USA

AP Calculus BC

College Board Advanced Placement Calculus BC exam. Extends AB with sequences, series, parametric, and polar topics.

Exam Format

Questions

45 multiple choice + 6 free response

Duration

3 hours 15 minutes (1h45m multiple choice, 1h30m free response)

Scoring

Scaled 1-5. Also generates an AB sub-score based on AB-level content within the BC exam.

Calculator

Graphing calculator permitted on Part B of both sections. No calculator on Part A.

Study Strategies

  • 1Master all AB topics first, since roughly 60-70% of the BC exam overlaps with AB content and generates your AB sub-score.
  • 2Prioritize series convergence tests (ratio, comparison, integral, alternating series) because series questions are heavily weighted in the BC-only portion.
  • 3Practice parametric and polar problems until converting between coordinate systems and computing arc length or area feels automatic.
  • 4When tackling free-response questions on sequences and series, always state which convergence test you are applying and verify its conditions explicitly.
  • 5Use your graphing calculator strategically on Part B to verify answers and sketch curves for parametric or polar problems.

How Math Zen Helps

Math Zen covers the foundational AB topics that make up the majority of the BC exam, giving you a strong base to build on. As BC-specific templates are added, you will be able to practice series, parametric, and polar problems in the same adaptive format.

Topics Covered

Limits

6 subtopics, 12 templates

Basic LimitsL'Hopital's RuleSqueeze TheoremLimits at InfinityContinuityEpsilon-Delta

Derivatives

12 subtopics, 24 templates

Power RuleProduct RuleQuotient RuleChain RuleTrigonometricImplicit DifferentiationHigher-OrderLogarithmicRelated RatesOptimizationLinearizationMean Value Theorem

Integrals

19 subtopics, 22 templates

Power RuleDefinite IntegralsTrigonometricu-SubstitutionConstant RuleIntegration by PartsPartial FractionsArea Between CurvesVolume (Disk/Washer)Volume (Shell)Arc LengthTrig SubstitutionImproper IntegralsTrapezoidal RuleSimpson's RuleSurface AreaWork & ForceReduction FormulasAdvanced Rational

Sequences & Series

7 subtopics, 17 templates

Arithmetic SequencesGeometric SequencesSeries SumsConvergence TestsPower SeriesTaylor SeriesRecursive Sequences

Parametric Curves

2 subtopics, 4 templates

Parametric DerivativesParametric Arc Length

Polar Coordinates

3 subtopics, 6 templates

Coordinate ConversionPolar AreaPolar Slope