MPT Technical Foundations 3 — Questions and Answers
Question 1: What is the GCF of 36 and 60?
- 6
- 9
- 12 (Correct answer)
- 18
Correct answer: 12
The greatest common factor of 36 and 60 is 12.
Question 2: Solve for x: x² − 9 = 0
- x = 3 only
- x = −3 only
- x = ±3 (Correct answer)
- x = ±9
Correct answer: x = ±3
x² = 9 gives x = ±3 (both positive and negative roots).
Question 3: Which expression is equivalent to (a + b)²?
- a² + b²
- a² + ab + b²
- a² + 2ab + b² (Correct answer)
- 2a + 2b
Correct answer: a² + 2ab + b²
Expanding (a+b)² using FOIL gives a² + 2ab + b².
Question 4: Convert 0.375 to a fraction in lowest terms.
- 3/8 (Correct answer)
- 3/7
- 37/100
- 5/12
Correct answer: 3/8
0.375 = 375/1000 = 3/8 after dividing numerator and denominator by 125.
Question 5: What is the LCM of 8 and 12?
- 16
- 24 (Correct answer)
- 36
- 96
Correct answer: 24
The smallest number divisible by both 8 and 12 is 24.
Question 6: Simplify: √75
- 5√3 (Correct answer)
- 3√5
- 15√3
- 5√15
Correct answer: 5√3
√75 = √(25·3) = 5√3.
Question 7: A rectangle has length 3x + 2 and width 4. What is its area?
- 12x + 2
- 12x + 6
- 12x + 8 (Correct answer)
- 3x + 6
Correct answer: 12x + 8
Area = length × width = 4(3x + 2) = 12x + 8.
MPT Technical Foundations 3
What is the GCF of 36 and 60?