Mathematics Past Questions and Answers

(a) Solve the equation, correct to two decimal places \(2x^{2} + 7x - 11 = 0\)
(b) Using the substitution \(P = \frac{1}{x}; Q = \frac{1}{y}\), solve the simultaneous equations : \(\frac{2}{x} + \frac{1}{y} = 3 ; \frac{1}{x} - \frac{5}{y} = 7\)

A man bought 5 reams of duplicating paper, each of which are supposed to contain 480 sheets. The actual number of sheets in the packets were : 435, 420, 405, 415 and 440.
(a) Calculate, correct to the nearest whole number, the percentage error for the packets of paper;
(b) If the agreed price for a full ream was N35.00, find, correct to the nearest naira, the amount by which the buyer was cheated.

Using a scale of 2cm to 1 unit on the x- axis and 1cm to 1 unit on the y- axis, draw on the same axes the graphs of \(y = 3 + 2x - x^{2}; y = 2x - 3\) for \(-3 \leq x \leq 4\). Using your graph:
(i) solve the equation \(6 - x^{2} = 0\);
(ii) find the maximum value of \(3 + 2x - x^{2}\);
(iii) find the range of x for which \(3 + 2x - x^{2} \leq 1\), expressing all your answers correct to one decimal place.

(a) Prove that the angle which an arc of a circle subtends at the centre is twice that which it subtends at any point on the remaining part of the circumference.
(b)
In the diagram, O is the centre of the circle, < OQR = 32° and < MPQ = 15°. Calculate (i) < QPR ; (ii) < MQO.

The table below shows the distribution of the waiting times for some customers in a certain petrol station.

Waiting time (in mins)	No of customers
1.5 - 1.9	3
2.0 - 2.4	10
2.5 - 2.9	18
3.0 - 3.4	10
3.5 - 3.9	7
4.0 - 4.4	2

(a) Write down the class boundaries of the distribution.
(b) Construct a cumulative frequency curve for the data;
(c) Using your graph, estimate: (i) the interquartile range of the distribution ; (ii) the proportion of customers who could have waited for more than 3 minutes.