NCDAP College-Level Math 4

Question 1

What is the period of y = 4 sin(3x)?

Accepted Answer

2π/3

Answer

Period = 2π/|b| = 2π/3.

Question 2

Solve: log₃(x) = 4

Accepted Answer

81

Answer

x = 3⁴ = 81.

Question 3

Which conic section is represented by x²/9 + y²/4 = 1?

Accepted Answer

Ellipse

Answer

This is standard ellipse form x²/a² + y²/b² = 1 with a ≠ b.

Question 4

Find the product (2 + 3i)(1 − 2i).

Accepted Answer

8 − i

Answer

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?

Accepted Answer

4

Answer

Let u = x²: u² − 5u + 4 = (u−1)(u−4) = 0, giving x = ±1, ±2 — four real roots.

(NCDAP) North Carolina Diagnostic Placement Test Practice Test