Question bank / Advanced Placement / AP Calculus AB AP Calculus AB practice questions Original, AI-authored English practice with worked guidance. Selected topics only; independent teacher review is pending. This is not a complete syllabus, official past-paper collection or predicted exam score. SubjectScout is not affiliated with or endorsed by College Board. SAT practice is not a full adaptive test; AP practice does not simulate an entire exam.
16 original questions across 8 selected topic areas. No account or payment required to practise.
All topics Unit 1: Limits and Continuity (2) Unit 2: Differentiation: Definition and Fundamental Properties (2) Unit 3: Differentiation: Composite, Implicit, and Inverse Functions (2) Unit 4: Contextual Applications of Differentiation (2) Unit 5: Analytical Applications of Differentiation (2) Unit 6: Integration and Accumulation of Change (2) Unit 7: Differential Equations (2) Unit 8: Applications of Integration (2) Official AP framework reference (framework only, not a source of copied questions).
Topic All topics Unit 1: Limits and Continuity Unit 2: Differentiation: Definition and Fundamental Properties Unit 3: Differentiation: Composite, Implicit, and Inverse Functions Unit 4: Contextual Applications of Differentiation Unit 5: Analytical Applications of Differentiation Unit 6: Integration and Accumulation of Change Unit 7: Differential Equations Unit 8: Applications of Integration Practice view All questions Unanswered Bookmarked Review mistakes Difficulty All levels Foundation Standard Challenge Search questions
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Loading saved progress Question 1 · Unit 1: Limits and Continuity · foundation
What is lim as x approaches 3 of (x^2 - 9)/(x - 3)? A. 0B. 3C. 6D. The limit does not existCheck answer Question 2 · Unit 2: Differentiation: Definition and Fundamental Properties · foundation
If f(x) = 4x^3 - 2x, what is f'(2)? A. 22B. 30C. 46D. 48Check answer Question 3 · Unit 3: Differentiation: Composite, Implicit, and Inverse Functions · foundation
If y = (3x + 1)^4, what is dy/dx? A. 4(3x + 1)^3B. 12(3x + 1)^3C. 12(3x + 1)^4D. (3x + 1)^3Check answer Question 4 · Unit 4: Contextual Applications of Differentiation · foundation
A particle's position is s(t) = t^3 - 6t^2 + 9t metres. What is its velocity at t = 2 seconds? A. -3 m/sB. -2 m/sC. 0 m/sD. 3 m/sCheck answer Question 5 · Unit 5: Analytical Applications of Differentiation · foundation
For f(x) = x^3 - 3x, on which interval is f decreasing? A. (-infinity, -1)B. (-1, 1)C. (1, infinity)D. All real numbersCheck answer Question 6 · Unit 6: Integration and Accumulation of Change · foundation
What is the definite integral from 0 to 2 of 3x^2 dx? A. 4B. 6C. 8D. 12Check answer Question 7 · Unit 7: Differential Equations · foundation
A function satisfies dy/dx = 2y and y(0) = 3. Which formula gives y? A. 3 + 2xB. 2e^(3x)C. 3e^(2x)D. 3e^(-2x)Check answer Question 8 · Unit 8: Applications of Integration · foundation
What is the area between y = x and y = x^2 on 0 <= x <= 1? A. 1/6B. 1/3C. 1/2D. 5/6Check answer Question 9 · Unit 1: Limits and Continuity · standard
Let f(x) = (x^2 - 4)/(x - 2) for x != 2, and f(2) = k. Which k makes f continuous at x = 2? A. 0B. 2C. 4D. No real kCheck answer Question 10 · Unit 2: Differentiation: Definition and Fundamental Properties · standard
If f(x) = x sin(x), with x measured in radians, what is f'(pi)? A. -piB. -1C. 0D. piCheck answer Question 11 · Unit 3: Differentiation: Composite, Implicit, and Inverse Functions · challenge
The point (3,4) lies on x^2 + y^2 = 25. What is dy/dx there? A. -4/3B. -3/4C. 3/4D. 4/3Check answer Question 12 · Unit 4: Contextual Applications of Differentiation · challenge
The radius of a circle increases at 2 cm/s. At the instant its radius is 3 cm, at what rate does its area increase? A. 6 pi cm^2/sB. 9 pi cm^2/sC. 12 pi cm^2/sD. 18 pi cm^2/sCheck answer Question 13 · Unit 5: Analytical Applications of Differentiation · challenge
A rectangle has perimeter 20. What is its maximum area? A. 20B. 24C. 25D. 100Check answer Question 14 · Unit 6: Integration and Accumulation of Change · challenge
If F(x) is the integral from 1 to x^2 of sqrt(1 + t^3) dt, what is F'(1)? A. sqrt(2)B. 2 sqrt(2)C. 3 sqrt(2)D. 4Check answer Question 15 · Unit 7: Differential Equations · standard
A function satisfies dy/dx = 2xy and y(0) = 1. What is y(1)? A. e^(-1)B. 1C. eD. e^2Check answer Question 16 · Unit 8: Applications of Integration · challenge
The region between y = x and y = 0, from x = 0 to x = 2, is revolved about the x-axis. What is the volume? A. 4 pi/3B. 8 pi/3C. 4 piD. 8 piCheck answer All Advanced Placement subjects
