NECO Mathematics 2025 Theory — Question 5

Question 5 of 12 from the National Examinations Council (NECO) Mathematics 2025 Theory paper, with the correct answer and a full explanation.

5. (a) Evaluate the integral of (4x^3-3x^2+2)dx from x=1 to x=3. (b) Find the value of x if log(5x-6) - log(2x-3) = 1. (8 marks)

Model answer

(a) Integral = [x^4-x^3+2x] from 1 to 3 = (81-27+6) - (1-1+2) = 60-2 = 58. (b) log[(5x-6)/(2x-3)]=1, so (5x-6)/(2x-3)=10. 5x-6=20x-30, -15x=-24, x=24/15=1 3/5 (1.6).

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