Paper 2 Section C Practice

Index Numbers • 10-Mark Mastery

SPM Paper 2 Section C Specialty

Form 4 Chapter 10: Index Numbers (Nombor Indeks)

Total Marks: 40 Marks • Time Allowed: 50 Minutes

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A Bahagian A: Chain Index & Component Rules [10 Marks]

Answer all questions
Soalan 1 [4 Marks]

The price index of a brand of industrial copper wire in the year 2022 based on the year 2018 is $125$. The price index of the copper wire in the year 2025 based on the year 2022 is $112$.

(a) Calculate the price index of the copper wire in the year 2025 based on the year 2018. [2 marks]

(b) If a roll of copper wire cost RM 280 in the year 2025, calculate its price in the year 2018. [2 marks]

Soalan 2 [6 Marks]

A bakery produces premium chocolate cakes using four ingredients $P, Q, R,$ and $S$. The pie chart shows the sector angles representing the proportion of ingredients used.

P (108°) Q (90°) R (72°) S (90°)

The price indices for ingredients $P, Q, R,$ and $S$ in the year 2024 based on the year 2020 are $130, 115, 140,$ and $120$ respectively.

(a) Calculate the composite index for the cost of making the cakes in the year 2024 based on the year 2020. [3 marks]

(b) The bakery aims to maintain a fixed total production cost in 2024 equal to the year 2020 by reducing the quantity produced. If 1,200 cakes were produced in 2020, how many cakes can be produced in 2024 with the same total budget? [3 marks]

B Bahagian B: SPM Paper 2 Section C Full Blueprint [20 Marks]

Answer both 10-mark questions
Soalan 3 (Paper 2 Section C Model) [10 Marks]

Table below shows the price indices and weightages of four components $K, L, M,$ and $N$ used to manufacture a robotic cleaning device.

Component Price in 2020 (RM) Price in 2023 (RM) Price Index in 2023 based on 2020 Weightage ($w$)
K (Motor) 80.00 104.00 p 5
L (Battery) 60.00 q 125 4
M (Sensors) r 54.00 120 3
N (Casing) 25.00 27.50 110 k

(a) Calculate the values of $p, q,$ and $r$. [3 marks]

(b) The composite index for the production cost of the cleaning device in 2023 based on 2020 is $122.5$. Calculate the value of weightage $k$. [3 marks]

(c) If the manufacturing cost of a robotic cleaner in 2023 was RM 490, calculate the cost in the year 2020. [2 marks]

(d) From the year 2023 to 2025, the price of component $K$ increases by $10\%$, while component $M$ decreases by $5\%$. The other components remain unchanged. Calculate the new composite index for the year 2025 based on the year 2020. [2 marks]

Soalan 4 (KBAT Inflation Impact Model) [10 Marks]
A school food catering service prepares lunch packages for students. The production cost comprises three main expense categories: Food Ingredients ($F$), Kitchen Labor ($L$), and Utility & Packaging ($U$). In the year 2021, the monthly expenses for $F, L,$ and $U$ were RM 12,000, RM 6,000, and RM 2,000 respectively.

(a) Determine the weightage ratio of $F : L : U$ in its simplest integer form. [1 mark]

(b) In the year 2024, the cost of Food Ingredients increased by $20\%$, Kitchen Labor increased by $10\%$, while Utility & Packaging increased by $15\%$. Calculate the composite index for the lunch package production cost in 2024 based on 2021. [3 marks]

(c) Each student was charged RM 5.00 per lunch package in 2021. If the catering service intends to maintain its profit margin percentage, calculate the new price per lunch package in 2024. [3 marks]

(d) In 2025, due to government utility subsidies, the cost of Utility & Packaging is projected to drop such that its index in 2025 based on 2021 is $105$. If the total composite index for 2025 based on 2021 is capped at $118.0$, calculate the maximum allowable price index for Food Ingredients in 2025 based on 2021, assuming labor costs remain at the 2024 level. [3 marks]