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0580/33 Oct/Nov 2021, Question 6: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 10 marks

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The question, in short

Pie chart from 600 people's favourite sport choices; use angles to find numbers, complete the chart, find a probability, and fill a Venn diagram for 80 people with hockey and netball data.

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

Part (ai) · 1 mark

Show that 100 people choose tennis, using the 60° sector and 600 total.

  1. 1Tennis = 60/360 × 600 = 100

Answer60/360 × 600

Part (aii) · 2 marks

Work out how many people choose rugby from its 27° sector.

  1. 1The whole circle, 360°, stands for all 600 people.
  2. 2Rugby = 27/360 × 600 = 45

Answer45

Part (aiii) · 2 marks

Given 125 choose cricket and the rest swimming, complete the pie chart.

  1. 1Cricket angle = 125/600 × 360 = 75°
  2. 2Draw a line from the centre making 75° with the edge of an existing sector; label cricket and swimming

AnswerCorrect straight line on the pie chart

Part (aiv) · 2 marks

Find the probability a randomly picked person chooses tennis or cricket, as a simplified fraction.

  1. 1Tennis = 60/360 × 600 = 100 people
  2. 2Cricket = 125 people
  3. 3Tennis or cricket = 100 + 125 = 225 people
  4. 4P = 225/600 = 3/8

Answer3/8

Part (b) · 3 marks

Complete the Venn diagram for 80 people: 36 hockey, 53 netball, 8 neither.

  1. 1In H or N = 80 − 8 = 72
  2. 2H ∩ N = 36 + 53 − 72 = 17
  3. 3H only = 36 − 17 = 19, N only = 53 − 17 = 36
  4. 4H only: 19, H ∩ N: 17, N only: 36, outside: 8

AnswerH only: 19 H ∩ N: 17 N only: 36 Outside H and N: 8

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Also searched as: 0580/33/O/N/21 · 0580_w21_qp_33 · 0580 w21 33 · question 6.
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