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Question 9
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(a) A curve has gradient 3x2 – 2x + 1 at point (x,y). If it passes through the point (1,3), find its equation.
(b) the first term of an Arithmetic Progression is 3 and the nth term is 48. If the sum of the first n terms is 255, find the:
- value of n
- smallest value of r for which the rth term exceeds 149.
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A good number of the candidates who attempted the question performed well in the part (a) of the question. They were able to integrate 3x2 – 2x+1 and applied the given conditions to get the required curve y = x3 – x2 + x + 2. However, some candidates argued wrongly that since 3x2 – 2x+1 is the gradient function of the required curve, then
y - y1 = 3 x2 – 2x + 1. This only holds when the gradient is a constant.
x - x1
The part (b) of the question was satisfactorily handled by the candidates. Majority of them were able to apply the formula Sn = n/2 (a + l), where a = 3, l = 48.
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