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0580/21 Oct/Nov 2023, Question 14: Set Problems

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 4 marks

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The question, in short

Use a two-set Venn diagram with expressions 5x, x + 5, 12 − x and 15, given n(ℰ) = 52, to find n(A ∩ B); then shade a three-set region.

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

Part (a) · 3 marks

Form an equation from the four regions summing to 52, solve for x, then calculate the value of x + 5 for the overlap of A and B.

  1. 15x + (x + 5) + (12 − x) + 15 = 52
  2. 25x + 32 = 52 → x = 4
  3. 3n(A ∩ B) = x + 5 = 4 + 5 = 9

Answer9

Part (b) · 1 mark

On the three-circle Venn diagram, shade the area common to all of C, D and E.

  1. 1C ∩ D ∩ E is the region inside all three circles
  2. 2Shade only the small central region common to C, D and E

AnswerRegion inside all three circles C, D and E shaded

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Also searched as: 0580/21/O/N/23 · 0580_w23_qp_21 · 0580 w23 21 · question 14.
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