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0580/31 May/Jun 2024, Question 3: Time Calculations

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 15 marks

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The question, in short

Use a train timetable, a clock face, bus timings, percentage rises, a Venn diagram and a room ratio to work out times, counts, costs and probabilities.

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

Part (ai) · 2 marks

Fill the missing entries in the Hinton to Jarmouth timetable, given every train takes the same journey time.

  1. 1Journey time = 11 15 − 10 47 = 28 minutes
  2. 212 35 − 28 minutes = 12 07

Answer12 07

Part (aii) · 1 mark

Draw hands on the blank clock to show when Marge reaches Hinton, 20 minutes before the 10 47 departure.

  1. 110 47 − 20 minutes = 10 27
  2. 2Draw the hour hand just under half way from 10 to 11
  3. 3Draw the minute hand at 27 minutes (between 5 and 6)

Answer10 27 drawn correctly on clock face

Part (b) · 3 marks

Buses leave Texford every 45 minutes from 07 10 until 22 10; find how many departures occur that day.

  1. 122 10 − 07 10 = 15 hours = 900 minutes
  2. 2900 ÷ 45 = 20 gaps
  3. 3Number of buses = 20 + 1 = 21

Answer21

Part (c) · 3 marks

A pass costing $50 rises 10% then 5%; find its price on 1st January 2024.

  1. 12023: 50 × 1.10 = 55
  2. 22024: 55 × 1.05 = 57.75
  3. 3$57.75

Answer57.75

Part (di) · 1 mark

Using the Venn diagram counts, find the total number of hotel workers.

  1. 131 + 9 + 85 + 107 = 232

Answer232

Part (dii) · 1 mark

Using the Venn diagram, find n(B ∪ T).

  1. 1B ∪ T = 31 + 9 + 85
  2. 2= 125

Answer125

Part (diii) · 1 mark

State in words what the value 85 in the Venn diagram tells you about the workers.

  1. 185 is inside T but outside B
  2. 2So 85 workers travel by train but not by bus

AnswerThe number of workers who travel to work by train but who do not travel on a bus

Part (div) · 1 mark

For a randomly picked worker, find the probability that they use both bus and train.

  1. 1Bus and train = 9 workers
  2. 2P = 9/232

Answer9/232

Part (e) · 2 marks

Single to double rooms are in ratio 3 : 8 with 75 more doubles; find how many single rooms there are.

  1. 1Difference in parts = 8 − 3 = 5 parts = 75
  2. 21 part = 75 ÷ 5 = 15
  3. 3Single rooms = 3 × 15 = 45

Answer45

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