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4024/21 Oct/Nov 2024, Question 4: Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

For integers 1 to 15, set A is multiples of 3 and set B is factors of 30; list A, fill a Venn diagram, and find values involving unions, complements and counts.

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

Part (a) · 1 mark

List all elements of set A, the multiples of 3 within 1 to 15.

  1. 1Multiples of 3 up to 15: 3, 6, 9, 12, 15

Answer3, 6, 9, 12, 15

Part (b) · 2 marks

Place the integers 1 to 15 into the correct regions of the Venn diagram for sets A and B.

  1. 1B = factors of 30 up to 15: 1, 2, 3, 5, 6, 10, 15
  2. 2A ∩ B: 3, 6, 15; A only: 9, 12; B only: 1, 2, 5, 10
  3. 3Outside both: 4, 7, 8, 11, 13, 14

AnswerA only: 9, 12 A ∩ B: 3, 6, 15 B only: 1, 2, 5, 10 Outside both: 4, 7, 8, 11, 13, 14

Part (c) · 1 mark

Given x is in the complement of A union B, find the smallest possible x.

  1. 1(A ∪ B)′ = {4, 7, 8, 11, 13, 14}
  2. 2Smallest x = 4

Answer4

Part (d) · 1 mark

Find the number of elements in A intersect the complement of B.

  1. 1A ∩ B′ = {9, 12}
  2. 2n(A ∩ B′) = 2

Answer2

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Also searched as: 4024/21/O/N/24 · 4024_w24_qp_21 · 4024 w24 21 · question 4.
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