Core Academic Skills Assessment Mathematics: Algebra and Functions

Question 1

If f(x) = 3x² − 2x + 1, what is f(−2)?

Accepted Answer

17

Answer

f(−2) = 3(4) − 2(−2) + 1 = 12 + 4 + 1 = 17.

Question 2

Which value of x satisfies |2x − 5| = 9?

Accepted Answer

x = 7 or x = −2

Answer

2x − 5 = 9 gives x = 7; 2x − 5 = −9 gives x = −2.

Question 3

A function is defined as g(x) = (x + 3)/(x − 2). For which value of x is g(x) undefined?

Accepted Answer

x = 2

Answer

The function is undefined when the denominator equals zero: x − 2 = 0, so x = 2.

Question 4

What is the slope of the line passing through (−1, 4) and (3, −4)?

Accepted Answer

−2

Answer

Slope = (−4 − 4)/(3 − (−1)) = −8/4 = −2.

Question 5

If 5(x − 3) = 2x + 6, what is x?

Accepted Answer

7

Answer

5x − 15 = 2x + 6 → 3x = 21 → x = 7.

Core Academic Skills Assessment Practice Test