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

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

Part V Content Review for the AP Calculus BC 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 Basic Differentiation
 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
 Rolleโs 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 ๐ฅ
 The Derivative of ๐^๐ฅ
 The Derivative of log_๐ (๐ฅ)
 The Derivative of ๐^๐ฅ

12 Other Topics in Differential Calculus
 The Derivative of an Inverse Function
 Derivatives of Parametric Functions
 LโHรดpitalโs Rule
 Differentials
 Logarithmic Differentiation

8 Basic Applications of the Derivative

Unit 3 Integral Calculus Essentials

13 The Integral
 The Antiderivative
 Integrals of Trig Functions
 Addition and Subtraction
 ๐ขSubstitution

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

15 Exponential and Logarithmic Functions, Part Two
 More Integrals of Trig Functions
 Integrating ๐^๐ฅ and ๐^๐ฅ

16 Integration by Parts
 The Formula

17 Trig Functions
 Inverse Trig Functions
 Advanced Integrals of Trig Functions

13 The Integral

Unit 4 Integral Calculus Applications

18 The Area between Two Curves
 Vertical Slices
 Horizontal Slices

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

20 Other Applications of the Integral
 Length of a Curve
 Parametric Functions
 The Method of Partial Fractions
 Improper Integrals
 Calculus of Polar Curves

21 Differential Equations
 Separation of Variables
 Eulerโs Method
 Slope Fields

22 Infinite Series
 Sequences and Series
 Geometric Series
 The Ratio Test
 Comparison Test
 Limit Comparison Test
 Conditional Convergence
 Alternating Series
 Integral Test
 Error Bound
 Power Series
 Taylor Series and Polynomials

18 The Area between Two Curves

Unit 1 Differential Calculus Essentials