SAT_Math_Essentials
NEW YORKSATMATHESSENTIALS® Copyright © 2006 LearningExpress.All rights reserved under International and Pan-American Copyright Conventions.Published in the United States by LearningExpress, LLC, New York.Library of Congress Cataloging-in-Publication Data:Cernese, Richard.SAT math essentials / Richard Cernese, Dave Smith.p. cm.Includes bibliographical references and index.ISBN 1-57685-533-3 (alk. paper)1. Mathematics—Examinations, questions, etc.2. College entrance achievement tests—United States—Study guides.3. Scholastic Assessment Test—Study guides. I. Smith, Dave.II. Title.QA43.C35 2006510.76—dc222005027526Printed in the United States of America987654321 ISBN 1-57685-533-3For more information or to place an order, contact LearningExpress at:55 Broadway8th FloorNew York, NY 10006Or visit us at:www.learnatest.com INTRODUCTION vCHAPTER 1 Taking the SAT 1CHAPTER 2 Preparing for SAT Math 7CHAPTER 3 Math Pretest 13CHAPTER 4 Techniques and Strategies 27CHAPTER 5 Numbers and Operations Review 37CHAPTER 6 Algebra Review 69CHAPTER 7 Geometry Review 95CHAPTER 8 Problem Solving 149CHAPTER 9 Practice Test 1 173CHAPTER 10 Practice Test 2 197CHAPTER 11 Practice Test 3 221GLOSSARY 245Contentsiii Whether you bought this book, borrowed it, received it as a gift, took it out of the library, stoleit (not a good idea!), or are simply reading it in a book store, you’re undoubtedly hoping to acethe Math sections of the SAT Reasoning Test. Well, you’ve come to the right place to get pre-pared! This book provides answers to any and all questions you may have about the Math sections of the SAT. Toget the most benefit from the book, work through it from cover to cover. Every hour you put into preparing forthe SAT will pay off on test day. Here is a breakdown of what to expect in each section of the book:Chapter 1 is an introduction to the SAT. It answers basic questions you may have about the exam.Chapter 2 provides information about what to expect on the Math sections of the SAT and how best toprepare for the SAT.Chapter 3 is a math pretest. This test serves as a warm-up, giving you a flavor for the range of math ques-tions found on the SAT. Answers and explanations follow the pretest.Chapter 4 teaches strategies and techniques for acing the Math sections of the SAT.Chapter 5 reviews concepts of numbers and operations and provides sample numbers and operationsSAT questions with explanations.Chapter 6 reviews algebra and provides sample algebra SAT questions with explanations.Chapter 7 reviews geometry and provides sample geometry SAT questions with explanations.Chapter 8 reviews problem-solving skills and provides sample SAT word problems with explanations.Chapters 9, 10, and 11 are Practice Tests 1, 2, and 3. These practice tests are similar to the Math sectionsof the SAT. Answers and explanations follow the practice tests.The Glossary provides definitions of all key math terms used in this book.Introductionv What Is the SAT?The SAT Reasoning Test is a standardized test developed by the Educational Testing Service for The College Board,an association of colleges and schools. It contains questions that test skills in math, reading, and writing.Why Take the SAT?Most colleges require prospective students to submit SAT Reasoning Test scores as part of their applications. Col-leges use SAT exam scores to help them evaluate the reading, writing, and math skills of prospective students. There-fore, it is important to do your best on the SAT so you can show colleges what you are capable of accomplishing.CHAPTERTaking the SAT11 Who Takes the SAT?The SAT Reasoning Test is the most common stan-dardized test that high school students take whenapplying to college. In fact, approximately two millionstudents take the SAT each year.Will My SAT Scores DetermineWhether I Get into College?No. Your SAT scores are only one small part of any col-lege application. In other words, your SAT scores alonewill not determine whether or not a college acceptsyou as part of its student body. Let’s say that again, a lit-tle louder: YOUR SAT SCORES ALONE WILL NOTDETERMINE WHETHER OR NOT A COLLEGEACCEPTS YOU AS PART OF ITS STUDENT BODY.Colleges look at individuals, not just test scores andgrades. They want fascinating, curious, motivated peo-ple on their campuses, not a bunch of numbers.When evaluating candidates, admissions officerslook at your academic performance, but they also lookat the rest of your life. What are your interests? How doyou spend your time outside of school? What are yourgoals? When you submit an application to college, youshould make sure it shows what makes you a uniqueperson. Colleges typically aim to fill their campuseswith a diverse group of individuals. Think about whatyou can best offer to a college community. What areyour strong points? Do you excel in music, theater, art,sports, academics, student government, communityservice, business, or other areas? It doesn’t matter whatyour interests are. It only matters that you have them.Let your best qualities shine through in your applica-tion and you can be confident that you are presentingyourself as a strong possible candidate for admission.So, don’t sweat the SAT. Getting nervous about itwon’t help you anyway. As long as you follow throughwith your plan to prepare for it, your score can help youbecome an attractive candidate.When Do I Take the SAT?The SAT is offered on Saturday mornings several timesa year. Your high school guidance office can give you aschedule. You can also find a schedule online atwww.collegeboard.com. Please note that Sundayadministrations will occur the day after each Saturdaytest date for students who cannot test on Saturday forreligious reasons.How Many Times Should I Takethe SAT?The number of times you take the SAT is up to you. Youmay register and take the exam as often as you wish.Most colleges will not hold an initial lower score againstyou, and some will be impressed by a substantiallyimproved score, so taking the SAT twice or three timeswith the goal of raising your score is recommended ifyou think you can do better. However, some studentsprepare hard for their first SAT and feel satisfied withtheir initial score.Regardless, you shouldn’t take the SAT more thanthree times. Chances are your score will not change sig-nificantly on your fourth test. If you are still disap-pointed after your third score, your time, money, andenergy will be better spent on other parts of your col-lege application.But no matter how many times you have takenthe SAT, you’re smart to be using this book. The onlyway to raise your SAT score is through preparationand practice.–TAKING THE SAT–2 Where Is the SAT Given?Many high school and college campuses host the SATs.When you register, you will be given a list of sites inyour local area, and you can pick one that is comfort-able and convenient for you.Where Do I Sign Up for the SAT?To sign up for the SAT, you can:1. Register online at The College Board’s website:www.collegeboard.com.2. Get the SAT Registration Bulletin from your highschool guidance office. The Bulletin contains a reg-istration form and other important informationabout the exam. If you are retaking the exam, youcan also register by phone at 800-SAT-SCORE.How Long Is the SAT?The SAT takes three hours and 45 minutes. In additionto the testing time, you will get two or three five- to ten-minute breaks between sections of the exam. You willalso spend up to an additional hour filling out forms.Overall, you can expect to be at the testing location forabout four and a half hours.What Is Tested on the SAT?The SAT has approximately 160 questions divided intoeight test sections:■three critical reading sections ■two 25-minute sections■one 20-minute section■three math sections ■two 25-minute sections■one 20-minute section■two writing sections■one 35-minute multiple-choice section■one 25-minute essayYour scores on these eight sections make up yourSAT scores.In addition to the core eight sections, there is oneunscored “variable,” or “equating,” section that the testwriters use to evaluate new questions before includingthem on future SATs. Thus, you will actually completea total of nine sections on test day. But it will be impos-sible for you to tell which section is the variable section:It can be critical reading, multiple-choice writing, ormath, and it can appear in any place on the exam. Soalthough the variable section does not affect your SATscore, you must treat each section as if it counts.In What Order Are the SectionsTested?The writing essay is always the first section of the SAT.The multiple-choice writing section is always the lastsection. The remaining sections can appear in anyorder.How Is the SAT Scored?SAT scores range from 600–2400. You can score a min-imum of 200 and a maximum of 800 on each subject:math, critical reading, and writing.A computer scores the math questions. For themultiple-choice math questions, the computer countsthe number of correct answers and gives one point foreach. Then it counts your incorrect answers anddeducts one-quarter point from the total of your cor-rect answers. For the grid-in math questions, the com-puter counts the number of correct answers and givesone point for each. No points are subtracted for incor-rect answers to the grid-in questions. If the score thatresults from the subtraction is a fraction of a point,–TAKING THE SAT–3 Four Steps to Scoring Math Questions on the SATFor multiple-choice questions:1. Correct answers are added: 1 point for each correct answer.2. Incorrect answers are subtracted: ᎏ14ᎏpoint for each wrong answer.3. Your raw score is the result of adding correct answers, subtracting incorrect answers, and thenrounding the result to the nearest whole number. For grid-in questions:1. Right answers are added: 1 point for each correct answer.2. Wrong answers receive zero points: No points are subtracted.3. Your raw score is the total number of correct answers.Once questions are scored, raw scores are converted to scaled scores, using an equating process.4your score is rounded to the nearest whole number.Your raw score for the math sections is then convertedto a scaled score (between 200 and 800), using the sta-tistical process of equating.Math Score Reporting The College Board will send you a report on yourscores. They will also send your scores to any schools(up to four) you requested on your application. Col-leges, naturally, are used to seeing these reports, butthey can be confusing to everybody else. Here’s how youlook at them:You will see your scaled math score in a columnheaded Score. There are also columns titled Score Rangeand Percentiles College-bound Seniors. The informa-tion in these columns can be useful in your prepara-tions for college.Score RangeImmediately following your total scaled math score,there is a score range, which is a 60-point spread. Youractual scaled score falls right in the middle of this range.Based on experience, The College Board believesthat if you retake the SAT without further preparation,you are unlikely to move up or down more than thirtypoints within each subject tested. In other words, if youscored a 550 in math on your first SAT, chances are youwon’t score less than 520 or more than 580 in math ifyou take the exam again without any extra preparation.For this reason, it presents your score within a 60-pointrange to suggest that those are the range of scores thatyou could expect to get on the SAT.Keep in mind that The College Board believesyour score won’t change if you retake the SAT withoutfurther preparation. With further preparation, such asusing this book, your score can improve by much morethan 30 points.PercentileYour score report will also include two percentile rank-ings. The first measures your SAT scores against thoseof all students nationwide who took the test. The sec-ond measures your scores against only the students inyour state who took the test.The higher your percentile ranking the better.For example, if you receive a 65 in the national category . enjoy. The point isSAT Math at a GlanceMath Sections■two 25-minute sections ■one 20-minute math section■total of 70 minutes for math sectionsMath Questions. at:www.learnatest.com INTRODUCTION vCHAPTER 1 Taking the SAT 1CHAPTER 2 Preparing for SAT Math 7CHAPTER 3 Math Pretest 13CHAPTER 4 Techniques and Strategies