(a) Simplify \((\frac{4}{25})^{-\frac{1}{2}} \times 2^{4} \div (\frac{15}{2})^{-2}\) (b) Evaluate \(\log_{5} (\frac{3}{5}) + 3 \log_{5} (\frac{5}{2}) - \log...

ABC is a triangle, right-angled at C. P is the mid-point of AC, < PBC = 37° and |BC| = 5 cm. Calculate : (a) |AC|, correct to 3 significant figures ; (b) < PBA.

(a) Given that \(\sin(A + B) = \sin A \cos B + \cos A \sin B\). Without using mathematical tables or calculator, evaluate \(\sin 105°\), leaving your answer ...

In the diagram, ABCD is a trapezium in which \(AD \parallel BC\) and \(< ABC\) is a right angle. If |AD| = 15 cm, |BD| = 17 cm and |BC| = 9 cm, calculate : (...

In the diagram, a ladder TF, 10 metres long is placed against a wall at an angle of 70° to the horizontal. (a) How high up the wall, correct to the nearest m...

(a) A cylindrical pipe is 28 metres long. Its internal radius is 3.5 cm and external radius 5 cm. Calaulate : (i) the volume, in cm\(^{3}\), of metal used in...

(a) If \(\varepsilon\) is the set \({1, 2, 3,..., 19, 20}\) and A, B and C are subsets of \(\varepsilon\) such that A = { multiples of five}, B = {multiples ...

(a) Solve the simultaneous equations 3y - 2x = 21 ; 4y + 5x = 5. (b) Six identical cards numbered 1 - 6 are placed face down. A card is to be picked at rando...

The table gives the frequency distribution of marks obtained by a group of students in a test. Marks 3 4 5 6 7 8 Frequency 5 \(x - 1\) \(x\) 9 4 1 If the mea...