AP® practice test

Free AP® Calculus AB Practice Test (2026)

This is a set of 25 original practice questions that follow the official AP® Calculus AB course units and their exam weights, each with a short explanation. All of them can be solved by hand, without a calculator.

  • 25 questions
  • 8 topics from the official outline
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The practice test

25 questions

Question 1 of 25On which interval is g(x) = x − 2 ln x decreasing?
Question 2 of 25What is lim x→4 of (√x − 2)/(x − 4)?
Question 3 of 25What is the value of ∫ from 0 to 1 of x(x² + 1)³ dx?
Question 4 of 25A 13-foot ladder leans against a vertical wall. Its bottom slides away from the wall at 2 feet per second. How fast is the top of the ladder sliding down the wall when the bottom is 5 feet from the wall?
Question 5 of 25Let f(x) = x³ − 2x. What is lim h→0 of [f(2 + h) − f(2)]/h?
Question 6 of 25A particle moves along a line with velocity v(t) = t² − 4t + 3 meters per second. What is the total distance it travels from t = 0 to t = 3?
Question 7 of 25What is the derivative of sin²(3x)?
Question 8 of 25The derivative of a function f is f′(x) = x²(x − 3)(x + 1)². At which value(s) of x does f have a relative minimum?
Question 9 of 25Let y = f(x) be the solution of dy/dx = xy² with f(0) = 1. What is f(1)?
Question 10 of 25Let f(x) = ax + 1 for x < 2 and f(x) = x² − a for x ≥ 2. For what value of a is f continuous at x = 2?
Question 11 of 25Let g(x) = ∫ from 1 to x² of √(t³ + 1) dt. What is g′(2)?
Question 12 of 25What is lim x→0 of (eˣ − 1 − x)/x²?
Question 13 of 25Let f(x) = x⁴ − 4x³. At which x-values does the graph of f have a point of inflection?
Question 14 of 25Let g(x) = x² ln x. What is g′(e)?
Question 15 of 25A solid has as its base the region bounded by y = √x, the x-axis and the line x = 4. Its cross sections perpendicular to the x-axis are squares. What is the volume of the solid?
Question 16 of 25A continuous function f has f(0) = 4, f(2) = 7, f(5) = 3 and f(6) = 1. Using a trapezoidal sum with the three subintervals given by these points, what is the approximation of ∫ from 0 to 6 of f(x) dx?
Question 17 of 25Let f(x) = x³ + x + 1, and let g be the inverse function of f. What is g′(3)?
Question 18 of 25What is the absolute maximum value of f(x) = x³ − 3x on the closed interval [−2, 3]?
Question 19 of 25What is lim x→∞ of (√(x² + 6x) − x)?
Question 20 of 25A particle moves along the x-axis with position x(t) = t³ − 6t² + 9t for t ≥ 0. For which values of t is the particle speeding up?
Question 21 of 25Consider the differential equation dy/dx = x − y. At the point (1, 3), the solution curve through that point is
Question 22 of 25Let f(x) = x² for x ≤ 1 and f(x) = 2x − 1 for x > 1. Which statement about f at x = 1 is true?
Question 23 of 25If ∫ from 2 to 5 of f(x) dx = 7 and ∫ from 2 to 9 of f(x) dx = 3, what is ∫ from 9 to 5 of 2f(x) dx?
Question 24 of 25A rectangle has its base on the x-axis and its two upper vertices on the parabola y = 12 − x². What is the largest possible area of the rectangle?
Question 25 of 25What is the average value of f(x) = 3x² on the interval [1, 3]?

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