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0580/31 Oct/Nov 2023, Question 9: Fractions of an Amount

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 11 marks

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The question, in short

Work with gold purity in carats, a metal ratio in a clock, and a Venn diagram of 110 people's jewellery ownership, plus set notation for a shaded region.

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

Part (a) · 4 marks

Compare the $204 bracelet price with the cost of its pure gold, given 9-carat, 16 g, and $42 per gram; show working.

  1. 1Pure gold = 9/24 × 16 = 6 g
  2. 2Cost of gold = 6 × 42 = $252
  3. 3$204 < $252, so the price is less than the cost of the gold

AnswerLess

Part (b) · 2 marks

Find the copper mass in a 1080 g clock using the ratio copper : zinc : other metals = 21 : 14 : 1.

  1. 121 + 14 + 1 = 36 parts
  2. 2Copper = 1080 ÷ 36 × 21 = 630 g

Answer630

Part (ci) · 2 marks

Complete the Venn diagram for 110 people using 18 in both, 46 in G, and 11 in neither.

  1. 1G ∩ S = 18, outside = 11
  2. 2G only = 46 − 18 = 28
  3. 3S only = 110 − 11 − 46 = 53

AnswerG only: 28 G ∩ S: 18 S only: 53 Outside G ∪ S: 11

Part (cii) · 1 mark

State n(G ∩ S) from the given information.

  1. 1n(G ∩ S) = 18

Answer18

Part (ciii) · 1 mark

Find the probability a randomly chosen person owns gold but not silver.

  1. 1Gold but not silver = G only = 28
  2. 2Probability = 28/110

Answer28/110

Part (d) · 1 mark

Express the fully shaded two-circle Venn diagram region using set notation.

  1. 1Everything in E or F (or both) is shaded: E ∪ F

AnswerE ∪ F

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Also searched as: 0580/31/O/N/23 · 0580_w23_qp_31 · 0580 w23 31 · question 9.
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