In the diagram, O is the centre of the circle. If < NLM = 74\(^o\), < LMN = 39\(^o\) and < LOM = x, find the value of x. 

Find the least value of x which satisfies the equation 4x = 7(mod 9)

(a) If A = {multiples of 2}, B = {multiples of 3} and C = {factors of 6} are subsets of \(\mu\) = {x:1 \(\leq\) x  \(\leq\)  10} find A ′ \(\cap\) B ′ \(\cap\) C′

(b) Tickets for a movie premiere cost $18.50 each while the bulk purchase price for 5 tickets is $80.00. If 4 gentlemen decide to get a fifth person to join them so that they can share the bulk purchase price equally, how much would each person save?

(a) Given that P = (\(\frac{rk}{Q} - ms\))\(^{\frac{2}{3}}\)

(i) Make Q the subject of the relation;

(ii) find, correct to two decimal places, the value of Q when P = 3, m = 15, s = 0.2, k = 4 and r = 10.

(b) Given that \(\frac{x + 2y}{5}\) = x - 2y, find x : y

(a} In the diagram, O is the centre of the circle ABCDE, = I\(\overline{BC}\)I = |\(\overline{CD}\)| and < BCD = 108°. Find < CDE. 

(b) Given that tan x = \(\sqrt{3}\), 0\(^o\) \(\geq\) x \(\geq\) 90\(^o\), evaluate 

\(\frac{(cos x)^2 - sin x}{(sin x)^2 + cos x}\)