MPT Core Knowledge 3 — Questions and Answers
Question 1: Factor completely: x² − 5x − 14
- (x+2)(x−7) (Correct answer)
- (x−2)(x+7)
- (x+14)(x−1)
- (x−14)(x+1)
Correct answer: (x+2)(x−7)
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?
- 3
- −3 (Correct answer)
- 4
- −4
Correct answer: −3
Set x=0: −4y=12 → y=−3.
Question 3: Simplify: (x² − 9)/(x − 3)
- x − 3
- x + 3 (Correct answer)
- x² − 3
- x + 9
Correct answer: x + 3
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?
- 5 (Correct answer)
- 5√3
- 10√3
- 5√2
Correct answer: 5
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?
- 2
- 4
- 5 (Correct answer)
- 7
Correct answer: 5
The degree is the highest exponent, which is 5.
Question 6: Solve the inequality: −3x > 12
- x > −4
- x < −4 (Correct answer)
- x > 4
- x < 4
Correct answer: x < −4
Dividing by −3 reverses the inequality: x < −4.
Question 7: The sum of three consecutive integers is 87. What is the largest integer?
- 28
- 29
- 30 (Correct answer)
- 31
Correct answer: 30
Let them be n, n+1, n+2; 3n+3=87 → n=28, so the largest is 30.
MPT Core Knowledge 3
Factor completely: x² − 5x − 14