AP Calculus AB
AP Calculus AB¶
The following outline was taken from the CollegeBoard website as of July 5, 2023.
Overview¶
Unit 1: Limits and Continuity¶
10-12% of exam score
Topics¶
- How limits help us handle change at an instant
- Definition and properties of limits in various representations
- Asymptotes and limits at infinity
- Reasoning using the Squeeze theorem and the Intermediate Value Theorem
Unit 2: Differentiation: Definition and Fundamental Properties¶
10-12% of exam score
Topics¶
- Defining the derivative of a function at a point and as a function
- Connecting differentiability and continuity
- Determining derivatives for elementary functions
- Applying differentiation rules
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions¶
9-13% of exam score
Topics¶
- The chain rule for differentiating composite functions
- Implicit differentiation
- Differentiation of general and particular inverse functions
- Determining higher-order derivatives of functions
Unit 4: Contextual Applications of Differentiation¶
10-15% of exam score
Topics¶
- Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change
- Applying understandings of differentiation to problems involving motion
- Generalizing understandings of motion problems to other situations involving rates of change
- Solving related rates problems
- Local linearity and approximation
- L'Hospital's rule
Unit 5: Analytical Applications of Differentiation¶
15-18% of exam score
Topics¶
- Mean Value Theorem and Extreme Value Theorem
- Derivatives and properties of functions
- How to use the first derivative test, second derivative test, and candidates test
- Sketching graphs of functions and their derivatives
- How to solve optimization problems
- Behaviors of Implicit relations
Unit 6: Integration and Accumulation of Change¶
17-20% of exam score
Topics¶
- Using definite integrals to determine accumulated change over an interval
- Approximating integrals using Reimann Sums
- Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals
- Antiderivatives and indefinite integrals
- Properties of integrals and integration techniques
Unit 7: Differential Equations¶
6-12% of exam score
Topics¶
- Interpreting verbal descriptions of change as separable differential equations
- Sketching slope fields and families of solution curves
- Solving separable differential equations to find general and particular solutions
- Deriving and applying a model for exponential growth and decay
Unit 8: Applications of Integration¶
10-15% of exam score
Topics¶
- Determining the average value of a function using definite integrals
- Modeling particle motion
- Solving accumulation problems
- Finding area between curves
- Determining volume with cross-sections, the disc method, and the washer method