Preparing for the Calculus AP Exam with Calculus

Part I: Introduction to the AP* AB and BC Calculus Exams Part II: Precalculus Review of Calculus Prerequisites Calculus Prerequisites: Precalculus - A Preparation of Calculus Functions Transformations Polynomial Functions Rational Functions Exponential Functions Sinusoidal Functions More Trigonometric Functions Inverse Trigonometric Functions Parametric Relations Numerical Derivatives and Integrals Part III: Calculus Review of AB and 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 Between the Graphs of f, f' and f" Points of Inflection Concavity of Functions Extreme Value of Functions Analysis of Parametric, Polar, and Vector Curves Optimization Related Rates Implicit Differentiation Derivative as a Rate of Change Slopefields Euler's Method L'Hopital's Rule Derivatives of Basic Functions Derivative Rules Chain Rule Explorations 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 Integration by Substitution Integration by Parts Integration 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, Comparison Test Taylor Polynomials Maclaurin and Taylor Series Manipulating Taylor Series Power Series Radius and Interval of Convergence Lagrange Error Bound Part IV: Practice Examinations AB Exam 1 AB Exam 2 BC Exam 1 BC Exam 2 Part V: Answers and Solutions Solutions for Part 2: Precalculus Review of Calculus Prerequisites Solutions for Part 3: Calculus Review of AB and BC Topics AB Exam 1 Solutions AB Exam 2 Solutions BC Exam 1 Solutions BC Exam 2 Solutions