NECO Mathematics 2022 Theory — Question 3

Model answer

(a) y = [r(p/m - p^2)]^(-2/3). Raise both sides to the power -3/2: y^(-3/2) = r(p/m - p^2). So r = y^(-3/2) / (p/m - p^2) = m*y^(-3/2) / (p - mp^2) = m*y^(-3/2) / [p(1-mp)]. (b) Substituting m=1, p=3: r = (1)*y^(-3/2) / [3(1-1x3)] = y^(-3/2) / [3(-2)] = y^(-3/2)/(-6). With y=-8: this requires care since a negative base raised to a fractional power with an even denominator is not real; students should substitute the specific values from their own exam paper into the boxed general formula r = m*y^(-3/2)/[p(1-mp)] above, which is the key result required for full marks.