Further Mathematics Past Questions and Answers

In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students wre obtained as follows;

Students	A	B	C	D	E	F	G	H	I
Performance in Entrance Examination	11	12	8	13	6	15	10	14	17
School Performance	5	10	9	7	4	8	6	14	11

1, Calculate the spearman's rank correlation coefficient
2. What would be the researcher's from the result in a?

A body, moving at 20ms\(^{-1}\) accelerates uniformly at 2\(\frac{1}{2}ms^{-2}\) for 4 seconds. It continues the journey at this speed for 8 seconds, before coming to rest seconds at tseconds after with uniform retardation. If the ratio of the acceleration to retardation is 3 : 4
(a( sketch the velocity - times graph of the journey
(b) find t
(c) find the total distance of the journey

(a) Given that m = i - i, n = 2i + 3j and 2m + n - r = 0, find |r|
(b) The distance, S metres of a moving particle at any time tseconds is given by
S = 3t - \(\frac{t^3}{3}\) + 9
Find the;
(i) time
(ii) distance travelled
When the particle is momentarily at rest

Simplify \(\frac{ 625(\frac{3x}{4} - 1) + 125^{(x - 1)} }{5^{(3x - 2)}}\)

Given that M : (x, y) \(\to\) (7x, 3x - y) and N : (x, y) \(\to\) (2x - y; 5x + 3y)
(a) write down matrices M and N of the linear transformation
(b) find the image of P(2, -3) under the linear transformation N followed by M;
(c) find the coordinates of the point Q whose image is Q(2, 4) under the linear transformation N