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AP Calculus AB/BC MCQs

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AP Calculus AB/BC practice questions by unit

Fiveable has 8,764 AP Calculus AB/BC multiple-choice practice questions across 10 units. Practice one unit or topic at a time.

  • Unit 1 – Limits and Continuity: 1,188 multiple-choice questions
  • Unit 2 – Fundamentals of Differentiation: 654 multiple-choice questions
  • Unit 3 – Composite, Implicit, and Inverse Functions: 380 multiple-choice questions
  • Unit 4 – Contextual Applications of Differentiation: 467 multiple-choice questions
  • Unit 5 – Analytical Applications of Differentiation: 1,207 multiple-choice questions
  • Unit 6 – Integration and Accumulation of Change: 1,205 multiple-choice questions
  • Unit 7 – Differential Equations: 1,003 multiple-choice questions
  • Unit 8 – Applications of Integration: 827 multiple-choice questions
  • Unit 9 – Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only): 799 multiple-choice questions
  • Unit 10 – Infinite Sequences and Series (BC Only): 1,034 multiple-choice questions

Sample AP Calculus AB/BC practice question

A student claims that the derivative of f(x) = 3e^x + 2sin x is f'(x) = 3e^x + 2cos x. Which reasoning completely justifies why this conclusion is correct?

The derivative of e^x is e^x and the derivative of sin x is cos x, so by the sum rule, f'(x) = 3e^x + 2cos x.

Correct answer

The derivative of e^x is e^x and the derivative of sin x is cos x, so f'(x) = 3e^x + 2cos x.

Since both e^x and sin x are transcendental functions, their derivatives follow the pattern of reducing the coefficient, giving f'(x) = 3e^x + 2cos x.

The derivative of 3e^x is 3e^x and the derivative of 2sin x is 2cos x because constants multiply through derivatives.

Explanation

Identifying the correct derivative rules and applying the sum rule to combine them forms a complete justification. The reasoning chains together three components: (1) the specific rule for e^x, (2) the specific rule for sin x, and (3) the sum rule that allows combining derivatives of individual terms.

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