SAT prep course

Additional educational titles from Nova Press:

GRE Prep Course (624 pages, includes software)

GMAT Prep Course (624 pages, includes software)

Master The LSAT (560 pages, includes an official LSAT exam)

The MCAT Physics Book (444 pages)

The MCAT Biology Book (416 pages)

Law School Basics: A Preview of Law School and Legal Reasoning (224 pages)

Vocabulary 4000: The 4000 Words Essential for an Educated Vocabulary (160 pages)

Copyright © 2005 by Nova Press

Previous editions 2004, 2003, 2002, 2001, 2000, 1999, 1998, 1996, 1994

All rights reserved.

Duplication, distribution, or data base storage of any part of this work is prohibited without prior written

approval from the publisher.

ISBN 1889057282

SAT is a registered trademark of the College Entrance Examination Board, which was not involved in the

production of, and does not endorse, this book.

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iii

ABOUT THIS BOOK

If you don’t have a pencil in your hand, get one now! Don’t just read this bookstudy it, scrutinize it! In

short, for the next six weeks, this book should be a part of your life.

Although the SAT is a difficult test, it is a very learnable test. This is not to say that the SAT is

beatable. There is no bag of tricks that will show you how to master it overnight. You probably have

already realized this. Some books, nevertheless, offer "inside stuff" or "tricks" which they claim will

enable you to beat the test. These include declaring that answer-choices B, C, or D are more likely to be

correct than choices A or E. This tactic, like most of its type, does not work. It is offered to give the

student the feeling that he or she is getting the scoop on the test.

The SAT cannot be beaten. But it can be masteredthrough hard work, analytical thought, and by

training yourself to think like a test writer. Many of the exercises in this book are designed to prompt you

to think like a test writer. For example, in the math section, you will find Duals. These are pairs of

similar problems in which only one property is different. They illustrate the process of creating SAT

questions.

The SAT is not easynor is this book. To improve your SAT score, you must be willing to work; if

you study hard and master the techniques in this book, yourscore will improvesignificantly.

This book will introduce you to numerous analytic techniques that will help you immensely, not only

on the SAT but in college as well. For this reason, studying for the SAT can be a rewarding and satisfying

experience.

Although the quick-fix method is not offered in this book, about 15% of the material is dedicated to

studying how the questions are constructed. Knowing how the problems are written and how the test

writers think will give you useful insight into the problems and make them less mysterious. Moreover,

familiarity with the SAT’s structure will help reduce your anxiety. The more you know about this test, the

less anxious you will be the day you take it.

v

ACKNOWLEDGMENT

Behind any successful test-prep book, there is more than just the author’s efforts.

I would like to thank Kathleen Pierce for her many contributions to the book and for her continued

support and inspiration.

Reading passages were drawn from the following sources:

Passage page 35, from The Two Faces of Eastern Europe, © 1990 Adam Michnik.

Passage page 38, from Deschooling Society, © 1971 Harper & Row, by Ivan Illich.

Passage page 45, from The Cult of Multiculturalism, © 1991 Fred Siegel.

Passage page 49, from Ways of Seeing, © 1972 Penguin Books Limited, by John Berger.

Passage page 54, from Placebo Cures for the Incurable, Journal of Irreproducible Results, © 1985 Thomas

G. Kyle.

Passage page 59, from Women, Fire, and Dangerous Things, © George Lakoff.

Passage page 63, from Screening Immigrants and International Travelers for the Human Immunodeficiency

Virus, © 1990 New England Journal of Medicine.

Passage page 67, from The Perry Scheme and the Teaching of Writing, © 1986 Christopher Burnham.

Passage page 69, from Man Bites Shark, © 1990 Scientific American.

Passage page 71, from Hemingway: The Writer as Artist, © 1952 Carlos Baker.

Passage page 73, from The Stars in Their Courses, © 1931 James Jeans.

CONTENTS

ORIENTATION 9

Part One: Reading

Reading Comprehension 21

Critical Reasoning 81

Sentence Completions 99

Vocabulary 4000 108

Etymology 190

Vocabulary Drills 213

Part Two: Writing

Grammar 235

The Essay 285

Punctuation 286

General Tips On Writing Your Essays 310

Present Your Perspective On An Issue 319

Part Three: MATH

Substitution 347

Defined Functions 351

Functions 356

Math Notes 368

Number Theory 373

Geometry 381

Coordinate Geometry 408

Elimination Strategies 417

Inequalities 420

Fractions & Decimals 427

Equations 434

Averages 440

Ratio & Proportion 443

Exponents & Roots 447

Factoring 453

Algebraic Expressions 458

Percents 463

Graphs 467

Word Problems 474

Sequences & Series 483

Counting 487

Probability & Statistics 490

Miscellaneous Problems 494

Grid-ins 496

Summary of Math Properties 499

Diagnostic/Review Math Test 509

9

ORIENTATION

• WHAT DOES THE SAT MEASURE?

• FORMAT OF THE SAT

• PACING

• SCORING THE SAT

• SKIPPING AND GUESSING

• ORDER OF DIFFICULTY

• THE PSAT

• THE 2 OUT OF 5 RULE

• HOW TO USE THIS BOOK

Shortened Study Plan

• QUESTIONS AND ANSWERS

Orientation 11

What Does the SAT Measure?

The SAT is an aptitude test. Like all aptitude tests, it must choose a medium in which to measure

intellectual ability. The SAT has chosen math and English.

OK, the SAT is an aptitude test. The question isdoes it measure aptitude for college? The SAT’s

ability to predict performance in college is only a little better than chance.

No test can measure all aspects of intelligence. Thus any admission test, no matter how well written,

is inherently inadequate. Nevertheless, some form of admission testing is necessary. It would be unfair to

base acceptance to college solely on grades; they can be misleading. For instance, would it be fair to admit

a student with an A average earned in easy classes over a student with a B average earned in difficult

classes? A school’s reputation is too broad a measure to use as admission criteria: many students seek out

easy classes and generous instructors, in hopes of inflating their GPA. Furthermore, a system that would

monitor the academic standards of every class would be cost prohibitive and stifling. So until a better

system is proposed, the admission test is here to stay.

Format of the SAT

The SAT is a three-hour and 45-minute test. Only three hours and twenty minutes of the test count toward

yourscorethe experimental section is not scored. There are ten sections in the test.

Section Type Time

Reading

19 Sentence Completions

48 Reading Comprehension

67 Total Questions

70 minutes

(two 25-minute sections and one

20-minute section)

Writing

49 Grammar

1 Essay

49 Total Questions + Essay

60 minutes

(two 25-minute sections and one

10-minute section)

Math

44 Multiple-choice

10 Grid-ins

54 Total Questions

70 minutes

(two 25-minute sections and one

20-minute section)

Experimental Reading, Writing, or Math 25 minutes

The order of the format is not fixed: the sections can occur in any order.

The SAT is a standardized test. Each time it is offered, the test has, as close as possible, the same

level of difficulty as every previous test. Maintaining this consistency is very difficulthence the experi￾mental section. The effectiveness of each question must be assessed before it can be used on the SAT. A

problem that one person finds easy another person may find hard, and vice versa. The experimental section

measures the relative difficulty of potential questions; if responses to a question do not perform to strict

specifications, the question is rejected.

The experimental section, which is not scored, can be a reading section, a writing section, or a math

section. You won’t know which section is experimental. You will know which type of section it is,

though, since there will be an extra one of that type.

Because the bugs have not been worked out of the experimental section, this portion of the test is

often more difficult and confusing than the other parts.

This brings up an ethical issue: How many students have run into the experimental section early in

the test and have been confused and discouraged by it? Crestfallen by having done poorly on, say, the

12 SAT Prep Course

firstthough experimentalsection, they lose confidence and perform below their ability on the rest of the

test. Some testing companies are becoming more enlightened in this regard and are administering experi￾mental sections as separate practice tests.

Knowing that the experimental section can be disproportionately difficult, if you do poorly on a

particular section you can take some solace in the hope that it may have been the experimental section. In

other words, do not allow one difficult section to discourage your performance on the rest of the test.

Pacing

Although time is strictly limited on the SAT, working too quickly can damage your score. Many

problems hinge on subtle points, and most require careful reading of the setup. Because high school can

put heavy reading loads on students, many will follow their academic conditioning and read questions

quickly, looking only for the gist of what each is asking. Once they have found it, they mark their answer

and move on, confident they have answered it correctly. Later, many are startled to discover that they

missed questions because they either misread the problems or overlooked subtle points.

To do well in your classes, you have to attempt to solve every, or nearly every, problem on a test. Not

so with the SAT. In fact, if you try to solve every problem on the test, you will probably decimate your

score. For the vast majority of people, the key to performing well on the SAT is not the number of

questions they answer, within reason, but the percentage they answer correctly.

Scoring the SAT

The three parts of the test are scored independently. You will receive a reading score, a writing score, and a

math score. Each score ranges from 200 to 800, with a total test score of 6002400. The average score of

each section is about 500. Thus, the total average score is about 1500.

In addition to the scaled score, you will be assigned a percentile ranking, which gives the percentage

of students with scores below yours. For instance, if you score in the 80th percentile, then you will have

scored better than 80 out of every 100 test takers.

Skipping and Guessing

Some questions on the SAT are rather hard. Many test takers should skip these questions. We’ll talk about

how to identify hard questions as we come to them.

Often students become obsessed with a particular problem and waste valuable time trying to solve it.

To get a top score, learn to cut your losses and move on because all questions are worth the same number of

points, regardless of difficulty level. So often it is best to skip the hardest questions and concentrate on the

easy and medium ones.

Though there is a small guessing penalty on the SAT, if you can eliminate even one of the answer￾choices it is to your advantage to guess.

Order of Difficulty

Like most standardized tests, the SAT lists problems in ascending order of difficulty. So deciding which

questions to skip is easyskip the last ones. Note, some SAT sections have subsections. Within these

subsections, the problems also ascend in order of difficulty. For example, one of the writing sections has

three subsections: error identification, improving sentences, and improving paragraphs. So if the section

starts with improving sentences, then Question 1 will be the easiest and Question 11 (the last of improving

sentences questions) will be the hardest. Then Question 12 (the first error identification question) will be

the easiest, and so on.

Orientation 13

The PSAT

The only difference between the SAT and the PSAT is the format and the number of questions (fewer),

except for Algebra II questions, which do not appear. Hence, all the techniques developed in this book

apply just as well to the PSAT.

The 2 out of 5 Rule

It is significantly harder to create a good but incorrect answer-choice than it is to produce the correct

answer. For this reason usually only two attractive answer-choices are offered. One correct; the other

either intentionally misleading or only partially correct. The other three answer-choices are usually fluff.

This makes educated guessing on the SAT immensely effective. If you can dismiss the three fluff choices,

your probability of answering the question successfully will increase from 20% to 50%.

How to Use this Book

The parts of this book are independent of one another. However, to take full advantage of the system

presented in the book, it is best to tackle each part in the order given.

This book contains the equivalent of a six-week course which meets two hours a day, five days a

week. Ideally you have bought the book at least four weeks before your scheduled test date. However, if

the test is only a week or two away, there is still a truncated study plan that will be useful.

Shortened Study Plan

Reading:

Reading Comprehension: (The Six Questions)

Sentence Completions

Writing:

Grammar

General Tips on Writing Your Essays

Present Your Perspective on an Issue

Math:

Substitution

Functions

Math Notes

Number Theory

Geometry

Elimination Strategies

14 SAT Prep Course

Questions and Answers

When is the SAT given?

The test is administered seven times a yearin October, November, December, January, March, May, and

Juneon Saturday mornings. Special arrangements for schedule changes are available.

IfI didn’t mail in a registration form, may I still take the test?

On the day of the test, walk-in registration is available, but you must call ETS in advance. You will be

accommodated only if space is availableit usually is.

How important is the SAT and how is it used?

It is crucial! Although colleges may consider other factors, the majority of admission decisions are based

on only two criteria: your SAT score and your GPA.

How many times should I take the SAT?

Most people are better off preparing thoroughly for the test, taking it one time and getting their top score.

You can take the test as often as you like, but some schools will average your scores. You should call the

schools to which you are applying to find out their policy. Then plan your strategy accordingly.

Can I cancel my score?

Yes. To do so, you must notify ETS within 5 days after taking the test.

Where can I get the registration forms?

Most high schools have the forms. You can also get them directly from ETS by writing to:

Scholastic Assessment Test

Educational Testing Service

P.O. Box 6200

Princeton, NJ 08541

Or calling

609-771-7600

Or through the Internet:

www.ets.org

Part One

Reading

Reading 17

Format of the Reading Section

The SAT includes 3 reading sections: Two 25-minute sections and one 20-minute section. Each section

consists of two types of questions: Sentence Completions and Reading Comprehension. They are designed

to test your ability to reason using the written word. The sentence Completion questions are listed in

ascending order of difficulty, but the reading comprehension questions are not. There is a total of 19

sentence completion questions, and a total of 48 reading comprehension questions, which are drawn from

both long passages (400850 words) and short passages (about 150 words). The long and short passages

have the same type of questions.

TYPICAL FORMAT

Questions 18: Sentence Completions

Questions 924: Reading Comprehension

(two short passages and one long passage)

Vocabulary

The reading section is essentially a vocabulary test. If you know the word, you will probably be able to

answer the question correctly. Thus, it is crucial that you improve your vocabulary. Yet, even if you have

a strong vocabulary, you will still encounter unfamiliar words on the SAT. Much of the reading portion of

this book is dedicated to studying techniques that will help you discern the meaning of words you barely

recognize.

Nevertheless, don’t rely on just these techniquesyou must study word lists. Obviously, you cannot

attempt to memorize the dictionary, and you don’t need to. The SAT tests a surprisingly limited number of

words. Toward the end of the reading portion of this book, you will find a list of 4000 essential words.

Granted, memorizing a list of words is rather dry, but it is probably the most effective way of improving

your performance on the reading section.

Attempt the reading comprehension only after you have completed the sentence completions. As

mentioned before, each question on the SAT is worth the same number of points, whether it is long and

hard or short and easy. Sentence completion questions take only a fraction of the time that the reading

comprehension questions do.