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0580/13 May/Jun 2021, Question 20: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 5 marks

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The question, in short

Given 120 students, 61 pass maths, 27 pass both maths and English, and 19 pass neither, complete a Venn diagram, find n(E), and describe a shaded overlap region in set notation.

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

Part (ai) · 3 marks

Fill all four regions of the Venn diagram for M and E using the totals 120, 61, 27 and 19.

  1. 1M ∩ E = 27
  2. 2M only = 61 − 27 = 34
  3. 3Outside both circles = 19
  4. 4E only = 120 − 34 − 27 − 19 = 40

AnswerM only: 34 M ∩ E: 27 E only: 40 Outside both circles: 19

Part (aii) · 1 mark

Using your completed Venn diagram, state the value of n(E).

  1. 1n(E) = 27 + 40
  2. 2= 67

Answer67

Part (b) · 1 mark

Write the set notation for the shaded region where circles A and B overlap.

  1. 1The shaded region is in both A and B.
  2. 2A ∩ B

AnswerA ∩ B

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Also searched as: 0580/13/M/J/21 · 0580_s21_qp_13 · 0580 s21 13 · question 20.
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