placement Program, AP, CLEP, College-Level Examination Program, CSS/Financial Aid PROFILE, SAT, Student Search Service and the acorn logo are registered trademarks of the College Board. inspiring minds, MyRoad, SAT Preparation Center, SAT Readiness Program, SAT Subject Tests, Score Choice, Skills InSight, The Official SAT Online Course, The Official SAT Question of the Day and The Official SAT Study Guide are trademarks owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Visit the College Board on the Web; www.collegeboard.com.

ISBN-13: 978-0-87447-852-5 ISBN- 10: 0-87447-852-9 I 2 3 4 5 6 7 8 9

15141312 II 1009

Distributed by Macmillan

Sincerely,

Gaston Caperton President, The College Board

CONTENTS

vii

Preface

PART I

Getting Started

1

Chapter 1

Introducing the SA~

3

Chapter 2

How to Do Your Best on the SAT

9

Chapter 3

21

PART II

27

Chapter 4

29

Chapter 5

Sentence Completion

31

Chapter 6

49

Chapter 7

Practice for the Critical Reading Section

87

,

PART III

The Writing Section

97

Chapter 8

99

Chapter g.

The Essay

103

Chapter 10

Improving Sentences

137

Chapter 11

Identifying Sentence Errors

153

Chapter 12

Improving Paragraphs

169

Chapter 13

Practice for the Writing Section

189

PART IV

The Mathematics Section

215

Chapter 14

217

Chapter 15

Number and Operations Review

227

Algebra and Functions Review

243

Chapter 17

Geometry and Measurement Review

263

Chapter 18

Data Analysis, Statistics and Probability Review

291

Chapter 19

Multiple-Choice Questions

303

. Chapter 16

v

Contents

vi

Chapter 20

Student-Produced Response Questions

343

Chapter 21

Practice for the Mathematics Section

365

PART V

10 Official Practice Tests with Answer Keys

377

SAT Practice Test #1

379

SAT Practice Test #2

441

SAT Practice Test #3

503

SAT Practice Test #4

565

SAT Practice Test #5

627

SAT Practice Test #6

689

SAT Practice Test #7

751

SAT Practice Test #8

813

SAT Practice Test #9

875

SAT Practice Test #10

937

PREFACE

The best way to prepare for the SAr is to take challenging high school classes, read extensively and write as often as possible. For more immediate help, you should review the concepts covered and practice problems similar to those you will see on the SAT. This guide from the College Board - the test maker - is the only place you'll fin d questions written to the SAT test specifications and actual SAT tests. As you read through and practice with The Official SAT Study Guide'": Second Edition, you will gain confidence in your abilities and will be more prepared to succeed. This gUide provides you with: • opportunities to familiarize yourself with the format of the test • practice on the different question types • hundreds of practice questions • instructional help with the concepts covered • approaches to use for answering different types of questions • experience taking official practice tests, helping you learn how to pace yourself • numerous opportunities to sharpen your skills in writing effective essays • feedback that will help you focus on areas that may need improvement

Special Features

r

This book is filled with helpful suggestions. This icon appears next to the "Keep in Mind" boxes. which are located in the margins to remind you of approaches and other points that will help you prepare for the test. Plus, for every chapter that describes specific sections of the test, you'll find a "Recap" section for review. appears next to info rmation you can find online A computer icon at www.collegeboard.com/SATstudyguide. You can even enter your test answers online and receive personalized feedback for each of this guide's 10 full -length practice tests. This feedback makes it easy for you to focus on the areas you need to study further. As a book owner, you can review explanations to the questions in this gUide's 10 official practice tests. Subscribers to The Official SAT Online Course- have access to interactive instruction. additional sets of practice quest ions. practice essay

Q

vii

Preface

questions and six additional official practice tests, and have responses to essays in this book and in The Official SAT Online Course scored automatically.

How The Official SAT Study Edition Is Organized

Guide~:

Second

viii

Preface

,

We're Here to Help The College Board hopes that you find this guide helpful and easy to use; please visit www.collegeboard.com for the most up-to-date information on the SAT. We wish you well as you work through the admissions process.

ix

PART I

Getting Started

1

CHAPTER 1

Introducing the SAT®

About the SAT' Are you thinking about going to college? If you are, there's probably an SAr in your future. Taking the SAT is the first step in find ing the right college for you - one where you'll best succeed in d iscovering the tools necessary to pursue your passions. The SAT helps colleges get to know you better by giving them insight into how you thin k, solve problems and communicate. The SAT measures what you've learned in the classroom - basic skills such as reading, writing and mathematics - and how well you apply that knowledge. Your SAT score is just one of ma ny factors that colleges look at when they consider your application. They also look at your academic record, you r involvement in school

activities, your application essay and your letters of recommendation. The SAT is taken by more than two million students every year at thousands of testing centers (usually high schools) around the world. Many high school students take the SAT twice - once in the spring of their junior year and again in the fall of their senior year.

Who Is Responsible for the SAT? The SAT is a program of the College Board, a not-for-profit membership association to which more than 5,600 schools, colleges and universities belong. The College Board, whose mission is to connect students to college success and opportun ity, was founded more than 100 years ago. Every yea r, the College Boa rd serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college ad missions, gu idance, assessment, fi nancial aid, enrollment, and teaching and learning. Among its best-known progra ms are the SAT, the Advanced Placement Program- (AP-) and the PSAT/NMSQT·.

3

GETTING STARTED

How Is the SAT Developed? The SAT Test Development Committees, made up of college professors and high school teachers who are experts in their fie lds, oversee all aspects of test development to ensure that the SAT is carefully designed to be a fair test for all students. All questions undergo a very thorough review process. In fact, each question is pretested before it is placed on the scored sections of the test. The goal is to make the questions dear, appropriately chal lenging and fair for all students regardless of gender or ethnicity. How do the SAT Test Development Committees know which skills should be measured? They do their homework! The College Board meets with college faculty. high school teachers and experts in different subjects from across the country and surveys educators about their reading, writi ng and mathematics curricula. The College Board also reviews research on what skills are necessary for success in college. The skills measured by the SAT align with the subjects that you're learn ing in your high school classroom. The SAT has evolved over time to keep up to date with current teaching practices and college and high school curricula. For example, in 1994, a new SAT mathematics section was introduced that allowed students to use calculators for the first time. Since writing is critical to succeeding in college. the College Board added a writ ing section to the SAT in 2005.

How Is the Test Organized? The SAT features eight types of questions in sections on critical reading, writing and mathematics. Table 1.1 provides an overview of each section. The table also shows the type of questions, the total number of questions in each section and the time allotted for each section. You have 3 hours and 45 minutes to complete the SAT. The SAT also includes a variable section in critical reading, writing multiple choice or mathematics for which 25 minutes is allotted. The variable section is used to help make sure that your scores are comparable to scores on other editions of the SAT. This variable sect ion will not count toward your final score. Still, because you won't know which section is the variable. you need to do your best on the entire test. Remember, the official practice tests in this book do not include the variable section.

4

Introducing the SAT

Table 1. 1 Number and Type of Questions with Time Allotted for Each Section of the SAT Sections o f the SAT Critic al Reading

Wri ting

Type o f Questio ns Sentence completion

'9

48

67

Identifying sentence errors

'8

Improving sentences

25

Improving paragraphs

6

Essay writing

Multiple choice Student- p~oduced

Time All o tted

70 minutes (two 25-minute sections and one 20-minute section)

1 essay

Total writing questions

M athem atics

N o. o f Questions

49+ Essay

60 minutes (one 25-minute essay, one 25-minute multiple-choice section and one 10-minute multiple-choice section)

44 response

(grid-ins)

'0

Total mathematics questions

54

70 minutes (two 25-minute sections and one 20-minute section)

How Is the SAT Scored? Here's how SAT scores are calculated. 1.

Multiple -choice questions: You receive one point for each question answered correctly. For each question that you attempt but answer incorrectly, 1;' point is subtracted from the total number of correct answers. No points are added or subtracted for unanswered questions. If the fi nal score includes a fraction, the score is rounded to the nearest whole number.

2. Student-produced response questions in the mathematics section: Nothing is subtracted for wrong answers. 3.

The essay will receive a score of 2 to 12. However, a blank essay. essays that are not written on topic, essays written in pen or essays deemed illegible after several attempts have been made to read them will receive a score of o.

Q

Essay Practice

To practice the essay, check out The Official SAT Online Course™ at www.collegeboard. com/satonlinecourse.

A stat istical process called equating scales your scores from 200 (lowest) to 800 (highest). Scores are equated to adjust for minor differences between test forms. Equati ng assures you and colleges that a score of 500 on the mathematics section of one form of the test indicates the same abi lity level as 500 on the mathematics section of another form of the test.

5

GETTING STARTED

Score Range No test can ever measure your skills precisely. but the SAT can provide good estimates. Students who take the SAT many times within a short period of time usually find that thei r scores tend to vary - but not too far above or below their true capabilit ies. The score range is an estimate of how your scores m ight vary if you were tested many times.

Percentiles In addition to the scaled scores 0(200 to 800 on each oflhe three sections oflhe test, you also will receive corresponding SAT percentile scores. The percentile score compares your scores to the scores of other students who took the test. The comparison is given as a number between I and 99 signifying what percentage of students earned a score lower than yOUfS. For example, suppose your percentile is 53. That means you performed better than 53 out of every 100 test-takers in the comparison group. Your percentile changes depending on the group with which you are being compared. The national percentile is based on all recently graduated college-bound seniors from across the nation who took the test. The state percentile is based on all recently graduated college-bound seniors from your state who took the test.

Additional Services The following services are available to you when you register for the SAT or when you receive your scores.

SAT" Skills

Insight~

SAT Skills InSight is a free online tool that shows you the skills you know and highlights those you need to know better, includ ing: • Skills tested on the SAT • Skills typical of students who score within a particular score band

6

Introducing the SAT

• Suggestions for how to sharpen those skills • Real SAT questions and answers You can use your real SAT scores and your practice test scores when using SAT Skills Insight.

My SAT Online Score Report My SAT Online Score Report is a free online tool that gives you the meaning behind your numbers and insight into your strengths and weaknesses. It offers: • Details of performance by question type and difficulty level • National, state and high school percentiles • Your essay question and scanned response • The ability to search for career and major possibilities

Score Choice™; A New Score-Reporting Feature The College Board has introduced Score Choice~, a new feature that gives you the option to choose the SAT scores you send to colleges by test date - in accordance with a college or university's score-use practice. Designed to reduce your stress and improve the test-day experience, Score Choice gives you an opportunity to show colleges the scores you feel best represent your abilities. Score Choice is optional, so if you don't actively choose to use it, all of your scores will be sent automatically. Since most colleges only consider your best scores, you should still feel comfortable reporting scores from all of your test dates. Each college. university and scholarship program has different score-use practices. Our new, easy-to-use score-reporting process displays score-use practices for each participating institution, but you should also check with colleges to ensure that you are following their score-reporting requirements. E-mail reminders will be sent to you if you have not sent SAT scores to any colleges by the typical deadlines. Remember: • Scores from an entire SAT test (critical reading. writing and mathematics sections) will be sent - scores of individual sections from different test dates cannot be selected independently.

,

• You can send any or all scores to a college on a Single report - it will not cost more to send one, multiple or all test scores. • You receive four free score reports with your registration. We continue to recommend that you take fuU advantage of these reports. • Score Choice is available via the Web or by calling Customer Service (toll free within the United States). 7

GETTING STARTED

Questiori-and-Answer Service (OAS) The Question-aod-Answer Service (QAS) provides a report that lists the question number, the correct answer, the answer you gave, the type of question and the difficulty level of that question. You will also receive the actual questions from the edition of the SAT you took. QAS is offered for specific testing dates only (usually October. January and May). For the testing dates for which the Question-andAnswer Service is available. please visit www.collegeboard.com. You can order QAS when you register for the SAT. or when you complete the order form sent with you r

score report. QAS can be ordered up to five months after the test dale.

Student Answer Service (SAS) The Student Answer Service (SAS) provides a report that lists the question number. the difficulty of each SAT question and whether you answered it correctly. incorrectly or did not answer. Also included are the question or content types for each test section. Actual test questions are not included. SAS is available for all test dates for which QAS is not available. SAS can be ordered when you register for the SAT. or when you complete the order form sent with your score report. SAS can be ordered up to five months after the test date.

8

CHAPTER 2

How to Do Your Best on the SAT

This chapter offers suggestions for how to get ready for the SAT, how to pace yourself while taking the test, how to approach each type of question and how to feel more confident on test day.

There's No Substitute for Studying Preparing for t he SAT is like studying for any exam. You'll feel a lot more confident if you review the test's format and become familiar with its content. You've actually been preparing for the SAT all of your academic life. The best way to get ready fo r the SAT is to work hard in school, take challenging courses, and read and write as much as you can.

• Learning to read effectively gives you the ability to figure out what the author means as well as what the author says.

• Improving your vocabulary gives you tools to fig ure out new words from the context in wh ich they are used.

• Developing your problem-solving abilities helps you figure out what to do and how to do it and helps you deal with challenging problems even when you think you're stumped.

• Strengthening your writing helps you develop and express your ideas clea rly and convi ncingly.

How to Get Ready for the SAT Practice may not make perfect, but it defi nitely helps. 'That's why taking the PSAT/NMSQT (Prelimi nary SAT/Nat ional Merit Scholarship Qualifying Test) is one of the best ways to get familiar with the SAT. It includes questions like those

9

GETTING STARTED

Online Resources The College Board offers a wide range of free and low-cost online tools to help you get ready for test day. Available at collegeboard.com, the leading Web site for SAT and college-planning information, these resources can help you get familiar with and practice for the SAT. THE OFFICIAL SAT QUESTION OF THE DAY ""

Practice a different question each day with the College Board's popular SAT Question of the Day. Visit our Web site or sign up to receive daily test questions via e-mail. THE OFFICIAL SAT PRACTICE TEST

Print or enter your answers online as you take an official SAT practice test. See how you score and get detailed answer explanations to help you better understand where you need to improve. THE OFFICIAL SAT ONLINE COURSe-""

The most comprehensive online tool to help you get ready for the SAT, The Offidal SAT Online Course'" features 18 interactive lessons, official practice questions and tests, sample essays, automated essay scoring, personalized score The OttJclaJ reports and more. ~AT OnHne Coul'Be™ By using The Official SAT Study Guide'"; Second Edition, and The This book entitles you to a Offidal SAT Online Course together, you'll benefit from the best of discount on The OHicial SAT both formats - print and Internet. As a book buyer, you're entitled Online Course. To learn more, to a $10 discount for The Offidal SAT Online Course. To receive the visit www.collegeboard.com/ satonHnecourse. d iscount, you will need to visit www.collegeboard.com/satonlinecourse and answer questions about your book. You may already have access to The Official SAT Online Course through your school. To learn whether your school subscribes, ask a teacher or a counselor. CJ 10 CHAPTER 2 How to Do Your Best on the SAT This chapter offers suggestions for how to get ready for the SAT, how to pace yourself while taking the test, how to approach each type of question and how to feel more confident on test day. There's No Substitute for Studying Preparing for the SAT is like studying for any exam. You'll feel a lot more confident if you review the test's format and become familiar with its content. You've actually been preparing for the SAT aU of your academic life. The best way to get ready for the SAT is to work hard in school, take challenging courses, and read and write as much as you can. • Learning to read effectively gives you the ability to figure out what the author means as well as wh at t he author says. • Improving your vocabulary gives you tools to figure out new words from the context in which they are used. • Developing your problem-solving abilities helps you figure out what to do and how to do it and helps you deal with challenging problems even when you think you're stumped. • Strengthening your writing helps you develop and express your ideas clearly and convincingly. How to Get Ready fOT the SAT Practice may not make perfect, but it definitely helps. That's why taking the PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) is one of the best ways to get familiar with the SAT. It includes questions like those 9 How t o Do Your Best on the SAT SAT SKILLS INSIGHT As mentioned previously, this free online tool can help you understand what's tested on the test and what skills you need to do well and to achieve your desired score. You'll see that the skills on the test are the same skills you've been learning in the classroom! MVSAT Online registration is easy to use and always available. Most students register for the test online. You choose your test date and test center, provide credit card in forma· tion and get immediate registration confirmation. After the test, visit My SAT to receive your scores, view your score history and see where you sent your scores. You can also view a copy of you r essay. BOOK OWNERS' AREA Available exclusively to owners of this book, the online book owners' area pro· yides vaJllabJe feedback and can be use-d as a SJudy Jool in ne¥>ing you identify where you need to focus your efforts. After you've taken an official practice test in this book, you can enter you answers online. We'll provide a practice score report and answer explanations for each practice test. For more information, go to www.collegeboard.com/SATstudygu ide. Col/ege PIBnning The College Board Web site (www.collegeboard.com) provides all of the information and tools you need to prepare for your move from high school to college. You'll find complete and up -to-date information on College Board tests, including the SAT, SAT Subject Tests"', CLEp· , AP and PSAT/NMSQT, as well as va luable resources for college planning. Among the most popular online college-plann ing features are: • My Organizer. This tool shows a personalized to·do list for important college planning activities. It will help you remember test and application deadlines and build and update college lists. • College Search. Look for a college by name or by criteria such as ~epinMind Regist er early for the test so you have the best chance of getting the test center nearest to your home. size or location. For all colleges that match you r search, we'll give you a College Profi le - a detailed record provid ing information on everyt hing from majors to financial aid. Save colleges to your personalized list, or search for similar ones with the LikeFinder tooL • Pay for College. This section features articles about paying and borrowing for college, as well as College Financing Calculators to help evaluate alternatives. Here, you'll also find the Scholarship Search tool for funding options, and an application for CSS/Financiai Aid PROFILE·, which you can complete online. 11 GETTING STARTED Before the Test Know what to expect from the test: the types of questions, the number of questions and their order on the test. Understand the directions for all eight types of quest ions. Take time to carefully read the directions for the questions. That way, you won't have to spend extra time studying the directions on the day you take the SAT. If you understand the instructions, you'll feel more confident and be less likely to make careless errors. Arrive at the test center by 7:45 a.m ., unless your admission ticket specifies a different time. Remember to take the following items: • your admission ticket • an acceptable photo ID (see Table 2.1) • several No.2 (soft lead) pencils and soft erasers • an acceptable calculator (see Chapter 14 for details on which types are acceptable) • a watch (wit hout an audible alarm), so you can keep track of your time • a snack that can be easily stowed under desks or chairs in the test room and can be consumed outside the test room during breaks Table 2.1 Acceptable Photo IDs 12 driver's license {with your photo} school identification card valid passport student ID form that has been prepared by your school on school stationery and includes a recognizable photo and the school seal, which overl aps the photo , How to Do Your Best on the SAT Table 2.2 Checklist: What to Take to the SAT I Need I Heve appropriate photo 10 admission ticket several No.2 pencils and soft erasers calculator with fresh batteries watch snack I know the way to the test center and have instructions for finding the entrance on Saturday or Sunday. I am leaving at _ _ a.m.This will give me plenty of time in case I run into delays. My alann is set. "'Be On Time or You Can't Take the Test.· .. Start your mental preparation the day before the test. • Get a good night 's sleep. • Have everything that you need for the test ready the night before. • Review Table 2.2 to make su re you have everything you'll need the next day. ~epinMlnd Make sure you use a No. 2 pencil. It is very important that you fill in the entire circle on the answer sheet darkly and completely. If you change your response, erase it as completely as possible. 13 GETTING STARTED During the Test Read and think carefully. Consider all the choices in each question. Don't lose points on easy questions through careless mistakes. Use your test booklet. Your answer sheet must be kept neat and free of stray marks, but you can mark up your test booklet. You can write whatever you want, wherever you want, in the sect ion of the booklet you're working on. You will not receive credit for anything written in the booklet. though. Here are some pointers for using you r test booklet. Time and Hassle Savers Mark skipped questions in your test booklet. Cross out choices to eliminate 8S you move through the test. When skipping questions, be sure you leave the right cin:les on the answer sheet blank (to avoid mar1l:ing answers to the wrong question!!). • Mark each question that you don't answer so that you ca n easily find it aga in. • Draw a line through each choice as you eliminate it when you work on a question. • Mark sections. sentences or word s in reading passages. • In mathemat ics, make drawings to help you figure oul word problems. Mark key information on graphs. Add information to drawings and diagrams as you v{()rk on them. Check your answer sheet regularly to make sure you are ;11 the rigllt place. losing your place on the answer sheet will affect your test results. Check the number of the question and the number on the answer sheet every few questions. Thi s is especially important when you skip a question . Pacing and Timing . Each question on the test takes a certai n amount of time to read and answer. That 's where pacing comes in. If you had un lim ited time, or very few questions to a nswer, pacing might not be important. But the test ends in 3 h.o urs and 45 minutes whether or not you finished answering every question. So you have to keep moving through the test. Remember that you are allotted a certa in amount of time for each section and are not allowed to move on to the next sect ion if you fin ish early. Skilled test-takers develop a sense of tim ing. They spend time on the questions they are most likely to answer correctly and leave some time for review. Easy Does It Work at an even. steady pace. but keep moving. Don't spend so much time working through hard questions that you lose time to find and answer the easier ones. Work on less time-consuming questions before moving on to those that demand more time. Save time by marking questions as you work on them and crossing out choices you can eliminate as you move through the test. 14 r How to Do Your Best on the SAT Most questions within a section range from easy to hard. Within a group of questions, such as Identifying Sentence Errors. the easier ones come first and the questions become more difficult as you move along. If you find that one kind of question is too difficult, qUickly read through the rest of the questions in that group. There might be others you can answer. Then go on to the nex t group of questions in that section. The questions in the passage-based reading and improving paragraph sets don't range from easy to hard. An easier passage-based reading question might follow a harder one. (See Chapters 4 through 6 for details on the critica l reading section of the SAT.) Keep track of time during the test. The SAT includes 10 sections for which you have a tota l of3 hours and 45 minutes to complete. First check to see how much time you have to complete each section. Then, while practicing for a nd taking the test, develop a habit of occasionally checking you r progress through the test. That way you know when you a re one-fou rth of the way through the time allotted for a section, when you are halfway through and when you have five minutes left. If you fin ish a section before time is called, use the remaining time to check your answers. Know which questions are best for you. After practicing the different kinds of questions on the tests in this book, you will probably know which you feel most comfortable with. Some types of questions may take you longer than others. You might want to begin with that type of question rather than at the beginning of the section. But you'll have to be careful. Be sure to ma rk in your test booklet what you skipped so that you can return to it. Getting Started Skip questions. All questions are worth the same number of points regardless of the type or difficulty. So if you can't answer a question without spending a long time figur ing it out, go on to the next one. If you aren't sure about how to answer a question, or you don't know where to begin , stop working on that question. You may have time to come back to it. Remember to mark the question in your test booklet so that you can find it later. Answer the easy ones first. Once you know where the easy and hard quest ions are, answer the easy questions before tackling the more time-consuming questions. All questions are worth the same number of points. Making an Educated Guess When you're not sure of an a nswer, try making an educated guess. This may be helpful for the multiple-choice questions and for the mathematics questions for which you come up with your own answer. Multiple-choice questions. When you are not sure of an answer to a multiplechoice question, eliminate all the choices that you know are wrong and make an 15 GETTING STARTED educated guess from the remaining ones. The more choices you can eliminate, the better your chance of choosing the right answer and earning one point. To correct for random guessing, J.A point is subtracted for each incorrect answer. Because of this, random guessing probably won't improve your score. In fact. it could lower you r score. If you can't eliminate any choice, move on. You can return to the question later if there is time. Student-produced respoIJse questions. For the mathematics questions that are not multiple choice. fill in your best educated guess. You lose no points for incorrect answers to these problems. If you have no idea how to approach a problem, move on. Again, you can return to it later if there is time. How to MBke Bn EducBted Guess Here are some SAT questions that show how to make an educated guess. EDUCATED GUESSING EXAMPLES 1. Sentence Completion He was ------- businessman, but in his personal life he was kind, thoughtful, and -------. (A) (8) (C) (D) (E) a competent .. self-centered an avaricious .. menacing a scrupulous .. tactful a ruthless .. magnanimous an amiable .. compassionate What to do Start with the second blank in the sentence: He was ------- businessman, but in his personal life he was kind, thoughtful. and The word must be positive because it is in a series with the words kind and thoughtful. The second words in (A) and (B) - self-centered and menacing - are both negative. so you can eliminate those two choices. That leaves (C). (D) or (E) as possible correct answers, giving you one chance in three of getting it right. Make an educated guess. Even though you may get this particular question wrong, it is to your advantage to make an educated guess if you can eliminate one or more of the answer choices as definitely wrong. The correct answer is (0). 16 How to Do Your Best on the SAT 2. Mathematics/Mu ltiple Choice ~ _ P . Q In the figure above, PQ is a straight line. Which of the following must be true about x andy? (A) x+y-180 (B) 90+x-180-y (el 90+x-y (D) 2x -y (El 2y - x What to do Which of the answer choices can you eliminate by estimation? • Clearly, the answer cannot be choice (A) because both 90°. Cross off choice (A). XO and y" are less than • Choice (B) looks possible, but what about (C)? • It's pretty obvious that (C) is not the answer because 90 + x is greater than y. Cross off choice (C). • Choice (D) looks possible, so don't cross it off. • But choice (E) is not possible, so cross it off. Now you're left with on ly two possible answers, (8) and (D). If you were simply guessing, you are now faced with only two choices. If you notice that XO + yO must equal 90° and examine choice (8), you will see t hat 90 + x = 180 - Y simplifies to x + Y = 90. The correct answer is choice (8). 3. Identifying Sentellce Errors Carefully designed programs of healthy diet and regular exercise has prOvided growing A B teenagers nOI only healthier lungs and hearts, but also improved skin, teeth, and hair. C 0 NQ error E What to do Read the sentence through entirely to see if the error is clear to you immediately. If it is not, consider the most common errors people make in writing sentences: grammar, usage, diction and idiom. Choice (A) is an adverb (ending in -Iy) and it does 17 GETTING STARTED indeed modify the adjective designed, so that potential error is eliminated. Likewise. the adjective improved in choice (D) correctly describes the nouns "skin, teeth, and ha ir." You can cross (0) off. You are now left with choices (B), (C) and (E), a"nd you might determine from those fewer choices which is the actual answer for this item. Even if you guess wrong, your chances of getting this question correct have been improved from one in five to one in three. The correct answer is (B) because the plura l subject programs requires a plural verb, which would be "have provided" rather than the Singular "has provided." Get Confident How you do on the SAT depends on how well you apply your knowledge. But your results can also reflect how you feel on the day you take the test. Your scores can be affected if you are nervous and distracted, if you are concentrating poorly or if you have negative feeli ngs. Think Positively Getting down on yourself during the test does more than make you feel bad. It can take away the confidence you need to solve problems. It can distract you. Keep up your confidence and focus on each question. The SAT shows what you know and what you know you can do. The test has no trick questions. If you have taken challenging course work in high school, you should be feeling good about yourself and your capabilities. Stay Focus!3d Ignore distractions. Think only of the question in front of you . If you catch yourself daydreaming, bring your focus back to the test. Concentrate on Your Own Progress Suppose you get stuck on a question. Suppose you run into a batch of questions that are particularly difficult for you. You m ight be tempted to look around to see how everyone else is dOing. Don't do it! You'll just see that others are filling in their answer sheets. Thi nk of this: • Everyone works at a different pace. Your neighbors may not be working on the same question that has puzzled you. 18 r How to Do Your Best on the SAT • Thinking about what someone else is doing takes away time you could be using on the lest. • Within a testing room, the sect ions of the test arc in different sequences. Students sitting ncar you may be working on different sections. Keep the Test in Perspective The SAT is important , but how you do on one lest won't decide whether you get into college. • The test is only one factor of many in the college admissions decision. • Nonacademic admissions criteria are important, too. These include ext racurricular activities and personal recommendations. College admissions officers at individual colleges will usually be glad to discuss their schools' admissions policies with you. • If you don't do as well as you hoped to, you can take the test again or use Score Choice to show colleges the scores that you feel best represent your abilities. Most colleges look at you r highest score on each section, so even if you opt to use Score Choice you should feel comfortable sending all of your scores. You're in Control Making a plan for taking the SAT will keep you in control during the test: Practice each type of question. Remember that the easier questions generally come first in each section. Learn how to pace yourself. Learn how to make an educated guess. If you're in control, you'll improve your chances of doing your best. Taking the Test Again Research shows that most students do better on the SAT if they take the test a second time. Again, as mentioned in Chapter 1, approximately one out of every two high school students taking the SAT takes it at least once. Most who repeat the test take it once in the spring of their junior year and once in the fall of their senior year. There is no evidence that taking the test more than twice is beneficial to your score. But remember, all of the work you've done in school - including your reading, writing and mathematics - is what really helps you to do your best on the test and to be better prepared for college. 19 GETTING STARTED 1.-:" ® .(iI =I .~ -.... Recap Before the Test • Learn the directions for all eight question types. • Get a good night's sleep. • Have everything that you need for the test ready the night before. • Make sure you know how to get to the test center and have any special instructions for finding the entrance on Saturday or Sunday. • Leave early enough so that you will have plenty of time in case of delays while traveling to the test center. During the Test • First answer all the easy questions you can. • Keep moving. • Keep in mind that most questions are arranged from easy to hard. • Remember which questions are best for you. • Remember that all questions are wort h the same point value. • Eliminate choices. • Make an educated guess. • Watch the time you spend on anyone question. • Use your test booklet as scratch paper, and mark questions to go back to. • Check your answer sheet regularly to make sure you're answering the right question. • Keep your answer sheet neat. Feeling Confident • Think positively. Negative t h oughts will just distract you from doing your best. • Stay focused. Think only about the question you are trying to answer. • Concentrate on your own progress. Don't pay attention to what others in the room are doing or how quickly they may be working. • Keep the test in perspective. The SAT is not the only factor in college admissions decisions, and you can always take the t e st again. • Remember, you're in controL You can always choose t he scores you send with Score Choice . 20 . CHAPTER 3 About the PSAT/NMSQT® If you want practice for the SAT, then the PSATlNMSQT is for you. (PSAT/NMSQT stands for Preliminary SAT/National Merit Scholarship Qualifying Test.) This test also gives you a chance to enter scholarship competitions sponsored by the National Merit Scholarship Corporation and, through the Student Search Service, a chance to hear from colleges looking for students like you. The PSAT/NMSQT measures the critical reading, mathematics and writing skills that you've been developing all your school years. The test is given by high schools in October. Your school counselor can help you sign up for the PSAT/NMSQT. Many students take the test during their sophomore and junior years - but only test scores from thei r junior year are used for scholarship competitions. Ask your school counselor for a copy of the Official Student Guide to the PSATINMSQT, which includes a complete practice test. Why You Should Take the PSAT/NMSQT Taking the test helps you to: • practice for the SAT • assess your critical reading, mathematics and writing skills. A comprehensive score report gives helpful feedback on the skills you need to work on. • compare you rself with other college-bound students from around the country • receive projected SAT scores • qualify for entry into scholarship competit ions sponsored by the National Merit Scholarship Corporation • participate in the Student Search Service to receive information from colleges and scholarship organizations 21 GETTING STARTED Types of Questions The PSAT/NMSQT includes critical reading, mathematics and writing skills questions. (See Table 3.1 for details.) The PSAT/ NMSQT allows 2 hours and 10 minutes and includes five sections: • Two 25-minute critical reading sections • Two 25-minute mathematics sections • One 30-minute writing skills sect ion Score Report Your PSAT/NMSQT Score Report gives you feedback on your test performance and other valuable information: • PSAT/NMSQT scores for critical reading. mathematics and writing skills • Score ranges • Percentiles (for juniors or sophomores) • Se1ection index used by the National Merit Scholarship Corporation for initialentry into their scholarship competitions (sum of your scores in all three sections) • Comprehensive question+by+question feedback • Academic skills feedback • Online access to questions and answer explanat ions • Basic eligibility criteria and status for National Merit Scholarships • Guidance information to help in college and career planning Preparing for the PSAT/NMSQT As in preparing for the SAT. the best way you can prepare for the PSAT/NMSQT is to take challenging academic courses. work hard in school and read extensively. To become familiar with the questions that appear on the test: • Review the SAT tesHaking reminders and approaches on these pages. • Read Chapter 2. "How to Do Your Best on the SAT." • Before the test. become familiar with question types and directions by doing practice questions. which are also covered in the Official Student Guide to the PSA TINMSQT. 22 About the PSATINMSQT • Take the complete Practice Test included with your Official Student Guide to the PSATINMSQT Table 3.1 Nu mber a ndTy pes of Qu estions w ith Time Allotted for Each Section of the PSAT/N MSQT Sec tion No. of Quest io ns Time Allotted Critical Reading (multiple-choice questions) Sentence completion 13 Passage·based read ing 35 Total critical reading questions 48 50 minutes (two 25·minute sections) M athematic s Multiple choice 28 Student-produced response (grid-ins) 10 Total mathematics questions 38 50 minutes (two 25-minute sections) Writing Skills (mu ltiple-cho ice questions) Identifying sentence errors 14 Improving sentences 20 Improving paragraphs 5 Total writing questions 39 30 minutes (one section) Pointers for the PSATINMSOT 1. Know the directions for each type of question. 2. Expect easy questions at the start ofeach group of questions (except in passagebased reading in the critical reading section and improving paragraphs in the writing skills section). 3. Answer as many easy questions as you can because all quest ions are worth the same number of points. 4. Read all the answer choices for multiple-choice questions. 5. Make sure you understand what the question is asking. 6. Do scratchwork in the test booklet. 7. Work steadily. 23 GETTING STARTED 8. Understand the concept of educated guessing - that is, if you cannot find the correct answer, eliminate the choice or choices that you know are wrong and make an educated guess from the remaining answers. 9. Bring a calculator that you are comfortable using. lO. Practice and have a thorough understanding afhow to complete math studentproduced response questions. I I. Relax. Preparing for the Critical Reading and Mathemati cs Sections The types of critical reading and mathematics questions on the PSAT/NMS QT are the same as on the SAT. Here's what you'll need to do to prepare: • Review the critical reading and mathematics chapters in th is book. • Go through the mathematics review chapters carefully (see Chapters IS to 18), If it is dose to exam time, concentrate on the mathematics sk ills and concepts that you've studied but may need to review. If you have time before the test, start lea rn ing some of the unfamiliar skills and concepts. • Practice applying the approaches and reminders on the sample tests. Preparing for the Writing Section The writing skills sect ion of the PSAT/NMS QT includes the three types of grammar and usage multiple-choice questions that appear on the SAT writing section: • Identifying sentence errors • Improving sentences • Improving paragraphs The writ ing section includes 39 quest ions on grammar a nd usage, and it assesses your ability to use language in a clear, consistent manner and to improve writing by revising and editing. Test questions do not ask you to define or use grammatical terms and do not test spelling or capitalization. The PSAT/NMSQT does not include an essay portion. Here are some ideas on how to approach the writing skills sect ion of the test: • If you cannot find the correct answer, eliminate the choice or choices that you know are wrong and make an educated guess from the remaining answers. • Review the writing multiple-choice chapters in this book (Chapters 8 and 10 to 13). 24 About the PSAT/NMSQT • Try to answer the sample writing questions in this book and study the explanations for each sample. Important Review in September When the Official Student Guide to the PSATINMSQT arrives at your school in September (ask your counselor for it), review the explanation sections and then take the full-length practice test. If any questions pose problems for you, use th is book again to review those question types to improve your understa nding. And. of course, work in class and with your teachers to hone your academic skills daily. 25 PART II The Critical Reading Section 27 CHAPTER 4 About the Critical Reading Section When you get to the critical reading section, you'll find two types of multiple-choice questions: • Sentence completion. There are 19 multiple-choice quest ions that test your vocabulary and your ability to understand fairly complex sentences . • Passage-based reading. There are 48 questions that are based on passages that range from 100 to 850 words. The content of the passages is drawn from the humanities, literary fiction, social studies, and natural sciences. Critical reading skills are fu.ndamental building blocks of academic success. The two types of critical reading questions test how well you understand the written word. Your ability to read carefully and to think about what you read is essential to your success in college. In college. you will have to learn a great deal on your own from your aSSigned reading, even in courses that are not language arts, such as mathematics and science. BUilding your vocabu lary is a va luable life skill. Having a large and varied vocabulary can help you better express yourself. The best way to improve you r vocabulary is by reading. Approaches to the Critical Reading Section )- Work on sentence completion questions first. About one-third of the critical reading quest ions are sentence completions. Work on these fi rst in a ny section that includes both types of ceitical reading quest ions. "!he sentence completion questions take less time to finish than the passagebased reading questions. But remember to save enough time to read the passages. ~ Keep in Mind Answer the sentence completion questions you're comfort able with before moving on to the passage-based reading questions. 29 THE CRITICAL READING SECTION )- Mark your test booklet. As you work on one of the critical reading test sections, you may want to use the following three·step approach: I. Begin with the first set of sentence completions. Answer as many questions as you can. In your test booklet, mark each question you don't answer so that you can easily go back to it. 2. After moving through the first set, go back and take a quick glance at the questions you marked. Answer the ones you can without spending a lot of time on anyone question. 3. Then move on to the passage-based readi ng quest ions. )- Remember that the difficulty of sentence completion questions increases as you move through a question set. When these questions become difficu lt to a nswer, give the rest of them a quick read before you skip ahead to the passage-based reading questions. All sentence complet ion quest ions a re based in part on your knowledge of vocabulary. It doesn't take long to read these questions, and you may pick up a correct answer or two. You may see a word that you know that might improve your chances of answering the question correctly. ~eplnMlnd Keep track of the questions you w ant t o go back to and read again by mar1l:ing the questions in your test booklet . When skipping questions, though, be sure to keep track of your place on the answer sheet. )0 Use the process of elimination. If you have time to go back to some of the difficult questions that you skipped. try eliminating choices you know are wrong. (This is a good approach for the entire test.) Sometimes you can get to the correct answer that way. If not, eliminating choices will at least allow you to make educated guesses. )0 Consider related words,familiar sayings and phrases, roots, prefixes and suffixes. If you don't k now what a word means right away, stop for a moment. Have you ever heard or seen a word that may be related to it? You can get help from common sayings and phrases. If you don't know a word but a re familiar with a ph rase that uses it. you might be able to figure out the word. For instance, you may not immediately remember what the words ovation and annul mean. But you probably wou ld recognize them in the phrases "a standing ovation" and "annul a marriage." If you can recall a ph rase or saying in which a word is used, you may be able to figure out what it means in another context. 30 CHAPTERS Sentence Completion Having a broad vocabulary always comes in handy, espedally when you're doing parts of the SAT such as the sentence completion questions. Having the ability to ~ understand the logic of complex sentences is also helpful in this section of the SAT. In addition, several approaches can help you work through even the toughest questions. The following box provides the directions that will appear on the test. The directions include a sample question. ~ep in Mind Be familiar with the test directions before test day. Each sentence below has one or two blanks, each blank indicating thai something has been omitted. Beneath the sentence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, best fits the meaning of the sentence as a whole. Example: Hoping to ------- the dispute, negotiators proposed a compromise that they felt would be ------- to both labor and management. (A) enforce .. useful (B) end .. divisive (C) overcome .. unattractive (D) extend .. satisfactory (E) resolve .. acceptable @®©@ . Types of Questions The SAT has two different types of sentence complet ion questions: vocabulary in context and logic based. FollOWing are some examples of each type of question. Vocabulary-in-Context Questions To answer this type of question, you need to know how the words are used in the context of the sentence. If you know the definitions of the words involved, you have a better chance of selecting the correct a n s~er. 31 THE CRITICAL READING SECTION There are both one-blank and two-blank vocabulary-in-context questions. EXAMPLE 1 Ravens appear to behave -------, actively helping one another to find food. (A) mysteriously (B) warily (e) aggressively (D) cooperatively (E) defenSively Answer: The correct answer is (D). Expiarlation: This sentence asks you to look for a word that describes how the ravens behave. The information after the comma restates and defines the meaning of the missing word. You are told that the ravens "actively help one another." Only one word among the choices accurately describes this behavior: cooperatively. EXAMPLE 2 Both ------- and -------, Wilson seldom spoke and never spent money. (A) (B) (C) (D) (E) vociferous .. generous garrulous .. stingy effusive .. frugal taciturn .. miserly reticent .. munificent A'iswer: The correct answer is (0). Explanation: In this sentence, you are looking for two words that describe Wilson. One of the words has to mean that he "seldom spoke" and the other that he "never spent money." The correct answer is "taciturn .. miserly." Taciturn means "shy, unwilling to talk." Miserly means "like a miser, ext remely stingy." Logic-Based Questions The follOWing questions require you to know the meanings of the words, know how the words are used in context and understand the logic of a rather complicated sentence. EXAMPLE 1 After observing several vicious territorial fights. Jane Goodall had to revise her earlier opinion that these particular primates were always •..••.. animals. (A) (6) (C) (D) (E) ignorant inquisitive responsive cruel peaceful Answer: The correct answer is (E). 32 Sentence Compl etion Explanation; To answer this question, you have to follow the logical flow of the ideas in the sentence. A few key words reveal that logic. First, the introductory word "After" tells you that the information at the beginning of the sentence is going to affect what comes later. The word after also gives an order to the events in the sentence. Second, the word revise tells you that something is going to change. It is going to change after the events described at the beginni ng of the sentence. So the events at the beginning really cause the change. Finally, the end of the sentence-"her ea rlier opin ion that these particu lar primates were always ------- animals" -tells you what is changing. The word filling the blank should convey a meaning you would have to revise after seeing the animals fight. Peaceful is the only such word among the five choices. EXAMPLE 2 Although its publicity has been -------, the film itseifis intelligent, well-acted, handsomely produced, and altogether ------., (A) tasteless .. respectable (8) extensive .. moderate (e) sophisticated .. amateur (D) risque .. crude (E) perfect .. spectacu lar Answer; The correct answer is (A). Explanation: The first thing to notice about th is sentence is that it has two parts or clauses. The first clause begins with "Although," the second clause begins with "the film." The logic of the sentence is determined by the way the two clauses relate to each other. The two parts have contrasting or conflicting meanings. Why? Because one of the clauses begins with "Although." The word although is used to introduce an idea that confl icts with something else in the sentence: Although somet hi ng is true, something else that you would expect to be true is not. The answer is "tasteless .. respectable." You wou ld not expect a film with "tasteless publicity" to be "altogether respectable." But the introductory word although tells you that you shou ld expect the unexpected. 33 THE CRITICAL READING SECTION Approaches to the Sentence Completion Questions ... Start out by reading the entire sentence, saying "blank"for the blank(s}, This gives you an overall sense of the meaning of the sentence and helps you figure out how the parts of the sentence relate to each other. )- Always begin by trying to determine the standard dictionary definitions of the words in the sentence and the answers. To answer sentence completion questions, you usually don't have to know a nonstandard meaning of a word . . . Keep in mind that introductory and transitional words are extremely important. They can be the key to figuring out the logic of a sentence. They tell you how the parts of the sentence relate to each other. For example, look at the following common introductory and transitional words: . • but • although • however • yet • even though These words indicate that the two parts of the sentence will contradict or be in contrast with each other. There are many other introductory and transitional words that you should watch for when working on sentence completion questions. Always read the sentences carefully, and don't ignore any of the details. )- Be aware that some of the most difficult sentence completion questions contain negatives, which can make following the logiC of the sentences challenging. Negatives in two clauses of a sentence can be even more of a challenge, as in this example: According to Burgess, a novelist should not preach, for sermon izing has no place in good fiction. A negative appears in each clause of this sentence. The transitional word for indicates that the second part of the sentence will explain the first. )- Figure out what sort of word(s) should fill the blank(s) before looking at the choices; then look for a choice that is similar to the one(s) you thought of For many oneblank questions, especially the easier ones, you'll find the word you thought of among the choices. Other times, a close synonym for your word will be one of the choices. 34 Sentence Completion For example, try answering the following sentence completion question without looking at the choices: Once Mu rphy left home for good, he wrote no letters to his worried mother; he did not, therefore, live up to her picture of him as her ------- son. The transit ional word therefore indicates that the informat ion in the second part of the sentence is a direct, logical result of the informat ion in theftrst part. What words might fit in the blank? The second pa rt of the sentence includes a negative (" he did not ... live up to her picture ..."), so the blank must be a positive term. Words li ke perfect, sweet, respectful, devoted-all could fit in the blank. Now, look at the actual choices: (A) . misunderstood (B) elusive (C) destructive (0) persuasive (E) dutiful Choice (E) dutiful is the on ly choice that is even close to the ones suggested. Therefore, (E) is the correct answer. You can also try this technique with two-blank questions. You are less likely to come up with as close a word match, but it will help you get a feel for the meaning and logic of the sentence. )- With two-blank questions, try eliminating some answers based on just one blank. If one word in an answer doesn't make sense in the sentence, then you can reject the entire choice. For example, try approaching two-blank questions like this: • Work with one of the blanks alone. Eliminate any choices in which the word doesn't make sense. • Work on the other blank alone. Eliminate any choices in which that word doesn't make sense. If only one choice is left. that is the correct answer. If more than one choice remains, go to the next step. • Work on both blanks together only for the remaining choices. • Always read the complete sentence witl! botl! words in place to make sure your choice makes sense. 35 THE CRITICAL READING SECTION Example 2 of the logic-based qu.estions shows how this approach works. Here it is again: Although its publicity has been -------, thefilm itselfis intelligent, well-acted, handsomely produced, and allogether -------, (A) tasteless .. respectable (B) extensive .. moderate ee) sophisticated .. amateur (D) risque .. crude (E) perfect .. spectacular As you can see, the first blank is not tightly controlled by the words immediately around it. The firs t word depends on the word in the second blank. So start with the second blank. The second blank is part of a list th at includes "intelligent, well-acted, handsomely produced, and altogether ____ _ . " The word and indicates that the last word in the list (i.e., the blank) should be a positive word, in general agreement with the others. With that in mind, examine the second words in the following answer choices: • intelligent, well-acted ... and altogether respectable • intelligent, well-acted ... and altogether moderate • intelligent, well-acted ... and altogether amateur • intelligent, well-acted ... and altogether crude • intelligent, well-acted . .. and altogether spectacular Amateur and crude are defin itely not complimentary. No matter what the rest of the sentence says, neither of these words makes sense in the second blank. So you can eliminate the answers that contain amateur and crude. With two choices eliminated, the question becomes much easier to deal with. )- Remember that the instructions for all the sentence completion questions ask you to choose the best answer. One choice may seem to make sense, but it still might not be the best of the five choices. Unless you read all the choices, you may select only the second best and thus answer incorrectly. )- Check your choice by reading the entire sentence with the answer you have selected in place to make sure the sentence makes sense. This step is extremely important, especially if you have eli minated choices while working through the question. For example, choice (A) in Example 2 is correct because the words respectable and tasteless contrast with each other. Such a contrast is logically consistent because of the although construction of the sentence. 36 Sentence Completion Sample Questions Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, httt fits the meaning of the sentence as a whole. Example: Hoping to ------- the dispute, negotiators proposed a compromise that they felt would be ------- to both labor and management. (A) enforce .. useful (B) end .. divisive (C) overcome .. unattractive (D) extend .. satisfactory (E) resolve .. acceptable ®®©@ . 1. A judgment made before all the facts are known must be called -------. (A) harsh (B) deliberate (C) sensible (D) premature (E) fair 2. Despite their -----.- proportions, the murals of Diego Rivera give his Mexican compatriots the sense that their history is ------- and human in scale, not remote and larger than life. (A) monumental .. accessible (8) focused .. prolonged (C) vast .. ancient (D) realistic .. extraneous (E) narrow .. overwhelming 3. The research is so ------- that it leaves no part of the issue unexamined. (A) comprehensive (B) rewarding (C) sporadic (D) economical (E) problematic 4. A dictatorship ------- its citizens to be docile and finds it expedient to make outcasts ofthose who do not -------. (A) forces .. rebel (8) expects .. disobey (C) requires .. conform (D) allows .. withdraw {El forbids .. agree S. Alice Walker's prize-winning novel exemplifies the strength of first-person narratives; the protagonist tells her own story so effectively that any additional commentary would be -------. (A) subjective (B) eloquent (e) superfluous (D) incontrovertible (E) impervious 37 THE CRITICAL READING SECTION 6. The Supreme Court's reversal ofits previous ruling on the issue of states' rights .. -.--its reputation for -------. (A) sustained .. infallibility (8) compromised .. consistency (e) bolstered .. doggedness (D) aggravated .. inflexibility (E) dispelled .. vacillation 38 Sentence Completion Answers and Explanations I. A judgment made before all the facts are known must be called -------. (A) harsh (8) deliberate (e) sensible (D) premature (E) fair Answer: The correct answer is (D). Explanation; Getting the correct answer to this question depends almost entirely on knowing the definitions of the five words you must choose from. Which of the choices describes a judgment made before "all the facts are known"? Such a judgment, by definition, is not "deliberate," and the sentence doesn't tell us whether the judgmen~ was "ha rsh:' or lenient. "sensible" or silly, "fair" or unfai r. Premature means hasty or early; therefore, it fits the blank perfectly. This is the kind of one-blank vocabula ry question for which you might be able to predict the answer based on the information given Know your vocabulary. Think in the sentence . You might have thought of other words that could carefully about the meanings have completed the sentence satisfactorily- for instance, rash, hasty of the words in the answer choices. or risky-but none of them nor any synonyms for them appear among the choices. When you see the choices, you should recognize that premature has connotations similar to the words you thought of. ~epinMlnd 2. Despite their ------- proportions, the murals of Diego Rivera give his Mexican compatriots the sense that their history is -- ----- and human in scale, not remote and larger than life. (A) monumental .. accessible (B) focused .. prolonged (e) vast .. ancient (D) realistic .. extraneous (E) narrow .. overwhelming Answer: The correct answer is (A). Explanation: The keys to this sentence are the word "Despite," the words "human in scale," and the words "not remote and larger than li fe." The word fi lling the first blank has to be one that would relate closely to something that seems "larger than life," as (A) monumental does, but so does (C) vast. The word filling the second blank has to fit wilh "human in scale," which (A) accessible does. If you focus on only one of the two blanks, you will be able to eliminate several choices before you even think about the other bla nk, as in this case, where it is possible to eliminate answers (B), (D) and (E) almost immediately. 0epinMind Watch for key introductory and transitional words that determine how the parts of the sentence relate. Then try answering two-blank questions one blank at a time. If you can eliminate one word in a choice, the entire choice can be ruled out. 39 THE CRITICAL READING SECTION 3. The research is so ------- that it leaves no pari of the issue unexamined. (AI comprehensive (BI reward ing (CI sporadic (DI economical (EI problematic ~epinMind A nswer: The correct answer is (A). Explanation: Try filling in the blank without read ing the answer choices. What kind of words would fit? Words like complete, thorough or extensive could all fit. Now look at the a nswer choices. Choice (A) comprehensive is very si m ilar to the words suggested , and none of the other choices fi t at all. If no possible answer occurs to you before you look at the choices. Think about the logic of the sentence without looking at the choices. Then look for the choice that has 8 s imilar meaning to the words you thought of. try to relate each choice to the details of the sentence. In this case you are looki ng for a word that would match the detail "it leaves no part of the issue unexamined." 4. A dictatorship ------- its citizens to be docile and finds it expedient to make outcasts of those who do not -------. (A) forces .. rebel (8) (C) (0) (E) expects .. disobey requi res .. conform allows .. withdraw fo rbids .. agree Answer: The correct answer is (C). (;.ep in Mind Think carefully about the standard dictionary definitions of the important words in the sentence. Small words such as not can make a big difference. When you choose your answ er, read the entire sentence with the blank(s) filled in to be sure that it makes sense. Explanation: Answering this question depends in part on your k nowledge of vocabulary. You have to k now what the words dictatorship, docile and expedient mean. You also have to watch out for key words such as not. The fi rst word in each of the five choices is an action a d ictatorship might take, so you are more likely to find the correct answer by first examining the second word. Recognizing that the second word refers to what happens to "outcasts," and observing the cr ucial word not, you can elim inate rebel and disobey. That leaves conform, withdraw and agree as behaviors a dictatorship m ight wa nt to see d isplayed in its people. Conformity and agreement a re certainly qualities a dictator would want in the people. The tendency to withdraw is less likely, because people who are out of sight might also be out of the dictator's control; also, it is illogica l to make outcasts of everyone who does not withdraw. So choice (D) can be eliminated. If a dictator wants the people to conform, requiring them to be docile would help, so choice (C) looks good. In choice (E), if the dic tator is going to cast out those who do not agree, 40 Sentence Completion which is a very possible political reality, the first part of the sentence is illogical: dictatorships do not forbid people to be docile (gentle). Choice (C) is clearly the most logical and meaningful of the choices. 5. Alice Walker's prize-winning novel exemplifies the strength of first-person narra- tives; the protagonist tells her own story so effectively that any additional commentary would be -------. subjective eloquent (C) superfluous (D) incontrovertible (E) impervious (A) (B) Answer: The correct answer is (C). ~epinMind Explanation; Words like prize-winning, strength and effectively tell you Think about the meaning of the that the writer thinks Alice Walker's novel is well written. Therefore, sentence before you look at the would "add itional commentary" be necessary or unnecessary? Once choices. Get a sense of what you're looking for before you you've figured out that it is unnecessary, you can look for an answer start looking. with a similar meaning, which is choice (C) superfluous. That way, you may be able to answer the question more quickly because you won't have to plug in each choice one by one to see if it makes any sense. This is another single-blank vocabulary question that is best approached by trying to supply a satisfactory completion before you read the answer choices. 6. The Supreme Court's reversal of its previous ruling on the issue of states' rights ------- its reputation for -------. (A) sustained .. infallibility (B) compromised .. consistency (Cl bolstered .. doggedness (0) aggravated .. inflexibility (El dispelled .. vacillation Answer: The correct answer is (8). Explanation: Getting the correct answer to this question depends mainly on your knowledge of the meanings of the word choices. You have to know the definitions of the words before you can try the choices one by one to arrive at the correct pair. You also need to think about the central idea in the sentence: the Court's "reversal" does what to its "reputation" for what? The logic is complicated, and the vocabulary in the choices is difficult. You have to think for a moment about the attitude the sentence is probably trying to communicate. Most people would agree that the Supreme Court members think long and hard before they make a ruling. Reversing one of those rulings is probably an unusual and undesirable event. In each choice, the second word suggests a "reputation" the Court might have. Which of those 41 THE CRITICAL READING SECTION Ge p In MInd words most probably names a reputation we most usually expect of the Supreme Court? When you read the sentence to you rself, s ubstitute the word blank for each blank. Try to fig· • Infallibility in choice (A) and consistency in choice (B) - perhaps. ure out what the sentence is • Doggedness in choice (C) is less likely: it suggests persistence more than correctness. saying before you start plugging in the choices. • Inflexibility in choice (D) implies an unwillingness to keep an open mind, which is not a quality we would admire at our highest levels of justice. • And vacillation. in choice (E), is something we do not want to see in the Court at all . Look more closely at (A) and (8). If we choose (A), the sentence says that the reversal of the previous ruling sustained the Court's reputation for infallibility. That is contradic tory, so it ca nnot be the right answer. If we choose (B), the sentence means that the reversal of its ruling compromised (or imperiled or jeopardized) one of its most valued qualities, its consistency. That sounds like a meaningful sentence, and it is in fact the correct answer. 42 Recap 1. Be familiar with the directions before test day. 2. Answer as many easy questions as you can before spending time on the harder ones. 3. Read the sentence, substituting the word blank for each blank, to give you an overall sense of the meaning of the sentence. 4. Always begin by trying to determine the standard dictionary definitions of the key words in the sentence and the answer choices. 5. Know your vocabulary: think carefully about the meanings of the words in the answer choices. 6. Watch for key introductory and transitional words (e.g., but, although, however, yet, even though). These determine how the parts of the sentence relate. Also watch carefully for negatives. 7. Think about the logic of the sentence without looking at the choices. Try figuring out words to fill in the blank or blanks without looking at the answer choices. Then look for the choice that is similar to the one you thought of. B. Try answering two-blank questions one blank at a time. If you can eliminate one word in an answer, the ent ire choice can be eliminated. 9. Always check all the answer choices before making a final decision. A choice may seem okay, but it may still not be the best answer. Make sure that the answer you select is the best choice. 10. Check' your answer to make sure it makes sense by reading the entire sentence with your choice in place. 11. Eliminate answers that you know are wrong, and make an educated guess from those remaining. 43 THE CRITICAL READING SECTION Practice Questions Each sentence below has one or two blanks. each blank indicating that something has been omitted. Beneath the senlence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, ~ fits the meaning of the sentence as a whole. Exam ple: Hoping to ------- the dispute, negotiators proposed a compromise that they fell would be ------- to both labor and management. (A) enforce .. useful (8) end .. divisive {el overcome .. unattractive (0) extend . . satisfactory (E) resolve .. acceptable ®®©@ . I. In many cases, the formerly ------- origins of diseases have now been identified through modern scientific techniques. (A) insightful (B) mysterious (C) cruel (0) notable (El useful 2. Freeing embedded fossils from rock has become less .... --- for paleontologists, who now have tiny vibrating drills capable of working with great speed and delicacy. CAl exploratory (8) conclusive (C) tedious (D) respected (El demeaning 3. Many people find Stanley Jordan's music not only entertaining but also .... ---; listening to it helps them to relax and to ·······t he tensions they feel at the end of a trying day. (Al soothing .. heighten (B) therapeutic .. alleviate (el sweet .. underscore (D) exhausting .. relieve (E) interesting .. activate 4. Marine biologist Sylvia Earle makes a career of expanding the limits of deep·sea mobility, making hitherto-impossible tasks ---- ... through the new technology deSigned by her company. (A) (8) (C) (D) (E) 44 famous feasible fantastic controversial captivating Sent ence Completion 5. 'TWo anomalies regarding her character are apparent: she is unfailingly •. ····· yet bursting with ambition, and she is truly ..... ·· but unable to evoke reciprocal warmth in those with whom she works. (A) aspiring .. generous (8) mercenary .. impartial (C) impulsive .. resolute (D) persistent .. reserved (E) humble .. compassionate 6. In many parts or East Africa at that lime, wild animals were so ......• that it was almost impossible for a photographer to approach dose enough to film them. (A) rare (B) large (C) wary (D) numerous (E) unsightly 7. The unflattering reviews that his latest recording received were ••...•. by his fans, who believe thai everything he performs is a triumph of artistic """'. (A) dismissed .. creativity (8) hailed .. responsibility (e) suppressed .. self·promotion (D) accepted .. genius (E) regretted .. pretension 8. The board members, accustomed to the luxury of being chauffeured to corporate meetings in company limousines, were predictably ...•••• when they learned thai Ihis service had been ....... . (A) satisfied .. annulled (8) (C) (D) (E) stymied .. extended displeased .. upheld disgruntled .. suspended concerned .. provided 9. Misrepresentative graphs and drawings ....... the real data and encourage readers to accept ....... arguments. (A) (8) (C) (D) (E) obscure .. legitimate distort .. spurious illustrate .. controversial complement .. unresolved replace .. esteemed 10. Conservative historians who represent a traditional account as ....... because of its age may be gUilty of taking on trust what they should have ....... in a conscientious fashion. (A) ancient .. established (8) false .. reiterated (C) , mythical .. fabricated (D) accurate .. examined (E) suspicious .. challenged 45 THE CRITICAL READING SECTION II . The art of Mile! Andrejevic often presents us with an idyllic vision that is subtly ------- by more sinister elements, as if suggesting the ------- beauty of OUf surroundi ngs. (A) enhanced .. pristine (B) invaded .. flawed (C) altered .. unmarred (D) redeemed .. hallowed (El devastated .. bland 12. State commissioner Ming Hsu expected that her Commission on international Trade would not merely ------- the future effects of foreign competition on local businesses but would also offer practical st rategies fo r successfully resisting such competition. (Al counteract (B) intensify (C) imagine (D) forecast (El excuse 13. Since many teachers today draw on material from a variety of sources, disciplines, and ideologies for their lessons, their approach could best be called ........ (A) (B) (C) (D) (E) eclectic simplislic invidious impromptu dogmatic 14. Unprecedented turmoil in the usually thriving nation has made the formerly .-----investors leery of any further involvement. (A) pessimistic (B) cautious (C) clandestine (D) reticent (E) sanguine 15. Despite its apparent ------., much of earl y Greek philosophical thought was actually marked by a kind of unconscious dogmatism that led to ------- assertions. (A) liberality .. doctrinaire (B) independence .. autonomous (C) intransigence .. authoritative (D) fundamentalism .. arrogant (E) legitimacy .. ambiguous 46 THE CRITICAL READING SECTION Answer Key I. B 2. C 3. B 4. B 5. E 6. C 7. A 8. D 9. B IO.D II. B 12. D 13. A 14. E 15. A Additional practice questions can be found in The Official SAT Online Course at www.collegeboard.comls&tonlinecourse. 48 CHAPTER 6 Passage-based Reading When you answer passage-based reading questions, how carefully you read and how well you understand the information in a passage are more important than how much you know about the subject. Like much of the reading you'll be doing in college, the passages will present important issues, ideas or events to think about. Types of Passages Here's what to expect from the passages. • The passages range in length from about 100 to 850 words. • Some selections are from a Single source, and others consist of a pair of related passages on a shared issue or theme. For each pair, one of the passages supports, opposes or complements the other's point of view. • The passages coyer subjects in the humanities, social studies, natural sciences and literary fiction . . • The passages vary in style and tone. They include narraJive, persuasive, expository andlor literary elements. • A set of questions follows each passage or pair of related passages. Approaches to Reading the Passages ... Mark the passages or make short notes. Be careful that' you don't mark too much. The idea of marking the passage is to help you find information quickly. Nothing will stand out if you underline or mark most of the passage. Some students scribble a short note in the margin - a few words at most - that summarizes what a paragraph or key sentence is about. But don't spend 49 THE CRITICAL READING SECTION ~ePlnMlnd more time marking the passage than you will save. The idea is to answer the q uest ions, not just mark your test booklet. All passages have numbered lines. When a question refers to a particular line or lines in the passage, it may be helpful to go back and read the matching !ine(s! before answering the question. )- Use your knowledge and experience carefully. No matter what you know or what you believe. you cannot change what the writer h~s sa id or suggested. You must distinguish between what you th ink the writer should have said or what you would like t he writer to believe and what the writer's words actually say or imply. )- Read actively. may find that asking you rself questions about the passage will help you stay more engaged and absorb more information. Here are some YOll questions you can ask yourself: Is the passage a factual account of an event? What is the purpose of the passage? Is the writer trying to in fo rm you, amuse you, influence you or what? )- If you are having a hard time with a passage. read the questions before you finish the passage. This will give you a sense of what to look for. Looking at the questions first, though. might be a waste of time if you don't know what the passage is about. You may want to try both methods when working through practice questions. Types of Questions Three types of questions may be asked about a passage: extended reasoning, vocabulary in context and literal comprehension. You will be asked questions involving single passages, paired long passages and paired paragraphs. Extended Reasoning Questions Extended reason ing questions ask you to draw conclusions from or evaluate the information in the passage. The answers to these questions may not be directly stated in the passage but can be inferred from it. Extended reasoning questions also ask about the overall theme or meaning of the passage, the author's purpose or attitude. or the tone of the passage. Extended reasoning questions often include words or phrases like: • probably • apparently • seems • suggests • it can be inferred • the author implies 50 Passage-based Reading For these types of questions, you need to be an especially careful reader if you want to understand the information in a passage and figure out what the writer is say ing. You should be able to follow the logic of the passage and to recogn ize points that would strengthen or weaken the writer's argument. Extended reasoning questions require you to do some or all of the follow ing: • Determine the main idea of a passage or the author's primary purpose in writing the passage. • Interpret a specific part of a passage, such as a particular word, image, phrase, example o r quotation. Infer what purpose it serves rather than what it means. • Figure out what the information presented in the passage suggests, what ca n be inferred about the author's views, or how the aut hor of one passage would be likely to react to or evaluate an idea expressed in a related passage. • Determine what the author's tone or attitude is in a specific section of the passage or in the passage as a whole. • Understand a specific idea or relationship in a passage by identifying a parallel or analogous idea. FACTS, ASSUMPTIONS AND INFERENCES To answer extended reasoning questions correctly, it helps to know the d ifference between facts, assumptions and inferences. Facts: Statements known to be true and that can be shown to be true are called facts. Here are some examples. • There are 31 days in July. • It is against the law to drive over the speed limit. Assumptions: These are suppositions o r propositions that writers make to reach their conclusions. Sometimes, the assumptions that writers make may not be stated within the passage. To read critically, you must be able to recognize these unstated assumptions. These assumptions may be accurate or inaccurate - at least from your point of view. For example, think about some of the underlying assumptions in the following three statements. 1. "The principal has promised a big victory dance after the championship game next week." Two possible assumptions here are: • The principal hopes the team will win the championship game. • The principa l is looking fo r a way to reward the whole school for the team's success. 2. "Let's have a picnic tomorrow." Two possible assumptions here are: • The speaker would like to spend time with the person he or she is talking to. 51 THE CRITICAL READING SECTION • Picnics are fun. 3. "Reducing the workforce will increase the profits." Two possible assumptions here are: • Profits are more important than people. • A connection exists between the number of employees and the amount of profit each employee produces. Inferences: These are concl usions you reach based on what has been said in a passage. To infer is to arrive at a conclusion through reasoning. In the paragraph that follows, for example, it can be inferred that all 'the examples are taken from the author's own life. Phrases such as "I've counted ... my mailbox," "promised me prizes" and "I wrote this con artist" show that the author's opinions are based on personal experience. though this is not stated outright. The problem of junk mail has grown to epidemic proportions. I've counted no fewer than 616 pieces of junk mail in my mailbox in a given month! Not only is the sheer magnitude appalling, but the antics of these "post office pirates" are equally disturbing. For example, one enterprising sa lesman promised me prizes ranging from a car to a transistor radio if I would drive 200 miles to look at a piece of property. I wrote this con art ist and told him I'd come ifhe paid for the gas, but I never heard from him. LOGIC, STYLE AND TONE Many extended reasoning questions will ask you about the way the author develops and presents the ideas in the passage. Some questions will ask you to consider the tone or attitude of the author. They may also ask you to think about how a reader may react. In well-w ritten material, the writer uses both style and tone to express what he or she has to say and to try to influence the reader. Recognizing the author's purpose - whether it is to tell an exciting story, to express enjoyment or to sta rt a revolution - is an important part of reading. Vocabulary-in-Context Questions Some passage-based reading questions ask about the meaning of a word as it is used in the passage. Even if you don't know the word, you can sometimes figure it out from the passage and the answer choices. The context - that is, the particular situation in which the word is used, including information given in neighboring sentences - helps determine its meaning. For example, you are likely to know that the word smart has several meanings. It can mean "intell igent," "stylish" and "sassy." In the sentence "We knew his smart mouth would get him into a lot of trouble some day," the context tells us that we are 52 Passage-based Reading not talking about intelligence or fashion sense. Chances are, neither of those will get someone into a lot of trouble. The context, or the association between the words smart and trouble. tells us that the meaning intended here is "sassy." Usually you can work out the answer to a vocabulary-i n-context question just by reading th,e sentence in which it is included. But sometimes you may also have to read the sentence that comes before or after it. When a word has several meanings, a vocabulary-in-context question won't necessarily use the most common meaning. When answering vocabulary-in-context questions, keep the following in mind: • One word can have many meanings. The answer choices will often include several different meanings of the word. • Quest ions asking for the meaning of a word or phrase refer to the mean ing in the context in which the word or phrase is being used in the passage. • It helps to go back to the passage and reread the surrounding text of the word that is used. Be sure to read enough of the context to thoroughly understand the meaning of the word. Literal Comprehension Questions For th is type of question, you need to understand information that is d irectly presented in the passage. These questions measure a skill you'll be using a lot in college: how well you read to acquire information. Here are some approaches to answering literal comprehension questions: • Find the place in the passage where the detail is discussed. Reread enough of the text to find the answer. Even if you know something about the subject of the passage, remember to answer the question based on what is actually stated in the passage. • Recognize different ways of stating the same fact or idea . Somet imes the description of the fact or idea in the question is different from the wording in the passage. • Cross out incorrect responses as you eliminate them. Remember. you may write anywhere in your test booklet. • Read questions ca refully, looking for words such as except, not and only, and for other words that describe exactly what yOll are asked to do with the info rmation. • Be sure you can support your answer by referring to words or ph rases withi n the passage that support it. Questions Involving Paired Passages and Paragraphs At least one long and one paragraph reading selection will involve a pair of passages. The pair of passages will have a common theme or subject. One of the passages will oppose, support or in some way relate to the other. 53 THE CRITICAL READING SECTION Table 6.1 KevWords and Phrases for Understanding the Questions Understanding the following key words and phrases will help you understand what the questions are really asking. When you see this ... Remember that ... Naccording to the Naccording to the You must answer the question in terms of the statements, assumptions, or inferences that the writer is making, even jf you disagree with w hat the writer has said. The Question is meant to see if you understand what the wri t er has written. passage author~ H This is an important word in test questions because it usually asks you to find the most suitable or most acceptable of the answer choices. This m eans that even though you may find a response t hat seems to fit, you still need to look at the rest of the responses in order to be sure that you have selected the best one. Sometimes you may think none of the answers are particularly good, but you must pick the one that is best. "ch iefl y~ This means "above the rest,~ ~mostly," ~mainly but not exclusively." When you see chiefly, you will probably be looking for the most central element or most important explanation of something. "except~ A question with except usually asks you to identify words or phrases that don't belong with the other choices. "(the author) implies" "(it can be) inferred" "(the author) suggests" These terms ask you to come to a conclusion that is suggested by the information in the passage but not directly stated by the author. Make sure that your inference is indeed based on the material in the passage and not only on your own ideas or opinions. Opposite of most. Most important, or chiefly. Frequently used as a qualifier, as in most likely, most frequently, most reasonable. A qualifier recognizes that there are exceptions to most situations and tries to allow for those except ions. Only means "just the one." For exam ple, "This is the only . .. for me.~ It also can indicate a restriction, as in "You can go only after you wash the car." "primarily" 54 Most important, o r chiefly. Passage-based Reading When a question asks you to compare two passages, don't try to remember everything from both passages. Instead. take one choice at a time. Review the relevant parts of each passage before you select your answer. Table 6.1 offers additional gUidance. Suppose a question asks you to identify something that is true in both passages. It is often easier to start by eliminating choices that are not true for one of the passages. Don't be fooled by a choice that is true for one passage but not for the other. Approaches to Passage-based Reading Questions . . Keep in mind that the answers corne from the passage. Every single answer to these questions can be found in or directly inferred from the passage. Read the passages carefully. . . Remember, every word counts. Be aware of words describing people, events and things. If someone's face is described as "handsome" or "scarred," if an event is "surprising" or if a word is "whispered" or "spoken with a smile," pay attention. Details like these are mentioned to give you an understanding of what the author wants you to feel or think. . . Read the questions and answers carefully. With most passage-based reading questions. you have to: 1. think about what the question is asking 2. look back at the passage for information that will help you with the question 3. think again about how you can use the information to answer the question correctly . . Don't forget that an answer choice can be both true and wrong. The correct choice is the one that best answers the question, not any choice that makes a true statement. To keep from selecting a choice that is true but wrong. carefully read the passage. the questions and the answer choices . . . Make sure the reading passage supports your answer. There should always be information and details in the passage that provide support for your answer. Look for specific words, phrases and sentences that help to prove your choice is correct. Even with the inference, tone and attitude question s - the ones in which you have to read between the lines - you can find evidence in the passage to support the correct choice. . . Try eliminating choices. Compare each choice to the passage and you'll find that some choices can be eliminated as definitely wrong. Then it should be easier to choose the correct answer from the remaining choices. 55 THE CRITICAL READING SECTION )- Double-check the other choices. When you have made your choice, qUickly read the other choices again to make sure there isn't a better answer. )- Don't jump from passage to passage. You will spend a lot of time reading some of the passages before you're ready to a nswer even one question.$0 take the time to answer as many questions as you can about each passage before you move on to another. Consider these suggest ions:

• Move around within a set of questions to find the ones you can answer

qUickly. • Stay with a passage until you are sure you have answered as many questions as you can. If you return to the passage later, you'll probably have to read it again. • Go back to any questions you sk ipped. When you've gone through all the questions about a passage, review any you left out or weren't sure of. Sometimes information you picked up while thinking about one question will help you answer another.

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Sample Questions The passages below are followed by questions based on their content; questions following a pair of related passages may also be based on the relationship between the paired passages. Answer the questions on the basis of what is ~ or imJ;!l.itd in the passages and in any introductory material that may be provided.

Questions 1-2 are based on the following passage. Art forgery is a peculiar curse. Reliant on camouflage and deception, on the rhetoric of the believable lie, it is an act both audacious and self-effacing. For the imitation Linll to succeed in fooling us, it must resemble one or more 5 works that we have been led to believe are undoctored originals. Without something to mimic, the fake could not exist. And the forger of old masters' drawings. like the forger of twenty-dollar bills or United States' passports, must be skilled enough to fool eyes that by now 10 are practiced at uncovering deceit. I. The primary purpose of the passage is to (A) describe the motivations of art forgers (8) indicate the artistic merit of particular forgeries (C) discuss the challenges facing art forgers (0) catalogue the skills of a successful art forger (E) illustrate the public's ignorance about art forgery 2. The author refers to art forgery as an act that is Kself-effaci ng» (line 3) because it reqUires that the forger (A) (B) (C) (0) (E)

undergo an arduous apprenticeship work in the style of another artist forgo many opportunities for financial gain never take his or her work too seriously regard original artworks with reverence

Questions 3-4 are based on the following passage. A cousin of the tenacious Asian longhorned beetlewhich since its initial discovery in 1996 in New York City has caused tens of millions of dollars in damage annually Unll -the citrus longhorned beetle was discovered on a juniper 5 bush in August 2001 in Tukwila, Washington. Exotic pests such as the longhorned beetle are a growing problem-an unintended side effect of human travel and commerce that can cause large-scale mayhem to local ecosystems. To stop the citrus beetle, healthy trees were destroyed 10 even though there was no visible evidence of infestation, and normal environmental regulations were suspended so that a rapid response could be mounted.

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3. Which best describes the function oflhe opening sentence ("A cousin .. Washington")?

(A) It underscores how frequently pests are lransfer~d from one geographical region to another. (B) It suggests the potential harm the citrus longhorned beetle could cause in the United States. (C) It illustrates how the Asian longhorned beetle was introduced into the United States. (D) It describes how the citrus longhorned beetle was first discovered. (E) It compares the destructiveness of the Asian longhorned beetle to that of the citrus beetle. 4. The passage suggests that the actions undertaken in lines 9-12 are best characterized as (A) tested and reliable

(B) deliberate and effective (e) costly and unpopular (D) preemptive and aggreSSive

(E) unprecedented and unfounded Questions 5-8 are based on the following passages. Passage 1 Today any accessible, fast-mOVing story written in unaffected prose is deemed to be "genre fiction n -at best an excellem "read- or a "page turner" but never literature lin. with a capital L. Everything written in self-conscious, 5 writerly prose, on the other hand. is now considered to be "literary fiction" -not necessarily good literary fiction, mind you, but always worthier of respectful attention than even the best-written thriller or romance. It is these works that receive full -page critiques, often one in the Sunday 10 book-review section and another in the same newspaper during the week. II is these works, and these works only, that make the anllual short lists of award comm ittees. Passage 2 One reason why most literary novels don't appeal to the ordinary reader looking for a "good story" is that 15 they aren't intended to. Just as nuclear physicists strive to impress other nuclear physicists and dog breeders value the admiration of fellow dog breeders over that of the uninitiated masses, so people who write serious fiction seek the high opinion of other literary novelists. of creative 20 writing teachers, and of reviewers and critics. They want very badly to be "literary," and for many of them this means avoiding techniques associated with commercial and genre fiction-specifically too much emphasis on plot. Who, after all, wants to be accused of writing "action 25 movies in book form"? 5. The author of Passage I implies that "literature with a capital L" (lines 3·4) is fiction that is (A) (B) (e) (D) (E)

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considered classic by scholars ofEngJish literature written in a mannered and pretentious style unafraid to address highbrow themes and weighty issues successful both critically and financially unfairly ignored by the book-buyi ng public

6. The author of Passage 2 suggests that authors who write ~self-conscious, writerly prose~ (lines 4·5, Passage 1) are (A) unlikely ever to produce great work (B) trying to improve their chances of popular success (e) more talented than writers of mainstream fiction (D) seeking the approval of like-minded writers (E) not capable of depicting a realistic fictional world 7. In the two passages, quotation marks are primarily used to (A) (B) (Cl (D)

call attention to some common ways of categoriz.ing fiction suggest that some literary terms are meaningless note labels to which writers typically object ridicule the modes of writing most popular with the public

IE) 'mph"'" th' 'mpo,,,n,, of, ,h",d ",m'no[ogy 8. Which of the following best describes the relationship between the two passages? (A) (B) (Cl (D) (E)

Passage 2 presents evidence that rebuts the argument made in Passage l. Passage 2 explicitly defines terms that Passage I assumes are well·known. Passage 2 supplies an explanation for a state of affairs described in Passage I. Passage 2 focuses on an exception to a general rule established in Passage \, Passage 2 provides a humorous view of a situation that Passage 1 finds inexplicable.

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Questions 9-19 are based on the following passages.

In Passage I, the author presents his view of the early years of the silent film industry. In Passage 2. the atahor draws on her experiences QS a mime to generalize about her art. (A mime is II performer who, without speak;'lg, entertains through

gesture,facial expression, and movement.) Passage I

Talk to those people who first saw films when they were silent, and they will tell you the experience was magic. The silent film had extraordinary powers to draw

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members of an audience into the story, and an equally 5 potent capacity to make their imaginations work. It required the audience 10 become engaged-to supply

Line

voices and sound effects. The audience was the final,

10

15

20

25

30

creative contributor \0 the process of making a film. The finest films of the silent era depended on two clements that we can seldom provide today-a large and receptive audience and a well-orchestrated score. For the audience, the fusion of picture and live music added up to more than the sum of the respective parts. The one word that sums up the attitude of the silent filmm akers is elJthusiasm, conveyed most strongly before formulas took shape and when there was more room for experimentation. This enthusiastic uncertainty often resulted in such accidental discoveries as new camera or editing techniques. Some films experimented with players; the 19l5 film Regeneration, for example, by using real gangsters and streetwalkers, provided startling local color. Other fi lms, particularly those of Thomas Ince, provided tragiC endings as often as films by other companies supplied happy ones. Unfortunately, the vast majority of silent films survive today in inferior prints that no longer reflect the care that the Original technicians put into them. The modem yersions of silent films may appea r jerky and flickery, but the vast picture palaces did not attract four to six thousand people a night by giving them eyestrain. A silent film depended on its visuals; as soon as you degrade those, you lose elements that go far beyond the image on the surface. The acting in silentswas often very subtle, very restrained, despite legends to the contrary. Passage 2

35 Mime opens up a new world to the beholder, but it does so insidiously, not by pu rposely injecting points of interest in the manner of a tour guide. Audiences are not unlike visitors to a foreign land who discover that the modes, manners, and thoughts of its inhabitants are not 40 meaningless oddities, but are sensible in context. I remember once when an audience seemed perplexed at what I was doing. At first, I tried to gain a more immediate response by using slight exaggerations. I soon realized that these actions had nothing to do with the 45 audience's understanding oflhe character. What J had believed to be a failure of the audience to respond in the

60

55

60

65

70

manner I expected was, in fact, only their concentration on what I was doing; they were enjoying a gradual awakening-a slow transference of their understanding from their own lime and place to one that appeared so unexpectedly before their eyes. This was evidenced by their growing response to succeeding numbers. Mime is an elusive art, as its expression is entirely dependent on the ability of the performer to imagine a character and to re-create that character for each performance. As a mime. Tam a physical medium, the instrument upon which the figu res of my imagination play their dance of life. The individuals in my audience also have responSibilities-they must be alert collaborators. They cannot sit back, mindlessly complacent, and wait to have their emotions titillated by mesmeric m usical sounds or yisual rhythms or acrobat ic feats, or by words that tell them what to think. Mime is an art that, paradoxically, appeals both to those who respond instinctively to entertainment and to those whose appreciation is more analytical and complex. Between these extremes lie those audiences conditioned to resist any collaboration with what is played before them, and these the mime must seduce despite themselves. There is only one way to attack those reluctant minds-take them unaware! They will be delighted at an unexpected pleasure. 9. Both passages are primarily concerned with the subject of (A) (B) (e) (D) (E)

shocking special effects varied dramatic styles visual elements in dramatic performances audience resistance to theatrical performances nostalgia for earlier fo rms of entertainment

10. The author of Passage I uses the phrase "enthusiastic uncertai nt y" in line 17to suggest that the filmmakers were (A) excited to be experimenting in a new field (B) delighted at the opportunity to study new technology (C) opti mistic in spite of the obstacles that faced them (D) eager to challenge existing conventions (E) eager to please but unsure of what the publiC wanted

11. In tines 19-24, Regeneration and the films of Thomas Ince are presented as examples of (A) formulaic and uninspired silent films (8) profitable successes of a flourishing industry (C) suspenseful action films drawing large audiences

(D) daring applications of an artistic philosophy (E) unusual products of a readiness to experiment 12. In context, the reference to "eyestrain" (line 30) conveys a sense of (A) irony regarding the incompetence of silent film technicians . (B) regret that modern viewers are unable to see h igh quality prints of silent films (e) resentment that Ihe popularity of picture palaces has waned in recent years (D) pleasure in remembering a grandeur that has passed (E) amalement at the superior quality of modern film technology 13. In line 34, "legends" most nearly means (A) ancient folklore (B) obscure symbols (C) history lessons (D) famous people (E) common misconceptions 14. The author of Passage 2 most likely considers the

contrast of mime artist and tour guide appropriate because both (A) are concerned with conveying factual information (B) employ artistic techniques to communicate their knowledge (e) determ ine whether others enter a strange place (D) shape the way others perceive a new situation (E) explore new means of self-expression 15. The incident described in lines 41-52 shows the

author of Passage 2 to be similar to the silent filmmakers of Passage 1 in the way she

16. In lines 41-52, the author most likely describes a

specific experience in order to (A) dispel some misconceptions about what a mime

is like (B) show how challenging the career of a mime can

b, (C) portray the intensity reqUired to see the

audience's point of view (D) explain how unpredictable mime performances can be (E) indicate the adjustments an audience must make in watching mime 17. In Jines 60-63, the author's description of techniques used in the types of performances is (A) disparaging (8) astonished (C) sorrowful (D) indulgent (E) sentimental 18. What additional information would reduce the apparent Similarity between these two art forms? (Al Silent film audiences were also accustomed to vaudeville and theatrical presentations. (B) Silent films could show newsworthy events as well as dramatic entertainment. (e) Dialogue in the form of captions was integrated into silent films. (D) Theaters running silent films gave many musicians steady jobs. (El Individual characters created for silent fi lms became famous in their own right. 19. Both passages mention which of the following as being important to the artistic success of the dramatic forms they describe? (A) Effective fusion of disparate dramatic elements (B) Slightly exaggerated characterization (C) Incorporation of realistic details (D) Large audiences (El Audience involvement

(A) required very few props (8) used subtle technical skills to convey universal truths (e) learned through trial and error (D) combined narration with visual effects (E) earned a loyal audience of followers

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Answers and Explanations I. The primary purpose of the passage is to (A) describe the motivations of art forgers (B) indicate the artistic merit of particular forgeries

(C) discuss the challenges facing art forgers (D) catalogue the skills of a successful art fo rger (E) illustrate the public's ignorance about art forgery

~eplnMlnd

Don't be misled by an answer

that looks correct but is not supported by the actual text. Choice (0) is attractive. but it's

not as accurate as choice Ie).

Explanatiml: The passage primarily calls attention to the difficulties inherent in art forgery. Choice (C) is correct because the passage primarily discusses several ch allenges inherent in art forgery. Here's why each of the other choices is incorrect: • Choice (A) is incorrect because the passage does not discuss why people become art forgers.

• Choice (8) is incorrect because the passage does not discuss individual fo rgeries or their artistic merit. • Choice (0) is incorrect. Although the passage indicates that forgers need to be skilled enough to fool people who are experienced at detecting forgeries, it does not list or discuss the particular skills that make art forgers successful. • Choice (E) is incorrect. The passage does not discuss the public's lack ofknowledge about art forgery.

2. The author refers to art forgery as an act that is requires that the forger (Al (8) (C) (D) (El

~setf-effacing"

(line 3) because it

undergo an arduous apprenticeship work in the style of another artist forgo many opportunities for financial gain never take his or her work too seriously regard original artworks with reverence

Answer: The correct answer is (8). Explanation: The reference to "self-effacing" in line 3 suggests that a successful art forgery cannot ca ll attention to the forger. It must appear to be a creation of the original artist. Choice (8) is correct because forgery involves employing the style of another artist rather than working in one'S own style. It requires removing oneself from one's work.

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~epinMind

Here's why each of the other choices is incorrect:

• Choice (A) is incorrect because the author does not discuss apprenticeships undertaken by art forgers. Moreover. if forgers did undertake arduous apprenticeships. the experience would not necessarily be self-effacing.

A key word in the question may

be the clue you need to arrive at the best answer. Pay attention to the words that carry the meaning of the sentence.

• ChOices (C) and (D) are incorrec t because the author does not discuss the financial rewards of forging art, nor does the author suggest that the art forgers should not take their work too seriously.

• Choice (E) is incorrect because the author does not indicate that art forge rs must view original art with reverence. In fact, the author states that art forgery is an "audacious" act. A forger might not perform this audacious act if he or she viewed the original work with reverence.

3. Which best describes the fu nction of the opening sentence (~A cousin . . . . Washington )? H

(A) It underscores how frequently pests are transferred from one geographical region to another. (8) It suggests the potential harm the citrus longhorned beetle could cause in the United States. (e) It illustrates how the Asian longhorned beetle was introduced into the United States. (D) It describes how the citrus longhorned beetle was first discovered. (E) It compares the destructiveness of the Asian longhorned beetle to that of the citrus beetle.

Answer: The correct answer is (8). Explanation: The open ing sentence of the passage indicates that the citrus longhorned beetle is a relative of the Asian longhorned beetle, which has wreaked havoc on the plant life in the United States. Choice (B) is correct because the opening sentence establishes that the Asian and citrus longhorned beetles are cousins and points out the devastation that the Asian beetle has caused; the implication is that the citrus beetle might be as damaging to plant life as its "tenacious" relative. Here's why each of the other choices is not the correct answer:

~ePiDMind In some questions the syntax, or structure, of the sentence will guide vou to the right answer. In this case, the structure of the sentence emphasizes the comparison between the two beetles, suggesting that the second is much like the first.

• Choice (A) is incorrect because the opening sentence does not discuss how frequently pests are transferred from different geographical regions. • Choices (C) and (0) are incorrect because the opening sentence, while mentioning both the Asian and citrus longhorned beetles. does not indicate how the Asian beet le was introduced to New York City. nor does it describe how the citrus beet le was initially discovered.

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• Choice (E) is incorrect because the opening sentence makes no direct compa rison between the damage caused by the Asian longhorned beetle and that caused by the citrus longhorned beetle; in fact, the passage does not provide information about the destructiveness of the citrus longhorned beetle.

4. The passage suggests that the actions undertaken in lines 9-12 are best characterized as

(A) tested and reliable (8) deliberate and effective (C) costly and unpopular (D) preemptive and aggressive (E) unprecedented and unfounded

~eplnMlnd

may be tempting to apply a personal opinion, as in choice (e), but your answer must be found in the passage itself.

Explanation: Lines 9-12 indicate that to contain the possible spread of the citrus longhorned beetle qUickly, such actions as killing hea lthy trees and relaxing environ mental regulations and procedures were executed. Choice (0) is correct because the actions described in lines 9-12 were both preventative and bold: energetic measures undertaken to avert a potential envi ronmental disaster. Here's why each of the other choices is not the correct answer:

• Choice (A) is incorrect because the actions in lines 9-12 are not described as having been employed before, nor is there evidence that the actions have been repeated successfully. • Choice (8) is incorrect because nothing in lines 9-12 suggests that the act ions were ca reful and unhurried, nor is there any discussion of the effect iveness of these actions. • Choice (C) is incorrect because although the actions described in lines 9-12 might be expensive and unpopular, nothing in the passage directly supports this interpretation. • Choice (E) is incorrect because the passage provides no evidence that the actions in lines 9-12 had not been undertaken before; furtherm ore, the actions were not unwarranted, given the awareness of the damage that the Asian longhorned beetle had al ready caused.

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5. The author of Passage I implies that "literature with a capita! L" (lines 3-4) is fiction that is (A) considered classic by scholars of English literature

(8) written in a mannered and pretentious style (e) unafraid to address highbrow themes and weighty issues

(D) successful both critically and financially . (E) unfairly ignored by the book-buying public

Explana tion: The author of Passage I uses the phrase "literature with a capital L" to describe fiction written in a particular kind of prose. Choice (8) is correct because the passage suggests that "literature wit h a capital L" is written in "self-conscious, writerly prose." Prose written this way ca n also be desc ribed as "mannered and pretentious." Here's why each of the other choices is not the correct answer: • Choice (A) is incorrect because the passage does not discuss either the opinion of scholars or the issue of what is considered "d assic." • Choice (C) is incorrect because the passage doesn't focus on the types of themes and issues addressed by literary fiction.

G.P

In MInd

Rereading the relevant part of 'the passage should lead you to the correct answer. This quest ion asks for an understanding of a remaril: in the context of its neighboring sentences.

• Choice (D) is incorrect because the passage doesn't discuss how literary fiction fares in the marketplace. • Choice (E) is incorrect. Although the passage focuses on the amount of critical attention paid to literary fiction, it doesn't suggest that such fiction is undeservedly ignored by the book-buying public.

6. The author of Passage 2 suggests that authors who write ~self-conscious, writerly prose" (lines 4-5, Passage I) are (A) unlikely ever to produce great work

(8) trying to improve their chances of popular success (e) more talented than writers of mainstream fiction

(D) seeking the approval of like-minded writers (E) not capable of depicting a realistic fi ctional world

Explanation: Passage I uses the phrase "self-conscious, writerly prose" to describe the style of "literary fiction ." The question asks what the author of Passage 2 suggests about writers who employ this style. Choice (D) is correct because Passage 2 argues that writers of literary fiction hope to appeal to other people well versed in literary tiction: literary novelists, creative writing teachers. book reviewers and critics. So these writers using "self-conscious. writerly prose" are "seeking the approval of like-minded writers."

G.P

In MInd

The correct answer is found by rereading the highlighted phrase in the context of the surrounding sentences.

65

Here's why each of the other choices is not the correct answer: • Choice (A) is incorrect because Passage 2 focuses on why literary novelists write as they do, not on whether they are likely to produce great novels.

• Choice (8) is incorrect because Passage 2 argues that literary novelists are interested in impressing a very specific audience; they are not seek ing greater , popular success. • Choice (C) is incorrect because Passage 2 does not suggest that authorsofliterary fiction are either more or less talented than writers of mainstream fiction. • Choice (E) is incorrect because Passage 2 doesn't consider the issue of realism in writ ing.

7. In the two passages, quotation marks are primarily used to (A) call attention to some common ways of categorizing fiction (8) suggest that some literary terms are meaningless (C) note labels to which writers typically object

(0) ridicule the modes of writing most popular with the public (E) emphaSize the importance of a shared terminology

~eplnMlnd

Consider all the infonnation before making a Judgment. This question asks you to make an inference from the writer's stylistic choices. By comparing the choices to the content and meaning of each passage in its entirety, you will be able to see the purpose of the quotation marks.

Explanation: Choice (A) is correct because the aut hors of both passages put quotation marks around these words and phrases to call attention to the terms frequently used to characterize different kinds of fiction. Here's why each of the other choices is not the correct answer: • Choice (B) is incorrect because neither passage suggests that these literary terms are without meaning. In fact, both imply that these terms are commonly used when talking about fiction. and that they refer to specific, identifiable types of writing.

• Choice (C) is incorrect. While these words and phrases can be considered labels. neither passage suggests that writers typically object to them. • Choice (D) is incorrect. Although Passage 1 offers a negative view of mannered "literary fiction," it does not criticize popular fiction. Passage 2 makes no judgment at all about the inherent quality of either literary or popular fiction. • Choice (E) is incorrect. Although the quoted words and phrases are a shared terminology. neither passage emphasizes the value of sharing these terms. In fa ct, Passage 1 implies that the use of such terms is unfortunate because only fiction considered to be "literary" is given serious attention.

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8. Which of the following best describes the relationship between the two passages? (A) Passage 2 presents evidence that rebuts the argument made in Passage 1. (B) Passage 2 explicitly defines terms that Passage I assumes are well known. (C) Passage 2 supplies an explanation for a state of affairs described in Passage 1. (D) Passage 2 focuses on an exception to a general rule established in Passage I. (E) Passage 2 provides a humorous view of a situation that Passage I finds inexplicable.

An.swer: The correct answer is (C).

Explanation: Passage 1 argues that literary fiction is reviewed more thoroughly than genre fiction and is the only kind of fiction recognized by award committees. Passage 2 argues that writers of literary fiction write to impress other literary novelists, reviewers and critics. This would explain why such fiction receives more serious attention from reviewers and award committees, as described in Passage 1. Therefore, choice (C) is correct. Here's why each of the other choices is not the correct answer: • Choice (A) is incorrect because Passage 2 does not rebut the argument made in Passage 1. In fact, it assumes that the situation described in Passage 1 is accurate. • Choice (B) is incorrect because. although Passage 2 uses some of the same terms as Passage 1. it does not define them any more explicitly. • Choice (0) is incorrect because Passage 2 does not focus on an exception to the situation described in Passage 1. In fact, it does not discuss a specific case at all. • Choice (E) is incorrect because Passage 1 does not indicate that the situation it describes is inexplicable. In addition. Passage 2 does not proVide a pa rticularly funny view of this subject.

(1,e

p in Mind

This is the type of question you might find easiest to answer if you eliminate answers that are wrong. Each of the incorrect answers is directly contradicted by material in the passages. You are left with the correct answer by process of elimination.

9. Both passages are primarily concerned with the subject of (A) shocking special effects (B) varied dramatic styles (C) visual elements in dramatic performances (D) audience resistance to theatrical performances (E) nostalgia for earlier forms of entertainment

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Explanation: This question asks you to think about both passages. Notice that the question asks you to look for the main subject or focus of the pair of passages, not simply to recognize that one passage is about silent film and the other about mime. ~ The discussion in Passage 1 is most concerned with the effective~ep in Mind ness of silent films for audiences of that era. The discussion in Passage 2 is most concerned with what makes a mime performance effective When comparing two reading passages, review the relevant for the audience. The main subject fo r both passages is how a silent, parts of each passage as you visual form of entertainment affects an audience. Choice (C) is correct consider the choices. because it refers to performance in a visual art form. Here's why each of the other choices is incorrect: • Choice (A) is incorrect because "shocking special effects" is not a main subject of eit her passage. • Choice (B) is incorrect because, although "varied dramatic styles" (used by film performers and in mime) is briefly touched on in both passages, it is not the main subject of the pair of passages. • Choice (D) is incorrect because. "audience resistance to theatrical performances" is too specific: both authors are making points about the overall role of audiences in the performance. Choice (D) is also incorrect because that topic is primarily addressed only in Passage 2. • Choice (E) is incorrect because a tone of nostalgia appears only in Passage 1.

10. The author of Passage I uses the phrase uenthusiastic uncertainty" in line 17 to suggest that the filmmakers were (A) excited to be experimenting in a new field (B) delighted at the opportunity 10 study new technology (C) optimistic in spite of the obstacles that faced them

(D) eager to challenge existing conventions (E) eager to please but unsure of what the public wanted

~.PInMlnd

Answer: The correct answer is (A). Explanation: Look at the beginning of the third paragraph of Passage L The fi lmmakers were "enthusiastic" about a new kind of art form in which they could experi ment. And experimentation led to "accidental discoveries" (line 18), which suggests "uncertainty," all of which is said, though in a slightly different way, in choice (A). Here's why each of the other choices is incorrect:

Read each choice carefully and compare what it says to the information in the passage.

.

• Choice (B) is incorrect because the filmmakers were delighted to use the new technology rather than to study it. • Choice (C) can be eliminated because the passage does not talk about "obstacles" faced by the filmmakers.

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• Choice (D) is specifically contradicted by line 16, which refers to these film- ' makers as working "before formulas took shape." The word formulas in this context means the same thing as "conventions." • Choice (E) is incorrect because the "uncertainty" of the filmmakers was related to the new technology and how to use it, not to "what the public wanted."

11. In lines 19-24, Regeneration and the films of Thomas lnce are presented as examples of (A) formulaic and uninspired silent films (B) profitable successes of a flourishing industry (e) suspenseful action films drawing large audiences (D) daring applications of an artistic philosophy (E) unusual products of a readiness to experiment

Answer: The correct answer is (E). Explanation: The author's argument in the third paragraph is that there was lots of "room for experimentation" (line 17) in the silent film industry. Both Regeneration and Inee's fi lms are specifically mentioned as examples of that "readi ness to experiment," as referred to in choice (E). H ere's why each of the other choices is incorrect:

~epinMind

• Choice (A) is directly contradicted in two ways by the information in the passage. First, line 16 says that the filmmakers worked "before formulas took shape," so their work could not be "formulaic." Second, the author refers to Regeneration as having some "startling" effects and indicates that the endings of Ince's films were different from the endings of other fi lms of the time. So it would not be correct to describe these films as "uninspired."

As you consider the choices, think of the words, phrases and sentences in the passage that relate to the question you are answering. Be aware of how the ideas in the passage are presented. What is the author's point? How does the author explain and support important points?

• Choices (B), (C) and (0) are incorrect because the author does not argue that these films were "profitable," "suspenseful " or "applications of an artistic philosophy." He argues that they are examples of a willingness to "experiment."

12. In context, the reference to "eyestrain" (line 30) conveys a sense of (A) irony regarding the incompetence of silent film technicians (B) regret that modern viewers are unable to see high-quality prints of silent films (C) resentment that the popularity of picture palaces has waned in recent years (D) pleasure in remembering a grandeur that has passed (E) amazement at the superior quality of modern film technology

Answer: The correct answer is (8). Explanation: The author draws a distinction between the way silent films look when viewed today - "jerky and flickery" (line 28) - and the way they looked

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&.ep MInd In

Try eliminating choices that you

know are incorrect. Rule out choices that don't answer the question being asked or that are contradicted by the information in the passage.

when they were originally shown. He implies that thousands of people would not have come to the movie houses if the pictures had given them "eyestrai n." The author indicates that the perception of silent films today is unfortunate. This feeling can be described as "regret," choice (8 ). Here's why each of the other choices is incorrect: • Choice (A) is incorrect because there is no indicat ion in the passage that silent film technicians were "incompetent." The author even mentions "the care" taken by "the original technicians" (lines 26-27).

• Both choices (C) and (D) are incorrect because they do not answer this question. Remember, the question refers to the statement about "eyest rain ." The remark about eyestrain concerns the technical quality of the films, not the "popularity of picture palaces" or a "grandeur that has passed." • Choice (E) is incorrect for two reasons. First, no sense of "a mazement" is conveyed in the statement about eyestrain. Second, the author does not say that modern films are "superior" to silent films , only that the "prints" of silent films are " inferior" to what they once were (lines 25-26).

13. In line 34, "legends" most nearly means (A) (8) (C) (0)

ancient folklore obscure symbols history lessons fa mous people (E) common misconceptions

&.epln~nd

This is a vocabulary-In·context question . Even if you don't know the meaning of the word, try to figure it out from the pas· sage and the choices. Examine the context in which the word is used. Think of some word!s) that would make sense in the sen· tence; then look at the answers to see if any choice is similar to the word!s) you thought of.

Explanatio,,: A legend is an idea or story that has come down from the past. A secondary meaning of legend is anything made up rather than based on fact. Throughout the fina l paragraph of Passage I, the author emphasizes that people today have the wrong idea about the visual quality of silent films. In the last sentence, the author states that the act ing was "often very subtle" and "very restrained," and then he adds, "despite legends to the contrary." According to the author, silent film acting is today thought of as unsubtle and unrestrained, but that is a misconcep tion, an idea not based on fact, a "legend." Choice (E) is the best of the answer choices. Here's why each of the other choices is incorrect:

• Choice (A) is incorrect because, although it is the most common meaning of legend. it doesn't make any sense here. Ther~ s no reference to or suggestion ... about "ancient folklore." • Choice (8) is incorrect because it has no support at all in the passage.

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• Choice (C) is incorrect because the author does not refer to "history lessons" in this sentence, but to mistaken notions about the performances in silent films. • Choice (D) is incorrect because it simply doesn't make sense. In line 34, the word legends refers to acting, not to people.

14. The author of Passage 2 most likely considers the contrast of mime artist and tour guide appropriate because both (A) (B) (C) (D) (E)

are concerned with conveying factual information employ artistic techniques to communicate their knowledge determine whether others enter a strange place shape the way others perceive a new situation explore new means of self-expression

Answer: The correct answer is (D). Explanation: To answer this question, you have to find a choice that desc ribes a similarity between the performances of a mime and the work of a tour guide. The author begins Passage 2 by saying that a mime "opens up a new world to the beholder," but in a "manner" (or way) different from that of a tour gUide. Thus the author assumes that contrasting the mime and the tour guide is appropriate because both of them "shape the way others perceive a new situation," choice (D). , Here's why each of the other choices is incorrect:

c;epinMind Pay close attention when authors make connections, comparisons or contrasts. These parts of passages help you identify the authors' points of view and assumptions.

• Choice (A) is incorrect because although it may correctly describe a tour guide, it doesn't fit the mime. Nowhere in the passage does the author say the mime conveys "factual information ." • Choice (B) is incorrect because although it is true for the mime, it is not true for the tour guide. • Choice (C) is incorrect because the aut hor of Passage 2 contrasts how mimes and tour gUides introduce others to "a new world," not how they determine entrance to "a strange place." • Choice (E) is incorrect because the author does not discuss "self-expression" as a tour guide's work, and because she indicates that, as a mime, she expresses a particula r character, not her own personality.

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15. The incident described in lines 41-52 shows the author of Passage 2 to he similar to the silent filmmake rs of Passage I in the way she (A) (B) (e) (D) (E)

~.PInMlnd

required very few props used subtle tcchnical skills to convey universal truths learned through trial and error combined narration with visual effects earned a loyal audience of followers

When a question following a

pair of passages as ks you to identify something that is common to both passages or true for both passages, eliminate any answ er that is tru e for only one of the two passages.

Here's

Explanation: The question focuses on the story related in Jines 41-52 and asks you to explain how that story shows that the mime is similar to silent filmmakers. $0 the correct answer has to express a point made about the mime in lines 41-52 that is also true for the film makers described in Passage 1. Lines 41-52 show the mime cha nging her performance when she found something that d id not work. Passage 1 says that filmmakers learned through "experimentation" and "accidental discoveries." So all of these people learned through trial and error, choice (C). why each of the other choices is incorrect: • Choices (A), (B), (D) and (E) are incorrect answers because they don't include traits both described in lines 41-52 and shared with the filmmakers. , • Choice (A) is incorrect because "props" aren't mentioned in eit her passage. • Choice (8) is incorrect because "conveying universal truths" is not discussed in Passage 1. • Choice (D) is incorrect because a mime performs without speaking or narration. • Choice (E) is incorrect because Passage I describes loyal aud iences but lines 41-52 do not. 16. In lines 41-52, the author most likely describes a specific experience in order to (A) (B) (C) (0 ) (E) dispel some misconceptions about what a mime is like show how challenging the career of a mime can be portray the intensity req uired to see the audience's point of view explain how unpredictable mime performances can be ind icate the adjustments an audience must make in watching mime A nswer: The correct answer is (E). Explanation: The correct answer must expla in why the author of Passage 2 described a particular experience in lines 41-52. The author's point is that she learned the audience was "enjoying a gradual awa kening." Only choice (E) indicates that the story shows the "adjustments" the audience had to make to appreciate her perfo rmance. 72 Passage-based Reading &ee Here's why each of the other choices is inc..orrect: • Choice (A) is' incorrect because the only "misconception" that is dispelled is the author's "misconception" about the audience. • Choice (B) is incorrect because, while the story might suggest that mime is a "challenging career," that is not the author's point in desc ribing the experience. p In MInd Every word counts. When you're asked about the author's intent in describing something, you have to pay close attention to how the author uses details to explain, support or challenge the point being made. • Choice (C) is incorrect because there is no reference to "intensity" on the part of the mime. • Choice (D) is incorrect because the emphasis of lines 41-52 is not on how "u npredictable" mime performance is but on what the author learned from her failure to understand the audience's init ial react ion. 17. In lines 60-63, the author's description of techniques used in the types of performances is (A) disparaging (B) astonished (C) sorrowful (0) indulgent (E) sentimental Answer: The cor~ect answer is (A). Explanation: The sentence beginning in line 60 says that when viewing m ime, the audience "cannot sit back, mindlessly complacent." The author then says that other types of performances "titillate" audience emot ions by "mesmeric musical sounds" or "acrobatic feats." The author uses these kinds of words to belittle other techniques - her tone is disparaging, which is the answer in choice ~A). Here's why each of the other choices is incorrect: d ~ePinMind To figure out the author's attitude or tone or how the author feels about something, think about how the author uses tanguage in the passage. • Choices (B), (C) and (E) are incorrect because no "astonishment," "sorrow" or "sentimentalism" is suggested in lines 60-63. • Choice (D) is incorrect because it is almost the opposite of what the author means. She is not at all "indulgent" toward these other types of performance. 73 THE CRITICAL READING SECTION 18. What additional information would reduce the apparent similarity between these two art forms? (A) Silent film audiences were also accustomed to vaudeville and theatrical presentations. (B) Si lent films could show newsworthy events as well as dramatic entertainment. (C) Dialogue in the fo rm of captions 'was integrated into silent films. (0) Theaters running si lent films gave many musicians steady jobs. (E) Individual characters created for silent films became famous in their own righl. Answer: The correct answer is (C). ~ePlnMind Explanation: This question asks you to do two things: first , figure out a similarity bet ween silent films and mime; second, choose an answer This question asks you to think wit h informat ion that isn't found in either passage but would make about the two reading passages together. Remember that you mime performance and silent films seem less similar. should also consider the inforIf you think about the art forms 4iscussed in the two passages, you mation in the introduction when you compare passages. should realize that neither uses speech. This is an important similarity. Silent films include music but not spoken words. As stated in the introduction to the two passages, a mime entertai ns "without speak ing." Choice (C) adds the informat ion that "d ialogue" between characters was part of silent films. Characters "spoke" to each other even though audiences read captions instead of hearing spoken words. So silent film indirectly used speech and thus was different from mime, which relies on gesture,jacial expression and movement. Here's why the other choices are incorrect: • Choices (A), (B), (D) and (E) are incorrect because they don't deal with the fundamental similarity between the two a rt forms - the absence of words. These may all be interesting things to know about silent film, but "vaudeville" performances (choice A), "newswort hy events" (choice B), "steady jobs" for musicians (choice D) and fame of "individual characters".{choice E) have nothing to do with m ime. None of these things is related to an apparent similarity between mime and silent fi lms. 19. Both passages ment ion which of the following as being important to the artistic success of the dra matic forms they describe? (A) (B) (C) (0) (E) Effective fusion of disparate dramatic elements Slightly exaggerated characterization Incorporation of realistic details Large audiences Audience involvement Answer: The correct answer is (E). Explanation: Passage I very clearly states in lines 5-8 that audience involvement was important to the success of silent films. In lines 58-60 of Passage 2, the author 74 PassageMbased Reading makes a similarly strong statement about how important it is for the audierlce to be involved in mime performance; thus choice (E) is correct. Here's why each of the other choices is incorrect: • Choices (A)-(D) are incorrect because they don't refer to ideas mentioned in both passages as "important to the artistic success of the dramatic forms." ~epinMind When comparing two passages, focus on the specific subject of the question. Don't try to remember everything from both passages. Refer to the passages as you work your way through the five choices. • Choice (A) is incorrect because Passage 1 talks about the "fusion" of pictures and music, but Passage 2 is not concerned at all wit h "dispa rate dramatic elements." • Choice (8) is incorrect because although it refers to something mentioned in Passage 2 (l ine 43), it is not something important to the success of a mime performance. And Passage 1 says that the "acti ng in silents was often very subtle, very restra ined" (lines 33-34), which is the opposite of "exaggerated." • Choice (C) is incorrect because it is mentioned only in Passage 1 (lines 20-22), and not as an element "important to the artistic success" of silent films in general. • Choice (D) is incorrect because the author of Passage 1 says that silent films did enjoy "la rge audiences," but he doesn't say that "large audiences" were critica l to the "artistic success" of the films. Passage 2 doesn't mention the size of the audiences at all. 75 Recap 1. Be familiar with the directions before test day. 2. Keep in mind that, in this section of the test (unlike other sections of the SAT), questions do not increase in difficulty from easy to hard. 3. Don't forget that all passages have numbered lines, so when a question refers to a particular line or lines in the passage, go back and read the matching line(s) before answering the question. 4. Think of all possible meanings of a word. One word can have many meanings; the answer choices of vocabulary-in-context questions will often include several different meanings of the word. 5. Remember that the information you need to answer each question is always in the passage(s) - specific words, phrases and! or sentences that help to prove your choice is correct. All questions ask you to base your answer on what you read in the passages, introductions and (sometimes) footnotes. Keep in mind that there should always be information in the passage(s) that supports your choice. 6. Bear in mind that every word counts. Details that explain, support or challenge a point in a passage can help you understand how the author wants you to feel or think. 7. Try marking up the passages or making short notes in the sample test and practice questions in this book. S. If you are having a hard time with a passage, read the questions before you finish the passage. 9. When comparing two reading passages, review the relevant parts of each passage as you consider the choices. 10. Read the questions and answers carefully - this is as important as reading the passage carefully. Read actively to absorb as much information as possible. 11. Remember that an answer can be true and still be the WTong answer to a particular question. 12. Don't be misled by an answer that looks correct but is not supported by the actual text. 13. Look for a key word in the question stem, which may be the clue you need to arrive at the best answer. 76 14. Pay attention to the syntax, or structure, of the sentence in some questions , which will guide you to the right answer. 15. Don't apply your personal opinion: instead, read carefully, bec ause you must find your answer in the text passage itself. 16. To figure out the author's attitude or tone or how the aut hor feels about something, think about how the author uses language in the passage . 17. Reread the relevant part of the passage to find the correct answer. Examine the context in which words are used. Also, don't try to remember everything from the passage(s): instead, refer back to the passage(s) as you work your way through the possible answers. 18. Pay close attention when authors make connections, comparisons or contrasts. These parts of the passages can help you identify the authors' points of view and assumptions. 19. Do not be too quick to make a judgment without considering all the information. 20. If you' re not sure of the correct answer, tty eliminating choices and make an educated guess. If a question following a pair of reading passages asks you to identify something that is common to both passages or true for both passages , eliminate any answer that is true for only one of the two passages. 21 . When you have made your choice, double-check the other choices to make sure there isn't a better one. 22. Don't get bogged down on difficult questions. You might want to skim a set of questions and start by answering those you feel sure of. Then concentrate on the harder questions. But don't skip between sets of reading q uestions, because when you return to a passage you'll probably have to read it again. 23 . When you have gone through all the questions associated with a passage , go back and review any you left out or weren't sure about. 77 THE CRITICAL READING SECTION Practice Questions The passages below are followed by questions based on their content; questions following a pair of related passages may also be based on the relationship between the paired passages. Answer the questions on the basis of what is ~ or ~ in the passages and in any introductory material that may be provided. Questions 1-2 are based on the following passage. The Internet is rapidly becoming another means of disseminating information traditionally made available through radio and television stations. Indeed, it is now Line possible for journalists and the public to access new 5 releases of audio- and videotapes, satellite media tours, and on-line news conferences via.their computers. The number of news sites on the Internet grows each day. As one media company executive notes, "With many of these Web sites generating new content every hour 10 and exponentially larger audiences, on-line news sites represent a dynamic and vital outlet for news," 1. In the passage, the author emphaSizes which aspect of the Internet? (A) Its speed (B) Its cost (C) Its growth (D) Its design (El Its accuracy 2. Which of the following best captures the attitude of the (line 8) toward the Internet? (A) (B) {Cl (D) (E) ~company Anxiety Distrust Ambivalence Excitement Curiosity Questions 3-6 are based on the following passages. Passage I A recent study comparing the DNA of Native Americans and central Siberians has established that the two populations share common ancestors, Many anthropolLine ogists see this as proof of the Bering Strait migration 5 theory, which holds that between 11,000 and 6,000 years ago, ancestors of Native Americans migrated southward from Asia to North America across a land bridge that had joined the two continents. Apache scholar Ramon Riley sees it differently, Noting that tribal legends locate Apache 10 origins squarely in the American Southwest, he offers an alternative explanation of the newfound genetic link, ~The migration was just the other way around," he says, "They spread north from here_" In ,support of this view, Riley argues that the Athabaskan languages spoken by the northern 15 tribes~in the Pacific Northwest, Canada, and Alaska-are "much more diluted" than that spoken by the Apache. 78 executive" Passage-based Reading Passage 2 Stanford University linguist Merritt Ruhlen has discovered st riking sim ilarities between Ket, a nearly extinct language spoken in central Siberia. and various languages 20 of the Athabaskan group, traditionally spoken by Native Americans living along the western edge of North America. including the Apache in the southwestern United States. Citing 36 separate instances of correspondences between Ket and Athabaskan words, Ruhlen concludes that both linguistic 25 traditions ultimately derive from a single language, one presumably spoken by a prehistoric population from which both the Siberians and Native Americans are descended. 3. The two passages are similar in that each one (A) (8) (C) (D) (E) traces the origins ofKet to a Native American language uses genetic evidence to support its position discusses research linking Native Americans to a population in Siberia attempts to reconcile traditional myth and historical fact hypothesizes that a land mass once connected Asia am' North America 4. The anthropologists mentioned in Passage I, lines 3-4, wou ld most likely claim that Merritt Ruhlen's conclusion (Passage 2, lines 24-27) is (A) inconsistent with the DNA evidence (B) further confirmation of the Bering Strait migration theory (C) a validation of some Native American legends (D) based on a misunderstanding of Siberian culture (E) evidence that Ket is no longer spoken in central Siberia 5. Ramon Riley (Passage I, li ne 8) would most likely argue that the "prehistoric population" (Passage 2, line 26) was origi nally located in (A) (B) (C) (D) (E) central Siberia the southwestern United States the Pacific Northwest Canada Alaska 6. Passage I differs from Passage 2 in that on ly Passage 1 (A) provides evidence of linguistic similarities between two languages (8) contends that d ifferent groups descended from the same population (e) questions the feasibility of a population migration between continents (D) discusses the multiple languages spoken in central Siberia (E) offers conflicting interpretations of a recent scientific discovery 79 THE CRITICAL READING SECTION Questions 7· 12 are based on tbe following passage. The followin.g passage is an excerpt from a book written by two female Iristori(H1s about professional women who begml their careers in science in the lale nineteel1th and early twentieth cellturies. The strong efforts to gain equality for women in the scientific workplace began to show results in the last quarter of the twentieth century; women have secured Line poSitions as research scientists and won recognition and 5 promotion within their fields. Though the modern struggle for equality in scientific fields is the same in many ways as it was in the early pari of the century, it is also different. 10 15 20 25 30 35 40 45 50 55 80 The women who first began undertaking careers in science had litlle support from any part of the society in wh ich they lived. This vanguard had to struggle alone against the social conditioning they had received as women members ofthat society and against the male-dominated scientific community. Women scientific researchers made a seemingly auspicious beginning. In the first quarter of the twentieth century, some women scientists who engaged in research worked at the most prestigious institutes of the period and enjoyed more career mobility than women researchers would experience again for several decades. Florence Sabin, an anatomist at the Rockefeller Institute of Medical Research noted for her research on the lymphatic system, is one important example. This encouraging beginning, however, was not to be followed by other successes for many decades. To have maintained an active role in research institutions, women would have had to share some of the decision-making power: they needed to be part of hiring, promotion, and funding decisions. Unfort unately, these early ~'omen scientists were excluded from the power structure of scienti fic research. As a resuit, they found it almost impossible to provide opportunities for a younge r set of female colleagues seeking employment in a research setting, to foster their productivity and facilitate their career mobility, and eventually to allow them access to the top ranks. Even those with very high profeSSional aspirations accepted subordinate status as assistants if doing so seemed necessary to gain access to research positions-and too often these were the only positions offered them in their chosen careers. Time and again they pulled back from offering any real resistance or chaltenge to the organizational structure that barred their advancement. But we must remember that these women scientists were few in number, their participation in dedsion-makingpositions was Virtually nil, and their political clout was minimal. Thus they could easily become highly visible targets for elimination from the staff, especially if their behavior was judged in the least imprudent. Women's awareness that they were unequal colleagues. included in professional settings only on the sufferance of male colleagues, who held the pOSitions of power, conOicted with their belief in meritocracy. They wanted to believe that achieving persons would be welcomed for their abilities and contributions. Yet they were surrounded hy evidence to the contrary. An assista nt professor of zoology observed that the men who were heads of departments were insistent on having other men in the department; they told her that women ought to be satisfied teaching high school. She relates that, during her ten years in the department. men were given at least six 60 positions that she was qualified for and wanted desperately, but for which she was not even considered because she was a woman. 7. The primary purpose of the passage is to (A) (8) (C) (D) (E) explain a situation refute an argument propose a change predict an outcome honor an achievement 8. The passage as a whole suggests that "career mobilityQ (lines 18 and 32-33) means the (A) freedom to work on projects that one is most interested in (8) freedom to publish research findings no matter how controversial they are (e) ability to obtain funding to travel to important professional meetings (D) ability to find ajob in any part of the country (E) ability to advance in one's chosen field 9. The statement that women could be eliminated from their jobs if their behavior was "the least imprudent" (line 47) suggests primarily that they (A) we re more likely than their m~le colleagues to be rebellious (8) participated in the creation of the standards by which the performance of researchers was judged (C) could gain advancement if they avoided political con frontations about their rights as wo men (D) were judged by a standard different ftom the one used to judge their male colleagues (E) were as critical of their colleagues as their colleagues were of them 10. The last paragraph of the passage suggests that for the majority of women scientists, the "belief in me ritocracy" (line 51) was (A) justified, conSidering the opportunities available to them (8) fortunate, because it provided them with attainable goals (C) inconsistent with the fact thaI they were discriminated against on the job (D) understandable, in that the concept had worked for the previous generation of women scientists (E) trend-setting. in that their views soon received universal acceptance Passage-based Reading I I. The example of the assistant professor of zoology (lines 54-62) serves primarily to indicate the (A) extent of male bias against women in scientific fields at a particular time (B) results of a woman's challenging male dominance in the early part of this centu ry (C) reasons for women's right to equal treatment (D) inability of men and women to work together in an academic setting (E) early attempts of women 10 achieve a share of scientific awards 12. All of the following questions can be explicitly answered 011 the basis of the passage EXCEPT: (A) What condit ions did women scientists find it necessary to struggle against in the first quarter of the twentieth century? (B) What specific steps were taken in the early part oflhe twentieth century to help women gain equality in the scientific workplace? (C) What changes in the organization of the scientific commun ity would have enhanced the position of women scientists as the twentieth century advanced? (D) What were the views of some women scientific researchers on the subject of meritocracy? (E) What degree of success was attained by the generation of women scientists who followed those who came into prominence earlier in the twentieth century? 25 30 35 40 45 50 55 Q uestions 13-25 are based on the following passage. 71ze following excerpt i5 the beginning of a memoir, published ill 1989, by a woman who emigrated with her family from Poland to Canada when she was a teenager. It is April 1959. I'm standing at the railing of the Salory's upper deck, and I feel that my li fe is ending. I'm looking out at the crowd that has gathLins ered on the shore to see the ship's departure from 5 Gdynia-a crowd that, all of a sudden, is irrevocably on the other side-and I want to break out, run back, run toward the familiar excitement, the waving hands, the exclamations. We can't be leaving all this behind-but we are. I am thirteen 10 years old, and we are emigrating. It's a notion of such crushing, definitive finality that to me it might as well mean the end of the world. My sister, four years younger than I, is clutching my hand wordlessly; she hardly understands 15 where we are, or what is happening to us. My parents are highly agitated; they had just been put through a body search by the customs police. St ill, the officials .....eren't clever enough, or suspicious enough, to check my sister and me-lucky for us, 20 since .....e are both carrying some silverware .....e were not allo .....ed to take out of Poland in large 60 65 70 75 p , A trumptt made from a ram's hom and sounded in the synagogue on the Jewish High Holy Days. 81 THE CRITICAL READING SECTION 80 No wonder. But the wonder is what you can make a paradise out of. I told her that I grew up in a lumpen~ apartment in Cracow, squeezed into three rudimentary rooms with four other people, surrounded by squabbles, dark political rumblings, memories of wartime suffering, and daily struggle 85 for existence. And yet, when it came time to leave, I, too, felt I was being pushed out of the happy, safe enclosures of Eden. • Pertaining to dispossessed, often displaced, individuals who have been cui off from the socioeconomic dass with which they would ordinarily have been identified. 13. This passage serves mainly to (A) provide a detailed description of what the author loved most about her life in Poland (B) recount the author's experience of leaving Cracow (C) explain why the author's family chose to emigrate (D) convey the author's resilience during times of great upheaval (E) create a factual account of the author's family history 14. In lines 2·3, "I feel that my life is ending" most nearly reflects the author's (A) overwhelming sense of the desperate life that she and her family have led . (B) "d ,,,Ii,,';on Ih'l ,h, ;""v;ng ,(,m;!;" lif, (C) unsettling premonition that she witt not survive the voyage to Canada (D) severe state of depression that may lead her to seek professional help (E) irrational fear that she witt be permanently separated from her family 15. In lines 5·6, the author's description of the crowd on the shore suggests that (A) her family does not expect to find a warm welcome in Canada (B) her relatives will not be able to visit her in Canada (C) her family's friends have now turned against them (D) she will find it difficult to communicate with her Polish friends (E) the step she is taking is irreversible 82 16. The passage as a whole suggests that the autho r diffe rs from her parents in that she (A) has happier memories of Poland than her parents do (B) is more sociable than they are (C) feels no response to the rhythms of the Polish anthem (D) has no desire to wave to the crowd on the shore (El is not old enough to comprehend what she is leaving behind 17. For the author, the experience of leaving Cracow can best be described as (A) (B) (C) (D) (E) enlightening exhilarating annoying wrenching ennobling 18. In lines 17-19, the author's description of the customs police suggests that the author views them with (A) alarm (B) skepticism (C) disrespect (D) caution (E) paranoia 19. In lines 29·37, the author indicates that "nostalgia" differs from "tesknota" in that CA) tesknota cannot be explai ned in English (B) tesknota denotes a gloomy, bittersweet yearning (C) tesknota is a feeling that neve r ends (D) nostalgia is a more painful emotion than tesknota (E) nostalgia connotes a greater degree of desire than tesknota 20. By describing her feelings as having "shades and degrees" (tine 33), the author suggests that (Al she is allowing herself to grieve only a little at a time (B) she is numb to the pain of her grief (C) she is overwhelmed by her emotions (D) her sadness is greatest at night (E) her emotional state is multifaceted Passage-based Reading 21. In lines 33-34, the phrase ''I'm destined to know intimately" implies that the author (Al cannot escape the path her father has chosen for the family (B) believes that the future will bring many new emotional experiences (C) will be deeply affected by the experience of emigrating (D) must carefully analyze her conflicting emotional reactions (E) has much to learn about the experience of emigrating 22. The author refers to the "camera eye" (line 46) and the "heavy curtain" (line 47) in order to suggest (A) (B) (C) (D) (E) the difference between reality and art the importance of images to the human mind the difference between Poland and Canada her inability to overcome her fear of death her inability 10 imagine her future life Questions 26-31 are based on the following passage. The followi,zg passage is adapted from the writings of a Nobel Prize-winning scientist. Line 5 10 15 23. The description of the author as '"engaged in a stubborn refusal to move" (lines 65-66) suggests her (A) determination to claim her space on the crowded deck of the ship (B) refusal to accept the change in her life (C) wish to strike back at her parents for taking her away from Poland (D) resolve not to become a Canadian citizen (E) need 10 stay in close proximity to her family 20 25 24. In lines 66·69, the author suggests that her parents' comforting gesture indicates (A) a recognition of feelings of distress over their departure (B) their exhilaration and relief at the thought of personal freedom (C) a great deal of ambivalence regarding their decision (D) pain so great that they can feel no joy in their departure (E) a complete loss of feeling due to the stressful events 30 35 40 25. The author mentions the anecdote about the person she met at a "stylish party in New York" (line 70) in order to (A) prove that the author had become less childlike and more sophisticated (B) demonstrate tha t the author's parents had become affluent in Canada (C) describe how wealthy children are raised in Asian countries (D) make an important point about childhood happiness (E) show that the author had ultimately lived in the United States as well as Canada 45 50 Any scientist who is not a hypocrite will admit the important part that luck plays in scientific discovery. Our estimate of the importance of luck is inherently biased: we know when we benefit from luck, but in the nature of things cannot assess how often bad luck deprives us of the chance of making what might have been an important discovery. A colleague and I carried out an experiment in which little tissue fragments, which were \'ery difficult to work with, were injected into mice of different strains. If we had been more experienced, we would have injected only white blood cells (which would have been easier to handle) into the mice. We now know that if we had done this, we would not have discovered actively acquired toler· ance because the grafts would have in effect rejected their hosts. ObViously, we were lucky, but our scientific training enabled us to recognize the Significance of the accident. I think, therefore, that there was no need for the distinguished neurophysiologist Hodgkin to refer to his "feeling of guilt about suppressing the part which chance and good fortune played in what now seems to be a rather logical development." It might nevertheless seem as ifluck plays a dominant role in scientific discovery. I would like to challenge this view fo r the following reasons: we sometimes describe as "lucky" a person who wins a prize in a lottery at long odds; but if we describe such an event as luck, what word shall we use to describe the accidental d iscovery on a park bench of a lottery ticket that turns out to be the winning one? The two cases are quite different. A person who buys a lottery ticket is putting himself or herself in the way of winning a prize. This individual has, so to speak, purchased candidacy for such a turn of events and all the rest is a matter of mathematical probabilities.$0 it is with scientists. A scientist is anyone who, by observations and experiments conducted, by the literature read, and even by the company kept, puts himself or herself in the way of making a discovery. These individuals, by deliberate action, have enormously enlarged their awareness-their candidacy for good fortune- and will now take into account evidence of a kind that a beginner or a casual observer would probably overlook or misinterpret. I honestly do not think that blind luck of the kind enjoyed by someone who finds a winning lottery ticket for which he or she has not paid plays an important part in ~cience or that many important discoveries arise from the casual intersection of two lines. "Evidence that transplanting living tissues between adult organisms is pOS5ible.

83

THE CRITICAL READING S ECTIO N

55

Nearly all successful scientists have emphasized the importance of preparedness of mind, and I wanllO emphasize that this preparedness of mind

60

is worked for and paid for by a great deal of exertion and reflection. If these exertions lead to a discovery, then I think it would be inappropriate to credit such a discovery to luck.

26. The outcome of the experiment described in lines 9-l2 suggests that (Al luck worked against the scientists at first (B) the injection of only white blood cells into the mice allowed the two scientists to make their

discovery (el the mice represented the perfect animals on which to conduct the experiment (0) the scientists involved were able to capitalize on luck (El scientific experiments occur in the concrete world, not in the abstract world of theory

27. In lines 35-40, the author uses the example of the lottery win ner in order to (A) suggest that blind luck occurs more frequently than people realize (B) suggest that luck plays a more important part in most events t han people realize (e) suggest that luck is not the correct term to use when referring to a significant scientific discovery (D) illustrate th~1I those who rely solely on,luck are unlikely to find success (E) illustrate that the two forms ofluck are analogous

28. In lines 44-45, "deliberate" most nearly means (A) cunning (B) slow (e) compelling (D) cautious (E) intentional

84

29. The author implies that a scientist achieves "candidacy for good fortune~ (line 46) by (A) making careful and repeated mathematical calculations (B) playing hunches rather than depending on research (C) performing enough experiments to increase the statistical probability of success (D) obtaining k nowledge that allows him or her to recognize important evidence (E) understanding the difference between luck and discovery

30. The meaning of the phrase "casual intersection of two lines" (line 54) is most dearly conveyed by which of the following? (A) Informal kinds of experiments (8) Two detailed plans (C) Geometrically precise experiments (D) Unanticipated coincidence (E) Predetermined events

3 1. The primary purpose of the passage is to (A) delineate a Single definition ofluck (8) show that scientists d iscover what they intend to find (e) compare science 10 a game (D) share the pleasure in making scientific discoveries (El discuss the role of luck in science

17. D

2. D

18.

e

e

19. B

4. B

20. E

5. B

2 1. C

6. E

22. E

7. A

23. B

8. E

24. A

9. D

25. D

e

26. D

11. A

27. C

12. B

28. E

13. B

29. D

14. B

30. D

15. E

31. E

3.

10.

16. A

Additional practice questions can be found in The Official SAT

On/;ne Course at www.collegeboard.com/satonlinecourse.

86

CHAPTER 7

Practice for the Critical Reading Section

Here's a chance to practice the test-taking skills and concepts you've been working on. Tryout diffe rent ways of approaching questions before you take the pract ice tests in the last section of this book. This chapter is intended to give you practice with the differe nt types of questions, so it isn't arranged in the same way as the actual SAT.

87

Practice Questions-Sentence Completion Each sentence below has one or two blanks, each blank indicating that something has been omitted. Beneath the sentence are five words or sets of words labeled A through E. Choose the word or set of words that, when inserted in the sentence, ~ fits the meaning of the sentence as a whole. Example: Hoping to -.----- the dispute, negotiators proposed a compromise that they felt would be ------- to both labor and management. (A) enforce .. useful (B) end .. divisive (el overcome .. unattractive (D) extend .. satisfactory (El resolve .. acceptable

1. Investigation of the epidemic involved determining what was ------- about the people who were affected, what made them differ from those who remained well. (Al chronic (B) unique (C) fortunate (D) misunderstood (E) historical 2. Because management ......• the fact that employees find it difficult to work alertly al repetitious tasks, it sponsors numerous projects to .•..... enthusiasm for the job.

(A) recognizes .. generate (B) disproves .. create (e) respects .. quench (D) controls .. regulate (E) surmises .. suspend 3. They did their best to avoid getting embroiled in the quarrel, preferring to maintain their .•.. -.. as long as possible. (A) consciousness (8) suspense (C) interest (0) decisiveness (E) neutrality

4. The strong affinity of these wild sheep for mountains is not .......; mountain slopes represent ....... because they effectively limit the ability of less agile predators to pursue the sheep. (A) (B) (C) (D) (El

88

useful .. peril accidental .. security instinctive .. attainment rest rained .. nourishment surprising .. inferiority

5. Even those who do not .•. -••• Robinson's views ....... him as a candidate who has courageously refused to compromise his convictions. (A) shrink from .. condemn (B) profit from .. dismiss (C) concur with .. recognize (D) disagree with .. envision (E) dissent from .. remember

6. The alarm voiced by the committee investigating the accident had a ....... effect, for its dire predictions motivated people to take precautions that ..•.... an ecological disaster. (A) trivial .. prompted (B) salutary .. averted

(C) conciliatory .. supported (D) beneficial .. exacerbated (E) perverse .. vanquished 7. At the age offorty·fj,·e, with a worldwide reputation

and an as yet unbroken string of notable successes to her credit, Carson was at the ....... of her career. (A) paradigm (8) zenith

(Cl fiasco (D) periphery

(El inception

8. The fact that they cherished religiOUS objects.more than most of their other possessions ....... the ..•.... role of religion in their lives. (A) (8) (C) (D) (El

demonstrates .. crucial obliterates .. vital limits .. daily concerns .. informal denotes .. varying

9. Mary Cassatt, an Impressionist painter, was the epitome of the ....... American; a native of Philadelphia who lived most of her life in Paris. (Al (8) (C) (D) (El

conservative provincial benevolent prophetic expatriate

10. In the nineteenth centu ry many literary critics saw themselves as stern, authoritarian figures defending society against the .... -.. of those ....... beings called authors. (A) (B) (C) (D) (E)

depravities .. wayward at rocit ies .. exemplary merits .. ineffectual kudos .. antagonistic indidments .. secretive

Practice for the Critical Reading Section

Practice Questions-Passage-based Reading The passages below are followed by questions based on their content; questions following a pair of related passages may also be based on the relationship between the paired passages. Answer the questions on the basis of what is ~ or ~ in the passages and in any introductory material that may be provided. Questions I-II are based on the following passage. Fear of communism swept through the United States in the years fol/owing the Russian Revolution of 1917. Several stares passed espionage acts that restricted Line political discussion, and radicals of all descriptions were 5 roul/ded up in so-called Red Raids cOl/ducted by the attorney general's office. Some were convicted and imprisoned; others were deported. This was the background of a trial in Chicago involving twenty men charged under lllinois's espionage statute with 10 advocating the violent overthrow of the government. The charge rested on the fact that all the defendants were members of the newly formed Communist Labor party. The accused in the case were represented by Clarence Darrow, one of the fo remost defense attorneys in the 15 country. Throughout his career, Darrow had defended the poor and the despised against exploitation and prejudice. He defended the rights of labor unions,for example, at a time whe71 many $Ought to outlaw the strike, and he was resolute in defending constitutional 20 freedoms. The following are excerpts from Darrow's sum mation to the jury. Members of the Jury. . . . If you want to convict these twenty men, then do it. I ask no consideration on behalf of any one of them. They are no better than any other 25 twenty men or women; they are no better than the mil· lions down through the ages who have been prosecuted and convicted in cases like this. And if it is necessary for my clients to show that America is like all the reSI, if it is necessary that my clients shaH go to prison to show it, 30 then let them go. They can afford it if you members of the jury can; make no mistake about that. The State says my clients ~dare to criticize the Constitution." Yet this police officer (who the State says is a fine, right-living person) twice violated the federal Con35 stitulion while a prosecuting attorney was standing by. They entered Mr. Owen's home without a search warrant. They overhaulrd his papers. They found a flag, a red one, which he had the same right to have in his house that you have to keep a green one, or a reHow onr, or any 40 other color, and the officer impudently rolled it up and put another flag on the wall, nailed it there. By what right was that done? What about this ki nd of patriotism that 45 50 55 60 65 70 75 80 85 violates the Constitution? Has it come to pass in this country that officers of the law can trample on constitu· tional rights and then excuse it in a court of justice? . Most of what has been presented to this jury to stir up feeling in your souls has not the slightest bearing on provo ing conspiracy in this case. Take Mr. Lloyd's speech in Milwaukre. It had nothing to do with conspiracy. Whether the speech was a joke or was serious, I will not attempt to discuss. But I will say that if it was serious it was as mild as a summer's shower compared with many of the statements of those who are responSible for work· ing conditions in this country. We have heard from people in high places that those individuals who express sympathy with labor should be stood up against a wall and shot. We have heard people of position declare that individuals who criticiu the actions of those who are getting rich should be put in a cement ship with leaden sails and sent out to sea. Every violent appeal that could be conceived by the brain has been used by the powerful and the strong. [ repeat, Mr. Lloyd's speech was gentle in comparison. Mr clients are condemned because they say in their platform that, while they vole, they believe the ballot is secondary to education and organization. Counsel sug· gests that those who get something they did not vote for are sinners, but I suspect you the jury know full well that my clients are right. Most of you have an eight·hour day. Did you get it by any vote you ever cast? No. It came about because workers laid down their tools and said we will no longer work until we get an eight·hour day. That is how they got the twelve· hour day, the ten· hour day, and the eight-hour day-not by voting but by laying down their tools. ·Then when it was over and the victory won .. then the politicians, in order to get the labor vote, passed legislation creating an eight-hour day. That is how things changed; victory preceded law.... You have been told thaI if you acquit these defendants you will be despised because you will endorse everything they believe. But I am not here to defend my clients' opin· ions. I am here to defend their right to express their opinions. I ask you, then, to decide this case upon the facts as you have heard them, in light of the law as you under· stand it, in light of the history of our country, whose in· stitutions ynu and I are bound to protect. I. Which best captures the meaning of the word "consideration~ in line 23? (A) Leniency (B) Contemplation (C) Due respect (D) Reasoned judgment (E) Legal rights 89 THE CRITICAL READING SECTION 2. By "They can afford it if you members of the jury can" (lines 30·31), Darrow means that (A) no harm will come to the defendants if they are convicted in Ihis case (B) the jurors witl be severely criticized by the press if they convict the defendants (e) the defendants are indifferent about the outcome of the trial (D) the verdict of the jury has financial implications for all of the people involved in the trial (El a verdict of guilt), would be a potential threat to everyone's rights 3. Lines 32·45 suggest that the case against Owen would have been dismissed if the judge had interpreted the Constitution in which of the following ways? (A) Defendants must have their rights read 10 them when they are arrested. (D) Giving false testimony in court is a crime. (C) Evidence gained by illegal means is not admissible in court. (D) No one can be tried twice for the same crime. (E) Defendants cannot be forced to give incriminating evidence against themselves. 4. In line 47, the word ~bearing" most nearly means (A) connection (B) posture (C) endurance (D) location (E) resemblance 5. In lines 46·62, Darrow's defense rests mainly on convincing the jury that (A) a double standard is being employed (B) the prosecution's evidence is untrustworthy (C) the defendants share mainstream American values (D) labor unions have the right to strike (E) the defendants should be tried by a federal rather than a state court 6. The information in lines 46-62 suggests that the prosecution treated Mr. Lloyd's speech primarily as (Al (B) (C) (D) (El sarcasm to be resented propaganda to be ridiculed criticism to be answered a threat to be feared a bad joke to be dismissed 7. Darrow accuses "people in high places" (lines 54-55) of (A) conspiring to murder members of the Communist party (B) encouraging violence against critics of wealthy business ol,'ners (C, pressuring members of the jury to convict the defendants (D) advocating crud and unusual punishment for criminals (E) insulting the public's intelligence by making foolish suggestions 8. The word "education" (line 65) is a reference to the need for (Al establishing schools to teach the ph ilosophy of the Communist Labor party (8) making workers aware of their economic and political rights (Cl teaching factory owners about the needs of laborers (D) creating opportunities for on-the-job training in business (E) helping workers to continue their schooling 9. the statement "victory preceded law" (line 77) refers to the fact that (Al social reform took place only after labor unions organized support for their political candidates (B) politicians need to win the support oflabor unions if they are to be elected (Cl politicians can introduce legislative reform only if they are elected to office (D) politicians did not initiate improved working conditions but legalized them after they were in place (El politicians have shown that they are more interested in winning elections than in legislative reform 10. Judging from lines 78-80, the jury had appare ntly been told that finding the defendants innocent would be the same as (A) (B) (Cl (D) (E) denying the importance of the Constitution giving people the right to strike encouraging passive resistance inhibiting free speech supporting communist doctrine 11. In order for Darrow to win the case, it would be most crucial that the jurors possess (A) a thorough understanding oflegal procedures and terminology (B) a thorough understanding of the principles and beliefs of the Communist Labor party (C) sympathy for labor's rights to safe and comfortable working conditions (D) the ability to separate the views of the defendants from the rights of the defendants (E) the courage to act in the best interests of the nation's economy 90 Practice for the Critical Reading Section Questions 12-17 are based on the following passage. The follow ing is adapted from a translation of a novel first published in 1894. The author of the novel was a Puerto Rican legislator. The thin crescent of the new moon was greeted by torrential rains. Juan del Sallo, confined by the weather, was at his desk amidst a sea of paper. He Lint! reached into one of the pigeonholes and extracted 5 a bundle wrapped in a rubber band: his son's letters. Gabriel, twenty-four years old, was in his final semester oflaw studies in Spain. Although Gabriel was away from Puerto Rico and already a man, TO Juan regarded as unfinished his mission as a father. He must prepare Gabriel for the disappointments of reality, and with consummate tact, without wounding his optimism, he sent him brief accounts of the island, entrusting him with the 15 maturity to form his own convictions. Juan removed the most recent letter from the bundle and began to reread it, tenderly. aDon't think," Gabriel wrote, "t hat I have come to believe our land is a paradise. I know all too 20 well that life is a st ruggle everywhere. But I cannot conceal from you the sorrow that your words have caused me, and a few paragraphs in your letter have struck me with the impact of cold water. 25 "In the first paragraph, Father, you wrote just as stirring the air with a fan will never split mountains, fits oflyrical passion will not solve arduous problfms. Those \\--ords caused me to tear up an 'Ode to the Patria' which J had written. In the ode, I sang the glories of my land, basing it upon its natural opulence and upon the romanticism of a great cloud of loving sentiment. I tore it up, wnvinced that it was like the breeze of a fan, spending its force in the void of futility. 35 ~Second paragraph .. . shrce Humanity owns 30 the world, as it grows it must becomf worthy of the splendor of its creation. Many societies succumb to theories without ever having the good fortune to put a Single one of their philosophical 40 speculations into practice. ... Natiom are like individuals: they achieve more when they plan to plant a tiny tret, and do it, than when they propose to raise an entire forest and then fall asleep in the furrows. Reality! Here you have the 45 great lever. We should concern ourselves with what already exists, in order to achieve what should be. By only singing of what we would like it to be, we accomplish nothing. I sense a severe loved him infinitely. as though Gabriel were made of fragi le Bohemian crystal. Thus passed the hours of that nostalgic day. 12, The passage is primarily concerned with a (Al father's attempt to regain his son's affection (B) son's skill at setti ng his father's mind at ease (e) father's desire for his son to include artistic sentiments in his life (D) son's ambition to return to his homeland as a successful lawyer and poet (E) father's efforts to guide his son's intellectual and emotional growth 13. Juan apparently considers "lyrical passion~ (line 27) to be (Al a necessary component in the creation of enduring poetry (B) an effective technique for inspiring action in others (C) an emotion that Gabriel needs to experience (D) of little consequence in practical malleTS (El less compelling than olher artistic feelings 14. Gabriel's stated reason for destroying his aOde to the Pat ria" most strongly suggests that (A) Gabriel's optimistic illusions had been shattered (8) (C) (D) (E) Gabriel's writing skills suddenly embarrassed him Gabriel had reversed his feelings about Puerto Rico Juan had preViously ridiculed similar pieces Juan had successfully turned Gabriel's attention back to his studies 15. Which of the following best paraphrases the point made by mentioning trees and forests in lines 42-43? (A) Detailed planning is essential in large operations. {Bl Even the strongest structure will come to ruin if it is built on a weak foundation. (e) Following through on a small project is preferable to simply conceiving a large one. (D) If individuals work together harmoniously, the entire commun ity will prosper. (El The most invigorating work is that Which is selfgenerated, not that assigned by others. criticism in these words. and since I know how much you love our land. that criticism is immensely important to me.Juan enjoyed rereading it all. His son had imagi· nation and wit. He loved everything with childlike candor, but was Simultaneously a thinker begin55 ning the great journey along life's rugged trail. Juan 50 91 THE CRITICAL REA DING SECTION 16. It can be inferred from th~ passage that Gabriel sees his father as a man who Questions 18-22 are based on the following passage. their heat budgets. But if they should stretch up as a tree does, they would lift their working parts, their leaves, into the streaming Arctic winds. Then it is likely that the plants could not absorb enough heat from the Sun to avoid being cooled below a critical temperature. Your heat budget does not balance if rou stand tall in the Arctic. Such thinking also helps explain other characteristics of plant design. A desert plant faces the opposite problem from that of an Arctic plantthe danger of overheating. It is short of water and so cannot cool itselfby evaporation without dehydrating. The familiar sticklike shape of desert plants represents one of the solutions to this prob· lem: the shape exposes the smallest possible surface to incoming solar radiat ion and provides the largest possible surface from which the plant can radiate heat. In tropical rain forests. by way of contrast, the scorching Sun is not a problem for plants because there is sufficient water. This ,"",orking model allows us to connect the general characteristics of the forms of plants in different habitats with factors such as temperature, availability of water, and presence or absence of seasonal diffe rences. Our Earth is covered with a patchwork qUilt of meteorological conditions, and the patterns of this patchwork are faithfully reflected by the plants. This excerpt discusses the rdatiollSlJip between plants and tlleir environments. 18. "[he passage primarily focuses on which of the following characteristics of plants? 30 (A) has strong views that arc well worth considering (8) has made great sacrifices to send him to law school (e) expects him to become a powerful and important leader (D) writes harsh observations that need to be moderated (E) is somewhat unsure of himself despite his confident manner 35 4(] 17. It can be inferred from the letters cited in the passage that which oflhe following exchanges has already occurred? (A) Juan voiced doubts abollt Gabriel's economic decisions. (B) Juan encouraged Gabriel to consider practicing law in Spain. (e) Gabriel sought his father's advice on affairs of the heart. (D) Gabriel displayed a dear reluctance to accept criticism. (E) Gabriel expressed some loftily idealistic thoughts. 45 50 55 Line 5 10 15 20 25 92 Why do some desert plants grow tall and thin like organ pipes? Why do most trees in the tropics keep their leaves year round? Why in the Arctic tundra are there no trees at all? After many years without convincing general answers, we now know much about what sets the fashion in plant design. Using terminology more characteristic of a thermal engineer than of a botanist, we can think of plants as mechanisms that must balance their heat budgets. A plant by day is staked out under the Sun with no way of sheltering itself. All day long it absorbs heat. If it did not lose as much heat as it gained, then eventually it would die. Plants get rid of their heat by warming the air around them, by evaporating water, and by radiating heat to the atmosphere and the cold, black reaches of space. Each plant must balance its heat budget so that its temperature is tolerable for the processes of life. Plants in the Arctic tundra lie dose to the ground in the thin layer of still air that dings there. A foot or two above the ground are the winds of Arctic cold. Tundra plants absorb heat from the Sun and tend to warm up; they probably balance most of their heat budgets by radiating heat to space. but also by warming the still air that is trapped among them. As long as Arctic plants are dose to the ground, they can balance (A) Their ability to grow equally well in all environments (B) lbeir effects on the Earth's atmosphere (C) Their ability to store water for dry periods (D) Their fundamental Similarity of shape (E) Their ability to balance heat intake and output 19. Which of the following could best be subs'tituted for the words sets the fashion in" (line 6) wi thout changing the intended meaning? u (A) (8) (C) (D) (E) improves the appearance of accounts for the uniformity of defines acceptable standards for determines the general characteristics of reduces the heat budgets of 20. According to the passage, which of the following is most responSible for preventing trees from growing tall in the Arctic? (A) (8) (C) (D) (E) The hard, frozen ground The small amount of available sunshine The cold. destructive winds The large amount of snow that falls each year The absence of seasonal differences in temperature Practice for t he Critical Reading Section 21. The author suggests that the "sticklike shape of desert plants" (lines 41-42) can be attributed to the (A) inability of the plants to radiate heat to the air around them (8) presence of irregular seasonal differences in the desert (C) large su rface area that the plants must expose to the Sun (D) absence of winds strong enough to knock down tall, thin plants (E) extreme heat and aridity of the habitat 22. The contrast mentioned in lines 46-48 specifically concerns the (A) (B) (C) (D) (E) availability of moisture scorching heat of the Sun seasonal differences in tem perature variety of plant species heat radiated by plants to the atmosphere see a dark woman in a flowered dress doing a bit of cakewalk to the lively notes of a mouth organ. 35 Her bare feet would raise the saffron dust that floated down on the coveralls and bunion-split shoes of the man breathi ng music in and out of his harmonica. The Black people watching her would laugh and rub their knees, and it would be easy for 40 the valley man to hear the laughter and not notice the adult pain that rested somewhere under the eyelids, somewhere under their head rags and soft felt caps, somewhere in the palm of lhe hand, somewhere behind the frayed lapels. somewhere in 45 the sinew's curve. He'd have to stand in the back of Greater Saint Matthew's Church and let the tenor's voice dress hi m in silk, or touch the hands of the spoon carvers (who had not worked in eight years) and let the fingers that danced on wood kiss 50 his skin. Otherwise the pain would escape him even though the laughter was part of the pain. 23. The author's perspective on the Bottom is that of Questions 23-28 are based on the following passage. (A) an unsympathetic outsider (B) an adult recalling early dreams (C) a participant defending a course of action (D) an angry protester trying to prevent an undesirable event (E) a sad observer of a transformation The following description of a small town is from a novel by an African American which was published in 1973. [n that place, where they tore the nightshade and blackberry patches from their roots to make room for the Medallion City Golf Course, there Line was once a neighborhood. It stood in the hills 5 above the valley town of Medallion and spread all the way to the river. It is called the suburbs now, but when Black people lived there it was called the Bottom. One road, shaded by beeches, oaks, maples, and chestnuts, connected it to the valley. 10 The beeches are gone now, and so are the pear trees where children sat and yelled down through the blossoms to passersby. Generous funds have been allotted to level the stripped and faded buildings that clutter the road from Medallion up to the 15 golf course. They are going to raze the Time and a Half Pool Hall, where feet in long tan shoes once pointed down from chair rungs. A steel ball will knock to dust Irene's Palace of Cosmetology, where women used to lean their heads back on 20 sink trays and doze while Irene lathered Nu Nile into their hair. Men in khaki work clothes will pry loose the slats of Reba's Grill, where the owner cooked in her hat because she claimed she couldn't remember the ingredients without it. 25 There will be nothing left of the Bottom (the footbridge that crossed the river is already gone), but perhaps it is just as well, since it wasn't a town anyway: just a neighborhood where on quiet days people in valley houses could hear singing 30 sometimes, banjoes sometimes, and, if a valley man happened to have business up in those hillscollecting rent or insurance payments-he might 24. The name "the Bottom" is incongruous because the neighborhood (A) contains only demolished bu ildings (B) has become more prosperous since it was named (C) is a fertile piece of land (D) has only recently been established (E) is located in hills above a valley 25. ~Generous" as used to describe Hfunds" (line 12) is intended to seem (A) ironic, because the funds are being used to destroy something (8) progreSSive, because the narrator is showing how times change (e) objective, because the narrator knows the amount (D) humorous, because the cleanup is not t ruly expensive (E) equivocal, because the funds are inadequate 93 THE CRITICAL READING SECTION 26. In th~ second paragraph, the author conveys a feeling of tension by juxtaposing which two of the following elements? (A) The assertion that the neighborhood's destruction is insignificant versus the carefully drawn richness of its life (B) The author's expression of affection for the neighborhood versus frustration at its reluctance 10 change (C) Nostalgia about the way the town used to be versus a sense of excitement about its future (D) Appreciation fo r the town's natural beauty versus disapproval of its ramshackle state (E) Sadness about the town's fate versus sympathy fo r the reasons for it 27. The author's statement that the valley man might no t perceive the pain underlying the laughter of t he Bottom's residen ts (lines 38-45) emphasizes that the Boltom's residents (A) had frequent contact with other reside nts of the valley (B) understood the valley man well, even though they did not see him often (C) were not the carefree people they might appear to be (D) concealed their real feelings from outsiders (E) were concerned about the destruction of their neighborhood 28. The author portrays the Bottom as a place (A) that lacked economic prosperity but had a rich emotionalJife (B) that was too filled with sadness to be able to survive (C) that needed to become more up-to-date in order to prosper (D) whose effect on its residents was difficult fo r them to understand (E) in which people paid more attention to the way things seemed to others than to the way th ings really were 94 Q uestio ns 29-30 are based on the following passage. MI am a very serious woman,B was Bella Savitzky Abzug's simple but powerful response to those who made light of her often boisterous activism. Abzug's Un" forceful manner and flamboyant appearance may 5 have drawn ridicule from some of her adversa ries in the American polit ical a rena, but this very serious woman dedicated her life to the public service on behalf of the oppressed and ignored. Abzug gained fame nationally as the first Jewish woman elected to the 1(1 United States Congress and later internationally as a leader in the global women's movement, where he r courage and indomitable spirit made a lasting impression on younger activists. 29. The tone of the q uotat ion in line 1 is best described as (A) (8) (C) (D) (E) dignified apologetic exhilarated hostile cynical 30. The primary purpose of the passage is 10 (A) provide a character sketch of a political figure (8) promote interest in the global women's movement (C) emphaSize the importance of public service to a society (D) explore both sides of a national controversy (E) champion the righls of those whose voices are not heard THE CRITICAL READING SECTION Answer Key Sentence Completion I. B 6. B 2. A 7. B 3. E 8. A 4. B 9. E 5. C 10. A Passage-based Reading I.A 16. A 2. E 17. E 3. C 18. E 4. A 19. D 5. A 20. C 6. D 21. E 7. B 22 . A 8. B 23. E 9. D 24. E 10. E 25. A I I. D 26. A 12. E 27. C 13. D 28. A 14. A 29. A 15. C 30. A Additional practice questions can be found in The Official SAT Online Course at www.c o llege board.com/satonlinecourse. 96 PART III The Writing Section 97 CHAPTER 8 About the Writing Section Writing is a skill needed for success in both college and the workplace. The writing section gives you a chance to demonstrate the writing skills you've developed through your high school course work, particularly in English class, and th rough writing outside of school, such as personal journal entries and letters. The sect ion is composed of: • An essay: You will have to write a firs t draft of an original essay, under timed conditions. • Multiple-choice questions: You will have to recognize sentence errors, choose the best version of a piece of writi ng and improve paragraphs within a writi ng context. The mult iple choice sections measure your ability to • comm un icate ideas clearly a nd effectively; • improve a piece of writing through revision and edit ing; • recognize and identify sentence-level errors; • understand grammatical elements and structures and how they relate to one another in a sentence; • recognize correctly fo rmed grammatical structures; • clearly express ideas through sentence combin ing and use of tra nsitional words and phrases; and • improve coherence of ideas within and among paragraphs. In the essay component of the writing section, the student-written essay assesses you r ability to develop and express ideas effectively. It evaluates your ability to do the kind of writing required in college - writing that develops a point of view, presents ideas logically and clearly, and uses precise la nguage. You're not expected to be an expert in any particular field, but the topic of the essay (also called a prompt) does allow you to support your ideas by using what you've learned from your course work, your readings outside of school and your experiences in and out of school. The 99 THE WRITING SECTION essay must be written in a lim ited time. which doesn't allow for many rev isions, so it is considered and scored as a first draft. The multiple-choice component includes 49 questions on grammar, usage, paragraph organization and multi-paragraph coherence, and assesses your ability to use language in a clea r, The multiple-choice questions consistent manner and to improve a piece of writing through include three types: revision and editing. 1. improving sentences (see Chapter 10) The mult iple-choice questions don't ask you to define or use 2. identifying sentence elTors grammatical terms and don't test spelli ng or capitalization. In (see Chapter 11) some questions, punctuation marks, such as the semicolon, may 3. improving paragraphs (see Chapter 121 help you choose the correct answer. But questions like those mainly test the structure in which the punctuation appears. ~eplnMlnd Approaches to the Multiple-Choice Questions )- Read the directions carefully, and then follow them. )- Look at the explanations for each correct answer when you use the practice materials in this book. Even if you got the question right, you may learn something from the explanation. )- Eliminate the choices you are sure are wrong when you are not sure of the answer. Make an educated guess from those that remain. How the Writing Section Is Scored You will be given two subscores for the writing section: a multiple-choice subscore that will range from 20 to 80 and an essay subscore that will range from 2 to 12. If you write a n essay that is not on the assigned topic, you will receive an essay subscore ofO. The essay subscore will contribute about 30 pe~cent toward the total writing score, and the score on the multiple-choice questions will contribute about 70 percent. The total writing score will be placed on the College Board 200 to 800 scale. Developing Writing Skills Good writing, especially in college, requires you to develop your ideas with relevant and appropriate information. This is true for any subject that you'll be studying, whether it 's English, history, science, social studies, mathematics or fi ne arts. Though each of your inst ructors may have different expectations for your writing assignments, every instructor will wa nt ideas that are well thought out and clearly expressed. 100 About the Writing Section To write better, you have to write more. Practice helps improve your writing ski lls. To write better, you have to read more. Reading helps improve the way you use language. Successful college writing The more you read - challenging material in particular includes: • weH-developed ideas, with - the more you'll be exposed to interest ing and provocative relevant and accurate supportideas and to varied, even unusual, ways of using language. If ing information you read well-written books and articles. you may be inspired • clearly expressed thesis statements to use similar language in your own writing. • good organization Table 8. 1 lists characteristics of effective writing and pro• appropriate, accurate and varied vocabulary vides examples of ineffective sentences and corrected sen• variety of syntax (sentence tences. You will need to recognize these charac teristics when structure) you work on the writing multiple-choice sect ions. ~ePlnMlnd Table S.1 Characteristics of Effecti ve Writing, with Examples Characteristics of Effective Writing Examples of Ineffective Writing Corrected Sentences 1. Consistency Sequence of tenses After he broke his arm, he is home for two weeks. After he broke his arm, he was home for two weeks. Shift of pronoun If you are tense, one should try to relax. If you are tense, you should try to relax. Parallelism The master carpenter showed us how to countersink the nails, how to varnish the wood, and getting a smooth surface was also demon· strated. The master carpenter showed us how to countersink the nails, varnish the wood, and get a smooth surface. Noun·number agreement Ann and Sarah want to be a pilar. Ann and Sarah want to be pilots. Subject-verb agreement There is eight people on shore. There are eight people on shore. 2. Logica l Expression of Ideas Coordination and subordination Nancy has a rash, and she is probably allergic to something. Nancy has a rash; she is probably allergic to something. Logical comparison Harry grew more vegetables than his neighbor'S garden. Harry grew more vegetables than his neighbor. Modification and word order Barking loudly, the tree had the dog's leash wrapped around it. Barking loudly. the dog had wrapped his leash around the tree. (continued) 101 THE WRITING SECTION Table 8 .1 (continued) Exam pl es of Cha racte r i stics of Effective Writing In effective Writing Corre cted Se nte nces 3. Clarity a nd Precision Ambiguous and vague pronouns In the newspaper they say that few Diction He circumvented the globe on his Wordiness people voted. The newspaper reported that few people voted. trip. He circumnavigated the globe on his trip. There are many problems in the contemporary world in which we There are many problems in our contemporary world. live. Missing subject towed away. If you park here and do not eat in the restaurant, your car will be towed away. When you bake 8 cake, the oven should be preheated. When you bake a cake, you should preheat the oven. If your car is parked here while not eating in the restaurant, it will be Weak passive verbs 4. Appropriate Use of Conventions 102 Adjective and adverb confusion His friends agree that he drives reckless. His (riends agree that he drives recklessly. Pronoun case He sat between you and I at the stadium. He sat between you and me at the stadium. Idiom Natalie had a different opinion towards her. Natalie had a different opinion of her. Comparison of modifiers Of the sixteen executives, Meg makes more money. Of the sixteen executives, Meg makes the most money. Sentence Whether or not the answer seems correct. The answer seems to be correct. fragment Comma splice or fused sentence$hawna enjoys crossword puzzles, she works on one every day.

Shawna enjoys crossword puzzles, and she works on one every day.

CHAPTER 9

The Essay

The ability to write effectively is one of the key factors in doing well in college. Writing is an essential part oflearning. Through the writ ing process, you develop, examine and refine your ideas. Through formal writing assignments, you demonstrate what you understand and how weJJ you are able to communicate it to others. The SAT essay measures you r ability to write effectively under timed conditions. The SAT essay is similar to the on-demand writing done in many college classes. You

103

THE WRITING SECTION

~eplnMlnd

reader, the scoring director, scores the e ssay.

104

The Essay

Exhibit 9.1 SAT Scoring Guide Score of 6

Score of 5

Score of 4

An essay in this category demonstrates cleaf and consistent mastery, although it may have a few minor errors. A typical essay

An essay in this category demonstrates reasonably consistent mastery, although it will have occasional errors or lapses in quality. A typical essay

An essay in this category demonstrates adequate mastery; although it will have lapses in quality. A typical essay

• effectively and insightfully develops a point of view on the issue and demonstrates outstanding critical thinking, using clearly appropriate examples, reasons and other evidence to support its position

• effectively develops a point of view on the issue and demon· strates strong critical thinking, generally using appropriate examples, reasons and other evidence to support its position

• develops a point of view on the issue and demonstrates competent critical thinking, using adequate examples. reasons and other evidence to support its position

• is well organized and clearly focused, demonstrating clear coherence and smooth progression of ideas

• is well organized and focused, demonstrating coherence and progression of ideas

• is generally organized and focused, demonstrating some coherence and progression of ideas

• exhibits skillful use of language, using a varied. accurate and apt vocabulary

• exhibits facility in Ihe use of language, using appropriate vocabulary

• exhibits adequate but inconsistent facility in the use of language, using generally appropriate vocabulary

• demonstrates meaningful variety in sentence structure

• demonstrates variety in sentence structure

• demonstrates some variety in sentence structure

• is free of m ost errors i n grammar, usage, and mechanics

• is generally free of most errors in grammar, usage, and mechanics

• has some errors in grammar. usage, and mechanics

Score of 3

Score of 2

Score of 1

An essay in this category demonstrates developing mastery, and is marked by ONE OR MORE of the following weaknesses:

An essay in this category demon· strates lirrle mastery, and is flawed by ONE OR MORE of the following weaknesses:

An essay in this category demonstrates very little or no mastery, and is severely flawed by ONE OR MORE of the following weaknesses:

• develops a point of view on the issue, demonstrating some critical thinking, but may do so inconsistently or use inadequate examples, reasons or other evidence to support its position

• develops a point of view on the issue that is vague or seriously limited, and demonstrates weak critical thinking, providing inap· propriate or insufficient examples, reasons, or other evidence to support its position

• develops no viable point of view on the issue, or provides linle or no evidence to support ils position

• is limited in its organization or focus, or may demonstrate some lapses in coherence or progression of ideas

• is poorly organized and/or focused, or demonstrates serious problems with coherence or progression of ideas

• is disorganized or unfocused, resulting in a disjointed or incoherent essay

• displays developing facility in the use of language, but sometimes uses weak vocabulary or inappropriate word choice

• displays very linle facility in the use of language, using very limited vocabulary or incorrect word choice

• displays fundamental errors in vocabulary

• lacks variety or demonstrates problems in sentence structure

• demonstrates frequent problems in sentence structure

• demonstrates severe flaws in sentence structure

• contains an accumulation of errors in grammar, usage and mechanics

• contains errors in grammar, usage and mechanics so serious that meaning is somewhat obscured

• conlains pervasive errors in grammar, usage or mechanics that persistently interfere with meaning

Essays not written on the essay assignment will receive 8 score of zero.

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THE WRITI NG SECTION

Approaches to the Essay )- Read the promp! carefully, and make sure you write on the topic given. Essays not on topic will receive a zero. ~ Decide your viewpoint on the topic. If you have trouble focusing on the ma in

point, try complet ing this sentence: "When people finish reading my essay, I want them to understand that

The student sample that scored a 6 may have been the result of an outline like this: • Thesis: An attribute can be either a vice or a virtue. depending on a person's point of view. • Point 1 - I had always believed that perfectionism was a virtue: it was a motivator to achieve high goals, which I had done. • Point 2 - Later, I discovered that others, including a teacher, perceived my perfectionism to be a vice, resulting in fatig ue, stress and illness. • Conclusion - There is always a "however." I realized that perfectionism is neither all good nor all bad. You have only 25 minutes to write you r essay, so don't spend too much time outlining. A little planning time, however, may be essential to make sure that your essay does not wander off topic or stray from your foc used thesis statement. 106

The Essay

. . Vary the sentence structure in your writing. Good writing uses a variety of sentence types to show the proper relationships between ideas. Simple sentences communicate single observations. Compound sentences show that two ideas are related and are roughly equal in weight, and complex sentences show that of two related ideas, one is more important than the other. Essays that receive high scores almost always use a variety of sentence structures. Sentence variety also makes your writing more engaging and easier to read! Remember that as you write. Here are samples of the three kinds of sentences: • Simple: "My best frie nd lives two blocks away from me," This sentence is called simple because there is one subject - "my friend" - and one verb - "lives." It makes a single observation. • Compound: "My best friend lives two blocks away from me, but her house is much nicer than mine," This sentence is compound because it comprises what could be two or more si~ple sentences that are connected with one of the words we call coordinating conjunctions - and, or, but, for or nor. These words indicate that there is a relationship between these two observations and that the two statements are of roughly equal importance. You may learn that the words so and yet sometimes function as coordinating conjunctions as well. Either half of the compound sentence could have been a simple sentence by itself. • Complex: "Although my friend lives two blocks away from me, I don't go to her house very often." This sentence is complex because it contains two observations but they are not of equal importance. The first one "although my friend lives two blocks away from me" - cannot be written as a simple sentence because of the connecting word "although." That word, called a subordinating conjunction, expresses the relationship between the two ideas and indicates that the other observation, the one that does not begin with a subordinating conjunction, is the more important one. The fact that you don't go to your friend's house very often is, in this sentence, more important than the fact that she lives only two blocks away.

All your ideas will not be related to each other in the same way, so you should vary the sentence structure that communicates how your ideas are related to each other. . . Use clear, precise and appropriate vocabulary. Appropriate words are accurate and specific, not necessarily long and obscure. Avoid too many abstract and indefinite words, a,nd seek concrete, specific ones in their place. Consider the differences in these two sentences: 1. The place where we stopped to eat was full of people dressed up more than

we were.

107

THE WRITING SECTION

2. The restaurant where we stopped for lunch was full of men wearing

0 e P IDMind You w on't be judged on your handwritin g, but essay readers m ust be able t o read w hat

jackets and ties and women wearing suits and dresses - a noticeable contrast to our jeans and T-shirts.

you w rote. so w rite clearly

Although the first sentence is grammatically correct, it is general and

and leg ibly.

unspe.cific. A reader will not easily see the contrast between the speaker

and the other people in the restaurant. The second version creates a much more concrete and vivid image in the reader's mind, and it communicates more effectively the contrast between the speaker and the other customers. The sentence is not improved by substituting unnecessarily fancy words where concrete, everyday ones do just fine: "The dining establishment where we rested for our midday repast was peopled with representatives of the paying public who wore garments more typically associated wit h the office and business world than our comfortable and casua l attire." Good writing uses mature and sophisticated language, but some writers think readers are impressed by fancy vocabulary and convoluted sentences. Those writers are wrong.

)- Leave time to review what you've written. Although you won't have time for fu ll scale revision, do leave time for rereading your essay and mak ing minor changes in the wording or even in the structure of what you have written. OccaSionally a more appropriate word, or a clearer way to make a point, will occur to you. Don't be afraid to make these minor changes if they improve your essay.

Writing Exercise: Using Action Verbs Writing exercises and practice can help you prepare further for the essay component of the SAT. One ofthe best ways you can improve your writing is to minim ize the use of the same verb - especially the verb to be. Reliance on the verb to be in any of its eight pa rts (be, am, are, is, was, were, being, been) makes you r writing sluggish and unclear. More than any other kind of word, the verbs you use communicate what is happening so, whenever possible, try to use a verb to convey the action of your sentence. For example, consider this sentence: "The decision of the manager to bring about an end to the p ractice of overtime assignments and schedule the right number of workers in the first place was greeted with approval by a unanimous number of workers:' What a horrible sentence! It limps along until the passive verb "was greeted," and it merCifully ends a few words later. (A verb or sentence is passive, or in the passive voice, if someone or something other than the subject performs its action s. In th is case, the actual subject of the sentence is "decision," but the act ion, the greeting, was done by the workers. A sentence in which the subject performs the action is called an active sentence.) The main idea of the sentence, however, has little to do with greeting. It is supposed to communicate the fact that workers approved something that the manager decided to do.

108

The Essay

If we examine the sentence for words that contain some potential for action, we'll see many: decision, bring, end, practice, assignments, scheduling, workers, greeting and approval. Unfortunately, none of these can be the verb of the sentence because they appear in other grammatical structures (Le., in this sentence, they appear as abstract nou ns, infinitives and gerunds, which are defined and illustrated in the section below). Each functions as the subject or the object of a preposition, but not as a verb. If you could revise the sentence so that one or more of these potential verbs becomes the action-bearing word, you will have a more dynamic and accurate sentence.

Quick Grammar Review Although you will not be asked to define or use grammatical terms on the SAT, familiarity with the precedi.ng grammatical terms wm make it easier to understand the pri nciples of this writing exercise on action verbs. Here are some definitions:

• Abstract nouns are those nou ns (Le., naming words) that refer to ideas, thoughts or intangible things. The abstract nouns in the sample sentence are decision , end, practice, assignments, and approval. They are general rather tha n specifi c. • Infinitives are verb forms that use the word to. In the sample sentence, the infinitive is "to bring." O ther examples are "We hoped to see our cousin during her visit," or "What do you want to do with the money you've earned?"

• Gerunds are specialized verb forms that end in "-ing," take the place of nouns and indicate an action of some kind. In the sentence "Running is an excellent form of exercise," running is a gerund because it takes the place of a noun and names an action. Not all words ending in "-ing" are gerunds, but all gerunds end in "-ing."

• Present participles are also verb forms that end in "-ing." Instead of naming an action, though, the participle describes a noun . For exa mple, the word singing can be either a geru nd or a present participle depending on its use. In the sentence "Singing makes me feel happy," it is a geru nd because it names a n action. In the sentence "The singing bi rd woke me up at four o'clock," it is a participle because it describes the bird. • A preposition is a word that shows a particular relationship, such as direction or location, between a noun and the rest of the sentence. Prepositions are usually very short words, such as in, of, to or by. Prepositions are usually followed by nouns, which are called their objects. In the following illustrations, the preposition is italicized and the object is underlined: • the rooms in my hQ.yg • the name of my friend • the trip to Chicago • the tree by my window • A prepositional phrase contai ns a preposition and its object and whatever describing words accompany that object.

109

THE WRITING SECTION

Revising Sentences to Use Action Verbs If you revise your sentences so that the verb indicates the action and the subject tells who or what performed that action. you will probably see three other improvements: 1. You will change the passive voice to active.

2. You will reduce the number of abstract nouns. 3. You will eliminate strings of prepositional phrases. If you decide that the real action of the sample sentence lies in the word approval. begin by making that the verb. Then decide who approved of what. You should be able to construct this much of the sentence so far: "Workers approved when the manager decided .. ," Now you can add the details from the original sentence that you think are necessary: "Workers unanimously approved when the manager decided to bring about an end to the practice of overtime assignments and schedule the right number of workers in the first place." This revision is much better, but it is not as good as it can be. There are st ill several abstrac t nouns: end. practice. assignments. Take a moment and determine if these nouns imply actions (they do), and who performs these actions. Do the workers end, practice and assign? Or does the manager do these things? Once you think about it, you'll realize it's the manager who ends, the manager who practices and the manager who assigns. Thisis a lot of activity hiding in nonaction words, and ali of it is bei ng done by someone who is not the subject of the sentence. How can you express this action with the manager as the subjec t? "The manager decided to end assigning overtime and to schedule the right number of workers in the first place." Instead of "to end assigning overtime," you would probably write: "The manager decided to stop assign ing overtime . .." You see that you don't need the word "practice" at all. You've eliminated one unnecessary abstract noun. Now you have two sentences: "The manager decided to stop assigning overtime and to schedu le the right number of workers in the fi rst place." "Workers unanimously approved the manager's decision." You can leave this revision as two sentences if you like. These two sentences are certain ly clearer than the original. But you might also realize that there is a relationship between them, and you want to combine them in a way that communicates that relat ionship. Because the relationship is chronological (Le., the decision came first, then the approval after) or causative (i.e., the decision caused the approval),

110

The Essay

you have a few choices available. Suppose you want to indicate the time sequence. You could write: "After the manager decided to stop assigning overtime and to schedule the right number of workers in the first place, the workers unanimously approved the manager's decision." On the other hand, if you want to indicate cause, you could write: "Because the manager decided to stop assigning overtime and to schedule the right number of workers in the first place, the workers unanimously approved the manager's decision." Yet you are not happy about the repeated word "decided/decision." Should you change one of them? Can you do that without confusing the reader? Yes, you can, when you realize that it is the decision of the first clause that the workers approve. What you have been trying to communicate is: "Workers unanimously approved the manager's decision to stop assigning overtime and to schedule the right number of workers in the first place." How much better that reads than the original version! Here's the original sentence aga in: "The decision of the manager to bring about an end to the practice of overtime assignments and schedule the right number of workers in the fi rst place was greeted with approval by a unanimous number of workers." To sum up, you have made the following improvements: • You have expressed the action of the sentence as a verb. • You have used the subject of the sentence to tell who performed that action. • You have reduced the number of abstract nouns. • You have reduced the number of prepositional phrases. Following are a few more unclear sentences that need the same type of revision as in the example. You may find this process slow at first, but with practice, you will make these revisions quickly. Work out your revisions, and then compare them to the suggested revisions that follow. Remember that there will be several good revisions available for each. Yours will be good if you follow these suggest ions: • Avoid the verb to be in favor of a verb that communicates action. • Reduce the number of abstract nouns. • Replace prepositional phrases with single-word adjectives and adverbs when you can.

'11

THE WRITING SECTION

Example Exercise: Rewriting Sentences Using Action Verbs 1. The price of the toy on the shelf of the store was intended to be a reflection of the hard work of many workers and the high cost of materials.

Rewrite:

2. Under the management of the new owners of the store the store is designed to serve the basic needs of the majority of the people in the neighborhood.

Rewrite:

3. The audience was impressed by the skill of the actors and the imagination of the director of the film at the theater around the corner from my house.

Rewrite:

4. The most important idea in the introduction of the essay is at the end of the paragraph that is found at the beginning of the paper.

Rewrite:

POSSIBLE REWRITES THAT IMPROVE THE ORIGINAL SENTENCES

Here are some possible responses to the exercise. Yours mayor may not look li ke these, but successful ones will sha re the features mentioned above. The original sentence comes first. followed by a suggested revision. The verbs are italicized and the prepositional phrases a.re placed within brackets.

112

The Essay

1. Original: The price lofthe toy] [on the shelf] (of the store] was intended to be a

reflection [of the hard workl [of many workers] and the high cost [of materials]. Rewrite: The toys [on the shelf} cost so much because a lot [of people) worked hard to make them and the materials were expensive.

2. Original: [Under the management] [of the new owners] [of the store] the store is designed to serve the basic needs [of the majority] [of the people] [in the neighborhood].

Rewrite: The new owners will manage the store so that it serves most (of the neighborhood people's needs].

3. Original: The audience was impressed [by the skill] [of the actors] and the imagination [of the director] [of the film ] [at the theater] [around the corner] [from my house]. Rewrite: The actors' skill and the director's imagination impressed the audience who attended the theater (around the corner] (from my house]. Or: The actors' skill and the director's imagination impressed the audience who attended the neighborhood theater. 4. Original: The most important idea [in the introduction] [of the essay] is [at the end] [of the paragraph] that is found [at the beginning] [of the paper]. Rewrite: In the introduction to the essay, the most important idea is found at the end of the first paragraph.

Writing Exercise: Using Abstract and Concrete Language Another way to improve you r writ ing is to recognize the difference between abstract language and concrete language - and to provide concrete illustrations whenever you write about someth ing abstract. For example, when you read a word like success, you know what it means, but you probably also know that the same word will mean something different to someone else. On the other hand, "a score of 520 on the SAT math section" means the same to anyone who reads it. This is true because success is an abstract word, whereas "a score of 520" is a concrete expression. What would you consider to be an example of success? For some, it might be a position on the varsity tennis team. F.or others, it might be passing a driver's test. All these examples can be seen as concrete illustrations of the abst ract term success. If you are wr iting about success, you do not clarify your meaning by providing synonyms, such as achievement, accomplishment or reaching a goal. You achieve clarity by providing specific illustrations so that your reader knows what you mean by the term.

113

THE WRITING SECTION

Example Exercise: Using Concrete Language How would you illustrate success? Write three concrete illustrations of success here:

1. _______________________________________ 2. ___________________________________________ 3. ___________________________________________

Example Exercise: Using Abstract Language Beauty, happiness and courage are three other abstract nou ns. How would you illustrate them? Provide three examples of each of them , and then, if possible, compare your respon ses to a fri end 's.

Beauty:

1. ------------------------------------------2. _________________________________________ 3. _____________________________________

Happiness:

1. ------------------------------------------2. _______________________________________

3. _________________________________________

Courage:

1. ------------------------------------------2. ___________________________________________ 3. _______________________________________

114

The Essay

Most of the time. you know a word is abstract because you have a sense of its meaning. In some cases, however, the end ofthe word tells us it is an abstract noun. Common abstract noun endings include -age (as you saw in courage), -ance, -ment, -ness (as you saw in happiness), -ity (or just -ty, as you saw in beauty) and -tion. Although many abstract nouns have no such endings, so many do that it is a good idea to become familiar with them. Can you think of examples of abstract nouns with each of these suffixes?

-age

-ance

-ment

-ness

-ity or -ty

-tion

Example Exercise: Writing Concrete Descriptions

of Abstract Concepts To help improve the cla rity of your writing. look again at several of the abstract words you provided, and think of illustrations that would make the terms more concrete for a reader:

Abstract word: Concrete illu.strations: _ _ ______ _______ _ _ ______

Abstract word: _ _ _ _ _ _ _ _ _ __ _ Concrete illu.strations: _______________________

115

THE WRITING SECTION

Abstract word: _ _ _ _ _ _ _ _ _ _ __ Concrete illustrations: ______________________ _

116

The Essay

the afternoon and into the evening make me wish for the placidity of a lake in the woods. A few weeks ago this krling got so strong I bought myself a couple of bass hooks and a spinner and returned to the lake where we used to go, for a week's fish ing and to revisit old haunts." White's abst ract ideas, especially success and placidity, are well illustrated by the many concrete details he prOVides (again, in italics). Although you may not consider a month of camping by a lake in Maine to be a successful family vacation - you might prefer an amusement park or a city's museums and theaters - you still know exactly what White is ta lking about and his opinion on that subject. How much less satisfying this paragraph wou ld be ifhe had written the following: "My father used to take us on vacation, butwe all got sick and he fell in the water. Even so, we had a good time. We always used to go to the same place around the same time of yea r. After I grew up I liked other things, but sometimes I miss the old family place, so I got some old fishing gear and went back." Obviously, the ability to manage abstract and concrete language makes a tremendous difference in the success of White's writing here. A point worth noting is that proper nouns (Le., those that begin with capita l letters) and numbers are very concrete. The presence of such concrete language, when possible, gives you r writing specificity - which makes your writing more interesting.

Example Exercise: Rewriting Sentences Using Concrete Language For each of the abstract statements below, rewrite the sentence and make it more concrete by provid ing specific language.

I. What we did yesterday afternoon was lots of fun. Rewrite:

2. I have strong feeli ngs about the attitude you are expressing on that topic. Rewrite:

117

THE WRITING SECTION

3. That is my favorite performer singing that song on the rad io.

Rewrite:

4. That book is the most amazing thing I have ever read.

Rewrite:

5. When my friend told me her news, I thought she was the luckiest girl in the world.

Rewrite:

6. If you want to be healthy. you have to take care of yourself.

Rewrite:

POSSIBLE REWRITES THAT IMPROVE THE ORIGINAL SENTENCES

Following are some possible revisions of the preceding sentences. Yours will certainly be qu ite different, depend ing on what conc rete details you have included. In these sample responses, the concrete details are printed in italics.

I. Original: What we did yesterday afternoon was lots of fun. Rewrite: The trip to the mall and the ride on the roller coaster were lots of fun .

2. Original: r have strong feelings about the attitude you are expressing on that topic. Rewrite: r feel very worried when I hear how stubbornly you defend the bullies who tease children.

118

The Essay

3. Original: That is my favorite performer singing that song on the radio. Rewrite: That is my favorite singer, Miley Cyrus, singing "See You Again" on the radio. 4. Original: That book is the most amazing thing I have ever read.

Rewrite: Of all the books I have ever read, The Samurai's Garden best showed me how selfless love can be. 5. Original: When my friend told me her news, I thought she was the luckiest girl in the world. Rewrite: When Louisa told me that she had wall a basketball scholarship, r thought she was the luckiest girl in the world. 6. Orighlal: If you want to be healthy, you have to take care of yourself. Rewrite: If you want to be healthy, you have to eat fruits arid vegetables, get at least a half hour of exercise every day and sleep seven hours a night.

Sample Essays The rest of this chapter offers examples from students that illustrate every possible score. Although all of the sample essays were handwritten by students, they are shown typed here, in boxes, for ease of reading. However, we a re present ing one in handwriting to remind you that it is important to write legibly and clearly. The essays have been typed exactly as each student wrote his or her essay, without a ny corrections to spelling, punctuation or pa ragraph breaks. The following is a sample prompt:

~ Automated Score To receive an automated score for your response to this essay question, check out The Official SAT Online Course at www.col1egeboard.com/ satonlinecourse.

Think carefully about the issue presented in the following excerpt and the aSSignment below. Some people believe that there is only one foolproof plan, perfect solutio n, or correct interpretation. But nothing is ever that Si mple. For better or worse, for every so-called fina l answer there is another way of seeing things. There is always a ~however." Assignment: Is there always another explanation or another point of view? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from you r reading, studies, experience, or observations.

119

THE WRITING SECTION

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120

The Essay

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WHY ESSAY #1 RECEIVED A SCORE OF 8

This response demonstrates clear and consistent mastery by insight fully exploring the writer's drive for perfectionism. The writer effectively develops the position that whether another person considers this perfectionism "a vice or virtue depends on his or her point of view," This response demonstrates outstanding critical thinking by not only describing the writer's own intense motivation and the resulting physical and emotional strain, but also by providing examples of ways that others negatively see the writer's drive. ("Others see me crying over the 'B+' I received on the math test and blame my 'emotional instability,' as they call it, on my perfectionism," "My perfectionism is my vice, accord ing to her and yet all this time I thought it was my greatest virtue.") By considering others' viewpoints, the writer is able to look more objectively at his or her motivation. ("Now I understand that my perfectionism is not 'a ll good,' it was after all responsible for the lack of plenty of sleep as well as being responsible for my head cold. However, I maintain that it is not 'all bad' either.") This weIlorganized essay smoothly moves from one idea to the next, demonstrating a dear coherence. Using a varied, accurate and apt vocabulary, the essay exhibits the skillful use of language and demonstrates a meaningful va riety in sentence structure ("May is AP test season and for me that means severely high levels of stress. I could be spotted walking down the halls of the school with my Barron's AP World History book under my right arm and a high lighter in my pocket. It was imperative that I study hard enough to receive a grade of'S' on the test"). This outstanding response scored a 6.

122

The Essay

. Essay #2: This essay also received B score of 6.

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,he Ro"'yi",~ ,we",ties w"'s '" J.ecMe J."yi"'~ which the AIMeyic",,,, eco",oIMY s"'w '" y",piJ. 'oOOIM. I", -P",ct; AIMeyic",'s '0,,11 IM",y\:.ets, s"ch "'s the New YOY\:. 'Stoc\:. E"ch",,,,~e hM 'oecoIMe so .\1",,,,,,,ci,,,l1y i"'viti",~ 'oy 1'i27 th",t eve", AIMeyic",'s IMiJ.J.le c1",ss po"yeJ. its IMo",ey i",to AIMeyic",'s .\1",,,,,,,d,,,1 -PoY"IMS. V",-POYt""''''tely, 0", octo'oey 4, 1'i2'i the BooIMi",~ ,we",ties c"'IMe to "'''' ",'oy"pt h",lt whe", the "lew YOY\:. 'Stoc\:. E"ch",,,,~e cY",sheJ.. \he Cy",sh h",J. IM"''''y ",e~",tive co",seq"e",ces. f-Iost ",ot",'oly, the stoc\:. IM",y\:.et cY",sh o-P I'i2'i 1",,,,,,cheJ. AIMeyic", i",to the Gye",t Depyessio"" '" tiIMe o-P st",vy",tio", ",,,,J. "",eIMploYIMe",t -POy IMillio",s o-P AIMeyic",,,, dtize",s. \he wiJ.espye",J. optiIMisIM o-P the 1'i20's q"ic\:.ly t"y",eJ. i",to "'''' ",IIMost s"iciJ.",1 pessiIMislM. 1",J.eeJ.,

the Gye",t Depyessio", yepyese",ts '" cYippli",~ co",seq"e",ce o-P the stoc\:. IM",y\:.et cY",sh o-P 1'i2'i. Howevey, Fy",,,,\:'li,,, Del",,,,o Roosevelt est",'olisheJ. i",stit"tio",s ",,,,J. Ye~"I"'tio",s to pyeye",t -P"t"ye eco>lOIMic c",t",stvophes.

COB",iz",,,,t o-P the Cy",sh's c",,,ses, s"ch "'S pool COYY"ptio"" oveypyiceJ. stoc\:. v",l"es, ",,,,J. """YBi", 'o"yi",~, Roosevelt iIMpleIMe",teJ. the 'Sod",1 'Sec"yity Act, the FDIC, ",,,,J. stvictey y"les IMo",itoyi"'B cYeJ.it. His "'BByessive policies ",ot o",ly "'IMelioy",teJ. the ""'COIM-Poyt",'ole c1iIM",te o-P the Gye",t Depyessio"" 'o"t ",Iso l",iJ. the BYo"",J.woy\:. -POy '" s",-Pe y, IMoye s"ccess-p,,1 eco",oIMY. ,he AIMeyic",,,, p,,'olic ",Iso Ye",lizeJ. the """"'y positive yes "Its o-P the stoc\:. IM",y\:.et cY",sh o-P 1'i2'i. I", p",ytic"l",y, AIMeyic",,,, citize",s >lOw h",ve "'''' e",tiyely J.i-P-Peye",t .\1sc",1 o"tloo\:. -PyoIM the

'23

THE WRITING SECTION

o'te \-hey h",J- 'oe-Poye \-he Cy",sh. Spec lAl",\-oys h",ve pyove't \-0 'oe ",oye pYIAJ-e't\- "''tJ\-Ye'tJ-s 'oe-Poye

i'tsi~hHIAI,

<'\S \-hey o-P\-e't yese",ych ",,,,y~e\­

i'tves\-i't~ . Peyh",ps "'OS\- i",poY\-"''t\-ly,

A"'eylc"''t

iwes\-oys ",ye 'to\- "'s e",sily sw",y eJ- loy pOPIAI",y op\-i",is'" "''tJ~ eY

",J-vey\-ise",e't\-.

While \-he s\-oc~ ",,,,y~e\- cY",sh o-P 1'12'1 w<'\S \-he e",'ovyo o.f'

\-he Gye",\- Depyessio't, \-he Cy",sh ",Iso se\- \-he -POIA'tJ-",\-io't -POY '" sOIA'tJ-ey eco'to",y. '-P we Yeco~'tiz.e \-he ~00J- "''tJ- \-he 'o",J- o-P

\-he Cy",sh, we ",ye J-es\-i'teJ- \-0

",,,,~e

-PeWey eco'to",ic

",is\-",~es.

WHY ESSAY #2 RECEIVED A SCORE OF 6

In this outstanding essay, the writer develops insightfully the ma in idea that "Each situation has its benefits and its drawbacks" by focusing on how the tragedy of the 1929 stock market crash and the Great Depression necessitated changes that led eventually to a sounder national economy. This response demonstrates outstanding critical thinking by demonstrating that while the 1929 Crash "launched America into the Great Depression," it also motivated Franklin Delano Roosevelt to instigate changes that "laid the groundwork for a safer, more successful economy" and provided Americans with valuable fi nancial lessons. Paragraphs two and three describe the devastation that followed the crash of the 1920s' booming economy. Paragraphs four and five explore the idea that while the Great Depression was a time of "almost suicidal pessimism," positive actions were taken to ensure that such a catastrophe would not occur again. This well-orga ni zed essay uses dearly focused and appropriate details to demonstrate a smooth progression of ideas. Using a varied, apt and accurate vocabulary, the writer exhibits a skillful use of language. ("The American public also realized the many positive results of the stock market crash of 1929. In particular, American citizens , now have an enti rely different fiscal outlook from the one they had before the Crash.") This essay demonstrates clear and consistent mastery and scored a 6.

124

I

The Essay

B

score of 5.

The sh"l-elMel\l- '~eve is ",I",,,,y s '" '\'owevev" is e>

",cc",v",l-e, {'ov 1M0sl- I-\'il\~s il\ He cOl'\e wit-\' cOI\.:I.i\-\ol\.S, I-I.ost- 0-1' I-\'e l-ilMe il- is 1\01- ",Iw",y s "'s e",sy "'s s",yil\B 1-\'",1- yo", W",I\I- 1-0 .:1.0 sOlMel-\,il\B "'1\.:1. I-\'el\ .:I.oil\B il-, Ov s",yil\B 1-\'",1- yo", W",I\I- sOlMel-\'il\B "'1\.:1. I-\'el\ ~el-\-\~ il-, Theve is ",I",,,,>,s sOlMe soY\- 0{' co".:I.i\-io" Ov s\-\p",I",\-\ol\ sel- b y SOlMeOl\e else 1-\'",1- yo", lM",sl- {'oil ow, This wov.:l. '\,oweve<' is especi",lIy velev"'l\l- 1-0 I-eel\",~evs, w\'ose p",vel\\-s "'1\.:1. I-e",c\'evs I-",'<-e ",.:I.v"'l\l-", e O{' il- 1-0 soil w\'",l-evev l"'l\s Ov "J-e"'s "''vIey """''1 'vI",ve 'viM, '-",'<-e {'ov e><"'lMple '" typic",1 l-eel\"'Be boy w\'o \,,,,s j",sl- beel\ ",ssi I\e.:l. '" vo'ed 1-0 .:1.0 il\ \'is \,isl-ov c\",ss. The I-e",c\'ev beBil\s t"e C\SsiBl\lMel\t wit", 'Yo", "",ve "",II t'YeedoolM to c"oose I-\'e 1-0 ic o{' o",v vo' ed." 1\.:1. \'eve ",,",v'<-s I-\'e el\tt"'l\ce o{' I-\'e .:I.ve",.:I.{,,,,1 '\'o",evev.' The I-e",c\'ev cOl\l-il\",es, "HowEvER, I-\'e ~jed lM",sl- \'",ve sOlMe velev"'l\ce 1-0

I-\'e c",yyel\l- sil-",,,,I-iol\ il\

t\'e l-I.i.:l.J-le E",sl-," The boy 's \'eM, w\'k\' I\M fveviol.\s\y beel\. swilMlMil\B wil-\, i.:l.e",s, w"'s I\OW .:I.v",il\e.:l. O{' ",II I-opics, {'ov \'e \'",.:1.

,,0 cl",e ",k",1- "'C\S k",p e"il\ i" t-ke Mido.:l.le E",sr. ,-he" t-he pO -\11\",11'1 cOlMes "'P wil-\, '" topk "'1\.:1. Boes to .:I.isc",ss it wil-I\ \'is I-e",c\'ev, The I-e",c\'ev beBil\s, '~",t is '" very il\l-elliBel\t "'1\.:1. well 1-\'0"'~\'1- 0",1- i.:l.e",." '-\'e boy is el",l-e.:l., '0",1- I-\'el\ I-k",1- wov.:l. ve",vs i\-s "'Bly \'e",.:I., The I-e",c\'ev cOI\\-iI\",es, "HowEvER, it is 1\01- velev"'l\l- el\o", \, 1-0 I-I\e sil-",,,,\-\ol\ ",I- \''''1\.:1.,'' 1\.:1. 1-\'",1- ol\e wov.:l. \,,,,s sil\ le\''''I\.:I.e.:l.1 v",il\e.:l. 1-\'",1- '00 's.:l.", , Al\ol-"ev e><"'lMple "'0",1.:1. be '" l-eel\"'Be Bivl Bet-t-il\B veMy {'ov '" I\i \'1- 0",1- ",iI-\' \'ev {'viel\.:I.s, S\'e is '",sl- ",'00",1- to w",I'<- 0",1- I-\'e .:I.oov w\'el\ \'ev 1M01-\,ev beBil\s, ''Io",v 0",\--l11- is very lov ely," A",to1M",\-ic",lIy I-I\e ~iv\ becolMes s",spicio",s, The 1M0t\'ev cOI\\-iI\",es,

125

THE WRITING SECTION

"\1oWEvER, I

c",,,,,ol-lel- YOtA le",ve I-I-Iis 1-I0tAse we",vi"~ il-." The

~ivl cl-l",,,~es I-Iev OtAt-!11-

",,,J, vel-tAv"s wl-le" I-Iev 1M01-I-Iev 'oe~i"s ~",i", l'(OtA lM"'y I-",\

"\1oWEvER, YOtA IMIASI- 'ovi,,~ il- 'o",c\< 'oy ~:~O." A"J, I-I-Ie Bivl's eve~ pl",,,s ",ve CtAl- sl-lovl- ",,,J, I-Iev "iBI-I1- is vtAi"eJ,. ,I-Ie wovJ, I-Iowevev is vevy powev.ptAl. II- I-I",s I-I-Ie ",'oility 1-0 vtAi"

e,,\-tve J,,,,ys ",,,J, "iBI-I1-s wl-le" tAseJ, i"covvec\-1y. ,I-Ie 1M0J,ev" l-ee""'Bev especi",ny .peels I-I-Ie I-I",vsl-l tAs"'Be o.p 'I-Iowevev', .pov I-lis Ov I-Iev I-e",cl-levs ",,,J, p",ve,,1-s ",lw",ys "",,\

pc'\vHdp",t-e l~.

WHY ESSAY #3 RECEIVED A SCORE OF 5

In this essay, the writer effectively develops the main idea that parents and teachers use the word however to destroy the plans of the modern teenager by making "some sort of condition or stipulation on every activity that he or she wants to participate in." The essay demonstrates strong critical thinking by providing four appropriate, focused examples of instances when an initial offer from an adult is ruined by a subsequent "however." This focused response is well organized, moving easily from example to example and demonstrating a progression of ideas. The writer consistently exhibits facility in the use of language and demonstrates variety in sentence structure. ("The teacher continues, 'HOWEVER, the project must have some relevance to the current situation in the Middle East: The boy's head, which had previously been swimming with ideas, was now drained of all topics, for he had no clue what was happening in the Middle East.") To receive a score of 6, thiS response needs to demonstrate outstanding critical thinking by using the evidence more insightfully to develop the position instead of simply providing one example after another. Overall, this effective response demonstrates reasonably consistent mastery and scored a 5.

126

The Essay

Essay #4: This essay also received a score of 5.

Theye is ",Iw", S '" "howevey." Is H- "ot- hl.\e t-h"'t- evey lit-t-Ie

sit-I.\",t-io" i" li-l'e seel'

we see t-hyol.\~h hey se",ych, -!;"J.i,,!) '" sel.f1ess J.eeJ. is "ot- "'s

e", "'s it- """ SOI.\"J.. This ",Iso ye\"'t-es t-o t-he i"-I'",,,,ol.\s 1101J.e" C"'I.\I-!;elJ. 0-1' J.D. S",li,,!)ey's "C"'t-chey i" t-he Rye" I" HolJ.e,,'s se",ych -I'OY "hl.\e people", he co"t-i"l.\ol.\sly e"J.s I.\p J.is",ppoi"t-eJ., -!;"J.i,,!) -I''''I.\It-s wit-h eveyy peySO" he ",eet-s ",,,J.

pl",ci,,~

t-he",

1.\"J.ey his "pho"y c",t-e!)oyy" A"J. i" t-his cv"'ty woylJ. 0-1' t-oJ.",y we ",11 shive t-o ",chieve ",,,J. "!)et- ",he",J.", 'ol.\t- wit-h e",c h t-hi,,!)

t-h"'t- o"e eySo" ",i"s it- 'oeco",es I.\"",v",il",'ole -I'OY ",,,ot-hey I" Phoe'oe's I.\est- t-O -IT,,J. '" sel.f1ess J.eeJ. she -!;"J.s it- ",I",osti", ossi'ole t-o yove oe wyO" "'s wit-h evey ooJ. J.eeJ. t-h"'t- we ey-l'oy", we -I'eel ooJ. ",'o01.\t- ol.\yselves. ve" i-l' t-he J.eeJ. is '" t-ot-",I s",cvi-!;ce o"t-o Yol.\ysel-l', yol.\ e"J. I.\p -I'eeli,,!) 'oet-t-ey ",'o01.\tyol.\ "'s '" peyso", ",,,J. how yol.\ helpeJ. ",,,,,,ki,,J. jl.\st- '" lit-t-Ie. A"J. sO t-his "howeve." pey",e"'t-es e",ch ",,,J. eveyy ",speet- 0-1' Ol.\y lives, eve" "'''''''''~ t-o 'ol.\t-t- i" t-o seW s",cvi-!;ces, ~ooJ. J.eeJ.s, ",,,J. y",,,J.o,,, "'C+-S 0-1' ki"J."ess. I" 1101J.e,,'s c",se he -!;"J.s t-he "howeve." i" eveyythi"~ . Seei"~ I",wyeys "Ot- "'s pyot-eet-oys 0-1' jl.\sl-ice ",,,J. t-he I",w, 'ol.\t- Y"'t-hey ~yeeJ.y

people who love t-he t-hyill ",,,J. powey 0-1' co"J.I.\et-i,,!)

t-hel'

127

r

THE WRITING SECTION

lit evey)'olte, "'1tJ. hl.\Y!-s hll'\Sel-l' by Itevey see'ItB I-he BOoJ. lit people. While I-hls "howevey" I'\'Bhl- eXIsl- "'1tJ. be -I'01.\1tJ. 1-0 Iltl-eyl-wllte l!-seW lit I'\osl- SII-I.\",I-IOItS 0-1' li-l'e, we "'s hl.\I'\"'lts C"'It'1- J.well Olt II-. Bec"'l.\se 1-0 J.well Olt ",l1l-he ''ol.\!-s'' "'1tJ. "howeveys" 0-1' li-l'e, wOl.\lJ. oltly bYllt~",Hve "'1tJ. J.epyess'ItB -I'eeliItBs, Wil-h eveyyI-h'ItB lit ll-l'e, y ol.\ C"'1t B""1t sOl'\el-h'ItB, bl.\l- lit cOltseql.\eltce, sOl'\eolte else wl1110se wh",1- Y0l.\ B""It. II- IS "'It oltBo'ItB cycle c",l1eJ. ll-l'e. LI-I'e IS '" h Y0I.\I-, "'It ",1.\J.IHolt, "'It ",pplic",Holt, "'1tJ. "'s 10ltB "'s y ol.\ h y YOl.\y besl- "'1tJ. ",I- le",sl- hy 1-0 ",VOIJ. I-he "howeveys", y ol.\ shol.\lJ. be o\r.",y.

WHY ESSAY #4 RECEIVED A SCORE OF 5

This response demonstrates reasonably consistent mastery by developing effectively the pOint of view that "every little situation in life seems to always have some sort of a catch to it," The writer demonstrates strong critical th inking by selecti ng two appropriate examples of how a character's search fo r "truth" is, for d ifferent reasons, u nsuccessful because of a "however." The writer uses an episode of Friends to illustrate the idea that, because there is always a n attachment,to the gratificat ion from helping others and perform ing "good deeds," perfect ly sel fless acts do not exist. The response also explores how Holden Caulfie ld's focus on the negative aspects of people prevents hi m from ever "seeing the good in people" or fin ding "true people." The writer concludes by acknowledging the inevitability of "howevers" and "buts" in the life cycle and advocates not letti ng them become d istractions from the positive aspects of li fe. There is a va riety in sentence structu re. ("Just one little example is all she had to find, but as we see through her search, fi ndi ng a selfless deed is not as easy as it may sound . Th is also relates to the infamous Holden Caulfiel d of]. D. Salinger's 'Catcher in the Rye' In Holden's search for 'true people,' he cont inuously ends up disappointed, fin d ing faults with every person he meets and placi ng them u nder his 'phony category."') To receive a score of 6, this essay would have to exhibit a stronger organizational structure and smoother progression of ideas by focusi ng on fu lly developing one example before moving to the next. This effective essay scored a S.

128

The Essay

Essay #5: This essay received a score of 4.

vee wit-I-. t-I-.e t-I-.esis '''''eve is ",lw", s '" 'I-.owevev.'-" Bot-I-. I-.ist-ovy "'I\J. lit-ev",t-\.\ve "e",v wit-l\ess t-o t-I-.e I IMOst- cevt-",il\l

'"

\.\I\J.el\i",,,le -{'",d t-I-.",t-

1\0

IM",t-t-ev I-.ow '" sit-\.\",\-iol\ """y seeIM,

t-I-.eve will ",lw",ys "e ",I\ot-I-.ev -{'",dov t-o cOl\siJ.ev t-I-.",t- IM"'y sl-.eJ. '" I\ew Ii I-.t-

01\

t-I-.e civC\.\IMSt-"'I\ce

The cOl\cl\.\siol\ o-{' t-I-.e '5ecol\J. WovlJ. W",V

C",I\

evl-.",ps e>

ovev .p.""scis""," t~eve w""s "" \\~oweve/' t~""t- wov.1J.. evl.'\."" s ""'"""vv t-I-.eiv vidovy. This "I-.owevev" w"'s t-I-.e est-","lisl-.il\~ t-I-.ve",to-{' COIMIM\.\I\islM.

es it-e t-I-.e coloss",l vido

t-I-.e

llies I-.",J.

",cl-.ieveJ., t-I-.eve w"'s st-ill ",I\ot-I-.ev ",spec+, '" "I-.owevev" t-I-.",tW<'\S il\evit-",,,le

\.it-ev",t-\.\ve "'s well is '" t-est-"'IMel\t- t-o t-I-.is t-I-.esis, "'s eviJ.el\ceJ." t-I-.e t-v"'~ic pl",y o-{' ROIMeo "'I\J. J\.\liet-. ovevcoIMil\~ ",IIMost- il\s\,\vIMo\.\I\t-",,,le oJ.J.s t-I-.e sciol\ ",I\J.

J.",\.\

I-.t-ev o-{' -{''''IMil

viv",lvies -{,,,,ll il\ J.eep "'I\J. t-v\.\e love. "Howevev:' t-I-.eiv love is set-" t-I-.e cOl\s\.\IMil\ 1-.",t-veJ. "et-weel\ t-I-.eiv -{''''IMilies.

.,.p.p.

It-I-.o\.\ I-.

t-I-.e sit-\.\",\-iol\ <'\S il\ t-I-.e el\J. o-{' WovlJ. W",V II seeIMeJ. I-.ope-{'\.\I "'I\J. "vi~I-.t-, t-I-.eve

",ve ",lw",y s "I-.owevev" t-I-.",t- o.('.('set- t-I-.e civ-

C\'\IMst-"'I\ces As "ot-I-. I-.ist-ovy ",I\J. ~ve",t- wov'<.s o-{' lit-ev",t-\.\ve ",t-t-est- t-o, t-I-.eve

C"'I\

"e

1\0

cOl\s\.\IMIM",t-ely pev-{'ed (ov J.is",st-evo\.\s sit-\.\",-

t-iol\ wit-I-.o\.\t- ",t- le",st- ol\e "I-.owevev." This st-",t-eIMel\t- is il\J.eeJ. pvovel\ vevit-",,,le.

129

THE WRITING SECTION

WHY ESSAY #5 RECEIVED A SCORE OF 4

This response demonstrates adequate mastery by developing the point of view that "Both history and literature bear witness to the undeniable fact that no matter how a situation may seem, there will always be another factor to consider that may shed a new light on the circumstance." The writer demonstrates competent critical thinking by selecting two adequate examples to illustrate situat ions that seem "hopeful and bright" but are clouded by the inevitable "however," Paragraph two discusses how the "colossal victory the Allies had achieved" at the end of World War II was marred by the "threat of Communism." Paragraph three briefly discusses Romeo and Juliet's forbidden love. The response is generally focused and demonstrates some progression of ideas and coherence. The writer exhibits adequate facility in the use of language and displays some variety in sentence structure. ("Although the Allied powers reigned triumphant over fascism, there was a 'however' that wou ld perhaps marr their victory. This 'however' was the establishing threat of Communism. Despite the colossal victory the Allies had achieved, there was still another aspect, a 'however' that was inevitable.") Although this response is competent, to achieve a higher score, the writer would need to develop the point of view more effectively by demonstrating clearer focus and providing more detailed evidence. This essay scored a 4.

130

The Essay

Essay #6: This essay also

rec8iv~d

a score of 4.

R",yel l" life ls I-heye '" sll-"",\-lo" INheye 0,,1 o"e "'''SINey ls conec\-. I" .p",c+, eve" ",ss""'l"~ I-heye ls 0,,1'1 o"e Yl~hl- o.f'\-e" leMs 1-0 "''' ill I-ho"~hl- 0,,1- .l.eclslo". So",e\-l",es I-he 'oesl- IN"'Y 1-0 le",y" ls 1-0 -11".1. I-he "holNevey" ",,,.I. eys"e ",11 ossl'ole "'''SINeys 1-0 I-he .p"llesl- exl-e"l-. -n.,ls ls '" lesso" Ile",y"e.l. l" "''1 E"BIlsh cl",ss I-hls ye",y As INe

ye",.I. l" 'ooo'<.s, INe INo"I.I. IN",,,I- 1-0 h",ve .l.lsc"sslo"s ",'00,,1- I-hely ",e",,,l"~

",,,.I. I-hely l",plie",\-lo"s l" O"y Ilves. These .l.lsc"sslo"s

le.l. 1-0 "'''''''1 he",l-e.l. .l.e'o",l-es 0" V",yloC\S I-oplcs I-hYO"Bo,,1- I-he ye",y. AI- -11 ysl-, "''1 cl",ss",,,,l-es ",,,.I. I INo"I.I. 'oeco",e "'''BYY ",Ie",ch ol-hey .pOY .l.ls"'Byeel"B ",,,.I. ",I- I-he I-e",chev .pOY sh"c\-"yl,,~ hls lesso"s so I-hese

peyspeC\-lve ch",,,~e.l.

"'YB"",e,,\-s INo"I.I. OCC"y. l),,1- I-he" "''1 I c",,,,e 1-0 cl...ss o"e .1."''1 ""s"ye o.p hOIN

I .pell- 0" I-he I-opie. As I s",1- l" cl",ss I Ilsl-e"e.l. 1-0 e",ch ",y~ "'e"l-, hyl"~ 1-0 le",y" INh",1- I-he coyyec\- "'''SINey IN"'S Eve"I-"",lly I .po"".I. '" OIN" .peeli" SO" I-he s,,'o·ec\- '0,,1- I ",Iso .po"".I. so",e~ else.

-n.,eye ve",lly IN"'S "0 \lyl~hl-" "'''SlNey, ",,,.I. "''1 opl"lo"

IN"'S she"~l-he"e.l. '0'1 'oel"~ I-esl-e.l. '0'1 opposl"~ vleINs. s I-he e",y INe,,1- 0" "''''''Y of "''1 cl",ss",,,,l-es see",e.l. 1-0 ye",ll~e I-hls "'s INell. E,,~lish ye"""l"e.l. '" .l.e'o",l-e, '0,,1- "01- "''' "'''~!Y.­

o"e. II- 'oec","'e '" \-l",e 1-0 sh",ye yo"y peyspec\-lve INhlle lisl-e"l,,~ 1-0 I-he ol-heys' "holNeveys."

131

THE WRITING SECTION

WHY ESSAY #6 RECEIVED A SCORE OF 4

This competent response develops the point of view that "Sometimes the best way to learn is to find the 'however' and pcrsue all possible answers to the fullest extent." The. writer demonstrates competent critical thinking by focusing on an adequate, personal example to support the position. The response describes the change from the writer's initial anger with other pOints of view in class to an understanding that his or her own "opinion was strengthened by being tested by opposing views." This essay is generally organized to chronicle the shift in the writer's posit ion and therefore demonstrates a progression of ideas. Using generally appropriate vocabulary, the writer exhibits adequate facility in the use oflanguage. ("These discussions led to many heated debates on various topics throughout the year. At first, my classmates and I would become angry at each other for disagreeing and at the teacher for structuring his lessons so these arguments would occur.") However, to receive a higher score, th is writer would need to develop the position more effectively by discussing in further depth the ways the example supports the point of view, in addition to retelling the anecdote. Thus, this response demonstrates adequate mastery and scored a 4.

132

The Essay

Essay #7: This essay received a score of 3 .

The sl-"l-elMelll- ''"T\-.eve is "Iw" s" hewevev" s" ~esl-s I-h,,1-

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This response demonstrates developing mastery by asserting the point of view that "in many cases there is only one solution to a problem, no matter how one looks at it." The writer demonstrates some critica l thinking by attempting to prove that "the statement 'There is always a however' is false." Although the writer attempts to support the main idea, evidence provided is too limited and repetitive to be adequate. ("If a teacher were to ask for the answer to the problem one plus one, the answer would be two. In this case there is no however. The answer is two and there is no other answer.") To receive a higher score, this essay needs to demonstrate dearer focus and stronger critical thinking by developing the position further. Therefore, the essay remains in the inadequate category and scored a 3.

133

THE WRITING SECTION

8

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WHY ESSAY #8 RECEIVED A SCORE OF 2

This seriously limited essay begin s to develop the point of view that "the truth is not always easy to see," but it provides only one vague and insufficient example to support this position. Although the writer does demonstrate some critical thinking by

selecting the appropriate example of Jay Gatsby's deception, the response lacks the focus and organization necessary to exhibit coherence and a progression of ideas. Furthermore, the response displays little facilit y in the use of language. using a limited vocabulary. ("However, Gatsby became a mobster in order to get wealthy. ... Da isy wanted to marry Gatsby, but he was not wealthy. When he became wealt hy, they cou ld not marry, because he became a mobster.") To receive a higher score, this essay would need to exhibit more facility in the use of language and demonstrate stronger critical thinking by providi ng more relevant evidence to support the point of view. Consequently, this response demonstrates little mastery and scored a 2.

134

The Essay

Essay #9: This essay received a score of 1.

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WHY ESSAY #9 RECEIVED A SCORE OF 1

This brief response is fundamentally lacking. Although the response attempts to develop a point of view ("There is always a 'however' in any point of view."), there is little ev idence provided to support this position. The sparse support is incomplete and simply too limited to be organized or focused, resulting in an incoherent essay. Vocabulary is vague ("Knowing the possibility of a 'however' in an important instance ca n be helpful, unpleasing or both.") and fails to further the progression of ideas. To achieve a higher score, this response would have to exhibit a clearer focus and provide further evidence to support its position. Thus, this response demonstrates only very little mastery and scored a L

135

CHAPTER 10

Improving Sentences

Improving or revising written English is a pivotal part of successful writing. The questions in this chapter focus on an important skill: the ability to recognize and write dear. effective and accurate sentences. This is a skill you'll need when writing and making revisions to your writing in high school, in college and beyond. The following box provides the directions and the example that will appear on the test.

The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence are five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices. In making you r selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence - clear and precise. without awkwardness or ambiguity. Example: Laura Ingalls Wilder published her first book and she was sixty.fiye years old then. (A) and she was Sixty-five years old then (B) when she was sixty·five (e) at age Sixty-five years old (0) upon the reaching of sixt }'·five years (E) at the time when she was sixty· five

Here's another example. This one includes an explanation to help you understand the reasoning behind the correct answer.

137

THE WRITING SECTION

EXAMPLE Although several groups were absolutely opposed to the outside support given the revolutionary government, other groups were as eQual in their adamant approval of that support. CAl (B) (C) (D) (El

Answer: The correct answe r 1$(C). Explana tion: Choice (C) is correct because it expresses the second part of the sentence in a way that is parallel to the first part. Two groups are being compared: groups "absolutely opposed to" and groups "equally adamant in." Both phrases now have a common structure: an adverb modifyi ng an adjective followed by a preposition . Approaches to Improving Sentences ). Read the entire sentence before you look at the choices. Choice A is always the same as the original sentence, so you may see that the right answer is to leave the sentence unchanged. ). Remember that the right answer will be the one correct version among the five choices. This is d ifferent from what you will be asked to do for Identifying Sentence Errors (Chapter 11). ). Read each choice along with the entire sentence. Don't read the choices on their own. ). Look for common problem areas in sentences. These include noun/verb agreement, parallelism, placement of modifiers and the use of relative clauses. ). Read allfive versions of the sentence aloud, ifpossible, while you're practicing. You will not be able to do this during the actual test, of course. Your ear may tell you what your eye initially misses. ). Read more slowly than you normal/ydo. Our brains sometimes make automatic corrections that we don't notice. Reading more slowly will help you pay closer attention. ). Use your test booklet to help you by marking each question that you don't answer. Then you can easily find it later. Writing Exercise: Using Parallelism You ca n improve your writing enormously by using paralleli sm, which is simply using similar structu res in a series. Because parallelism puts the content of a sentence 138 Improving Sentences into a recognizable pattern. it's easier to understand a parallel sentence. For example. note the parallelism in these sentences: • Hawaii is famous for its beautiful beaches. and Montana is well known maiestic mountains . fur...!.u . • Sharon wanted to have the party at her house on Saturday night rather than in a restaurant on Sunday afternoon. In the first sentence. Hawaii and Montana a re the two subjects. They are both described with adjectives (which are italicized - Le.,famous a nd well known), and what they are famou s and well known for in each case follows in a prepositional phrase (which is underlined). The parallelism extends to the fac t that the noun in each prepositional phrase is preceded by an adjective: Hawaii is famous fQ[ its; Q!::I!!.!tif!.!i 2!::I!o!;;bC:i Montana is well known fQ[ its; maj!:s:ti!;; m~!lmt i!,il]:i and How would you describe the parallelism of the second sentence? Sharon wanted to have the party rather than (where?) at her house (when?) 2n S5!,t!.![gay night (where?) in a restaurant (when?) 2n Sundi!,y aflC[D2QI]. In general, try to balance a word with a word, a phrase with a phrase and a clause with a clause. W ithin those patterns. if you want to be a careful w riter, try to bala nce similar types of words - for example, adjectives wit h adjectives, prepositional phrases with prepositional phrases, or noun clauses with noun clauses. For example, notice the clumsiness of this sentence: "On a hot day, I like swimming or to sit in the shade:' A better, clearer way to write this sentence would use a parallel expression: "On a hot day, I like to swim or sit in the shade:' Often the para llelism involves items in a series: "The telephone message was short. quiet and what I couldn't understand." This sentence would be clea rer if it had three adjectives (italicized); "The telephone message was short, quiet and hard to understand." 139 THE WRITING SECTION Example Exercise: Rewriting Sentences Using Parallelism Rewrite these sentences, using parallelism: 1. Our vacation plans include exploring the city, visiting old friends, and to spend a few days doing nothing at all. Rewrite: 2. Sean had to choose between his brother's baseball game and going to his girlfriend's recital. Rewrite: 3. A teacher needs patience and to be fa ir. Rewrite: 4. I decided to buy the gift whether the store took credit cards or even making me pay cash. Rewrite: 140 Improving Sentences 5. The movie was not entertaining or an experience that was pleasant. Rewrite: 6. She is hoping fo r a career in med icine, law, or to be an engineer. Rewrite: 7. I try to be honest. hardworking, and to pay attention to my friends. Rewrite: 8. The produce in that store is fresh, well displayed, and costs too much. Rewrite: 141 THE WRITING SECTION POSSIBLE REWRITES THAT IMPROVE THE ORIGINAL SENTENCES In the following rewritten sentences, the parallel items are italicized, and an explanation follows each rewrite. 1. Origillal: OUf vacation plans include exploring the city. visiting old friends. and to spend a few days doing nothing at all. Rewrite: Our vacation plans include exploring the city. visiting old friends and spending a few days doing nothing at all. Rationale: The three parallel words are all gerunds - that is, verbs ending in -ing - that are doing the job of a noun: in this case, telling what the vacation n plans include. Nouns often answer the question "what. Gerunds look like present participles, which are also verbs ending in -ing, but part iciples do the work of an adjective, which is to descr ibe a noun. If you want an even more thorough understanding of grammar, consider this: the gerund is not only a noun but is Simultaneously performing as a verb. In this case, like the transitive verbs they are, each one takes an object (underlined): exploring the city. visit ing old friends, and spending a few days. 2. Original: Sean had to choose between his brother's baseball game and going to his girlfriend's recital. Rewrite: Sean had to choose between his brother's baseball game and his girl- friend's recital. Rationale: The parallel items a re in similar form : his brother's this and his girlfriend's that. 3. Original: A teacher needs patience and to be fair. Rewrite: A teacher needs patience and fairness. Or: A teacher needs to be patient and fair. Rationale: The teacher needs two qualities. It does not matter whether they are expressed as nou·ns (i.e., patience and fairness) or infinitives (i.e., to be patient and [to belfair). Either parallel expression is fine. 142 Im proving Sentences 4. Original: I decided to buy the gift whether the store took credit cards or even making me pay cash. Rewrite: I decided to buy the gift whether the store took credit cards or even made me pay cash. Rationale: I decided to buy the gift whether the store did this or did that took credit cards or (even) made me pay. You achieve the parallelism when you put both expressions into the same form, in this case, the past tense verb following the subject "store." 5. Original: The movie was not entertaining or an experience that was pleasant. Rewrite: The movie was not entertaining or pleasant. Or: The movie was neither entertaining nor pleasant. Rationale: Two words tell what the movie was not: entertaining and pleasant. Those two adjectives would make the sentence parallel in structure. Also, remember that when you use the negative word neither, you must use the equally negative word nor. That pair of connectors emphasizes the parallelism of the sentence. 6. Original: She is hoping for a career in medicine, law or to be an engineer. Rewrite: She is hoping for a career in medicine, law or engineering. Rationale: The series following "in" tells of three choices, so they should be expressed in parallel structure: medicine, law and engineering. Another possible parallel expression is to name the three professions: She is hoping to be a doctor, a lawyer or an engineer. 7. Original: I try to be honest, hardworking and paying attention to my friends. Rewrite: 1 try to be honest, hardworking and attentive to my friends. Rationale: What three qualities do "I" claim to have? 1 am hardworking, I am honest and 1 am attentive. The parallel structure uses three adjectives rather than two adjectives and an infinitive verb (the form of the verb that begins with to), as in the original sentence. 143 THE WRITING SECTION 8. Original: The produce in that store is fresh, well displayed and they charge too much. Rewrite; The produce in that store isfresh, well displayed, and too costly. Rationale: What three words describe the produce in that store? Fresh, well displayed and too costly. Use these three adjectives to ach ieve parallelism. 144 Improving Sentences Sample Quest ions The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence are five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternat ives, select choice A; if not, select one of the other choices. In making your selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence - clear and precise, without awkwardness or ambiguity. Exam ple: Laura Ingalls Wilder published her firsl book and she was sixty-five years old then. CA) (B) (C) (D) (E) and she was sixty-five years old then when she was sixty-five at age sixty-five years old upon the reaching of sixty-five years at the time when she was sixty-five @.©@@ l. Alice Walker, one of America's best-known writers. she has published both poetry and prose. CA) (B) (C) (D) (E) writers, she has published writers, has published writers, and publishing writers since publishing writers when she published 2. Consumers are beginning to take notice of electric cars because they are quiet, cause no air pollution. and gasoline is not used. CAl (B) (C) CD) (E) cause no air pollution, and gasoline is not used air pollution is not caused, and gasoline is not lIsed cause no air pollution, and use no gasoline causing no air pollution and using no gasoline air pollution is not caused, and no gasoline is used 3. The convenience and availability of watercolor paint account for itS popularity with amateur artists. (A) account for its popularity (B) account for their popularity (C) accounts for its popularity (D) is why it is popular (E) are a reason for its popularity 145 THE WRITING SECTION Answers and Explanations 1. Alice Walker, one of America's best-known writers, she has published both poetry and prose. (A) writers, she has published (B) writers, has published (e) writers, and publishing (D) writers since publishing (E) writers when she published ~eplnMind Answer: Choice (8) is the correct answer. Restating the subject with a pronoun is a common mistake. Usually the pronoun is both unnecessary and distracting. Explanation: This sentence describes Alice Walker, one of America's best-known writers, who has published both poetry and prose. Choice (8) makes this correction so the sentence is written properly. Here's why each of the other choices is nol the correct answer: • Choice (A) is incorrect because the pronoun "she" is redundant. Simply dropping "she" will correct this problem . • Choices (C), (D) and (E) are incorrect because they do not contai n verb forms that produce grammatically complete sentences. 2. Consumers are beginning to take notice of electric cars because they are quiet, cause no air pollution. and gasoHne is not used. (A) cause no ai r pollution, and gasoline is nOI used (B) air pollut ion is not caused, and gasoline is not used (C) cause no air pollution, and use no gasoline (D) causing no air pollution and using no gasoline (E) air pollution is not caused, and no gasoline is used ~eplnMlnd Parallelism is one sign of clear writing. When you see a pair or a series of items joined by and or or,. make sure the grammatical structure is the same. The words, in most cases, should all be nouns, or all adjectives, or all verbs in the same tense. Answer: Choice (C) is the correct answer. Explanation: In this sentence, you must recognize that pa rt sofa series separated by commas should parallel each other, as in the sentence produced by choice (C): Consumers are beginning to take notice of electric cars because they are quiet, cause no air pollution, and use no gasoline. Here's why each of the other choices is not the correct answer: • In the original sentence and choice (A), the first two items in the series ("are quiet" .a nd "cause") take the plural subject "they" and use active verbs, but the third item ("gasoline is not used") introduces a new subject and the passive voice. To follow the structure set forth by the phrase "they are quiet," the words "cause" and "use" - which also take "they" as their subject - should be used. 146 Improving Sentences • Choices (B), (D) and (E) do not follow this parallel structure and so are incorrect. J. The convenience and availability of watercolor paint account for its popularity with amateur artists. (A) account for its popularity (B) account for their popularity (C) accounts for its popularity (D) is why it is popular (E) are a reason for its popularity Answer: The co rrect answer is (A). Explanation : This sentence requires you to pay close attention to the plu ral subject. The original sentence is correct, so the answer is (A). Here's why each of the other choices is not the correct answer: • In (B), the verb "accou nt" correctly refers back to the plu ral subject "convenience and availability,n but the plural pronoun "their" is incorrect - what is popular is "watercolor paint," not "convenience and availability." {J;ep in Mind Singular and plural parts of your sentences should match. If your subject is plural, your verb should also be plural. for example. You might mali!: the subject with an S or a P to remind yourself that it is singular or plural. • In (C) and (D), the verb is singular rather than plural. • In (E), the si ngular noun "reason" does not agree with the plura l subject. 147 Recap 1. Read the entire sentence before you look at the choices. 2. Remember that the right answer will be the one correct version among the five choices. 3. Read each choice along with the entire sentence; don't read the choices on their own. 4. Look for common problem areas in sentences, such as noun! verb agreement, parallelism. placement of modifiers and the use of relative clauses. 5. Read all five versions of the sentence aloud, if possible , while you 're practicing. 6. Read more slowly than you nonnally do to help you pay closer attention. 7. Be sure that your subjects and verbs agree. 8. Mark each question that you don't answer in your test booklet, so you ca n easily return to it later. 148 Improving Sentences Practice Questions The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence a re five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices. In making your selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should resuit in the most effective sentence - dear and precise, without awkwardness or ambiguity. Example: Laura Ingalls Wilder published her first book and she was Sixty-five yeafs old then. (A) (B) (C) (D) (E) and she was Sixty-five years old then when she was sixty-five at age Sixty-five years old upo n the reaching of Sixty-five years at the time when she was sixty-five I. He arranged the gems on the counter, the sales assistant proceeded to tell us about the origins of each stone. (A) He arranged the gems (B) (C) (D) (E) The gems, which were arranged The gems were first arranged After arranging the gems He, having arra nged the gems 2. Some of t he Smithsonian Institution's most prized items, from Duke Ellington's musical transcripts to First Ladies' gowns, coming from unsolicited donations. (Al (B) (C) (D) (El comi ng from they come from they have come from came from which came from 3. Brought to the United States at the age of thirteen to receive a Western education, his first bOQk discusses Lee ¥an Phou's childhood in China. (Al (B) (C) (D) (E) his first book discusses Lee Yan Phou's childhood in China Lee Yan Phou's childhood in China is the subject of his first book the subject of his first book is Lee Yan Phou's childhood in China l.ee Yan Phou discusses his childhood in China in his first book Lee Yan Phou, whose childhood was in China, discusses this in his first book 4. Only since t he publication of her first novel Olivia has been considering herself a genuine writer. (Al (B) (C) (D) (E) Olivia has been considering Olivia considered has Olivia considered was Olivia considering could Olivia be able to 149 THE WRITING SECTION 5. Scientists predict technological changes in the next century. they will be as dramalic as was the development of the transcontinental railroad in the last century. (A) century, they will be as dramatic as was (8) centu ry, these will be as dramatic as (e) century; being as dramatic as was (D) century will be dramatic as is (El century as dramatic as 6. Anita liked to watch television. ofwhjcb she fQuod the science proGrams especially fascinating. (A) (8) (el (D) (E) television, of which she found the science programs especially fascinating television; she found the science programs especially fascinating television, and it was especially the science programs that were of fascination television; the fascination of the science programs especially television, especially fascinating to her were the science programs 7. Although gale force winds often pass through the Eiffel Tower, (ausin\: it to sway no more than four inches. (A) causing it to sway no more (8) and yet it sways no more (e) they do not cause it to sway more (0) and they do not cause it to sway (E) yet causing it to sway no more 8. Underestimaling its value. breakfast is a meal many people skip. (A) Underestimating its value, breakfast is a meal many people skip. (B) Breakfast is skipped by many people because of their underestimating its value. (e) Many people, underestimating the value of breakfast, and skipping it. (0) Many people skip breakfast because they underestimate its value. (E) A meal skipped by many people underestimating its value is breakfast. 150 THE WRITING SECTION Answer Key 1. D 2. D 3. D 4. C 5. E 6. B 7. C 8. D Additional practice questions can be found in The Official SAT Online Course at www.collegeboard.comlsatonlinecourse. 152 CHAPTER 11 Identifying Sentence Errors When you're writing and making revisions. being able to find mistakes in sentences is one of the most important ski lls you can have. Even writers who know the rules of good written English may need to correct m istakes while they're making revisions. To clearly express your written ideas. you must know gramma r, usage, word choice and idioms. The following box provides the directions and the example that will appear in the section on Identifying Sentence Errors. The following sentences test your ability to recognize grammar and usage errors. Each sentence contains either a single error or no error at all. No sentence contains more than one error. The error, if there is one, is underlined and lcuered. If the sentence contains an error, select the one underlined part that must be changed to make the sentence correct. If the sentence is correct, select choice E. In choosing answers, follow the requirements of standard written English. Example: The other delegates and him immediately A B C accepted the resolution drafted by the D neutral states. No error E Here's another example. This one includes an explanation to help you understand the reasoning behi nd the correct answer. EXAMPLE In the following question, you are asked to identify the grammatical error. 153 THE WRITI NG SECT ION II is likely that the opening of the convention center, ~reviQusly illi2r July 1, would be postponed A' C because of the bricklayers' strike. No error D E Answer: The correct answer is (C). Explanation: Choice (C), "would be," is the wrong tense of the verb in this sentence. The'sentence concerns when the convention center is going to open. This is a time in the future. either July I or later if there is a strike. Because the opening will defi· nitely take place, the future tense, "will be," is needed. "Would be" (which is the conditional tense) indicates only that an event might happen. Approaches to Identifying Sentence Errors The questions in this section are different from most other multiple-choice questions. For Identifying Sentence Errors, you will have to choose the answer that contains a mistake. Here are some approaches to try as you work through Identifying Sentence Errors . ... Read each sentence qUickly but carefully. The error may be obvious as soon as you see it. ... Consider each question as a cluster of truejalse questions, each to be considered separately. Only one can be false, and that is the one containing the error. If there are no false responses, the answer is (E) - no error. ... Read aloud, if possible, during your practice sessions. You won't be able to do this during the actual test, of course. If you read aloud, you may hear the error immediately. Keep in mind, however. that the rules for written English are stricter than those for everyday spoken English . ... Examine the underlined choices A to D. Consider which kind of correction may be needed for each one (and refer to the table in Chapter 8 on "Characteristics of Effective Writing"). ... Develop the habit of looking for the most common mistakes people make in grammar: subject/verb agreement. pronoun agreement and adjective/adverb confusion . ... Look for errors in idiom - words or phrases that are particular to our language because of what they mean when used together. We say that we listen to someone. not listen at someone or by someone; a song is by a composer. not from a composer. We say at the top of the hill, not at the top on the hill. 154 Identifying Sentence Errors ... Remember that some sentences have no error. Don't spend time looking for what is not there. Mark (E), No error, on your answer sheet if you believe the sentence is correct as written . ... Correct errors even in questions for which you have only to identify the error. As you practice, correcting the error may help you keep in mind the language principles . . . Move quickly through questions about Identifying Sentence Errors. The other kinds of questions - Improving Sentences (Chapter 10) and Improving Paragraphs (Chapter 12) - will likely take more time . . . Mark questions in your test booklet that you've skipped. Then you can return to them later. Writing Exercise: Avoid Dangling Participles To improve your writing, make sure you avoid using participial phrases that have no subjevt; they are a frequen t cause of confusion. Ouick Grammar Review: Participles Participles are verb forms that function as adjectives. In the present tense, participles always end in "-ing" (e.g., laughing, falling, gusting). In the sentence "The laughing child played with the falling leaves that the gusting breeze shook loose from the quivering branches," the italicized words are all present participles, and they describe nouns, which are underlined. These are the present participles of the verbs laugh,fall, gust and quiver. In the past tense, partic iples often end in -ed, -en or -t (e.g., cooked, washed; broken, written; spent, lost), and some are irregular (e.g., bought, wrung). In the follOWi ng sentences, the past participles are again italicized, and they describe nouns, which are again underlined: • Raw vegetables are more nut ritious than cooked Q.Il.e.£. • The newly washed car glistened in the afternoon sunshine. • The jury had a hard time ignoring the written J2!.QQf of the defendant's alibi. • He had nothing to show for his road trip but receipts for all his spent~. • Lost opportunities rarely come around a second time. • You have to declare the value of all the bought goods you bring home from your trip. • Tightly wrung laundry will dry faster but will need more ironing. These are past participles of the verbs cook, wash, write, spend, lose, buy and wring. 155 THE WRITING SECTION Quick Grammar Review: Participial Phrases A group of words that begins with a participle is known as a participial phrase. Because participial phrases are adjectives, they are used to modify nouns. Because they are verbs, they need subjects. Read this sentence and see if you detect a problem in its clarity: Tourists see statues of many famous patriots walking a long Boston's Freedom Trail. It appears that the statues are walking, not the tourists. In English, modifiers are usually placed as dose as possible to the words they describe, so this sentence should read: Tourists walking along Boston's Freedom Trail see statues of many famous patriots. Example Exercise: Rewriting Sentences to Improve the Participial Phrase's Location Revise each of the follOWing sentences so that the participial phrase's location does not cause confusion. The first six are present participles; the last four are past participles. I. I thought I heard a strange rattle driving my car. Rewrite: 2. Strumming on his guitar, we suddenly remembered where we had seen this fo lk singer before. Rewrite: 156 Identifying Sentence Errors 3. I turned the corner and bumped into an elderly gentleman paying no attention to where I was going. Rewrite: 4. Orbiting between Mars and Jupiter, research astronomers discovered a new group of asteroids. Rewrite: 5. I saw a long line of traffic looking both ways before I tried to cross the street. Rewrite: 6. The caterer served refreshments to the guests wearing a frilly white apron. Rewrite: 7. Raised in an open field without any pesticides, I prefer vegetables and fruits. Rewrite: 157 THE WRITING SECTION 8. Cooked too long, she thought the pasta did not taste good any more. Rewrite: 9. Spiced with Italian herbs, I had never tasted anything quite like Imelda's salad. Rewrite: 10. Wrapped in brightly colored paper, Mickey lore open the birthday present. Rewrite: POSSIBLE REWRITES THAT IMPROVE THE ORIGINAL SENTENCES In the following rewritten sentences (others are possible), the participial phrase is italicized and the noun it describes is underlined. In each case, the participial phrase describes that noun and is located as close to it as the sentence will allow. l. Origillal: I thought I heard a strange rattle driving my car. Rewrite: Driving my car, I thought I heard a strange rattle. Ratiollale: The st range rattle was not d riving the car. Relocating the parti cipial phrase so it is next to the word I removes that confusion. The sentence "W hile J was driving my car, I thought J heard a strange rattle" is a perfectly good English sentence; it does not use a participial phrase. 2. Original: Strumming on his guitar, we suddenly remembered where we had seen this folk singer before. Rewrite: Hearing thefolk singer strumming on his guitar, ~suddenly remembered where we had seen him before. Rationale: Whatever revised sentence you write, be sure that you do nol make it sound like "we" were strumming on the guitar. 158 Identifying Sentence Errors 3. Orighwf: I turned the corner and bumped into an elderly gentleman paying no attention to where I was going. Rewrite: Paying no attention to where I was going.l turned the corner and bumped into an elderly gentleman. Rationale: Who was paying no attention? It is not the elderly gent leman. so the pa rticipial phrase cannot be placed next to "gentleman." 4. Original: Orbiting between Mars and Jupiter, research astronomers discovered a new group of asteroids. Rewrite: Research astronomers discovered a new group of asteroids orbiting between Mars and Jupiter. Rationale: The original sentence says that the ast ronomers were orbiting between Mars and Jupiter. It's more likely that the asteroids were. 5. Original: I saw a long line of traffic looking both ways before I tried to cross the street. Rewrite: Looking both ways before I tried to cross the street, 1 saw a long line of traffic. Rationale: Is the traffic looking both ways? Place the participia l phrase by the noun (in this case, pronoun) it actually describes. 6. Origillai: The caterer served refreshments to the guests wearing a frilly white apron. Rewrite: The~, wearing a frilly white apron, served refreshments to the guests. Or: Wearing a frilly white apron, the ~ served refreshments to the guests. Rationale: The original sentence makes it sou nd li ke on ly guests wearing frilly white apron s received refreshments. Probably the apron belonged to the caterer, so relocate the part icipial phrase to a posit ion near the noun it describes. 7. Origj1wi: Raised in an open fiel d without any pesticides, Tprefer vegetables and fruits. Rewrite: I prefer vegetables and frujts raised in all open field without any pesticides. Rationa le: It is not the subject "I" who was raised in a field, but the vegetables and fru its. Rephrase the sentence so that point is clear. 8. Original: Cooked too long, she thought the pasta did not taste good any more. Rewrite: She thought the~, cooked too long, did not taste good any more. Rationale: "She" was not cooked too long; the pasta was. Placing the participial phase next to "pasta" will correct that misstatement. You can also write, "Because the pasta was cooked too long, she thought it did not taste good any more." This is also accurate, but there is no participial phrase in this version. 159 THE WRITING SECTION 9. Original: Spiced with Italian herbs, I had never tasted anything quite like Imelda's salad. Rewrite: I had never tasted anything quite like Imelda's ~ which was spiced with Italian herbs. Rationa le: "I" am not spiced with Italian herbs, so the sentence needs rewriting. Place the descriptive participial phrase near the word it describes. to. Original: Wrapped in brightly colored paper, Mickey tore open the birthday present. Rewrite: Mickey tore open the bi rthday present wrapped in brightly colored paper. Rationale: Although it is possible that Mickey was wrapped in brightly colored paper, it is much more likely that the birt hday present was. Placing the participial phrase near "present" will make that clear. In several of these examples, you might have revised the sentence and removed confusion by some means other than relocat ing the participial phrase. That's perfectly fine. The lesson here is to recogn ize when the participial phrase is badly located and to take steps to correct the problem. 160 Ide ntifying Sentence Errors Sample Questions The following sentences test your ability to recognize grammar and usage errors. Each sentence contains either a single error or no error at all. No sentence contains more than one error. The error, if there is one, is underlined and lettered. If the sentence contains an error, select the one unde rlined part that must be changed to make the sentence correct. If the sentence is correct, select choice E. In choosing answers, follow the requirements of standard written English. Exam ple: The other delegates and him immediately ABe accepted the resolution drafted by the o neulral states. No error E I. The 1Wib1 fiberglass sculptures of Luis Jimenez has received critical A B acclaim nOI only in his home state, New Mexico, but also in New York. e No errQr E 2. Even with a calculator, you must have a basic understanding of A B mathematics if one expects to solve complex problems correctly. No error e E 3. People who dislike cats sometimes criticize them for beine aloof and A B independent; people who are fimd.cl cats often admire them for the same e qualities. No error E 4. The decision that basjusl been agreed with by the committee members A B should serve as a hasis for their work in the years to come. No error e E 16 1 THE WRITING SECTION Answers and Explanations I. The b.r.iihl fiberglass sculptures of Luis Jimenez has received B A critical acclaim not only in his home state, New Mexico, but also in C D New York. NQ error E Answer: 1he correct answer is (B). GePinMind answer might be immediately Explanation: The problem with th iS sentence lies in (B): the subject of the sentence, "sculptures," is plural and requires the plural verb "have apparent because the error is received," Read the entire sentence. The a common one of punctuation or grammar. The other choices are all correct: • The word "bright" in choice (A) is used properly as an adjective . • In (C), "not only" is part of the combination "not only ... but also," • The preposition in (D), " in," begins a phrase that effectively parallels the preceding phrase "in his home state." The best answer. then. is (8). The corrected sentence reads: "The bright fiberglass sculptures of Luis Jimenez have received crit ica l accla im not only in his home state, New Mexico, but also in New York." 2. Even with a calculator, you must have a basic understandi ng of A B mathematics if onc cxpects to solve complex problems correctl y. C D No error E Answer: The correct answer is (C). Explarlation: The first part of the sentence addresses "you." Because this pronoun is not underlined, it cannot be changed, and subsequent pronouns must also use the second person. In (C), the third-person pronoun "one" is used incorrectly; choice (C) shou ld be worded "you expect." 162 Identifying Sentence Errors The other choices are all appropriate: • Choice (A) introduces the conditional relationship set forth in the rest of the sentence. • Choice (B) appropriately uses the preposition "of" with "understanding." • The adverb "correctly" in (D) modifies the verb "solve." The corrected sentence reads: "Even with a calculator, you must have a basic understanding of mathematics if you expect to solve complex problems correctly." ~eplnMlnd As you read a sentence, ask yourself if the error is obvious. If it isn't, consider the common problems: it's not subject/verb agreement (you must have is good) or adjective/adverb confusion (correctly is right, not co,. rect!o But the pronouns do not agree (you/one). Once again, the error is a common one. 3. People who dislike cats sometimes criticize them for bejnK aloof and A B independent; people who are fund..cl cats often admire them for the same C D qualities. No error E Answer: The correct answer is (E). Explanation: All of the underlined choices in this sentence are appropriate: • The word "sometimes" in (A) properly modifies the verb "criticize." • In (8), "being" is the verbal form that fits idiomatically with the phrase "criticize ... for." ~ • The preposit ion "of" in (C) is appropriate to use after "fond." • In (D), the plural pronoun, "them," is used appropriately to refer to "cats," and "for" is the correct preposition to use with the verb "admire." ~ep in Mind If you can't find an error In a sentence, the correct answer may be (E), "No error." Therefore, because all of the underlined parts of this sentence are correct, the best answer is (E), "No error." 4. The decision that bas just been agreed with by the committee members A sbould serve as a basis for thei r work in tbe years to come. No error C D E Answer: The correct answer is (8). 163 THE WRITING SECTION ~.PInMlnd Explanation: The error is the preposition used in choice (B). In the context of this sentence, the correct idiomatic expression is "agreed to" rather than "agreed with," The other choices are correct: While practicing, read sentences aloud if you can. The error may then become obvious. • In (A), the present-perfect verb phrase is used appropriately to indicate an action that is completed in the present. • In (e), "for" appropriately completes the expression "basis for," and "their" properly refers to the plural noun "members." • Choice (D) properly expresses the time reference in the sentence. The corrected sentence reads: "The decision that has just been agreed to by the committee members shou ld serve as a basis for their work in the years to come," 164 Recap 1. Consider each question as a cluster of true-false questions , each to be considered separately. 2. Read each sentence quickly but carefully, and the error may become obvious. 3. Read aloud during your practice sessions if possible . 4. Examine the underlined choices A to D; then think of which correction may be needed for each. 5. Develop the habit of looking for the most common mistakes people make in punctuation, grammar and other areas. 6. Look for errors in idioms - that is, expressions whose meanings may not be clear from the individual words, but that mean something when used together. 7. Remember that some sentences have no error and that the COfrect answer may be (E), "No error." B. Correct errors when you practice, even if you are asked only to identify the error. 9. Move quickly through questions about Identifying Sentence Errors, because the questions on Improving Sentences and Improving Paragraphs will probably take more time. 10. Mark questions in your test booklet that you've skipped so you can go back to them later. 165 THE WRITING SECTIO N Practice Questions The following sentences lest your ability to recognize grammar and usage errors. Each sentence contains either a single crror or no error at all. No sentence contains more than one error. The error, if there is one, is underlined and lettered. If the sentence contains an error, select the onc underlined part that mus t be changed to make the sentence correct. If the sentence is correct, select choice E. In choosing answers, follow the requirements of standard written English. Example: The other delegates and him immediately ABC accepted the resolution drafted by the D , neutral states. NQ error @~©@® I. Since ~ two pencils, a pad of paper, and a ruler on each desk, students A do nol have to brina thei r own supplies. NQ error BCD E 2. Each time Caroline turns on her computer, she bM to enter a company code, then A her initials, and then enters a password.l:W2rk she can beiin working. NQ error B C D E 3. Flints found in the region extending from the Nile Valley!.Q the highlands of eastern A B Iraq attests to the presence of people there as lonK aio as one hundred thousand C D , years. No error 4. By virtue of~ size and supersensitive electronics, modern radio telescopes are able A to gather more waves and discriminate among 1hgn with greater precision thm B C D , earlier versions could. No error 5. Delgado's dilemma was like many other young writers: he had to choQse between A B assured publication in a student magazine illi! ~robable rejection by a popular C , magazine. No error 166 D Identifying Sentence Errors 6. Air pollution caused by industrial fumes has been studied for years, 1llu only A B recently his the harmful effects of noise pollution ~ known. No error C E 7. No matter how cautioys snowmobiles ill driven, they are capable ofdamagjng the A B C D land over which they travel. No error E 8. The starling isiY.ili...a pest in rural areas that it bas become necessary 10 find ways of A B C controlling the growth cl.1b.rir population. No error o E 167 THE WRITING SECTION Answer Key I. A 2. B 3. C 4. A S. A 6. C 7. B 8. D Additional practice questions can be found in The Official SAT Online Course at www.collegeboard.comisatonlinecourse. 168 CHAPTER 12 Improving Paragraphs If you think you do a great amount of writing now, just wait until you're in college. That's the main reason the College Board added a writing section to the SAT in 2005. The improving paragrap hs questions call on all you r ski lls in writi ng and rev is· ing. After you read a draft of a short essay, you will be asked to understand how the sentences and the paragraphs work together. You will have to make revisions by combining sentences and by altering structures within sentences. Though you may not realize it, that's the process you go through as you edit and revise your own school essays until they're fina l. The fo lloWing box p rOV ides the directions for Improving Paragraphs that will appear on the test. Di rections: The following passage is an early draft of an essay. Some parts of the passage need to be rewritten. Read the passage and select the best answers fo r the questions that follow. Some questions are about particular sentences or parts of sentences and ask you to improve sentence structure or word choice. Other questions ask you to consider organization and development. In choosing answers, follow the requirements of standard written English. Here's an example of an improving paragraphs question. EXAMPLE (l) At one point in the movie Raiders of the Lost Ark, the evil archaeologist Belloq shows the heroic Indiana 'ones a cheap watch. (2) If the watch were to be buried in the desert for a thousand years and then dug up, Belloq says, it would be considered priceless. (3) I often th ink of the scene whenever I consider the record album-collecting phenomenon, it being one of the more remarkable aspects of popular culture in the United States. (4) Collecting record albums gives us a chance to make a low-cost investment that might pay dividends in the future. (5) When my aunt collected them in the mid-sixties, nobody regarded them as investments. (6) A young fan shelled out dollar after dollar al the corner record store for no other reason than to assemble a complete collection of her fa\·orite musical groups - in my aunt's case, the Seatles and the Supremes. (7) Sycommitting so much of her allowance each week to the relentless pursuit of that one group not yet in her coiled ion the immortal Yardbirds, let us say - she was proving her loyalty to her superstars. 169 THE WR ITING SECTION (8) The recordi ng industry is a capitalist enterprise and so th is hobby has become one. (9) Just as everyone has heard oflhe exorbitant prices being paid for the Beatles' first album in mint condition, so everyone is certain that a payoff is among each stack of old records. (IO) But if thaI album was buried somewhere in my aunt's closet of dusty records, she never knew it. (I l ) Long before she learned it, she had t hrown them out. In the context of the first paragraph, which revision is most needed in sentence 3? (A) Insert ~As a matter offaet" at t he beginning. (8) Omit the words "it being". Om it the word "scene". CD) Change the comma to a semicolon. (El Change "t h ink~ to "thought" and "consider" to "considered". eel A nswer: The correct answer is Choice (B). Expla nation: The words "it being" are unnecessary. Approaches to Improving Paragraphs ).- Read the essay thoroughly to determine its overall meaning before you look at tile questions. It's important to have a sense of the enti re essay's organization and meaning before you deal with any changes. The essay is mea nt to be a draft, so there will be errors in it, but don't linger over those errors. ).- Read more slowly than you usuaIIy do, to help you pay closer attention . ).- Try all of the options before you decide on your answer. The di rections tell you to choose the best answer. That means one may be sat isfactory but not as good as another. Don't overlook any possibilities. ).- Make sure that your answer about a particular sentence or sentences makes sense in the context of the preceding and foIIowing sentences and of the passage as a whole. ).- Use your test booklet to help you by marking each question that you don'f answer. Then you can easily find it later. Writing Exercise: Avoiding Wordiness A great way to improve you r writing is to si mplify it. Why use lots of words when just one or two well-chosen words will convey exactly what you want to say? Wordiness results from using unnecessary words and phrases and from adding empty expressions to a sentence. Unnecessa ry words a re someti mes the result of redundancy, or surplus words. For exa mple, expressions such as "two in number" are redundant because two is a number, so the ph rase "in number" does not add any 1 70 Improving Pa ragraphs mea ning to the sentence. Similarly, "sadly unhappy" is redundant. Finally, empty expressions, such as "if you know what I mean," add little to your writi ng except to fill up space - which should not be your goal. Eliminate those unnecessary words and phrases from your writing. Example Exercise: Rewriting Sentences to Avoid Wordiness Here's some practice. Revise the following sentences so that no unneeded words remain: 1. Ou r most favorite balloons were those that were red in color. Rewrite: 2. We put off until later in time the decision about whether or not the funny comedians would be appropriate and fitting for our evening of after-dinner entertainment performers. Rewrite: 3. Snow continued to keep on falling, so we had to repeatedly shovel the sidewalk over and over again. Rewrite: '7' THE WRITING SECTION 4. Working so aSSiduously hard left her tired, fatigued, and exhausted; she could barely stay awake and avoid falling asleep. Rewrite: 5. We considered his behavior rude, in the truest sense of the word. Rewrite: 6. The driver witnessed a fema le person as she parked a blue-colored veh icle, exited out of it, and proceeded to make her wayan foot in a northerly direction toward the blinking red light that was flashing on and off and on and off. Rewrite: 7. The American WaI of Independence is principally the most important historic event that grade school children in elementary schools have to learn about and study. Rewrite: 8. If you come to think about it, green vegetables ought to be a part of everyone's daily diet. Rewrite: 172 Improving Paragraphs POSSIBLE REWRITES THAT IMPROVE THE ORIGINAL SENTENCES Following are some suggested rewrites (though others are possible, too). The rationales show that many of the sentences displayed redundancy, or unnecessa ry repetition. I. Original: Our most favorite balloons were those that were red in color. Rewrite: Our favorite balloons were red. Or: We like the red balloons best. Rationale: "Favorite" means the one most liked, so "most favorite" is redundant. And because red is a color, the words "in color" are unnecessary. 2. Original: We put off until later in time the decision about whether or not the funny comedians would be appropriate and fitting for our eveni ng of after-dinner entertainment performers. Rewrite: We put off [or delayed] deciding whether the comedians would be appropriate for our after-dinner entertainment. Rationale: Firstofa\l, " 'aterin time" is redundant in thesameway"redincolor" and "ra iny weather" are. Second, unless they are not funny, we assume comedians are funny, so we don't have to say so. Third, "appropriate" and "fitting" are two words that say the same thing; we only need one. Finally. "entertainment performers" is also redundant, and because dinner is the evening meal. "after-dinner entertainment" already tells us that this is an evening event. 3. Original: Snow continued to keep on falling, so we had to repeatedly shovel the sidewalk over and over again. Rewrite: Snow kept on falling, so we had to shovel the sidewalk over and over. Or; Because it kept snowing, we had to shovel the sidewalk over and over. Rationale: "Continued to keep on" is redundant, as are "over and over again" and "repeatedly." 4. Original: Working so aSSiduously hard left her tired, fatigued, and exhausted; she could barely stay awake and avoid falling asleep. Rewrite: She was exhausted from working so hard, and she could hardly stay awake. Or; Because she worked herself into exhaustion, she could hardly stay awake. Rationale: "AsSiduously" means "working hard," so "aSSiduously working hard" is redundant. "Tired," "fatigued" and "exhausted " all mean the same thing, as do "stay awake" and "avoid falling asleep." 173 THE WRITING SECTION 5. Original: We considered his behavior rude. in the truest sense of the word. Rewrite: We considered h im rude. Rationa le: The word "behav ior" is implied by the rest of the sentence, and the expression "in the truest sense ofthe word" does not add any meaning to the sentence. Why would a writer use a word in an u nt rue sense? 6. Original: The driver witnessed a female person as she parked a blue-colored vehicle. exited out of it, and proceeded to make her wayan foot in a northerly direction toward the blinking red light that was fl ashing on and off and on and off. Rewrite: The driver saw a woman park a blue car, get out, and walk north toward the blinking red light. Rationale: "A fem ale person" is a woman. "Blue-colored," like "red in color," is redundant. "Exited" means "went out." "Proceeded to make her wayan foot" is a multiword version of "wa lked." "In a northerly direct ion" is more simply (and just as accurately) said by writing "north." "Blinking" is the same as "flashing on and off a nd on and off." It is true that, in another context, the expression "proceeded to ma ke her way on foot" might be appropriate. If the writer were calling attention to the distinction between one mode of travel, for example. by bicycle or car, and foot travel, the phrase might tell something important. But in th is simple sentence, there is no such need to make that d istinction . Don't try to be fancy when being simple will do. 7. Original: The American War ofIndependence is principally the most important historic event that grade school children in elementary schools have to learn about and study. Rewrite: The American War of Independence is the most important historic event that elementary students have to study. Rationale: "Pri ncipally" means the same as "the most important." Grade school and elementary school are the same, so there is no need to say it twice. The same is true of "learn about" and "study." 8 .. Original: If you come to think about it, green vegetables ought to be a part of everyone's daily diet. Rewrite: Everyone should eat green vegetables daily. Rationale: "If you come to think about it" is an empty expression, unnecessary for the meaning of the sentence. "Green vegetables ought to be a part of everyone's daily diet" is satisfactory. The other suggested answer, "Everyone shou ld eat green vegetables daily," uses a different subject and verb, so it offers another good possible rev ision. 174 Improving Pa ragraphs ADDING DESCRIPTIVE WORDS THAT ARE NOT REDUNDANT The previous exercise asked you to eliminate unnecessary words. words that are repetitive or words that add nothing to the sentence's meaning. If these sentences seem too simple, you can make them more interesting by adding descriptive details. For example. the first one could be revised in any of the following ways: • "W hen we spent a day at the circus, our favo rite balloons were red and starshaped." • "Our favorite balloons were red, but the kids in front of us liked the blue ones better." • "Red balloons decorated with silver sparkles caught the sunshine the best, so we decided they were our favorites." Now try improving the sentences by adding descriptive details. 1. Original: Our favorite balloons were red. Your rewrite: 2. Original: We did not go swimming because it rained. Your rewrite: 3. Orighlal: We put off deciding whether the comedians would be appropriate for our after-dinner entertainment. Your rewrite: 175 THE WRITING SECTION 4. Original: Snow kept on falling. so we had to shovel the sidewalk over and over. Your rewrite: 5. Original: She was exhausted from working so hard. and sh e could hardly stay awake. Your rewrite: 6. Original: We considered him rude. Your rewrite: 7. Original: The driver saw a woman park a blue car, get out, and walk north toward the blinking red light. Your rewrite: 176 Improving Paragraphs 8. Original: The American War of Independence is the most important historic event that elementary students have to study. Your rewrite: 9. Original: Everyone should eat green vegetables daily. Your rewrite: 10. Original: My neighbor, Tony, is a doctor in a nearby hospital. Your rewrite: Now that you've had some practice adding descriptive words, let's look at the sample questions from this sect ion of the SAT. 177 THE WRITING SECT ION Sam ple Q u estions Directions: The following passage is an early draft of an essay. Some parts of the passage need 10 be rewritten. Read the passage and select the best answers for the questions that follow. Some questions are about particular sentences or paris of sentences and ask you to improve sentence structure or word choice. Other questions ask you to consider organization and development. In choosing answers, follow the requirements of standard written English. Questions 1-6 are based on t he following passage. (I) My father has an exceptional talent. (2) The ability 10 understand people. (3) When I have a problem that I think no one else will unde rstand, I lake it to my father. (4) He listens intently, asks me some questions, and my feelings are seemingly known by him exactly. (5) Even my twin sister can talk to him more easi ly than to me. (6) Many people seem too busy to take the time to unde rstand one another. (7) My father, by all accounts, sees taking time to listen as essential to any relationship, whether it involves family, friendship, or work. (8) At work, my father's friends and work associates benefit from this talent. (9) His job requires him to attend social events and sometimes I go along. (10) I have watched him at dinner; his eyes are fixed on whoever is speaking, and he nods his head at every remark. (II) My father emerges from such a conversation with what I believe is a true sense of the speaker's meaning. (12) In the same way, we choose our friends. (13) My father's ability to listen affects his whole life. (14) His ability allows him to form strong relationships with his coworkers and earns him lasting friendships. (15) It allows him to have open conversations with his children. (16) Furthermore, it has strengthened his relationship with my mother. (17) Certainly, his tale nt is one that I hope to develop as 1 mature. I. Of the following, which is the best way to revise and combine sentences I and 2 (reproduced below) ? My father has an exceptional talent. The ability to rmderstand people. (A) My father has an exceptional talent and the ability to understand people. (B) My father has an exceptional talent that includes the ability to understand people. (e) My father has an exceptional talent: the ability to understand people. (D) My father has an exceptional talent, it is his ability to understand people. (E) Despite my father's exceptional talent, he still has the ability to understand people. 2. Of the following, which is the best way to phrase sentence 4 (reproduced below) ? He listens intently, asks me some questiol15, and my feelings are seemingly known by him exactly. (A) (As it is now) (B) Listening intently, he will ask me some questions and then my exact feelings are seemingly known to him. (C) As he listens to me and asks me some questions, he seems to be knowing exactly my feelings. (D) He listened to me and asked me some questions, seeming to know exactly how I felt. (E) He listens intently, asks me some questions, and then seems to know exactly how I feel. 178 Improving Paragraphs 3. In sentence 7, the phrase by all accounts is best replaced by (Al however (8) moreover (C) to my knowledge (D) like my sister (E) but nevertheless 4. Which of the following sentences should be omitted to improve the unity of the second paragraph? (A) Sentence 8 (B) Sentence 9 (C) Sentence 10 (D) Sentence II (E) Sentence 12 5. In context, which of the following is the best way to phrase the underlined portion of sentence 16 (reproduced below) ? Fllrthermore, it has strengthened his relationship with my mother. (A) (As it is now) (8) Further strengthening (C) But it strengthens (D) However, he is strengthening (E) Considering this, he strengthens 6. A strategy that the writer uses within the third paragraph is to (A) make false assumptions and use exaggeration (B) include difficult vocabulary (e) repeat certain words and sentence patterns (D) argue in a tone of defiance (E) turn aside (rom the main subject 179 THE WRITING SECTION Answers and Explanations I. Of the following, which is the best way to revise and combine sentences I and 2 (reproduced below)? My father has an exceptional talent. The ability to understand people. (A) My father has an exceptional talent and the ability to understand people. (B) My father has an exceptional talent that includes the ability to understand people. (C) My father has an exceptional talent: the abi lity to understand people. (D) My father has an exceptional talent, it is his ability to understand people. (E) Despite my father's exceptional talent, he still has the ability to understand people. ~epinMind Answer: Choice (C) is correct. Explanation: The passage shows that the father's exceptional talent is his ability to understand people. Because sentence 2 is a fragment, sentences make sure that the relationship I and 2 must be combined in a way that clearly indicates the correct relabetween them is clear. tionship between the father's talent and ability. The use of a colon to join sentences 1 and 2 corrects the error of the original and signifies that the father's talent is his ability to understand people. When you combine sentences, • Choice (A) is unsatisfactory because the passage suggests that the father's talent is his abi lity to understand people; his talent and his ability are not two separate things. • Choice (8) is unsatisfactory because, as the passage shows, the father's talent does not include his ability to understand people; it is his ability to understand people. • Choice (D) is unsatisfactory because it joins two independent thoughts with only a comma. • Choice (E) is unsatisfactory because it contrasts the father's talent with his ability, when in fact, as the passage shows, they are the same thing .. 2. Of the following, which is the best way to phrase sentence 4 (reproduced below)? He listens intently, asks me some Questiolls, and my feelings are seeminglv known by him exactly. . (A) (As it is now) (B) Listening intently, he will ask me some questions and then my exact feelings are seemingly known to him. (e) As he listens to me and asks me some questions, he seems to be knowing exactly my feelings. (D) He listened to me and asked me some questions, seeming to know exactly how I felt. (El He listens intently, asks me some questions, and then seems to know exactly how I feel. 180 Improving Paragraphs Answer: Choice (E) is correct. Explanation: Sentence 4 shou ld use a parallel const ruction of present-tense verbs to denote the series of events the father typically performs. This sentence properly follows sentence 3 by indicating, in a man ner consistent with p In Mind the rest of the paragraph, how the father typically responds to his Don't reject a choice because child 's problems. Ge - Choice (A) is unsatisfactory because the sentence shifts unnecessa rily from the active voice to the passive voice. the language is simple. Often the simplest expression of an idea is the clearest - and the best. - Choice (B) is unsatisfactory because it awkwardly shifts the subject of the sentence from the father (" he") to the chi ld 's feelings. - Choice (C) is unsatisfactory because it uses an improper verb form; "to know" is preferable to "to be knowing." - Choice (D) is unsatisfactory because the sentence switches to the past tense; the context suggests that these are habitual, ongoing act ions that require the present tense. 3. In sentence 7. the phrase by all accounts is best replaced by (A) however (B) moreover (e) to my knowledge (D) like my sister (E) but nevertheless Answer: The correct answer is choice (A). Explanation: Sentence 7 draws a contrast between the fathe r and the people described in sentence 6. With the inclu sion of the word "however," the sentence properly indicates that the father, unlike the busy people of sentence 6, is NOT too busy to spend time listening. - Choice (8) is unsatisfac tory because the word "moreover" suggests that the thought about to be expressed supports and is consistent with the previous thought - but instead. sentence 7 draws a contrast with sentence 6. Ge p In Mind The revised sentence must make sense in the context of the passage as 8 whole. - Choice (C) is unsatisfactory because the phrase "to my knowledge" is unnecessa ry; we know from the writer's use of the first person that these claims are a reflection of his or her knowledge. 181 THE WRITING SECTION • Choice (D) is unsatisfactory because the subject of the paragraph is the father. It would be inappropriate al thi s point in the paragraph to int roduce new inform ation about the sister. • Choice (E) is unsatisfactory because the word "but" is unnecessary. The word "nevertheless" by itself would be sufficient to express the idea. 4. Which oftne following sentences should be omitted to improve the unity of tne second paragraph? (Al Sentence 8 (B) Sentence 9 (el Sentence 10 (D) Sentence 11 (El Sentence 12 Answer: Choice (E) is correct. Explanation: Paragraph 2 conti nues the discussion of the father's abilit y to understand people by explaining how he uti lizes this talent at work. Sentence 12 stands out from the paragraph because it introduces a new idea: how we choose our friends. • Choice (A) is unsatisfactory because sentence 8 introduces an idea - how the father uses his talent at work - that is suppo rted in the follow ing sentences. • Choice (B) is unsatisfactory because sentence 9 properly follows sentence 8 by expla in ing one aspect of the father's job. ~PInMlnd A concluding remark covers the entire essay, not just one part of it. Choice (C) is unsatisfactory because the dinner discussed in sentence 10 is clearly one of the social events introduced in sentence 9. Choice (D) is unsatisfactory because the phrase "such a conversation" in sentence I I refers clearly to the previous sentence. 5. In context, which of the following is the best way to phrase the underlined port ion of sentence 16 (reproduced below)? Furthermore, it lias strengtlrened his relationsllip with my rnotlrer. (A) (B) (e) (0) (E) (As it is now) Further st rengthening But it strengthens However, he is strengthening Considering this, he strengthens Answer: Choice (A) is correct. Explanation: The idea expressed in sentence 16 offers further support for the idea specified in sentence 13 and supported in sentences 14 and IS. The language of the sentence shou ld indicate this. 182 Improving Paragraphs The word "Furt hermore" properly indicates that the information about the father's relationship with the mother offers further support for the statement made in sentence 13. • Choice (B) is unsatisfactory because it creates a sentence fragment; the result ing sentence has no subject. • Choice (C) is unsatisfactory because the word "But " indicates a contrast between the ideas expressed in sentences 15 and 16 where a contrast does not exist. • Choice (0) is unsatisfactory because the word "However" indicates, illogically, that the st rengt hening of the fat her's relationship wit h the mother is somehow in contrast with the strengthening of his relationships with children and friends. • Choice (E) is unsatisfactory because the phrase "C.onsidering this" makes no sense in context. The resulting sentence implies that the strengthening of the relation ship with the mother is separate from the father's ability to understand others, while the progression of support in the paragraph suggests the opposite. ~ Keep in Mind Adding material to an essay can be an excellent revision technique, as long as the new material is relevant and d evelops the ideas of the essay. 6. A st rategy that the writer uses within the third paragraph is to (A) make false assumptions and use exaggeration (B) include difficult \'ocabulary (C) repeat certain words and sentence patterns (D) argue in a tone of defiance (E) turn aside from the main subject Answer: Choice (C) is correct. Explanation: The writer makes the point that the fathe r's ability to understand people affects his whole life by specifying those particular areas of his life that have benefited. The writer emphasizes the point that the fa ther's abi lity has benefited him in relationships with many different people (friends, co-workers, children, spouse) by ut ilizing a parallel structure in sentences 14, IS and 16. The writer also repeats the words "abi lity" and "allows" and uses the same subject (the father's ability or talent) for each sentence in the paragraph. • Choice (A) is unsatisfactory because nothing about this paragraph is exaggerated or shown to be false. • Choice (B) is unsatisfactory because there is no evidence that vocabulary in the third paragraph is particularly difficult. • Choice (D) is unsatisfactory because the tone of this paragraph is not defiant. • Choice (E) is unsat isfactory because the pa ragraph continues the discussion of the main subject of the essay - the father's except iona l talent. 183 ;1Rl:1 ""':J' \!!: Recap 1. Read the es~ay through to determine its overall meaning before you look at the questions. 2. Read more slowly than you usually d o, to help you pay closer attention. 3. Make sure that your sentence revisions make sense in the context of the passage as a whole. 4. Don't reject a possible answer because the language is simple. Often, the simplest expression of an idea is the clearest and therefore the best answer. 5. Try all the suggestions before you decide on your answer. 6. Make sure that the relationship between the two sentences is clear when you combine sentences. 7. Remember that pronouns should always clearly refer back to a word or phrase. 8. Keep in mind that adding material to an essay can be an excellent revision technique, but the new material must be relevant and develop the ideas of the essay. 9. Use your test booklet to help you by marking each question that you don't answer. Then you can easily find it later. 184 Improving Paragraphs Practice Questions , Directions: The following passage is an early draft of an essay. Some parts of the passage need to be rewritten. Read the passage and select the best answers for the questions that follow. Some questions are about particular sentences or parIs of sentences and ask you to improve sentence structure or word choice. Other questions ask you to consider organization and development. In choosing answers, follow the requirements of standard written English. Questions 1-5 are based on the following passage. (I) I have just read an excellent book called "Having Our Say: The Delany Sisters' First 100 Years." (2) Usually I do not enjoy autobiographies. (3) r could hardly put this one down. (4) It is about Sadie Delany, who is 103 years old, and her "little" sister Bessie, she is 101. (5) The sisters grew up in North Carolina in times that were not easy for African Americans. (6) Around 1916 they moved to New York City and went to Columbia University at their father's urging. (7) He tells them, "You are college material. (8) And if you don't go, shame on you!" (9) Sadie became a teacher and Bessie a dentist. (10) The second Black woma n dentist ill New York. (1 1) They lived through an incredible amount of history. ( 12) For instance, Bessie participated in civil rig hts marches and protests in New York for decades, starting in the 1920s. (13) Imagine having people like Paul Robeson over to dinner! ( 14) One aspect of the book that I especially liked was its humor; though Sadie is not as irreverent as Bessie, both are full of wisecracks. (IS) The Delany sisters seem livelier than many twenty-year-olds. (1 6) They care deeply about what is going on around them - and they laugh at things whenever possible. I. What is the best way to deal with sentence 3 (reproduced below)? I could hardly pilI this one down. (A) Leave it as it is. (B) (C) (D) (E) Connect it to sentence 2 with the word "but". Place it before sentence 2. Change "this one" to "this a~tobiography". Omit it. 2. In context, which is the best version of "He tells below)? them~ in sentence 7 (reproduced He tells them, "You are college material. (A) (As it is now) (B) Their father tells them, (C) Th is is because he tells them, (D) He had told them, (E) His suggestion was: 3. Which of the following sentences is best to insert between sentences 12 and 13? (A) The two sisters also knew many famous figures personally. (B) Sadie usually did not march, but protested by other means. (C) Many young people seem to think this did not begin until the 19605. (D) The last hundred years have seen many changes in civil rights laws. (E) Paul Robeson was a promine nt Singer, actor, and political activist. 4. In context, what is the best way to deal with sentence 14? (A) Move it to the beginning of the first paragraph. (B) Move it to the beginning of the second paragraph. (C) Start a new sentence after "irreverent" and delete "though~. (D) Connect it to sentence 15 with a comma. (E) Follow it with an example. 185 THE WRITING SECTION 5. Which of the following, if placed after sentence 16, would be the most effective concluding sentence for the essay? (Al (B) (el (D) (El They eat healthy food and do yoga every day. Therefore, it is no small thing to survive past age toO. This book is a remarkable story made even bettcr by the way it is told. Finally, young people should definitely commu nicate with their elders. Much as ! enjoyed the rest of the book, the final chapter is my favorite. Questions 6-11 are based on the following passage. (1) Becoming the best is very difficult. (2) No matter if you are trying to become a bettcr athlete, student, or musician. (3) !fyou want to be the best, sacrifices must he made by you. (4) You lose a lot of time that you would otherwise have for just relaxing. (5) This time could also have been spent exercising outdoors. (6) You must also be willing to cut down on time spent with family and friends. (7) If your goal is to become a fine jazz pianist, you must be willing to work hard. (8) Many people think jazz musicians just sit down and play, this is a mistake. (9) Practicing demands many hours in a week. (10) Most of the exercises done are of repetition and become boring, but that is the price you must pay for success. (11) You must practice fingering techniques and le~rn about both classical and jazz harmonics and chords. (I2) The reason you need to know about these harmonies is that so much of jazz involves improvisation, making up new sequences of notes to play. (13) You are not just playing notes that a composer wrote but are almost like a composer yourself. (14) Sometimes you will feel discouraged. (15) When you can playa classic like Dizzy Gillespie's ~Manteca" the way it really should be played, the long hours and hard work seem worthwhile. 6. Of the following, which is the best way to write the underlined portion of sentences I and 2 (reproduced below)? Becoming the best is very difficult. No matter ifyou are trying to become a betler athlete, student, or musician. (A) (As it is now) (8) difficult, never mind if (e) difficult, whether (D) difficult. Regardless of whether (El difficult; whether or not ( 7. In context, which of the following is the best way to phrase the underlined portion of sentence 3 (reproduced below)? If you want to be the best, sacrifices must be made by you. (Al (As it is now) (B) one must sacrifice some things (el you must make sacrifices (D) one will have to make sacrifices (E) sacrifices are necessary to make 186 • Improving Paragraphs 8. Which of the following is the best way to revise and combine sentences 4 and 5 (reproduced below)? You fose a lot of time that you would otherwise have for just relaxing. This time could also have been spent exercising outdoors. (A) Time that could have been spent exercising outdoors or jusl to relax will be lost. (8) Spending time exercising outdoors or relaxation are things for which you will have less time. (C) Yo u will have much less time for exercising outdoors or for just relaxing. (D) Sacrificing outdoor exercise and just relaxing, because you will not have lime. (E) As examples of the things you will have to cut down on would be outdoor exercise or just relaxing. 9. Of the following, which would be the best way to revise the underlined portion of sentence 8 (reproduced below)? Many people think jazz musicians just sit down and play, this is a mistake. (A) and, this is a mistake however (8) (C) (D) (E) this would be a mistake what a mistake that would be it is mistaken but they are mistaken 10. In context, which of the following is the best way to phrase sentence 10 (reproduced below)? Most of the exercises done are of repetition and become boring, but that is the price you must pay for success. (A) (As it is now) (B) The price you must pay consists mostly of repetitious and boring exercises for success. (C) Doing repe titious and boring exercises; this is the price of success. (D) Repetition and boredom are the inevitable res ult when having done most of the exercises. (E) Doing repetitious and boring exercises is the price you must pay for success. II . In context, which of the followi ng is the best way to phrase the underlined portion of sentence 11 (reproduced below)? You must practice tinzerirJ.i techniques and /earn about both classical and jazz harmonies and chords. (A) (6) (C) (D) (E) (As it is now) You must practice fingering techniques and learning One would practice techniq ues fo r fingering and learn Fingering techniques must be pract iced and learning There must be practice of finger ing techniques and you learn 187 THE WRITING SECTION Answer Key I. B 2. D 3. A 4. E 5. C 6. C 7. C 8. C 9. E 10. E 1 I. A Additional practice questions can be found in The Official SAT Online Course at www.colle geboard.comfsatonlinecourse. 188 CHAPTER 13 Practice for the Writing Section You can never practice too much. Th is chapter gives you additional practice in writing essays and answering questions. This chapter includes nine sample essays with scores ranging from 6 through 1. There are practice quest ions on improving sentences, ident ifying sentence errors and improving paragraphs. These are all in addition to the sample quest ions in Chapters 9,10.11 a nd 12. g Automated Score To receive a n automated score f or your response to this essay question, check out The Official SAT Online Course at www.collegeboard.com/ saten Ii neeau rse .com. Practice for the Essay The following is a typical essay prompt that you might find on the SAT. Follow the instructions and try writing an essay. Think carefu lly about the issue presented in the follow ing excerpt and the assignment below. Honesty is important. of cou rse. but deception can actually make it easier for people to get along. In a recent study. for example. one out of every four of the lies told by participants was told solely for the benefit of another person. In fact, most lies are harmless social untruths in wh ich people pretend to like someone or something more than they actually do ("Your muffins are the best!"). Adapted from Allison Kom et. "The Truth About Lying" Assignment: Is deception ever just ified? Plan and write an essay in which you develop your point of view on this issue. Support YOUT position with reasoning and examples taken from your reading. studies. experience, or observations. 189 THE WRITING SECTION Practice Questions: Improving Sentences The following sentences test correctness and effectiveness of expression. Part of each sentence or the entire sentence is underlined; beneath each sentence are five ways of phrasing the underlined material. Choice A repeats the original phrasing; the other four choices are different. If you think the original phrasing produces a better sentence than any of the alternatives, select choice A; if not, select one of the other choices. In making your selection, follow the requirements of standard written English; that is, pay attention to grammar, choice of words, sentence construction, and punctuation. Your selection should result in the most effective sentence - dear and precise, without awkwardness or ambiguity. Example: Laura Ingalls Wilder published her first book and she was Sixty-five years old then. (Al (B) (C) (D) and she was Sixty-five years old then when she was sixty-five at age sixty-five years old upon the reaching of Sixty-five years (E) at the time when she was Sixty-five 1. To ensure that the bread will have the same consistency from batch to batch, il...i..UM. Quality control spedalist who checks small random samples of dough from each lot. (Al it is the quality control specialist who checks small random samples of dough from each lot (8) the quality control specialist checks small random samples of dough from each lot (C) small random samples of dough are checked from each lot by the quaHty control specialist (D) the quality control specialist checks samples of dough - small and randomly - from each lot (E) the quality control specialist is the one checking small random samples from each lot of dough 2. Although Central Park in Manhattan is better known than Prospect Park in Brooklyn, the designer of both parks, Frederick Law Olmsted, preferred Prospect Park. (A) Although Central Park in Manhattan is better known than Prospect Park in Brooklyn, the designer of both parks, Frederick Law Olmsted, preferred Prospect Park. (B) Central Park in Manhattan being better known than Prospect Park in Brooklyn, the deSigner of both, Frederick Law Olmsted, preferred the latter. (C) Although not as well known as Central Park, Frederick Law Olmsted, who designed both parks, preferred Prospect Park. ~ (D) The deSigner of both Central Park and Prospect Park was Frederick Law Olmsted, he preferred Prospect Park. (E) Although more people know about Manhattan's Central Park than Prospect Park in Brooklyn, Frederick Law Olmsted, having designed both, has preferred the latter. , 3. Growing up in a family where music was a daily part of life, Steve and Rick shared a determination to become singing duos known nationwide. (A) to become singing duos (8) to become a singing duo (Cl of becoming Singing duos (D) that they would become singing duos (E) ofbecoming a singing duo 190 Practice for the Writing Section 4. The bagpipe originated in ancient Sumer, many people assume tha t it was the Scottish Highlands. (Al many people assume t hat it was (B) many people assuming (C) not, as many people assume, in (D) not what many people assume (E) but many people assume it to be 5. Certain shipwrecks have a particular fascination for those people which have a belieOn finding the treasure in them. (A) which have a belief in finding the treasure in them (B) that belief there is treasure to be found in them (Cl who belie\-e they hold treasure and that they can find it (D) who believe that there is treasure 10 be found in them (El who believe about treasure to be found in them 6. Many of the instruments used in early operations of the United States Ar my Signal Corps were adaptations of eQuipment used by the Plains Indians. particularly that of the heliograph. (A) Corps were adaptations of equipment used by the Plains Indians, particularly that of the heliograph (B) Corps, there were adap tations of equipment used by the Plains Indians, particularly t he heliograph {Cl Corps, and in particular the heliograph, was an adaptation of equipme nt used by the Plains Indians (D) Corps, and in part icular the heliograph, were adaptations of equipment used by the Plains Indians (E) Corps being adaptations, the heliograph in particular, of those used by Plains Indians 7. Marie and Pierre Cu rie discovered rad ium but refused to patent the process they ysed nor otherwise profiling fro m the commercial exploitation of radium. (A) used nor otherwise profiting {Bl had used nor otherwise did they profit (C) have used or otherwise to have profited (D) used or otherwise profited (E) had used o r otherwise to profit 8. Many drivers violale t raffic laws knowingly and openly, in other respec ts they are law-abiding citizens. however. (A) Many drivers violate t raffic laws knowing ly and openly, in other respec ts they are law-abiding citizens, however. (B) Many drive rs who are otherwise law-abiding citizens violate traffic laws knowingly and openly. (Cl Many drive rs violate traffic laws knowingly and openly and arc otherwise lawabiding citizens. (D) Although otherwise law-abid ing citizens, many drivers, howeve r, violate t raffic laws knOW ingly and open ly. (E) Many drivers which violate traffic laws kn owingly and openl y are in other respects law-abiding citizens. 9. The primatologist has argued that sustai ned observation of a few animals provides better behavioral data tban does intermittent observation ofmany animals. (A) provides better behavioral da ta t han does intermittent observation of many ani mals (ll) provides beller behavioral da ta than Olany a nimals are observed intermittently (C) prOViding better behavioral data than does intermittent observation of ma ny animals (D) do provide better behavioral data than intermittent observation of many animals do (E) in cont rast to intermittent observation of many animals, provides better behavioral da ta 191 THE WRITING SECTION Practice Questions: Identifying Sentence Errors The following sentences test your ability to recognize grammar and usage errors. Each sentence contains either a single error or no error at all. No sentence contains more than onc error. The error, if there is one, is underlined and letlered. If the sentence contains an error, select the one underlined pari that must be changed to make the sentence correct. If the sentence is correct, select choice E. [n choosing answers, follow the requirements of standard written English. Example: The other delegates and him immediately ABC accepted the resolution drafted by the D neutral slales. No error ®. ©@@ E 10. One challenge that writer Eleanor Wong Telemaque faced was bow preserving her A ethnic identity while becomina more accessible to readers who are accustomed to B C D writers from other cultural backgrounds. No error E 11. Lions and tigers~ identical in size. h1l1 the tiger is the fiercer animal and the A B C lion the strotlaest. No errQr D 12. Ms. Jordan E ~ demonstrated her company's most popular product. a watch thaI A flashes the lime in ~ numerals when pressjna a butto!}. No error C D E 13. In the 1920s. Dl!.I..dl critical approval was aiven to a group of English writers A B known as the Bloomsbury group. the most famous ofwhoOl was Virgin ia Woolf. C D No error E 14. Maude Adams, after her spectacular triumph as the original Peter Pan, went about A B beavy veiled and was accessible to only a handful of intimate friends. No error C D E 192 Practice for the Writing Section IS. All states ~ severe penalties 00 drivers who do not stop when he or she is A B C involved in accidents. No error o E 16. If one is interested in learning even more about Zora Neale Hurston, yoy should ABC read Robert Hemenway's biography. No error E 17. !fhe had begun~, he might have succeeded in finishjng the extremely A B C complex project before the deadline. No error E 18. In the early twentieth century, new thinking iiliQ.uj symbolism and the unconscious A ~ greatly inspired ~ the writings QfSigmund Freud and Carl Jung. No errQr BCD E 193 THE WRITING SECTION Practice Questions: Improving Paragraphs D ir~c lion s: The following passage is an ea rl y draft of an essay. Some parts of the passage need to be rewritten. Read the passage and select the best answers for the questions that follow. Some questions are about pa rticular sentences or parts of sentences and ask you to improve sentence structure or word choice. Other questions ask you to consider organization and development. In choosing answers, follow the requi rements of standard written English. Questions 19- 23 a re based on the following passage. (I) Living in a city in central Alaska, I have become accustomed to extreme weather cond itions, these are a parI of living in a remote, northern region. (2) To us Alaskans, a 70 mph wind is something that messes up our hair. (3) Temperatures of20 degrees Farenheit mean that we can take off our coats. (4) We are used 10 wi nter days with only 4 hours of sunlight, or summer baseball games that can sta rt at \0:30 PM without artificial lighting. (5) Adj usting to such conditions is not too difficult. (6) But, Alaska's remote location creates challe nging economic circumstances. (7) Alaska is tremendously rich in natural resources, such as lumber, oil, and fish. (S) We must import processed goods from the lower forty-eight states. (9) Most goods are shipped all the way to t he port of Anchorage; the cost is nearly triple that of sendi ng goods from New York to Seattle by rail. (10) The state of Alaska is the number one harvester of seafood in the United States. (I I) But processed seafood can be bought more inexpensively in the state of Washington because Alaska does not have enough fish processing plants of its own and so must ship a great deal of seafood to Seattle for processing. (12) Thus, the cost of long distance transportation drives up the price of the product. (13) One solution that Alaskans definitely should consider is having built more local processing facilities. (14) Afte r all, there is plenty of fish to keep them running. (15) Ultimately, th is solution can benefit Alaskans by providing jobs, lower prices, and healthycompetition. 19. In the context of the first paragraph, which of the following would be the best way to combine the underlined portions of sentences 5 and 6 (reproduced below)? Adjusting to su.ch condilions is not 100 difficult. Bul. Alaska's remote loco/ion creates clW/ICllgillg economic circumstances. (A) difficult, and Alaska's remote locat ion (B) difficul t, but Alaska's re mote location (el difficult: the remote location of Alaska (D) difficult; indeed, its remote location (E) difficult, and the remoteness of our location 20. Which of the follOWing would be the most logical insertion at the beginning of sentence 8? (A) In other words, (B) Not surprisingly, (C) Invariably, (D) Hence, (E) Unfortunately, 194 Practice for the Writing Section 2 1. In context, which oftne following sentences would best fit between sentences 10 and II? (A) Many years ago the fishing was better than it is today. (B) I do nol personally care for seafood. (el Fishing can he a dangerous business because of the squalls that can blow up sudden ly in this part of the world. (D) OUf coastal waters contain an abundance of king crab, salmon, and other sea creatures. (E) Some fish nelS drift out to sea. 22. In context, which of the following is thc best way to phrase the underlined portion of sentence 13 (reproduced below)? One solutio" /lull Alaskans definitely shOldd consider is IlRyjng built more Weed processing fad/ities. (A) (As it is now) (B) is building more local processing faci lities (e) is this: more local processing facilities should be built locally (D) is that more should be built locally (E) is that we should build mo re of them 23. The func tion of the third paragraph (sentences 13-15) is to (A) offer further evidence supporting the view presented in the first paragraph (sentences 1-6) (B) describe the result of problems listed in the second paragraph (sentences 7-12) (C) propose a way 10 remedy the situation described in the second paragraph (D) unify the essay by resolvi ng a contradic tion between the first and second paragraphs (E) end the essay with an ironic twist 195 - THE WRITING SECTION Answer Key The Essey To prepare for the essay section, it is helpful to review sample essays written by other students and the explanat ions of the scores they received, ranging from 6 to I. To receive a n a utomated score for you r respons e to this Although all of the sample essays were handwritten by students. essay quest ion, check out The they are shown typed here. in boxes. for ease of reading. However. we Official SAT Online Course at www.collegeboa rd.com/ are presenting one in handwriting to remind you that it is important satonli necourse. to write legibly and clea rly. The essays have been typed exactly as each student wrote his or her essay, without any correct ions to spelling, punc tuation, syntax or paragraph breaks. The following is a sample prompt: Q Automated Score Think carefully about the issue presented in the following excerpt and the assignment below. Honesty is important, of course, but deception can actually make it easier for people to get along. In a recent study, for example, one out of every four of the lies told by participants was told solely for the benefit of another person. In fac t, most lies are harmless social un truths in which people pretend to like someone or something more than they actually do ("Your muffins are the best!"). Adapted from Allison Komet, "The Truth About Lying" Assignment: Is deception ever justified? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, studies, experience, or observations. 196 --- --------------------------------------Practice for the Writing Section Essay #1: This essay received Pan A (Wrltm 5ampIej , """) Mt + score of 6. lDoaon'lftieI!4IJ. &.11,")'0\1' , B J, Ti,..,.. ~ If AMO ~ IPIU. COfIWIW On U\t . . . . . • ~. v.!h.... "'. , d ,,~ "" < J. ~ , .;." -, 1;~"'1ut< L.;, ...." ~.H " U e , ""'" .. .If.. ; ,.,. II .f ~. """" ~ (~ r ~ ...H., -r '" ... ""~ J w'wt- -n-. -~' e~'; N\,tn, llo-.... ot- 11 ... ' U9=4 \ , " '" .,.. I , .- Ge./lt:r. , IAA QC..""""Qt\ .I: ,,; s. I~ ce<..... "-J ...~. -t. Condnue on the reven;e side if necNSII (continued) 197 THE WRITING SECTION -">We g·/So ~,,-n.. .. M<~.ui~ oF- cf.t.cf'(1l1V1 Ds-GM.e'r MWa", ""~ E;h'1"'I'D I,l'& .k.Ca.dc!:.- of p« : (~. T. .§"'\ .!.r..Ie~ •• t:: f"" rt- -h-t IM--)", .Tt V.R[ tt.. 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.p"I-"ye. l.p yeve",le,A y",,A,,,,,11 h"I-" o-P-Peys v",I"",'Dle "'"owle,ABe . ...,,"s o"e c"''' view ,Aec e Ho" "'s '" sweel- he",l-. II- is li"'e '" coo"'ie 1-"",1- s",l-is-lle s "",,~ey ",,,,A !jives i""""e,Ai",l-e ple",s"ye. owevey I-"e coo"'ie will 0,,1 c",,,se OOy "e",ll-" i" I-" e .p"I-"ye. $i""l1",yl ,Aece I-io" '" e",ys 1-0 'De '" . "sl-i-ll",'Dle ",,,,A so""el-i""es eve" CO"" ",ssio"",l-e 'D"I- il- 0,,1 "ol,As .p"I-"ye yo'Dlel<'\S. WHY ESSAY #2 RECEIVED A SCORE OF 6 In all ways, this well-organized and clea rly focu sed essay demonstrates clear and consistent mastery. The writer demonstrates outstanding critical thi nking by developing in sight fully the main idea "that decept ion does not offer the same long-term benefits as honesty does," wh ile also acknowledging and discussing the temptation to use decept ion "to escape immediate repercussions." Pa ragraphs 2 and 3 offer personal examples of instances when the use of deception led to unfortunate consequences. Paragraph 4 uses the example of protecting a ch ild 's innocence to describe a time when decept ion can be tempting. Th roughout this essay. the writer exhibits skillful use of language and demonstrates variety in sentence structure. Thus, this outstanding response scored a 6. 201 THE WRITING SECTION Essay #3: This essay received a score of 5. I" '" wovlJ. wheve hovvi·lk ",,,J. "e~",\-ive i"dJ.e"ts o>'l-e" OCCl.\v I-he ~e"ev",1 pl.\'blic is ot>l-e" J.ecieveJ.. So"'e 'believe I-he shielJ.i"~ Ov \-wis\-i,,~ ot' ceY\-",i" i">'ov",,,,\-io,, "''''y 'be 'be"e-i1d",1. How- evev, "'s show" I-hvol.\~h """jov hisl-ovie",1 eve"ts, J.ecepl-io" is "e ev ·l.\sl-i-i1",'ble. ellow ·ol.\v"",lis", ",,,J. I-he ce"sovshi 0>' >'",cts pvoves jl.\sl- I-his. I" I-he wee~s pveviol.\s 1-0 I-he Sp",,,ish-A,,,evic,,,,, w"'v i" I-he . I",I-e I gOOs, "''' ",vol.\si,,~ ",,,~ev ",~",i" sp",i" WO\$ vis,,,~ ",,,,0":JI-he pl.\'blic. AJ.voc",l-es 0>' w"'v I-oo~ I-he "'",\-\-ev i"l-o I-heiv OW"

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lie wO\$pl.\'blisheJ. ",,,J. I-he "ewsp"'pevs '"sisl-eJ. 1-1.,,,,1- I-he le\-\-ev w"'s i"sl.\ll-i"~ I'\cki"ley. Soo" I-he e"Hve pl.\'blic w"'s lieJ. 1-0 ",,,J. ",I",osl- evevyo"e e"col.\v",~eJ. w"'v. The pl.\'blic w"'s ",,,,,,ipl.\l,,,l-eJ. ",,,J. J.ecieveJ.. ,hey weve hic~eJ. i"l-o w"'v, ",,,J. hisl-ovy h",s '" l",vBe "I.\",'bev 0>' A",evic",,, ",,,J. Sp",,,ish J.e",l-hs which de",vly show how hl.\ely h",v",>'1.\1 J.ecep\-io" Dl.\vi,,~ c"''' 'be. I-he s",,,,e pevioJ. 0>' H",e, "'s A",evie",,,s ye",v"eJ. >'ov i"'pevi",lisl'\ The Fillipi"o I"sl.\vec\-io" occl.\veJ.. As I-hol.\s",,,J.s ot' A",evic",,, solJ.ievs 'bec","'e e"B"'BeJ. i" ~ovill", w",v>,,,,ve, '" I",v~ . "I.\",'bev ot' J.e",l-hs occl.\veJ.. B",c~ ho"'e, 0" V"il-eJ. SI-",I-es soil, I-he A",evic",,, pl.\'blie wo"J.eveJ. ",'bOI.\I- I-he pvo~vess i" I-his >'ov~" I",,,J.. I-hey 202 weve lieJ. 1-0. Fe",v>'1.\1 1-1.,,,,1- I-he -i1Bh\-i"B wOI.\IJ. Practice for the Writing Section 'oecolMe lA"poPlAl",., ilMpevi",lisl- polil-io"s 1-01.1. I-he PIA'olic 0-1' Bve",1...J.v",,,celMe,,\-s ",,,.I. "ew I-evvil-ov ",,,.I. eo Ie CO" lAeveJ.. s lMevic",,,s ",,,.I. filii i"os weve 'oei" 'ovlAl-",l1 sl"'lA hl-eveJ. e",ch J.",y, ce"sovship ",,,.I. J.eciel- vev",ileJ.. B I-he I-ilMe I-he \-vlAl-h w"'s lA"v",ileJ. I-he J."'IM'" e h",J. ",lve",J. bee" J.o"e. \"he \-vlAl-h cOlA1J. h",ve s",veJ. lives, veSOlAvces, ",,,.I. J.iB"iry -I'ov I-he ~, 'o1A1il- w"'s sheilJ.eJ. J.ece I-io" is "evev ",cce I-",'ole. E",ch evso" ve ",vJ.less 0-1' olil-ic",l Ov sod",l v",,,\<. J.esevves I-he ",'osollAl-e \-vlAl-h 0" """,,,,,evs I-h",1- ve",\-1 e.f'.f'ec\- I-heiv lives. s show" I-hvolA h hisl-ov WHY ESSAY #3 RECEIVED A SCORE OF 5 This detailed e,ssay uses examples of events in history to develop effectively the point of view that "deception is never justifiable." The writer displays strong critical think ing by describing two separate instances when the American public was led deceptively into supporting a war. The second paragraph describes how the media distorted the truth, provoking Americans into backing the Spanish-American War. In paragraph 3, the writer explores the use of "censorsh ip and deciet" to ma intain American support during the "Fillipino Insurection." This respon se is focused, and the writer uses appropriate vocabula ry and displays a progression of ideas. Thus. the essay demonstrates reasonably consistent mastery and scored a 5. 203 THE WRITING SECTION Essay #4: This essay also received a score of 5. Decep\-tc", Cv \-he ",isvepvese"\-",\-ic,, c.p \-vv.e pV.vpcses, is '" .pcv", c.p '" lie. AI\-hcv.Bhliei,,~h\- pcse i",,,,eJ.i,,,\-e be"e-l!\-s i" \-he Ic" +ev", i\- si", I cve",\-es vcblel'\S. Thv.s J.ece \-tc" c",,, "evev be jv.s\-i-l!eJ.. Thvcv.~hcv.\-li\-ev"'\-v.ve, \-heve ",ve """"y i"s\-",,,ces c.p "e.p",vi- cv.s ch",v",c\-evs v.si"B J.ecep\-ic". Fcv e><"''''ple, i" """,cbe\-h by Sh",~espe",ve, \-he wi\-ches c-P-Pev "h",I.p-\-vv.\-hs" i" \-he .pcv", c.p cc".pv.si" ",,,J. "'isle",J.i" viJ.J.les \-c """,cbe\-k Obvicv.sly, \-he wi\-ches ",ve cve",\-v.ves c.p evil, i,,\-e,,\- c" cve",\-t"B p",i" ",,,J. wve",~i" h",vcc. The J.ece \-ive \-hi" s \-he wikhes \-ell """,c- be\-h J.vive hi", \-c J.c \-hi" s he wcv.lJ. "c\- cvJ.i"",vil J.c sv.ch "'s ~iII \-he v."c",,, ",,,J. "''' v.c. ThvCv. . h \-his ",,,J. "v."'evcv.s c\-hev e><",'" les i\- becc"'es '" ",ve,,\- \-h",\- J.ece \-tc" ",,,J. \-vic~ev ",ve \-he \-ccls c-P evil. Thv.s, b y yel",\-tc", J.ecep\-tc" is evil. Hcw, \-he" c"''' J.ece \-tc" evey be . v.s\-i-l!eJ. "'s ",cy",11 vi hI-? I" \-he .pcl~\-",Ie, The I>cy whc CyieJ. Wcl.p, '" bcy i"\-e"\-ic,,,,,lIy J.ecieves c\-hevs .pCY his cw" ",,,,v.se,,,e,,\-. Hcwevey, whe" he sevicv.sly "eeJ.s help ",,,J. c",lIs .pCY it; "c c"e will help hi", bec",v.se \-hey J.c "c\- believe hi",- His pyevicv.s J.ecep\-ic"s h",ve ",,,,J.e hi", Icse ",II cveJ.ibility i" \-he e yes c.p \-he \-ow"specple. H",J. he "c\- pyevicv.sly J.eceiveJ. \-he"" sv.yely \-hey wcv.lJ. help hi", "cw. This \-",Ie pyese,,\-s '" s\-vc"B "'ess",~e: J.ecep\-ic" c"''' c"ly c",V.se \-vcv.ble. v.yi" The W",\-ev ",\-e sc",,,J.,,,1 i> "''''0'' c\-hey \-hi" s J.eceiveJ. \-he A"'eyic",,, people. As "''' elec\-eJ. o-P-l!ci",l, he w",S e> 204 Practice for the Writing Section ",isvepvese","eJ. ,",,-e ",c\-io"s o{' "-is people i" '-"'e W",,"ev~,,,,"e i"ciJ.e,,\-, ,,-e co",,,,it-t-eJ. "''' ",c\- o{' J.ecep\-io". Al\-"-ol.\~"- \-,,-e ,"e",pov",vy vew",vJ.s o{' ,""-is ",ppe",leJ. C",,,J. i"covvec\-) w"'y ,"001: '" "-I.\~e 01.\,". PI.\e ,"0 \-0 "-i",, ,""-is w"'s ,",,-e e",sy \-,,-is J.ecept-io", Nb,o,,'s i"'",~e "-it-, ",,,J. ,,-e e"J.eJ. I.\p vesi~"i,,~ ,",,-e pvesiJ.e"cy o{' ,",,-e V"i,"eJ. 'S,"",,"es. E-P-Pec\-ively, J.ecept-io" leJ. ,"0 ,",,-e J.ow"{',,,l1 o{' Ric"-"'vJ. Nb,o". '-"'is is w"-y I believe J.ecept-io" c"''' "evev bejl.\st-i-11eJ.. WHY ESSAY #4 RECEIVED A SCORE OF 5 This well-organized and foc used essay demonstrates reasonably consistent mastery. The writer develops effectively the point of view that "deception can never be justified" and demonstrates strong critica l thinking by providing three appropriate examples to support th is position: • In the second paragraph, the writer provides evidence from the play Macbeth to illustrate the idea that because deception is evil, it cannot be "justified as morally right." • Paragraph 3 uses the folktale TIle Boy Who Cried Wolf to show that deception leads to trouble. • Paragraph 4 describes how Richard Nixon's deception of the American people eventually led to his downfall . Th is response exh ibits facility in the use of language, demonst rates variety in sentence st ructure and is generally free of errors. Therefore, this essay is categori zed as effective and received a score of 5. 205 THE WRITING SECTION Essay #5: This essay received a score of 4. "E"J.s j\.\sti~y t\-.e ..,e",,,s." This 9\.\ote si~"i.fies t\-.",t i" so..,e c",ses, J.ecept-io" is j\.\st-i.fieJ.. Decept-io" occ\.\vS w\-.e" '" pevso,,'s t-v\.\st i" ot\-.evs is t",~e" ",J.v"'''t~e ot I" sped",l c",ses, t\-'is e> '" .., \-.eM. 1 ot e> to be. Fov t\-.e "e> .., ..,o\.\t\-' w"'s '" lie. 1J.iJ.,,'t ~"ow "'\\ o~ \-.ev ~vie"J.s ~o.., 0\.\1siJ.e o~ sc\-.ool so 1 \-.M to lie w\-.e" s\-.e ",s~eJ. w\-. 1w",,,teJ. to 'oo..ow \-.ev ",J.J.vess 'ooo~. "I lost ..,i"e ",,,.,I. 1w",,,t to co people ~o.., yo\.\v 'ooo~." S\-.e ve\\.\c",,,t-\y t\-.e ",~veeJ., ",,,.,I. ,,,It\-.o\.\~ ~elt '" p~\.\i\1; 1w"'s ",'ole to cve",te '" co..,plete ~\.\est list. Th\.\vsJ.", "i \-.t 1c",\\e.l. \-.ev ",,,.,I. vete"J.eJ. 1w"'-S sic~. \\ J."'y FviJ.", i"ste",J. o~ oi" to sc\-'ool 1 \-.",.,1. to et t\-.e c",~e "0 t\-.e 'o",\\oo"s ",,,.,I. ot\-.ev J.ecov",t-io"s. Theve w"'s w'" s\-.e co\.\IJ. \-.",ve s\.\spect-eJ. '" s\.\pvise p",vty i~ \-.ev best ~vie"J. w"'s sic~. The ..,i,,\.\te s\-.e t\-.eve ",,,.,I. ~ov 206 i"to t\-.e vOO.., \-.ev 'oivt\-.J.",y< s\-.e st",vteJ. evevy J.eceptio" ~",ce ",,,.,I. e"J.s w",l~eJ. .,1.0 j\.\st-i~y cvyi,,~ S",w "'\\ t\-.e eople wit\-. joy. EvevY....lk- 0" bee" j\.\st-i~eJ. by t\-.e loo~ \-.ev i" \-.ev e es. So..,et-i..,es i" He t\-.e \-.",.,1. t\-.e \-.'" ~i"ess ",,,.,I. t\-.e "'e",,,s. Practice for the Writing Section WHY ESSAY #5 RECEIVED A SCORE OF 4 Th is generally focused essay demonstrates adequate mastery. The writer develops the point of view that "in some cases, deception is justified" by prov iding a personal, detailed example of an instance when the "ends do justify the means." By describing how the deception involved in planning a surprise party is justified by the ultimate happiness the friend fee ls because of the party, the writer demonstrates competent critical th inking. The support is adequate and genera lly organized, exhibiti ng some coherence and progression of ideas. This response displays some variety in sentence structu re and uses generally appropriate vocabulary. Thus, the essay is competent and scored a 4. 207 THE WRITING SECTION Essay #6: This essay also received a score of 4. The lise o-P J.eceptiol\ is I.\sl.\",l1y I-hol.\,hl- o-P "'s '" 'bM I-hil\B. BI.\I-I-heve ",ve ti",es whel\ J.eceptiol\ isjl.\sl-i-l1eJ.. 11\ I-he c",ses o-P HolJ.el\ C"'I.\-l1elJ. "'I\J. A'biB",il Wi\Ii",\'o\S I-heiv l.\Se o-P J.ecepl-iol\ is ",cce I-",'ble 'bec"'I.\se o-P I-he sil-I.\",tiol\s il\ which I-he ",ve pl",ceJ.. The ",,,,il\ ch",v",c\-ev o-P The C",I-chev il\ I-he R e 'b S",lil\~ev is olJ.el\ C"'I.\-l1elJ.. HolJ.el\ is '" J.e vesseJ. ch",v",c- I-ev I-h"'1\ el\J.s I.\~oil\B cv",z.y. 11\ I-he wee\:.el\J. I-h",1- I-he 'boo\:. I-",\:.es I",ce HolJ.el\ is co"sl-",,,t-I I.\si" J.ece tio". He vel-e"J.s 1-0 'be olJ.ev ",,,J. ",ove sl.\-l1stic",l-eJ. I-h",,, he ve",l1y is. This is '" vO vi",l-e -Pov hi", 'bec"'I.\se he is tv i" 1-0 -Peel ",cce l-eJ. il\ I-he veJ.o"'i"",,,t-I MI.\II- ",I-\'\os heve I-h",1- he I.\\-s hi\'o\SeI-P i"l-o. olJ.e" w",,,\-s 1-0 'be s",,",vl-ev ",,,J. 'bel-l-ev ",I- evev I-hi" I-h"'1\ ",11 I-he people he ",ee\-s, so he ",c\-s I-h",1- w"'y. Eve" I-hol.\Bh HolJ.e" is I.\si"~ J.eceptio", he is l.\Si"B il- 1-0 -Peel 'bel-l-ev ",'bOl.\1- hi\'o\Sel-P whe" he is ",I- '" vev J.i-P-llcl.\11- ",vI- o-P his Ii-Pe. -PI-ev 'bei" \:.ic\:.eJ. 01.\1- o-P -POl.\v schools, h",vi"B his 'bvol-hev J.ie, ",,,J. "01- h",vi" "''''1\ -Pvie"J.s olJ.e"s I.\se o-P J.ece tio" is vi. ht-l ·I.\sti-l1eJ.. A"ol-hev ch",v",c\-ev -Pvo", '" 'boo\:. I-h",1- I.\ses J.eceptio" is A'bi- ",iI Wi\Ii",\'o\S -Pvo", The CVl.\ci'ble. 'bi ",iI is '" Ov h",,, chilJ. who h",s sl-", eJ. wil-h "'''''' J.i-P-Peve,,1- -P",,,,ilies "ol\e o-P which h",ve li\:.eJ. hey. A'bi,,,,il is ",Iso i" love wil-h '" "'''''' "",,,,eJ. Joh" PvocI-ov who J.oes "01- love hey 'b",c\:.. 'bi ",iI I.\ses J.ece tiOl\ 1-0 "",,\:.e hey I-ow" o-P s",le", viii", e I-hi,,\:. she sees wil-ches. 'bi . ",il J.oes I-his I",v el 1-0 el- ",I-I-e"tio" -Pvo", I-he eo Ie who I\evev ",ve il1-0 hey, ",,,J. 1-0 Bel- 'b",c\:. ",I- Joh" Pvoc\-ov -Pov "01- 10vi"B hey. A'bi- ",iI vl.\i"s ol-hev eo les lives I-hvol.\ h J.ece I-iol\ 1-0 ",,,,\:.e hevsei-P 208 Practice for the Writing Section -Peel 'oet+ev. Eve", I-ho"~h I-he .A.eeepl-io", is 'o",.A., il- is j"sH.fI",'ole i", 'oi "'ils sil-"",Ho", 'oee",,,se o-P I-he h",vsh li-Pe she h",s Iive.A.. As see", i", I-he eh",v",c\-evs Hol.A.e", (",,,.fIel.A. ",,,,.A. A'oi~",i1 Wil- .A.eee Ho", is so"'eH"'es ·"sH.fI",'ole. I", 'ool-h I-hese eh",v",eI-evs e",ses il- w"'s 'oee",,,s I-heiv lives weve 0", '" .A.ow",w",v.A. s iv",1 ",,,,.A. I-hey weve j"sl- \-vyi"'~ 1-0 eli",'o 'o",e,", "p. 1i",1MS WHY ESSAY #6 RECEIVED A SCORE OF 4 This competent essay develops the point of view that "there are times when deception is justified." The writer demonstrates competent critical thinking by providing two adequate examples from literature when the characters' use ofdecept ion was justified "becaus their lives were on a downward spiral and they were just trying to climb back up." Evidence provided is generally organized and .focused, demonstrating some coherence and progression of ideas. This writer uses generally appropriate vocabulary and displays some variety in sentence structure. Conseq uently, this response demonstrates adequate mastery and scored a 4. 209 THE WRITING SECTION Essay #7: This essay received a score of 3. I believe I-h",1- .Aecepl-io" c"''' be jl.\5l-i-fleJ.; il- si",ply ",,,,I-I-evs wh",1- I-he civc"...sl-",,,ces. Cevl-",i"ly il- c",,,,,ol- h"vl-I-o co",pli",e,,1- '" -Pvie".A 0" his "ew h",ivc"l-, whe" pevso"",11y yo" -fI".A ilvevoll-i,,~. S"ch s"pev-flci",l .Aecepl-io"s occ"v i" evevy J.",y li{'e, ",,,.A c"'l.\5e "0 ve",l h",v"," B"I- i" I-he l",v~ev se"se, I {'eel .AecepI-io" c"''' be sep",v",l-eJ. i"l-o!-wo c"'l-e~evies: I-hej"sl-i-fl",ble J.ecepl-io" I-h",1- o"e "'1.\51- "se 1-0 B",i" "'.Av"'''I-",~e i" '" co"'pel-iI-ive -flel.A, ",,,.A I-he "'li"sH-fI",ble J.ecepl-io" o"e "ses ",I- I-he el< e"se o{' ol-hevs {'ov his ov hey OW" evso"",l ",i". The biBBesl- "ews sl-ovy 1-0.A",y is I-h",1- o{' I-he ):"vo" b",,,"'v"pl-cy. Gv",,,l-e.A we J.o "01- el- "'"ow ",11l-he {'",C\-S b,,1- il- is obvio"s I-h",1- .Aecepl-io" 1-00'" pl",ce.'" He",.As o{' I-he co",P"'''y "'"owi" I lieJ. 1-0 I-heiv sh",veholJ.evs e"co"v", i" I-he", 1-0 b" "'ove sl-oc"', while I-he he....As I-he...selves ",,,,J.e "'illio"s by shov\selli" . I-he l"",,,,el-i,, sl-oc.... -rho"s",,,.As o{' wov"'evs losl-I-heiv li{'e-s"'vi,,~s bec",,,se o{' I-he co",p",,,y's .Aecepl-io". "'Theve is ",lve....Ay eviJ.e"ce I-h",1- sevev",l ",e,,\-s weve eil-hev shve.AJ.eJ. ov coveveJ. " ",cco""I-i"~ .Aoc,,- ~ WHY ESSAY #7 RECEIVED A SCORE OF 3 This limited essay demonstrates developing mastery. The writer offers a point of view ("l feel deception can be separated into two categeries: the justifiable decept ion that one must use to gain advantage in a competitive field. and the unjustifiable decep~ tion one uses at the expense of others for his or her own personal gain") but fails to provide adequate evidence to support this main idea. By compa ring a personal example of when deception is justified to the recent Enron scandal when deception caused harm to thousands of innocent people, the writer demonstrates some critical thin king. The writer displays a developing facility in the use of language. However, this response simply lacks the evidence to support the main idea or establish a progression of ideas. Therefore, the essay remains in the inadequate category and scored a 3. 210 Practice for the Writing Section Essay #8: This essay received a score of 2. I" I-v.e I",I-e seve"l-ee" v.",,,J.veJ.s, I-v.e A"'evic",,, colo"ies v.",J. e"l-eveJ. '" W"'V .pov i"J.epe"J.e"ce ",~",i"sl- I-v.e oppvessio" o.p ki" Geov . e III. Ge"ev",1 Geov e W",sv.i" 1-0" le",J.ev o.p I-v.e A"'evic",,, \-voops, e"'i'loyeJ. '" yo",,,~ """" 1-0 i"-llI\-v,,,l-e I-v.e Bvit-isv. Ii"es i" ovJ.ev 1-0 J.el-ev",i"e I-v.eiv ",v"'is posit-io". l1 WHY ESSAY #8 RECEIVED A SCORE OF 2 This spa rse response demonstrates little mastery. The writer develops a point of view ("deception ca n someti mes be justified") that is seriously limited by providing only insufficient evidence to support this position. The response demonstrates weak critical thinking by offeri ng the appropriate but brief example of Washi ngton's use of secrecy to win "freedom and liberty" for the American people. Although this response is focused, the writer fails to provide sufficient support to demonstrate a progression of ideas. Thus, the essay is seriously limited and scored a 2. 211 THE WRITING SECTION Essay #9: This essay received a score of 1. Decept-io" c"''' sOlMet-ilMes 'be j",st-i-lleJ.. Evevyt-it.i,,~ is sOlMehlMes ",Iw",ys j",st-i-lleJ., eve" t-it.i"~s yo", wo",IJ.,,'t- t-it.i,,\< ",,,hi yo", ve",ny 100\ o"e e""'lMPle t-it.",t- c"'lMe t-o lMi"J. w"'s it.ow o",v wovlJ. wov\ WHY ESSAY .9 RECEIVED A SCORE OF 1 This brief response demonstrates only very little mastery. Although there is a main idea present ("Deception can sometimes be justified"), the example of speeding offered as support is too unfocused to develop this point of view. Ideas Automated Score are d isorganized and unclear, resulting in a disjointed and incoherent To receive an automated score for your essay response online, check out The Official SAT Online Course at www.coUegeboard.com/ satonlinecourse. 212 essay. Furthermore, the response demonstrates severe fl aws in sentence struc ture. ("Like if someone was driving down the st reet and speeding." "Instead of putt ing him/her in jaiL") Consequent ly, this essay is fundamentally lacking and received a score of I. THE WRITING SECTION Answet Key Improving Sentences I. B 6. D 2. A 7. E 3. B 8. B 4. C 9. A 5. D Identifying Sentence Errors 10. A 15. C II. D 16. D 12. D 17. E 13. E 18. B 14. C Improving Paragraphs 19. B 22. B 20. E 23. C 2 1. D Additional practice questions can be found in The Official SAT Online Course at www.collegeboard.comlsatonlinecour••. 214 PART IV The Mathematics Section 215 CHAPTER 14 About the Mathematics Section Just about every part of your life requires math skills, and math skills will be especially important for success in college. The questions on the SAT emphasize mathematical reasoning and eva luate how well you can think through math problems. You will need to know some specific math concepts and math skills. The mathematics section evaluates how well you use these concepts and ski lls to solve real-life math problems. The mathematics section has the following questions: • 44 multiple-choice questions • 10 student-produced response questions, which require you to fill in a response The mathematics section has four categories of questions: 1. Number and operations (reviewed in Chapter 15) 2. Algebra and functions (reviewed in Chapter 16) 3. Geometry and measurement (reviewed in Chapter 17) 4. Data analysis, statistics and probability (reviewed in Chapter 18) Mathematics Reference Information The SAT mathematics section includes reference information. You may find these facts and formu las helpful as you answer some of the test questions, but don't let the reference in formation give you a fa lse sense of sec urity. It won't tell you how to solve math problems. To do well on the mathematics section, you have to be comfortable working with these facts and formulas. If you get a lot of practice using them before the test, you will be a lot more relaxed using them during the test. 217 THE MATHEMATICS SECTION jG Dw~ ~h E}b~ _ " A - ". .. 1 8 C:2n r ~ ~ ~ -'" t A=w I A=-2bh . V=lwh a c 2 :::a 1 +b 1 V:: Jrr 2h 2>~x ,I:A. ,.12 ~[~ x..[3 s Special Right Triangles TIle number of degrees of arc in a circle is 360. TIle sum of the measures in degrees ofthc angles of a triangle is 180. Example: Multiple Choice If2x+2x+2x= 12,whatisthevalueof2x-l? (A) (B) (C) (D) (E) 2 3 4 5 6 A"swer: The correct answer is (B). Chapter 19 gives you ideas on answering specific kinds of multiple-choice questions. Example: Student-Produced Response Student-produced response questions are not multiple choice. Instead, you must figure out the correct answer and fill it in on the answer sheet. St udent-produced response question s (also ca lled grid-ill questions) are solved just like any other math problems. Here's the same question presented above, but as a grid-in question . lf2x .... 2x .... 2x = 12, what is the value of 2x - I ? Answer: The answer is still 3, but instead of fi ll ing in choice (A), (B), (C), (0 ) or (E), you have to write "3" at the top of the grid and fill in the circle contain ing "3" below. I(.)I~ , 3 • •· ·• • ,• ,• 0 ' , , • • • • •, •, 0) ,• 1* 218 '. II About the Mathematics Section Note: No question in tllis format has an answer that is negative, greater than 9999 or irrational because there is no way to grid this response. Specific ideas on completing student-produced response questions are presented in Chapter 20. Approaches to Mathematics Questions )- Familiarize yourself with tile directions ahead of time. Also, learn how to complete the grids for student-produced response questions (see Chapter 20). )- Ask yourself the following questions before you solve each problem: • What is the question asking? • What do I know? )- Limit your time on anyone question. All quest ions are worth the same number of points. If you need a lot of time to answer a question, go on to the next one. Later, you may have time to return to the question you skipped. )- Keep in mind that questions are arranged from easy to hard. Within any group of questions - for example, the multiple-choice questions - the easier ones come first and the questions become more difficult as you move a long. If you find that the questions of one type are becoming too difficult, quickly read through the rest of the questions in that group to see if you can answer others. Then go on to the next group of questions in that sect ion. )- Don't make mistakes because of carelessness. No matter how frustrated you are, don't pass over questions wit hout at least reading them, and be sure to consider all the choices in each question. If you're careless, you could choose the wrong answers even on easy questions. Take each question as it comes and avoid careless mista kes by making sure you do the fo llowing: • Answer the question asked. For example, if the question asks for the area of a shaded region, don't give the area of the unshaded region. • Check that your answer makes sense. For example, is a discount higher than the original price? Is the average age of a high school student 56 years old? In both cases, obViously not - so think about your answer instead of just calculating automatically. Check your work from the beginning. If you can, use a different method from the one you used 10 get the answer. If you use the same method. you may make the same mistake twice. )- Work out the problems in your test booklet. You will not receive credit for anything written in the booklet, but you will be able to check your work easily later: • Draw figures to help you think through problems that involve geometric shapes, segment lengths, dista nces, proportions, sizes and so on . 219 THE MATHEMATICS SECTION • Mark key information on graphs, and add information to drawings and diagrams, as you work through the questions. • Mark each question that you don't answer so that you can easily go back to it later. )- Eliminate choices. If you don't know the correct answer to a question, try eliminating wrong choices. It's sometimes easier to find the wrong answers than the correct one. On some questions, you can eliminate all the incorrect choices. Draw a line through each choice as you eliminate it until you have on ly the one correct answer left. )- Make an educated guess whenever you can eliminate at least one' tHlswer choice. On multiple-choice questions, if you ca n eliminate even one incorrect answer choice, you increase your chances of getting a question right. With each correct answer choice, you gain one point; if you leave the answer blank you get no points; if you r answer is wrong you lose only one-fourth of a point. (t) )- Keep in mind that, on grid-in questions, you don't lose points for wrong answers. Make an educated guess if you don't know the answer. )- Always eIIter your answer by filling in the circles on the grid. One of the most important rules to remember about grid-in questions is that olllyanswers entered on the grid are scored. Your handwritten answer at the top of the grid isn't scored. However, writing your answer at the top of the grid may help you avoid gridding errors. Approaches to Finding the Right Answer If you absolutely can't figure out how to approach a problem, you may find it helpful, when appropriate, to try to answer the question either by substituting numbers or by trying each of the a nswer choices to determine the answer. Note that these approaches are quick fixes as you prepare to take the SAT and don't help you learn what you need to know to solve problems. Also, keep in mind that these approaches somet imes take considerable time. so keep track of your time and remember to pace yourself. )- Substitute numbers for variables. Some questions use variables (indicated by letters) to represent the values you are asked to consider. You can sometimes approach these problems by substituting numbers for the variables. For example, consider the follOWing question: 220 About the Mathematics Section Exa mple w+p o w+r In the triangle above, which of the following must he true? (A) p (C) p>r (D) p=O (E) r = 0 How to solve: Because the question involves p and r, try substituting a number for w. Then th ink about what you are given and what you know: • Suppose w = 3 . • Then the side opposite the angle measuring 70 0 has length 3 + r. • The side opposite the angle measuring 80 0 has length 3 + p. • Because 70 < 80, you know that 3 + r < 3 + P . • Sor )- Use each of the answer choices to help you solve a problem. Sometimes working through a question using the same format used in the answer choices will help you save time. For example. if the answer choices to a question are in the form of decimals, you may choose to do your work in decimals instead of fractions. This could save time because you won't have to convert you r answer to a decimal. Also, some questions can be answered by working backward from the answer choices. This approach is often useful when the question includes a condition that you ~can express in the form of a formu la - even a verbal one. (Keep in mind that this method can be time-consuming.) For example, look at the fol lowing multiple-choice question: Example If the product of three consecutive integers is equal to the middle integer, what is the LEAST of the three integers? (A) 2 (B) 1 (C) 0 (D) - I (E) - 2 221 THE MATHEMATICS SECTION How to solve: Use the answer choices to figure out which choice satisfies the conditions of the question: • Can the answer be (A)? If so, then it m ust be true that 2 x 3 x 4 ::: 3 (the middle integer). Clearly, this is not true. • Ask yourself the same question for the other choices. • When you get to choice (D), the consecutive integers ilre -I, 0 and L The product of these three integers is 0, which is the middle integer. • The correct answer is (D). Calculators Are Recommended You should bring a calculator to use on the mathematics section of the SAT. Every question on the PSAT/NMSQT and the SAT can be solved without a calculator; however, using a calculator on some questions may be helpfu l to students. A scient ific or graphing ca lcu lator is recommended . Using a calculator can help you avoid missing a question because of computation errors. Bring Your O w n Calculator You are expected to provide your own calculator. You may not use any of the following: • calculators that have QWERTY keypads (e.g., TI-92 Plus, Voyage 200) or have pen-input, stylus" or touch-screen capability • calcu lators that have wireless, Bluetooth, cellular, audio/video recording a nd playing, camera or any ot her cell phone-type feature • calc ulators that make noise or "talk," require a n electrical outlet or use paper tape • calculators that can access the Internet ~The use of the stylus with the Sharp EL-9600 calculator will not be perm itted. The Sharp EL-9600 remains on the list of approved graphing calculators. What to Keep in Mind When Using Calculators on the SAT 1. Bring a calculator with you when you take the SAT, even if you're not sure that you will use it. Calculators will not be available at your test center. 2. Practice on the calculator you plan to use before the test so that you're used to it. 3. Remember that all questions on the test can be answered without a calculator. Complicated or tedious calculations won't be requi red. 222 About the Mathematics Section 4. Don't buy an expensive. sophisticated calculator just for the test. If you already have one. though, that's fine. 5. Don't try to use a calcu lator on every question. Before you start using the calculator, think through how you will solve each problem. Then decide whether to use the calculator. , 6. Use common sense. The calculator is meant to help you in problem solving, not to get in the way. 7. Do scratch work in the test booklet before you use your calculator so that you'll get your thoughts down on paper quickly. 8. Check that you r calculator is in good working order and that its batteries (if needed) are fresh. If you r calculator fails during the test, you'll need to complete the test without it. 223 ® .1-'1.11 ::t : l 00 Recap 1. Familiarize yourself (ahead of time) with the directions and the reference information that will be on the SAT and that is shown at the beginning of this chapter. 2. Study the concepts and skills in Chapters 15 to 18, which cover mathematics reviews. 3. Bring a calculator that you know how to use fresh batteries. ~ and don't forget 4. Keep in mind that questions a re arranged from easy to hard. 5. Pace yourself. Don't spend too much time on anyone question. 6. Before you solve each problem, ask yourself: What is the question asking? What do I know? 7. Make notes in your test booklet: Draw figures to help you think through problems with geometric shapes, distances, proportions and so on. • Write out calculations to check later. • For questions that contain figures, note any measurements or values you calculate right on the figure in the test booklet. 8. Use the answer choices to your advantage - for example, look at the form of the answer choices if you can't figure out how to approach a problem. 9. Substitute real numbers for variables, to make the problem more concrete. 10. Make an educated guess when you can eliminate at least one incorrect answer choice in a multiple-choice question. 11. Remember that figures that accompany questions are drawn to scale unless otherwise noted. 12. However, if you're told that a figure is not drawn to scale, remember that lengths and angles may not be shown accurately. 13. Don't panic when you're faced with special symbols: read the definition carefully and use it as your instruction for working out the answer. 14. Take each solution one step at a time. Some seemingly difficult questions are really just a series of easy questions. 224 15. Keep in mind that the answer sheet will be scored by a computer, so you will receive credit only if you fill in the circles correctly on the student-produced response questions, (Although it 's not required, it's a good idea to write your answer in the boxes at the top of the column, t o help you fill in the circles correctly.) 16. Avoid careless mistakes. 17. Answer the question asked. 18. Check that your answer makes sense. 19. If you have time to check your work, t ry to rework your calculations differently from t h e way you first did them. 225 CHAPTER 15 Number and Operations Review Concepts You Need to Know Though you've been preparing for the mathematics section of the SAT all during your high school years, here's a chance to review what you know. For mathematics questions cover ing number and operations, you should be familia r with all of the following basic skills and concepts: • Properties of integers • Arithmetic word problems • Number lines • Squares and square roots • Fractions and rational numbers • Elementary number theory • Factors, multiples and remainders • Prime numbers • Ratios, proportions and percents • Sequences • Sets (u nion, intersection. elements) • Counting problems • Logical reasoning The SAT doesn't include • Tedious or long computations • Matrix operations 227 THE MATHEMATICS SECTION Properties of Integers You will need to know the fo llowing information for. some questions in the mathematics section: • Integers consist of the whole numbers and their negatives (including zero) . ...• -3, -2, - I, 0,1,2,3,4, ... • Integers extend infinitely in both negative and positive directions. The following are negative integers: -4, -3, -2,-1 The following a re positive integers: 1, 2, 3, 4 The integer zero (0) is neither positive nor negative. Odd Numbers ... ,-5,-3,-\, 1,3,5, ... Even Numbers ... , -4, -2, 0,2,4, ... The integer zero (0) is an even number. Consecutive Integers Integers that follow in sequence, where the difference between two successive integers is 1, are consecutive integers. Here are th ree examples of some consecutive integers: - 1,0,1,2,3 1001, 1002, 1003, 1004 -14, -13, -12,-11 The following is an expression representing consecutive integers: n, n + 1, n + 2, n + 3, ... , where n IS any integer. Addition of Integers even + even = even odd + odd = even odd + even = odd 228 Number and Operations Review Adding zero (0) to any number doesn't change the value: 8+0 = 8 -1+0= - 1 Multiplication of Integers even x even =even odd x odd = odd odd x even = even Multiplying any number by one (1) doesn't change the value: 3 x 1= 3 -lOxI =-1O Arithmetic Word Problems The SAT often has arithmetic word problems that do not require you to write down an algebraic equation or expression. Such questions test your ability to apply correct ly arithmetic operations in a problem situation. To solve these problems, you need to identify which quantities are being given, what is being asked for and which arithmetic operations must be applied to the given quantities to get the answer. Examples EXAMPLE 1 Ms. Griffen is making bags of Halloween treats. If she puts 3 treats in each bag, she will make 30 bags of treats and have no treats left over. If instead she puts 5 treats in each bag, how many bags of treats can she make? How to solve: If Ms. Griffen puts 3 treats in each bag, she makes 30 bags of treats. There are 30 x 3 = 90 treats in the bags and none left over. Therefore, Ms. Griffen has a lotal of 90 I reats. If Ms. Griffen puts 5 treats in each bag, she can make 90 + 5 = 18 bags of treats. EXAMPLE 2 Jorge bought 5 pencils from the store. He gave the cashier a five-dollar bill and got back$0.75 in change. Jorge saw that he had gotten too much change, and he gave $0.25 back to the cashier. What was the price, in dollars, of each pendl? How to solve: Jorge gave the cashier$5.00 for the 5 pencils, and he got $0.75 back. At this point, Jorge had 'paid$5.00 - 0.75 = $4.25. Then Jorge gave the cashier$0.25. 229

THE MATHEMATICS SECTION

Therefore, Jorge paid a total of $4.25 + 0.25 =$4.50 for the 5 pencils. Each pencil cost $4.50 + 5 =$0.90.

Number Lines A number line is used to graphically represent the relationships between numbers: integers, fractions or decimals. -6

-5

_4

-3

-2

-1

o

,

3

4

5

(

,

• Numbers on a number line always increase as you move to the right, and tick marks are always equally spaced. • Negative numbers are always shown with a negative sign (-). For positive numbers, the plus sign (+) is usually not shown. • Number lines are drawn to scale. You will be expected to make reasonable approximations of positions between labeled points on the line. Number line questions generally require you to figure out the relationships among numbers placed on the line. Number line questions may ask: • Where a number should be placed in relation to other numbers; • The difference or product of two numbers; • The lengths and the ratios of the lengths of line segments represented on the number line.

Example Here is an example of a number line question: A

-,

8

c

-1 .

o

a

E

F

G

,

3

4

On the number line above, the ratio of AC to AG is equal to the ratio of CD to which of the following?

BD

(C) CG (DI DF (EI EG

How to solve: In this quest ion, the number line is used to determine lengths: AC =2, AG =6, CD =1 . Once you have these lengths, the quest ion becomes a ratio and proportion problem.

230

Number and Operations Review

• The ratio of AC to AG is 2 to 6. • The ratio of AC to AG is equal to the ratio of CD to what? 2

I

· 6=x · x=3 Now you have to go back to the number line to find which of the given segments has length 3. Because AD = 3, the answer is (A).

r

0.425

0.430

The number line show n above is from a quest ion that appeared on the SAT. The question requires that you figure out the coord inate of point P. given that the tick marks are evenly spaced. The units of measure are thousandths. (The distance between adjacent tick marks is 0.001.) Point P has coordinate 0.428 on this number line.

~epinMind The dist ances between tick marks on II number line m ay not be m easured in w hole units.

Squares and Square Roots Squares of Integers Although you ca n always figure them out with paper and pencil or with your calculator. it's helpful if you know or at least can recognize the squa res of integers between - 12 and 12. Here they are:

,

I

2

3

I

4

9

-I

-2

-3

I

4

9

4 16

5

6

25

36

7 49

B

9

to

64

BI

100 121 144

II

12

-4 -5 - 6 -7 -B -9 -10 -II - 12 16 25 36 49 64 BI 100 121 144

You ca n see, for example, that S2 =2S and ..J64 =8. Your knowledge of common squares and square roots may speed up your solution to some math problems. The most common types of problems fo r which this knowledge will help you will be those involving: • Factoring andlor simpli fying expressions • Problems involving the Pythagorean theorem (a 1 + b1 = 2) • Areas of ci rcles or squares

231

THE MATHEMATICS SECTION

Squares of Fractions Remember that if a positive fraction with a value less than 1 is squa red, t he result is always smaller than the original fraction: I(O

Then n 2 < n

Try it. What are the values of the following fractions?

~ and 614' respectively. Each of these is less than the original fraction.

4 2 For example, "'9 < 3'

Fractions and Rational Numbers You should know how to do basic operations with fractions: • Adding, subtracting. mu ltiplying and dividing frac tions • Reducing to lowest terms • Fi nding the least common denominator • Expressing a value as a mixed number (2t) and as an improper fraction

(t)

• Working with complex fractions - ones that have fractions in their numerators or denom inators You shou ld know that a rational number is a number that can be represented by a frac tion whose numerator and denominator are both integers (a nd the denom inator must be nonzero). The following are rational numbers:

1

2

15

"4

3

(or 3.)

_ll 13

5

T (or 5) As you can see from the last example, every integer is a rational number.

232

Number and Operations Review

Decimal Fraction Equivalen ts You may have to work with decimal frac tion equivalents. That is, you may have to be able to recognize common fract ions as decimals and vice versa. To change any fraction to a decima l, divide the numerator by the denominator. Although you can figure out the decimal equivalent of any fraction (a calculator will help here), you'll be doing yourself a favor if you know the following: Fraction

1 4

Decimal

0.25

2

2

3

3

3

4

0.3~

0.5

0 .6~

0.75

!

1

"The bar notation indicates that the 3 and the 6 repeat infinitely.

Reciprocals The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 5 is Note that 5 x = l. The product of a number and its reciprocal is always I.

t

t.

Here is another example: The reciprocal of

to

t is I divided by t, which is equal

t. Note that you can find the reciprocal of any nonzero fraction by switching its

numerator and denominator. How do you find the reciprocal of2t? Write it as an improper fract ion: 2t Now sw itch the numerator and denominator: the reciprocal of 2t is

t.

=~.

You can also find the reciprocal of a negative number. For example, the reciprocal of -2 is _~ =

-to

Note that the reciprocal of a negative number is negative.

The number zero (0) has no reciproca l. The number 1 is its own reciprocal. Also, the number - I is its own reciproca l.

Place Value and Scientific Notation The number 123 can be written as 100 + 20 + 3 or as (I x IO l ) + (2 X 10 1) + (3 x I). The digit I stand s for 1 times 100; the d igit 2 stands for 2 times lOj and the digit 3 stands for 3 times 1. We say these digits have the follOWing place values: I is in the hundreds place. 2 is in the tens place. 3 is in the units (ones) place. Every digit in a decimal number has a place value. The nex t places to the left of 123 are the thousands place, the ten-thousands place, the hundred-thousands place, the millions place and so on. Digits to the right of the decimal point also have place values. For example 0.56 =0.5 + 0.06 =(5 x 10- 1) + (6 x 10-2 ); the digit 5 is in the tenths place, and the digit 6 is in the hundredths place.

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THE MATHEMATICS SECTION

Sometimes, usi ng t he concept of place value ca n lei you write a very big or small number in a much shorter form. For example: 2,300,000,000,000 = 2.3 x lOll 0.0000000007 = 7 x to-IO

Because such numbers often occur in scientific calculations, writi ng a number as t he product of a power of 10 and a number greater t ha n o r equal to 1 and less than 10 is called scientific notatiot!.

Elementary Number Theory Factors, Multiples and Remainders On the SAT, you'll find questions that requi re you to understa nd and work with these three related concepts: factors. mu ltiples and remainders. FACTORS

The factors of a number are positive integers t hat can be divided evenly into t he

number - that is, without remainder. For instance, consider the number 24: The nu mbers 24, 12,8,6, 4,3,2 and I are all factors of the number 24. Each of these numbers can be d ivided even ly into 24 with no remainder. The term divisible by mea ns divisible by without any remainder or with a

remainder of zero. For instance. 15 is divisible by 5 because 15 divided by 5 is 3 with a remainder ofO. But 15 is not divisible by 7 because 15 divided by 7 is 2 with a remainder of 1.

Com mon fa cto rs: Common factors are factors that two (or more) numbers have in common. For instante, 3 is a common facto r of 12 and 18. The largest com mon factor of two (or more numbers) is called their greatest commotl factor (GCF). For example, 6 is the GCF of 12 a nd 18. MULTIPLES

The multiples of any given number are those numbers that ca n be d ivided by that given number without a remainder. You can find the mu ltiples of a n umber by mu ltiplying it by 1, 2, 3, 4 and so on. For instance, 8, 16. 24, 32. 40 and 48 are some of t he mu ltiples of8. Notice that the multiples of 8 are also multiples of2 and 4 (factors of8). Remember, the mu ltiples of any nu mber wil l always be mult iples of all the factors of that number. For instance: • The numbers 30, 45, 60 and 75 are all m ultiples of the nu mber 15. • Two factors of 15 are the numbers 3 and 5. • That means that 30, 45, 60 and 75 a re all multiples of 3 and 5.

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Number and Operations Review

Common multiples; Suppose you have two (or more) numbers. Any number that is a multiple of all the given numbers is called a common multiple. For instance, 48 and 96 are both common multiples of 8 and 12. The smallest multiple of two (or more) numbers js called their least common multiple (LCM). For example, 24 is the LCM of8 and 12.

Examples EXAMPLE 1 What is the least positive integer divisible by the numbe rs 2, 3, 4 and 5?

How to solve: • To find one example of a number that is divisible by several other numbers, multiply those numbers together. You could multiply 2 x 3 x 4 x 5 and the result would be divisible by all those factors. • But the question asks for the least positive number divisible by all four (in other words, the LCM of the four numbers). To find that, you have to eliminate any extra factors. • Any number divisible by 4 will also be divisible by 2, so you can eliminate 2 from your initial multiplication. If you multiply 3 x 4 x 5, you will get a smaller number than if you multiply 2 x 3 x 4 x 5, and the number will still be divisible by 2. • Because the remaining factors (3, 4 and 5) have no common factors, the result of 3 x 4 x 5 will give you the answer. So 3 x 4 x 5 = 60 is the least positive integer divisible by 2, 3, 4 and 5. EXAMPLE 2 Which of the follow ing cou ld be the remainders when four consecutive positive integers are each divided by 3? (A) (8) (C) (D) (E)

1,2,3,1 1,2,3,4 0, 1,2,3 0,1,2,0 0,2,3,0

How to soLve: Remember, the question asks only for the remainders. • When you divide any positive integer by 3, the remainder must be less than or equal to 2. • All the choices except (0) include remainders greater than 2, so (0) is the only possible correct choice. If the first and fourth of the consecutive integers are multiples of3, the remainders will be 0,1,2 and O. Exam ining only the rema inders of numbers is sometimes called modular arithmetic.

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THE MATHEMATICS SECTION

EXAMPLE 3

Does the equation 3x + 6y= 47 have a solution in which x and yare both positi"e integers?

How to solve: Note that 3x + 6y = 3(x + 2y). Therefore, fo r any positive integers x and y. the sum 3x + 6y = 3(x + 2y} is a mUltiple of 3. But 47 is not a mu ltiple of 3. Therefore, no matter what posit ive integers you choose for x and y. the sum will not be 47. Thus. the equation 3x + 6y = 47 does not have a solution in which x and yare both posit ive integers. This question is an example of a Diophantine equation - that is, it is an equat ion with integer coefficients for which you arc seeking integer solutions.

Prime Numbers A prime nu mber is a positive integer greater than 1 that has exactly two wholenumber factors - itself and the number l. The number I itself is not prime. The fi rst eight prime numbers are: 2,3,5,7, Il, 13, 17, 19 (Note that 2 is the on ly even prime number.)

Prime factors: Prime fac tors are the factors of a number that are prime numbers. That is, the prime fac to rs of a number cannot be factored further. For example, the prime factors o f the number 24 are 2 and 3. 24=2x2x2x3

Ratios. Proportions and Percents A ratio expresses a mathematical relationsh ip between two quantit ies. Specifically, a ratio is a quot ient of those qua ntities. The following are all relationships that can be expressed as rat ios: • My serving of pizza is

t of the whole pie.

• There are twice as ma ny chocolate cookies as va nilla cookies in the cookie ja r. • My brother earns $5 for each$6 I earn . The preceding ratios can be expressed in several different ways. They can be stated in words: • The ratio of my serving of pizza to the whole pie is one to four. • The rat io of chocolate to vanilla cookies is two to one. • The ratio of my brot her's earnings to mine is five to six.

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Number and Operations Review

They can be expressed as fract ions:

.I

4

2

'T

.5

6

They can be expressed with a colon (:). as follows: • 1:4

· 2:1

· 5:6 Or they can be expressed using the word to: • I to 4 · 2 to I

· 5 to 6 A percent (%) is a ratio in which the second quantity is 100: for example. I got 75 percent of all the questions right. (The ratio of questions I got right to all the questions .

IS

75 )

100.

A proportion is an equation in which two ratios are set equal to each other. YOli may be asked to answer questions that require you to set up a proportion and solve it.

Examples EXAMPLE 1

The .....eight of the tea in 100 identical tea bags is 8 ounces. What is the weight, in ounces, of the tea in 3 tea bags?

How to solve: You solve this problem using a proportion, which is two ratios set equal to each other. Start by setting up two ratios. • The ratio of the tea in 3 tea bags to the tea in 100 tea bags is 3 to 100 (or

I~O).

• Lei x equal the weight, in ounces, of the tea in 3 tea bags. • The ratio of the weight of the tea in 3 tea bags to the weight of the tea in 100 tea bags is x ounces to 8 ounces

(i).

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THE MATHEMATICS SECTION

The ratio of x ounces to 8 ounces is equal to the ratio o f 3 to 100:

x_ 3

"8- 100 iOOx = 24

x = 120~ or 0.24 Therefore t he weight of the tea in 3 tea bags is 0.24 ounces. EXAMPLE 2

You may find questions that involve ratios in any of the following situations: • Lengths af line segments • Sizes of angles • Areas and perimeters • Rate/time/distance • Numbers on a number line You may be asked to combine ratios with other mathematical concepts. For instance:

The ratio oftne length of a rectangular floor to its width is 3:2. If the length oftne floor is 12 meters, what is the perimeter of the floor, in meters?

How to solve: The ratio of the length to the width of the rectangle is 3:2, so set that ratio equal to the ratio of the actual measures of the sides of the rectangle: l_ length 2 - width

l=ll 2

x

3x= 24 x = 8 (the width)

Now that you have the width of the rectangle. it is easy to find the perimeter: 2(length + width) = 2(12 + 8). The perimeter is 40 meters.

Sequences A sequence is an ordered list of numbers. Some sequences follow a specific pattern. For example, the sequence 3,7, 11, 15, ...

follows the pattern add 4. That is, each term in the sequence is 4 more than the one before it. The first term is 3, the second term is 7 and, in general, if n is a positive integer,

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Number and Operations Review

the nth term in this sequence is 3 + 4(n - I). The three dots ( ... ) indicate that this sequence goes on forever. Not all sequences go on indefinitely. The sequence 2,4,6, ... ,22,24 contains even numbers only through 24, where the sequence ends. The mathematics section will include geometric sequences, which are sequences for which there is a constant ratio between consecutive terms. For example. 7,21,63, 189, ...

is a geometric sequence in which the first term is 7 and the constant ratio is 3. Note thatl!. = 3 63 = 3 and 189 = 3 7

'21

63'

For any positive integer n, the nth term of this sequence is 7 x 3"-1. These sequences have real-life applications. and there may be questions in the mathematics sect ion using geometric sequences in contexts such as population growth. Because the nth term of geometric sequences can be written using exponential notation. the growth of such sequences is somet imes called exponential growth. The mathematics section does not ask you to figure out the rule for determ ining the numbers in a sequence without giving the information in some way. For instance, in the preceding example. if you were given that the nth term of the sequence was 7 X 3"-1 , you may be asked to determine that each term after the first was 3 times the term before it. On the other hand, if you were given that the first term in the sequence was 7 and that each term after the first was 3 times the term before it, you might be asked to find that the nth term of the sequence was 7 x 3"-1 . Number sequence questions might ask you for the following: • The sum of certain terms in a sequence • The average of certain terms in a sequence • The value of a specific term in a sequence

Sets (Union. Intersection. Elements) A set is a collection of things. and the th ings are called elements or members of the set. Questions in the mathematics section might ask about the union of two sets (Le .• the set consisting of the elements that a re in either set or both sets) or the intersection of two sets (i.e.• the set consisting of the common elements). For example, if set A = /2, 4, 6, 8, lO} and set B = {8, 10, 12, 14} then the union of sets A and B would be {2, 4, 6, 8,10, 12, 14}

and the intersection of sets A and B would be {8, to}.

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THE MATHEMATICS SECTION

Counting Problems Counting problems involve figuring out how many ways you can select or arrange members of groups, such as letters of the alphabet, numbers or menu selections.

Fundamental Counting Principle The fundamental counting principle is the principle by which you figure out how many possibilities there are for selecting members of different groups: If one event can happen in n ways, and a second, independent event can happen in m ways, the total ways in which the two events can happen is n times m. For example: On a res taurant menu, there are three appetizers and four main courses. How many different dinners can be ordered if each dinner consists of one appet izer and one main course?

• The first event is the choice of appetizer, and there are three choices available. • The second event is the choice of main course, and there are four main courses. • The total number of different dinners is therefore 3 x 4 = 12. This idea can be extended to more than two events. If you had two choices for beverage added to your choices for appetizer and main course, you would multiply the total by 2:

2x3x4=24

If you also had three choices for dessert, you would multiply by 3: 3x2x3x4=72

Permutations and Combinations If )'ou select member after member from the same group, the number of possible choices will decrease by 1 for each choice. Some counting problems involve permutations. A permutation of a set is a reordering of the elements in the set. A security system uses a four-letter password, but no tetter can be used more than once. How many possible passwords are there? • For the first letter, there are 26 possible choices - one for each letter of the alphabet. • Because you cannot reuse any letters, there are only 2S choices for the second letter (26 minus the letler used in the first letter of the password).

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Number and Operations Review

• There are only 24 choices for the third leiter, and only 23 choices for the fourth. The total number of passwords will be 26 )( 2S )( 24 )( 23. If the order in which the members are chosen makes no difference, the counting problem involves combinations. For example: There are 12 st udents in the school theater class. Two students will be responsible for finding the props needed for the skit the class is performing. How many different pairs of students can be chosen to find the props? • The first student chosen can be any of the 12 students. • The second student chosen can be any of the 11 remain ing students. • Suppose Amy and Juan are in the class. There are two ways Amy and Juan could be chosen: Amy first and Juan second, or Juan first and Amy second. • To get the answer, you first multiply 12 by 11 to get the number of ways of choosing a pair of students, and then you divide by 2 because each pa ir of students can be chosen in two different ways. The answer is 66.

Logical Reasoning Some mathematics questions emphasize logical thinking. You have to figure out how to draw conclusions from a set of facts.

Exsmple Here's an example:

c In the figure above, ci rcular region A represents the set of all numbers of the form 21n, circular region 8 represents the set of all numbers of the form ,,1 and circular region C represents the set of all numbers of the form 10k, where In, nand k are positive integers. Which of the following numbers belongs in the set represented by the shaded region? (A) (8) (C) (D)

2 4

JO 2S

(E) 100 How to solve: Answering this question correctly depends on understanding the logic of the figure.

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THE MATHEMATICS SECTION

• The question is asking about the shaded region. • The shaded region is part of all of the ci rdes. • Therefore. any numbers in the shaded region have to obey the rules for all the circles: The ru le for A: The numbers must be of the form 2m, which means that they must all be even numbers. And the rule for B: The numbers must be of the form /1 2 , which mea ns that they must all be perfect squares. And the rule for C: The numbers must also be of the form 10 k , which means they have to be some whole-number power of 10 (10, 100. 1,000, 10,000, etc.). • When you realize that the numbers in the shaded area must obey all the individual ru les, yOli have figured out the logic of the question, and the answer is easy. The only choice that obeys all the rules is 100. The answer is (E).

242

CHAPTER 16

Algebra and Functions Review

Concepts You Need to Know Many mathematics questions require a knowledge of algebra. This chapter gives you

some further practice. You have to manipulate and solve a simple equation for an unknown. simplify and evaluate algebraic expressions, and use algebraic concepts in problem-solving situations. For the mathematics questions covering algebra and functions content, you should be familia r with all of the following basic skills and topics: • Operations on algebraic expressions • Factoring • Exponents • Evaluating expressions with exponents and roots • Solving equations • Determining if an equation has a solution • Solving for one variable in terms of another • Solving equations involving radical expressions • Absolute value • Direct translation into mathematical expressions • Inequalities • Systems of linear equations and inequalities • Solving quadratic equations by factoring • Rational equations and inequalities • Direct and inverse variation

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THE MATHEMATICS SECTION

• Word problems

• Functions • Function notation and evaluation • Domain and range • Using new definitions • Functions as models • Linear functions: their equations and graphs • Quadratic functions: their equations and graphs • Qualitative behavior of graphs and functions Translations and their effects on graphs of functions The SAT does not include: • Complex numbers • Logarithms • Trigonometry

Operations on Algebraic Expressions You will need to be able to apply the basic operations of arithmetic - addition, subtraction, multiplication and division - to algebraic expressions. For example: 4x+5x=9x IOz-3y-(-2z)+2y= 12z-y (x+3)(x-2)=x'+x-6

l ~? = 5x

Factoring The types of factoring included on the mathematics sect ion are: • Difference of two squares: a 2 _ b2 = (a + b)(a - b) • Finding common factors, as in:

r

+ 2x =x(x+ 2)

2x+4y=2(x+2y)

• Factoring quadratics: x' - 3x- 4 = (x- 4)(x+ I)

r

244

+ 2x + I = (x + 1)(x + 1) = (x + 1)2

Algebra and Functions Review

You are not likely to find a question instructing you to "factor the following expression." However, you may see questions that ask you to evaluate or compare expressions that require factOring.

Exponents Definitions

1.1 P P

'r

'r:: ( vx)~ x -l>=vx"=

"nd

Three Points to Remember I. When multiplying expressions with the same base, add the exponents: a 2 • a 5 = (a . a)(a . a . a . a . a)

= a'

Th is rule also holds for exponents that are not positive integers:

t5 •

r 2 = (t·

t· t . t· t) .

(t· t)= t

3

2. When dividing expressions with the same base, subtract exponents: / r.r.r.r.r , = '-'-'-'-'''--'--'-'- = r 2 r r· r· r

3. When a number raised to an exponent is raised to a second exponent, multiply the exponents:

(a mt = amI!

245

TH E MATHEMATICS SECTION

Evaluating Expressions with Exponents and Roots

,

You will need to know how to evaluate expressions involving exponents and roots. For instance: If y ::: 8, what is y1" ? 2

lr.:;

J~

y 3=VS- = v 64=4

,

Here is an example afhow to work the reverse problem. If x T = 64, what is the value of x?

,

,

By the rules of exponents, xi = (X l)! = 64.

,

Taking the cube root of both sides of this equation, you find x T ::: 4. Squaring both sides, you get x = 16.

Solving Equations Most of the equations that you will need to solve are linear equations. Equations that are not linear can usually be solved by factOring or by inspection.

Working with " Unsolvable" Equations At first, some equations may look like they can't be solved. You will find that although you can't solve the equation, you can answer the question. For instance: If a + b = S. what is the value of2a + 2b? You can't solve the equation a + b = 5 for either a or b . But you can answer the question: • The question doesn't ask for the value of a or b . It asks for the value of the entire quantity 2a + 2b .

• 2a + 2b can be factored: 2a + 2h = 2(a + b) a+b=5 You a re asked what 2 times a + b is. That's 2(a + b) = 2 x 5 = 10.

Solving for One Variable in Terms of Another You may be asked to solve for one variable in terms of another. Again. you're not always going to be able to find a specific, numerical value for all of the variables. For example: If3x+ y= z, what isx in termsofyand z?

246

Algebra and Functions Review

You aren't asked to find a numerical value for x. You are asked to manipulate the expression so that you ca n isolate x (put it by itself) on one side of the equation. That equation will tell you what x is in terms of the other variables: · 3x+y=z

• Subtract y from each side of the equation. 3x=z-y

• Divide both sides by 3 to get x.

'-=1' x =-----yThen x in terms of y and z is ~.

Solving Equations Involving Radical Expressions The expression 5..& is a radical expression because it involves a root; in particular, the square root of x. The equation S..Jx + 14 = 29 is a radical equation because it involves a radical expression. You can solve this equation: 5'" + 14 = 29

5'" = 15

"'=

3 x=9

~epinMind Be careful when solving radical equations such as ..[X 5 . There is one solution to this equation: 25. (However, there are two solutions to the equation x2 25 : 5 and -5.)

=

=

Absolute Value Being familiar with both the concept and notation of absolute value will be helpful to you when solving the mathematics questions. The absolute value of a number is its distance from zero on the number line. The absolute va lue of the number w is denoted Iwi. For example, 16.51 = 6.5 and 1-321 = 32. You can think of the absolute value of a number as the "size" of the number, disregardi ng whether it is positive or negative. You may be asked to work with expressions and solve equations that involve absolute value. For example, you can solve the equation 17 - II = 10 by thinking of it as either: 7-t=1O

or

i

-(7 - t) = 10

r

I

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THE MATHEMATICS SECTION

In the first case: 7-t=1O -t=

3

r =-3 In the second case: -(7-1}=1O

-7 + t = 10 t = 17 $0,t=-30rt= 17. Direct Translation into Mathematical Expressions Many word problems requ ire you to translate the verbal description of a mathemat icai fact or relationship into mathematical terms. Always read the word problem ca refully a nd double-check that you have translated it exactly. For example: ~eplnMind Be especially careful with sub- traction and division because the order of these ope rations is important. 5 - 3 is not the same as 3 - 5 . Addition and multiplication are commutative, but subtraction and division are not! "3 times the quantity 4x + 6" translates to 3(4x + 6). "A number y decreased by 60" translates to y - 60 . "S iess than a number k" translates to k - 5 . "x less than 5" translates to 5 - x . "20 d"ddb IVI e yn ",20 15--;:;- , "20 divided into a number y" is [0 . See the "Keep in M ind" ideas in the Word Problems section of this chapter. Inequalities An inequality is a statement that one quantity is greater than or less than a nother. Inequalities are show n using four symbols: • Greater than : > 5 >3, 1 > -2 • Greater than or equa l to: 2= 7 32=2, 4+5 2= 9 0<1. -7 <-6 • Less than: < • Less than or equal to: S 8- 4 248 5 s: 5, "2 s 2.5 Algebra and Functions Review Most of the time, you can work with si mple inequalities in exact ly the same way you work with equalities. Consider the following: 2x+I>11 If th is were an equation. it would be pretty easy to solve: 2x + I = II 2x = ll -l 2x = 10 x=5 ~ePinMlnd Remember that multiplying or dividing both sides of an inequality by a negative number reverses the direction of the inequality: If - x < 3,thenx >-3. ¥ou can use a similar process to solve inequalities: 2x+I > 11 2x> I I - I 2x > 10 x>5 Systems of Linear Equations and Inequalities ¥ou may be asked to solve systems of two or more linear equations or inequalities. For example: For what values of a and b are the following equat ions both true? a + 2b = I -3a-8b= 1 You can solve this system of equations by el iminating one of the variables. Say you decide to eliminate h. Multiply both sides of the fi rst equation by 4: 4a+8b =4 - 3a-8b = 1 Adding the Iwo equations gives: -3a- J =4-4a a=5 Substituting a = 5 into the original equation gives 5 + 2b = I . ¥ou ca n solve this equation to find b = -2 . The answer is that the fi rst two equations are true if a = 5 and b = -2 . 249 THE MATHEMATICS SECTION Solving Quadratic Equations by Factoring You may be asked to solve quadrat ic equations that can be factored. (You will not be expected to know the quadratic formula.) For instance: For what values of x is r - lOx + 20 = -4 ? Add 4 to both sides of the equation to get a standard quadratic equation: x! - lOx + 24 = O. Now factor: r - lOx+24=D (x - 4)(x - 6) = 0 Therefore, either x - 4 = 0 or x - 6 = O. The values x =4 and x = 6 satisfy the original equation. Rational Equations and Inequalities A rational algebraic expression is the quotient of two expressions. An example is 3y+ 5 y-2 You may be asked to solve equations or inequalities involving such expressions. For example: For what value of x is the following equation true? x-I 3=2x+3 Multiplying both sides by 2x + 3 gives 3(2x+3)=x-l 6x+9=x - l 5x =-10 x = -2 Direct and Inverse Variation The quantities x and yare directly proportional if y = kx for some constant k. For example: x and yare directly proportional. When the value x is 10. Y is equal to -5. Ifx= 3, what isy? Because x and y are directly proportional, y = kx for some constant k. You know y is -5 when x is 10; you can use th is to find k. y= kx -5 = k(lO) k= -t So, the equation is y = -tx . When x = 3, you get y = (-t)(3) = -~. 250 Algebra and Functions Review The quantities x and yare inversely proportional if y =! for some constant k . For x example: If xy = 4. show that x and yare inversely proportional. Divide both sides of the equation xy = 4 by x: y=ix Therefore. x and yare inversely proportional, with k = 4 . Word Problems Some mathematics questions are presented as word problems. They requ ire you to apply math skills to everyday situations. With word problems you have to: • Read and interpret what is being asked. • Determine what information you are given. • Determine what information you need to know. • Decide what mathematica l skills or formulas you need to apply to find the answer. • Work out the answer. • Double-check to make su re the answer makes sense. When checking word problems. don't substitute your answer into your equations, because they may be wrong. Instead, check word problems by checking your answer with the original words. Translate as You Read As you read word problems. translate the words illto mathematical expressions and equations: • When you read "Jane has three dollars more than Tom," translate to J = T + 3 . • When you read "the average (arithmetic mean) of the weights of three children . IS 80 pounds," translate to a+b+c 3 = 80 . • When you read "Jane buys one clown fish and two guppies for$3." translate to c+2g=3. When you've finished reading the problem, you will have already translated it into mathematical expressions and equations. Table 16.1 will help you with some of the more common phrases and mathematical translations:

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THE MATHEMATICS SECTION

Table 16.1 Mathematical Expressions

Worda

Symbol

Translation

15, was, has: The number of days Jane worked is the number of days Tom worked.

J=T

More than, older than, farther than, greater than, sum of:

+

Jane has 2 more dollars than Tom.

+

J=2+ TorJ=T+2

Tom ran 10 mil es farther than Jane.

T=10+JorT=J+10

The sum of two integers is 36.

Lass than, difference, younger then, fewer;

Subtraction

Tom has 5 fewer marbles than twice the number Jane has.

T = 2J - 5 (Don't make the ~5 - 2J" mistake!)

The difference between Tom's height and Jane's height is 22 centimeters.

Multiplication 20% otTom's socks are red. Jane ata

%

R=.2)( T

%of the candy.

For. per:

Jane won 3 games for every 2 thatTom won.

ratio

Division

+

J:::: 3 T

2

50 miles per hour

50 miles/hour

2 bleeps per revolution

2 bleeps/revolution

Examples Figuring out these problems takes more than just knOWing all of the formulas. You have to th ink about what sk ills and tools you will apply to the questions in order to reason your way through to the correct answer. EXAMPLE 1 'The price of a sweater went up 20% since last year. If last year's price was x, what is this year's price in terms of x?

How to solve: • Last year's price,=, 100% of x • This year's price is 100% of x plus 20% of x . x+20% ·x=x+O.2x'=' 1.2x

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Algebra and Functions Review

EXAMPLE 2

One year ago, an average restaurant meal cost $12. Today, the average restaurant meal costs$15. By what percent has the cost of the average restaurant meal increased?

How to solve: You can figu re percent increase by taking the difference in prices first and then expressing it as a percentage of the original price: $15 -$12 = $3 d ifference What percentage of the original price is$3? 3 x TI = 100 12x = 300 x= 2S

The cost increased by 25%. Or you can figure what percent the new price is of the old price: IS is what percent of 12?

15=(1~0)12 15

TI =

x 100

x= 125

Therefore, IS is 125 percent of 12. This tells you what percent the current price ($15) is of the old price ($12). But the question asks for the percent increase, so you have to subtract 100 percent from 125 percent. 125% - 100% = 25% increase

EXAMPLE 3

The average height (arithmetic mean) of 4 members of a 6-person volleyball team is 175 cm. What does the average height in centimeters of the other 2 players have to be if the average height of the entire team equals 180 cm?

How to solve: Start with the formula for the average: Sum of values Number of values = average Use what you know to find out the sum of the heights of the 4 members whose average is 175 cm. Sum of heights 4

175

Sum of heights = 4(175) = 700

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THE MATHEMATICS SECTION

The average of all 6 players is 180 em. Average 0 f6 payers 1

'h . h sum of 4 players' heights + sum 0£2 players' heights clg Is ::: 6 180 =

700 + sum of 2 players' heights 6

1080 ::: 700 + sum of 2 players' heights 1080 - 700::: sum 0£2 players' heights 380::: sum 0(2 players' heights What is the average of the heights of the 2 players? sum Average::: number of players Average = 3~O

= 190 em EXAMPLE 4 A car traveling at an average rale of 55 kilometers per hour made a trip in 6 houTs. Ifit had traveled at an average rale 0(50 kilometers per hour, the trip would have taken how many /til/lUtes longer?

How to solve: • How long was the trip?

Distance ::: rate x time Distance ::: S5 kph x 6 hours Distance ::: 330 km • How long does the 330-kilometer tr ip take if the car is traveli ng at SO ki lometers per hour? ' _ d istance T Ime rate , 330km Tlme= 50 kph Time = 6~ hours • What does the question ask? The difference ill minutes between the two trips, Difference = ~ hour Difference = x minutes 3

x

5= 60 = 180 x = 36 minutes

5x

254

Algebra and Functions Review

Examples The test may include quest ions that involve quantit ies that are directly proportional to each other and quantities that are inversely proportional to each other. Look at the next two examples: EXAMPLE 1 The number of juice packs that Rambling Pines Day Camp buys each day is directly proportional to the number of children at the camp that day. If the camp bought 150 juice boxes yesterday for 60 children. how many juice boxes will they buy today for 52 children?

Howto solve: If two quantities x and yare directly proportional (another way to say this is that one varies d irect ly wit h the other), then there is a constant k for which y = kx. In this case, the number of juice boxes varies directly with the number of children. There are 150 juice boxes when there are 60 children: ISO = k(60)

(j.ep in Mind

You can solve for k to get 5

k=Z What does the question ask? How many juice boxes for 52 child ren? 5

Recall that two quantities x and yare inversely proportional if there is a nonzero constant k for which y:::

!.

k x 52 = '2 x 52 = 5 x 26 = 130

The camp will buy 130 juice boxes for 52 children. EXAMPLE 2 If c and d are inversely proportional and c = 10 when d:::: 6, what is d when c = 30?

How to solve: The quantities c and d are inversely proport iona l, so

,

d=! for some constant k. Because c :::: 10 when d = 6, you get

k

6=\0and so k = 60. You now can find d when c =30 :

60 d =30 =2 So d= 2 when c= 30.

255

THE MATHEMATICS SECTION

Functions Function Notation Bnd Evaluation A function can be thought of as a rule or formula thai tells how to associate the elements in o ne set (the domain) with the elements in another set (the range), For example. the squaring function can be thought of as the rule "take the square of x" or as the rule;c. You should be familiar w ith function notation. The squari ng function can be written in funct ion notation asJ(x) = x?-. Function notation lets you write complicated funct ions much more easily. For example, you ca n write that the funct ion g is defined by g(x) = J" + ~. Then g(2) = 32 +

-t

= 9t·

Domain and Range • The domain of a function is the set of all the va lues for which the function is defined . • The range of a function is the set of all values that are the output, or result, of applying the function. EXAMPLE What are the domain and range of j(x) = I +.fX ?

How to solve: The domain of I is the set of all values of x for which the formula I + ...Jx' is defined. This formula makes sense if x is zero or a positive number. But if x is negative, I is not defined, the square root of a negative number is not a real number. Therefore, the domain ofI(x) = I + -.fX is all nonnegative numbers x . What is the range off? In other words, what is the set of all possible values of fix) = ~ + -JX ? A square root is always nonnegative, so every value ofI must be at least 1. The question now remains: Is every number r 2: 1 equal to 1(5) for some 5 ? Let's try a va lue, say r = 9. /(5)=I+is=9 is =8 5

= 64

You can see that for any r;:: I, you can find 5 such that r = f(5) : f(5) = I +is =r

-.JS =r-

I

5=(r-l)2

So, the range oflis all numbers greater than or equal to I.

256

Algebra and Functions Review

y

8 7 6 range

5 4

3 y =/(x)_ I

2

-< -s

-4

-3 -2 - 10

2

3

4

S

6

+-IX

7

,

- 1

domain

-2 -3 -4

-s

-< -7

Using New Definitions For functions. especially those involving more than one variable. a special symbol is sometimes introduced and defined. §) so you won't conThese symbols generally have unusual looking signs (-tT, fuse them with standard mathematical symbols. The key to these questions is to make su re that you read the definit ion carefully. A typical special symbol quest ion might look something like this:

*,

w

x

z

y

Let ~--1'--~ =

wy - xz

where w, x, y and z are integers.

What is the value of ~--1I--c7' 4

257

THE MATHEMATICS SECTION

To answer this question, substitute the numbers according to the definition: • Substitute 2 for

W,

3 for x, 4 for

z and

1 for y.

3

" E------1f----7

= (2)(1) - (3)(4) = -10

Some questions will ask you to apply the definition of the symbol to more complicated situations. For instance: • You may be asked to compare two values, each of which requi res the use of the symbol. • You may be asked to evaluate an expression that involves mult iplying, dividing, adding, squaring or subtracting terms that involve the symbol. • You may be asked to solve an equation that involves the use of the symbol.

Functions as Models Functions can be used as models of real-life situations. Here is an example: The temperature in City X is W(t) degrees Fahrenheit t hours after sundown at 5:00 p.m. The function Wet) is given by W(,) = 0.1 (400 - 40, + f) for 0 <,

< 12

You can draw a graph of this fUnction:

I: ~

3 20

o

1C

E 10

~

o

258

2

3

4

7 6 Time (hours)

5

8

9

10

II

12

Algebra and Functions Review

Linear Functions: Their Equations and Graphs You may be asked to answer quest ions involving linear equations and their graphs. Therefore. you will need to understand the concepts of slope and intercepts: y = mx + b. where m and b are constants, is a linear function. and the graph of y = mx + b in the xy-plane is a line with slope m a nd y-intercept b.

For example: y p

e

In the figu re above. points A. Band C lie on a vertical line segment that intersects line at B and line pat C. OA = 1. DE = I, BA = I and BC = 2 . What are the coordinates of the point D where lines and p intersect?

e

The slope of

e

e is ~~

= 1 . Because

e passes through the origin, its equation is

y=x.

You can find the slope of p in a few ways. For instance, it is ~~ = 2 . The y-intercept of pis 1. and so the equation of pis y = 2x + 1 . From the equations of lines dinates (-1. - 1).

eand p, you can see their intersection at D has coor-

Quadratic Functions: Their Equations and Graphs You may be asked to answer questions involving quadratic equations and their graphs. You will need to be able to identify some of the basic features of the graph of a quadratic equation. such as its highest or lowest point, its zeros and its direction.

259

THE MATHEMATICS SECTION

For example, which of t he following is the graph of y = -x?- - 1 ? (A)

( 8)

(C)

( D)

(E)

\

) I

\

Because the square of any number is nonnegat ive, -:xl - 1 must always be a negative number. This eliminates all choices except (8) and (E). The largest value of y must occur when x = O. This eliminates (E). The correct answer is (6).

Qualitative Behavior of Graphs Bnd Functions You will need to understand how the properties of a function and its graph are related. For example, the zeros of the function f are given by the points where the graph of f(x) in the xy-plane intersects the x-axis. Or you could be asked a question such as the followin g: The graphs of y = j(x) and y = 2 are shown below. (Note th at

the domai n of the fun ction f is the interval from x = -3 to x = 4 .) For how many va lues of x doesf(x) = 2?

26 0

Algebra and Functions Review

,• ,

,

• -,~-,h~~TT~~r ' -6 -S ~ -3-2-1 0 2)4S67

-,

-, -,

The value offix) equals 2 exactly when the graph of y = fix) has height 2. This graph has height 2 at the points where it intersects the line y = 2 . The figure shows that there are three points of intersection, so you know thatj(x) = 2 for three values of x .

Translations and Their EHects on Graphs of Functions You may be asked question s on the 'effects of simple translations on the graph of a function. For example, if you are given the graph ofg(x), you should be able to identify the graph of g(x + 3) . For example: The graph of y = j(x) is shown below.

,

,• , , ,• , ,

-,~-.-:.-,~~~~c-, ,~,,".~,'-T,-;,- ·· -' -, '0

--

-,

-, -, -, -' -,

'"

-,--

• 261

THE MATHEMATICS SECTION

Which of the following could be the graph of y = l(x - 1) ? (A)

.... -S ....

(B)

·' l -'O .,

....

(e)

~

.... -3 _/

-'0.,

I

I

l

,

6

1

.... -S ... -J _I " 0

.,

., -,

'

I

I

,

1

-'0-, '

I

I

,

1

-,

., "

"-, .,

"

~

(D)

(E)

• •

-6 -S ....

-J _I

-'0-,

-,

-,

I

I

J

,

1

-
,

....

...J _I

~

-,

The graph of y = l(x - 1) is the graph of y = fix) sh ifted 1 unit to the right. The correct choice is (E). You can also check the values of the functions at specific points. The original graph shows that!(3} = O. Therefore, the graph of y = l(x - 1) m ust contain the poi nt (4,0). Only the graphs in (C) and (E) contain (4,0). Butj(O) = 1 . Therefore, the graph of y = I(x - I) must contai n the point (1, 1); the graph in (C) doesn't contain (1, I), so the correct answer is (E).

262

........... Geometry and Measurement Review ",..

,

Concepts You Need to Know For the mathematics questions covering geometry and measurement concepts, you should be familiar with all of the following basic ski lls, topics and formulas: • Geometric notation • Points and lines • Angles in the plane • Triangles (including special triangles) • Equilateral triangles • Isosceles triangles • Right triangles and the Pythagorean theorem

• 30°_60°_90° triangles • 45°_45°_90° triangles • 3-4-5 triangles • Congruent triangles • Similar triangles • The triangle inequality • Quadrilaterals • Parallelograms • Rectangles • Squares • Areas and perimeters • Areas of squares and rectangles • Perimeters of squares and rectangles • Area of triangles • Area of parallelograms

263

THE MATHEMATI CS SECTION

• Other polygons • Angles in a polygon • Perimeter

• Area • Circles • Diameter

Tangent to a circle • Circumference

• A rea • Solid geometry • Solid fi gu res and volumes • Surface area • Geometric perception • Coord inate geomet ry • Slopes, paraUellines and perpendicular lines • The m idpoint formula • The dista nce formula • Transformations The SAT doesn't include: • Formal geomet ric proofs • Trigonometry • Radian measure

264

Geometry and Measurement Review

Geometric Notation You will need to be able to recognize and use geometric notation for points and li nes, line segments, rays, angles and t heir measures, and lengths.

e

)'

6 m

5 E 4 p

M

2 8 -6 - 5 -4

- 3 -2

2

3

4

5

6

x

-2 -3 -4

-5 -6

In the figure above. the xy-coordinate plane has origin O. The values of x on the horizonta l x-ax is increase as you move to the right, and the values of yon the vertical y-axis increase as you move up. Line contains point P, which has coordinates

e

(- 2, 3), and point E, which has coord inates (0, 5). Line m passes through the origin 0(0,0) and the point Q (I, I). Unes and mare parallel - they never meet. This is written ell m. You will also need to know the mean ing of the follOWing notation:

e

el

PE

the line containing the points Pand E (this is the same as line

PE

the line segm ent with endpoints P and E

PE

the length of the line segment PE (you can write PE '" 2.J2)

fiE

the ray starting at P and extending infinitely in the direction of E

EP

the ray starting at E and extending infinitely in the direction of P

L ODC

the angle formed by 00 and OC

mL ODC

the measure of L ODe (you can write mL DOC ", 90°)

flOaC

the triangle with vertices 0 , C and

8PMD

the quadrilateral with vertices 8, P, M and

8P .l PM

the relation that 8Pis perpendicular to PM (you should also recognize that the small square within L BPM means this is a right angle)

a a

265

THE MATHEMATICS SECTION

Points and Lines There is a unique line that contains any two distinct points. Therefore, in the following diagram, line

eis the only line that contains both point A and point B . ---------c.~--------~.c_--------

A

B

e

The midpoint of a line segment is the point that div ides it into two segments of equal length. The diagram below shows the midpoint M of line segment AB .

A

e

B

M

Because M is the midpoint of AB, you know that AM = MB. You will also need to understand how to add the lengths afline segments along the same line. For example. in the following diagram, PR = PQ + QR = 2 + 3 = 5 .

P 2 Q

3

e

R

You may also be given the lengths afline segments along a common line and be asked a question that requires you to find the order of points along the line.

Example Points E, Fand G all lie on line m, with E to the left of F. EF"" 10, FG "" 8 and EG:> FG. What is EG?

How to solve: You can start to solve the problem by drawing the foJlowing d iagram ofEandFonm.

r-- 10 E

266

-----1 •

F

m

Geometry and Measurement Review

The diagram uses the given information that E is to the left of F and that EF = 10 . Now the question is where to place point G on m. You a re given that FG = 8, but is G to the left or to the right of F? Try putt ing G to the left of F. Using FG =8, you get the following diagram.

f - - IO- - j • • • F E2G S

m

In the diagram, EG = 2 . But you are given that EG must be greater than FG, and in the diagram, EG < FG. Therefore, G cannot be to the left of F . This means G must be to the right of F, as shown below.

s--1

f - - IO •

I

E

F

G

m

1-1- - - IS - - - I

Now EG > FG, as required. Therefore, this diagram shows the correct order of points E, F, and G along line m, and EG = 18 .

Angles in the Plane In order to work th rough some of the mathematics questions, you will need to know the basic facts about the angles formed in a plane by lines, line segments and rays .

• Vertical angles and supplementary angles. Two opposite angles formed by two intersecting lines a re called vertical angles.

65"

115'

Vertical angles have the sa me measure. In the figu re above.y = 115 and x = 65. Note that any pa ir of angles next to each other in the figure have measures that add up to 180°. (This is the measure of a straight angle, the angle formed by a straight line.) Two angles whose measures have a sum of 180° are called supplementary angles.

267

THE MATHEMATICS SECTION

• Para lie/lines. When a line intersects a pair of parallel lines. the eight angles formed are related in several ways .

a

. bO

CO dO e

.r

8· hO

e

m

The measures of corresponding angles are equa l; fo r example, a and e arc equal, as arc d and h. Also. several pairs of angles each add up to a straight angle; for example, d +f = ISO and a + g = 180. Finally, alternate interior angles have equal measures; in the fi gure, c and! are equal, as arc d and e .

• Righi angles, perpendicular lines, and complementary angles. A right angle is an angle wit h a measure of90", If two lines intersect and one of the four angles formed is a right angle, the lines are perpendicular. In this case, a ll four angles that are formed a re right angles. Two angles whose measures have a sum of 90° are called complementary angles.

Triangles (Including Special Triangles) The sum of the measures of the angles in any triangle is 180°.

Equilateral Triangles The three sides of an equilateral triangle (a, b, c) are equa l in length. The three angles are also equal, and they each measure 60° (x = y = z = 60).

C

268

Geometry and Measurement Review

Isosceles Triangles An isosceles triangle is a triangle with two sides of equal length (m = n). The angles opposite the equal sides are also equal (x = y).

Right Triangles and the Pythagorean Theorem A right triangle is a triangle with a right angle. {Note that the other two angles in a right triangle are complementary angles.} You can get a lot of information from figures that contain right triangles. This information frequently involves the Pythagorean theorem: The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

B

c

a C

A b

The hypotenuse is the longest side of the triangle and is opposite the right angle. The other two sides are usually referred to as legs. In the figure above: • AB is the hypotenuse with length c .

• BC and AC a re the two legs, with lengths a and b, respectively. • The Pythagorean theorem leads to the equation: 2

a +b

2

=r

• If you know the lengths of any two sides, you can use the Pythagorean theorem to find the length of the third side.

269

THE MATHEMATICS SECTION

The lengths of the sides of a 30°-60°-90° triangle are in the ratio of 1:..[3 : 2. as shown in the figure: • Short leg = x

• Long leg = x..J3 • Hypotenuse = 2x

B

o x-i3

2x

A

60"

C

x

If you know the lengths of anyone side, you can find the lengths of the other two sides. For instance, if you know the length of the short leg is 1, then the length of the hypotenuse is 2. and the Pythagorean theorem gives you the length of the longer leg:

c2=a 2 +b 2 c=2,b=I 22 =a Z + 1 4=a 2 + 1 3 = a2 ,f3 = a

The lengths of the sides of a 45°_45 0 _90° triangle are in the ratio of 1:1:..J2. as shown

in the figure below. To verify this ratio when the equal sides are of length 1. apply the Pythagorean theorem to find the length of the hypotenuse:

B

xfi

x

45 " AL.:!"-------'-1C

c=a

+b 2 a = I, b = 1

2=

2

}2+ 12

2=1+1

c=2

,= fi

270

Geometry and Measurement Review

3-4-5 Tr;snglss The sides of a 3-4-5 right triangle are in the ratio of 3:45. For example, in the figure below, if x = 2, the sides of the triangle have lengths 6, 8 and 10. It is easy to use the Pythagorean theorem to verify this:

ov1:

A~C 4x 2=a 2 +b 2

102 = 62 +8 2 100 = 36+64 100 = 100

Congruent Triangles Congruent triangles are triangles that have the same size and shape.

, A

E

B y'

,

s

s

D ~x,-·___--,-___-"Z~' F

t

{

c In the figure, each side of MBC has the same length as the corresponding side of llDEF. AB=D£=r

BC=EF=s CA = FD = t

Each angle of MBC is also equal to its corresponding angle in llDEF . Two triangles a re congruent if a ny of the following is true: • Each pair of correspond ing sides has the same length. • Two pairs of corresponding sides each have the same length, and the angles fo rmed by these sides have the same measure. • One pair of corresponding sides has the same length, and two pairs of corresponding angles each have the same measure.

271

THE MATHEMATICS SECTION

Similar Triangles Similar triangles have the same shape. Each corresponding pa ir of angles has the same measure.

B y'

16

E

10

sA,

DL----.iF

A L-~------b~------~C

7

In the figure, rnLA = mLD, rnLB = mLE and mLC = mLF. An important fact about similar tria ngles is that the ratio of the lengths of any pair of correspondi ng sides is the sa me. (In other words. the lengths of corresponding sides are in propor6 tion.) For example, in the figure 18 = ISO. We can also find b in the figure: 16

b

8="7 Sb = 112 b = 14

Two triangles are similar if • Two pairs of corresponding angles each have the same measure . • One pair of corresponding angles has the same measure, and the pairs of correspondi ng sides that for m those angles have lengths that a re in the same ratio.

The Triangle Inequality The triangle inequa lity is an important fact about triangles. It states that the sum of the lengths of any two sides of a triangle is greater than the length of the thi rd side. E

9

DL-------,,-------'F 13

In the figure. forexampie, 9 + 13> DE . Therefore. you know DE must be less than 22.

272

Geometry and M easurement Review

Quadrilaterals In some special quadrilaterals - parallelograms. rectangles and squares - there are relat ionships among the angles and sides that can help you solve geometry problems.

Par allelograms In a pa rallelogram, the opposite angles are of equal measure and the opposite sides are of equal length. Angles A and C are equal, and angles Band D are equal. AB = CD and AD = BC.

Rectangles A rectangle is a special case of a parallelogram. In rectangles, all the angles are right angles.

Squares A square is a special case of a rectangle in which the lengths of all the sides are equal.

Notice that if you know the length of any side of a square. you also know the length of a diagonal. A diagonal makes two 45 0 _45 0 _90 0 triangles with the sides of the square. You can figure out the lengths of the sides from the length of a d iagonal or the length of a diagona l from the length of a side.

8[2J: A

,

273

THE MATHEMATICS SECTION

~eplnMlnd

Areas and Perimeters

Remember the reference infor-

mation . Fonnulas for areas of common figures are given in

the reference material that is printed in the test booklet.

Areas of Rectangles and Squares The formula for the a rea of any rectangle is:

Area = length x width

B

e

r----"----,

C

• A'-------'0

Because all sides of a square a re equal. the length and width are often both referred to as the length of a side. s. So, the area of a square can be written as: Area =

s-

Perimeters of Rectangles and Squares The perimeter of a polygon is the sum of the lengths of its sides. Because the opposite sides of rectangles are equa l, the fo rmula for the perimeter of a rectangle is: Perimeter of a rectangle = 2{length + width) = 2(C + w) The same is true for any parallelogram. For a squa re, it's even easier. Because all four sides of a squa re are equal, the perimeter of a square is: Perimeter of a square

Area of Triangles The area of a triangle is:

274

=4{length of any side) =4$Geometry and Measurement Review • b is the base. &-ep In Mind • h is the height, a perpend icu lar segment drawn from a vertex of the triangle to the base. Arsa of Parallelograms To find the area of a parallelogram, you drop a perpendicular - segment BE in the figu re shown below. Th is makes a right triangle ABE . If you take this triangle away from the pa rallelogram and add it to the ot her side (6.DCF), you have a rectangle with the same area as the original parallelogram. The area of the rectangle is length x width. The width of this rectangle is the same as the height of the para llelogram, so the formula for the area of a para llelogram is: You can start with anv verte Kof the triangle. The side opposite the vertex you choose becomes the base and the perpendicular line from that vertex to the seg· ment becomes the he ight. For instance, the area of the triangle in the figure could be calculated using point A as the vertex instead of point B. Area == length x height B,, -__-C~"~g'~h____ C ij heighl !! • U~E~-------!; D 'O F Other Polygons Occasionally, a question will ask you to work with polygons other than triangles and quadr ilaterals. A regular polygon is a polygon whose sides all have the same length and whose angles all have the same measure. Here are a few other things to remember about other polygons. Angles in a Polygon You can fig ure out the tota l nu mber of degrees in the interior angles of most polygons by divid ing the polygon into triangles: • From any vertex, d ivide the polygon into as many nonoverlapping triangles as possible. Use only straight lines. Make sure that all the space inside the polygon is divided into tria ngles. • Count the tria ngles. In th is figure, there are four tria ngles. 275 THE MATHEMATICS SECTION • There is a total of 180" in the angles of each triangle. so multiply the number of triangles by 180. The product will be the sum of the angles in the polygon (720" in the hexagon shown below). ':--. '. ", .. . Sid •• . '" " ·· Interior Angle Sum 3 4 5 540 0 6 720" n 180(n - 2) Example ~B~~ __________________~C \''2". A~~-------------~~Z~'YD In the figure shown above. lengths AB, BD and CD are all 3-./2 units. Angles A and C are both 45". What is the perimeter of ABeD? What is the area of ABeD? How to solve: You are asked for the perimeter and the area of the figure. For the perimeter you will need to know the lengths of Be and AD. For the area you will also need to know the heights of f}.ABD and t.BCD. PERIMETER • You are given the lengths of3line segments, all of which arc the same: 3-12. • You are given two angles, both of which have the same measure: 45°. • t.ABD is a triangle with two equa l sides. 276 Geometry and Measurement Review • 6.BCD is a triangle with two equal sides. • Therefore, they are both isosceles triangles. • The measure of angle C is 45°, so y = 45, because angles opposite equal sides are equaL • In the same way, you can show that z = 45. • Both triangles are 45°_45°_90° triangles. • You can figure out the lengths of AD and BC by the Pythagorean theorem: AD' = (3-./2)' + (3-./2)' = 36, so AD = 6 • Do the same for the length of BC to find that BC = 6 . • You can now add up the lengths of the sides to gel the perimeter: 2(6 + 3-./2) = 12 + 6-./2. AREA • ABCD is a parallelogram. You know thiS because both sets of opposite sides are equal: AB = CD and AD = Be. • That means that you ca n use the formula for the area of a pa rallelogram: area = length x height. • To find the height, drop a perpendicular from B . • That creates another 45°_45°_90° triangle whose hypotenuse is AB. • The ratio of the sides of a 45°_45°_90° triangle is l:l:..J2 . • From that ratio, you know the height of the figure is 3. • With the height, you can then ca lculate the area: 3 x 6 = 18. If you label everything you figure out as you go along, you will end up with a figure that looks like the one below. 6 277 THE MATHEMATICS SECTION Circles Diameter The diameter of a circle is a line segment that passes through the center and has its endpoints on the circle. All diameters of the same circle have equal lengths. Radius The radius of a circle is a line segment extending from the center of the circle to a point on the circle. In the figure shown below, DB and OA are radii. All radii of the same ci rcle have equal lengths, and 'the radius is half the diameter. In the figure, DB = OA. A C Arc An arc is a part of a circle. In the figure above, the points on the circle from A to B form an arc. An arc can be measured in degrees or in units oflength. If you form an angle by drawing radii from the ends of the arc to the center of the circle, the number of degrees in the arc (arc AB in the figure) equals the number of degrees in the angle formed by the two radii at the center of the circle (LAOB), called the central angle. Tangent to a Circle A tangent,!? a circle is a line that intersects the circle at exactly one point. In the figure, line AC is a tangent. A tangent to a circle is ahvays perpendicu lar to the radius that contains the one point of the line that touches the circle. In this case, OA.l AC. Circumference The circumference is the d istance around a circle, and it is equal to diameter, d (or Jr times twice the radius. r). Circumference = ltd Circumference = 2Jrr 278 1r times the Geometry and Measurement Review If the diameter is 16. the circumference is 16Jr. If the radius is 3. the circumference is 2(3)Jr, or 6Jr. d , Area The area of a circle is equal to Jrtimes the square of the radius. Area = Jr, 2 Example In the figure shown below, A is the center of a circle whose area is 2511'. B and Care points on the circle. The measure of angle ACB is 45°. What is the length of line segment Be? B How to solve: • Point A is the center of the circle. • That makes both AB and AC radii, which means that they have equal length. • Because AB = AC, MBC is an isosceles triangle. The angle opposite AB has a measure of 45°. • That means the angle opposite the other equal side is also 45°. • The remaining angle is 90°. • The area of the circle is 25Jr. • The formula for the area of a circle is Jrr 2 • You can use that fo rmula to figure out the length of the radius, r. • That length, r. is also the length of the legs of the triangle whose hypotenuse (BC) has the length you are trying to figure out. 279 L - - _ _ _ __ __ __ _ THE MATHEMATICS SECTION • , A L-;''''~ C What is the value of r ? Area = 25n = 25 rrr trr =" S=r • , A ,--,;.",,--' , 1c Figuring out the final an swer to the problem is a simple matter of working through the Pythagorean theorem or remembering that the ratio of the sides of 45°_45°_90<> triangles is 1:1:'-'2. The answer is s..J2. Solid Geometry Solid Figures and Volumes You may be asked questions about the basic Iypes of solids: cubes. rectangular solids. prisms. cylinders, cones, spheres and pyramid s. You will be given the for mulas for the volume of a recta ngula r solid and a right ci rcular cylinder in the Reference Information box in the SAT. You a re not expected to memori ze complicated formu las involving solids, but you may be asked questions that require logic and applying you r knowledge in new ways. Cubes and rectangular solids. The simplest type of solid is a cube. Every edge of a cube has the same length. If the edge length of a cube is 5, then the volume of the cube i s~. 280 Geometry and Measurement Revi ew I""'1----+-[,,""'---" ,, ,, , ~"------------,,----"'--"" , Note that the dashed lines indicate edges of the cubes that a re hidden from your view. Remember, on the SAT, you will be told if a figure does not lie in a plane. Just because you see a dashed line in a figure does not mean it is a solid. In a rectangular solid. the length, width and height may be different. f--/-----{I h II- L--_"_----" The volume is given by the formu la V = Cwh . Prisms and cylinders. A rectangular solid is one example of a right prism, which is a solid in wh ich two congruent polygons are joined by rectangular faces that are perpendicular to the polygons. The congruent polygons are called the bases of the prism, and the length of an edge joining the polygons is called the height, even if the prism is not standing on its base. T height A prism may be named after its polygonal base: for example, triangular prism, hex- agonal prism. 281 THE MATHEMATICS SECTION The volume of a prism is given by the product of its height and the area of its base. You should also be familiar with a right circular cylinder, a solid in which two congruen! ci rcles are joined by a curved surface that meets the circles at a right angle. , h In the figure. r is the radius of the circular base, and h is the height of the cylinder. (As with a prism, this length is called the height and the circles are called the bases, no matter how the cyli nder is o riented.) The volume of a right circular cylinder is given by the for mula V;:; nrh ; note t hat this is the same as the a rea of the base times the height. Spheres, cOll es and pyramids. You might see spheres, cones or pyramids in a question. ~ ' " :i, . _., -r" " . " Sphere Cone '. Pyramid A sphere is the solid analogue of a circle. All radii of a sphere are equal. A circular cone has a circular base, which is connected by a curved surface to its vertex. If the line from the vertex of the circular cone to the center of its base is perpendicu lar to the base, then the cone is called a right circular cone. A pyramid has a base that is a polygon, which is connected by tria ngu lar faces to its vertex. If the base is a regular polygon and the triangu lar faces are all congruent isosceles triangles, then the pyramid is called a regular pyramid. 282 Geometry and Measurement Review Surface Area If you make cuts in a sol id that allow you to open it up to form a plane figure, the result is called a net of the solid. A solid may have many different nets. The figure below shows one net for a cube. x x x x Sometimes, you can find the surface area of a solid by working with one of its nets. For example, from the net of the cube with edge length x, you can see its su rface consists of six squares, each with side x. The surface area of the cube is the sum of the areas of these six squares, which is 6r. Geometric Perception The SAT may ask you quest ions that require you to visualize a plane figure or a solid from different views or orientations. These are questions in geometric perception. For example: B A Blue c The wire frame above is made of three wires permanently joined together: a red wire. a blue wire and a green wire. Three beads, labeled. A, Band C, are attached to the frame so that each of them can move all around the frame. However, none of the beads 283 THE MATHEMATICS SECTION can be taken off the frame, nor can they be moved past one anot her. Which of the following configurations cannot be reached by sliding the beads around the frame or changing the position of the frame? (A) (B) Green Red--.. c Green ___ R,d B c A A B Blue Blue (D) R,d Green Red--.. A B B A Blue Blue c (E) Blue ___ R,d c A B Green The configuration in (A) can be reached by sliding each bead clockw ise to the next wire piece. The configurat ion in (C) can be reached by sliding each bead counterclockwise to the next wire piece and then flipping the frame over. The configuration in (D) is reached simply by sliding bead A clockw ise to the green wire. The configurat ion in (E) comes from turning the wire frame a th ird of a revolution clockwise. The configuration in (8) cannot be reached no matter how you slide the beads or rotate and flip the frame. The correct answer is (B). 284 Geometry and Measurement Review Coordinate Geometry Slopes, Parallel Lines and Perpendicular Lines Some of the geometry questions on the test will involve points, lines and figures in the coord inate plane. For example, you may be given the equat ion y = ~ x + 2 and be asked which of five lines in the coordinate plane has a graph parallel to the graph of that equation. Two of the choices m ight look like th is: y y and Because the line that is the graph of y = i x + 2 has slope t, you would choose the second of the choices above because the slope of the line in that figu re is ~. Lines in the xy-plane are parallel exactly when their slopes are equal. You sho uld also know the following fact about slopes: Two lines are perpendicula r when the product of thei r slopes is - I. For exa mple, look at the fi gu re below: y e 4 -2 In -3 -4 285 THE MATHEMATICS SECTIO N Line eis the graph of y = 2x . It has slope 2 and passes through P (I, 2) . Line m is the graph of the equation y = - ~ x . It has slope The product of the slopes of lines -+ and passes through Q (-2, 1) . eand m is -1. Therefore, it should be true that lines eand m are perpendicular. Triangles aBO and PAD are congruent, so x = w. ¥ou know z + w = 90, so you can conclude that z + x = 90 . That implies LQOP is a right angle. So lines and m are indeed perpendicular. e The Midpoint Formula You might also be asked to find the midpoint afline segments in the coordinate plane. If AB has endpoints A (3,4) and B (7, 8), then th~ midpoint of AB has coordinates (3;7, 4;8)=(5,6) The midpoint (x"" y"J is simply the average of the x's and average of the y's: Xl +Xl Yl = x'" 2 + Y2 2 = Ym The Distance Formula In the coordinate plane, the Pythagorean theorem can be used to find the d istance between any two points. For example, you can find the distance between A (I, 2) and B (4, 6), as indicated in the figure below: y 8 7 B (4.6) 6 , 4 3 2 -<; -, -4 -3 -2 -I 0 -I -2 -3 -4 -, -<; -7 288 A (1.2) C (4,2) Geometry and Measurement Review Clearly, MBC is a right triangle, AC = 3, and CB theorem: = 4 , Applying the Pythagorean AB2 = 32 + 4 2 'AB 2 = 25 AB=5 In genera l, if (XI' YI) and (X2' ' 2) are two points in the coordinate plane, the distance between them is given by the formula: d = ..J(x 2 - XI)2 + (Y2 _ YI)2 Transformations Understanding the concepts of simple geometric transformations - translations, rotations and reflections - will help you work through some of the mathematics questions, A translation moves a shape without any rotation or reflection, For example, the square on the left has been translated 2 units up (that is, in the positive y-d irection) to get the square on the right. , , 8 8 , , 7 , l , 7 , l , --c-~c-~~~~~~-+~~~o-~. --6 -~ -4 -3 -2 - \ 0 1 2 3 4 ~ 6 7 _I -, -l L-..J -- -, -4 -l -, - 10 -I -, -l -4 -, -, -- -- -7 D -7 287 THE MATHEMATICS SECTION Rotating an object means turning it around a point, which is called the center of rotation. For example, when the dock face on the left is rotated 90° counterclockwise, the result is the dock face on the right: 12 • 6 To reflect an object means to produce its mirror image with respect to a line. which is called the line of reflection. The figure below shows a triangle reflected A mirror image is produced on the other side of the line. across the line e. e If you reflect a figure twice across the same line. you get back the original figure. Look at the figure below to review the concept of symmetry: no < i ) The dashed line m divides the hexagon into two halves. If the left half is reflected ac ross line m, the result is the right half - and vice versa. In other words, if you 288 Geometry and Measurement Review reflect the hexagon across line m, the result is the sa me hexagon. The hexagon is said to be symmetrica l about the line m, and m is called a line of symmetry for the hexagon. A geometric figure may have more than one line of symmetry (for example, a recta ngle), or it may have no lines of symmetry. There is another type of symmet ry. Look at the rectangle below, with poi nt P at its center: •p If you rotate the rectangle 180 0 (clockwise or cou nterclockwise) around P, then the result is the same rectangle. The rectangle is said to be symmetric around the point P, and P is ca lled a point of symmetry for the rectangle. Note that symmetry about a line and symmetry about a point are different properties. A given figure may have either type of symmetry and not the other, or it may have both types of symmetry (for example, a circle) or neither type. 289 CHAPTER 18 Data Analysis Statistics and Probability Review I Concepts You Need to Know For the mathematics questions covering data analysis. statistics and probability concepts, you should be familiar with all of the following basic skills and topics: • Data interpretation • Statistics • Arithmetic mean • Median • • • • Mode Weighted average Average of algebraic expressions Using averages to find missing numbers • Elementary probabil ity • Geometric probability The SAT doesn't include • Computation of standard deviation Data Interpretation Your primary task in these questions is to interpret information in graphs, tables or charts. and then compare quantities, recognize trends and changes in the data, or perform calculations based on the information you have found. You should be able to understand information presented in a table or in various types of graphs. 291 THE MATHEMATICS SECTION Circle Graphs (Pie Charts) MUNICIPAL EXPENSES FOR THE TOWN OF WESTON IN 2004 ,... Police Schools Depanmenl 23 % S~W Removal 6% NO Dcpanmcn~ 12% Sanitation Depanment 15% Waler Supply Other Exp"nses 18% 6% The pie chart above shows the percentages of its total expenditures that Weston spends on va rious types of expenses. Suppose you are given that Weston's total expenses in 2004 were$10 million, and Y,ou are asked for the amount of money spent on the police department and fire department combined. You can see that together these two categories account for 23% + 12% = 35% of the town's expenses. Therefore, Weston spends 35% 0($10 million =$3.5 million on the police and fire departments combined.

Line Graphs Information can be displayed in a line graph. Below is an example of a double line graph that shows the high and low temperatures in Weston for the first seven days of February. 45 40

High

Low

E 20

~E

~ 15

10

Feb. I Feb. 2 Feb.3 Feb.4 Feb. 5 Feb.6 Feb. 7 Date

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Data Analysis. Statistics and Probability Review

From the graph you ca n see, for example, that on February 5 the high was 25 degrees Fah renheit a nd the low was to degrees Farenheit. So you also know that the difference between the high a nd low temperatures on that day was 15 degrees Fahrenheit.

Bar Graphs Bar graphs can also be used to present data. The bar graph below shows the amount of snow that fell each day in Weston for the first seven days of February. For example, you can see that no snow fell on February 2 and that 6 inches of snow fell the next day.

8 7

r5

r-

3

r-

2

rI

I Feb,

Feb.

Feb.

Feb.

Feb. Feb.

Feb.

1234567 Date

Pictographs A pictograph presents data using pictorial symbols. For example, the pictograph below shows the number of snowpeople built each day in Weston during the fi rst seven days of February. For example, you can see that 40 snowpeople were built on February 7 and that about 25 were built the day before. Dale

Number of Snowpeop\e

February I February 2 February 3 February 4 February 5 February 6 February 7

[j = \0 snowpcople 293

THE MATHE MAnes SECTION

There is another type of graph you may see on the SAT: a scatterplot. Scatterplots will be discussed a little later in this chapter. The questions you are asked may require you to do more than read the data pre-

sented in a graph or chart. A question on a graph like the one shown below m ight require you to identify specific pieces of information (data), compare d ata from dif-

ferent parts of the graph and manipulate the data.

,, _

COMI'AR!$O,' l OF MONTHLY PROFITS When working with data interpretation questions, you have to: • Look at the graph , table or chart to make sure you understand it. Make sure you know what type of information is being displayed. • Read the labels. • Make sure you know the units. • Make SUfe you understand what is happening to the data as you move through the table, graph or chart. • Read the question carefully. Examples The graph below shows profits over time. The greater the profits, the higher the point on the vertical axis will be. (Each tick mark on the vertical axis is another$1,000.) As you move to the right along the horizontal axis, months are passing.

,, _

COMPA RISON OF MONTltlY PROFITS

:g •

"0 ~

,, ., .1

~I

'-

~,"+-~-4--r-~~

'"

~~

f

~

s

1. In what month or months did each company make the greatest profit?

How to solve: Follow the line labeled Company X to its highest point. Then check the month at the bottom of the graph. Follow the same procedure for Company Y.

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Data Analysis. Statistics and Probability Review

For Company X, the greatest profit was made in April. For Company Y, the greatest profit was made in May. 2. Between which two consecutive months did each company show the greatest increase in profit?

How to solve: The increase (or decrease) in profit is shown by the steepness, or slope. of the graph. For Company X, it's easy to see that the biggest jump occurred between March and April. For Compa ny Y, you have to be a little more careful. The biggest increase in profits occurred between January and February. You know this because the slope of the line connect ing January and February is the steepest. The increase between January and February is about $},500, which is greater than the increase for any other pair of consecutive months. 3. In what month did the profits of the two companies show the greatest difference? How to solve: To figure th is out, you have to compare one company to the other, month by month. The month in which the points are farthest apa rt is the one in which there is the greatest difference between the two companies. The distance between the two graph points is greatest in April. CO'IPARISO:O: OFMO~THLY PROFITS if • ~ , ,• ,," , ~ 0 ~ , :? i ,- --. /-"• ,, " )j' , 0: ~ ,> ~ 4. If the rate of increase or decrease for each company conti nues for the next six months at the same rate shown between AprH and May, which compa ny would have higher profits at the end of that time? How to solve: This question is asking you to look at the graph and project changes into the future. To project changes, extend the lines between April and May for each company. The lines cross pretty qUickly - well before six more months have passed. So the answer is that Company Y would have higher profit in six months if the rales of change from month to month stay the same as they were between April and May. 295 THE MATHEMATICS SECTION J~ . CQ.'1 PAR ISON Of M01 :-", : . ~\ J :, i/ 1 ,. • ,• i f ". . '" " ~ , < , > ~ f , z From graph to table. The same information presented in the profit chart could be presented in a profit table, which might look something like this: PROFIT (IN DOLLARS) Jan Fab Company X 2,000 2,750 1,500 4,000 3,750 Company Y 1,000 2,500 1,500 2,500 3,000 May W it h a table it's a little harder to make the comparisons and see the trends. But the table is much more precise. The graph does not show the exact numbers the way the table does. Scatterplots. One way of presenting data graphically is a scatterpiot. A scatterplot compa res two characteristics of the same group of people or things. For example, the scatterplot below plots the years of experience against the weekly salaries for each of20 sa lespeople who work at Company X . . '" • • • 900 'i': 'a 850 5 800 • • • • ~ 1:0 ~ 750 .!' ~ ~ 700 • • 650 296 600 2 3 4 5 Years of Experience 6 D ata Ana lysis, Statistics and Probability Review From the scatter plot, you can see m.any things. For example: • There are 20 sa lespeople: 4 with one yea r of experience, 3 with two years, 4 with three years, 2 with four years, 3 with five years and 4 with six years. • The median level of experience is 3 years. There are three modes for experience level: 1 yea r, 3 years and 6 years. • Salary tends to increase with experience. • Th ree people make$700 a week and 3 others make $850 a week. These are the two modes for salary level. • The middle two salaries are$775 and $800. Therefore, the median of the salaries is$787.50. If you do not know what a med ian or a mode is, you can lea rn about them in the

nex t section.

Statistics Arithmetic Mean Arith metic mean is what is usually thought of when talking about averages. If you want to know the arithmetic mean of a list of values, the formu la is: The sum of a list of values The number of values in the list For exa mple, if there a re th ree children, aged 6, 7 and 11, the arithmetic mean of thei r ages is: 6 + 7 + 11 = 24

3

3

or 8 years.

Median The media n is the middle value of a list when the numbers a re in order. To fi nd the media n, place the values in ascending (or descend ing) order and select the middle value. For insta nce, what is the median of the fo llowing values? 200,2,667, 19,4,309,44,6, 1

• Place the values in ascend ing order: 1,2,4,6, 19,44,200,309,667 • Select the value in the middle. • There are nine values listed. The middle value is the fifth . • The med ian of these va lues is 19. 297

THE MATHEMATICS SECTION

THE MEDIAN OF A LIST WITH AN EVEN NUMBER OF VALUES

When the number of values in a list is an even number, the median is the average (arithmetic mean) of the two middle values when the numbers are placed in order. For example, the median of 3,7, 10,20 is 7+10_ 2 -85 .

Mode The mode of a list of values is the value or values that appear the greatest number of times. Consider the following list: I. 5. 5. 7. 89. 4. 100.276.89.4.89. 1.8

• The number 89 appears three times, which is more times than any other number appears . • The mode of this list is 89. MULTIPLE MODES

It is possible to have more than one mode in a list of numbers:

1.5.5.7.276.4. 10004.89.4.276. 1.8 In the list above. there are four modes: 1,4,5 and 276.

Weighted Average A weighted average is the average of two or more groups that do not all have the same number of members. For instance: Fifteen members of a class had an average (arith metic mean) SAT math score of 500. The remaining 10 members of the class had an average of 550. What is the average score of the entire class? You can't simply take the average of 500 and 550, because there are more students ~ w ith SODs than with 550s. The correct average has to be weighted ~ep in Mind toward the group with the 'greater number. To find a weighted average, multiply each individual average by A calculator may help you find the answer to this question its weighting factor. The weighting fac tor is the number of values that more quickly. correspond to a pa rticular average. In this problem. you multiply each average by the number of students that corresponds to that average. Then you divide by the total number of students involved: (500 x 15);5(550 x 10) = 520 Thus the average score for the entire class is 520.

298

D~ ta

Ana lysis, Statistics and Probability Review

Average of Algebraic Expression s Algebraic expressions can be averaged in the same way as any other values: What is the average (arithmetic mean) of 3x + 1 and x - 3 ? There are two expressions, 3x + 1 and x - 3, to be averaged. Find the sum of the expressions and divide by the number of expressions: (3x + 1) + (x - 3) _ 4x - 2 _ 2 -1 2 2 - x

Using Averages to Find M issing Numbers You can use simple algebra in the basic average formula to find missing values when the average is given: • The basic average formula is: The sum of a list of values The number of values in the list = average • If you have the average and the number of values, you can figure out the sum of the values:

Average x number of values = sum of values

Example Try putting this knowledge to work w ith a typical question on averages:

The average (arithmetic mean) of a list of 10 numbers is 15. If one of the numbers is removed, the average of the remaining numbers is 14. What is the number that was removed? How to solve:

• You know the average a nd the number of values in the list, so you can fi gure out the sum of all the values in the list. • The difference between the sum before you remove the number and after you remove the number will give you the value of the ·number you removed. • The sum of all the values when you start out is the average times the number of values: 10 x 15 = 150. • The sum of the va lues after you remove a number is 9 x 14 = 126. • The d iffe rence between the sums is 150 - 126 = 24. • You only removed one number, so that number is 24.

299

THE MATHEMATICS SECTION

Probability Some questions in the mathematics section will involve elementary probability. You may be asked, for example, to find the probability of choosing an even number at random from the set: {6, 13, 5, 7, 2, 9}

Because there are 6 numbers in the set and 2 of them are even, the probability of choosing an even number at random is 2 out of 6, or = Remember: The probability of an event is a number between 0 and 1, inclusive. If an event is certain, it has probability 1. If an event is impossible (Le., it cannot occur), it has probability o.

i t·

Independent/Dependent Events You may be asked to find the probabil ity that two (or more) events will both occur. To answer such a question, you need to understand the difference between independent and dependent events.

Two events are independent if the outcome of either event has no effect on the other. For example, if you toss a penny, it has probability then toss a nickel, it has probability

t of landing heads. If you

t of la nding heads. Neither event affects the

probability of the other. To find the probability of two or more independent events occurring together. you multiply together the probabilities of the individual events. For example, in the previous situation, the probability of the penny landing heads and the nickel land'hd,lll Illg ea slsIxI="4'

Two events need not be independent. For example, if you toss a fair coin, the probability that it lands tails is and the probability it lands heads is But these are not independent events - if the coin lands heads, it cannot land tails at the same time! If the outcome of one event affects the probability of another event, the events are called dependen t events. You must use logical reasoning to help figu re out probabilities involving dependent events.

t

t.

Here's an example: O n Monday, Anderson High School's basketball team will play the team from Baker High School. On Wednesday, Baker's team will play the team from Cole High School. On Friday, Cole will play Anderson. In each game, either team has a 50 percent chance of winn ing. (a) What is the probability that Anderson will win both its games? (b) What is the probability that Baker will lose both its games? (c) What is the probability that Anderson will win both its games and Baker will lose both its games?

300

Data Analysis, Statistics and Probability Review

How to solve: (a) The probability that the team from Anderson High School will win on Monday against Baker is t. The probability they will win on Friday against

t. These two games are independent events. abi lity that Anderson will win both games is therefore t x! = t.

Cole's team is also

The prob-

(b) The probability that Baker will lose its game against Anderson on Monday is the same as the probability that Anderson will win: !. The probabi lity that Baker will lose on Wednesday against Cole is also

t. These two games are

independent events. The probability that Baker will lose both games is thereforetxt=t(c) In (a), you found that the probability that Anderson will win both games

t. In (b), you found that the probability that Baker will lose both games is t- Can you multiply t by t to find the probability that Anderson will win is

both its games and Baker wiJIlose both its games? The answer is no. Because Anderson plays Baker on Monday, the event that Anderson wins both its games and the event that Baker loses bOth its games are dependent events. You must analyze the situat ion logically to answer (c). If Anderson wi ns both its games, that means that Anderson defeats Baker on Monday and Anderson defeats Cole on Friday. So you already know Baker has lost one of its games. For Baker to lose both its games, Cole must defeat Baker on Wednesday. So the results of the three games must be as follows: Monday: Anderson wins its game with Baker. Wednesday: Cole wins its game with Baker. Friday: Anderson wins its game with Cole. The results of these games are independent events. Each outcome has probability

t of occurring, so the probability that the three games will have the .

above resu lts IS

I

I

I

I

'2 x '2 x '2 = S·

Therefore the answer to (c) is that the probabili ty Anderson will win both its games and Baker will lose both its games is

k. 301

THE MATHEMATICS SECTION

Geometric Probability Some probability questions in the mathematics section may involve geometric figures. For example, you may be given a figu re like this

o and be told that the large circle has radius 8 and the small circle has radius 2. If a point is chosen at random from the large circle, what is the probabil ity that the poi nt chosen will be in t he small ci rcle? • The area of the large circle is 64n. • The area of the sma ll circle is 4n. Area of the small circle 41C 4 1 Area of the large circle = 64n = 64 = 16 So the probability of choosing a point from the small circle is

302

l~ .

CHAPTER 19

Multiple-Choice Questions

The SAT mathematics section includes 44 multiple-choice questions and covers the content you reviewed in Chapters 15 to 18: number and operations; algebra and functions; geometry and measurement; and data analysis. statistics and probability. You may find a calculator helpful on some problems, but none of the problems requires the use of one. While you're doing the sample questions in this chapter. practice using the calculator you plan to take to the test. It is important that you be familiar with your own calculator and know when it can be helpful to you.

Approaches to Multiple-Choice Questions

)to- Ask yourself the following questions before you solve each problem: I. What is the quest ion ask ing?

2. What do I know?

)- Ollce you've answered the preceding questions, do the following: • Answer the question asked. • Check that your answer makes sense. • Check your work from the beginning. If you can, use a different method from the one you used to get the answer. If you use the same method, you may make the same mistake again .

... Work the problems in your test booklet. You will not receive credit for anything written in the booklet, but you will be able to check your work if you have time. Here are some suggestions on how to use your test booklet: • Draw figures to help you think through problems that involve geometric shapes, segment lengths, distances, proportions, sizes and so on.

303

THE MATHEMATICS SECTION

• Mark key information on graphs and add information to drawings and diagrams as you work through the problems. • Mark each question that you don't answer so that you can easily go back to it later. • When you're working on a question, draw a line through each choice you eliminate.

)- Substitute numbers. Some questions use variables (indicated by letters) to represent the values you are asked to consider. You can 'm ake the problem more concrete by substituting numbers for the variables. • Use common sense when picking numbers to substitute. • Substitute numbers that are easy to work with.

(!)

304

Multiple-Choice Questions

Sample Questions Directions: For this section, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork. Notes 1. The use of a calculator is permitted.

2. All numbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. All figu res lie in a plane unless otherwise indicated. 4. Unless otherwise specified. the domain of any function/is assumed to be the set of all real numbers x for whichf(x) is a real number.

iGD·~~'G'·~~··~ 1

-§ "'C.2..-r ...."

j

"'- t..

"'. bh

y .. twll

y ...,'~

c'_a'+b'

Spoci.ol RllbtTrianJlOl

~

The numb<.- at dcJRlel of in I cin:1c ;'360. The JIIm nr the IIlUJIII"U In dcp-ees or the lIlIIea or. triancJe;1 180.

I.

1. 2

(A)

2x3456

3'4'5y'6'7 = X

7y

(B)

3x 7y

(C)

~'xy

(D)

6x

(E)

!x.

27 7

8x

305

THE MATHEMATICS SECTION

x 2. If"]

=:r, the value of x can be which of the following? I.

-"'3I

II.

III.

(A) (B) (e) (D) (E)

3

Ionly II only III only II and III only I, II, and III

3. All numbers divisible by both 4 and 15 are also divisible by which of the following? (A) (S) (C)

6 8

18

(D) 24

CE) 45

4. If United States imports increased 20 percent and exports decreased 10 percent during a certain year, the ratio of imports to exports at the end of the year was how many times the ratio at the beginning of the year?

CA) (S)

12

If 4

3 II (C) 8 (D)

l2

CE) 2

306

Multiple-Choice Questions

',m 5. The figure above shows how a rectangular piece of paper is rolled into the shape of a cylinder. If it is assumed that the 4·centimeter sides of the rectangle meet with no overlap, what is the area, in square centimeters, of the base of the cylinder? (A) 16Jr

(8) 9Jf

(C) 4Jr

(D) (E)

9 Jr

4 Tr

6. The odometer of a new automobile functions improperly and registers only 2 miles for every 3 miles driven. If the odometer ind icates 48 miles, how many miles has the automobile actually been driven? (A) 144 (B) 72 (C) 64 (D) 32 (E) 24

307

THE MATHEMATICS SECTION

s

, R ~

7

L-------'r Figure not drawn to scale.

7. If the perimeter of /J.RSTabove is 3 limes the length of RS, then RT == (A) (B) (0)

3 5 8 9

(E)

10

(e)

8. A, B, C and D are points on a line. with D the midpoint of Be. The lengths of AB, ACand BCare 10,2 and 12, respectively. What is the length of AD?

308

(A)

2

(B) (C) (0) (E)

4

6 10 12

Multiple-Choice Questions

y

;;;-c;;;t~~~-~";;;-> x (0,0) (5, 0 )

9. What is the area of the triangle in the figure above? (A) (8) (C) (D) (E)

4.0 7.5

8.0 8.5 \5.0

10.

A={3, 6, 9} B= {S, 7, 9} C= 17,8, 9J

If three different numbers are selected, one from each of the sets shown above, what is the greatest sum that these three numbers could have? (A) (8) (C) (D) (E)

22 23 24 25 27

11. Let the symbol@representthenumberofdifferentpairsof positive integers whose product is x. For example,@=3,becausethereare3differentpairsof positive integers whose product is 16: 16 x 1,8 x 2 and 4

x 4.

What does@equal? (AI (B) (C) (D) (E)

5 6 8 10 12

309

THE MATHEMATICS SECTION

12. Several people are standing in a straight line. Starting at one end of the line, Bill is counted as the 5th person, and starting at the other end, he is counted as the 12th person. How many people are in the line? (Al IS (8) 16 (C) 17 (D) 18

(El 19

EXPENDITURES BY COMPANY Y

13. In the graph above, the tolal expenditures by Company Ywere $1,000,000. If each of the following pie charts represents the lotal expenditures of Company Y, in which of the charts does the shaded region best represent the expenditu res other than shiooing and energy? (A) (B) (C) (D) (E) 310 ~ <!> e. e ~ Multiple-Choice Questions y • Q(k, 7) • P(1. 1) ~o~--~~------_x 14. In the figure above, the slope of the line through points Pand Q is value of k? ~. What is the (A) 4 (B) 5 (C) 6 (0) 7 (E) 8 15. In the xy-plane, point R (2, 3) and point S (5, 6) are two ve rtices of triangle RST. If the sum of the slopes of the sides of the triangle is 1, which of the following angles could be a right angle? I.LR II. LS III. LT (A) (B) (C) (0) (E) None I only III only I and II only I, II, and III 311 THE MATHEMATICS SECTION 16. For pumpkin carving, Mr. Sephera will not use pumpkins that weigh less than 2 pounds or more than 10 pounds. If x represents the weight of a pumpkin, in pounds, he willllQ1 u'se, which of the following inequalities represents all possible values of x? (A) IX-21> 10 (B) Ix-4 1>6 (C) IX-51>5 (D) Ix-61>4 (E) Ix- 101>4 , , , SI .200 -, -.,- ','.$ I,()()()

.~.

...- ..:..

',

,

-,.-~~l~t

.: - ~- -!--

, , ,

'1-~--,--

-~- : ·c(n) = an

+ "b"' __ _._ ....... • • .1._ " " " , , ' $60() -f- , -:--t-':--:'-H--:--H-~-, , , , , , , , , _.' ... -,. -•. ..... -,. -,' -r-, , , , , , , , , ,$400 - , , , , , , , , , -, -lt -1- -:,. • ,~ 'l'-:"~ - t·~·, -:- ,)-, , , , , , , $200 -. -.,, -,., ", -.,' , -.-' , ,r·,·.,· , , 'r-. , , -.- . S800 ~ ~ 8 , ' , ' ',' , ~.' _~_ . . . . ......................... ...... . . . .. . " ~- •• - ~- . p • • - . - ...... - • • • - ~-- ... -. - • • -' • ' ~'>--i''''''~''';''~''''''-:,;',.;.'~':;-<.n$0 0±-;.'-,i2 4 6 8 10 12 Units Produced

17. The cost, in dollars, of producing n units of a certain product is given by the function c as c(n) = an + b, where a and b are positive constants. The graph of c is given above. Which of the follow ing fu nctions,j. re presents the average (arith metic mean) cost per un it, in dollars, when n un its are produced? (A) j(n) = 50 +

n50

(B) j(n)=50+

n

500

(C) j(n) :: 500 + SOn (D) fin) = 500 +

n50 500

(E) j(n) = 500 + 11

312

Multiple-Choice Questions

, 18. For all positive values of x, the func tionfis defined by j(x) = X l ~ X -I , Of the following, which is the best app roximation off(x) for values of x greater than I,OOO?

(A)

Xl

(B) x~ (e) x 5 (D) x 6 (E) x 9

313

THE MATHEMATICS SECTION

12x3456

1.

2')'4" Sy'Ii'? "" (A)

..:!.. 7y

(8) 3x 7y

21

(C) 27' xy 6x (D) - , (E)

?l 8x

~epinMind

Answer: The correct answer is (A). Expfarlation: In this question, all the fractions are being multiplied.

H you have a question in which all of the fraction s are being multiplied. canceling may be a possibility.

so canceling is a possibility. The denominators cancel diagonally with the numerators that follow. • The 2 from

• The 3 from

t cancels wilh the 2 from l

t cancels with the 3 from ~.

• And so on, right down to the equa l sign.

Note that the x in the numerator and the y in the denominator can be rearranged as ~ . After you have canceled everything that can be canceled, you are left with the fract ion

t.

~ = ;,.

2. If; ,. xl, the value of xean be which of the following?

- "3

II.

o

III. (A) (B) (e) (D) (E)

I

I.

3

Ionly II only III only II and III only J, II, and III

314

Multiple-Choice Questions

Explanation: Question 2 uses what is referred to as the Roman numera l answer format. This form at is used in both the mathematics and critical reading questions. The way to approach these is to work on each Roman numeral as a separate a nd independent true-false question. O nce you have decided (a nd marked) each Roman numeral as true or false, it's easy to find the correct answer. To answer this question, let's look at each of the three possible values.

~epinMind

ROMAN NUMERAL I: CAN THE VALUE OF x BE

-t

-~1

You could test this answer by substituting for x in the equation a nd seeing whether the result is true. But you can also reason this question out without substituting numbers:

When you're checking the values of expressions, remember the rul es for muttiplying positive and negative numbers: 1+)(+) = 1+)

1-11. ) -1-1 1-11-1-1. )

·r

has to bea positive number because any nonzero number squared is positive.

• If x were negative, ~ wou ld be negative. • So

1" is negative and r

is positive. I

• Therefore, x cannot be -3'Mark Roman numeral r with an F for fa lse. ROMAN NUMERAL II : CAN THE VALUE OF ]( BE 01

This is a very easy substitution to make: x

"3=-<'

o

3=02 =0

~ePinMind

Roman numeral II is true, so mark it with a T for true. 1

ROMAN NUMERAL III: CAN THE VALUE OF ]( BE 3'1

Substitute

t for

x:

Also, xl

I =('3I)' ='9'

Roman numeral III is true, so mark it with a T for true.

Remember the approaches to Roman numeral fonnat answers: • Take each Roman numeral statement as a separate true! false question. • Marti: each Roman numeral with a T for true or an F for fal se as you evaluate it. • Look for the answer that matches yourTs and Fs.

You now know whet her each of the Roman numeral statements is true or fa lse: • I is false. • II is true. • III is true. Find the answer that says only II and III a re true, choice (D).

315

THE MATHEMATICS SECTION

3. All numbers divisible by both 4 and 15 are also divisible by which of the following? (A) (B)

(1.e

6 8

(C)

18

(D) (E)

24 45

Explanation: One way to solve this problem is to first find a number that is d ivisible by both 4 and 15. "Divisible by" means that the remainder is zero after the division. For example, 8 is divisible by 4, but it is not divisible by 3. O ne such nu mber is 60. Now check each choice to see if 60 is

When the arithmetic is simple and you understand what the

• checking each choice • eliminating choices

In more complicated problems.

divisible by that choice; 60 is d ivisible by choice (A) but is not divisible by any of the other choices. The answer must be (A).

this can take more time than find!ng a solution through mathematical reasoning .

4. If United States imports increased 20 percent and exports decreased 10 percent during a certain year, the ratio of imports to exports at the end of the year was how many ti mes the ratio at the beginning of the year? (A)

12 II

(B)

4 ,-

(C)

II

8

3

(D) ,(E)

2

Answer: The correct answer is (B). Explanation: To solve this problem, express what you know in mathematical terms: • State the ratio of imports to exports as

i.

• At the end of the year, imports were up by 20 percent. So imports at the end of the year can be expressed as 100 percent of beginni ng-of-the-year imports plus 20 percent: 100% of 1+ 20% of 1= I + 0.21 = 1.21

• At the end of the yea r, exports were down by 10 percent. So exports at the end of the year can be expressed as 100 percent of beginning-of-the-year exports minus 10 percent: 100% of E - lO%ofE = 90% of E=0.9E

316

Multiple·Choice Questions

• Express the ratio of imports to exports at the end of the year: 1.21 12 1 0.9E =9· E • Reduce the fraction: 12

4

9=} • The ratio of imports to exports at the end of the year was the ratio at the begin ni ng of the year: 1.21 4 1 0.9E=}· E

t times

~eplnMlnd Read word problems carefully. • "x is n times y" does not mean

the same thing as .. x is n times greater than y ." • "x is ntimes y" means x: ny. • ~ x is n times greater than y" meansx:y + ny. 4

For example: 120 is '3 times 90 (120: ~ . gOl. but 120 is greater than 90 (120:90 + t·90l.

t

'

5. The figure above shows how a rectangular piece of paper is rolled into the shape of a cylinder. If it is assumed that the 4-centimeter sides of the rectangle meet with no overlap, what is the area, in squa re centimeters, of the base of the cylinder? (A) 16K (8) , . (e) (0)

IE)

'",

• 4

Explanation: To solve this problem, follow these three steps: 1. Ask yourself: what do you know?

2. Then ask: are there any formu las that will solve the problem? 3. Finally, apply the formula to get the answer. WHAT DO YOU KNOW?

• You know the circumference of the circle. • Label the middle and the right-hand figures in the diagram.

317

THE MATHEMATICS SECTION

Notice that the 4-centimeter sides meet to form the seam in the cylinder and the 6-centimeler sides curl around to become the top and bottom of the cylinder. • So the circumference of the circle is 6 centimeters. ARE THERE ANY FORMULAS THAT WILL SOLVE THE PROBLEM?

The question has now become a rather simple one. You know the circumference of the circle, and you have to figure out the area. • You need to calculate the area, and you can get there in two sleps. I. Relate the radius to the circumference by the formula: Circum ference = 27fr 2. Relate the area to the radius by the formula: Area =

nr

• You know the circumference, so start there and work toward the area. The radius r is the common term in the two formulas. so start by solving for r. APPLY THE FORMULA TO GET THE ANSWER

Ci rcumference = 2nr

6 = 2nr 6 2rr = r

.l n; = r

0eplnMlnd Label diagrams a nd figures with the infonnation you have. This often revea ls key infonnation that you need to answer the question.

Now use the va lue for r in the formu la for the area. A=

If'" .l

r = rr

6. The odometer of a new automobile functions improperly and registers only 2 miles for every 3 miles driven. If the odometer indicates 48 miles. how many miles has the automobile actually been driven? (A) (8) (C) (D) (E)

144 72

6' 32 24

Multiple-Choice Questions

Explanatior,: In this problem you are told that the odomete r registers only 2 miles for every 3 miles driven. So the rat io of m iles registered to miles driven is 2 to 3, or This can be expressed as

t.

2 miles re~istered 3 mi les riven

48 miles registered x miles driven

If the odometer indicates 48 miles, the actual miles can be found using the above relationship, as fo llows:

1= 48 3

x

2x = 144 x= 72

If the odometer indicates 48 miles, the actual number of miles driven is 72. HOW TO AVOID ERRORS WHEN WORKING WITH PROPORTIONS

The most importa nt thing wit h proport ions is to be consistent in the way you set them up. There are severa l correct ways to set up a proport ion, but if you mix up the terms, you will not get the correct answer. For instance, if you put the registered mileage in the numerator of one ratio but the actual mileage in the numerator of the other rat io, you will come up with a wrong answer: 3 _ 48

2'-X3x

= 96

x = 96 = 32 miles 3

But this answer is wrong, which you should realize if you do a "make-sense" check, as described in the next sect ion. MAKE A " DOES-IT-MAKE-SENSE?" CHECK

When you arrive at an answer to a word problem, check to see whether it makes sense. The question states that the actual mileage is greater tha n the registered mileage, so the actual mileage has to be a number larger tha n 48. Your check shou ld warn you not to choose the incorrect answer, (D) 32, that was obtained by setting up the wrong proportion.

~eplnMlnd A quick " make-sense" check before you start working on a question can help you eliminate some of the answers right away. H you realize that the actual miteage has to be greater than the registered mileage, you ca n eliminate answers (OJ and IE) immediately.

319

THE MATHEMATICS SECTION

PUT IN THE UNITS OF MEASUREMENT

One way to help you set up proportions correctly and to avoid mixing up the terms is to put in the units of measurement. For example: If 10 cans of peas cost $4.80, how much will 7 cans cost at this rate?$4.80 =~ to cans 7 cans

Note that dollars are in the numerators of both ratios, and cans are in the denominators of both ratios. To solve for x: 4.80' 7 = lOx 33.60 = lOx 3.36 = x

$0 7 cans will cost$3.36.

s

R ~

'--- ---'T

Figure not drawn to scale.

7. If the perimeter of I1RSTabove is 3 times the length of RS, then RT "" (A) (B)

3 5

(e)

8

(D) (E)

JO

9

A nswer: The correct answer is (A). "Note: Figure not drawn to scale" means that the points and angles are in their relative positions, but the lengths of the sides and the sizes of the angles may not be as pictured.

Explanation: To solve this p roblem, again, first ask yourself what you already know, and then express the problem using an equation. WHAT DO YOU KNOW?

• The perimeter of the triangle is the sum of the lengths of the 3 sides. • The question states that the perimeter is 3 times the length of RS . • RS is 5 units long.

• ST is 7 units long.

320

Multiple·Choice Questions

~eplnMlnd

EXPRESS THE PROBLEM USING AN EQUATION

• The perimeter is equal to 3 times the length of RS . • That means that the perimeter is 3 times 5, or IS. • S05+7+RT= 15.orRT= 3.

It's always a good idea to draw the lines and figures that are described in a question if a fig ure is not given. Make sure that what you draw fits the information in the question. Don't worry about how pretty the figure is. It only has to be neat enough for you to work with it.

8. A, B, Cand Dare points on a line, with D the midpoint of BC. The lengths of AB, ACand BCare 10, 2 and 12, respectively. What is the length of AD? (AI (B) (C)

2 4

6

(0)

10

(E)

12

Explanatioll: The key to this question lies in not jumping to incorrect conclusions. The question names the points on a line. It gives you a variety of information about the points. The one thing it does not do is tell you the order in which the points fall. Many students assume that the order of the points is A, then B, then C, then D. As you will see, if you try to locate the points in th is order, you will be unable to answer the question. WHAT IS THE QUESTION ASKING?

The question asks for the length of AD. In order to find this length, you have to establish the relat ive posit ions ofthe four points on the line. WHAT DO YOU KNOW?

Try to draw the figure. You might be tempted to locate point A fi rst. Unfortunately. you don't have enough information about A, yet. to place it. • You can place B, C and D becau se D is the midpoint of BC .

B

o

C

I

I

I

• You know the lengt hs of th ree of the line segments: AB = 10 AC=2 BC= 12

321

THE MATHEMATICS SECTION

• Because you know where Be is, you can label the length of Be.

B

D

c

I

I

I

f--12----1 BUILD THE FIGURE, ADDING WHAT YOU KNOW AND WHAT YOU CAN FIGURe OUT

Because D is the midpoint of Be, you know that BD and DC a re each 6 units long.

I

c

D

B

6

I

6

I

f - - 12 ----1 Where can you place point A ? • It has to be 2 units from C, because AC = 2 . • It also has to be 10 units from B, because AB = 10 . • $0 the only location for A is between Band C, but closer to C. • Place point A and mark the d istances. It is now an easy matter to figure out the answer to the question: • DC is 6 units. • A is 2 units doser to D than C is to D, so AD is 4 units. f------ 10 --+ 21 B D A C I I I I I 12 I f-6--+-6-! (J,•• PInMlnd H you have time, always check that the picture you have drawn is consistent with the information given in the problem. Also check that you answered the question . Check: 8 D.... C I I II 6 " - A. B, C and D are on the line. - D is the midpoint of BC . -AB: 10, AC", 2 and BC= 12. -AD:4 . 322 Multiple-Choice Questions y (0,3) ~~~--~~~~,-.x (0,0) (S,O) 9. What is the a rea of the triangle in the figure above? (A) 4.0 (8) 7.5 (C) 8.0 (0) 8.5 (E) 15.0 Answer: The correct answer is (B). Explanation: The figu re provides all the information you need to answer the question. WHAT IS THE QUESTION ASKING? You are asked to figure out the area of a triangle that is defined by three points on a coord inate plane. WHAT DO YOU KNOW? • The tria ngle in the figure is a right triangle with the right angle at the lower left. • Because it is a right triangle, its base and height are the two sides that form the right angle. • The area of a triangle is tbh, where b is the length of the base and h is the height. • The base of the triangle extends from point (0, 0) to point (5, 0), so b = 5 . • The height of the triangle extends from point (0, 0) to point (0, 3), so h = 3 . I Area = "2bh I = '2 (5)(3) I = '2 (IS) = 7.5 323 THE MATHEMATICS SECTION If you are presented with a question that shows the grid li nes of a graph, you may rely on the accuracy of those lines. ~ ~ : : Q~ 'iB, , :;., . .... . . . . .. , ...... '.....,.... .. ......,........ ~ : :. +.+.+. .[..:... : : . . . . . . . . . Ai . , , ' , !C You can use the grid on the graph above to determine the following information: ~epinMind • AC is 6 unit s long. The coordinate system provides essential infannation for solving t his problem . Your knowledge of the coordinate system can give you infannation about lengths a nd a ngles. such as: • Whether lines are parallel, perpendicular or neither • ADEC is a recta ngle. • Side AD is 4 units long. • The height of triangle ABC is the sa me as the width of the rectangle (ADEC), so the height of the triangle is 4 un its. • The area of the triangle is t the area of the rectangle. • Whether figures are squares, s pecial triangles. etc. • How long line segments are • Whether angles are right angles or other special angles • The area of a rectangle::; width x length ;:: AD x AC ::; 4 x 6 ;:: 24 square units. • The area of the triangle ::; t (base x height) ::; ;:: 12 square units. t (AC x AD) ::; t (6 x 4) A={3, 6, 9J B = {S, 7, 9} C = {7, 8, 9J 10. If three diffe rent nu mbers are selected, one from each of the sets shown above, what is the greatest sum that these three numbers could have? (A) 22 (B) 23 (C) 24 (D) 25 (E) 27 Answer: The correct answer is (C). Explanation: This question cha llenges your ability to reason with numbers. In other words, it is more a quest ion of logic than of a rithmetic. WHAT IS THE QUESTION ASKING? The question asks what is the largest sum you ca n get if you choose one number from each set and add those numbers together. Each nu mber you select must be diffe rent, so you cannot ta ke the largest number, 9, from each set, add the nines together and come up with choice (E) 27. 324 Multiple·Choice Questions WHAT DO YOU KNOW? • The number 9 is the largest number in each set. • You can only take one 9. This means that you will have to take the second-largest or thi rd-largest number from two of the sets. MAKE YOUR SELECTIONS • The second· la rgest number in set A is 6, which is smaller than the second-largest number in sets Band C, so select 9 from set A . Ge p In MInd If you have time, go back and check that you have observed the conditions of the problem: • Did you choose one number from each of the sets? (Yes, 9 is in set A, 7 is in set 8 and 8 is in set C.l • Did you choose three different numbers? (Yes, 9, 7 and 8 are all different.) • The ot her two choices are now easy. Ta ke the largest numbers avai lable from sets Ba nd C . • The greatest sum is 9 + 7 + 8 = 24. II . Let the symbol@represent the number of differe nt pairs of positive integers whose product is x. For example,@= 3, because there are 3 d ifferent pairs of positive integers whose product is 16: 16xl,8x2and4x4 What does @equa l? (A) (8) (C) (D) (E) 5 6 8 10 12 A nswer: The correct answer is (A). Explanation: Most SAT mathematics sections have at least one question involVing a newly defined symbol. Somet imes there will be an easy question, li ke th is one, fo llowed by a more d ifficult one in wh ich you might have to use the new symbol in an equation. To answer these questions. you have to read the definition of the special symbol carefu lly and follow the instruct ions. It is not expected that you have ever seen the new symbol before. The quest ion asks you to fi gure out how ma ny different pairs of posit ive integers can be multiplied together to give you the number in the circle. 325 THE MATHEMATICS SECTION ~eplnMlnd PUT THE SPECIAL SYMBOL TO WORK When you're faced with a spe- • To figure out@, list the pairs of positive integers whose product is 36: cialsymbol, read the definition carefully and use it as your I )( 36 2 x 18 instruction for working out the answer. 3 )( 12 4x9 6x6 • Count up the pairs. The answer is 5. 12. Several people are standing in a straight ti ne. Slarting at one end oflhe line, Bill is counted as the 5th person, and starting at the other end, he is counted as the 12th person. How many people are in the line? (A) 15 (B) 16 (C) 17 (0) IS (E) 19 Answer: The correct answer is (B). ~eplnMlnd Problems like this one focus on your ability to reason logically. There's nothing wrong with drawing a fjgure using dots to Explanation: You can answer this question by careful reasoning, or you can draw it out and count. Either way. be careful that you don't leave Bill out or count him twice. WHAT DO YOU KNOW? represent the people in line. Just make sure that you follow the instructions carefully when you draw your figure. • Bill is the 5th person from one end of the line. • Bill is the 12th person from the other end. USING LOGICTO SOLVE THE PROBLEM • If Bill is the 5th person from one end of the line, there are 4 people (not counting Bill) between him and that end of the line. • If Bill is the 12th person from the other end of the line, there are II people (not count ing Bill) between him and that end of the line. • The sum of 4 people between Bill and one end plus II people between Bill and the other end equals 15 people. Then you have to add in Bill. So, there are 16 people in line. 326 Multiple-Choice Questions EXPENDITURES BY COMPANY Y Catea<>rIeo 13. In the graph above, the total expenditures by Company Y were$1,000,000. If each of the following pic charts represents the total expenditures of Company Y, in which of the charts does the shaded region best represent the expenditures other than shipping and energy? (A)

~

(B)

<!l

(0)

e e

(E)

(C)

Explanation: In this question you have to interpret information from one type of graph (ba r graph) and translate that information into anot her type of graph (pie chart). Questions that involve interpreting data presented on graphs or in tables wi ll be common on the SAT.

0ep

in Mind

If you are presented with a math question that shows the grid lines of a graph, you may rely on the accuracy of those

lines. WHAT IS THE QUESTION ASKING?

The question asks you to identify the pie chart that shows all of Company V's expenses other than shipping and energy. That "Miscellaneous" category is important. It's easy to overlook. WHAT DO YOU KNOW?

All you need to know to answer the question is the amount of money spent on shippi ng and energy and the tota l expenses for the company. • You are given the total expenses: $1,000,000. (You also could have figured that total from the graph by adding all the expenses from the individual categories.) • The graph shows you that the expenditures for sh ipping and energy amount to$250,000.

327

THE MATHEMATICS SECTION

TRANSLATING THE INFORMATION

• The question really asks you to identify approximately what fraction of the total costs did not go for shipping and energy. Although the question does not ask this specifically, the pie charts in the answer choices show fractions of the whole, so that's the way you will have to express the information you have. • Shipping and energy expenses amount to 5250,000 of the $1,000,000 of total expenses. " d$250,000 I f h I • Sh IpplOg an energy cost $1,000,000 or '4 0 t e tota . • That means the answer is (8) because the pie chart in (8) shows about total, right? No, this answer is wrong. t of the • Remember, the question asks which pie chart "best represents expend itu res other than shipping and energy," 1 3 • If"4 goes for shlppmg and energy, that leaves 4" fo r other thmgs. y • Q(k, 7) OP(!. I) -;Orr----'''--''----~ x 14. In the figure above, the slope of the line through points P and Q is value of k? i. What is the (A) 4 (8) 5 (C) 6 (D) 7 (E) 8 Answer: The correct answer is (8). Explanation: Your ability to answer this quest ion depends on knOWing and bei ng able to apply the definition of slope. The slope of a line in the xy-coordinate plane is: The change in y between any two points on the line The change in x between the same points on the line The question asks for the value of k, which is the x coordinate of point Q. 328 Multiple-Choice Questions WHAT DO YOU KNOW1 • The slope of the line that goes through P and Q is t. • That means for every 3 units that y changes. x will change 2 units. • The coordinates of P are (I. I). &ee • The coordinates of Q are (k, 7). • The change in the value of y between P and Q is 6 units (7 - I = 6). APPLY WHAT YOU KNOW • y changes 6 units between the two points. • That means that x will change 4 units, since for every 3 units that y changes. x changes 2 units. • The x coordinate of point P is I. ~ p In MInd Re membe r to check that your answer fits t he conditions of ·the problem. • If k '" 5, then point Q lias coordinates (5, 7). • Is the s lope of the line through the points P (1 ,1) a nd Q (5, 7) equal to t1 7- 1 Yes'5_ 1 6 3 ="4 ="2. I • The x coordinate of point Q will be I + 4 = 5. 15. In the xy-plane. point R (2. 3) and point S (5, 6) are two vertices of triangle RST. If the sum of the slopes of the sides of the triangle is 1. which of the following angles could be a right angle? I. II. III. LR LS LT (A) None (8) Tonly (e) ITT on ly (0) Tand II only (E) I, II, and III Answer: The correct answer is (A). _ 6-3 3 Explanation: Given the coordinates of points Rand S, the slope of RS is 5 _ 2 ="3 = l. If LR is a right angle. then RS and RT would be perpendicular. The slope of RT would be -I because the slopes of RT and RS wou ld have to be negative reciprocals of each other. Because it is given that the sum of the slopes of RS, ST and RT is I, the slope of ST would have to be 1. Then RS and ST would have the same slope, which means that they would be parallel. or that points R, Sand T would be collinear. Neither of these is possible if RST is a triangle. Similarly. if LS is a right angle. then the slope of ST would be -1. Because the sum of the slopes of RS. ST and RT is I, the slope of RT would have to be l. Then RS and RT would have the same slope. which means that they would be parallel, or that points R, Sand T would be collinear. Neither of these is possible if RST is a triangle. 329 THE MATHEMATICS SECTION &ee If L T is a right angle, let the slope of RTbe k. The slope of ST would p In Mind -i. Because the sum of the slopes of the three sides oftriRST ST RT will k- t or k t . k k= have to be In questions with three Roman numeral choices, consider each of I, II and III separately. • Consider each as a separate true-false question. • After you have decided which are true and which are false, you can answer the question . angle is 1, the sum of the slopes of =0 and Solving this equation for = yields be zero, so that :t I . In either case, the ,result is that one of the two sides would again be paraliel to RS, or pOints R, Sand T would be collinear. Neither of these is possible if RST is a triangle. 16. For pumpkin carving, Mr. Sephera will not use pumpkins that weigh less than 2 pounds or more than 10 pounds. If x represe nts the weight of a pumpkin, in pounds, he will IlQ1 use, which of the following inequalities represents all possible values of x? (A) Ix - 21> IO (B) IX-41>6 (C) Ix-51>5 (0) Ix- 6 1>4 (E) Ix- 10 1> 4 Answer: The correct answer is (D). Explanation: If x represents the weight of the pumpkins Mr. Sephera will not use, then x < 2 or x > 10. This is represented graphically as follows: , , 2 : 6 10 . Because 6 is midway between 2 and 10, each point in the solution is more than 4 units from 6. This is equivalent to the statement 1x - 61 > 4 . ~ Another way to solve the problem is to rewrite both x < 2 and ~eep in Mind x> 10 . Algebraically, the expression x < 2 is equivalent to -x > -2 or Remember I a I > 4 means that either B > 4 or - a > 4 . Check your answer: -I x - 6 1> 4 means that either x - 6 > 40r - (x - 6»4. -If x - 6 > 4, then x> 10 . -If - (x - 6) > 4, then -x + 6 > 4, so - x >-2,andx <2. - Because Mr. Sephera will not use pumpkins that weigh more than 10 pounds or less than 2 pounds, I x - 6 I > 4 is the correct answer. 330 -x + 6 > 4 or -(x - 6) > 4 . The expression x > 10 is equivalent to x _ 6 > 4 . Combining the two expressions yields I x - 6 I > 4 . Multiple-Choice Questions , , , , , , , , , , , , , , , " " " , '-,",, " -,"".....$1,000 .;.~ .+ .;.~ .. ~.~ . . ~. ,':+' , , , , , " ", ·,··r·.· .. ·· $800 +~.++~.: ·c(n)"" an + "b. _~$600 _J_', ·:--t·i-·: . , , ,.. ,~-i-~--~-t-~-, , , . ' SI,200

"'~"~""","

"

"'~","""'i'"'r' ~._ ....

~

. .......~ • • • J ••

-,, - .,··r· , , •. , ,, ...., 'r-, , , -.,-, -r-' , , - ..' --~ - ~- -:- -: - ~. -;-. ~ - ~- -:. -~ - ~ -~-­

$400 -t - ~_.:- - ~ -~ •.:• . ~.~. ~.-~. t - .. -- .$200 .;, - ~-, -:-.;, -~";""; --:. -~-; -..:-, , , , , , , ' , , , , , , , , , , ' ...... -- -

••• -

.

..... -

.

... -

•••• •

j

••

SO 0!-+-;2--+-.;.4...;....6.,..;.-;S-'':0.....'2=- n Units Produced

17. The cost, in dollars, of producing n units of a certain product is given by the function c as = an + b, where a and b are positive constants. The graph of c is given above. Which of the following functions,f, represents the average (arithmetic mean) cost per unit, in dolla rs, when n units are produced?

,en)

50 (A) j(n) = 50 + -;;-

500

(B) j(n) = 50 + --;(C) j(n) = 500 + SOn

50

(0) j(n) = 500 + -;;-

500

(E) j(n) = 500 + --;-

Explanation: To solve this problem, start by findi ng the values of a and b . Because c is a linear func tio n , a is the slope of the line and b is the y-intercept. The y· intercept of the line is 500 because the line contains the point (0, 500). To find the slope, take any two points on the line and the slope is

c~ange ~n Y . Two such points are (0, 500) and (12, 1100). c angemx

The slope of the line is 1100 - 500 = 600 = 50. Because a = 50 and b =

'2

12

500, the cost to produce n units of the product is given by c(n) = SOn +

~eplnMlnd • If the function 9 is given by g(xj = ax + b, for constants B and b, then 9 is a linear func· tion . • The graph of 9 in the xy-plane isa line. • The slope of the graph of 9 is 8 . • The y-intercept (i.e., the point where the line crosses the y-axis) is (0, b) .

500 . The average cost per unit is the total cost divided by the number of units produced, or fl.n) = c(n) = SOn

n

+ 500 = 50 + 500 . n

n

331

THE MATHEMATICS SECTION

18. For all positive values of x, the functionfis defined by fix) = x' - X-l , Of the following, which is the best approximation ofj(x) for values of x grealer than

I,OOO? (AI

x'

(BI x' (C) x' (DI ,.

(EI x'

A,rswer: The correct answer is (A). Explana tion: To answer this quest ion, you need to understand the notation x- 2 , In ge nera l, x-'" means ;'" . Because x-2 is equivalent to rewritten as fix) = xl -

-tr, t he defi n ition o ff can b e

~ . For large values of x, the value of r

is very large; therefore

the value of ~ is very small, but greater than o. For example. when x = 10, ~ = and when x = 30, ~ =

160'

960 .If you keep trying larger and larger values of x, you can

probably convince yourself that

?- is a very small positive number for all x values

greater than 1.000. For large values of x, xl is very large. For large values of x, the value of (x) is xl minus a very small positive number. Th is means that for x > 1,000 , j{x) is just a bit less than xl. Of the answer choices given, xl is the best approximation

of fix) for large values of x .

~epinMind • Re member that x -1 ::..!. . x • If x is pos itive, then as x becomes larger, ..!. becomes x closer to O. -In general, x- m :: ~. X - If x is positive, and m is a positive integer, then as x becomes larger, x~'" becomes closer to O.

332

Recap 1. Ask yourself these questions before you solve each problem: What is the question asking? What do I know?

6. Draw figures and lines to help you think through problems. 7. Mark key information on graphs and add information to drawings and diagrams. 8. Mark each question that you don't answer so you can return to it later. 9. Draw a line through each choice you eliminate. to. Make problems more concrete by substituting numbers for the variables.

11. Work backward and substitute the answer choices to see which one works.

12. Make an educated guess when you can e liminate at least one answer choice. 13. If you have a question in which a group of fractions is being multiplied, canceling may be a possibility. 14. When you're checking the values of expressions, remember the rules for multiplying positive and negative numbers. 15. Consider each Roman numeral answer choice as a separate false question.

true ~

16. Read word problems carefully. 17. Label diagrams and figures with the information you have. 18. If a figure is not given, draw the lines and figures that are described in a question. 19. Check that the picture you have drawn is consistent with the information given in the problem. 20. Find information about lengths and angles from your knowledge of the coordinate system. 21. Check that your answer observes the conditions of a problem.

(continued)

333

When faced with a special symbol, read the definition carefully. 23. Make sure that you follow the instructions carefully when you draw figures to help you solve logic problems. 24. Rely on the accuracy of the grid lines shown in a graph.

334

Multiple-Choice Questions

Practice Questions Directions: For this section, solve each problem and decide which is the best oflhe choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork. Notes I. The use of a calculator is permitted. 2. All numbers used are real numbers. 3. Figures that accompany problems in this test are intended to provide informa. tion useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated. 4. Unless otherwise specified, the domain of any funct ion/is assumed to he the set of all real numhersx for whichJ(x) is a real number.

IGD·~B.·8··~

'i.

I

-

t

II

1

.04 .....

C. 2o:r

.o4 .

t..

.o4 ·

IM

..

v••,JI!

V.t"'"

cJ ... JtIl J

,.. "".~ .. ~ " ' Speeitl Ri&hl 1'l"ian&*

'tI TIM: nurMer of dctroes or...: i~ • cilcle ;'360.

The sum or die me.uwa ill dev- of tK ........ of. triaII&k: if 1150.

• I -2

R

I

I

I,

-1

I

1

o

I I I

I I

2

1. On the number line above, whal number is the coordinate of po inI R ? J (A) - 1"4

(8) - I ! (C) (D)

(E)

J 4

-, I

4

335

THE MATHEMATICS SECTION

2. If a certain number is doubled and the result is increased by 7, the number obtained is 19. What is the original number? (A) (8) (C) (D) (E)

2.5 6 13 16.5 2.

3. For the two intersecting lines above, which orthe follow ing must be true? T.

II. il L

a:>,

a,. 2b a+60=b+c

(A) I only (8) II only (C) I and II only (D) II and III only (E) I, II, and III

4. Three consecutive integers are listed in increasing order. If their sum is 102, what is the second integer in the list? (A) 28 (8) 29 (C) JJ

(0) 3' (E) J5

336

Multiple-Choice Questions

5. If 10,000 microns = I centimeter and 100,000,000 angstrom uni ts = I centimeter, how many angstrom units equal I micron? (A) (B) (C) (D) (E)

0.000000000001 0.0001 10,000 100,000 1,000,000,000,000

c

A

~~x a

6. In the figure above, OX is a radius of the circle wit h center O. Which of the following triangles has the kia area? (A) (B) (C) (D) (E)

MOX aBOX

'COX llDOX llEOX

7. If the product of five integers is negative, then, at most, how many of the five inte-

gers could be negative? (A) One (B) Two (C) Three

(D) Four (E) Five

337

THE MATHEMATICS SECTION

8. If x - 7 = 2yandx = 5 + 3y, what is the value of y? (A) -5 (B) - 2 (C) 2 (D) 5 (E) 12

--~.~-- e

p

e

9. In the figure above, if two points S and Tare to be placed on line on opposite

sides of po In! P so that 2SP = PT, what will be the value of

~~

?

(A) 2

3

(B) .,

2

(C)

J

(D)

!2

(E)

!3

,

j(x) = (x+ 1)4

10. For the function f, defined1above, what are all the values of x for which j(x) is a real number? (A) All real numbers (8) X£!:-J (C) x<!:O 3 (0) xC!:"4 (E)

338

xc::

1

Multiple~Choic e

Questions

11. There a re g gallons of paint available to paint a hous~. After 71 gallons have been used, then, in terms of g and 71, what percent of the paint has ruu been used? (A)

10071%

g

g

(B) 10071%

(Cl lOOg%

" (0)

g " JOO(g-rl)

12. If x is an integer and 2 < x < 7, how many different triangles are there with sides of lengths 2, 7 and x? (A) One (B) Two

(C) Three (D) Four (E) Five

13. If2 1x + 31 '" 4 and J Y+ J EXCEPT

iJ "" 2, then Ix + yl could equal each of the following

(A) 0 (8) 4 (C) 8 (0) 10

(E) 12

339

THE MATHEMATICS SECTION

14. If a> band a(b - a) = 0, whic h of the following must he true?

a=O

I.

b< 0 a-h>O

II. ,III. (A) I only (B) II only

eel

II I o n ly

(D) I and II only (El I, II , and III

y

(-2,0)

~~~-O~-----+x

15. The graph above is a parabola that is symmetric about the x-axis. W hich of the following could be an equatio n of the parabola?

(B)

x=I-2 x=-y-2

(C)

X ..

(Al

(y_2)l

(D) x= (y-

,!if

(El x = -(y - Ji) l

340

THE MATHEMATICS SECTION

e

2. B 3. D 4. D 5.

e

6. A 7. E

8.

e

9. B 10. B II. E 12. A 13. D 14. E 15. A

Additional practice questions can be found in The Officia' SAT Online Course at www.collegeboard.comlsatonlinecourse.

342

CHAPTER 20

Student-Produced Response Questions

On the SAT, you will find 10 student- produced response or grid-in questions. These questions require the same math skills and reasoning abilities as the multiple-choice math quest ions. In fact, many st udent-produced response questions are similar to multiple-choice questions. The big difference: no answers are provided. You must work out each problem yourself and enter your answer onto a special math grid . Use the sample grids at the end of this chapter to practice gridd ing techn iques.

Guidelines for Completing the Grid Become very fam iliar with the gUidelines for answering and gridding studentproduced response questions. You can save time and improve your con fidence by knowin g the rules before the test.

Calculators May Help Here If you are asked to calculate the answer of a grid-in problem, be carefu l to check your work. Without answers to choose from, you may make ca reless mistakes. That's why it is a good idea to use a calculator for this section.

Practicing with the Grid Before the test, practice completing the grids. You don't have to write your answer in the boxes above the grid , but it's a good idea to do so to avoid errors. Rem ember that only the answers you put in the grid will be scored. Be careful to mark no more th an one circle in any column because answer sheets are m achine scored and you

will receive credit only if t he circles are filled in correctly.

343

THE MATHEMATICS SECTION

Positive Numbers and Zero Only The grid can only hold four places and can accommodate only positive numbers and zero. It is not possible to grid a negative number of any type. If you obtain a negative answer for a student-produced response question, you will know that you have made a mistake. Rework the problem:

Place Answer in Any Column Don't worry about which column to use when you begin writing the answer. As long as the answer is gridded completely, you will receive credit. For example, 156 can be gridded as shown below; both answers are correct. 1 5 6 ~

or

5 6

~

~

1(.) 0 0 '"

•'",, ,,• •,, ,• , , •, • •• • • • •

~~

0 . ®® ' 0 @0 '~ @0 0 '

®® 00 @@ ®® @@

• • I~

. ® ®. 0fll ®. ®®

~ r• •

Integers You can grid onc-, Iwo-, three- or four-digit positive integers or zero as follows. 2

4 3

Ir:> f.<~ · . Ir. 0 f.< ~

• I~ \ I~ , , , I~, ,• • ' 0 •, • • • ~ • (i) • • • • • • 2

2

';; 7

7

If. If.<

.f£'" I~0 I~® '"®~

••

~ 00 ~ il5 il5 ® il5 ®

0 0 0 0

® ® ® ® ®

6 9 1

::;

'" f.<

~

8

7 510

1i:lIGl

Ir:>

I", ~

• If.< ,, ~, ,, Ir. I~ , 1)1 , • • • • III ,

• I~

o

If.< ::; b

'"0 •0 ~® ® 0. ~ 0 00

I• • •II I'i '. :l; ,' • ill , ,

~ .

:i: ' •

I~

• • I~ ~ ~'

~

®

~

~

il5 ®

~ ~ ®® 0 ®

Decimals and Fractions The grids include decimal points (.) and fraction lines (I) so that you can enter answers both in decima l and fraction form. You can grid your answer as a decimal or a fraction.

344

Student-Produced Response Questions

Decimal Points If the answer is O. grid it in column 2, 3 or 4. Zero has been omitted from column 1 to encourage you to grid the most accurate values for rounded answers. For example, an answer of tcould also be gridded as .125 but not as 0.12, which is less accu rate.

No Mixed Numbers You can grid both proper and improper fractions. However, it is not possible to grid mixed numbers. If your answer is a mixed number, convert it to an improper fraction or to a decimal. For example. if you get the answer 2t. grid ~I or 2.75, as shown.

The fraction line appears

in the first shaded row of circles.

If you grid 2t. the scoring machine will read the answer as

2i.

which is wrong.

2 3 /1 4

,

I~ I ",

.''.

1'" •

0/ll :~ , , Ol . ' , 00

®®

@@

00 ~0 '0

'( ~: • •

Repeating Decimals If the answer you are gridd ing is a repeating decimal, you must grid the most accurate possible decimal. The easiest way to follow the rule for repeating decimals is to completely fill the grid with the answer. If you obtain a decimal answer with more digits than the grid can accommodate. it may be either rounded or truncated. but it must fill the entire grid. For example, if you obtain an answer such as 0.6666 ... , you should record your result as .666 or .667. A less accurate va lue such as .66 or .67 will be scored as incorrect.

345

THE MATHEMATICS SECTION

9/11 = .8181

8

I.

I~

1/6=.166

2/3

=.66

111617

51. 5

·' ,., ~~

1(.' ~I ~ 1(.

1 8

,

l?i , 1%1 ' 1*1* s ~ . I~ . 'I~ • 'I~ ,• 2

l,eJ

o~

CD

I• .166 will also be

.666 will also be

correct. B ill,

correct. But. .6, .7,.66 or .67

.16or .l1will not be COIttCt.

entered on the grid, and not the answer handwritten at the top of the grid, is scored. You must decide whether to first write your answer in at the top of the grid and then transfer it to the grid, or to transfer your answer directly from notes in your test booklet or in your head to the grid. You might practice both approaches

II..!'

'I~

~

4

1 ~4

~~~~ ®~.~

: ® • ®

.81 or .82 will not be correct

~ ~ : 1&

2

3

, Ij

51/2=5.5

(NOT a repeating decimal.)

w ill not be.

Multiple Answers Some of the student-produced response q uestions may have more than one correct answer. These questions may say somethi ng like, "What is one possible value of x?" Th is wordi ng indicates that there may be more than one value of x that is correct. Under these circum stances, simply choose one of the possible answers to grid on YOUf answer sheet.

There Is No Penalty for Wrong Answers

a nd see which one wolts best for you. You want to make sure you enter your answer cOlTectly. While

it might be more time-cons uming to first write your answer in at the top of the grid, you may find this approach helps you avoid errors.

346

On student-produced response questions, unlike multiple-choice questions, no points are subtracted for wrong answers. Feel comforta ble gridding whatever answer you get without fear that it may subtract from your fi nal score if it is wrong.

Student-Produced Response Questions

Sample Questions For Student-Produced Response questions 1- 9, use the grids at the bottom of the answer sheet page.

An~wcr:

-

112

7/ I 2

.I~ Ii'

_

• • •

(irid in ...... ",.ult.

Frnct;"n

O{l

Ei!he r

line

,i linn

2 0

1-.Jij2;1i~5~ -

i~

rome!.

20

Dt:.::imal poim

0 . 0 10 @@ • 00 00 00 0@ CD CD @0

00 (0)(0) . 0 00 00 0@ • • • • • Mar\:

AMwe.: 2.5

more than ORC drde in any column.

• Because the answer sheet w;lI be machinescored, you will rt<:e;"e c .... dit only irtht eirel"" a .... 1i111'd in cUI","""1Iy. • Altoougll 00l n:

JSQtt; You may

~!an your answers in any rulumn . 'plIa permiuing. CoI~mm not needed should be leO

'~{~~J§~~:~" an answer your ",",ult a~. k.... H<'CUnlte ~Mlue sud> 1OS.66 ur .67 will "" sron;d lOS inco, .....,t. Ae<:epl3ble ways to grid

~

are:

• Somc prohlems may ha,·. more than one COITeC! an,w~r.

In such cases. grid only one anSwer.

• Noquestinn ha.< a RCgati,·. answer. • Mixed nUn1hcrs i uch as 3 ~ rnu" be gri d

J5 or 7/2. Ilf 1ii.1~1 ~ is gridded. il win bo: interp"'ted as

31

,

T' not 3 2,)

l. In a restaurant where the sales tax on a $4.00 lunch is$0.24, what will be the sales tax due, in dollars, on a $15.00 dinner? (Disregard the$ sign when gridding your

answer. For example, if the answer is $1.37, mark 1.37 on the grid.) 347 THE MATHEMATICS SECTION 2. A team has won 60 percent of the 20 games it has played so far this season. If the team plays a 10la1 0(50 games all season and wins 80 percent of the remaining games, how many games will the team win for the entire season? 3. If n is a two-digit number that can be expressed as the product of two consecutive even integers, what is one possible value of n? 4. [{the ratio of a to b iS~, what is the ratio of2a to b? 5. [{the population of a town doubles every 10 years, the population in the year X + 100 will be how many limes the population in the year X ? 348 Student-Produced Response Questions Number of Donuts Total Price$0.40 Box of 6

$1.89 Box of 12$ 3.59

6. According to the information in the table above, what would be the least amount of money needed, in dollars, to purchase exactly 21 donuts? (Disregard the S sign when gridding your answer. For example, if the answer is $1.37, mark 1.37 on the grid.) P , -----'l<---- m --/'''----\----, N2Ri Figure not drawn to scale. 7. In the figure above, line m is parallel to line If x = y. what is the value of x? eand is perpendicu lar to line p. 8. Iff =Y and 2y =y, what is the value of x? 349 THE MATHEMATICS SECTION y B 9. The figu re above shows the graph of y = k ~ABC is 64, what is the value of k ? 350 r, where k is a constant. If the area of •c ~ III o '" '; •• CI ~ c o a. ~ ." • • U £.. c G0eeeeeeeee ,ye. eeeeeeeee • • ~ ." , ooeeeee@E>@@ . eeeeeeeee '" M <> - .. ~eeeeee • <> - ~ • <> - .. · .. @eee 8C· 0eeeeeeeee C· eeeeeeeee " eeeeeeee ooeeeeeeee :>C. ooeeeeeee@ -G eeeeeeee@ , 0eeeeeeeee o_~ <> o_~~ <> .1 .; N @0@@G@@ ee8@G@@ sx· :>C. eeeeeeeee@ G eeeeeooe@ <> - 10@@e08 8e@0@@ "l(.,X.. X...)@@ .... ~--. :9\.. olf o X - )(N'If .. eee8e@8@@ <> - .. oci "' C· 9G .. N c· eeeeeeeee@ , . eeeeeeeee@ , . eeeeeeooee C· 0080eeeee C·3eeeeeeeee , . eeeeeeeeee , . oeeeeeeeee . eeeeeeeee to .. SX· C· (=:J~8@@6@@ <-' oeeeE)@@E)ee <> <> Gee0E)@eee - " . . --, -@ ~ THE MATHEMATICS SECTION Answers and Explanations I. In a restaurant where the sales tax on a$4.00 lunch is SO.24, wha t will be the sa les tax due, in dolta rs, on a $15.00 din ner? (Disregard the$ sign whe n gridding you r

answer. For example, jfthe answer is $1.37, mark 1. 37 on the grid.) ~epinMind Answer: The correct answer is .90 or .9. Do not grid zeros before the decimal point. For example, don 't try to grid 0.90; just grid .90 or .9. The question asks for the number of dollars, so 90 for 90 cents would be wrong. Explmwtion: One way to solve this problem is to determine the tax on each$1.00 and then multiply this amount by 15 to get the tax on $15.00. The tax on a$4.00 lunch is $0.24. Then the tax on$l.00 would be

i

this amount, which is $0.06. So the tax on$15.00 wou ld be $15 x .06 =$0.90.

2. A team has wo n 60 percent of the 20 games it has played so far this season. If the team plays a total of 50 games all season and wi ns 80 percent of the remain ing games. how many games will the team win for t he entire season?

~.PlnMind

When working problems, especially student-produced respons e problems, it is a good idea to check your answers if you have time. For e xample: Games

Games

Woo Plaved 12_60% of20 So far: 20 24_80%of30 Remaining: 30 Tota l: 50 3.

You don't have to use a table, but you should find some way to check that your answer fits the informatio n in the problem.

Explanation: Express the information in mathematical terms: How many games has the team won so far? 60% of 20 games

=

60

100 x 20 = .6 x 20 = 12 games How ma ny ga mes will the team win the rest of the season? The total number of games left is 50 - 20 = 30. The tea m will win 80 percent of 30 games during the rest of the season.

80

100 x 30 = .8 x 30 = 24 games The total number of wins is: 12 + 24 = 36. Grid in 36.

3. lf II is a two-digit number that can be expressed as the produc t of two consecutive even integers. what is one possible value of II ?

Answer: There are three acceptable correct answers: 24, 48 and 80. You have to find only one. Explanatioll: Although there are several values fo r n that will work, you have to find only onc.

352

Student-Produced Response Questions

{;eplnMlnd is the product of two consecutive even integers. In other words, the question tells you to mu ltiply consecutive even integers.

• Tl

• Tl

is also a two-digit number.

Some questions have more than one correct answer. You can grid anyone of the correct answers and get full credit.

TRY SOME VALUES

• 8 is not a two-digit number, so n can not be 8. Try the next two consecutive even integers, 4 and 6. · 4x6=24 • 24 is a two-digit number. • 24 is the product of two consecutive even integers. Therefore, 24 is an acceptable value for

Tl.

Grid in 24.

The other possible values are 48 (6 x 8) and 80 (8 x 10). You can grid in anyone of these three values and get credit for answering the question correctly.

4. If the ra tio of 11 10 b is

f. whal is the ratio of21l to b ?

4 A nswer: The correct answer is 13 ,4.66 or 4.67. Explanation: This question requires that you know how to work with ratios. EXPRESS THE RATIO

a

The ratio of a to b can be written as Ii

.

The ratio of a to b iS~, which can be expressed as ~ = ~. a

7

If1J = 3' then Grid in the answer

Ii as 14/3.

a

(7)= '3' 14

21J= 23

Here are some facts you should know about gridding:

14 can-

not be gridded as

The grid-

4l 4i

re ading system cannot tell the difference between

How ever, if you change

and

~2 .

14 t o a

decimal, either 4.66 or 4.67 is an acceptable answer.

353

THE MATHEMATICS SECTION

5. If the population of a town doubles every 10 years, the population in the year X + 100 will be how many times the population in the year X?

A nswer: The correct answer is 1024. Explana tiorl; Express the population growth in mathematical terms. Each time the population doubles, multiply it by 2. Let p represent the population in year X . • In 10 yea rs, the population increases from p to 2p. • In 10 more years, it increases to 2(2p). • In 10 more years, it increases to 2!2(2p)], and so on for 100 years. This repeated doubling can be expressed by using powers of 2: • Another way to express 2(2) is 22 , • So a populat ion of2(2p)

='

(2 2)p.

• In 10 more years, the population is 2(2 1)p. or (2 3)p. • In 10 more years, the population is 2(2 3 )p. or (2 4 )p. etc. HOW MANY GROWTH CYCLES ARE THERE?

• The population doubles (is raised to another power of 2) every 10 years. • This goes on for 100 years. 100

• So there are 10 = 10 cycles. • The population increases to 2LO times what it was in year X . FIGURE OUT THE ANSWER

~

Keep In MInd

A calculator can help speed up getting the answer to some questions.

You ca n multiply ten 2s, but this invites error. You may want to use you r calculator to find 210. Some calculators have an exponent key that allows you to find y directly. If your calculator does not have this feature, you can still quickly get the value of 210 on your calculator as follows. 2'= 2x 2x 2 x 2 x2 =32

354

StudentwProduced Response Questions

Number of Donuts

Tot a l Price

$0.40 Box of 6$ 1.89

Box of 12

$3.59 6. According to the information in the table above, what would be the least amount of money needed, in dollars, to purchase exactly 21 donuts? (Disregard the S sign whe n gridding your answer. For example, if the answer is S1.37, mark 1.37 on the grid.) Answer: The correct answer is 56.68. Explanation: WHAT DO YOU KNOW1 • You can save money by purchasing donuts by the box. A box of 6 donuts costs 51.89, but 6 ind ividual donuts cost$2.40. • You can save more money by purchasing the larger box. A box of 12 donuts costs $3.59, but 2 boxes of 6 donuts cost 2($1.89) = $3.78 . • The question says you have to buy exactly 21 donuts. USE YOUR HEAD You want to buy as few ind ividual donuts as you can. You want to buy as many donuts in large boxes as you can. You cannot buy 2 boxes of 12 because that wou ld put you over the 21 donut limit. So start with 1 box of 12 donuts. w • Ma rk down 12 donuts, so you ca n keep track as you add more donuts. • Ma rk down 53.59, so you ca n keep track as you spend more money. You have 12 donuts, so there are 9 left to buy. You can save money by buying a box of 6 donuts. (1.e p In MInd When you're working out an answer, jot down your calculations in the space provided in your test booklet. • Add 6 to your donut total. • Add$1.89 to you r money total. You now have 18 donuts, which mea ns you will have to buy 3 ind ividual donut s. • Add 3 to your donut total. You now have exactly 21 donuts. • Add 3 x $.40 =$1.20 to your money total. • Add up the dollar figures: $3.59 +$1.89 + $1.20 =$6.68. Grid in 6.68. Remember to disregard the $sign. No te: Do not grid 668 without the decimal mark - it will be interpreted as 355 THE MATHEMATICS SECTION$668! p

,

----';1'---.

--1'-'---1--- 1 ~

Figure not d rawn \0 scale.

7. In the figure above, li ne m is parallel to line f and is perpendicu lar 10 line p. If x = y, what is the value of x?

{;ePlnMlnd Write relevsnt facts (angles. lengths of sides) on the figure as you pick up more informa-

tion. look for special properties

Explanation: This question requires that you use you r knowledge of li nes, angles and triangles to calculate values for parts of the fig ure that are not labeled. As you work on the question, remember:

question. If it is about angles. look for special properties of angles. If it is about areas, look for special properties of areas. Special properties that help you translate between different kinds of measurements can be especially useful . For example: • If you know two sides of a

triangle are of equal length,

then you know that the meaSUTes of the angles opposite

• It's helpfu l to label pa rts of the fig ure as you work. • Use what you know about parallel lines, vertical a ngles, a nd special types of triangles and their properties. WHAT DO YOU KNOW?

• Lines eand m are pa rallel . • Line p is perpendicu la r to line m.

those two sides are equal. • If you know two s8gments are radii of the same circle, you know that they are of equal length.

WHAT CAN YOU FIGURE OUT FROM THE FIGURE?

You ca n use the pa rallel lines in the figu re to label another angle that has Illeasure XO because correspondi ng angles are congruent. P

,

------';1F---. --1"-+--- 1 Because line p is perpendicula r to line m, Therefore,

XO

+ yO= 90°. You are told that x = y .

2x = 90 x = 4S

Grid the answer, 45. Disregard the degree symbol (0).

356

Student-Produced Response Questions

8.

If; '" y and 2y '" y, what is the value of x ?

Answer: The correct answer is O. Explanation: Th is is another question that takes some reasoni ng in addition to

some simple mathematical manipulation. LOOK AT THE EQUATIONS

The second equation may look a little unusua l to you: 2y=y

~epinMind

If 2y = y, then y = O. Therefore: 2y= 0

To grid zero, just enter 0 in a s ingle column (any column where o appearsl . leave the other three columns blank.

x=O Grid in the answer, O. y B

____A~-o~~C~-x

o

9. The figure above shows the graph of y == k 6ABC is 64, what is the value of k?

r, where k is a constant. If the area of

Explanation: The area of 6ABC is equal to "2(AC)(OB), which is equivalent to (OC)(OB) because the parabola is symmetric about the y-axis and ±AC = OC . So

you know that (OC)(OB) = 64 . Because the length of OB can be determined from the y-intercept of the graph of y = k -

r,

it fo llows that OB = k . Similarly. the

length of OC can be determ ined from the x-intercepts of the parabola. To fin d the x-intercepts, set y = k - :xl = 0 . Solving this equatio n for x gives the two intercepts

x = ~...fk, which correspond to the pOint A (-...fk, 0) and the point C (...fk, 0). Therefore, OC = ...fk, and you can now substitute into the equation (OC)(OB) = 64 to get that "

,

(.Jk)(k) = 64. But since (.JkHk) = klk = kl, it follows that kl = 64, and you can now

solve, this equation for k by ra ising both sides to the two-thirds power. Therefore, k = (64)' =

[%"4)' = 4' = 16. 357

~~ ~:i~

~:f~~ r-~------------------------. ~ Recap 1. Remember that only the answer entered on the grid is scored; the answer that is handwritten on the top of the grid is not

scored. 2. Don't grid zeros before the decimal pOint.

3. Take each question one step at a time because some questions that seem difficult are just a series of easy questions. 4 . Think about what you need to know in order to answer a question. 5. Make sure you answer the question that has been asked. 6. Double-check your answers, especially on grid-in questions, if you have time. 7 . Remember that some questions have more than one correct answer; you can grid any of the correct answers and get full

,

credit.

8. State an answer as a fraction or a decimal: You can grid or .5.

1

1

Zas '2

3 9 . Write mixed numbers as improper fractions. For example, 1"5 is 8 "5. The grid-reading system cannot distinguish bet ween 3 13 1"5 and 5'

10. Grid as much of a repeating decimal as will fit in the grid. You may need to round a repeating decimal, but round only the last digit: grid .66.

~ as~,

.666 or .667. Do not grid the value

~ as

.67 or

11. Use a calculator to help speed up getting an answer. 12. Jot down your calculations in your test booklet. 13. Write relevant facts (about angles, lengths of sides, etc.) on figures as you pick up more information. 14. Look for special properties that may help you answer questions. 15. Grid zero by entering 0 in a single column (any column where 0 appears) .

358

Student-Produced Response Questions

Practice Questions - Student-Produced Response Questions For Student-Produced Response questions 1-8, use the grids at the bottom of the answer sheet page.

\!Irit~:::'"'''r=·t';t:~~~iJ·--: ::o". .""

Answer: 201 Either ,ition IS correct.

An,we" 2.5

2 0

"

line

Grid in =ult. Not~: Y011 ma)" stan yOllr answers in any column. 'I"'<"" permilling. Columns 001 neWed should be ~ft

blank . • Mark no more than one circle in any eolumn.

• Becau.o;e tile answer sheel will be machine· ~d. yuu will r<:<:e,,'e crnHi unly ir Ihe ci rdes arc filled in COf're<:tly. • Although no( require<!. it i< ,uueMed that you wrile y""r an.we. in the boxc.. at the top oftbc columns to help you fin;n the c;n.:les accurately.

• Some prQbkms m"y 1>/"" mOre than one com:ct anSwer. In such cases. grid OIlly one anSwer,

• I)e(:lmul A.",,'ers: [fyou obtain a decimal answer with mQrc digilS than tloe grid can acc'QnulIoomc. it may be either rounded or truncated. but it mUlt lillthe entirc grid. For eumple. if you obtain an allSWer such as 0.6660 .... you should record your ~uI13' ,66/\ or .667. A Ieo." Mc-cursl~ value su~h a~.66 or .67 "ill be scorW lIS inCOf'ffl:t. o Accepta~le way. TO grid j are:

2 /3

• No question has a ""&atiYe ,,"Swe •.

• Mi~ed uumbers loch 3, 3 ~ ,nuS! be ~dded as

3.~ or 7/2. (If D~ ~l~

is gridded. it will be

b b b o

bb7

000 0000 G)@G)G) 0000 <!)<!)<!)<!)

I. In 2 weeks, 550 cartons of juice were sold in Ihe school cafeleria. At Ihis rate, how many cartons of juice would one expecl to be sold in 5 weeks?

2. For what integer value of x is 3x + 5 > 11 and x - 3 < 1

359

THE MATHEMATICS SECTION

3. The number 0.008 is equivalent to the ratio of 8 to what number?

x

4

y

1

9

36

3

4. If Y is directly proportional to the square foot of x, what is the missing value of y in the table above?

o

5. In the figure above, if 0 is the center of the circle, what is the value of x ?

6. The average (arithmetic mean) of 4 numbers is greater than 7 and less than 11. What is one possible number that could be the sum of these 4 numbers?

360

Student-Produced Response Questions

7. A line twith a slope oft passes through the points (0, value of y?

t) and

(4,y) . What is the

..,J>?-r=2t-x 8. If x and t are positive numbers that satisfy the equation above, what is the value of

-=-, I .

361

THE MATHEMATICS SECTION

,--------,

I

I.

2

3

,

~

1(;) >:<

~

I~ :~

-as •- 0- 0

00

1 '0 '0

®® 0~' 0 0' ®®

~

, I~

~• • o0~'. 0' 0 o . ~r. ®® 7.

, . ~

~(15 0~ ®®

00' 000-

- - 00

-0 !-0 0

-0 0' '0 '0 0~ 0 ' ®® 8

, ,

,. 0. k

I~

0 , 0 0- 0 0

~~ ~ ~ ~~ 00 0~

®® 0

~~ 0 ~

--00 • 0

•'~•

®®

6

Id8

00 01~ ®® , , 00 ~0

362

-0 0~ 0 ' '0

0 0 0 0

5

00 1*1(1)

0 ®® 0

4.

(;)

. ,. I~ b

0 ~ ~0 -0 0

0 0 0

.fl.:,

,

. ,.

1(;) I~i~ '~

0 '0 0 -0

~ ~~

0 00

0 0 ~~ 0 ~0 0 '0

.

0 0 0 0 0 0 0 0 0 0

, I~b

Cl :

00 I~ I~ -0 0~ 0 ' '0 00 0 -0 0~

-

0 ' -0 00 ' 0 0~ 0 ' ~0 '0

THE MATHEMATICS SECTION

2. 3 3. 1000

4. 312 or 1.5 5. 55

6. 28

8 . 5/4 or 1.25

Additional practice questions can be found in The Official SAT Online Course at www.collegeboard.comlaatonlinecourse .

364

CHAPTER 21

Practice for the Mathematics Section

The questions in Ihis chapter give you a chance to practice the approaches you've learned so far. Use the approaches on the questions in this chapter before you take the practice tests in the last section of this book. This chapter will give you practice on different types of math questions that are on the SAT.

365

THE MATHEMATICS SECTION

Multiple-Choice Questions This section contains two types of questions. For questions 1- 12, solve each problem and decide which is the best of the choices given. Fill in the corresponding circle on the answer sheet. You may use any available space for scratchwork.

Notes 1. The use of a calculator is permitted.

2. All numbers used are real numbers. 3. Figures that accompany problems in Ihis lest aTe intended to provide information useful in solving the problems.

They are drawn as accurately as possible EXCEPT when it is stated in a specific problem Ihal the figure is not drawn to scale. All figures lie in a plane unless otherwise indicated.

4. Unless otherwise specified, the domain of any function/is assumed to be the set of all real numbers x for whichflxl is a real number.

IGD·6~·8··~

...

.!;

§

{

A_V

1

A .lw

C_2M

b

..

I A ," }:M

V_M

V_VI~

c'."l+b f

The IIUI1Iber of dec-s of an:: in I tirde is 360. rnea5urt$in degrees oflhc ....1es of. tnansJe is 180. to: The sum of~ CABLE TELEVI SION SUBSCRIBERS IN TOWN T BY REGION Ion Region M RcgionN Region 0 Region P = 1.000 subscribe rs OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ I. If the four regions shown in the graph above are the only regions in Town T, the total of which two regions accounts for exactly 70 percent of all cable television subscribers in Town T? (Al (8) (C) (D) (El 366 Regions M and N Regions M and 0 Regions Nand 0 Regions Nand P Regions 0 and P Practice for the Mathematics Section 2. If xl: k, where x and k aTe integers, which of the following could be the value of k? (A) 3 (6 ) 6 (e) 9 (0) 12 (E) 15 3. For which of the follow ing graphs off doesj(x) '" j(-x) for all values of x shown? (A) y 2 -2 - I (C) f 01 -I Y 2 y (B) f 2 x 2 -2 - 10 x y (D) f f x - 2 _I 0 -I (E) 1 2 -I 1 2 x y 2 -2-10 -I 2 fx 4. A class has twice as many boys as girls. The students in the class stand in one line, with a girl at the front of the line. Which of the following must be true? (A) (B) (C) (D) (E) The last person in line is a girl. The last person in line is a boy. There are more girls than boys in the class. There are at least two girls standing next to each other. There are at least two boys standing next to each other. 367 THE MATHEMATICS SECTI ON 5. Wh ich orlbe following is an equation oflhe line that has a y-inlerccpt of2 and an x-intercept of3? (A) -2x+3yo:=4 (B) -2x+3y=6 (C) 2x+3y=4 (D) 2x+3y",6 (El 3x+2y=6 6. In a certain game, each orS players received a score between 0 and 100, inclusive. If their average (arithmetic mcan) score was 80. what is the greatest possible number oflhe 5 players who could have received a score orSO? CAl None (8) One (C) 1\"'0 (D) Three (E) Four 7. On the staircase shown above, both the depth and the height of each step are s, and each step forms a right angle. What is the value of t in terms of s? (A) lOs (B) 14s (C) 7s..fi (D) 7,.,fj (El 368 2S1 Practice for the Mathematics Section y 8. The figure above shows a portion of the gra ph of the function f If fix + 5) = fix) for all values of x, thenf(x) = 0 for how many different values of x between 0 and 12? (A) Eight (B) Nine (C) Ten (D) Eleven (E) l\ve\ve 9. The sum offour consecutive odd integers w, x,y and z is 24. What is the median of the set {w, x,y, z, 24j? (A) (B) (C) (D) (E) 3 5 7 9 24 I ( 369 THE MATHEMATICS SECTION x fix) g(x) 5 2 1 4 2 2 3 3 4 1 4 1 5 5 3 10. According to the table above, if k '" j(3), what is the value of g(k) ? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 k classes with n students in each class. If a total of p pencils are distributed equally among these students, how many pencils are there for each student? 11. In a certain school, there are (A) Lk, (B) k, p , (C) kp (D) np k (E) npk 370 Practice for the Mathematics Section 12. In the figure above, the four circles have the same center and their radii are 1,2,3 and 4, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring? (A) 1;2 (B) 1:4 (C) ' " (D) 3:7 (E) 5;7 37' THE MATHEMATICS SECTION Student-Produced Response Questions For Student-Produced Response questions 1-8, use the grids al the bollom of the answer sheet page. '"Write .,,":.:. . . ·(I*~~~H-::'' ' lioc Qrid in ",sul l. ~ You onay sian your answers in ony col um n•• pare pc'nniuing. Colurnns IlOI "ecdr(l .,hoo ld be le ft blank. • Becllu!.e ,,,,= aM,"'"" !.heel will be machi ... • • ,Mart no tnI'N"e than ODe circle in any oolumn. scortd, you .. iIl ~>'t ertdit only irt~ circle . l~~~~~~~~~~'~""~'~~'~: III _'" nUfli i n rorn<:Uy. • Although flnt O"eI.!uiml. il is ""J!MCil<.-d thai you "'me your ansWCT III the bo~~ at tJ>c, I(IJI of the columns 00 help you fill in !he c;n:1e. K<:umdy. Acctplahlc 2 • Some problems may h.we nlOf'C than one t:Ofre<;I ,"",wcr. In such C3'JCS, gnd only one ""'''"Cr. • No qllUli<> J.' or 7/ 2. (If ~,,~ . cd Inlerpn:1 U i. gri 31 ) 1) 2'I'l0l 2" 1\ will be ''''1''' , • • (!) ~~ . ", • 1 (!)@@@ ·0 1. A store has 660 books in stock. If 30 percent of these books are on sale, how many books are.!l2.t on sale? 372 Practice for the Mathematics Section einches I.. in'hes '------------' N2k;. Figure not drawn to scale. 2. The perimeter of the rectangle above is p inches and the area of the rectangle is 36 square inches. If and ware integers. what is one possible value of p ? e 3. Ifx+~=2.whatisthevalueofr+~? 4. If{of f is subtracted from 2. what is the resulling value? 5. Tim wrote a seven-digit phone number on a piece of paper. He later tore the paper aCcidentally and the last two digits were 1051. What is the maximum number of arrangements of two digits. using the digits 0 through 9. that he could use in attempting to reconstruct the correct phone number? 373 THE MATHEMATICS SECTION 6. If the slope of the line that passes through the points (a, 0) and (I, -2) is l, what is the value of a ? 2 7. One adult and to children are in an elevator. If the adult's weight is 4 times the average (arithmetic mean) weight of the children, then the adult's weight is what fraction of the total weight of the 11 people in the elevator? y e (0 ,4) (- 5,0) ~~~~ O~-----+x 8. The fi gure above shows line C in the xy-coordinate plane. Line m (not shown) is obtained by horizontally tra nslating each point on line 2 units to the left. If the equation of m is y = + k, what is the value of k? tx 374 e Practice for the Mathematics Section 3 2. Idr. 18 '-' .(j) I~ I~ • • 0 '-' , '0 0 0 • •® ® •' 0 ® 0 ® ~~ ® '31 :, :b o0~• ~I~ ®® ®® @@ 00 ®® ®® <;) ®® ®® @® 0~ 0 ' ®® 00 00 ® ® 0 0 0 , ,---, 4 '-' IGl Ir. Ir.< ~ ® ~ 'i ~ 0~ . . I~, : Ii 6 ,----, 8 18 b ct I~ I~ ~~~ ~~~~ 0 0 0 0 0 ~0 0® ~ ~ 7 8 '-' 8, 18 b I~ I~ ~ 0 ~ 0~ ®00 ~ 0 0 0 ~ 0 ® i <;) b 18 8, '-', 0) I~ 0) 0) 0 0 0 ® 0 0 0 ® 0 ® 0 ® 0 0 0 0 0 ® 0 ® 0 0 ® 0 0 ® 0 ~ ~ I 375 THE MATHEMATICS SECTION Answer Key Multiple-Choice Questions l.A 2. C 3. C 4. E 5.0 6. C 7. C 8. B 9. C 10. E 11. A 12. 0 Student-Produced Response Questions (Grid-ins) l. 462 2. 24.26,30,40 or 74 3. 2 4.5/3, 1.66or 1.67 5. 100 6. 5 7. 2/7, .285 or .286 8. 28/5 or 5.6 Additional practice questions can be found In The Official SAT Online Course at www.coliegeboard.comJsatonlinecours• . 376 PART V 10 Official Practice Tests with Answer Keys 377 10 COMPLETE PRACTICE TESTS WITH ANSWER KEYS Taking the Practice Tests Part V offers 10 practice tests for the SAT. Each version includes only 9 of the 10 sections in the actual test. The variable sections have been omitted. You'll get the most Qut of the practice tests if you take them under conditions that are as close as possible to those of the real test: • Leave you rself3 hours and 20 minutes to complete each sample test. (The actua l test is 3 hours and 45 minutes. The omitted variable section is 25 minutes.) • Sit at a desk or table cleared of any other papers or books. Items such as dictionaries, books, or notes won', be allowed when you take the actua l SAT. • For the math quest ions, use the calculator that you plan to use on the test. • Set a timer or use a watch or dock to time you rself on each section. • Tear out or make a copy of the 8-page practice answer sheet located just before each practice test and fill it in just as you will on the day of the actual test. • When you complete a practice test. use the corresponding answer key, scoring instructions, scoring worksheet. and conversion tables to determine your score ranges. Q After you complete each test: • Use this book to its full potential! Get exclusive access answer explanat ions. free practice score reports and free sample student essays to help you score your essay in the Book Owners' Area at www.collegeboard.com/satstudyguide. • Want more practice? Get 10 more officia l practice tests, auto essay scoring and lesson pla ns from the lest maker by subscribing to The Official SAT Online Course. As a book owner. you're entitled to a$10 discount. Sign up at www.collegeboard.com/satstudyguide.

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