Core Academic Skills Assessment Mathematics: Algebra and Functions 4

Question 1

Simplify: (x² − 9)/(x + 3) for x ≠ −3.

Accepted Answer

x − 3

Answer

Factor the numerator: (x − 3)(x + 3)/(x + 3) = x − 3.

Question 2

Which of the following tables of values represents a linear function?

Accepted Answer

x: 0,1,2,3 → y: 4,7,10,13

Answer

The differences between consecutive y-values are constant (3), confirming a linear function.

Question 3

If 2^x = 32, what is x?

Accepted Answer

5

Answer

32 = 2⁵, so x = 5.

Question 4

Which system of equations has no solution?

Accepted Answer

y = 2x + 1 and y = 2x − 3

Answer

Two lines with the same slope (2) but different y-intercepts are parallel and never intersect.

Question 5

What is the range of f(x) = x² + 3?

Accepted Answer

y ≥ 3

Answer

Since x² ≥ 0 for all real x, the minimum value of f(x) is 3, so y ≥ 3.

Core Academic Skills Assessment Practice Test