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AP Calculus AB/BC MCQs

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AP Calculus AB/BC practice questions by unit

Fiveable has 16,707 AP Calculus AB/BC multiple-choice practice questions across 10 units. Practice one unit or topic at a time.

  • Unit 1 – Limits and Continuity: 2,259 multiple-choice questions
  • Unit 2 – Fundamentals of Differentiation: 1,325 multiple-choice questions
  • Unit 3 – Composite, Implicit, and Inverse Functions: 737 multiple-choice questions
  • Unit 4 – Contextual Applications of Differentiation: 1,042 multiple-choice questions
  • Unit 5 – Analytical Applications of Differentiation: 2,161 multiple-choice questions
  • Unit 6 – Integration and Accumulation of Change: 2,239 multiple-choice questions
  • Unit 7 – Differential Equations: 1,688 multiple-choice questions
  • Unit 8 – Applications of Integration: 1,805 multiple-choice questions
  • Unit 9 – Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only): 1,317 multiple-choice questions
  • Unit 10 – Infinite Sequences and Series (BC Only): 2,134 multiple-choice questions

Sample AP Calculus AB/BC practice question

A table shows values of a continuous function h(x) at selected points. At x = 1, 2, 3, 4, 5, the values are h(1) = 0.5, h(2) = 1.2, h(3) = 0.8, h(4) = 0, h(5) = -0.6. Let H(x) = ∫₁ˣ h(t) dt. Which of the following correctly describes the relationship between the table values and the shape of H?

H increases from x = 1 to x = 3 and decreases from x = 3 to x = 5

Correct answer

H is increasing on the entire interval [1, 5] because all h values are nonzero

H has a local minimum at x = 3 because h(3) = 0.8 is the largest value

H decreases from x = 1 to x = 4 and increases from x = 4 to x = 5

Explanation

Applying the Fundamental Theorem, H'(x) = h(x). The table shows h(x) > 0 for x ∈ [1, 3) and h(x) ≤ 0 for x ∈ [3, 5]. Therefore H increases where h is positive and decreases where h is negative or zero. This translation from numerical data to function behavior demonstrates understanding of how the sign pattern of h determines monotonicity of H.

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