AP Calculus AB – Scheme of Work

Course Duration: One Academic Year (40 Weeks)

Level: Advanced Placement (Grade 11–12)

Term 1: Limits and Continuity (Weeks 1–6)

Weeks 1–2 – Introduction to Limits

  • Concept of a limit
  • Evaluating limits graphically and algebraically
  • Continuity and its properties

Weeks 3–4 – One-Sided & Infinite Limits

  • One-sided limits
  • Infinite limits and vertical asymptotes
  • Limits at infinity and horizontal asymptotes

Weeks 5–6 – Intermediate Value Theorem

  • Applications of the theorem
  • Analyzing function behavior on intervals

Term 2: Derivatives (Weeks 7–16)

Weeks 7–8 – Definition and Basic Rules

  • Derivative definition and interpretation
  • Power, constant, and sum/difference rules
  • Derivatives in context: motion and rates of change

Weeks 9–10 – Product, Quotient & Chain Rules

  • Product and quotient differentiation
  • Chain rule and composite functions
  • Implicit and inverse function differentiation

Weeks 11–12 – Applications of Derivatives

  • Related rates
  • Motion problems
  • Optimization problems

Weeks 13–16 – Curve Analysis

  • First and second derivative tests
  • Concavity and points of inflection
  • Curve sketching

Term 3: Integrals (Weeks 17–26)

Weeks 17–19 – Antiderivatives & Riemann Sums

  • Indefinite and definite integrals
  • Riemann sum approximations
  • Integration techniques: substitution

Weeks 20–22 – Fundamental Theorem of Calculus

  • Connection between derivatives and integrals
  • Accumulation functions
  • Net change interpretation

Weeks 23–26 – Applications of Integration

  • Solving differential equations
  • Growth and decay models
  • Area between curves
  • Volumes of solids of revolution

Term 4: Advanced Topics & Review (Weeks 27–40)

Weeks 27–30 – Advanced Topics

  • Parametric, polar, and vector functions (BC only)
  • Sequences and series (BC only)

Weeks 31–36 – Review & AP Questions

  • Review of all major units
  • Past AP exam questions
  • Mock exams

Weeks 37–40 – Final AP Exam Preparation

  • Targeted practice and concept reinforcement
  • Strategy for multiple-choice and free-response sections