(a) 

In the Venn diagram, P, Qand R are subsets of the universal set U. If n(U) = 125, find : (i) the value of x ; (ii) n(\(P \cup Q \cap R'\)).

(b)  In the diagram, O is the centre of the circle. If WX is parallel to YZ and < WXY = 50°, find the value of (i) , WYZ 

(ii) < YEZ.

(a) Solve : \((x - 2)(x - 3) = 12\).

(b)  In the diagram, M and N are the centres of two circles of equal radii 7cm. The circle intercept at P and Q. If < PMQ = < PNQ = 60°, calculate, correct to the nearest whole number, the area of the shaded portion. [Take \(\pi = \frac{22}{7}\)].

The table shows the distribution of outcomes when a die is thrown 50 times. Calculate the : 

(a) Mean deviation of the distribution ; (b) probability that a score selected at random is at least a 4.

(a) Given that \(5 \cos (x + 8.5)° - 1 = 0, 0° \leq x \leq 90°\), calculate, correct to the nearest degree, the value of x.

(b) The bearing of Q from P is 0150° and the bearing of P from R is 015°. If Q and R are 24km and 32km respectively from P : (i) represent this information in a diagram;

(ii) calculate the distance between Q and R, correct to two decimal places ; (iii) find the bearing of R from Q, correct to the nearest degree.

(a) Two functions, f and g, are defined by \(f : x \to 2x^{2} - 1\) and \(g : x \to 3x + 2\) where x is a real number.

(i) If \(f(x - 1) - 7 = 0\), find the values of x.

(ii) Evaluate : \(\frac{f(-\frac{1}{2}) . g(3)}{f(4) - g(5)}\).

(b) An operation, \((\ast)\) is defined on the set R, of real numbers, by \(m \ast n = \frac{-n}{m^{2} + 1}\), where \(m, n \in R\). If \(-3, -10 \in R\), show whether or not \(\ast\) is commutative.