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4024/22 May/Jun 2023, Question 5: Compound Measures

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Use a table of populations and areas for three countries to compare values, find a difference in standard form, and work out the largest population density.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 1 mark

State the smallest population value from the table.

  1. 1Smallest population: Sri Lanka, 2.18 × 10⁷

Answer2.18 × 10⁷ or 21 800 000

Part (aii) · 1 mark

Calculate the area difference between Sri Lanka and Pakistan, giving the result in standard form.

  1. 18.82 × 10⁵ − 6.56 × 10⁴ = 882 000 − 65 600 = 816 400
  2. 2= 8.164 × 10⁵ km²

Answer8.16 × 10⁵ or 8.164 × 10⁵

Part (aiii) · 2 marks

Compute population density for each country and identify the largest value.

  1. 1Sri Lanka: 2.18 × 10⁷ ÷ 6.56 × 10⁴ = 332.3…
  2. 2South Korea: 5.17 × 10⁷ ÷ 1.00 × 10⁵ = 517
  3. 3Pakistan: 2.17 × 10⁸ ÷ 8.82 × 10⁵ = 246.0…
  4. 4Largest population density = 517 people per km²

Answer517 or 5.17 × 10²

Part (bi) · 1 mark

Subtract B from A, giving the result in standard form in terms of n.

  1. 1B = 1.5 × 10ⁿ⁻¹ = 0.15 × 10ⁿ
  2. 2A − B = (8.6 − 0.15) × 10ⁿ = 8.45 × 10ⁿ

Answer8.45 × 10ⁿ

Part (bii) · 2 marks

Multiply A by B, giving the result in standard form in terms of n.

  1. 1A × B = 8.6 × 1.5 × 10ⁿ × 10ⁿ⁻¹ = 12.9 × 10²ⁿ⁻¹
  2. 2= 1.29 × 10²ⁿ

Answer1.29 × 10²ⁿ

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