College Math Placement Test College Algebra 2

Question 1

Which of the following is the solution set of |2x - 3| < 7?

Accepted Answer

-2 < x < 5

Answer

Solving |2x-3| < 7 gives -7 < 2x-3 < 7, so -4 < 2x < 10, meaning -2 < x < 5.

Question 2

What is the vertex of the parabola y = 2(x - 3)² + 5?

Accepted Answer

(3, 5)

Answer

The vertex form y = a(x-h)² + k has vertex (h, k), so the vertex is (3, 5).

Question 3

If f(x) = x² - 4 and g(x) = x + 2, what is f(g(x))?

Accepted Answer

x² + 4x

Answer

f(g(x)) = (x+2)² - 4 = x² + 4x + 4 - 4 = x² + 4x.

Question 4

What is the domain of f(x) = √(x² - 9)?

Accepted Answer

x ≤ -3 or x ≥ 3

Answer

The radicand x²-9 ≥ 0 factors as (x-3)(x+3) ≥ 0, giving x ≤ -3 or x ≥ 3.

Question 5

Solve for x: log₂(x) + log₂(x - 2) = 3

Accepted Answer

x = 4

Answer

Combining logs gives log₂(x(x-2)) = 3, so x(x-2) = 8, x²-2x-8 = 0, giving x = 4 (rejecting x = -2).

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