AP® Calculus AB & BC | Complete Course Index

Concepts of limits, one-sided limits, continuity, types of discontinuities, and the formal definition of a limit. Includes evaluation using algebra, tables, and graphs, Squeeze Theorem, asymptotes, and the Intermediate Value Theorem.

Definition of the derivative, relationship to graphs and tables, rules and notations, power, product, quotient rules, derivatives of trig, exponentials, logs, and basic applications.

Advanced derivative rules: chain rule, implicit differentiation, derivative of inverse functions (including trig). Includes higher-order derivatives and procedures for selecting rules.

Applying derivatives to motion, real-world rates, related rates, interpretation in context, linearization, and L'Hospital's Rule for limits.

Mean Value Theorem, finding and classifying extrema, intervals of increase/decrease, candidate’s test, concavity & inflection points, sketching graphs, and optimization problems.

The concept of accumulation, Riemann sums, definite/indefinite integrals, area, Fundamental Theorem of Calculus, substitution, and BC depth with improper and partial fractions.

Modeling with differential equations, slope fields, separation of variables, initial conditions, exponential and logistic models, Euler’s Method (BC), and verifying solutions.

Average value, accumulated change, areas between curves, volumes with cross-sections and solids (disc/washer), arc length and surface area (BC).

Parametric equations, derivatives and second derivatives, vector-valued functions, motion in plane, polar coordinates, area/arc length for parametric and polar curves.

Convergence/divergence of series, geometric and p-series, integral/comparison/ratio/alternating series tests, Taylor/Maclaurin polynomials, power series, radius & interval of convergence, error estimation.