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0580/31 May/Jun 2022, Question 7: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 7 marks

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The question, in short

Using a table of Paper 1 and Paper 2 scores for 15 students, complete and interpret a scatter diagram, draw a line of best fit, estimate a Paper 2 score, and solve a Venn diagram probability problem.

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

Part (ai) · 1 mark

Plot the two remaining students' scores on the scatter diagram, which already shows thirteen points.

  1. 1Plot the last two students: (23, 30) and (42, 58)

Answer2 points correctly plotted

Part (aii) · 1 mark

State the type of correlation visible in the completed scatter diagram.

  1. 1Higher paper 1 scores go with higher paper 2 scores: positive correlation

AnswerPositive

Part (aiii) · 1 mark

Draw a line of best fit on the scatter diagram grid.

  1. 1Draw a ruled line through the middle of the points, e.g. through the mean point (32.7, 47.6)
  2. 2Keep about as many points above the line as below it, following the upward trend

AnswerA ruled line of best fit within tolerance

Part (aiv) · 1 mark

For a Paper 1 score of 24, use the line of best fit to estimate the Paper 2 score.

  1. 1Go up from 24 on paper 1 to the line and across to paper 2
  2. 2Estimate ≈ 37

Answer37 (accept 32 to 42)

Part (bi) · 2 marks

Complete the Venn diagram for 140 students, with 122 choosing biology, 55 choosing chemistry, and 2 choosing neither.

  1. 1n(B ∪ C) = 140 − 2 = 138
  2. 2n(B ∩ C) = 122 + 55 − 138 = 39
  3. 3B only = 122 − 39 = 83, C only = 55 − 39 = 16, outside = 2

AnswerB only: 83 B ∩ C: 39 C only: 16 Outside B and C: 2

Part (bii) · 1 mark

Find the probability that a randomly chosen student chooses both biology and chemistry.

  1. 1P(B and C) = 39/140

Answer39/140

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Also searched as: 0580/31/M/J/22 · 0580_s22_qp_31 · 0580 s22 31 · question 7.
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