General Mathematics Paper 2,May/June. 2010  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 Main
General Comments

Question 2

(a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120 m from the foot of the cliff, calculate the height of the cliff.

(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.


This question was also reported to have been attempted by majority of the candidates. Furthermore, the report stated that in part (a), majority of the candidates could not draw the diagram correctly and this affected their performance significantly. A few others were unable to apply the trigonometric ratios correctly. Candidates were expected to draw the diagram.
From the diagram, I FMI :: 120 tan 35° = 84.02m. Therefore the height of the cliff:: 2 x 84.02 = 168.04.
In part (b), the most observed weakness was their inability to convert from minutes to hours. They were expected to recall that time :: distance (i.e. t:: ~) and apply this to the problem.
                                                         speed         v
Time taken by faster motorist « ~ while that of the other motorist = ~ where x is the distance
                                                             60                                                                   80
                     X x
from P to Q. - - - = Y2 (30 rnlnutes « Y2 hr). Simplifying this expression gave x = 120km.
                       60 80
Candidates' responses to this question were reported to be generally below average.

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