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0580/32 Oct/Nov 2024, Question 7: Venn Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 11 marks

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The question, in short

Use a 142-student group with sets M and S, given 105 pass maths, 82 pass both, 17 pass neither, to complete a Venn diagram and answer set, probability, error interval, percentage and ratio questions.

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

Part (ai) · 2 marks

Fill in the two-circle Venn diagram for sets M and S using the 142 students, 105 maths passes, 82 both passes and 17 neither.

  1. 1M ∩ S = 82
  2. 2M only = 105 − 82 = 23
  3. 3Outside = 17
  4. 4S only = 142 − 17 − 105 = 20

AnswerM only: 23 M ∩ S: 82 S only: 20 Outside M and S: 17

Part (aii) · 1 mark

Work out n(M ∪ S), the number of students in the union of sets M and S.

  1. 1n(M ∪ S) = 23 + 82 + 20 = 125

Answer125

Part (aiii) · 1 mark

For a randomly chosen student, find the probability of passing science but not mathematics.

  1. 1S only = 20 out of 142
  2. 2P = 20/142

Answer20/142

Part (b) · 1 mark

State the set notation for the shaded region of the two-circle Venn diagram with sets A and B.

  1. 1The shaded region is in both A and B
  2. 2A ∩ B

AnswerA ∩ B

Part (c) · 2 marks

Given n = 10 600 rounded to the nearest hundred, complete the lower and upper bounds for n.

  1. 1Nearest hundred means the true value is within 50 either side.
  2. 2Lower bound = 10 600 − 50 = 10 550
  3. 3Upper bound = 10 600 + 50 = 10 650
  4. 410 550 ≤ n < 10 650

Answer10 550 ≤ n < 10 650

Part (d) · 2 marks

Find the percentage increase in science test students from 15 800 in 2022 to 17 064 in 2023.

  1. 1Increase = 17 064 − 15 800 = 1264
  2. 21264 ÷ 15 800 × 100 = 8%

Answer8

Part (e) · 2 marks

With 18 400 students and a pass to fail ratio of 4 : 1, calculate how many students passed.

  1. 118 400 ÷ (4 + 1) = 3680 per part
  2. 2Passed = 4 × 3680 = 14 720

Answer14 720

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Also searched as: 0580/32/O/N/24 · 0580_w24_qp_32 · 0580 w24 32 · question 7.
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