College Math Placement Test College Algebra 5

Question 1

Which inequality represents the range of f(x) = -x² + 4x - 1?

Accepted Answer

y ≤ 3

Answer

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?

Accepted Answer

-6

Answer

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?

Accepted Answer

2/3

Answer

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)?

Accepted Answer

3

Answer

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)

Accepted Answer

x^(2/3)

Answer

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).

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