SPM 2020 Add Maths Paper 2, Question 15Index Numbers

Solved on video in English and Bahasa Melayu · Form 4, Index Numbers · 6:59 video

The question

(a)

Syarikat Jus Segar manufactures canned drinks. Table 3.1: the price of sweetener per kg was RM2.00 in 2016 and RM x in 2018; the price index for 2018 based on 2016 is 110, and the price index for 2021 based on 2018 is a 25% increase. Table 3.2 gives the price index for 2021 based on 2016 for four ingredients: Sweetener = y, Lychee = 115, Mango = 108, Grape = 112. Diagram 9 is a bar chart of the percentage of each ingredient used: Sweetener = 40, Lychee = m, Mango = m + 2, Grape = 28 (m is a constant). (a) Find the value of x.

(b)(i)

1, find the value of y (the price index of sweetener for 2021 based on 2016).

(b)(ii)

(b)(ii) Calculate the composite index for the price of the mixed fruit drink for the year 2021 based on the year 2016.

(c)

(c) The company estimated that the cost of manufacturing the mixed fruit drink will increase at a constant rate of 2% per year from the year 2021. Estimate the corresponding price of a can of mixed fruit drink for the year 2026 if the price of a can in 2016 was RM1.30.

SPM 2020 Add Maths Paper 2, Question 15: the question as drawn in Eduly's video6:59

Part (a)

Step 1

Price index 2018 based on 2016 = (P2018/P2016) * 100 = 110.

Why this step

The base year is always on the bottom. Here 2016 is the base, so its RM2.00 goes under x. Flipping it gives the wrong x.

1 more step, with the reason for it, in the full solution

Final answer

x = RM2.20

Where students lose marks

Watch out: give the price to two decimal places, RM2.20, not RM2.2.

Part (b)(i)

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

Final answer

y = 137.5

Where students lose marks

Watch out: a 25% rise means index 125, and it must be chained with the 110 from 2018 based on 2016.

Part (b)(ii)

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

Final answer

Composite index = 121.97

Where students lose marks

Watch out: solve for m first, and use y = 137.5 for the sweetener, not 125, or the composite index will be wrong.

Part (c)

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

Final answer

RM1.75 (RM1.76 if the 2021 price is rounded first)

Where students lose marks

Watch out: 2% a year for 5 years compounds as (1.02)⁵, not a flat 10% rise.

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