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0580/33 Oct/Nov 2022, Question 4: Dividing in a Given Ratio

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 11 marks

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The question, in short

Use a travel graph of Tia cycling from Bay Park to Ocean Park via Sandy Cove to compare speeds, draw Andy's journey, find when they meet, and answer percentage and ratio questions.

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

Part (ai) · 1 mark

Identify the two times between which Tia's cycling speed is greatest, using the travel graph.

  1. 1Steepest part of Tia's graph: 12 km in 20 minutes
  2. 2Between 10 20 and 10 40

Answer10 20 and 10 40

Part (aii) · 2 marks

Draw Andy's journey on the graph: leaves Bay Park at 10 20, runs 8 km/h to Sandy Cove, then rests until 12 00.

  1. 1Time to Sandy Cove = 12 ÷ 8 = 1.5 h, so arrives 10 20 + 1 h 30 min = 11 50
  2. 2Line from (10 20, 0) to (11 50, 12), then horizontal at 12 km to 12 00

AnswerLine from (10 20, 0) to (11 50, 12) and from (11 50, 12) to (12 00, 12)

Part (aiii) · 2 marks

State the time and distance from Bay Park where Tia and Andy pass each other.

  1. 1The lines cross at 11 30
  2. 2Andy at 11 30: 8 × 70/60 = 9.33… km
  3. 3Time 11 30, distance ≈ 9.3 km

AnswerTime 11 30, Distance 9.2 to 9.6 km

Part (b) · 2 marks

Calculate the percentage increase in cyclists from 3546 in June to 4067 in July.

  1. 1Increase = 4067 − 3546 = 521
  2. 2521 ÷ 3546 × 100 = 14.69… ≈ 14.7%

Answer14.7 or 14.69…

Part (ci) · 1 mark

Express the ratio of 432 walkers to 528 runners in simplest form.

  1. 1432 : 528, divide by 48
  2. 2= 9 : 11

Answer9 : 11

Part (cii) · 3 marks

Given cyclists : walkers = 14 : 3 and 432 walkers, find the total number of cyclists, walkers and runners.

  1. 1Cyclists = 432 ÷ 3 × 14 = 2016
  2. 2Total = 2016 + 432 + 528 = 2976

Answer2976

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Also searched as: 0580/33/O/N/22 · 0580_w22_qp_33 · 0580 w22 33 · question 4.
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