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Free AP Calculus AB/BC Study Guide

AP Calculus AB/BC · All Units

Master AP Calculus from limits and continuity through integration, differential equations, and (for BC) infinite series. Flashcards, cheat sheets, essential terms, practice questions, and visual reviews for every unit, all completely free.

10 units (8 AB + 2 BC)
AB & BC exams covered
College Board aligned
100% free

Choose your unit

Each unit has 6 study resources: flashcards, cheat sheet, essential terms, practice questions, visual review, and FRQ practice. Units 9–10 are BC only.

Unit 1
Limits & Continuity
Limits and Continuity
Limits, one-sided limits, evaluating limits algebraically, the squeeze theorem, continuity, discontinuities, asymptotes, and the IVT.
AB 10–12% · BC 4–7%
Start Unit 1 →
Unit 2
Definition of the Derivative
Differentiation: Definition & Fundamental Properties
The derivative as a limit, differentiability, and the basic rules: power, product, quotient, and derivatives of common functions.
AB 10–12% · BC 4–7%
Start Unit 2 →
Unit 3
Chain, Implicit & Inverse
Differentiation: Composite, Implicit & Inverse Functions
The chain rule, implicit differentiation, and derivatives of inverse and inverse trigonometric functions.
AB 9–13% · BC 4–7%
Start Unit 3 →
Unit 4
Applying the Derivative
Contextual Applications of Differentiation
Rates of change, motion, related rates, linear approximation, and L'Hospital's Rule.
AB 10–15% · BC 6–9%
Start Unit 4 →
Unit 5
Analyzing Functions
Analytical Applications of Differentiation
The Mean Value Theorem, increasing/decreasing, extrema, concavity, curve sketching, and optimization.
AB 15–18% · BC 8–11%
Start Unit 5 →
Unit 6
Integration
Integration and Accumulation of Change
Riemann sums, the definite integral, the Fundamental Theorem of Calculus, antiderivatives, and u-substitution.
AB 17–20% · BC 17–20%
Start Unit 6 →
Unit 7
Differential Equations
Differential Equations
Slope fields, separation of variables, and modeling with differential equations (plus BC methods).
AB 6–12% · BC 6–9%
Start Unit 7 →
Unit 8
Applications of Integration
Applications of Integration
Average value, area between curves, and volumes of solids by cross sections and revolution.
AB 10–15% · BC 6–9%
Start Unit 8 →
Unit 9
Parametric, Polar & Vectors
Parametric, Polar & Vector-Valued Functions
Calculus of parametric and vector-valued functions and polar curves. BC only.
BC only · 11–12%
Start Unit 9 →
Unit 10
Sequences & Series
Infinite Sequences and Series
Convergence tests, power series, and Taylor and Maclaurin series. BC only.
BC only · 17–18%
Start Unit 10 →

About AP Calculus AB & BC

AP Calculus is a college-level introductory calculus course centered on the big ideas of limits, derivatives, integrals, and the Fundamental Theorem of Calculus. Calculus AB covers Units 1–8; Calculus BC covers all the AB content plus two additional units: parametric/polar/vector functions and infinite series, at a faster pace.

The course builds from the idea of a limit to differentiation (rates of change and its applications), then to integration (accumulation of change), differential equations, and applications of integrals. Throughout, you learn to work across graphical, numerical, analytical, and verbal representations, and to justify conclusions with proper notation.

Every page on this site is aligned to the College Board's official AP Calculus AB and BC Course and Exam Description and completely free. Use what works for your study style: flashcards for active recall, the cheat sheet for a one-page overview, or practice questions to test yourself before the exam.

What's included in each unit

Every unit has the same 6 study resources, designed for different learning styles.

Flashcards
Interactive cards per unit
Cheat Sheet
One-page visual summary
Essentials
Key terms and core concepts
Visual Review
Slide-by-slide walkthrough
Practice MCQ
Exam-style questions
FRQ Practice
Free-response practice

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