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0580/32 May/Jun 2021, Question 7: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 9 marks

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The question, in short

Use a frequency table of 135 boys' favourite sports to work out pie chart angles, complete a pie chart, and find a probability; then use set notation with n(S)=53, n(H)=68, n(S ∪ H)=110 to fill a Venn diagram.

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

Part (ai) · 2 marks

Calculate the missing pie chart sector angles for hockey, rugby and other from their frequencies out of 135.

  1. 1Angle per boy = 360 ÷ 135 = 8/3°
  2. 2Hockey = 45 × 8/3 = 120°, Rugby = 27 × 8/3 = 72°, Other = 9 × 8/3 = 24°

Answer| Favourite sport | Pie chart sector angle | | Hockey | 120° | | Rugby | 72° | | Other | 24° |

Part (aii) · 2 marks

Draw the remaining sectors on the pie chart using the calculated angles, with soccer already shown.

  1. 1From the soccer sector, draw sectors of 120° (Hockey), 72° (Rugby) and 24° (Other)
  2. 2Label each sector

AnswerCorrect pie chart

Part (aiii) · 1 mark

Work out the probability that a randomly chosen boy's favourite sport is soccer.

  1. 1P(soccer) = 54/135 = 2/5

Answer2/5

Part (bi) · 3 marks

Fill in the four regions of the Venn diagram for 135 girls using the given set sizes.

  1. 1n(S ∩ H) = 53 + 68 − 110 = 11
  2. 2S only = 53 − 11 = 42, H only = 68 − 11 = 57
  3. 3Outside both = 135 − 110 = 25

AnswerS only: 42 S ∩ H: 11 H only: 57 Outside both circles: 25

Part (bii) · 1 mark

State the value of n(S ∩ H) from the completed Venn diagram.

  1. 1n(S ∩ H) = 11

Answer11

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Also searched as: 0580/32/M/J/21 · 0580_s21_qp_32 · 0580 s21 32 · question 7.
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