In a certain class, 22 pupils take one or more of Chemistry, Economics and Government. 12 take Economics (E), 8 take Government (G) and 7 take Chemistry (C). Nobody takes Economics and Chemistry and 4 pupils take Economics and Government. 

(a)(i) Using set notation and the letters indicated above, write down the two statements in the last sentence; (ii) Draw a Venn diagram to illustrate the information.

(b) How many pupils take (i) both Chemistry and Government ? (ii) Government only?

A man has 9 identical balls in a bag. Out of these, 3 are black, 2 are blue and the remaining are red.

(a) If a ball is drawn at random, what is the probability that it is (i) not blue? (ii) not red?

(b) If 2 balls are drawn at random, one after the other, what is the probability that both of them will be (i) black, if there is no replacement? (ii) blue, if there is a replacement?

ABCDE is a regular pentagon and a rectangle AXYE is drawn on the side AE such that the vertices X and Y lie on the sides BC and CD respectively. Calculate the size of 

(i) an interior angle of the pentagon ; 

(ii) < BXA.

(a) Solve the equation, correct to two decimal places \(2x^{2} + 7x - 11 = 0\)

(b) Using the substitution \(P = \frac{1}{x}; Q = \frac{1}{y}\), solve the simultaneous equations : \(\frac{2}{x} + \frac{1}{y} = 3 ; \frac{1}{x} - \frac{5}{y} = 7\)

A man bought 5 reams of duplicating paper, each of which are supposed to contain 480 sheets. The actual number of sheets in the packets were : 435, 420, 405, 415 and 440. 

(a) Calculate, correct to the nearest whole number, the percentage error for the packets of paper;

(b) If the agreed price for a full ream was N35.00, find, correct to the nearest naira, the amount by which the buyer was cheated.