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WAEC 2019 Mathematics · Question 4

If m : n = 2 : 1, evaluate 3m2−2n2m2+mn\frac{3m^2 - 2n^2}{m^2 + mn}

Options

  1. A.43\frac{4}{3}
  2. B.53\frac{5}{3}
  3. C.34\frac{3}{4}
  4. D.35\frac{3}{5}

Answer: B. 53\frac{5}{3}

Explanation written with AI and checked against the answer key

Analyze the question: We're given the ratio m : n = 2 : 1 and need to evaluate an algebraic expression in m and n. Concept: If m : n = 2 : 1, then m/n = 2, so m = 2n. We can substitute this into the expression and cancel n. Solution: Let m = 2n. Numerator: 3m² − 2n² = 3(2n)² − 2n² = 12n² − 2n² = 10n² Denominator: m² + mn = (2n)² + (2n)(n) = 4n² + 2n² = 6n² So the expression is: (10n²) / (6n²) = 10/6 = 5/3 Check with numbers: Take m = 2, n = 1. Numerator = 3(4) − 2(1) = 12 − 2 = 10 Denominator = 4 + 2 = 6 10/6 = 5/3 ✓ Answer: The correct option is B. **Tip: For ratio questions like this, plug in the simplest numbers that fit the ratio (m = 2, n = 1). This saves time and reduces errors, especially in an exam hall.

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