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4024/21 Oct/Nov 2023, Question 1: Standard Form

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 12 marks

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The question, in short

Use percentages, ratios and standard form to work out town, village and city population figures, then compare population densities of four countries.

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

Part (a) · 2 marks

Find how many residents of the town are older than 18, given 36 400 people and 23% aged 18 or under.

  1. 1Aged 18 and under = 23/100 × 36 400 = 8372
  2. 2Over 18 = 36 400 − 8372 = 28 028

Answer28 028

Part (b) · 2 marks

With ages split 4:11:5 and 890 people over 60, find the village total aged 60 or under.

  1. 11 part = 890 ÷ 5 = 178
  2. 2Aged 60 and under = (4 + 11) × 178 = 2670

Answer2670

Part (ci) · 2 marks

Find the percentage fall in the city's population from 702 800 in 2015 to 678 202 in 2020.

  1. 1Decrease = 702 800 − 678 202 = 24 598
  2. 2Percentage decrease = 24 598/702 800 × 100 = 3.5%

Answer3.5

Part (cii) · 2 marks

Given a 12% rise to 702 800 by 2015, work out the city's 1980 population.

  1. 11.12 × population in 1980 = 702 800
  2. 2Population = 702 800 ÷ 1.12 = 627 500

Answer627 500

Part (di) · 1 mark

Subtract the Maldives population 3.92 × 10⁵ from Bahrain's 1.54 × 10⁶, giving the result in standard form.

  1. 11.54 × 10⁶ − 0.392 × 10⁶ = 1.148 × 10⁶

Answer1.148 × 10⁶

Part (dii) · 3 marks

Using the table, compare people per km² for the four countries and state which is highest, showing your working.

  1. 1Bangladesh: 1.63 × 10⁸ ÷ 148 000 ≈ 1101 per km²
  2. 2Bahrain: 1.54 × 10⁶ ÷ 760 ≈ 2026 per km²
  3. 3Maldives: 3.92 × 10⁵ ÷ 298 ≈ 1315; Lebanon: 5.30 × 10⁶ ÷ 10 400 ≈ 510
  4. 4Highest population density: Bahrain

AnswerBahrain

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Also searched as: 4024/21/O/N/23 · 4024_w23_qp_21 · 4024 w23 21 · question 1.
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