MPT Standards 5

Question 1

If a polynomial P(x) has a root at x = -4, which factor must P(x) contain?

Accepted Answer

(x + 4)

Answer

If x = -4 is a root, then (x - (-4)) = (x + 4) is a factor by the Factor Theorem.

Question 2

What is the distance between points (-1, 2) and (3, 5)?

Accepted Answer

5

Answer

d = √((3-(-1))² + (5-2)²) = √(16 + 9) = √25 = 5.

Question 3

Which transformation maps f(x) to f(x) + 3?

Accepted Answer

Vertical shift up 3

Answer

Adding a constant outside the function shifts the graph vertically upward by that amount.

Question 4

Simplify: (x³)² / x⁴

Accepted Answer

x²

Answer

(x³)² = x⁶; then x⁶/x⁴ = x⁶⁻⁴ = x².

Question 5

What is the sum of the interior angles of a hexagon?

Accepted Answer

720°

Answer

Using (n-2)·180° with n=6: (6-2)·180 = 4·180 = 720°.

(MPT) UCF Math Placement Test Practice Test