AP® practice test

Free AP® Calculus BC Practice Test (2026)

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

  • 25 questions
  • 10 topics from the official outline
  • No timer
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The practice test

25 questions

Question 1 of 25What is the sum of the series Σ from n = 1 to ∞ of 3(−2/5)ⁿ?
Question 2 of 25What is lim x→0 of sin(5x)/tan(2x)?
Question 3 of 25What is the value of ∫ from 0 to 1 of x eˣ dx?
Question 4 of 25A curve is given by x = t² and y = t³ − 3t. What is d²y/dx² at t = 2?
Question 5 of 25A function g has derivative g′(x) = (x² − 4)e^(−x). At which x does g have a relative maximum?
Question 6 of 25The point (1, 2) lies on the curve x² + xy + y² = 7. What is dy/dx at that point?
Question 7 of 25What is the length of the curve y = (2/3)x^(3/2) from x = 0 to x = 3?
Question 8 of 25Which of the following series converges?
Question 9 of 25Let y be the solution of dy/dx = x + y with y(0) = 1. Using Euler's method with two steps of equal size, what is the approximation of y(1)?
Question 10 of 25What is an equation of the line tangent to y = x eˣ at x = 1?
Question 11 of 25What is the value of ∫ from 2 to 3 of 1/(x² − 1) dx?
Question 12 of 25What is the area enclosed by one petal of the polar curve r = cos(2θ)?
Question 13 of 25On which interval is the graph of f(x) = x e^(−x) concave up?
Question 14 of 25Using the line tangent to f(x) = √x at x = 16, what is the approximation of √16.2?
Question 15 of 25A function f has f(2) = 1, f′(2) = 3 and f″(2) = −4. What is the approximation of f(2.1) given by the second-degree Taylor polynomial for f about x = 2?
Question 16 of 25A function f is continuous on [1, 4], with f(1) = 6 and f(4) = −2. Which statement must be true?
Question 17 of 25What is the value of the improper integral ∫ from 0 to ∞ of x e^(−x²) dx?
Question 18 of 25A population P satisfies dP/dt = 0.3P(1 − P/600) with P(0) = 100. At what population is P growing the fastest?
Question 19 of 25Let f(x) = arctan(x²). What is f′(1)?
Question 20 of 25A particle moves in the plane with position vector ⟨t², 4t − t³/3⟩. What is its speed at t = 1?
Question 21 of 25The region between y = x and y = x² for 0 ≤ x ≤ 1 is revolved about the x-axis. What is the volume of the resulting solid?
Question 22 of 25Which x-coordinate gives the point on the curve y = √x that is closest to the point (3, 0)?
Question 23 of 25What is lim h→0 of [ln(e + h) − 1]/h?
Question 24 of 25If f is continuous and ∫ from 0 to 3 of f(x) dx = 6, what is ∫ from 0 to 1 of f(3x) dx?
Question 25 of 25What is the interval of convergence of the power series Σ from n = 1 to ∞ of (x − 3)ⁿ/(n·2ⁿ)?

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