Mathematics Past Questions and Answers

(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 are 4 fives and 2 red nines in a pack of 52 cards]
(b) P, Q and R are points in the same horizontal plane. The bearing of Q from P is 150° and the bearing of R from Q is 060°. If /PQ/ = 5m and /QR/ = 3m, find the bearing of R from P, correct to the nearest degree.

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) mean ; (ii) median ; (iii) mode of the marks;
(b) percentage of the students who scored at least 8 marks.

(a) Using mathematical tables, find ; (i) \(2 \sin 63.35°\) ; (ii) \(\log \cos 44.74°\);
(b) Find the value of K given that \(\log K - \log (K - 2) = \log 5\);
(c) Use logarithm tables to evaluate \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)

(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 \(x^{2} - 6x + 7 = 0\), correct to 1 decimal place.
(c) The product of two consecutive positive odd numbers is 195. By constructing a quadratic equation and solving it, find the two numbers.

(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 /BD/ : /DC/ is 3 : 2.
(c) Through D, construct a line I perpendicular to BC.
(d) If the line I meets AC at P, measure /BP/.