Volume I
AP Calculus BC
Unit Directory
Complete Framework Index
Curriculum Units
Navigate the complete AP/BC Calculus framework — twelve units spanning differential, integral, and advanced calculus.
Limits and Their Properties
An intuitive understanding of the limiting process, continuity, and the Intermediate Value Theorem.
Differentiation
The derivative, tangent line problem, Chain Rule, implicit differentiation, and related rates.
Applications of Differentiation
Extrema, Mean Value Theorem, curve sketching, optimization, and linear approximations.
Introduction to Integral Calculus
Antiderivatives, Riemann sums, the Fundamental Theorem of Calculus, and u-substitution.
Transcendental Functions
Natural logarithmic and exponential functions, inverse trig functions and their calculus.
Differential Equations
Slope fields, Euler’s Method, growth/decay, separation of variables, and the Logistic Equation.
Applications of Integration
Area between curves, volumes via disk/washer/cross-section methods, and arc length.
Integration Techniques
Integration by parts, partial fractions, L’Hôpital’s Rule, and improper integrals.
Infinite Series
Sequences, convergence tests, Taylor polynomials, power series, and Maclaurin series.
Parametric, Polar, and Calculus
Parametric equations and calculus, polar coordinates, area and arc length in polar.
Vector-Valued Functions
Vectors in a plane, vector-valued functions, differentiation/integration, velocity and acceleration.
AP Exam Preparation
Past AP exams, free response practice, and comprehensive cumulative review.
SEMESTER OVERVIEW
AP EXAM
The AP Calculus BC Exam is administered in May. All twelve units contribute to the exam’s multiple-choice and free-response sections.