Core Academic Skills Assessment Mathematics: Algebra and Functions 3

Question 1

A line has equation 4x − 2y = 8. What is its slope and y-intercept?

Accepted Answer

slope = 2, y-intercept = −4

Answer

Rewrite as y = 2x − 4; slope is 2 and y-intercept is −4.

Question 2

Which of the following is a factor of x² − x − 12?

Accepted Answer

(x − 4)

Answer

x² − x − 12 = (x − 4)(x + 3), so (x − 4) is a factor.

Question 3

If h(x) = 2x + 1 and k(x) = x², what is k(h(3))?

Accepted Answer

49

Answer

h(3) = 7, then k(7) = 7² = 49.

Question 4

Solve the inequality: −3x + 6 > 12.

Accepted Answer

x < −2

Answer

−3x > 6 → x < −2 (inequality flips when dividing by a negative).

Question 5

Which equation represents a line parallel to y = (2/3)x − 5?

Accepted Answer

y = (2/3)x + 7

Answer

Parallel lines have the same slope (2/3) but different y-intercepts.

Core Academic Skills Assessment Practice Test