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0580/31 May/Jun 2024, Question 2: Bar Charts and Composite Bar Charts

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 15 marks

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The question, in short

Use a pie chart of holiday preferences with sector angles to find fractions, percentages, ratios and probabilities, complete a frequency table and bar chart, and compare holiday costs in euros using an exchange rate.

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

Part (ai) · 2 marks

Find the fraction of people preferring a mountain holiday from its 120° sector, in simplest form.

  1. 1Mountain sector = 120°
  2. 2120/360 = 1/3

Answer1/3

Part (aii) · 1 mark

Find the percentage preferring a beach holiday from its 135° sector.

  1. 1Beach sector = 135°
  2. 2135/360 × 100 = 37.5%

Answer37.5

Part (aiii) · 2 marks

Write the ratio beach : cruise : lake : mountain using the sector angles, in simplest form.

  1. 1Angles beach : cruise : lake : mountain = 135 : 30 : 75 : 120
  2. 2Divide by 15: 9 : 2 : 5 : 8

Answer9 : 2 : 5 : 8

Part (aiv) · 2 marks

Find the probability a randomly chosen person prefers cruise or lake.

  1. 1Cruise + lake = 30° + 75° = 105°
  2. 2P = 105/360 = 7/24

Answer105/360 or 7/24

Part (av) · 1 mark

Given 675 people prefer beach, show the total number asked is 1800.

  1. 1Beach sector 135° represents 675 people
  2. 21° represents 675 ÷ 135 = 5 people
  3. 3Total = 5 × 360 = 1800

Answer675 × 360 / 135 = 1800

Part (avia) · 2 marks

Complete the frequency column for Lake and Mountain using the sector angles.

  1. 11° represents 1800 ÷ 360 = 5 people
  2. 2Lake = 75 × 5 = 375
  3. 3Mountain = 120 × 5 = 600

AnswerLake 375, Mountain 600

Part (avib) · 3 marks

Complete the bar chart for all four holidays, including a suitable scale on the frequency axis.

  1. 1Choose a linear scale, e.g. 0, 100, 200, …, 700
  2. 2Draw bars to heights Beach 675, Cruise 150
  3. 3Lake 375, Mountain 600

AnswerCorrect bar chart with linear scale labelled: Beach 675, Cruise 150, Lake 375, Mountain 600

Part (b) · 2 marks

Work out how many more euros Mr Shah pays than Mr Gibb, given $2208 and 2050 euros at 1 euro = $1.15.

  1. 1Mr Gibb in euros = 2208 ÷ 1.15 = 1920
  2. 22050 − 1920 = 130 euros

Answer130

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Also searched as: 0580/31/M/J/24 · 0580_s24_qp_31 · 0580 s24 31 · question 2.
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