NBT Mathematics Proficiency 2 — Questions and Answers
Question 1: Solve for x: 2x² - 8 = 0
- x = ±2 (Correct answer)
- x = ±4
- x = 2 only
- x = 4 only
Correct answer: x = ±2
Dividing both sides by 2 gives x² = 4, so x = ±2.
Question 2: Which expression is equivalent to (3x - 2)(x + 4)?
- 3x² + 10x - 8 (Correct answer)
- 3x² - 8x - 8
- 3x² + 10x + 8
- 3x² - 2x - 8
Correct answer: 3x² + 10x - 8
Using FOIL: 3x·x + 3x·4 + (−2)·x + (−2)·4 = 3x² + 12x − 2x − 8 = 3x² + 10x − 8.
Question 3: A car travels 240 km in 3 hours. At the same speed, how long will it take to travel 400 km?
- 5 hours (Correct answer)
- 4 hours
- 6 hours
- 4.5 hours
Correct answer: 5 hours
Speed = 80 km/h; time = 400 ÷ 80 = 5 hours.
Question 4: What is the value of 3⁻² + 9⁰?
- 10/9 (Correct answer)
- 1/9
- 2
- 10
Correct answer: 10/9
3⁻² = 1/9 and 9⁰ = 1, so 1/9 + 1 = 10/9.
Question 5: Simplify: (x² − 9) ÷ (x − 3)
- x + 3 (Correct answer)
- x − 3
- x² + 3
- x + 9
Correct answer: x + 3
Factor the numerator as (x−3)(x+3); canceling (x−3) leaves x+3.
Question 6: If 5x − 3 = 2x + 12, what is x?
- 5 (Correct answer)
- 3
- 4
- 6
Correct answer: 5
Subtracting 2x and adding 3 gives 3x = 15, so x = 5.
Question 7: A mixture of 20 liters contains 30% alcohol. How many liters of alcohol does it contain?
- 6 (Correct answer)
- 8
- 4
- 10
Correct answer: 6
30% of 20 = 0.30 × 20 = 6 liters.
