| |
| |
| About the Authors | |
| |
| |
| About Your Pearson AP Guide | |
| |
| |
| Acknowledgments | |
| |
| |
| |
| Introduction to the AP AB and BC Calculus Exams | |
| |
| |
| |
| Precalculus Review of Calculus Prerequisites | |
| |
| |
| Calculus Prerequisites | |
| |
| |
| Precalculus - A Preparation for Calculus! | |
| |
| |
| Functions | |
| |
| |
| Transformations | |
| |
| |
| Polynomial Functions | |
| |
| |
| Rational Functions | |
| |
| |
| Exponential Functions | |
| |
| |
| Sinusoidal Functions | |
| |
| |
| More Trigonometric Functions | |
| |
| |
| Inverse Trigonometric Relations and Functions | |
| |
| |
| Parametric Relations | |
| |
| |
| Numerical Derivatives and Integrals | |
| |
| |
| |
| Review of AP Calculus AB and Calculus BC Topics | |
| |
| |
| Functions, Graphs, and Limits | |
| |
| |
| Analysis of Graphs | |
| |
| |
| Limits of Functions | |
| |
| |
| Asymptotic and Unbounded Behavior | |
| |
| |
| Function Magnitudes and Their Rates of Change | |
| |
| |
| Continuity | |
| |
| |
| Intermediate and Extreme Value Theorems | |
| |
| |
| Parametric, Polar, and Vector Functions | |
| |
| |
| Derivatives | |
| |
| |
| Concept of the Derivative | |
| |
| |
| Differentiability and Continuity | |
| |
| |
| Slope of a Curve at a Point | |
| |
| |
| Local Linearity | |
| |
| |
| Instantaneous Rate of Change | |
| |
| |
| Relationships between the Graphs of f and f' | |
| |
| |
| The Mean Value Theorem | |
| |
| |
| Equations Involving Derivatives | |
| |
| |
| Correspondences among the Graphs of f, f', and f" | |
| |
| |
| Points of Inflection | |
| |
| |
| Concavity of Functions | |
| |
| |
| Extreme Values of Functions | |
| |
| |
| Analysis of Parametric, Polar, and Vector Curves | |
| |
| |
| Optimization | |
| |
| |
| Related Rates | |
| |
| |
| Implicit Differentiation | |
| |
| |
| Derivative as a Rate of Change | |
| |
| |
| Slope Fields | |
| |
| |
| Euler's Method | |
| |
| |
| L'Hopital's Rule | |
| |
| |
| Basic Derivatives | |
| |
| |
| Derivative Rules | |
| |
| |
| Chain Rule | |
| |
| |
| Derivatives of Parametric, Polar, and Vector Functions | |
| |
| |
| Integrals | |
| |
| |
| Riemann Sums | |
| |
| |
| Definite Integral of a Rate of Change | |
| |
| |
| Basic Properties of Definite Integrals | |
| |
| |
| Applications of Integrals | |
| |
| |
| Fundamental Theorem of Calculus | |
| |
| |
| Antiderivative Basics | |
| |
| |
| Antidifferentation by Substitution | |
| |
| |
| Antidifferentation by Parts | |
| |
| |
| Antidifferentation by Simple Partial Fractions | |
| |
| |
| Improper Integrals | |
| |
| |
| Initial Value Problems | |
| |
| |
| Separable Differential Equations | |
| |
| |
| Numerical Approximations to Definite Integrals | |
| |
| |
| Polynomial Approximations and Series | |
| |
| |
| Concept of Series | |
| |
| |
| Geometric, Harmonic, and Alternating Series | |
| |
| |
| Integral Test, Ratio Test, and Comparison Test | |
| |
| |
| Taylor Polynomials | |
| |
| |
| Maclaurin and Taylor Series | |
| |
| |
| Manipulating Taylor Series | |
| |
| |
| Power Series | |
| |
| |
| Radius and Interval of Convergence | |
| |
| |
| LaGrange Error Bound | |
| |
| |
| |
| Practice Examinations | |
| |
| |
| Calculus AB Exam 1 | |
| |
| |
| Calculus AB Exam 2 | |
| |
| |
| Calculus BC Exam 1 | |
| |
| |
| Calculus BC Exam 2 | |
| |
| |
| |
| Answers and Solutions | |
| |
| |
| Part II: Precalculus Review of Calculus Prerequisites | |
| |
| |
| Part III: Review of AP Calculus AB and BC Topics | |
| |
| |
| Functions, Graphs, and Limits | |
| |
| |
| Derivatives | |
| |
| |
| Integrals | |
| |
| |
| Polynomial Approximation | |
| |
| |
| Practice Examinations | |
| |
| |
| Calculus AB Exam 1 | |
| |
| |
| Calculus AB Exam 2 | |
| |
| |
| Calculus BC Exam 1 | |
| |
| |
| Calculus BC Exam 2 | |