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4MA1/1H Jun 2023, Question 16: Three-Set Venn Diagrams

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks

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The question, in short

Use the Venn diagram numbers and x with n(A ∪ B) = 42 to find x, then find n(A′) and n(B′ ∩ C).

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

Part (a) · 1 mark

Use n(A ∪ B) = 42 with the diagram regions to find x.

  1. 1A ∪ B is made up of the regions 9, x, 12, 5, 3 and 7
  2. 2n(A ∪ B) = 9 + x + 12 + 5 + 3 + 7 = 36 + x
  3. 336 + x = 42
  4. 4x = 6

Answer6

Part (b) · 1 mark

Find the number of elements outside set A.

  1. 1Total number of elements = 9 + 6 + 12 + 5 + 3 + 7 + 10 + 7 = 59
  2. 2n(A) = 9 + 6 + 5 + 3 = 23
  3. 3n(Aʹ) = 59 − 23 = 36

Answer36

Part (c) · 1 mark

Find the number of elements in C but not in B.

  1. 1Bʹ ∩ C is the part of C that lies outside B
  2. 2That is the 5 in A and C only together with the 10 in C only
  3. 3n(Bʹ ∩ C) = 5 + 10 = 15

Answer15

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