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AP Calculus AB Study Guide — Complete Review by Unit
Complete AP Calculus AB study guide. Unit-by-unit summaries from limits to integration, FRQ strategies, calculator tips, and common mistakes to avoid.
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AP Calculus AB covers differential and integral calculus through 8 units. About 20% of students score a 5 — the highest rate of any AP math exam. The 6 FRQs (Part A with calculator, Part B without) account for 50% of your score. Here's what each unit tests and what to prioritize.
Unit 1: Limits and Continuity (10–12% of exam)
Understand limits graphically, numerically, and analytically. Know the three conditions for continuity at a point (limit exists, function defined, they're equal). Key theorems: Intermediate Value Theorem (if a continuous function equals different values at two endpoints, it must equal every value in between) and Squeeze Theorem. Asymptotic behavior using limits.
Unit 2 & 3: Differentiation (17–20% of exam)
Power rule, product rule, quotient rule, chain rule. Implicit differentiation. Derivatives of trig functions, inverse trig, natural log, and exponential functions. Know these cold — they appear in every FRQ set. The most common mistake: applying chain rule incorrectly or forgetting the derivative of the outer function when composing.
Unit 4 & 5: Applications of Differentiation (15–18% of exam)
Related rates, optimization, Mean Value Theorem, and L'Hôpital's Rule. Critical points and inflection points from the first and second derivative test. Curve sketching: given f′ or f″, describe behavior of f. This is heavily tested on both MCQ and FRQ — practice reading sign charts.
Unit 6: Integration and Accumulation of Change (17–20% of exam)
Riemann sums (left, right, midpoint, trapezoidal). The Fundamental Theorem of Calculus Parts 1 and 2 — understand both. Substitution (u-substitution) is the only integration technique required for AB. Know how to set up and evaluate definite integrals from graphs using area geometry.
Unit 7: Differential Equations (6–12% of exam)
Slope fields and what they represent. Separation of variables — the only method required for AB. Initial value problems. Exponential growth and decay models (dy/dt = ky → y = Cekt). Slope field questions appear on almost every exam.
Unit 8: Applications of Integration (10–15% of exam)
Area between curves, volume of solids of revolution (disk/washer method), and accumulation problems. Context problems: if a rate function r(t) is given, the total accumulated quantity is ∫r(t)dt. This connects directly to FRQ Part A (calculator-active), where you set up and evaluate definite integrals in context.
FRQ Strategy
- Show every step. A correct answer with no work earns no credit. An incorrect answer with correct method earns partial credit.
- Use correct notation. Write dy/dx, not just d. Write ∫f(x)dx with the dx. Use interval notation for domains.
- Justify your answers. "f has a relative minimum at x=2 because f′ changes from negative to positive" earns full justification credit. "Because f′=0" does not.
- 3 decimal places on calculator answers unless the problem specifies otherwise.
AP Calculus AB Practice Questions · AP Calc AB Practice Test · How to Get a 5 on AP Calc AB
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