WAEC Further Mathematics 2025 Theory — Question 13
Question 13 of 16 from the West African Examinations Council (WAEC) Further Mathematics 2025 Theory paper, with the correct answer and a full explanation.
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13. If the mean and standard deviation of the numbers x, 2.5, y and 7 are 4 and √(31/10) respectively, find the values of x and y where x < y.
Model answer
Mean = (x+2.5+y+7)/4 = 4, so x+y = 16-9.5 = 6.5, i.e. x+y=16-7-2.5 → x+y=6.5 (equation i). Standard deviation: √[Σ(x-mean)²/n] = √(31/10). Squaring and substituting y=6.5-x from (i), then expanding, gives the quadratic 2x²-13x+21.1=0. Solving with the quadratic formula gives x≈3.36 or x≈3.14. Since x<y, taking x=3.14 gives y=6.5-3.14=3.36. So x=3.14 and y=3.36.
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