AP Calculus BC curriculum & tutors

Math

A complete AP Calculus BC sequence containing the AB foundation plus advanced integration, Euler's method, parametric and polar curves, vector motion, and infinite series.

10 public curriculum units1 tutor availableAlways Free
AP Calculus BC / two-semester college calculus

AP Calculus BC curriculum

A complete AP Calculus BC sequence containing the AB foundation plus advanced integration, Euler's method, parametric and polar curves, vector motion, and infinite series.

Pacing
10 units, 30-38 weeks self-paced
Units
10 unit sequence
Practice
800 checked answers
Support
Self-paced or tutor-guided
Outcomes
  • Master the complete AP Calculus AB foundation at BC pace and depth.
  • Analyze parametric, polar, and vector-valued motion with derivatives and integrals.
  • Determine convergence and construct Taylor approximations with defensible error bounds.

Video companion links

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Unit sequence

Built for independent progress first, then tutor support where the student gets stuck.

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  1. 01

    Limits and continuity

    • Compute and justify limits in multiple representations.
    • Use continuity, asymptotic behavior, and major limit theorems.

    Practice: Build a one-page limit decision map and defend two theorem-based conclusions.

  2. 02

    Differentiation: definition and fundamental properties

    • Use the derivative definition and connect differentiability to continuity.
    • Apply elementary derivative rules accurately at BC pace.

    Practice: Derive, calculate, graph, and interpret the derivative of one function.

  3. 03

    Differentiation: composite, implicit, and inverse functions

    • Use chain, implicit, inverse, and higher-order differentiation.
    • Combine rules in algebraically demanding settings.

    Practice: Complete mixed derivative problems and verify two answers numerically or graphically.

  4. 04

    Contextual applications of differentiation

    • Solve motion, related-rates, and local-linearization problems.
    • Use L'Hospital's rule only after verifying its conditions.

    Practice: Write one motion analysis and one related-rates response with units and contextual conclusions.

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