SPM Mathematics 2016, Paper 2 (Questions 5 & 6)


Question 5 (4 marks):
Diagram 5 shows a cylindrical tank in a residential area which have 125 houses. Each house received equal volume of water.

Diagram 5

The diameter of the cylindrical tank is 4 m. It is given that each house has a cuboid tank with a base area of 0.8 m2.
Using  π= 22 7 , calculate the height of the water level, in m, of each tank in the house.


Solution:
Volume of water in cylindrical tank =π r 2 h = 22 7 × 2 2 ×3.5 =44  m 3 Volume of water in each cuboid tank= 44 125 0.8×h= 44 125 h=0.44 m Height of water level in each  cuboid tank=0.44 m.


Question 6 (5 marks):
Diagram 6 shows two parallel straight lines, POQ and RMS drawn on a Cartesian plane.

Diagram 6

Find
(a) the equation of the straight line RMS,
(b) the x-intercept of the straight line MN.


Solution:
(a)
m RMS = m POQ        = 10 20        = 1 2 At point ( 4, 6 ) y 1 =m x 1 +c 6= 1 2 ( 4 )+c 6=2+c c=8 The equation of straight line RMS is y= 1 2 x+8


(b)
When y=0, 1 2 x+8=0 1 2 x=8 x=16 x-intercept of straight line MN is 16.


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