Core Academic Skills Assessment Mathematics: Algebra and Functions 5

Question 1

Which expression is equivalent to 3(x − 2)² − 5?

Accepted Answer

3x² − 12x + 7

Answer

Expand: 3(x² − 4x + 4) − 5 = 3x² − 12x + 12 − 5 = 3x² − 12x + 7.

Question 2

If f(x) = 5x − 3, what is f⁻¹(x)?

Accepted Answer

(x + 3)/5

Answer

To find the inverse, swap x and y then solve: x = 5y − 3 → y = (x + 3)/5.

Question 3

A sequence is defined by aₙ = 3n − 2. What is the 10th term?

Accepted Answer

28

Answer

a₁₀ = 3(10) − 2 = 30 − 2 = 28.

Question 4

Which inequality is represented by the graph of a dashed line y = x + 2 with shading below it?

Accepted Answer

y < x + 2

Answer

A dashed boundary means strict inequality, and shading below means y is less than the line.

Question 5

What are the x-intercepts of y = x² − 4x − 5?

Accepted Answer

x = 5 and x = −1

Answer

Factor: (x − 5)(x + 1) = 0, giving x = 5 and x = −1.

Core Academic Skills Assessment Practice Test