MPT Core Knowledge 3

Question 1

Factor completely: x² − 5x − 14

Accepted Answer

(x+2)(x−7)

Answer

Find two numbers that multiply to −14 and add to −5: those are +2 and −7, giving (x+2)(x−7).

Question 2

What is the y-intercept of the line 3x − 4y = 12?

Accepted Answer

−3

Answer

Set x=0: −4y=12 → y=−3.

Question 3

Simplify: (x² − 9)/(x − 3)

Accepted Answer

x + 3

Answer

x²−9=(x+3)(x−3); dividing by (x−3) leaves (x+3), provided x≠3.

Question 4

A 30-60-90 triangle has a hypotenuse of 10. What is the length of the shorter leg?

Accepted Answer

5

Answer

In a 30-60-90 triangle, the shorter leg is half the hypotenuse: 10/2=5.

Question 5

What is the degree of the polynomial 4x⁵ − 3x² + 7x − 1?

Accepted Answer

5

Answer

The degree is the highest exponent, which is 5.

(MPT) UCF Math Placement Test Practice Test