AP Calculus AB/BC Formula Sheet Overview

The AP Calculus AB and BC formula sheets provide essential formulas and theorems fundamental to solving problems in calculus. While the AB course focuses on differential and integral calculus, the BC course extends these concepts and includes additional topics such as sequences, series, and parametric equations. Key formulas included in the sheets are:

• Derivative rules (product, quotient, and chain rules)

• Fundamental Theorem of Calculus

• Integration techniques (substitution, integration by parts)

• Limits and continuity concepts

• Series convergence tests (ratio test, root test)

Key Sections of the Formula Sheet

1. Limits

• Definition of a Limit:

  

• Properties of Limits: Includes limit laws such as the sum, difference, product, and quotient of limits.

2. Derivatives

• Definition:

  

• Basic Derivative Rules:

  • Power Rule:

    

  • Product Rule:

    

  • Quotient Rule:

    

  • Chain Rule:

    

3. Integrals

• Definite Integral:

  

• Fundamental Theorem of Calculus:

  • Part 1:

    

  • Part 2:

    

4. Applications of Integrals

5. Applications of Integrals

6. Series and Sequences (BC Only)

7. Parametric Equations and Polar Coordinates (BC Only)

8. Differential Equations (BC Only)

9. Additional Important Concepts