10 exam-style questions with answers and explanations, straight from our 1,030-question bank. Tap an answer to check yourself. When you're ready, take the scored version in the free practice test.
The AP Calculus AB exam has 42 questions and runs 3 hours 10 minutes.
These 10 free AP Calculus AB questions are organized by exam domain, so you can see how each part of the Advanced Placement Calculus AB blueprint is tested. Reveal the answer and explanation under each question.
The function f is given by f(x) = (x² - 3x - 10)/(x² - 4). Which of the following correctly describes the graph of f at x = 2 and at x = -2?
Correct answer: A - A vertical asymptote at x = 2 and a removable discontinuity at x = -2
The function h is continuous on the closed interval [2, 9], with h(2) = -4 and h(9) = 11. Which of the following is guaranteed by the Intermediate Value Theorem?
Correct answer: B - There is at least one value c in (2, 9) for which h(c) = 0
lim(h→0) [(2 + h)⁵ - 32] / h =
Correct answer: C - 80
The function f is defined by f(x) = x² + 1 for x ≤ 3 and f(x) = ax + b for x > 3. If f is differentiable at x = 3, what is the value of a + b?
Correct answer: B - -2
The functions f and g are differentiable, with f(2) = 5, f'(2) = -3, f(4) = 1, f'(4) = 6, g(2) = 4, and g'(2) = 7. If h(x) = f(g(x)), then h'(2) =
Correct answer: D - 42
The function f is differentiable and increasing, with f(3) = 8, f'(3) = 5, f(8) = 20, and f'(8) = 2. If g is the inverse function of f, then g'(8) =
Correct answer: A - 1/5
A particle moves along a horizontal line. At time t = 3 seconds, the velocity of the particle is -6 meters per second and its acceleration is -2 meters per second squared. Which statement about the particle at t = 3 is true?
Correct answer: B - The particle is moving to the left, and its speed is increasing
A 13-foot ladder leans against a vertical wall. The base of the ladder slides away from the wall at a constant rate of 2 feet per second. At the instant the base is 12 feet from the wall, at what rate is the top of the ladder sliding down the wall?
Correct answer: D - 24/5 feet per second
The derivative of the function f is given by f'(x) = (x - 1)²(x - 4). Which of the following describes the behavior of f?
Correct answer: A - f is decreasing on (-∞, 4), with a relative minimum at x = 4 only
The function f is given by f(x) = x³ - 6x² + 9x + 2. What is the absolute maximum value of f on the closed interval [0, 5]?
Correct answer: D - 22
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