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0580/12 Oct/Nov 2021, Question 23: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks

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The question, in short

Airport survey of 216 people: 125 speak English, 43 speak both English and French, 61 speak neither. Complete a Venn diagram, find n(F), and shade A ∩ B on another diagram.

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

Part (ai) · 2 marks

Complete the Venn diagram for 216 people, with 125 English speakers, 43 speaking both languages, and 61 speaking neither.

  1. 1E ∩ F = 43
  2. 2E only = 125 − 43 = 82
  3. 3Outside both = 61
  4. 4F only = 216 − 82 − 43 − 61 = 30

AnswerE only 82, E ∩ F 43, F only 30, outside both 61

Part (aii) · 1 mark

Using the completed Venn diagram, find n(F), the number of people who speak French.

  1. 1n(F) = 43 + 30 = 73

Answer73

Part (b) · 1 mark

On the given Venn diagram with sets A and B, shade the region A ∩ B.

  1. 1A ∩ B is the overlap of the two circles: shade only the region inside both A and B

AnswerCorrect shading for A∩B

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Also searched as: 0580/12/O/N/21 · 0580_w21_qp_12 · 0580 w21 12 · question 23.
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