AP Calculus AB curriculum & tutors

Math

A complete AP Calculus AB sequence centered on limits, derivatives, integrals, differential equations, applications, multiple representations, and written justification.

8 public curriculum units1 tutor availableAlways Free
AP Calculus AB / first-semester college calculus

AP Calculus AB curriculum

A complete AP Calculus AB sequence centered on limits, derivatives, integrals, differential equations, applications, multiple representations, and written justification.

Pacing
8 units, 28-36 weeks self-paced
Units
8 unit sequence
Practice
640 checked answers
Support
Self-paced or tutor-guided
Outcomes
  • Connect limits, derivatives, and integrals across symbolic, graphical, numerical, and verbal representations.
  • Solve change and accumulation problems while stating units, assumptions, and conclusions.
  • Write AP-ready free-response solutions with visible reasoning and correct notation.

Video companion links

Use these linked courses for video instruction and mastery practice, then return here for PeerTutor original checks and tutor help on the exact unit that got stuck.

External video content is linked or embedded through provider-hosted players, not copied. PeerTutor practice is original and cites each source path separately.

Unit sequence

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

View full curriculum
  1. 01

    Limits and continuity

    • Estimate and compute limits from graphs, tables, and formulas.
    • Use continuity, asymptotes, the Squeeze Theorem, and the Intermediate Value Theorem.

    Practice: Complete a mixed limit set and justify one continuity or existence claim in words.

  2. 02

    Differentiation: definition and fundamental properties

    • Use the derivative definition as an instantaneous rate and local linear model.
    • Differentiate elementary functions with product and quotient rules.

    Practice: Derive one derivative from the limit definition, then connect it to a graph and contextual rate.

  3. 03

    Differentiation: composite, implicit, and inverse functions

    • Apply chain, implicit, and inverse-function differentiation.
    • Use higher derivatives and select efficient rule combinations.

    Practice: Solve a mixed differentiation set and annotate which rule controls every nontrivial step.

  4. 04

    Contextual applications of differentiation

    • Model motion, related rates, and local linearity.
    • Interpret derivative values and units in context.

    Practice: Write a complete related-rates solution with diagram, variables, equation, derivative, substitution, and conclusion.

Need the complete source list and remaining units? Open the full AP Calculus AB curriculum.

STEM, coding, and test-prep tutor support

Free

Nikhil supports students working through the public STEM, coding, and test-prep curriculum. Sessions focus on diagnosing the exact gap, working probl…

Pre-AlgebraAlgebraPrecalculusAP Precalculus+2 more
4 yrs experience Online

Ready to work through AP Calculus AB?

Start with the public curriculum. If a unit stalls, get targeted one-on-one support from a tutor.