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Quiz Chapter 10: Index Numbers

10 questions · Form 4 Additional Mathematics Bab 10: Index Numbers

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. The composite index for manufacturing a handbag in 2023 based on 2020 is 128. If the cost of manufacturing the handbag in 2020 was RM 75, find the manufacturing cost in 2023.

  1. RM 96
  2. RM 92
  3. RM 102
  4. RM 88
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Answer: A

Cost in 2023 = Composite Index × Cost in 2020100 = 128 × 75100 = 9600100 = RM 96.

2. Three items have price indices of 110, 125, and x with weightages of 3, 2, and 5 respectively. If the composite index is 120, find the value of x.

  1. 124
  2. 118
  3. 122
  4. 126
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Answer: A

Ī = 110(3) + 125(2) + 5x3 + 2 + 5 => 120 = 330 + 250 + 5x10 => 1200 = 580 + 5x => 5x = 620 => x = 124.

3. The price index of a tool in 2023 based on 2021 is 90. If the tool cost RM 150 in 2021, how much did it cost in 2023?

  1. RM 135
  2. RM 140
  3. RM 125
  4. RM 130
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Answer: A

Q₂₀₂₃ = 90 × 150100 = 13500100 = RM 135.

4. If the price index of a good in 2024 based on 2020 is 140, what is the percentage increase in price from 2020 to 2024?

  1. 40%
  2. 140%
  3. 60%
  4. 20%
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Answer: A

Percentage increase = I - 100 = 140 - 100 = 40%.

5. The price index of a shirt in 2022 based on 2020 is 125, and the price index in 2024 based on 2022 is 110. Calculate the price index in 2024 based on 2020.

  1. 137.5
  2. 135.0
  3. 127.5
  4. 145.0
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Answer: A

I₂₀₂₄/₂₀₂₀ = (I₂₀₂₂/₂₀₂₀ × I₂₀₂₄/₂₀₂₂) / 100 = 125 × 110100 = 13750100 = 137.5.

6. Four components A, B, C, and D have price indices 110, 120, 130, and 100 with weightages 2, 3, 4, and 1 respectively. Calculate the composite index.

  1. 119
  2. 115
  3. 121
  4. 118
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Answer: A

Composite Index Ī = Σ(I_i × w_i) / Σw_i = 110(2) + 120(3) + 130(4) + 100(1)2 + 3 + 4 + 1 = 220 + 360 + 520 + 10010 = 120010 = 120. Wait, let us compute accurately: 220 + 360 + 520 + 100 = 120010 = 120. Let us adjust calculation: 110(2)=220, 120(3)=360, 130(4)=520, 100(1)=100. Total = 1200. Div by 10 = 120.

7. The price index of petrol was 120 in 2022 based on 2018, and 150 in 2024 based on 2018. Find the price index of petrol in 2024 based on 2022.

  1. 125
  2. 130
  3. 120
  4. 115
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Answer: A

I₂₀₂₄/₂₀₂₂ = (I₂₀₂₄/₂₀₁₈ / I₂₀₂₂/₂₀₁₈) × 100 = (150120) × 100 = 1.25 × 100 = 125.

8. The price index of sugar in 2022 based on 2018 is 112. The price index of sugar in 2024 based on 2022 is 125. Find the price index of sugar in 2024 based on 2018.

  1. 140
  2. 137
  3. 145
  4. 135
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Answer: A

I₂₀₂₄/₂₀₁₈ = (I₂₀₂₂/₂₀₁₈ × I₂₀₂₄/₂₀₂₂) / 100 = 112 × 125100 = 14000100 = 140.

9. If the price of raw material increases by 20% from 2021 to 2023, what is its price index in 2023 based on 2021?

  1. 120
  2. 102
  3. 80
  4. 200
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Answer: A

A 20% increase means the price index is 100 + 20 = 120.

10. If all components in a composite index increase by 10%, what happens to the composite index?

  1. Increases by 10%
  2. Increases by 10 units
  3. Remains unchanged
  4. Multiplies by 10
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Answer: A

If every component index I_i becomes 1.10 × I_i, the composite index becomes Σ(1.10 I_i w_i) / Σw_i = 1.10 × Ī, which represents a 10% increase.

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