SPM 2022 Add Maths Paper 2, Question 14Index Numbers

Solved on video in English and Bahasa Melayu · 6 marks · Form 4, Index Numbers · 7:59 video

The question

(a)

Table 2 shows the information related to four ingredients used to produce a type of biscuit, with prices (RM) per kg in 2019 and 2021 and the weightage.

Ingredient | Price 2019 | Price 2021 | Weightage P | 15.00 | z | 5 Q | x | y | p R | 7.50 | 12.00 | q S | 8.00 | 8.80 | 3

(a) (i) Given that the price index of ingredient P for the year 2021 based on the year 2019 is 130, find the value of z. (ii) The price index of ingredient Q for the year 2021 based on the year 2019 is 140. The price per kg of ingredient Q in the year 2019 is RM6 less than its corresponding price in the year 2021. Calculate the value of x and of y.

(b)

(b) Given that the composite index to produce the biscuit for the year 2021 based on the year 2019 is 132, express p in terms of q.

[3 marks]

(c)

(c) The price of the biscuit in the year 2019 is RM40. The prices of all the ingredients have increased by 20% from the year 2021 to the year 2022. Find the selling price of the biscuit in the year 2022, if the company is targeting a profit of 15%.

[3 marks]

SPM 2022 Add Maths Paper 2, Question 14: the question as drawn in Eduly's video7:59

Part (a)

Step 1

Price index I = (P_2021 / P_2019) × 100. For ingredient P: (z/15) × 100 = 130.

Why this step

The base year (2019) always goes on the bottom, the year we're comparing (2021) on top. Flip them and you get the wrong index.

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

Final answer

z = RM19.50; x = RM15, y = RM21

Where students lose marks

Watch out: “RM6 less” means the 2019 price is smaller, so x = y − 6, not x = y + 6.

Part (b)

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

Final answer

p = 9.5 − 3.5q

Where students lose marks

Watch out: use every weightage (5, p, q, 3) in both the top and the bottom of the composite index, then simplify p fully.

Part (c)

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

Final answer

≈ RM72.86

Where students lose marks

Watch out: first raise the 2021 price by 20% to get the 2022 cost, then add the 15% profit to that cost.

Watch every step of this question solved on video (7:59), with the reason behind each step and a box that checks your own answer.

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