Table of Contents
 Part I Using This Book to Improve Your AP Score
 Part II Practice Test 1
 Part III About the AP Calculus AB Exam

Part IV TestTaking Strategies for the AP Calculus AB Exam
 1 How to Approach MultipleChoice Questions
 2 How to Approach FreeResponse 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

4 Continuity
 The Definition of Continuity
 Types of Discontinuities

5 The Definition of the Derivative
 Deriving the Formula
 Differentiability

6 Differentiability
 Notation
 The Power Rule
 The Addition Rule
 Higher Order Derivatives
 The Product Rule
 The Quotient Rule
 The Chain Rule
 Derivatives of Trig Functions
 Graphical Derivatives

7 Implicit Differentiation
 How to Do It
 Second Derivatives

3 Limits

Unit 2 Differential Calculus Applications

8 Basic Applications of the Derivative
 Equations of Tangent Lines and Normal Lines
 The Mean Value Theorem for Derivatives
 Rolleβs Theorem

9 Maxima and Minima
 Applied Maxima and Minima Problems
 Curve Sketching

10 Motion
 Related Rates
 Position Velocity, and Acceleration

11 Exponential and Logarithmic Functions, Part One
 The Derivative of ln π₯
 The Derivative of π^π₯
 The Derivative of log_π(π₯)
 The Derivative of π^π₯

12 Other Topics in Differential Calculus
 The Derivative of an Inverse Function
 Differentials
 LβHΓ΄pitalβs Rule

8 Basic Applications of the Derivative

Unit 3 Integral Calculus Essentials

13 The Integral
 The Antiderivative
 Integrals of Trig Functions
 Addition and Subtraction
 π’Substitution

14 Definite Integrals
 Area Under a Curve
 Tabular Riemann Sums
 The Mean Value Theorem for Integrals

15 Exponential and Logarithmic Functions, Part Two
 Inverse Trig Functions
 More Integrals of Trig Functions
 Integrating π^π₯ and π^π₯

13 The Integral

Unit 4 Integral Calculus Applications

16 The Area between Two Curves
 Vertical Slices
 Horizontal Slices

17 The Volume of a Solid of Revolution
 Washers and Disks
 Cylindrical Shells
 Volumes of Solids with Known CrossSections

18 Differential Equations
 Separation of Variables
 Slope Fields

16 The Area between Two Curves

Unit 1 Differential Calculus Essentials