AP Calculus BC Classes

1. Limits and Continuity

  • Understanding the concept of a limit.

  • Limits at infinity.

  • Continuity and the Intermediate Value Theorem.

  • Limits of indeterminate forms (L'Hopital’s Rule).

2. Differentiation

  • Definition of the derivative.

  • Basic differentiation rules (power, product, quotient, chain rule).

  • Implicit differentiation.

  • Derivatives of trigonometric, exponential, logarithmic, and inverse functions.

  • Applications of the derivative:

    • Related rates.

    • Optimization problems.

    • Linear approximation and differentials.

3. Integration

  • Definition of the integral (antiderivative).

  • Fundamental Theorem of Calculus.

  • Techniques of integration:

    • Substitution.

    • Integration by parts.

    • Trigonometric integrals.

    • Partial fractions.

  • Improper integrals.

  • Numerical methods for integration (e.g., trapezoidal rule, Simpson's rule).

4. Applications of Integrals

  • Area under curves.

  • Volume of solids of revolution (disk and washer methods).

  • Work, fluid pressure, and other physical applications.

  • Average value of a function.

  • Arc length and surface area.

5. Series

  • Sequences and series.

  • Convergence and divergence.

  • Power series.

  • Taylor and Maclaurin series, including their radius and interval of convergence.

  • Error bounds for approximating functions using series.

6. Polar Coordinates and Parametric Equations

  • Parametric equations and their derivatives.

  • Polar coordinates and graphs.

  • Calculus with parametric and polar equations (area, length, etc.).

7. Differential Equations

  • Solving separable differential equations.

  • Slope fields.

  • Euler’s method.

8. Applications of Derivatives and Integrals

  • Analyzing functions using the first and second derivatives (increasing/decreasing, concavity, and points of inflection).

  • Optimization and motion problems.

  • Work and related physical applications.

These topics make up the majority of what is assessed on the AP Calculus BC exam. The test consists of multiple-choice questions and free-response questions, with a focus on problem-solving, conceptual understanding, and mathematical reasoning.

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