Preface Acknowledgments About the Author Introduction: The Five-Step Program STEP 1 Set Up Your Study Plan 1 What You Need to Know About the AP Calculus AB Exam 1.1 What Is Covered on the AP Calculus AB Exam? 1.2 What Is the Format of the AP Calculus AB Exam? 1.3 What Are the Advanced Placement Exam Grades? How Is the AP Calculus AB Exam Grade Calculated? 1.4 Which Graphing Calculators Are Allowed for the Exam? Calculators and Other Devices Not Allowed for the AP Calculus AB Exam Other Restrictions on Calculators 2 How to Plan Your Time 2.1 Three Approaches to Preparing for the AP Calculus AB 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 AB Diagnostic Test 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 Review of Precalculus 5.

1 Lines Slope of a Line Equations of a Line Parallel and Perpendicular Lines 5.2 Absolute Values and Inequalities Absolute Values Inequalities and the Real Number Line Solving Absolute Value Inequalities Solving Polynomial Inequalities Solving Rational Inequalities 5.3 Functions Definition of a Function Operations on Functions Inverse Functions Trigonometric and Inverse Trigonometric Functions Exponential and Logarithmic Functions 5.4 Graphs of Functions Increasing and Decreasing Functions Intercepts and Zeros Odd and Even Functions Shifting, Reflecting, and Stretching Graphs 5.5 Rapid Review 5.6 Practice Problems 5.7 Cumulative Review Problems 5.8 Solutions to Practice Problems 5.

9 Solutions to Cumulative Review Problems Big Idea 1: Limits 6 Limits and Continuity 6.1 The Limit of a Function Definition and Properties of Limits Evaluating Limits One-Sided Limits Squeeze Theorem 6.2 Limits Involving Infinities Infinite Limits (as x → a) Limits at Infinity (as x → ±∞) Horizontal and Vertical Asymptotes 6.3 Continuity of a Function Continuity of a Function at a Number Continuity of a Function over an Interval Theorems on Continuity 6.4 Rapid Review 6.5 Practice Problems 6.6 Cumulative Review Problems 6.7 Solutions to Practice Problems 6.

8 Solutions to Cumulative Review Problems Big Idea 2: Derivatives 7 Differentiation 7.1 Derivatives of Algebraic Functions Definition of the Derivative of a Function Power Rule The Sum, Difference, Product, and Quotient Rules The Chain Rule 7.2 Derivatives of Trigonometric, Inverse Trigonometric, Exponential, and Logarithmic Functions Derivatives of Trigonometric Functions Derivatives of Inverse Trigonometric Functions Derivatives of Exponential and Logarithmic Functions 7.3 Implicit Differentiation Procedure for Implicit Differentiation 7.4 Approximating a Derivative 7.5 Derivatives of Inverse Functions 7.6 Higher Order Derivatives 7.7 L''Hôpital''s Rule for Indeterminate Forms 7.

8 Rapid Review 7.9 Practice Problems 7.10 Cumulative Review Problems 7.11 Solutions to Practice Problems 7.12 Solutions to Cumulative Review Problems 8 Graphs of Functions and Derivatives 8.1 Rolle''s Theorem, Mean Value Theorem, and Extreme Value Theorem Rolle''s Theorem Mean Value Theorem Extreme Value Theorem 8.2 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 8.3 Sketching the Graphs of Functions Graphing without Calculators Graphing with Calculators 8.

4 Graphs of Derivatives 8.5 Rapid Review 8.6 Practice Problems 8.7 Cumulative Review Problems 8.8 Solutions to Practice Problems 8.9 Solutions to Cumulative Review Problems 9 Applications of Derivatives 9.1 Related Rate General Procedure for Solving Related Rate Problems Common Related Rate Problems Inverted Cone (Water Tank) Problem Shadow Problem Angle of Elevation Problem 9.2 Applied Maximum and Minimum Problems General Procedure for Solving Applied Maximum and Minimum Problems Distance Problem Area and Volume Problems Business Problems 9.

3 Rapid Review 9.4 Practice Problems 9.5 Cumulative Review Problems 9.6 Solutions to Practice Problems 9.7 Solutions to Cumulative Review Problems 10 More Applications of Derivatives 10.1 Tangent and Normal Lines Tangent Lines Normal Lines 10.2 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 10.3 Motion Along a Line Instantaneous Velocity and Acceleration Vertical Motion Horizontal Motion 10.

4 Rapid Review 10.5 Practice Problems 10.6 Cumulative Review Problems 10.7 Solutions to Practice Problems 10.8 Solutions to Cumulative Review Problems Big Idea 3: Integrals and the Fundamental Theorems of Calculus 11 Integration 11.1 Evaluating Basic Integrals Antiderivatives and Integration Formulas Evaluating Integrals 11.2 Integration by U-Substitution The U-Substitution Method U-Substitution and Algebraic Functions U-Substitution and Trigonometric Functions U-Substitution and Inverse Trigonometric Functions U-Substitution and Logarithmic and Exponential Functions 11.3 Rapid Review 11.

4 Practice Problems 11.5 Cumulative Review Problems 11.6 Solutions to Practice Problems 11.7 Solutions to Cumulative Review Problems 12 Definite Integrals 12.1 Riemann Sums and Definite Integrals Sigma Notation or Summation Notation Definition of a Riemann Sum Definition of a Definite Integral Properties of Definite Integrals 12.2 Fundamental Theorems of Calculus First Fundamental Theorem of Calculus Second Fundamental Theorem of Calculus 12.3 Evaluating Definite Integrals Definite Integrals Involving Algebraic Functions Definite Integrals Involving Absolute Value Definite Integrals Involving Trigonometric, Logarithmic, and Exponential Functions Definite Integrals Involving Odd and Even Functions 12.4 Rapid Review 12.

5 Practice Problems 12.6 Cumulative Review Problems 12.7 Solutions to Practice Problems 12.8 Solutions to Cumulative Review Problems 13 Areas and Volumes 13.1 The Function 13.2 Approximating the Area Under a Curve Rectangular Approximations Trapezoidal Approximations 13.3 Area and Definite Integrals Area Under a Curve Area Between Two Curves 13.4 Volumes and Definite Integrals Solids with Known Cross Sections The Disc Method The Washer Method 13.

5 Rapid Review 13.6 Practice Problems 13.7 Cumulative Review Problems 13.8 Solutions to Practice Problems 13.9 Solutions to Cumulative Review Problems 14 More Applications of Definite Integrals 14.1 Average Value of a Function Mean Value Theorem for Integrals Average Value of a Function on [a, b] 14.2 Distance Traveled Problems 14.3 Definite Integral as Accumulated Change Business Problems Temperature Problem Leakage Problem Growth Problem 14.

4 Differential Equations Exponential Growth/Decay Problems Separable Differential Equations 14.5 Slope Fields 14.6 Rapid Review 14.7 Practice Problems 14.8 Cumulative Review Problems 14.9 Solutions to Practice Problems 14.10 Solutions to Cumulative Review Problems STEP 5 Build Your Test-Taking Confidence AP Calculus AB Practice Exam 1 AP Calculus AB Practice Exam 2 Appendix Bibliography Websites.