(a) A pack of 52 playing cards is shuffled and a card is drawn at random. Calculate the probability that it is either a five or a red nine. [Hint : There ar...

The frequency table shows the marks scored by 32 students in a test. Marks scored 1 2 3 4 5 6 7 8 9 10 No of students 2 3 4 4 4 4 5 3 2 1 Find the : (a)(i) m...

The quantity y is partly constant and partly varies inversely as the square of x. (a) Write down the relationship between x and y. (b) When x = 1, y = 11 and...

(a) Given that \(p = x + ym^{3}\), find m in terms of p, x and y. (b) Using the method of completing the square, find the roots of the equation \(x^{2} - 6x ...

(a) Copy and complete the table for the relation \(y = 2 \cos 2x - 1\). x 0° 30° 60° 90° 120° 150° 180° \(y = 2\cos 2x - 1\) 1.0 0 1.0 (b) Using a scale of 2...

(a) Using a ruler and a pair of compasses only, construct triangle ABC with /AB/ = 7.5cm, /BC/ = 8.1cm and < ABC = 105°. (b) Locate a point D on BC such that...

(a) Factorise : \(px - 2px - 4qy + 2py\) (b) Given that the universal set U = {1, 2, 3, 4,5, 6, 7, 8, 9, 10}, P = {1, 2, 4, 6, 10} and Q = {2, 3, 6, 9}; show...

(a) In the diagram, PQSR and SRYZ are parallelograms and PQYZ is a straight line. If /QY/ = 2cm and /RS/ = 3cm, find /PZ/. (b) P and Q are two towns on the e...

(a) Using mathematical tables, find ; (i) \(2 \sin 63.35°\) ; (ii) \(\log \cos 44.74°\); (b) Find the value of K given that \(\log K - \log (K - 2) = \log 5\...