AP Calculus AB

Course overview

AP Calculus AB develops core ideas of change and accumulation. You begin with limits and continuity, build derivative techniques and interpretations, then use integration and differential equations to model and solve problems.

Syllabus

1. 01

   Limits and Continuity

   Define limits numerically, graphically, and algebraically, and decide when a function is continuous at a point or over an interval.

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2. 02

   Differentiation: Definition and Basic Rules

   Build the derivative from first principles, interpret derivative values, and use core differentiation rules for common function forms.

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3. 03

   Composite, Implicit, and Inverse Functions

   Differentiate composite functions with the chain rule, handle implicit relationships, and compute derivatives of inverse functions.

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4. 04

   Contextual Applications of Differentiation

   Use derivatives to model rates in context, including motion and related rates, with careful attention to units and interpretation.

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5. 05

   Analytical Applications of Differentiation

   Analyze function behavior using first and second derivatives, then solve optimization and curve-analysis problems.

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6. 06

   Integration and Accumulation of Change

   Introduce antiderivatives, Riemann sums, and definite integrals, then use the Fundamental Theorem of Calculus to connect accumulation with derivatives.

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7. 07

   Differential Equations

   Model rates with differential equations, visualize slope fields, and solve separable equations with initial conditions.

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8. 08

   Applications of Integration

   Apply definite integrals to area, accumulated change, and simple geometric or physical quantities derived from rates.

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