Mathematics Past Questions and Answers

(a)
In the diagram, BA is parallel to DE. Find the value of x.
(b) Illustrate graphically and shade the region in which inequalities \(y - 2x < 5 ; 2y + x \geq 4 ; y + 2x \leq 10\) are satisfied.

(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 ACDB. If < CAO = 26° and < AOB = 130°. Calculate : (i) < OBC ; (ii) < COB.

(a) What is the 25th term of 5, 9, 13,... ?
(b) Find the 5th term of \(\frac{8}{9}, \frac{-4}{3}, 2, ...\).
(c) The 3rd and 6th terms of a G.P are \(48\) and \(14\frac{2}{9}\) respectively. Write down the first four terms of the G.P.

(a) Copy and complete the following table of values for \(y = 3\sin 2\theta - \cos \theta\).

\(\theta\)	0°	30°	60°	90°	120°	150°	180°
y	-1.0			0			1.0

(b) Using a scale of 2cm to 30° on the \(\theta\) axis and 2cm to 1 unit on the y- axis, draw the graph of \(y = 3 \sin 2\theta - \cos \theta\) for \(0° \leq \theta \leq 180°\).
(c) Use your graph to find the : (i) solution of the equation \(3 \sin 2\theta - \cos \theta = 0\), correct to the nearest degree; (ii) maximum value of y, correct to one decimal place.

The table below shows the frequency distribution of the marks scored by fifty students in an examination.

Marks (%)	0-9	10-19	20-29	30-39	40-49	50-59	60-69	70-79	80-89	90-99
Freq	2	3	4	6	13	10	5	3	2	2

(a) Draw the cumulative frequency curve for the distribution.
(b) Use your curve to estimate the : (i) upper quartile; (ii) pass mark if 60% of the students passed.