General Mathematics Paper 2,Nov/Dec. 2010
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Question9

1. Using ruler and a pair of compasses only, construct:
2. a quadrilateral PQRS such that |PQ| = 5.9 cm, |QR| = 7.1 cm, ∠PQR = 135o,                 |SR| = 11 cm and |PS| = 6 cm;
3. a perpendicular,l1, from S to ;
4. the locus, l2 of points equidistant from  and .
1. Locate a point T such that T is the intersection of l1 and l2.

1. Measure
2. |TQ|;
3. ∠PSR.
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Observation

This question was reported to be very unpopular among the candidates and majority of those who attempted it did not perform very well. Some of them drew the diagram instead of constructing it using ruler and a pair of compasses as instructed in the question. Candidates were expected to draw line PQ using a ruler such that |PQ| = 5.9 cm. Candidates would then construct ∠135o (∠90o + ∠45o) at Q such that ∠PQR = 135o and then measure the length of the line QR to be 7.1 cm. Using the pair of compasses with a radius of 11 cm and R as centre, draw
an arc. Similarly, with radius of 6 cm and P as centre, draw another arc to cut the first arc. Their point of intersection would be the point S. Join the points P, Q, R and S to form the required quadrilateral. To construct a perpendicular from S to the line PR, candidates were expected to use the compass with S as the centre and draw an arc to cut the line PR at two points. Using the same radius and centres at the two points, candidates would then bisect the line PR. This would be locus l1. The locus l2 was gotten by bisecting angle QPS. The point T was the point of intersection of l1 and l2. Using ruler, TQ was measured as 4.5 cm while ∠PSR was measured to be 85o using a protractor.