SPM 2023 Add Maths Paper 2, Question 15Index Numbers

Solved on video in English and Bahasa Melayu · Form 4, Index Numbers · 8:34 video

The question

(a)

Table 4 shows information about four ingredients (A, B, C, D) used to make a type of cake: prices (RM per kg) in 2021 and 2023, and the price index for 2023 with 2021 as the base year. A: 2021 price 25.00, 2023 price 27.50, index x B: 2021 price 16.00, 2023 price 18.00, index 112.5 C: 2021 price y, 2023 price 22.50, index 150 D: 2021 price 7.50, 2023 price 9.00, index 120

(a) Find the value of x and of y.

(b)

The price indices (2023 with 2021 as base) are: A = 110, B = 112.5, C = 150, D = 120.

(b) The composite index for the cost of making the cake in 2023 with 2021 as the base year is 127.5. The ratio of the ingredients A, B, C and D used is 3 : 2 : m : 4. Find the value of m.

(c)(i)

The composite index for the cost of making the cake in 2023 with 2021 as base is 127.5.

(c) It is expected that the price of the cake will increase by 20% from the year 2023 to the year 2025. (c)(i) Find the composite index for the cost of making the cake in the year 2025 with 2021 as the base year.

(c)(ii)

The composite index for the cake in 2025 with 2021 as base is 153.

(c)(ii) State the price of the cake in the year 2025, if the price in the year 2021 is RM100 per kg.

(c)(iii)

The composite index for the cake in 2025 with 2021 as base is 153; the ratio of ingredients A : B : C : D is 3 : 2 : 5 : 4, with 2025 indices (base 2021) for A, B, D equal to 110, 112.5, 120.

(c)(iii) Find the percentage increase in the price of ingredient C from the year 2021 to the year 2025, if the prices of the other ingredients remain unchanged from the year 2023 to the year 2025.

SPM 2023 Add Maths Paper 2, Question 15: the question as drawn in Eduly's video8:34

Part (a)

Step 1

Price index I = (P_2023 / P_2021) × 100.

Why this step

Index compares the new price with the base year, so the current-year price goes on top and the base-year price at the bottom.

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

Final answer

x = 110, y = 15

Where students lose marks

Watch out: check your division carefully. 27.50 ÷ 25.00 × 100 gives 110, not 108.

Part (b)

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

Final answer

m = 5

Where students lose marks

Watch out: pair each index with its own weight (A with 3, B with 2, C with m, D with 4).

Part (c)(i)

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

Final answer

Composite index = 153

Where students lose marks

Watch out: chain the indices, 120 × 127.5 ÷ 100. Don't just add 20 to 127.5.

Part (c)(ii)

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

Final answer

RM153 per kg

Where students lose marks

Watch out: use I = (P_2025 / P_2021) × 100 with the composite index 153, not an ingredient's index.

Part (c)(iii)

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

Final answer

121.4% increase

Where students lose marks

Watch out: only C changes. Let C's index be k in the composite equation; the shortcut answer of 53% is wrong.

Watch every step of this question solved on video (8:34), with the reason behind each step and a box that checks your own answer.

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