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0580/13 May/Jun 2024, Question 21: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 4 marks

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The question, in short

Using set ℰ = {1, 4, 5, 8, 9, 12, 16, 64}, place cube and square numbers in a Venn diagram, find n(C ∪ S), and shade A ∩ B on a second 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 by placing each element of ℰ into the correct region for cube numbers C and square numbers S.

  1. 1Cube numbers in ℰ: 1, 8, 64
  2. 2Square numbers in ℰ: 1, 4, 9, 16, 64
  3. 3Both: 1 and 64 go in the overlap
  4. 48 in C only; 4, 9, 16 in S only
  5. 55 and 12 go outside both circles

AnswerC only: 8; C ∩ S: 1, 64; S only: 4, 9, 16; outside both circles: 5, 12

Part (aii) · 1 mark

Find n(C ∪ S), the number of elements in the union of C and S.

  1. 1C ∪ S = {1, 4, 8, 9, 16, 64}
  2. 2n(C ∪ S) = 6

Answer6

Part (b) · 1 mark

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

  1. 1A ∩ B is the region inside both A and B
  2. 2Shade only the overlap of the two circles

AnswerOverlap of A and B shaded

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Also searched as: 0580/13/M/J/24 · 0580_s24_qp_13 · 0580 s24 13 · question 21.
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