General Mathematics Paper 2,May/June. 2009

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General Comments
Weakness/Remedies
Strength

Question 12

(a)Copy and complete the table of values for y = sin x + 2 cos x, correct to one decimal place.

X	0°	30º	60°	90°	120°	150°	180°	210°	240
Y		2.2				-1.2	-2.0		-1.9

(b) Using a scale of 2 cm to 30° on the x – axis and 2 cm to 0.5 units

on the y-axis, draw the graph of y = sin x + 2cos x for 0° ≤ x ≤ 240°
(c)     Use your graph to solve the equation:
          (i)     sin x + 2cos x = 0;
         (ii)     sin x = 2.1 – 2cos x.
(d)     From the graph, find y when x = 171°.

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Observation

This was another question where candidates’ performance was reported to be very poor. Majority of them could not complete the table of values correctly. The few who drew the graph correctly could not read from it. More work should be done by teachers on this area of the syllabus. The expected the table is as shown:

X	0	30	66	90	120	130	180	210	240
Y	2.0	2.2	1.9	1.0	-0.1	-1.2	-2.0	-2.2	-1.9

They were also expected to use the given scale and the table to draw the graph, locate the line y = 2.1 and use it to solve the equation, sin x = 2.1 – 2cos x, to obtain x = 9°, 45°. When x = 171°, y = – 1.75.