NBT Mathematics Proficiency 2

Question 1

Solve for x: 3x - 7 = 14

Accepted Answer

x = 7

Answer

3x = 14 + 7 = 21. x = 21 ÷ 3 = 7.

Question 2

Factorise: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

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)?

Accepted Answer

2

Answer

Gradient = (y₂ - y₁) / (x₂ - x₁) = (11 - 3) / (6 - 2) = 8 / 4 = 2.

Question 4

Simplify: (2x³)(3x²)

Accepted Answer

6x⁵

Answer

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?

Accepted Answer

x² + 3x - 10 = 0

Answer

With roots r₁ = 2 and r₂ = -5: sum = -3, product = -10. Equation: x² - (sum)x + product = x² + 3x - 10 = 0.

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