, Mastering
* the
SAT
Math
Jerry Bobrow, Ph.D.
Contributing Authors
Dale Johnson, M.A.
Joe Skinner, M.A.
*SAT is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.
, About the Author Publisher’s Acknowledgments
Jerry Bobrow, Ph.D., is a national authority in the field of Editorial
test preparation. As executive director of Bobrow Test Project Editor: Suzanne Snyder
Preparation Services, he has been administering the test
Acquisitions Editor: Greg Tubach
preparation programs at more than 25 California institutions
for the past 30 years. Dr. Bobrow has authored more than 30 Copy Editor: Tere Stouffer
national best-selling test preparation books, and his books Production
and programs have assisted more than two million test-takers.
Proofreader: Henry Lazarek
Each year, Dr. Bobrow personally lectures to thousands of
students on preparing for graduate, college, and teacher cre- Wiley Publishing, Inc. Composition Services
dentialing exams.
Author’s Acknowledgments
I would like to thank Dr. Suzanne Snyder, of Wiley, for her
assistance and careful attention to the production process.
Finally, I would like to thank my wife, Susan; daughter,
Jennifer; and sons, Adam and Jonathan, for their patience,
moral support, and comic relief.
Mastering the SAT®: Math Note: If you purchased this book without a cover,
Published by: you should be aware that this book is stolen property.
It was reported as “unsold and destroyed” to the
Wiley Publishing, Inc. publisher, and neither the author nor the publisher
111 River Street has received any payment for this “stripped book.”
Hoboken, NJ 07030-5774
www.wiley.com
Copyright © 2007 Jerry Bobrow, Ph.D.
Published by Wiley, Hoboken, NJ
Published simultaneously in Canada
Library of Congress Cataloging-in-Publication Data
Bobrow, Jerry.
Mastering the SAT : math / by Jerry Bobrow.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-470-03660-0 (alk. paper)
ISBN-10: 0-470-03660-5 (alk. paper)
1. Mathematics—Examinations—Study guides. 2. Mathematics—Examinations, questions, etc. 3. SAT (Educational test)—Study guides. 4. Universities and col-
leges—United States—Entrance examinations—Study guides. 5. Achievement tests—Study guides. I. Title.
QA43.B649 2007
510.76—dc22
2006029556
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
1O/SR/RR/QW/IN
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, record-
ing, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of
the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400, fax 978-646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Legal Department,
Wiley Publishing, Inc., 10475 Crosspoint Blvd., Indianapolis, IN 46256, 317-572-3447, fax 317-572-4355, or online at http://www.wiley.com/go/permissions.
THE PUBLISHER AND THE AUTHOR MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETE-
NESS OF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDING WITHOUT LIMITATION WAR-
RANTIES OF FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES OR PROMOTIONAL
MATERIALS. THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY SITUATION. THIS WORK IS SOLD
WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN RENDERING LEGAL, ACCOUNTING, OR OTHER PROFESSIONAL
SERVICES. IF PROFESSIONAL ASSISTANCE IS REQUIRED, THE SERVICES OF A COMPETENT PROFESSIONAL PERSON SHOULD BE SOUGHT.
NEITHER THE PUBLISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM. THE FACT THAT AN ORGANIZATION
OR WEBSITE IS REFERRED TO IN THIS WORK AS A CITATION AND/OR A POTENTIAL SOURCE OF FURTHER INFORMATION DOES NOT
MEAN THAT THE AUTHOR OR THE PUBLISHER ENDORSES THE INFORMATION THE ORGANIZATION OR WEBSITE MAY PROVIDE OR REC-
OMMENDATIONS IT MAY MAKE. FURTHER, READERS SHOULD BE AWARE THAT INTERNET WEBSITES LISTED IN THIS WORK MAY HAVE
CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRITTEN AND WHEN IT IS READ.
Trademarks: Wiley, the Wiley Publishing logo, CliffsNotes, the CliffsNotes logo, Cliffs, CliffsAP, CliffsComplete, CliffsQuickReview, CliffsStudySolver,
CliffsTestPrep, CliffsNote-a-Day, cliffsnotes.com, and all related trademarks, logos, and trade dress are trademarks or registered trademarks of John Wiley & Sons,
Inc. and/or its affiliates. SAT is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. All
other trademarks are the property of their respective owners. Wiley Publishing, Inc. is not associated with any product or vendor mentioned in this book.
For general information on our other products and services or to obtain technical support, please contact our Customer Care Department within the U.S. at
800-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information
about Wiley products, please visit our web site at www.wiley.com.
, Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Special Notes for the New SAT I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Questions Commonly Asked about the New SAT I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Taking the New SAT I: Successful Overall Approaches for Multiple-Choice Questions . . . . . 5
I. The “Plus-Minus” System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
II. The Elimination Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
III. The “Avoiding Misreads” Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
IV. The Multiple-Multiple-Choice Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
A Summary of General Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
PART I: ANALYSIS AND STRATEGIES
Introduction to the Mathematics Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Using Your Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Basic Skills and Concepts That You Should Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Number and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Algebra and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Geometry and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Data Analysis, Statistics, and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Basic Skills Necessary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Analysis of Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Suggested Approach with Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Grid-In Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Basic Skills Necessary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Directions with Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Practice Grid-Ins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Suggested Approaches with Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
PART II: REVIEW WITH SAMPLE PROBLEMS
A Quick Review of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Symbols, Terminology, Formulas, and General Mathematical Information . . . . . . . . . . . . . . 39
Common Math Symbols and Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Math Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Important Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Math Words and Phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Mathematical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Numbers and Operations, Data Analysis, Statistics, and Probability . . . . . . 45
Arithmetic Diagnostic Test (Including Numbers and Operations,
Data Analysis, Statistics, and Probability) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
* the
SAT
Math
Jerry Bobrow, Ph.D.
Contributing Authors
Dale Johnson, M.A.
Joe Skinner, M.A.
*SAT is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.
, About the Author Publisher’s Acknowledgments
Jerry Bobrow, Ph.D., is a national authority in the field of Editorial
test preparation. As executive director of Bobrow Test Project Editor: Suzanne Snyder
Preparation Services, he has been administering the test
Acquisitions Editor: Greg Tubach
preparation programs at more than 25 California institutions
for the past 30 years. Dr. Bobrow has authored more than 30 Copy Editor: Tere Stouffer
national best-selling test preparation books, and his books Production
and programs have assisted more than two million test-takers.
Proofreader: Henry Lazarek
Each year, Dr. Bobrow personally lectures to thousands of
students on preparing for graduate, college, and teacher cre- Wiley Publishing, Inc. Composition Services
dentialing exams.
Author’s Acknowledgments
I would like to thank Dr. Suzanne Snyder, of Wiley, for her
assistance and careful attention to the production process.
Finally, I would like to thank my wife, Susan; daughter,
Jennifer; and sons, Adam and Jonathan, for their patience,
moral support, and comic relief.
Mastering the SAT®: Math Note: If you purchased this book without a cover,
Published by: you should be aware that this book is stolen property.
It was reported as “unsold and destroyed” to the
Wiley Publishing, Inc. publisher, and neither the author nor the publisher
111 River Street has received any payment for this “stripped book.”
Hoboken, NJ 07030-5774
www.wiley.com
Copyright © 2007 Jerry Bobrow, Ph.D.
Published by Wiley, Hoboken, NJ
Published simultaneously in Canada
Library of Congress Cataloging-in-Publication Data
Bobrow, Jerry.
Mastering the SAT : math / by Jerry Bobrow.
p. cm.
Includes bibliographical references and index.
ISBN-13: 978-0-470-03660-0 (alk. paper)
ISBN-10: 0-470-03660-5 (alk. paper)
1. Mathematics—Examinations—Study guides. 2. Mathematics—Examinations, questions, etc. 3. SAT (Educational test)—Study guides. 4. Universities and col-
leges—United States—Entrance examinations—Study guides. 5. Achievement tests—Study guides. I. Title.
QA43.B649 2007
510.76—dc22
2006029556
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
1O/SR/RR/QW/IN
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, record-
ing, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of
the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923,
978-750-8400, fax 978-646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Legal Department,
Wiley Publishing, Inc., 10475 Crosspoint Blvd., Indianapolis, IN 46256, 317-572-3447, fax 317-572-4355, or online at http://www.wiley.com/go/permissions.
THE PUBLISHER AND THE AUTHOR MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETE-
NESS OF THE CONTENTS OF THIS WORK AND SPECIFICALLY DISCLAIM ALL WARRANTIES, INCLUDING WITHOUT LIMITATION WAR-
RANTIES OF FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES OR PROMOTIONAL
MATERIALS. THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY SITUATION. THIS WORK IS SOLD
WITH THE UNDERSTANDING THAT THE PUBLISHER IS NOT ENGAGED IN RENDERING LEGAL, ACCOUNTING, OR OTHER PROFESSIONAL
SERVICES. IF PROFESSIONAL ASSISTANCE IS REQUIRED, THE SERVICES OF A COMPETENT PROFESSIONAL PERSON SHOULD BE SOUGHT.
NEITHER THE PUBLISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM. THE FACT THAT AN ORGANIZATION
OR WEBSITE IS REFERRED TO IN THIS WORK AS A CITATION AND/OR A POTENTIAL SOURCE OF FURTHER INFORMATION DOES NOT
MEAN THAT THE AUTHOR OR THE PUBLISHER ENDORSES THE INFORMATION THE ORGANIZATION OR WEBSITE MAY PROVIDE OR REC-
OMMENDATIONS IT MAY MAKE. FURTHER, READERS SHOULD BE AWARE THAT INTERNET WEBSITES LISTED IN THIS WORK MAY HAVE
CHANGED OR DISAPPEARED BETWEEN WHEN THIS WORK WAS WRITTEN AND WHEN IT IS READ.
Trademarks: Wiley, the Wiley Publishing logo, CliffsNotes, the CliffsNotes logo, Cliffs, CliffsAP, CliffsComplete, CliffsQuickReview, CliffsStudySolver,
CliffsTestPrep, CliffsNote-a-Day, cliffsnotes.com, and all related trademarks, logos, and trade dress are trademarks or registered trademarks of John Wiley & Sons,
Inc. and/or its affiliates. SAT is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product. All
other trademarks are the property of their respective owners. Wiley Publishing, Inc. is not associated with any product or vendor mentioned in this book.
For general information on our other products and services or to obtain technical support, please contact our Customer Care Department within the U.S. at
800-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information
about Wiley products, please visit our web site at www.wiley.com.
, Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Special Notes for the New SAT I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Questions Commonly Asked about the New SAT I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Taking the New SAT I: Successful Overall Approaches for Multiple-Choice Questions . . . . . 5
I. The “Plus-Minus” System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
II. The Elimination Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
III. The “Avoiding Misreads” Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
IV. The Multiple-Multiple-Choice Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
A Summary of General Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
PART I: ANALYSIS AND STRATEGIES
Introduction to the Mathematics Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Using Your Calculator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Basic Skills and Concepts That You Should Know . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Number and Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Algebra and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Geometry and Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Data Analysis, Statistics, and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Multiple-Choice Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Basic Skills Necessary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Analysis of Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Suggested Approach with Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Grid-In Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Ability Tested . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Basic Skills Necessary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Directions with Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Practice Grid-Ins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Suggested Approaches with Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
PART II: REVIEW WITH SAMPLE PROBLEMS
A Quick Review of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Symbols, Terminology, Formulas, and General Mathematical Information . . . . . . . . . . . . . . 39
Common Math Symbols and Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Math Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Important Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Math Words and Phrases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Mathematical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Numbers and Operations, Data Analysis, Statistics, and Probability . . . . . . 45
Arithmetic Diagnostic Test (Including Numbers and Operations,
Data Analysis, Statistics, and Probability) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
