SPM Mathematics 2017, Paper 2 (Questions 3 & 4)


Question 3 (4 marks):
Diagram 2 shows a composite formed by joining a quarter cylinder and a right prism at the rectangular plane EFGH. The trapezium ABGF and the quarter circle FGK are the uniform cross sections of the solid.

Diagram 2

Using   π= 22 7 , calculate the volume, in  cm3, of the composite solid.


Solution:
Volume of FGK = 1 4 ( π r 2 h ) = 1 4 ( 22 7 × 5 2 ×7 ) = 1 4 ( 22 7 ×25×7 ) =137 1 2  cm 3 Volume of ABGF =[ 1 2 ( 10+5 )5 ]×7 = 5 2 ( 15 )×7 = 525 2 =262 1 2  cm 3 Total volume of solid =137 1 2  cm 3 +262 1 2  cm 3 =400  cm 3


Question 4 (5 marks):
Solution by matrix method is not allowed to answer this question.
Diagram 3 shows a bicycle and a tricycle.

Diagram 3

Calculate the number of bicycles and the number of tricycles if there are 64 pedals and 74 tyres.


Solution:
Let bicycle = x and tricycle = y
So,
2x + 2y = 64 …………. (1)
2x + 3y = 74 …………. (2)
(2) – (1)
3y – 2y = 74 – 64
y = 10

When y = 10
From (2)
2x + 3(10) = 74
2x = 7430
2x = 44
x = 22

Thus, the number of bicycles are 22 and the number of tricycles are 10.


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