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0580/32 Feb/Mar 2022, Question 1: Tally Charts and Frequency Tables

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Complete frequency tables from tallies and given data for cycling and travel to school, then calculate a percentage, a probability, and pie chart angles and sectors.

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

Part (ai) · 1 mark

Use the tally marks to fill in the missing frequency for teachers and students.

  1. 1Teachers: one gate = 5
  2. 2Students: 4 gates + 3 = 4 × 5 + 3 = 23

AnswerTeachers 5, Students 23

Part (aii) · 2 marks

Find the percentage of all people cycling who are students.

  1. 1Total who cycle = 5 + 23 = 28
  2. 223/28 × 100 = 82.14…
  3. 382.1%

Answer82.1 or 82.14…

Part (bi) · 3 marks

Fill the two-way table for 120 Year 1 and Year 2 students using the given counts and 4/9 of bus users in Year 1.

  1. 1Year 1 bus = 4/9 × 36 = 16, Year 2 bus = 36 − 16 = 20
  2. 2Year 2 total = 120 − 48 = 72, Year 2 walk = 72 − 5 − 20 = 47
  3. 3Year 1 walk = 77 − 47 = 30, Year 1 cycle = 48 − 30 − 16 = 2
  4. 4Cycle total = 2 + 5 = 7

AnswerYear 1: 30, 2, 16, 48; Year 2: 47, 5, 20, 72; Total: 77, 7, 36, 120

Part (bii) · 2 marks

Find the probability a randomly chosen student does not travel by bus.

  1. 1Not by bus = 120 − 36 = 84
  2. 2P = 84/120 = 7/10

Answer7/10

Part (ci) · 2 marks

Work out the pie chart sector angle for each of the three complaint frequencies.

  1. 1360 ÷ 24 = 15° per complaint
  2. 2Late 10 × 15 = 150°, Price 6 × 15 = 90°
  3. 3Crowded 8 × 15 = 120°

Answer150, 90, 120

Part (cii) · 2 marks

Draw the completed pie chart using the calculated sector angles on the given circle.

  1. 1Measure 150° from the given radius and label it Late
  2. 2Measure a further 90° and label it Price
  3. 3The remaining 120° is Crowded; label it

AnswerCorrect pie chart drawn: sectors of 150°, 90° and 120°, labelled

Stuck on a step? Read the free lesson: Tally Charts and Frequency Tables

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Also searched as: 0580/32/F/M/22 · 0580_m22_qp_32 · 0580 m22 32 · question 1.
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