MPT Algebra 5

Question 1

Which expression is equivalent to (x³ · x⁻¹)²?

Accepted Answer

x⁴

Answer

x³ · x⁻¹ = x² and (x²)² = x⁴.

Question 2

The sum of three consecutive integers is 54. What is the largest integer?

Accepted Answer

19

Answer

If the integers are n, n+1, n+2, then 3n + 3 = 54, n = 17, and the largest is 19.

Question 3

What is the vertex of the parabola y = (x - 2)² + 5?

Accepted Answer

(2, 5)

Answer

The vertex form y = (x - h)² + k gives vertex (h, k) = (2, 5).

Question 4

Solve for x: (x/3) - 2 = (x/6) + 1

Accepted Answer

18

Answer

Multiplying through by 6 gives 2x - 12 = x + 6, so x = 18.

Question 5

If g(x) = x² - 4 and h(x) = x + 2, what is g(x)/h(x) simplified (x ≠ -2)?

Accepted Answer

x - 2

Answer

g(x) = (x-2)(x+2) and dividing by h(x) = (x+2) gives (x - 2).

(MPT) UCF Math Placement Test Practice Test