College Math Placement Test College Algebra 5 — Questions and Answers
Question 1: Which inequality represents the range of f(x) = -x² + 4x - 1?
- y ≤ 3 (Correct answer)
- y ≥ 3
- y ≤ -1
- y ≥ -1
Correct answer: y ≤ 3
Completing the square: f(x) = -(x-2)² + 3, so the maximum value is 3 and the range is y ≤ 3.
Question 2: What value of k makes the system kx + 2y = 4 and 3x - y = 1 have infinitely many solutions?
- -6 (Correct answer)
- 6
- 3
- -3
Correct answer: -6
For infinitely many solutions the equations must be proportional: k/3 = 2/(-1) = 4/(-1) — checking ratios gives k = -6.
Question 3: What is the product of the roots of 3x² - 7x + 2 = 0?
- 2/3 (Correct answer)
- 7/3
- 3/2
- -7/3
Correct answer: 2/3
By Vieta's formulas, the product of roots = c/a = 2/3 for ax²+bx+c = 0.
Question 4: If f(x) = 5x - 2, what is f⁻¹(13)?
- 3 (Correct answer)
- 63
- 7
- 5
Correct answer: 3
Solve 5x - 2 = 13 → 5x = 15 → x = 3, so f⁻¹(13) = 3.
Question 5: Simplify: (x^(1/2) · x^(1/3)) / x^(1/6)
- x^(2/3) (Correct answer)
- x^(1/6)
- x
- x^(7/6)
Correct answer: x^(2/3)
x^(1/2) · x^(1/3) = x^(5/6); dividing by x^(1/6) gives x^(5/6 - 1/6) = x^(4/6) = x^(2/3).
Question 6: A function f is even. If f(3) = 7, what is f(-3)?
- 7 (Correct answer)
- -7
- 0
- Cannot be determined
Correct answer: 7
An even function satisfies f(-x) = f(x), so f(-3) = f(3) = 7.
Question 7: What is the y-intercept of the exponential function f(x) = 4 · (1/2)^x?
- 4 (Correct answer)
- 1/2
- 2
- 8
Correct answer: 4
At x = 0: f(0) = 4 · (1/2)⁰ = 4 · 1 = 4, so the y-intercept is 4.
College Math Placement Test College Algebra 5
Which inequality represents the range of f(x) = -x² + 4x - 1?