NCDAP College-Level Math 2 — Questions and Answers
Question 1: What is the domain of f(x) = √(2x − 6)?
- x ≥ 3 (Correct answer)
- x > 3
- x ≥ 6
- x ≥ −3
Correct answer: x ≥ 3
Set 2x − 6 ≥ 0, giving x ≥ 3.
Question 2: Which expression is equivalent to log₂(32)?
Correct answer: 5
2⁵ = 32, so log₂(32) = 5.
Question 3: If f(x) = 3x² − 5 and g(x) = x + 2, what is f(g(1))?
Correct answer: 22
g(1) = 3, then f(3) = 3(9) − 5 = 22.
Question 4: Solve for x: 2^(x+1) = 16
Correct answer: 3
16 = 2⁴, so x + 1 = 4, giving x = 3.
Question 5: What is the vertex of the parabola y = −(x − 4)² + 9?
- (4, 9) (Correct answer)
- (−4, 9)
- (4, −9)
- (9, 4)
Correct answer: (4, 9)
The vertex form y = a(x − h)² + k gives vertex (h, k) = (4, 9).
Question 6: What is the sum of the roots of 2x² − 8x + 6 = 0?
Correct answer: 4
By Vieta's formulas, sum of roots = −(−8)/2 = 4.
Question 7: Simplify: (x² − 9)/(x − 3)
- x + 3 (Correct answer)
- x − 3
- x² + 3
- x + 9
Correct answer: x + 3
Factor the numerator as (x−3)(x+3) and cancel (x−3).
