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General Mathematics Paper 2,May/June. 2009  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 Main
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°.

_____________________________________________________________________________________________________
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.

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