Mathematics Past Questions and Answers

(a) Using logarithm table, evaluate \(\frac{\sqrt[3]{1.376}}{\sqrt[4]{0.007}}\) correct to three significant figure.
(b) Without using Mathematical tables, find the value of \(\frac{\log 81}{\log \frac{1}{3}}\).

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 : \(\frac{2}{x} + \frac{1}{y} = 3 ; \frac{1}{x} - \frac{5}{y} = 7\)