Y is 60 km away from X on a bearing of 135°. Z is 80 km away from X on a bearing of 225°. Find the : (a) distance of Z from Y ; (b) bearing of Z from Y.

Out of the 24 apples in a box, 6 are bad. If three apples are taken from the box at random, with replacement, find the probability that : (a) the first two a...

(a) Evaluate, without using mathematical tables or calculator, \((3.69 \times 10^{5}) \div (1.64 \times 10^{-3})\), leaving your answer in standard form. (b)...

(a) Simplify : \(\frac{x^{2} - 8x + 16}{x^{2} - 7x + 12}\). (b) If \(\frac{1}{2}, \frac{1}{x}, \frac{1}{3}\) are successive terms of an arithmetic progressio...

The diagram shows the cross- section of a railway tunnel. If |AB| = 100m and the radius of the arc is 56m, calculate, correct to the nearest metre, the perim...

(a) Using a ruler and a pair of compasses only, construc : (i) a triangle PQR such that /PQ/ = 10 cm, /QR/ = 7 cm and < PQR = 90° ; (ii) the locus \(l_{1}\) ...

(a) A cylinder with radius 3.5 cm has its two ends closed, if the total surface area is \(209 cm^{2}\), calculate the height of the cylinder. [Take \(\pi = \...

(a) With the aid of four- figure logarithm tables, evaluate \((0.004592)^{\frac{1}{3}}\). (b) If \(\log_{10} y + 3\log_{10} x = 2\), express y in terms of x....

(a) Simplify : \(\frac{3\frac{1}{12} + \frac{7}{8}}{2\frac{1}{4} - \frac{1}{6}}\) (b) If \(p = \frac{m}{2} - \frac{n^{2}}{5m}\) ; (i) make n the subject of t...