AP Calculus AB

381 Pages·2002·3.95 MB·English

by  William Ma

0267-00 FM 12/18/2001 17:22 Page i
M GRAW-HILL
C
5 Steps to a 5
AP Calculus AB
0267-00 FM 12/18/2001 17:22 Page ii
Other books in McGraw-Hill’s 5 Steps to a 5 Series include:
AP Biology
AP English Language
AP English Literature
AP Spanish Language
AP U.S. History
0267-00 FM 12/18/2001 17:22 Page iii
M GRAW-HILL
C
5 Steps to a 5
AP Calculus AB
William Ma
M G -H
C RAW ILL
New York Chicago San Francisco Lisbon London Madrid Mexico City
Milan New Delhi San Juan Seoul Singapore Sydney Toronto
abc
McGraw-Hill
Copyright ©2002 by the McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under
the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a data-
base or retrieval system, without the prior written permission of the publisher.
0-07-140624-7
The material in this eBook also appears in the print version of this title: 0-07-137714-X.
All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we
use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such
designations appear in this book, they have been printed with initial caps.
McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training pro-
grams. For more information, please contact George Hoare, Special Sales, at [email protected] or [phone].
TERMS OFUSE
This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all rights in and to the work. Use of
this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work,
you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate,
sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial
and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these
terms.
THE WORK IS PROVIDED “AS IS”. McGRAW-HILLAND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE
ACCURACY, ADEQUACYOR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY
INFORMATION THATCAN BE ACCESSED THROUGH THE WORK VIAHYPERLINK OR OTHERWISE, AND EXPRESSLYDISCLAIM
ANYWARRANTY, EXPRESS OR IMPLIED, INCLUDING BUTNOTLIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITYOR
FITNESS FOR APARTICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work
will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you
or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has
no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be
liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even
if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether
such claim or cause arises in contract, tort or otherwise.
DOI: 10.1036/0071406247
Want to learn more?
We hope you enjoy this McGraw-Hill eBook! If you’d like more
information about this book, its author, or related books and
websites, please click here.
0267-00 FM 12/18/2001 17:22 Page v
Dedication
To my mother, Lai-ping, who borrowed money
to hire a tutor for me when I was in 7th grade.
v
0267-00 FM 12/18/2001 17:22 Page vi
This page intentionally left blank.
0267-00 FM 12/18/2001 17:22 Page vii
For more information about this title, click here.
Contents
Preface / xiii
Acknowledgments / xv
PART I HOW TO USE THIS BOOK
How Is This Book Organized? / 3
Introduction to the Five-Step Program / 3
Three Approaches to Preparing for the AP Calculus AB Exam / 4
Overview of the Three Plans / 4
Calendar for Each Plan / 5
Graphics Used in the Book / 9
PART II WHAT YOU NEED TO KNOW ABOUT THE
AP CALCULUS AB EXAM
Background on the AP Exam / 13
What Is Covered in the AP Calculus AB Exam? / 13
What Is the Format of the AP Calculus AB Exam? / 13
What Are the Advanced Placement Exam Grades? / 13
How Is the AP Calculus AB Exam Grade Calculated? / 14
Which Graphing Calculators Are Allowed for the Exam? / 14
Calculators and Other Devices Not Allowed for the AP Calculus Exam / 14
Other Restrictions on Calculators / 15
How Much Work Do I Need to Show When I Use a Graphing Calculator in
Section II, Free-Response Questions? / 15
What Do I Need to Bring to the Exam? / 15
Tips for Taking the Exam / 15
Getting Started! / 17
Diagnostic Test / 19
Answers and Solutions / 27
Scoring and Interpretation / 39
PART III COMPREHENSIVE REVIEW
Chapter 1 Review of Pre-Calculus / 43
1.1 Lines / 43
Slope of a Line / 43
Equations of Lines / 44
Parallel and Perpendicular Lines / 45
1.2 Absolute Values and Inequalities / 47
Absolute Values / 47
Inequalities and the Real Number Line / 48
Solving Absolute Value Inequalities / 49
vii
Copyright 2002 The McGraw-Hill Companies, Inc. Click Here for Terms of Use.
0267-00 FM 12/18/2001 17:22 Page viii
viii • Contents
Solving Polynomial Inequalities / 50
Solving Rational Inequalities / 51
1.3 Functions / 53
Definition of a Function / 53
Operations on Functions / 53
Inverse Functions / 56
Trigonometric and Inverse Trigonometric Functions / 58
Exponential and Logarithmic Functions / 61
1.4 Graphs of Functions / 64
Increasing and Decreasing Functions / 64
Intercepts and Zeros / 65
Odd and Even Functions / 67
Shifting, Reflecting, and Sketching Graphs / 68
1.5 Rapid Review / 72
1.6 Practice Problems / 73
1.7 Solutions to Practice Problems / 74
Chapter 2 Limits and Continuity / 76
2.1 The Limit of a Function / 76
Definition and Properties of Limits / 76
Evaluating Limits / 77
One-Sided Limits / 78
Squeeze Theorem / 81
2.2 Limits Involving Infinities / 83
Infinite Limits (as x→a) / 83
Limits at Infinity as (x→±∞) / 85
Vertical and Horizontal Asymptotes / 87
2.3 Continuity of a Function / 90
Theorems on Continuity / 90
2.4 Rapid Review / 92
2.5 Practice Problems / 93
2.6 Cumulative Review Problems / 95
2.7 Solutions to Practice Problems / 95
2.8 Solutions to Cumulative Review Problems / 97
Chapter 3 Differentiation / 99
3.1 Derivatives of Algebraic Functions / 99
Definition of the Derivative of a Function / 99
Power Rule / 102
The Sum, Difference, Product, and Quotient Rules / 103
The Chain Rule / 104
3.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and
Logarithmic Functions / 105
Derivatives of Trigonometric Functions / 105
Derivatives of Inverse Trigonometric Functions / 107
Derivatives of Exponential and Logarithmic Functions / 108
3.3 Implicit Differentiation / 110
3.4 Approximating a Derivative / 112
3.5 Derivatives of Inverse Functions / 113
3.6 Higher Order Derivatives / 115
3.7 Rapid Review / 116