These eight questions are original. They start with the basic price index and move to weights and base years, so work through them in order and show every line.
Cover the answer, attempt the question, then open the answer and compare your method as well as your result.
Use a scientific calculator that cannot be programmed. The ministry’s circular allows one in SPM papers other than any it names separately, and marks still go to the working you write 1. Confirm the current rule on the Lembaga Peperiksaan site.
Questions
Question 1. A kilogram of rice cost RM4.00 in 2020 and RM5.20 in 2024. Find the price index for 2024 based on 2020.
Answer
I = 5.20 ÷ 4.00 × 100 = 130.
Rice was 30% dearer in 2024 than in 2020.
Question 2. The price index of a magazine in 2024 is 125, based on 2020. It cost RM7.50 in 2024. Find its price in 2020.
Answer
Price in 2020 = 7.50 ÷ 125 × 100 = RM6.00.
Check: RM6.00 × 125 ÷ 100 = RM7.50.
Question 3. Three items have indices 120, 150 and 90 with weights 4, 1 and 5. Find the composite index.
Answer
ΣIw = 120×4 + 150×1 + 90×5 = 480 + 150 + 450 = 1 080.
Σw = 4 + 1 + 5 = 10.
Composite index = 1 080 ÷ 10 = 108.
The index is pulled down because the heaviest weight belongs to the item with index 90.
Question 4. Two items have indices 110 and 140, with weights 3 and k. The composite index is 125. Find k.
Answer
(110×3 + 140×k) ÷ (3 + k) = 125.
330 + 140k = 125(3 + k) = 375 + 125k.
15k = 45, so k = 3.
Check: (330 + 420) ÷ 6 = 750 ÷ 6 = 125.
Question 5. The composite index for 2021 is 120 and for 2025 is 156, both with base year 2018. Find the index of 2025 based on 2021.
Answer
156 ÷ 120 × 100 = 130.
Costs in 2025 were 30% higher than in 2021. The subtraction 156 − 120 = 36 is not the percentage change.
Question 6. A composite index is 118. Item A has index 100 and weight 2, item B has index 120 and weight 3, and item C has weight 5. Find the index of item C.
Answer
Let the index of C be x. Then (100×2 + 120×3 + 5x) ÷ 10 = 118.
200 + 360 + 5x = 1 180, so 5x = 620 and x = 124.
Check: (200 + 360 + 620) ÷ 10 = 118.
Question 7. The index for 2022 is 125, based on 2019. The index for 2024 is 115, based on 2022. Find the index for 2024 based on 2019.
Answer
Multiply the two ratios: 125 ÷ 100 × 115 = 143.75.
Reason: costs rose 25% from 2019 to 2022, then 15% from 2022 to 2024. Changes from different bases multiply, they do not add, so the total is not 140.
Question 8. With base year 2020, the composite index is 120 for 2023 and 138 for 2024. Farid says costs rose 18% from 2023 to 2024. Is he correct?
Answer
No. Re-base to 2023: 138 ÷ 120 × 100 = 115.
Costs rose by 15%. Farid subtracted the indices, but both are measured against 2020, while the question asks for the change from 2023.
If you got these wrong
- Questions 1 and 2: revisit calculating a price index from two values.
- Questions 3, 4 and 6: read combining weighted indices and finding missing weights or component indices.
- Questions 5, 7 and 8: study reading a composite index without mixing up base years.
Log the step where each mistake started in the mistake log, then repeat those questions after a few days. The timed practice session builder sets up a timed version.
For a teacher to go through your working, see online one-to-one Additional Mathematics tuition, or return to the index numbers chapter.