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;

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