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0580/41 Oct/Nov 2023, Question 3: Calculating a Percentage of a Quantity

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 14 marks

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The question, in short

Use the planet table to convert and calculate distances, diameters, ratios and percentages, then work with light years and light travel time from Andromeda.

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

Part (ai) · 1 mark

Write Mars's average distance from the Sun, 2.279 × 10⁸ km, as an ordinary number.

  1. 12.279 × 10⁸ = 227 900 000 km

Answer227 900 000

Part (aii) · 2 marks

Find Uranus's diameter, given it is 35.8% of Jupiter's diameter of 143 000 km.

  1. 135.8/100 × 143 000 = 51 194 km
  2. 2≈ 51 200 km

Answer51 200 or 51 190 or 51 194

Part (aiii) · 1 mark

Express Neptune's diameter to Saturn's diameter as 1 : n and find n.

  1. 1n = 120 500 ÷ 49 500 = 2.434… ≈ 2.43

Answer2.43 or 2.434…

Part (aiv) · 2 marks

Find Neptune's average Sun distance as a percentage of Earth's 1.496 × 10⁸ km.

  1. 1(4.495 × 10⁹)/(1.496 × 10⁸) × 100
  2. 2= 3004.67…%

Answer3000 or 3004 to 3005

Part (av) · 2 marks

Given Jupiter is 5.20 AU away, find Mars's average distance from the Sun in AU.

  1. 1Mars/Jupiter = (2.279 × 10⁸)/(7.786 × 10⁸)
  2. 2Mars = 2.279/7.786 × 5.20 = 1.522… ≈ 1.52 AU

Answer1.52 or 1.522…

Part (avi) · 2 marks

Mars's diameter is 39.2% greater than Mercury's; calculate Mercury's diameter.

  1. 1d × (1 + 39.2/100) = 6800
  2. 2d = 6800 ÷ 1.392 = 4885.05… ≈ 4890 km

Answer4890 or 4885…

Part (bi) · 2 marks

Using light speed 2.9979 × 10⁵ km/s and 365.25 days per year, show one light year is 9.461 × 10¹² km to 4 s.f.

  1. 1Seconds in a year = 60² × 24 × 365.25 = 31 557 600
  2. 2Distance = 2.9979 × 10⁵ × 31 557 600
  3. 3= 9.4606… × 10¹² ≈ 9.461 × 10¹² km

Answer2.9979 × 10⁵ × 60² × 24 × 365.25 = 9.4606… × 10¹²

Part (bii) · 2 marks

For Andromeda at 2.40 × 10¹⁹ km, calculate light travel time to Earth in millions of years.

  1. 1One light year = 2.9979 × 10⁵ × 60 × 60 × 24 × 365.25 km
  2. 2= 9.461 × 10¹² km
  3. 3Time = 2.40 × 10¹⁹ ÷ (9.461 × 10¹²) = 2 536 800 years
  4. 4In millions of years: 2.5368… ≈ 2.54

Answer2.54 or 2.536 to 2.537

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