NBT Mathematics Proficiency 2 — Questions and Answers
Question 1: Solve for x: 3x - 7 = 14
- x = 5
- x = 6
- x = 7 (Correct answer)
- x = 9
Correct answer: x = 7
3x = 14 + 7 = 21. x = 21 ÷ 3 = 7.
Question 2: Factorise: x² - 9
- (x - 3)(x + 3) (Correct answer)
- (x - 9)(x + 1)
- (x + 3)²
- (x - 3)²
Correct answer: (x - 3)(x + 3)
x² - 9 is a difference of squares: a² - b² = (a - b)(a + b). Here, a = x and b = 3. Result: (x - 3)(x + 3).
Question 3: What is the gradient (slope) of the line passing through (2, 3) and (6, 11)?
- 1
- 1.5
- 2 (Correct answer)
- 2.5
Correct answer: 2
Gradient = (y₂ - y₁) / (x₂ - x₁) = (11 - 3) / (6 - 2) = 8 / 4 = 2.
Question 4: Simplify: (2x³)(3x²)
- 5x⁵
- 6x⁵ (Correct answer)
- 6x⁶
- 5x⁶
Correct answer: 6x⁵
Multiply coefficients: 2 × 3 = 6. Add exponents: x³ × x² = x⁵. Result: 6x⁵.
Question 5: A quadratic equation has roots x = 2 and x = -5. Which equation matches?
- x² + 3x - 10 = 0 (Correct answer)
- x² - 3x - 10 = 0
- x² + 3x + 10 = 0
- x² - 3x + 10 = 0
Correct answer: x² + 3x - 10 = 0
With roots r₁ = 2 and r₂ = -5: sum = -3, product = -10. Equation: x² - (sum)x + product = x² + 3x - 10 = 0.
Question 6: Evaluate: 2³ + 3² - 4¹
- 12
- 13 (Correct answer)
- 14
- 15
Correct answer: 13
2³ = 8. 3² = 9. 4¹ = 4. Result: 8 + 9 - 4 = 13.
NBT Mathematics Proficiency 2
Solve for x: 3x - 7 = 14