SPM 2021 Add Maths Paper 2, Question 13Index Numbers

Solved on video in English and Bahasa Melayu · Form 4, Index Numbers · 5:06 video

The question

(a)

Table 3 shows information on three ingredients used in producing a type of food. Ingredient A: price RM20.00 (2018), RM21.60 (2020), price index 108, percentage of usage 60. Ingredient B: price RM12.50 (2018), RM13.00 (2020), price index 104. Ingredient C: price RM y (2018), RM2.00 (2020), price index x, percentage of usage 5. (a) The price of ingredient C decreased by 20% from 2018 to 2020. (a)(i) State the value of x. (a)(ii) Find the value of y.

(b)

Using Table 3 (with price index of ingredient C = 80, and percentages of usage A = 60, C = 5): (b) Calculate the composite index for the cost of making the food in the year 2020 based on the year 2018.

(c)

Given the composite index for the cost of making the food in 2020 based on 2018 is 105.2: (c) The cost of making a packet of food increases by 40% from the year 2020 to the year 2021. The selling price of a packet of food is RM43 with a profit of RM5 in the year 2021. Calculate the cost of making a packet of food in the year 2018.

SPM 2021 Add Maths Paper 2, Question 13: the question as drawn in Eduly's video5:06

Part (a)

Step 1

A 20% decrease means the price index = 100 − 20 = 80, so x = 80.

Why this step

A price index is the new price as a percentage of the old one. A 20% fall leaves 80%, so the index is 80, not 20.

2 more steps, each with the reason for it, in the full solution

Final answer

x = 80, y = RM2.50

Where students lose marks

Watch out: y is money, so write it to 2 decimal places, RM2.50, not just 2.5.

Part (b)

4 more steps, each with the reason for it, in the full solution

Final answer

Composite index = 105.2

Where students lose marks

Watch out: use x = 80 from part (a) for ingredient C. A wrong index there, like 83.33, ruins the composite index.

Part (c)

4 more steps, each with the reason for it, in the full solution

Final answer

RM25.80

Where students lose marks

Watch out: back-calculate from the cost RM38 (selling price minus profit), not RM43, and round the final answer to 2 decimal places.

Watch every step of this question solved on video (5:06), with the reason behind each step and a box that checks your own answer.

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