Free CLEP Calculus Practice Test (2026)

What is the average value of f(x) = sin x on the interval [0, π]?

An open-top box with a square base must hold 32 cubic feet. What is the smallest possible total area of its base and four sides, in square feet?

A car traveling at 48 feet per second brakes with a constant deceleration of 4 feet per second squared. How far does it travel from the moment braking starts until it stops?

Let h(x) = f(g(x)). Suppose g(1) = 3, g′(1) = −2, f(1) = 4, f′(1) = 5 and f′(3) = 4. What is h′(1)?

Let f(x) = x^(2/3)·(x − 5). Which statement describes f at x = 0 and at x = 2?

Let f(x) = x + 4/x. What value of c in the interval (1, 4) satisfies the conclusion of the Mean Value Theorem for f on [1, 4]?

Let G(x) = ∫ from 1 to x of (t² − 4) dt. Which gives all values of x for which G is decreasing?

A particle moves along a line with position x(t) = t³ − 9t² + 24t for t ≥ 0. What is its acceleration at the first moment it is at rest?

Water flows into a tank at a rate of r(t) = 6√t liters per minute, where t is in minutes. The tank holds 20 liters at t = 0. How many liters does it hold at t = 9?

What is the area of the region enclosed by the graphs of y = x² and y = 4 − x²?

Water is poured at 8 cubic feet per minute into a tank shaped like an inverted cone that is 8 feet tall with a top radius of 4 feet. How fast is the water level rising when the water is 4 feet deep?

If f(x) = arcsin(x/2), what is f′(1)?

What is lim h→0 [cos(π/3 + h) − 1/2]/h?

What is lim x→0 (tan x − x)/x³?

A function f is twice differentiable, f″(x) > 0 for every real number x, and f′(3) = 0. Which statement must be true?

What is the value of lim n→∞ of the sum Σ (i = 1 to n) of (3/n)·(1 + 3i/n)²?

If f is an odd function and ∫ from 0 to 3 of f(x) dx = 5, what is ∫ from −3 to 3 of [f(x) + 2] dx?

What is lim x→0 (1 − cos 3x)/x²?

Let f(x) = (x² + ax − 6)/(x − 2) for x ≠ 2, and f(2) = b. For which values of a and b is f continuous at x = 2?

A quantity y changes according to dy/dt = ky. If y(0) = 200 and y(2) = 600, what is y(5)?

F is an antiderivative of f(x) = x·e^(x²), and F(0) = 2. What is F(1)?

The point (0, 1) lies on the curve eʸ + xy = e. What is dy/dx at that point?

What is lim x→−∞ √(4x² + 1)/(x + 3)?

The line y = kx is tangent to the curve y = eˣ. What is k?

What is ∫ from 0 to π/2 of sin x·cos²x dx?