Dedication and Acknowledgments Preface About the Authors Introduction: The Five-Step Program STEP 1 Set Up Your Study Plan 1 What You Need to Know About the AP Calculus BC Exam 1.1 What Is Covered on the AP Calculus BC Exam? 1.2 What Is the Format of the AP Calculus BC Exam? 1.3 What Are the Advanced Placement Exam Grades? How Is the AP Calculus BC Exam Grade Calculated? 1.4 Which Graphing Calculators Are Allowed for the Exam? Calculators and Other Devices Not Allowed for the AP Calculus BC Exam Other Restrictions on Calculators 2 How to Plan Your Time 2.1 Three Approaches to Preparing for the AP Calculus BC 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 BC 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 Big Idea 1: Limits 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 Big Idea 2: Derivatives 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 L''Hôpital''s Rule for Indeterminate Forms 6.7 Rapid Review 6.8 Practice Problems 6.

9 Cumulative Review Problems 6.10 Solutions to Practice Problems 6.11 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 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 Big Idea 3: Integrals and the Fundamental Theorems of Calculus 10 Integration 10.1 Evaluating Basic Integrals Antiderivatives and Integration Formulas Evaluating Integrals 10.2 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 10.3 Techniques of Integration Integration by Parts Integration by Partial Fractions 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 11 Definite Integrals 11.1 Riemann Sums and Definite Integrals Sigma Notation or Summation Notation Definition of a Riemann Sum Definition of a Definite Integral Properties of Definite Integrals 11.2 Fundamental Theorems of Calculus First Fundamental Theorem of Calculus Second Fundamental Theorem of Calculus 11.3 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 11.

4 Improper Integrals Infinite Intervals of Integration Infinite Discontinuities 11.5 Rapid Review 11.6 Practice Problems 11.7 Cumulative Review Problems 11.8 Solutions to Practice Problems 11.9 Solutions to Cumulative Review Problems 12 Areas, Volumes, and Arc Lengths 12.1 The Function F(x) = f (t)dt 12.2 Approximating the Area Under a Curve Rectangular Approximations Trapezoidal Approximations 12.

3 Area and Definite Integrals Area Under a Curve Area Between Two Curves 12.4 Volumes and Definite Integrals Solids with Known Cross Sections The Disc Method The Washer Method 12.5 Integration of Parametric, Polar, and Vector Curves Area, Arc Length, and Surface Area for Parametric Curves Area and Arc Length for Polar Curves Integration of a Vector-Valued Function 12.6 Rapid Review 12.7 Practice Problems 12.8 Cumulative Review Problems 12.9 Solutions to Practice Problems 12.10 Solutions to Cumulative Review Problems 13 More Applications of Definite Integrals 13.

1 Average Value of a Function Mean Value Theorem for Integrals Average Value of a Function on [a, b] 13.2 Distance Traveled Problems 13.3 Definite Integral as Accumulated Change Business Problems Temperature Problem Leakage Problem Growth Problem 13.4 Differential Equations Exponential Growth/Decay Problems Separable Differential Equations 13.5 Slope Fields 13.6 Logistic Differential Equations 13.7 Euler''s Method Approximating Solutions of Differential Equations by Euler''s Method 13.8 Rapid Review 13.

9 Practice Problems 13.10 Cumulative Review Problems 13.11 Solutions to Practice Problems 13.12 Solutions to Cumulative Review Problems Big Idea 4: Series 14 Series 14.1 Sequences and Series Convergence 14.2 Types of Series p-Series Harmonic Series Geometric Series Decimal Expansion 14.3 Convergence Tests Divergence Test Integral Test Ratio Test Comparison Test Limit Comparison Test Informal Principle 14.4 Alternating Series Error Bound Absolute and Conditional Convergence 14.

5 Power Series Radius and Interval of Convergence 14.6 Taylor Series Taylor Series and MacLaurin Series Common MacLaurin Series 14.7 Operations on Series Substitution Differentiation and Integration Error Bounds 14.8 Rapid Review 14.9 Practice Problems 14.10 Cumulative Review Problems 14.11 Solutions to Practice Problems 14.12 Solutions to Cumulative Review Problems STEP 5 Build Your Test-Taking Confidence AP Calculus BC Practice Exam 1 AP Calculus BC Practice Exam 2 Formulas and Theorems Bibliography Websites.