(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 

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

The total surface area of a cone of slant height 1cm and base radius rcm is 224$\pi$ cm$^2$. If r : 1 = 2.5, find: 

(a) correct to one decimal place, the value of r

(b) correct to the nearest whole number, the volume of the cone [Take $\pi$ = $\frac{22}{7}$]

A die was rolled a number of times. The outcomes are as shown in the table 

If the probability of obtaining 2 is 0.15, find the: 

(a) value of m;

(b) number of times the die was rolled;

(c) probability of obtaining an even number. 

(a) Copy and complete the table of values for the relation y = 3 sin 2x. 

(b) Using a scale of 2 cm to 15° on the x-axis and 2cm to I unit on the y-axis, draw the graph of y = 3 sin 2x for 0° $\geq$ x $\geq$ 150°.

(c) Use the graph to find the truth set of;

(i) 3 sin 2x + 2 = 0;

(ii ) $\frac{3}{2}$ sin 2x = 0.25. 

(a) The diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is 48 m and the base radius is 14. Calculate, correct to three significant figures, the surface area of the structure, [Take $\pi = \frac{22}{7}$]

(b) Five years ago, Musah was twice as old as Sesay. If the sum of their ages is 100, find Sesay's present age.

(a) Ms. Maureen spent $\frac{1}{4}$ of her monthly income at a shopping mall, $\frac{1}{3}$ at an open market and $\frac{2}{5}$ of the remaining amount at a Mechanic workshop. If she had N222,000.00 left, find:

(i) her monthly income.

(ii) the amount spent at the open market.

(b) The third term of an Arithmetic Progression (A. P.) is 4m - 2n. If the ninth term of the progression is 2m - 8n. find the common difference in terms of m and n. 

(a)  Two cyclists X and Y leave town Q at the same time. Cyclist X travels at the rate of 5 km/h on a bearing of 049° and cyclist Y travels at the rate of 9 km/h on a bearing of 319°.

(a) Illustrate the information on a diagram.

(b) After travelling for two hours, calculate. correct to the nearest whole number, the:

(i) distance between cyclist X and Y;

(ii) bearing of cyclist X from Y.

(c) Find the average speed at which cyclist X will get to Y in 4 hours.

The table shows the distribution of marks obtained by students in an examination. 

(a) Construct a cumulative frequency table for the distribution.

(b) Draw the cumulative frequency curve for the distribution.

(c) Using the curve, find correct to one decimal place, the:

(i) median mark;

(ii) lowest mark for the distinction if 5% of the students passed with distinction