WAEC Further Mathematics 2025 Objective — Question 15

Question 15 of 40 from the West African Examinations Council (WAEC) Further Mathematics 2025 Objective paper, with the correct answer and a full explanation.

Given that d²y/dx² = x-1, y'(1)=5 and y(0)=6, find y(x).

A. x³/2 - x + 11/2
B. x³/2 - x²/2 + 11x/2 + 5
C. x³/6 - x²/2 + 11x/2 + 6Correct
D. x³/6 - x²/2 + 11x + 6

Explanation

Integrate once: dy/dx = x²/2 - x + c1. Using y'(1)=5 gives c1=11/2. Integrate again: y = x³/6 - x²/2 + 11x/2 + c2. Using y(0)=6 gives c2=6, so y(x) = x³/6 - x²/2 + 11x/2 + 6.

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