AP Calculus BC

What Students Learn

Students use derivatives to describe rates of change and integrals to study accumulation, connecting graphical and analytical representations. Parametric and polar representations and series convergence and approximation extend their learning, with emphasis on reasoning and mathematical communication.

Course Units

The units and learning focuses below follow the official AP course framework.

Unit 1: Limits and continuity

Unit 2: Differentiation: definition and fundamental properties

Unit 3: Differentiation of composite, implicit, and inverse functions

Unit 4: Contextual applications of differentiation

Unit 5: Analytical applications of differentiation

Unit 6: Integration and accumulation of change

Unit 7: Differential equations

Unit 8: Applications of integration

Unit 9: Parametric equations, polar coordinates, and vector-valued functions

Unit 10: Infinite sequences and series

AP Assessment

Under the 2027 format, the AP exam includes 42 multiple-choice questions in 100 minutes, worth 50%, and six free-response questions in 90 minutes, worth 50%. It assesses calculations and conceptual understanding, including interpretation of representations and justification of conclusions. Some sections use a graphing calculator. BC-specific content includes parametric and polar calculus and infinite series.

References (2026–2027): College Board course framework; assessment information