AP Calculus AB Syllabus

The curriculum is structured into eight official units. For study purposes, these topics can be grouped into three main areas: Limits and Continuity, which sets the foundation; Differentiation, which deals with rates of change; and Integration, which deals with accumulation. Mastering them in this order provides a logical progression through the course material.

Limits and Continuity

• Understanding Limits Estimating limits from graphs and tables, and determining them using algebraic manipulation.
• Continuity Defining continuity at a point and applying theorems like the Intermediate Value Theorem (IVT).
• Asymptotic Behavior Using limits to describe vertical and horizontal asymptotes of a function.

Differentiation

• The Derivative Understanding the derivative as a limit, a rate of change, and the slope of a tangent line.
• Differentiation Rules Applying the Power, Product, Quotient, and Chain Rules to various functions.
• Implicit Differentiation Finding derivatives of relations that are not explicitly defined as functions.
• Contextual Applications Solving problems involving rates of change, such as motion (position, velocity, acceleration).
• Analytical Applications Using derivatives to find extrema, intervals of increase/decrease, and points of inflection.

Integration

• Integrals and Antiderivatives Understanding integration as antidifferentiation and approximating areas with Riemann sums.
• Fundamental Theorem of Calculus Connecting differentiation and integration to evaluate definite integrals.
• Integration Techniques Using u-substitution as the primary method for finding antiderivatives.
• Applications of Integration Calculating the area between curves and the volume of solids with known cross-sections.
• Differential Equations Solving basic separable differential equations and interpreting slope fields.