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0580/33 May/Jun 2022, Question 2: Square Numbers

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 10 marks

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The question, in short

Use set notation for a shaded Venn region, then work with ℰ = natural numbers ≤ 16, listing squares and primes, and complete and use Venn diagrams for multiples of 3 and factors of 15.

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

Part (a) · 1 mark

Describe the shaded region of the Venn diagram using set notation.

  1. 1Everything in A or B (or both) is shaded
  2. 2A ∪ B

AnswerA ∪ B

Part (bi) · 2 marks

List every square number that belongs to the universal set ℰ.

  1. 11 = 1², 4 = 2², 9 = 3², 16 = 4²
  2. 2Square numbers: 1, 4, 9, 16

Answer1, 4, 9, 16

Part (bii) · 2 marks

List the six prime numbers contained in the universal set ℰ.

  1. 1Primes ≤ 16 (1 is not prime)
  2. 22, 3, 5, 7, 11, 13

Answer2, 3, 5, 7, 11, 13

Part (biiia) · 2 marks

Place the elements of M and F, multiples of 3 and factors of 15, into the Venn diagram.

  1. 1M = {3, 6, 9, 12, 15}, F = {1, 3, 5, 15}
  2. 2M ∩ F = {3, 15}
  3. 3M only: 6, 9, 12; F only: 1, 5
  4. 4Outside M and F: 2, 4, 7, 8, 10, 11, 13, 14, 16

AnswerM only: 6, 9, 12 M ∩ F: 3, 15 F only: 1, 5 Outside M and F: 2, 4, 7, 8, 10, 11, 13, 14, 16

Part (biiib) · 1 mark

List all odd numbers lying outside both set M and set F.

  1. 1Odd numbers in ℰ: 1, 3, 5, 7, 9, 11, 13, 15
  2. 2Remove those in M or F (1, 3, 5, 9, 15)
  3. 37, 11, 13

Answer7, 11, 13

Part (biiic) · 1 mark

Find n(M ∩ F), the number of elements common to M and F.

  1. 1M ∩ F = {3, 15}
  2. 2n(M ∩ F) = 2

Answer2

Part (biiid) · 1 mark

For a random pick from ℰ, find the probability the number is in F.

  1. 1n(F) = 4 (1, 3, 5, 15) out of 16 numbers
  2. 2P(in F) = 4/16

Answer4/16

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Also searched as: 0580/33/M/J/22 · 0580_s22_qp_33 · 0580 s22 33 · question 2.
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