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0580/31 May/Jun 2021, Question 3: Direct Proportion in Real Life

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

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The question, in short

Use a 1 cm to 5 km scale drawing with R marked and North shown to locate town M, then work through cost, workforce, speed and bearing calculations for the railway.

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

Part (a) · 2 marks

Convert 36 km to centimetres on the drawing and plot M at a bearing of 163° from R.

  1. 1Distance on map = 36 ÷ 5 = 7.2 cm
  2. 2Measure 163° clockwise from the North line at R.
  3. 3Mark M 7.2 cm from R along this direction.

AnswerM marked correctly

Part (bi) · 2 marks

Using the 36 km track length and $1070 per metre, calculate the total build cost.

  1. 136 km = 36 × 1000 = 36000 m
  2. 2Cost = 36000 × 1070
  3. 3= $38520000

Answer38520000

Part (bii) · 3 marks

Given 15 people lay 60 m daily, find how many days 45 people need for the full track.

  1. 1One person builds 60 ÷ 15 = 4 m per day
  2. 245 people build 45 × 4 = 180 m per day
  3. 3Days = 36000 ÷ 180 = 200

Answer200

Part (c) · 2 marks

For 36 km at 75 km/h average speed, find the journey duration in minutes.

  1. 1Time = 36 ÷ 75 = 0.48 hours
  2. 20.48 × 60 = 28.8 minutes

Answer28.8

Part (d) · 2 marks

Given K lies on a bearing of 312° from R, determine the bearing of R as seen from K.

  1. 1Back bearing = 312 − 180
  2. 2= 132°

Answer132

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