NCDAP College-Level Math 4 — Questions and Answers
Question 1: What is the period of y = 4 sin(3x)?
- 2π/3 (Correct answer)
- 3π/2
- 2π
- 4π/3
Correct answer: 2π/3
Period = 2π/|b| = 2π/3.
Question 2: Solve: log₃(x) = 4
- 81 (Correct answer)
- 12
- 64
- 27
Correct answer: 81
x = 3⁴ = 81.
Question 3: Which conic section is represented by x²/9 + y²/4 = 1?
- Ellipse (Correct answer)
- Circle
- Hyperbola
- Parabola
Correct answer: Ellipse
This is standard ellipse form x²/a² + y²/b² = 1 with a ≠ b.
Question 4: Find the product (2 + 3i)(1 − 2i).
- 8 − i (Correct answer)
- 8 + i
- 2 − i
- 5 − i
Correct answer: 8 − i
2(1) + 2(−2i) + 3i(1) + 3i(−2i) = 2 − 4i + 3i + 6 = 8 − i.
Question 5: How many distinct real roots does x⁴ − 5x² + 4 = 0 have?
Correct answer: 4
Let u = x²: u² − 5u + 4 = (u−1)(u−4) = 0, giving x = ±1, ±2 — four real roots.
Question 6: What is the range of f(x) = −x² + 6?
- y ≤ 6 (Correct answer)
- y ≥ 6
- all real numbers
- y ≤ −6
Correct answer: y ≤ 6
The parabola opens downward with vertex at (0, 6), so range is y ≤ 6.
Question 7: Simplify: (3a²b)(2ab³)²
- 12a⁴b⁷ (Correct answer)
- 6a⁴b⁷
- 12a³b⁵
- 6a³b⁵
Correct answer: 12a⁴b⁷
(2ab³)² = 4a²b⁶; then 3a²b · 4a²b⁶ = 12a⁴b⁷.
