NCDAP College-Level Math 3

Question 1

What is the slope of the line perpendicular to y = (2/3)x − 5?

Accepted Answer

−3/2

Answer

Perpendicular slopes are negative reciprocals: −3/2.

Question 2

Evaluate: lim(x→2) (x² − 4)/(x − 2)

Accepted Answer

4

Answer

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?

Accepted Answer

x − 3

Answer

x³ − 27 = (x − 3)(x² + 3x + 9), so (x − 3) is a factor.

Question 4

Solve the inequality: |2x − 3| < 7

Accepted Answer

−2 < x < 5

Answer

−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?

Accepted Answer

y = 3x + 1

Answer

Slope = (10−4)/(3−1) = 3; using point (1,4): y − 4 = 3(x−1) → y = 3x + 1.

(NCDAP) North Carolina Diagnostic Placement Test Practice Test