(a) Make q the subject of the relation \(t = \sqrt{\frac{pq}{r} - r^{2}q}\). (b) If \(9^{(1 - x)} = 27^{y}\) and \(x - y = -1\frac{1}{2}\), find the value o...

(a) Simplify : \(\frac{\frac{1}{2} of \frac{1}{4} \div \frac{1}{3}}{\frac{1}{6} - \frac{3}{4} + \frac{1}{2}}\). (b) Given that \(\sqrt{x} = 10^{\bar{1}.6741}...

A sector of a circle with radius 21 cm has an area of 280\(cm^{2}\). (a) Calculate, correct to 1 decimal place, the perimeter of the sector. (b) If the secto...

(a) Divide \(\frac{x^{2} - 4}{x^{2} + x}\) by \(\frac{x^{2} - 4x + 4}{x + 1}\). (b) The diagram below shows the graphs of \(y = ax^{2} + bx + c\) and \(y = m...

A library received $1,300 grant. It spends 10% of the grant on magazine subscriptions, 35% on new books, 15% to repair damaged books, 30% to buy new furnitur...

In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 passed Mathematics and Accounts only, 6 Mathematics only, 9 Acco...

(a) In the diagram, PQRST is a quadrilateral. PT // QS, < PTQ = 42°, < TSQ = 38° and < QSR = 30°. If < QTS = x and < POT = y, find: (i) x ; (ii) y. (b) In th...

(a) Given that \(\sin x = 0.6, 0° \leq x \leq 90°\), evaluate \(2\cos x + 3\sin x\), leaving your answer in the form \(\frac{m}{n}\), where m and n are integ...

Using ruler and a pair of compasses only, (a) construct a rhombus PQRS of side 7 cm and < PQR = 60°; (b) locate point X such that X lies on the locus of poin...