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0580/31 Oct/Nov 2021, Question 6: Distance-Time Graphs

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

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The question, in short

Use a train travel graph from Wengen to Kleine Scheidegg to interpret a stop, a time gap, an average speed, and a second train's path, then find a meeting time and work out temperatures from a rise and a height formula.

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

Part (ai) · 1 mark

State what the train is doing during the one-minute interval from 14 09 to 14 10.

  1. 1The graph is horizontal from 14 09 to 14 10
  2. 2The train is stopped (at Wengernalp)

AnswerTrain stopped

Part (aii) · 1 mark

Work out how many minutes the train takes to travel between Allmend and Wengernalp.

  1. 1Leaves Allmend at 13 59
  2. 2Arrives at Wengernalp at 14 09
  3. 314 09 − 13 59 = 10 min

Answer10

Part (aiii) · 3 marks

Work out the train's average speed over the whole trip from Wengen to Kleine Scheidegg, giving it in km/h.

  1. 1Distance = 6.4 km
  2. 2Time = 13 54 to 14 19 = 25 min = 25/60 h
  3. 3Speed = 6.4 ÷ 25/60
  4. 4= 15.36 km/h

Answer15.36

Part (aiv) · 3 marks

Plot the second train's journey on the graph using its departure, arrival and stop times at the stations.

  1. 1Rule a line from Kleine Scheidegg (14 01, 6.4) to Allmend (14 18, 1.9)
  2. 2Horizontal line at 1.9 km from 14 18 to 14 20
  3. 3Rule a line from (14 20, 1.9) to Wengen (14 30, 0)

AnswerThree correct ruled lines: (14 01, 6.4) to (14 18, 1.9), then (14 18, 1.9) to (14 20, 1.9), then (14 20, 1.9) to (14 30, 0)

Part (av) · 1 mark

State the clock time at which the two trains meet on the graph.

  1. 1The two lines cross near Wengernalp
  2. 2Read the time at the crossing: 14 09

Answer14 09

Part (b) · 1 mark

Work out the 4 pm temperature given that it started at −3 °C and rose by 10 °C.

  1. 1−3 + 10
  2. 2= 7 °C

Answer7

Part (c) · 1 mark

Use T = 2 − h/130 with h = 780 to work out the temperature at Kleine Scheidegg.

  1. 1T = 2 − 780/130
  2. 2= 2 − 6 = −4 °C

Answer−4

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Also searched as: 0580/31/O/N/21 · 0580_w21_qp_31 · 0580 w21 31 · question 6.
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