AP Calculus BC Syllabus

Course Structure

AP Calculus BC is equivalent to a full year of college calculus. It covers all the material from AP Calculus AB and then extends it with three additional units. Because of this structure, students who take the BC exam also receive an AB subscore, which reflects their performance on the AB-only portion of the content. The exam tests understanding of concepts, methods, and their applications.

Core Calculus Topics (Shared with AB)

• Limits and Continuity Defining and determining limits and understanding the behavior of functions.
• Differentiation: Definition and Basic Rules Finding derivatives using rules like the product, quotient, and chain rule.
• Differentiation: Composite, Implicit, and Inverse Functions Applying derivative rules to more complex function types.
• Contextual Applications of Differentiation Using derivatives to solve problems involving rates of change and optimization.
• Integration and Accumulation of Change Finding definite and indefinite integrals and applying the Fundamental Theorem of Calculus.
• Differential Equations Modeling and solving simple differential equations, including slope fields.
• Applications of Integration Using integrals to find the area between curves and volumes of solids.

Advanced Topics (BC Only)

• Advanced Integration Techniques Using methods like integration by parts and linear partial fractions.
• Parametric, Polar, and Vector-Valued Functions Analyzing motion and curves in different coordinate systems.
• Infinite Sequences and Series Determining convergence or divergence and understanding geometric and p-series.
• Taylor and Maclaurin Series Representing functions as power series and using them for approximation.