Page 24 - Spotlight A+ SPM Additional Mathematics Form 4 & 5

Form
4
Chapter 10 Index Numbers Additional Mathematics

Example 11 If the composite index of the four items in the
year 2019 based on the year 2015 was 136,
The table below shows the price indices for the calculate the value of p.
four ingredients, A, B, C and D used in making a
cake in 2017 based on 2014. Solution:

Ingredient A B C D ∑I w = 115(2) + 150(3) + 135p + 140(1)
i
i
= 820 + 135p
Price index in 2017 80 140 150 100 ∑w = 2 + 3 + p + 1
based on 2014 i
= 6 + p
Bar chart below represents the relative amount ∑Iw i –
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i
of the ingredient A, B, C and D, used in making ∑w = I
a cake. i
820 + 135p = 136
Weightage
6 + p
820 + 135p = 136(6 + p)
140
820 + 135p = 816 + 136p
120
p = 4
80
Try question 5 in Formative Zone 10.2
60
Ingredients
0 A B C D
Calculate the composite index for the cost of Solving problems involving index numbers
making a cake in the year 2017 based on the
year 2014. and composite index
Example 13
Solution:
∑I w = 80(140) + 140(80) + 150(120) + 100(60) The table below shows the price indices of
i
i
= 46 400 four raw materials, P, Q, R and S which used to
∑w = 140 + 80 + 120 + 60 produce a tin of drink A in a factory.
i
= 400 Raw Price index in 2019
– ∑Iw material based on 2017
I = i i
∑w
i P 120
46 400
=
400 Q 145
= 116 R
Thus, the composite index for the cost of making
a cake in the year 2017 based on the year 2014 S 130
was 116. Pie chart represents the proportion of the raw CHAP
Try question 4 in Formative Zone 10.2 material used in the drink. 10

P Q
Example 12
85°
140°
The table below shows the price indices and 20°
their corresponding weightage of four items, E, 115° R
F, G and H in 2019 using 2015 as the basis year.
S
Price index in 2019
Item Weightage (a) If the composite index for the cost of
based on 2015
making a tin of drink A in the year 2019
E 115 2 based on the year 2017 is 132, what is the
F 150 3 price index of raw material R?
(b) If the price of raw material R in the year
G 135 p
2017 was RM15, calculate the price of raw
H 140 1 material R in the year 2019.

10.2.1 10.2.2 203