Calculus AB Examination
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Advanced Placement · Practice Examination

Calculus AB
Derivatives & Integrals

One hundred questions, arranged from foundational to advanced

SubjectAP Calculus AB
UnitDerivatives → Integrals
Grade Level11–12
Date Created260808
Total Questions100
FormatMultiple Choice

Work through all ten sections at your own pace. Each question offers a hint, a difficulty rating, immediate scoring, and a full explanation. Flag questions for later review, jump between sections with the navigator, or answer by keyboard.

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100 Questions · Self-Graded · Printable · Grade 11–12
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Quick Reference

Core Rules · All 10 Sections
Section 01

Average Rate of Change

ARC = [f(b) − f(a)] / (b − a) — the slope of the secant line through (a, f(a)) and (b, f(b)).

Section 02

The Limit Definition of the Derivative

f′(x) = lim(h→0) [f(x+h) − f(x)] / h — the instantaneous rate of change.

Section 03

Power Rule and Basic Derivatives

d/dx[xⁿ] = nxⁿ⁻¹. Sum, difference, and constant-multiple rules apply term by term.

Section 04

Product and Quotient Rules

(fg)′ = f′g + fg′. (f/g)′ = (f′g − fg′) / g².

Section 05

The Chain Rule

d/dx[f(g(x))] = f′(g(x)) · g′(x) — outside derivative times inside derivative.

Section 06

Trigonometric, Exponential and Logarithmic Derivatives

d/dx[sin x]=cos x, d/dx[cos x]=−sin x, d/dx[eˣ]=eˣ, d/dx[ln x]=1/x.

Section 07

Implicit Differentiation and Tangent Lines

Differentiate both sides with respect to x, treating y as a function of x, then solve for dy/dx.

Section 08

Riemann Sums and the Definite Integral

Σ f(xᵢ)·Δx, Δx = (b−a)/n. As n→∞ the sum converges to ∫ₐᵇ f(x) dx.

Section 09

Antiderivatives and Integration Rules

∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1). Also ∫eˣdx=eˣ+C, ∫(1/x)dx=ln|x|+C.

Section 10

The Fundamental Theorem of Calculus

∫ₐᵇ f(x)dx = F(b) − F(a). Second FTC: d/dx ∫ₐˣ f(t)dt = f(x).

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AP Calculus AB — Practice Examination

SUBJECT: AP Calculus AB  |  UNIT: Derivatives to Integrals
GRADE LEVEL: 11-12 (Advanced Placement)  |  QUESTIONS: 100
DATE CREATED: 260808  |  NAME: _______________________   DATE: ____________

Answer Key

AP Calculus AB — Quick Reference Sheet

1. Average Rate of ChangeARC = [f(b) − f(a)] / (b − a) — the slope of the secant line through (a, f(a)) and (b, f(b)).
2. The Limit Definition of the Derivativef′(x) = lim(h→0) [f(x+h) − f(x)] / h — the instantaneous rate of change.
3. Power Rule and Basic Derivativesd/dx[xⁿ] = nxⁿ⁻¹. Sum, difference, and constant-multiple rules apply term by term.
4. Product and Quotient Rules(fg)′ = f′g + fg′. (f/g)′ = (f′g − fg′) / g².
5. The Chain Ruled/dx[f(g(x))] = f′(g(x)) · g′(x) — outside derivative times inside derivative.
6. Trigonometric, Exponential and Logarithmic Derivativesd/dx[sin x]=cos x, d/dx[cos x]=−sin x, d/dx[eˣ]=eˣ, d/dx[ln x]=1/x.
7. Implicit Differentiation and Tangent LinesDifferentiate both sides with respect to x, treating y as a function of x, then solve for dy/dx.
8. Riemann Sums and the Definite IntegralΣ f(xᵢ)·Δx, Δx = (b−a)/n. As n→∞ the sum converges to ∫ₐᵇ f(x) dx.
9. Antiderivatives and Integration Rules∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1). Also ∫eˣdx=eˣ+C, ∫(1/x)dx=ln|x|+C.
10. The Fundamental Theorem of Calculus∫ₐᵇ f(x)dx = F(b) − F(a). Second FTC: d/dx ∫ₐˣ f(t)dt = f(x).