AP Calculus AB

524 indexed practice questions across 8 units. Open a unit for a summary and question list with links to full explanations.

easy 195medium 209hard 120

Units

AP Calculus AB Universal Cheatsheet

Exam Format (College Board)

  • • 45 MC + 6 FRQ · 3h 15m · each section 50% of the score
  • • Section I: 30 MC no calculator (60 min) + 15 MC calculator (45 min)
  • • Section II: 2 FRQ calculator (30 min) + 4 FRQ no calculator (60 min)
  • • Unit weights: U6 Integration 17–20% · U5 15–18% · U4 & U8 10–15% each · U1–U2 10–12% · U3 9–13% · U7 6–12%

Key Formulas

Power rule: d/dx xⁿ = nxⁿ⁻¹
Product rule: (fg)′ = f′g + fg′
Quotient rule: (f/g)′ = (f′g − fg′)/g²
Chain rule: d/dx f(g(x)) = f′(g(x))·g′(x)
Derivative of inverse: (f⁻¹)′(a) = 1/f′(f⁻¹(a))
d/dx e^x: e^x · d/dx ln x = 1/x
d/dx sin x: cos x · d/dx cos x = −sin x
d/dx arcsin x: 1/√(1−x²) · d/dx arctan x = 1/(1+x²)
FTC Part 1: d/dx ∫ₐˣ f(t)dt = f(x)
FTC Part 2: ∫ₐᵇ f(x)dx = F(b) − F(a)
Average value: (1/(b−a))∫ₐᵇ f(x)dx
∫ xⁿ dx: xⁿ⁺¹/(n+1) + C (n ≠ −1)
Volume (disc): π∫[r(x)]²dx
Volume (washer): π∫(R² − r²)dx
Euler step: yₙ₊₁ = yₙ + h·f(xₙ, yₙ)
dy/dt = ky: solution y = Ceᵏᵗ

Exam Tips

  • • +C on every indefinite integral: it is worth points
  • • Related rates: differentiate first, substitute constants after
  • • Speed is |v(t)|: never negative; distance = ∫|v|dt, displacement = ∫v dt
  • • L'Hôpital only for 0/0 or ∞/∞: check the form first
  • • FRQ: justify with a theorem name (MVT, IVT, EVT) and verify its hypotheses

AP Calculus AB FAQ

›How many AP Calculus AB practice questions does Apentix have?

524 questions across 8 units: every question includes a full explanation and is tagged by difficulty (easy, medium, hard).

›Are these questions like the real AP Calculus AB exam?

Yes, questions follow College Board's unit weighting and format for AP Calculus AB, including stimulus-based and standalone multiple choice with AP-style distractors.

›Is it free?

Yes. Browsing questions, unit guides, and cheatsheets is free; a free account adds progress tracking, assignments, and classroom games.