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Extend your calculus knowledge with advanced integration, sequences, series, parametric/polar calculus, and vector-valued functions.
This AP Calculus BC course on Study Mondo covers 42 topics organized across 13 categories. Each topic includes detailed written explanations, worked examples, practice problems with step-by-step solutions, flashcards for review, and interactive lessons to help you master the material.
Since AP Calculus BC is a superset of AB, this page includes all Calculus AB topics as your foundation, followed by the BC-exclusive topics.
All content is completely free. Start with any category below, or jump to a specific topic that you need help with.
Take a diagnostic test covering AB foundations and BC-exclusive content. Get your BC score, AB subscore, and a personalized study plan.
Jump into high-impact topics and keep your study momentum moving.
Evaluating limits, squeeze theorem, continuity, and the Intermediate Value Theorem
Definition of the derivative, basic rules, chain rule, and implicit differentiation
Derivative as a limit, differentiability, graphical interpretation, and tangent lines
Critical points, curve sketching, optimization, and linearization
Critical points, first/second derivative tests, concavity, and curve sketching
Setting up and solving optimization problems in business and geometry
Linear approximation, differentials, error estimation, and tangent line approximation
Mean Value Theorem, Rolle's Theorem, Extreme Value Theorem, and IVT applications
Position, velocity, acceleration, speed, displacement, and distance
Riemann sums, definite integrals, FTC, antiderivatives, and u-substitution
Riemann sums, definite integral definition, properties, and the Fundamental Theorem of Calculus
Antiderivative basics, power rule for integration, trig antiderivatives, and initial value problems
Basic u-substitution, definite integrals with u-sub, and complex substitutions
Accumulation concept, interpreting integrals, FTC connections, and rate in vs rate out
Area, volumes, average value, and real-world integration applications
Slope fields, separation of variables, and exponential models
FRQ strategies, tables/data analysis, and full exam review
Integration by parts, partial fractions, improper integrals, and advanced methods
IBP formula, LIATE strategy, repeated IBP, tabular method, and applications
Decomposition with distinct, repeated, and irreducible quadratic factors
Type I and II improper integrals, convergence tests, and comparison test
Trig substitution, advanced u-sub, integration strategies, and reduction formulas
Calculus with parametric, polar, and vector-valued functions
Parametric derivatives, second derivatives, arc length, speed, and area
Polar derivatives, area in polar, arc length, and intersections
Vector functions, derivatives, integrals, velocity, acceleration, and planar motion
Arc length in rectangular, parametric, and polar; surface area of revolution
Infinite sequences, series, convergence tests, and error bounds
Sequence basics, convergence, bounded/monotonic sequences, and limits
Geometric series, telescoping series, nth term test, and harmonic series
Direct comparison, limit comparison, ratio test, root test, and choosing tests
Alternating series test, error bound, conditional vs absolute convergence
Power series, Taylor/Maclaurin series, Lagrange error, and applications
Power series basics, radius and interval of convergence, differentiation and integration
Taylor series, Maclaurin series, common series, and Taylor polynomials
Error bound formula, finding maximum error, choosing polynomial degree
Function approximation, solving DEs with series, physics applications, and error analysis
Euler method, logistic models, and advanced DE techniques
BC-specific strategies, exam tips, and comprehensive review