NCDAP College-Level Math 2

Question 1

What is the domain of f(x) = √(2x − 6)?

Accepted Answer

x ≥ 3

Answer

Set 2x − 6 ≥ 0, giving x ≥ 3.

Question 2

Which expression is equivalent to log₂(32)?

Accepted Answer

5

Answer

2⁵ = 32, so log₂(32) = 5.

Question 3

If f(x) = 3x² − 5 and g(x) = x + 2, what is f(g(1))?

Accepted Answer

22

Answer

g(1) = 3, then f(3) = 3(9) − 5 = 22.

Question 4

Solve for x: 2^(x+1) = 16

Accepted Answer

3

Answer

16 = 2⁴, so x + 1 = 4, giving x = 3.

Question 5

What is the vertex of the parabola y = −(x − 4)² + 9?

Accepted Answer

(4, 9)

Answer

The vertex form y = a(x − h)² + k gives vertex (h, k) = (4, 9).

(NCDAP) North Carolina Diagnostic Placement Test Practice Test