AP Calculus AB: 8 units covered
Unit 1: Limits and Continuity
10–12% of exam scoreLimits from graphs, tables and algebra, limits at infinity, the squeeze theorem, continuity and the Intermediate Value Theorem.
What it covers (4)- Estimating limits from graphs and tables
- Algebraic limits and the squeeze theorem
- Limits at infinity and asymptotes
- Continuity and the Intermediate Value Theorem
Key formulaStudy Unit 1: Limits and ContinuityUnit 2: Differentiation: Definition and Fundamental Properties
10–12% of exam scoreThe derivative as a limit and as a rate of change, differentiability, and the power, product and quotient rules.
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
9–13% of exam scoreThe chain rule, implicit differentiation, derivatives of inverse and inverse trigonometric functions, and higher-order derivatives.
Unit 4: Contextual Applications of Differentiation
10–15% of exam scoreRates of change in context, straight-line motion, related rates, local linearization and L'Hôpital's rule.
Unit 5: Analytical Applications of Differentiation
15–18% of exam scoreThe Mean Value Theorem, the Extreme Value Theorem, increasing and decreasing intervals, the first and second derivative tests, concavity and optimization.
Unit 6: Integration and Accumulation of Change
17–20% of exam scoreRiemann sums, the definite integral as accumulation, the Fundamental Theorem of Calculus, antiderivatives and substitution.
Unit 7: Differential Equations
6–12% of exam scoreWriting and checking differential equations, slope fields, separation of variables and exponential growth and decay.
Unit 8: Applications of Integration
10–15% of exam scoreAverage value, motion from velocity, accumulated change, area between curves and volumes by cross-sections and revolution.