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A full-length 1-hour AP Precalculus practice test covering functions, polynomials, quadratics, absolute value, complex numbers, and more. Includes MCQs, free-response questions, and a live timer
AP Precalculus Practice Test
Time Allowed: 1 Hour | Total Marks: 40
Time Left: 60:00
Section A – Multiple Choice
10 questions × 1 mark = 10 marks
1. Piecewise Functions
f(x) = 2x + 1, when x < 0
f(x) = x², when x ≥ 0
f(x) = x², when x ≥ 0
Find the value of f(−2).
2. Average Rate of Change
The function is:
f(x) = x² − 3x
Find the average rate of change on the interval from x = 1 to x = 4.
3. Composition of Functions
f(x) = 2x − 1
g(x) = x²
g(x) = x²
Find (f ∘ g)(2).
4. Odd and Even Functions
Which of the following functions is odd?
5. Synthetic Division
Find the remainder when:
x³ − 4x² + x + 6 is divided by (x − 2)
Section B – Short Answer
5 questions × 2 marks = 10 marks
6. Polynomial Function
State the degree and leading coefficient of:
f(x) = −4x⁵ + 3x² − x + 7
7. Rational Function
Find the vertical asymptote of:
f(x) = 2 ÷ (x − 3)
8. Composite Functions
f(x) = x + 1
g(x) = 2x
g(x) = 2x
Find f(g(x)).
9. Absolute Value Function
Write the function f(x) = |x − 2| as a piecewise function.
10. Quadratic Function
Find the x-intercepts of:
y = x² − 9
Section C – Free Response
2 questions × 10 marks = 20 marks
11. Piecewise Continuity
f(x) = ax + 1, when x < 2
f(x) = x² − 3, when x ≥ 2
f(x) = x² − 3, when x ≥ 2
Find the value of a so that f(x) is continuous at x = 2.
12. Quadratic Model
A ball is thrown upward and its height (in meters) is given by:
h(t) = −5t² + 20t + 3
a) Find the maximum height.
b) Find the time when the ball hits the ground.
📘 View Answer Key
MCQs: 1–B, 2–C, 3–C, 4–B, 5–D
Short Answers: Degree 5, LC −4 | x = 3 | 2x + 1 | piecewise form | x = ±3
Free Response: a = 0 | Maximum height = 23, time ≈ 4.1 seconds