General Mathematics Paper 2,May/June. 2012
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 Main
Weakness/Remedies
Strength

Question 9

Three towns X, Y and Z are such that Y is 20 km from X and 22 km from Z.  Town X is 18 km from Z.  A Health Centre is to be built by the government to serve the three towns.  The Centre is to be located such that patients from X and Y will always travel equal distances to access the Health Centre while patients from Z will travel exactly 10 km to reach the health Centre.

(a)      Using a Scale of 1cm to 2km, find by Construction, using a pair of compasses and ruler only, the possible positions the Health Centre can be located.

(b)     In how many possible locations can the health Centre be built?

(c)      Measure and record the distances of the locations from town X.

(d)     Which of these locations would be convenient for all the three towns?

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Observation

The Chief Examiner reported that this question was not popular among the candidates. It was avoided by majority of the candidates.  The few who attempted it did not use the scale given.  Others were not able to locate the possible location of the health centre.
Candidates were expected to use a pair of compasses, ruler and the scale given to construct a triangle XYZ where /XY/ = 10cm, /YZ/ = 11cm and /XZ/ = 9 cm. Candidates would then construct the perpendicular bisector of the line XY and a circle with Centre at Z and radius 5cm. The points of intersection of the loci would be the possible locations of the Health Centre.  There were two such possible locations and their distances from X were 27.8 km and 12.4 km respectively.  The location that would be more convenient was the location with the shorter distance from X.