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0580/31 Oct/Nov 2022, Question 5: Circumference and Area of a Circle

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 13 marks

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The question, in short

Use a frequency table for 60 customers' item counts to find range, mean and a probability, then handle a 96 cm rounded length and wheel revolutions over 1.4 km.

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

Part (ai) · 1 mark

Find the range of the number of items sold using the frequency table.

  1. 1Range = 7 − 0 = 7

Answer7

Part (aii) · 3 marks

Calculate the mean number of items sold per customer from the table.

  1. 1Σfx = 0×3 + 1×6 + 2×12 + 3×8 + 4×14 + 5×10 + 6×3 + 7×4 = 206
  2. 2Mean = 206 ÷ 60 = 3.43

Answer3.43 or 3 13/30

Part (aiii) · 2 marks

Find the probability a randomly chosen customer bought more than 4 items.

  1. 1More than 4 items: 10 + 3 + 4 = 17 customers
  2. 2P = 17/60

Answer17/60

Part (bi) · 2 marks

Complete the inequality bounds for l, given as 96 cm to the nearest centimetre.

  1. 1Half a centimetre either side of 96
  2. 295.5 ≤ l < 96.5

Answer95.5, 96.5

Part (bii) · 5 marks

With wheel diameter 46 cm, calculate the number of complete revolutions in a 1.4 km ride.

  1. 1Circumference = 46 × π = 144.51… cm
  2. 21.4 km = 140 000 cm
  3. 3140 000 ÷ 144.51… = 968.7…
  4. 4Complete revolutions = 968

Answer968

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Also searched as: 0580/31/O/N/22 · 0580_w22_qp_31 · 0580 w22 31 · question 5.
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