Free CLEP Precalculus Practice Test (2026)

A function f has these values: f(1) = 2, f(2) = 7, f(3) = 16, f(4) = 29 and f(5) = 46. Which formula fits all five values?

Which set lists every real solution of √(x + 7) = x − 5, and nothing else?

Angle α lies in Quadrant I with sin α = 3/5, and angle β lies in Quadrant II with cos β = −5/13. What is the value of sin(α + β)?

Let f(x) = 1/(x − 2) and g(x) = √(x + 1). What is the domain of the composite function f(g(x))?

At what value of x does the graph of y = log₃(x − 1) + 2 cross the x-axis?

A cup of coffee at 90°C is placed in a room that stays at 20°C. The difference between the coffee's temperature and the room's temperature is cut in half every 10 minutes. What is the coffee's temperature after 30 minutes?

What are all the solutions of sin(2x) = cos x in the interval 0 ≤ x < 2π?

Two functions have these values: f(0) = 3, f(1) = 0, f(2) = 4, f(3) = 1 and f(4) = 2; g(0) = 2, g(1) = 4, g(2) = 1, g(3) = 0 and g(4) = 3. For which value of x does f(g(x)) = 4?

Which equation describes the set of all points in the xy-plane whose distances from (−3, 0) and (3, 0) add up to 10?

Suppose f is an odd function and g is an even function, both defined for all real numbers, and neither one is the zero function. Which of the following must be an odd function?

A bicycle wheel has a radius of 0.35 meter and turns at 4 revolutions per second as it rolls without slipping. About how fast is the bicycle moving?

As x increases without bound, the graph of f(x) = (x² + 3x − 1)/(x − 1) gets closer and closer to which line?

For which values of x is (x² − 4)/(x − 1) ≥ 0?

The graph of a sinusoidal function has a maximum at (0, 5), and the nearest minimum to the right of it is at (π/2, −1). Which equation could define the function?

Let f(x) = 2x + 3. If f(g(x)) = 6x − 1 for all x, what is g(x)?

Two sides of a triangular garden measure 8 meters and 10 meters, and the angle between them measures 150°. What is the area of the garden?

For which values of k does the equation |x² − 4| = k have exactly four real solutions?

What is the solution of the equation 2^(x + 3) = 5^x?

A circle has its center at (2, −1) and is tangent to the line y = 3. Which is an equation of the circle?

What is the value of arcsin(sin(5π/6))?

Which of the following functions has an inverse that is also a function?

For all values of x for which the expression is defined, sec x − sin x tan x is equal to

A polynomial p of degree 3 has real coefficients, and both 2 and 1 + i are zeros of p. Which of the following could be p(x)?

For which values of b does the line y = x + b meet the circle x² + y² = 8 in exactly one point?

A Ferris wheel is 40 meters in diameter, and its center is 25 meters above the ground. It turns at a constant speed and makes one full turn every 8 minutes. A rider boards at the lowest point at time t = 0. Which function gives the rider's height h, in meters, above the ground t minutes later?