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0580/32 Feb/Mar 2022, Question 7: Scale Drawings

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 13 marks

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The question, in short

Convert 6 miles to metres using 1 mile = 1.609344 km, find a reverse bearing, work out an arrival time from speed and distance, and use two scale drawings to measure and mark positions.

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

Part (a) · 3 marks

Using 1 mile = 1.609344 kilometres, express 6 miles in metres, rounded to the nearest metre.

  1. 16 × 1.609344 = 9.656064 km
  2. 29.656064 × 1000 = 9656.064 m
  3. 3= 9656 m to the nearest metre

Answer9656

Part (bi) · 2 marks

Given a boat's bearing of 322° from a harbour, determine the bearing of the harbour seen from the boat.

  1. 1Back bearing = 322 − 180
  2. 2= 142°

Answer142

Part (bii) · 3 marks

With the boat 12 km away, leaving at 2.30 pm at 5 km/h, find when it reaches the harbour.

  1. 1Time = 12 ÷ 5 = 2.4 h = 2 h 24 min
  2. 22.30 pm + 2 h 24 min = 4.54 pm

Answer4.54 pm or 1654

Part (ci) · 1 mark

On the drawing scaled 1 cm to 4 km, measure and state the bearing of M from S.

  1. 1Measure clockwise from North at S to the line SM: 107°

Answer107 (accept 105 to 109)

Part (cii) · 4 marks

On the map scaled 1 cm to 5 km, draw Mairi's house M at the correct position relative to S.

  1. 1SM measures 9 cm, so the distance is 9 × 4 = 36 km
  2. 2On the new map: 36 ÷ 5 = 7.2 cm
  3. 3Draw a bearing of 107° from S and mark M 7.2 cm from S

AnswerThe position of M correctly marked on the diagram

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