Every rates and speed question from 8 Cambridge IGCSE Mathematics (0580) past papers (Oct/Nov 2025 to May/June 2026), syllabus section 1.12. 8 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/31/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Number past paper questions.
0580 Rates and Speed past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 3 · 0580/31/M/J/26 · Q24
Ali drives 56 km at an average speed of 48 km/h. He then drives for 30 minutes at 54 km/h. Calculate the average speed for his whole journey.
Show solution
- Average speed = total distance ÷ total time.
- First part: time = distance ÷ speed = 56 ÷ 48 = 1.1666… hours = 70 minutes.
- Second part: distance = speed × time = 54 × 0.5 = 27 km.
- Total distance = 56 + 27 = 83 km. Total time = 70 + 30 = 100 minutes = 100⁄60 hours = 12⁄3 hours.
- Average speed = 83 ÷ 12⁄3 = 83 ÷ 1.666… = 49.8 km/h
- Tip: Do not just average the two speeds, 48 and 54. The car spends different amounts of time at each speed.
May/June 2026 · Paper 3 · 0580/32/M/J/26 · Q21
Sam leaves home at 14 30 and drives 106 km to town A. His average speed is 40 km/h. Calculate the time he arrives at town A.
Show solution
- Time = distance ÷ speed = 106 ÷ 40 = 2.65 hours.
- Change the decimal part to minutes: 0.65 × 60 = 39 minutes. So the journey takes 2 h 39 min.
- 14 30 + 2 h = 16 30. Then 16 30 + 39 min = 17 09.
- He arrives at 17 09
- Tip: 2.65 hours is not 2 h 65 min. Always multiply the decimal part by 60.
May/June 2026 · Paper 3 · 0580/33/M/J/26 · Q17
Town A has population 4680 and area 104 km². Town B has area 760 km². The population density of the two towns is the same. Calculate the population of town B. (Population density = population ÷ area.)
Show solution
- Population density of town A = 4680 ÷ 104 = 45 people per km².
- Town B has the same density, so its population = density × area.
- 45 × 760 = 34 200
Feb/Mar 2026 · Paper 3 · 0580/32/F/M/26 · Q9(b)
A bus takes 1 hour 15 minutes to travel 45 km between two towns. Work out the average speed of the bus in kilometres per hour.
Show solution
- Change the time to hours: 15 minutes = 15⁄60 = 0.25 hours, so 1 h 15 min = 1.25 hours.
- Speed = distance ÷ time = 45 ÷ 1.25 = 36 km/h
0580 Rates and Speed past paper questions: Extended (Papers 2 and 4)
May/June 2026 · Paper 4 · 0580/43/M/J/26 · Q10(b)
Llew cycles to school at an average speed of 18.9 kilometres per hour. Write this speed in metres per second.
Show solution
- 1 km = 1000 m, so 18.9 km = 18 900 m.
- 1 hour = 60 × 60 = 3600 seconds.
- 18 900 m in 3600 s: 18 900 ÷ 3600 = 5.25 m/s
- Tip: A quick way is to divide km/h by 3.6: 18.9 ÷ 3.6 = 5.25.
Oct/Nov 2025 · Paper 4 · 0580/41/O/N/25 · Q9
An athlete runs at a speed of 9.5 m/s. Convert this speed into km/h.
Show solution
- 9.5 m/s means 9.5 metres every second.
- There are 60 × 60 = 3600 seconds in one hour, so in one hour the athlete runs 9.5 × 3600 = 34 200 m.
- Change metres to kilometres (÷ 1000): 34 200 m = 34.2 km.
- The speed is 34.2 km/h
- Tip: A quick rule is m/s × 3.6 = km/h. 9.5 × 3.6 = 34.2 ✓
Oct/Nov 2025 · Paper 4 · 0580/42/O/N/25 · Q4
Pedro makes cards. (a) He makes cards at a rate of 9 cards every 20 minutes. Work out the number of cards he makes in 8 hours.
(b) Each card costs 12 cents to make. Pedro sells each card for 50 cents. Work out his percentage profit on each card.
Show solution
- Change 8 hours to minutes: 8 × 60 = 480 minutes.
- Number of 20-minute blocks = 480 ÷ 20 = 24.
- He makes 9 cards in each block: 24 × 9 = 216 cards
- Profit on each card = 50 − 12 = 38 cents.
- Percentage profit = profit⁄cost × 100 = 38⁄12 × 100 = 316.6…
- 317%
- Tip: Percentage profit is always worked out from the cost price (12 cents), not the selling price.
Oct/Nov 2025 · Paper 4 · 0580/43/O/N/25 · Q21
A dressmaker takes 75 hours to make 31 dresses. In week 1, she takes 12 hours 30 minutes to make the first 4 dresses. In week 2, she makes the remaining 27 dresses at a constant hourly rate. Work out the percentage increase in her hourly rate of making dresses from week 1 to week 2.
Show solution
- Change 12 hours 30 minutes to hours: 12.5 hours.
- Week 1 rate = dresses ÷ hours = 4 ÷ 12.5 = 0.32 dresses per hour.
- Week 2 time = 75 − 12.5 = 62.5 hours. Week 2 rate = 27 ÷ 62.5 = 0.432 dresses per hour.
- Increase = 0.432 − 0.32 = 0.112.
- Percentage increase = 0.112⁄0.32 × 100 = 35%
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