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AP Calculus AB/BC MCQs

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AP Calculus AB/BC practice questions by unit

Fiveable has 8,138 AP Calculus AB/BC multiple-choice practice questions across 10 units. Practice one unit or topic at a time.

  • Unit 1 – Limits and Continuity: 951 multiple-choice questions
  • Unit 2 – Fundamentals of Differentiation: 597 multiple-choice questions
  • Unit 3 – Composite, Implicit, and Inverse Functions: 280 multiple-choice questions
  • Unit 4 – Contextual Applications of Differentiation: 432 multiple-choice questions
  • Unit 5 – Analytical Applications of Differentiation: 1,239 multiple-choice questions
  • Unit 6 – Integration and Accumulation of Change: 1,139 multiple-choice questions
  • Unit 7 – Differential Equations: 1,015 multiple-choice questions
  • Unit 8 – Applications of Integration: 794 multiple-choice questions
  • Unit 9 – Parametric Equations, Polar Coordinates, and Vector–Valued Functions (BC Only): 734 multiple-choice questions
  • Unit 10 – Infinite Sequences and Series (BC Only): 957 multiple-choice questions

Sample AP Calculus AB/BC practice question

A biologist models the population of bacteria in a petri dish using the series ∑n=1∞(−1)n+1⋅500n\sum_{n=1}^{\infty}\frac{(-1)^{n+1}\cdot 500}{n}, where each term represents the net change in population (in thousands) during the nn-th hour. Using the alternating series test, the biologist determines this series converges. What does the convergence of this series mean for the bacteria population?

The population oscillates but approaches a stable limiting value over time.

Correct answer

The population grows without bound because the series has infinitely many terms.

The population reaches zero after finitely many hours.

The population alternates between positive and negative values indefinitely.

Explanation

Recognizing that convergence of the series means the sum of all population changes stabilizes at a finite limit. The alternating terms represent growth and decline alternating each hour, but their magnitudes decrease (satisfying both AST conditions), so the cumulative effect approaches a fixed population level rather than growing unbounded or oscillating wildly.

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