STEP 1 Set Up Your Study Plan
1 What You Need to Know About the AP Calculus ABBC Exams
1.1 What Is Covered on the AP Calculus Exams?
1.2 What Is the Format of the AP Calculus APBC Exams?
1.3 What Are the Advanced Placement Exam Grades?
How Is the AP Calculus Exam Grade Calculated?
1.4 Which Graphing Calculators Are Allowed for the Exam?
Calculators and Other Devices Not Allowed for the AP Calculus
Exam
Other Restrictions on Calculators
2 How to Plan Your Time
2.1 Three Approaches to Preparing for the AP Calculus Exam
Overview of the Three Plans
2.2 Calendar for Each Plan
Summary of the Three Study Plans
STEP 2 Determine Your Test Readiness
3 Take a Diagnostic Exam
3.1 Getting Started!
3.2 Diagnostic Test
3.3 Answers to Diagnostic Test
3.4 Solutions to Diagnostic Test
3.5 Calculate Your Score
Short-Answer Questions
AP Calculus ABBC Diagnostic Exam
STEP 3 Develop Strategies for Success
4 How to Approach Each Question Type
4.1 The Multiple-Choice Questions
4.2 The Free-Response Questions
4.3 Using a Graphing Calculator
4.4 Taking the Exam
What Do I Need to Bring to the Exam?
Tips for Taking the Exam
STEP 4 Review the Knowledge You Need to Score High
5 Limits and Continuity
5.1 The Limit of a Function
Definition and Properties of Limits
Evaluating Limits
One-Sided Limits
Squeeze Theorem
5.2 Limits Involving Infinities
Infinite Limits as x → a
Limits at Infinity as x → ±∞
Horizontal and Vertical Asymptotes
5.3 Continuity of a Function
Continuity of a Function at a Number
Continuity of a Function over an Interval
Theorems on Continuity
5.4 Rapid Review
5.5 Practice Problems
5.6 Cumulative Review Problems
5.7 Solutions to Practice Problems
5.8 Solutions to Cumulative Review Problems
6 Differentiation
6.1 Derivatives of Algebraic Functions
Definition of the Derivative of a Function
Power Rule
The Sum, Difference, Product, and Quotient Rules
The Chain Rule
6.2 Derivatives of Trigonometric, Inverse Trigonometric,
Exponential, and Logarithmic Functions
Derivatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
Derivatives of Exponential and Logarithmic Functions
6.3 Implicit Differentiation
Procedure for Implicit Differentiation
6.4 Approximating a Derivative
6.5 Derivatives of Inverse Functions
6.6 Higher Order Derivatives
6.7 Indeterminate Forms
L’H?opital’s Rule for Indeterminate Forms 97
6.8 Rapid Review
6.9 Practice Problems
6.10 Cumulative Review Problems
6.11 Solutions to Practice Problems
6.12 Solutions to Cumulative Review Problems
7 Graphs of Functions and Derivatives
7.1 Rolle’s Theorem, Mean Value Theorem, and Extreme Value
Theorem
Rolle’s Theorem
Mean Value Theorem
Extreme Value Theorem
7.2 Determining the Behavior of Functions
Test for Increasing and Decreasing Functions
First Derivative Test and Second Derivative Test for Relative
Extrema
Test for Concavity and Points of Inflection
7.3 Sketching the Graphs of Functions
Graphing without Calculators
Graphing with Calculators
7.4 Graphs of Derivatives
7.5 Parametric, Polar, and Vector Representations
Parametric Curves 130
Polar Equations
Types of Polar Graphs
Symmetry of Polar Graphs
Vectors
Vector Arithmetic
7.6 Rapid Review
7.7 Practice Problems
7.8 Cumulative Review Problems
7.9 Solutions to Practice Problems
7.10 Solutions to Cumulative Review Problems
8 Applications of Derivatives
8.1 Related Rate
General Procedure for Solving Related Rate Problems
Common Related Rate Problems
Inverted Cone Water Tank Problem
Shadow Problem
Angle of Elevation Problem
8.2 Applied Maximum and Minimum Problems
General Procedure for Solving Applied Maximum and Minimum
Problems
Distance Problem
Area and Volume Problem
Business Problems
8.3 Rapid Review
8.4 Practice Problems
8.5 Cumulative Review Problems
8.6 Solutions to Practice Problems
8.7 Solutions to Cumulative Review Problems
9 More Applications of Derivatives
9.1 Tangent and Normal Lines
Tangent Lines
Normal Lines
9.2 Linear Approximations
Tangent Line Approximation or Linear Approximation
Estimating the nth Root of a Number
Estimating the Value of a Trigonometric Function of an Angle
9.3 Motion Along a Line
Instantaneous Velocity and Acceleration
Vertical Motion
Horizontal Motion
9.4 Parametric, Polar, and Vector Derivatives
Derivatives of Parametric Equations
Position, Speed, and Acceleration
Derivatives of Polar Equations
Velocity and Acceleration of Vector Functions
9.5 Rapid Review
9.6 Practice Problems
9.7 Cumulative Review Problems
9.8 Solutions to Practice Problems
9.9 Solutions to Cumulative Review Problems
10 Integration
11 Definite Integrals
12 Areas and Volumes
13 More Applications of Definite Integrals
14 Series For Calculus BC Students Only
STEP 5 Build Your Test-Taking Confidence
Appendixes
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