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Quiz Chapter 10: Index Numbers

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

Question 1 of 10Score: 0

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

Full Question List & Answer Key

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

1. 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.

2. 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.

3. 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.

4. 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.

5. A price index of 85 indicates that the price of an item has:

  1. Decreased by 15%
  2. Increased by 15%
  3. Decreased by 85%
  4. Increased by 85%
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Answer: A

Since 85 is less than 100, the price decreased by (100 - 85)% = 15% compared to the base year.

6. 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.

7. In a pie chart representing weightages, component X occupies an angle of 90°. What is the weightage of component X as a fraction of the total?

  1. 14
  2. 13
  3. 12
  4. 38
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Answer: A

Weightage fraction = 90° / 360° = 14.

8. 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.

9. The price index of a textbook in 2024 based on 2020 is 115. If the textbook costs RM 46 in 2024, find its price in 2020.

  1. RM 40
  2. RM 38
  3. RM 42
  4. RM 35
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Answer: A

115 = (46Q₂₀₂₀) × 100 => Q₂₀₂₀ = 46 × 100115 = 4600115 = RM 40.

10. The prices of a commodity in 2019 and 2023 are RM 15.00 and RM 18.75 respectively. Calculate the price index in 2023 based on 2019.

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

I = (18.7515.00) × 100 = 1.25 × 100 = 125.

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