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4024/12 Oct/Nov 2021, Question 25: Three-Set Venn Diagrams

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 7 marks

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The question, in short

Use given counts of 40 students across Art, Dancing and Gardening to fill a Venn diagram, find x, y, z from a ratio, identify an empty region in set notation, and evaluate n((D ∪ G) ∩ A).

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

Part (a) · 2 marks

Complete the Venn diagram using the given numbers, including 5 outside all circles and 1 in all three.

  1. 1Put each number in the region that matches its fact.
  2. 212 do Art only → A only; 1 does all three → centre (A ∩ D ∩ G).
  3. 3Dancing and Gardening but not Art → D ∩ G only; none of them → outside.
  4. 4A only: 12; A ∩ D ∩ G: 1; D ∩ G only: 4; outside all circles: 5

AnswerA only: 12; A ∩ D ∩ G: 1; D ∩ G only: 4; outside all circles: 5

Part (b) · 3 marks

Given x : y : z = 1 : 2 : 3 and the total of 40, find the values of x, y and z.

  1. 1x + y + z = 40 − 12 − 1 − 4 − 5 = 18
  2. 21 + 2 + 3 = 6 parts, one part = 18 ÷ 6 = 3
  3. 3x = 3, y = 6, z = 9

Answerx = 3, y = 6, z = 9

Part (c) · 1 mark

Identify which subset of the Venn diagram contains no students and write it in set notation.

  1. 1The empty region is in A and G but not D: A ∩ G ∩ D′

AnswerA ∩ G ∩ D′

Part (d) · 1 mark

Using the completed regions, find n((D ∪ G) ∩ A).

  1. 1(D ∪ G) ∩ A = regions of A that are also in D or G: x + 1 + 0
  2. 2= 3 + 1 + 0 = 4

Answer4

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Also searched as: 4024/12/O/N/21 · 4024_w21_qp_12 · 4024 w21 12 · question 25.
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