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4024/22 May/Jun 2024, Question 6: Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Venn diagram questions: shade a union, write set notation for a shaded region, then work with sets ℰ = {1,...,10}, A = factors of 40, B = odd numbers, completing a diagram and finding elements and a probability.

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

Part (a) · 1 mark

On the two-circle Venn diagram with sets P and Q, shade the area belonging to P or Q.

  1. 1P ∪ Q is everything in P or Q or both
  2. 2Shade the whole of both circles

AnswerP ∪ Q shaded (the whole of both circles P and Q)

Part (b) · 1 mark

For circles X and Y where all but the overlap is shaded, express that shaded region in set notation.

  1. 1Everything except X ∩ Y is shaded
  2. 2(X ∩ Y)′

Answer(X ∩ Y)′

Part (ci) · 2 marks

Place the elements of ℰ into the Venn diagram for A (factors of 40) and B (odd numbers).

  1. 1A = {1, 2, 4, 5, 8, 10}, B = {1, 3, 5, 7, 9}
  2. 2A only: 2, 4, 8, 10; A ∩ B: 1, 5; B only: 3, 7, 9
  3. 3Outside A and B: 6

AnswerA only: 2, 4, 8, 10 A ∩ B: 1, 5 B only: 3, 7, 9 Outside A and B: 6

Part (cii) · 1 mark

Give the elements that lie outside A but inside B.

  1. 1In B but not in A: 3, 7, 9

Answer3, 7, 9

Part (ciii) · 1 mark

For a random pick from ℰ, work out the probability of landing in both A and B.

  1. 1A ∩ B = {1, 5}: 2 elements out of 10
  2. 2P = 2/10

Answer2/10

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Also searched as: 4024/22/M/J/24 · 4024_s24_qp_22 · 4024 s24 22 · question 6.
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