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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. 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.

2. 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
Show answer

Answer: A

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

3. The prices of a bicycle in 2018 and 2022 were RM 400 and RM 520 respectively. Find the price index for 2022 based on 2018.

  1. 130
  2. 120
  3. 125
  4. 135
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Answer: A

I = (520400) × 100 = 1.3 × 100 = 130.

4. 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.

5. The price index of an item in 2023 based on 2021 is 135. If the price in 2021 was RM 80, what was its price in 2023?

  1. RM 108
  2. RM 100
  3. RM 112
  4. RM 115
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Answer: A

I = (Q₁ / Q₀) × 100 => 135 = (Q₂₀₂₃ / 80) × 100 => Q₂₀₂₃ = 135 × 80100 = RM 108.

6. 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.

7. 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
Show answer

Answer: A

Q₂₀₂₃ = 90 × 150100 = 13500100 = RM 135.

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
Show answer

Answer: A

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

9. 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.

10. The price of a laptop in the year 2020 was RM 2,500. In 2024, its price increased to RM 3,000. Calculate the price index of the laptop in 2024 based on the year 2020.

  1. 120
  2. 125
  3. 80
  4. 115
Show answer

Answer: A

Price Index I = (Q₁ / Q₀) × 100 = (30002500) × 100 = 1.2 × 100 = 120.

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