AST Algebra and Functions 3

Question 1

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

Accepted Answer

3x² - 13x - 10

Answer

FOIL: 3x² - 15x + 2x - 10 = 3x² - 13x - 10.

Question 2

If p(x) = 4x - 6, for what value of x does p(x) = 18?

Accepted Answer

6

Answer

4x - 6 = 18 → 4x = 24 → x = 6.

Question 3

What is the vertex of the parabola y = x² - 6x + 5?

Accepted Answer

(3, -4)

Answer

x = -b/2a = 6/2 = 3. y = 9 - 18 + 5 = -4. Vertex: (3, -4).

Question 4

If 3(x + 2) = 2(x + 7), what is x?

Accepted Answer

8

Answer

3x + 6 = 2x + 14 → x = 8.

Question 5

Two functions: f(x) = x² and g(x) = 3x - 2. At what positive x-values do they intersect?

Accepted Answer

x = 1 and x = 2

Answer

x² = 3x - 2 → x² - 3x + 2 = 0 → (x-1)(x-2) = 0. Intersections at x = 1 and x = 2.

AST - ACT Scaling Test Practice Test