WAEC Further Mathematics 2025 Theory — Question 9

Question 9 of 16 from the West African Examinations Council (WAEC) Further Mathematics 2025 Theory paper, with the correct answer and a full explanation.

9. Given that ∫₁ₘ⁻(2x²-x-3)dx = -9/2 where m is an integer, find the value of m.

Model answer

Integrating: [2x³/3 - x²/2 - 3x] evaluated from -1 to m = -9/2. Substituting the limits and simplifying leads to the cubic equation 4m³-3m²-18m+16=0. Testing integer values, m=2 satisfies the equation (4(8)-3(4)-36+16=0). So m = 2.

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