AP Calculus BC
Mathematics
AP Calculus BC: everything in AP Calculus AB, plus parametric/polar/vector-valued functions and infinite sequences and series.
Unit 1: Limits & Continuity
Limits, continuity, and the formal definition of a limit.
1 topic
Unit 2: Differentiation — Definition & Fundamental Properties
The definition of the derivative and basic differentiation rules.
1 topic
Unit 3: Differentiation — Composite, Implicit & Inverse Functions
The chain rule, implicit differentiation, and derivatives of inverse functions.
1 topic
Unit 4: Contextual Applications of Differentiation
Related rates, linearization, and L'Hôpital's Rule.
1 topic
Unit 5: Analytical Applications of Differentiation
Extrema, concavity, curve sketching, and optimization.
1 topic
Unit 6: Integration & Accumulation of Change
Riemann sums, the definite integral, and the Fundamental Theorem of Calculus.
1 topic
Unit 7: Differential Equations
Slope fields, separable equations, and logistic models.
1 topic
Unit 8: Applications of Integration
Average value, area between curves, volumes, and arc length.
1 topic
Unit 9: Parametric Equations, Polar Coordinates & Vector-Valued Functions
Calculus with parametric, polar, and vector-valued functions.
2 topics
Unit 10: Infinite Sequences & Series
Convergence of sequences and series, power series, and Taylor series.
2 topics