NCDAP College-Level Math 3 — Questions and Answers
Question 1: What is the slope of the line perpendicular to y = (2/3)x − 5?
- −3/2 (Correct answer)
- 3/2
- 2/3
- −2/3
Correct answer: −3/2
Perpendicular slopes are negative reciprocals: −3/2.
Question 2: Evaluate: lim(x→2) (x² − 4)/(x − 2)
- 4 (Correct answer)
- 0
- 2
- undefined
Correct answer: 4
Factor as (x+2)(x−2)/(x−2) = x+2; at x=2, the result is 4.
Question 3: Which of the following is a factor of x³ − 27?
- x − 3 (Correct answer)
- x + 3
- x² − 9
- x + 9
Correct answer: x − 3
x³ − 27 = (x − 3)(x² + 3x + 9), so (x − 3) is a factor.
Question 4: Solve the inequality: |2x − 3| < 7
- −2 < x < 5 (Correct answer)
- x < −2 or x > 5
- x > −2
- x < 5
Correct answer: −2 < x < 5
−7 < 2x − 3 < 7 gives −4 < 2x < 10, so −2 < x < 5.
Question 5: A line passes through (1, 4) and (3, 10). What is its equation?
- y = 3x + 1 (Correct answer)
- y = 2x + 2
- y = 3x − 1
- y = 2x + 4
Correct answer: y = 3x + 1
Slope = (10−4)/(3−1) = 3; using point (1,4): y − 4 = 3(x−1) → y = 3x + 1.
Question 6: If sin θ = 5/13, what is cos θ (assuming θ is in the first quadrant)?
- 12/13 (Correct answer)
- 5/13
- 13/12
- 5/12
Correct answer: 12/13
In a 5-12-13 right triangle, cos θ = 12/13.
Question 7: What is the inverse function of f(x) = 2x − 4?
- f⁻¹(x) = (x + 4)/2 (Correct answer)
- f⁻¹(x) = (x − 4)/2
- f⁻¹(x) = 2x + 4
- f⁻¹(x) = x/2 − 2
Correct answer: f⁻¹(x) = (x + 4)/2
Swap x and y: x = 2y − 4, then solve for y = (x + 4)/2.
NCDAP College-Level Math 3
What is the slope of the line perpendicular to y = (2/3)x − 5?