AP®︎ Calculus AB | College Calculus AB | Khan Academy

AP®︎ Calculus AB Course Overview

This Khan Academy course covers the standard AP®︎ Calculus AB curriculum, organized into 10 units of study.

• Unit 1: Limits and Continuity
  • Covers limit estimation (graphs/tables), algebraic properties, direct substitution, trigonometric limits, the Squeeze Theorem, continuity, infinite limits, and the Intermediate Value Theorem.
• Unit 2: Differentiation (Definition and Basic Rules)
  • Covers rates of change, the derivative as a slope, differentiability, power rule, and derivatives of trigonometric, exponential, and logarithmic functions.
• Unit 3: Composite, Implicit, and Inverse Functions
  • Focuses on the Chain Rule, implicit differentiation, derivatives of inverse functions, and second derivatives.
• Unit 4: Contextual Applications of Differentiation
  • Covers motion problems, related rates, local linearity, and L'Hôpital's Rule.
• Unit 5: Applying Derivatives to Analyze Functions
  • Covers the Mean Value Theorem, critical points, extrema (min/max), concavity, inflection points, and optimization.
• Unit 6: Integration and Accumulation of Change
  • Covers Riemann sums, the Fundamental Theorem of Calculus, antiderivatives, and $u$-substitution.
• Unit 7: Differential Equations
  • Covers slope fields, separable differential equations, and exponential growth models.
• Unit 8: Applications of Integration
  • Covers average value of a function, motion problems, area between curves, and volumes of solids (cross-sections, disc/washer methods).
• Unit 9: AP Exam Prep
  • Contains solved free-response questions from past AP exams.
• Unit 10: Standards Mapping
  • Provides alignment between the course content and official AP®︎ Calculus AB standards.