AP®︎ Calculus BC | College Calculus BC | Khan Academy

AP®︎/College Calculus BC Curriculum Overview

This page outlines the comprehensive course structure for Khan Academy's AP®︎ Calculus BC curriculum, organized into 10 units:

• Unit 1: Limits and Continuity: Covers limit estimation, algebraic limit laws, the Squeeze theorem, continuity, infinite limits, and the Intermediate Value Theorem.
• Unit 2: Differentiation (Definition and Basic Rules): Focuses on the derivative as a slope, differentiability, power rule, product/quotient rules, and derivatives of trigonometric, exponential, and logarithmic functions.
• Unit 3: Composite, Implicit, and Inverse Functions: Covers the chain rule, implicit differentiation, derivatives of inverse functions, and second derivatives.
• Unit 4: Contextual Applications of Differentiation: Explores motion problems, related rates, local linearity, and L'Hôpital's rule.
• Unit 5: Applying Derivatives to Analyze Functions: Includes the Mean Value Theorem, critical points, extrema, concavity, inflection points, and optimization.
• Unit 6: Integration and Accumulation of Change: Covers Riemann sums, the Fundamental Theorem of Calculus, antiderivatives, u-substitution, integration by parts, partial fractions, and improper integrals.
• Unit 7: Differential Equations: Focuses on slope fields, Euler's method, separable differential equations, and exponential/logistic growth models.
• Unit 8: Applications of Integration: Covers average value of a function, motion problems, area between curves, volumes of solids (disc/washer methods), and arc length.
• Unit 9: Parametric, Polar, and Vector-Valued Functions: Explores differentiation and integration techniques applied to parametric equations, polar coordinates, and vector-valued functions, including planar motion.
• Assessment Structure: Each unit contains multiple topic-specific quizzes and a concluding unit test to track student progress.