Mathematics Past Questions and Answers

(a) If p varies directly as \(r^{2}\) and p = 3.2 when r = 4, find the value of p when r = 6.5.
(b) Solve the simultaneous equations :
\(\frac{x}{2} + \frac{y}{4} = 1 ; \frac{x}{3} - \frac{y}{4} = \frac{-1}{6}\)

Without using Mathematical tables or a calculator, simplify :
(a) \(\sqrt{50} - 3\sqrt{2}(2\sqrt{2} - 5) - 5\sqrt{32}\)
(b) \(\frac{1}{2} \log_{10} \frac{25}{4} - 2 \log_{10} \frac{4}{5} + \log_{10} \frac{320}{125}\).

(a) Simplify : \(625^{\frac{3}{8}} \times 5^{\frac{1}{2}} \div 25\)
(b) Solve the following equations correct to one decimal place.
(i) \(\tan (\theta + 25)° = 5.145\)
(ii) \(5\cos \theta - 1 = 0\), where \(0° \leq \theta \leq 90°\).

In the diagram, PQRS is a circle with centre O and radius 7cm. SQ and PR intersect at K and < SKR = 90°. If the length of the arc SR is four times that of arc PQ, find the length of the arc SR. [Take \(\pi = \frac{22}{7}\)].

The table shows the number of suitcases possessed by a group of travellers.

No. of suitcases	0	1	2	3	4	5
Travellers	2	7	7	2	3	6

(a) Calculate the (i) median (ii) mean, correct to the nearest whole number.
(b) Draw a bar chart to represent the information.