# Cracking the AP Calculus AB Exam, 2018 Edition Genres:

## Book Preface

YOUR GUIDE TO USING THIS BOOK

This book is organized to provide as much—or as little—support as you need, so you can use this book in whatever way will be most helpful for improving your score on the AP Calculus AB Exam.

• The remainder of Part I will provide guidance on how to use this book and help you determine your strengths and weaknesses.
• Part II of this book contains Practice Test 1, and its answers and explanations. (Bubble sheets can be downloaded as PDFs here.) We strongly recommend that you take this test before going any further, in order to realistically determine
which question types you’re ready for and which you might need to practice
which content topics you are familiar with and which you will want to carefully review
Once you have nailed down your strengths and weaknesses with regard to this exam, you can focus your test preparation, build a study plan, and be efficient with your time.
• Part III of this book will
provide information about the structure, scoring, and content of the AP Calculus AB Exam.
• Part IV of this book will explore the following strategies:
how to attack multiple-choice questions
how to write a high scoring free-response answer
how to manage your time to maximize the number of points available to you
• Part V of this book covers the content you need for your exam.
• Parts VI and VII of this book contain four additional Practice Tests, their answers and explanations, and an Appendix containing formulas you should know. If you skipped Practice Test 1, we recommend that you do all five (with at least a day or two between them) so that you can compare your progress between them. Additionally, this will help to identify any external issues: if you get a certain type of question wrong both times, you probably need to review it. If you only got it wrong once, you may have run out of time or been distracted by something. In either case, this will allow you to focus on the factors that caused the discrepancy and to be as prepared as possible on the day of the test.
You may choose to use some parts of this book over others, or you may work through the entire book. This will depend on your needs and how much time you have. Let’s now look at how to make this determination.

Contents

Cover
Title Page
Acknowledgments

Part I: Using This Book to Improve Your AP Score

Your Guide to Using This Book

How to Begin

Part II: Practice Test 1
Practice Test 1

Practice Test 1: Answers and Explanations

Part III: About the AP Calculus AB Exam
AB Calculus vs. BC Calculus

The Structure of the Calculus Exam

How the AP Calculus AB Exam is Scored

Overview of Content Topics

General Overview of This Book

How AP Exams Are Used

Other Resources

Part IV: Test-Taking Strategies for the AP Calculus AB Exam

1 How to Approach Multiple-Choice Questions

2 How to Approach Free-Response Questions

Part V: Content Review for the AP Calculus AB Exam

Unit 1: Differential Calculus Essentials

3 Limits
What is a Limit?

Limits of Trigonometric Functions

Practice Problem Set 1

4 Continuity
The Definition of Continuity

Types of Discontinuities

Practice Problem Set 2

5 The Definition of the Derivative
Deriving the Formula

Differentiability

Practice Problem Set 3

6 Differentiability
Notation

The Power Rule

Higher Order Derivatives

Practice Problem Set 4

The Product Rule

The Quotient Rule

The Chain Rule

Practice Problem Set 5

Derivatives of Trig Functions

Graphical Derivatives

Practice Problem Set 6

7 Implicit Differentiation
How to Do It

Second Derivatives

Practice Problem Set 7

Unit 1 Drill

Unit 2: Differential Calculus Applications

8 Basic Applications of the Derivative
Equations of Tangent Lines and Normal Lines

Practice Problem Set 8

The Mean Value Theorem for Derivatives

Rolle’s Theorem

Practice Problem Set 9

9 Maxima and Minima
Applied Maxima and Minima Problems

Practice Problem Set 10

Curve Sketching

Practice Problem Set 11

10 Motion
Related Rates

Practice Problem Set 12

Position, Velocity, and Acceleration

Practice Problem Set 13

11 Exponential and Logarithmic Functions, Part One
The Derivative of ln x

The Derivative of ex

The Derivative of logax

The Derivative of ax

Practice Problem Set 14

12 Other Topics in Differential Calculus
The Derivative of an Inverse Function

Practice Problem Set 15

Differentials

Practice Problem Set 16

L’Hôpital’s Rule

Practice Problem Set 17

Unit 2 Drill

Unit 3: Integral Calculus Essentials

13 The Integral
The Antiderivative

Integrals of Trig Functions

Practice Problem Set 18

u-Substitution

Practice Problem Set 19

14 Definite Integrals
Area Under a Curve

Tabular Riemann Sums

Practice Problem Set 20

The Mean Value Theorem for Integrals

Practice Problem Set 21

15 Exponential and Logarithmic Functions, Part Two
Inverse Trig Functions

Practice Problem Set 22

More Integrals of Trig Functions

Integrating ex and ax

Practice Problem Set 23

Unit 3 Drill

Unit 4: Integral Calculus Applications

16 The Area Between Two Curves
Vertical Slices

Horizontal Slices

Practice Problem Set 24

17 The Volume of a Solid of Revolution
Washers and Disks

Cylindrical Shells

Volumes of Solids with Known Cross-Sections

Practice Problem Set 25

18 Differential Equations
Separation of Variables

Slope Fields

Practice Problem Set 26

Unit 4 Drill

19 Solutions to Practice Problem Sets and Unit Drills

Part VI: Practice Tests 2 and 3
Practice Test 2

Practice Test 2: Answers and Explanations

Practice Test 3

Practice Test 3: Answers and Explanations

Practice Test 4

Practice Test 4: Answers and Explanations

Practice Test 5

Practice Test 5: Answers and Explanations

Appendix