| |
| |
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 | |