Using a scale of 2cm to 1 unit on the x- axis and 1cm to 1 unit on the y- axis, draw on the same axes the graphs of \(y = 3 + 2x - x^{2}; y = 2x - 3\) for \...

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 th...

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)....

(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 sim...

Simplify : (i) \(2\frac{2}{3} - (2\frac{1}{2} - 1\frac{4}{5})\) (ii) \(\frac{3.25 - 1.64}{2.47 - 2.01}\)

(a) Using logarithm table, evaluate \(\frac{\sqrt[3]{1.376}}{\sqrt[4]{0.007}}\) correct to three significant figure. (b) Without using Mathematical tables, f...

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 probabil...

(a) Prove that the angle which an arc of a circle subtends at the centre is twice that which it subtends at any point on the remaining part of the circumfere...

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,...