AP Calculus BC practice
33 original lessons and 221 questions with hints and worked feedback. Practice and save progress on your own device.
Topics you can study
- Limits and Continuity: Limits across representations; Limit laws and algebraic repair; Infinite limits and end behavior; Continuity, discontinuity, and IVT.
- Differentiation: Definition and Fundamental Properties: Derivative definition and local behavior; Elementary derivatives and higher derivatives; Products, quotients, and derivative representations.
- Differentiation: Composite, Implicit, and Inverse Functions: Composition and rule selection; Implicit relations and higher implicit derivatives; Inverse-function and inverse-trigonometric derivatives.
- Contextual Applications of Differentiation: Rates, units, and rectilinear motion; Related rates and evolving constraints; Linearization and indeterminate-rate limits.
- Analytical Applications of Differentiation: MVT, EVT, critical points, and extrema; Concavity, inflection, and derivative graph synthesis; Optimization under contextual constraints.
- Integration and Accumulation of Change: Accumulation, definite integrals, and numerical sums; FTC and accumulation-function reasoning; Antiderivatives, substitution, and definite evaluation; Parts, partial fractions, and improper integrals.
- Differential Equations: Differential-equation models and slope fields; Separable initial-value problems; Euler approximation and logistic models.
- Applications of Integration: Average value, motion, and contextual accumulation; Areas between curves; Cross-section, disc, and washer volumes; Arc length for explicit planar curves.
- Parametric Equations, Polar Coordinates, and Vector-Valued Functions: Parametric derivatives and planar motion; Parametric length and vector distance; Polar differentiation and polar area.
- Infinite Sequences and Series: Sequences, geometric series, and convergence tests; Absolute and conditional convergence with error bounds; Power series, Taylor approximation, and endpoint analysis.
How practice works
Use mixed practice or focus on a chapter. Multiple-choice and numeric responses receive objective feedback. Written, graph and code responses use an analytic self-review checklist; code is not compiled and graph work is not automatically graded.
Coverage and review
Formative original practice aligned to the preparation topic map. This is an incomplete preparation beta with provisional difficulty, written self-review and no official score prediction.
Original questions and lessons have independent AI review. Human academic approval, empirical difficulty calibration and measured score improvement are not established. Our examples and questions are not official assessment items. Read the full practice scope.
What is free?
All included questions, explanations, lessons, normal practice and question reporting are free. The optional Apple Practice Toolkit adds custom controls across the courses included in that app version. The purchase does not include future courses, tutoring, AI or cloud services.
Specification sources
- College Board course framework and current unit weights — specification facts checked 2026-10-02.
- College Board course topic outline — specification facts checked 2026-10-02.
- College Board current May 2027 exam format — specification facts checked 2026-10-02.