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4024/21 May/Jun 2023, Question 8: Distance-Time Graphs

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 6 marks

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The question, in short

Maya travels from an office to a factory, stays 1 1/2 hours, then returns at 35 km/h; a cyclist rides to a lake and back, with speeds related by a fraction, to find d.

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

Part (ai) · 2 marks

Extend the distance–time graph: hold at 42 km for 1 1/2 hours, then draw the return to the office at 35 km/h.

  1. 1Horizontal line at 42 km from 11 00 to 12 30 (1 1/2 hours)
  2. 2Time to return = 42 ÷ 35 = 1.2 hours = 1 hour 12 minutes
  3. 3Straight line from (12 30, 42) down to (13 42, 0)

AnswerLine from (11 00, 42) to (12 30, 42); line from (12 30, 42) to (13 42, 0)

Part (aii) · 1 mark

Read from your completed graph the time of day when Maya reaches the office again.

  1. 112 30 + 1 hour 12 minutes = 13 42

Answer13 42 or 1 42 pm

Part (b) · 3 marks

Using the times 08 00, 08 36, 09 10 and 09 55, the distance d − 7200 at 08 36, and the speed ratio 4/5, work out d.

  1. 108 00 to 08 36: speed = (d − 7200)/36 m per minute
  2. 209 10 to 09 55: speed = d/45 m per minute
  3. 3(d − 7200)/36 = 4/5 × d/45 = 4d/225
  4. 4225(d − 7200) = 144d, so 81d = 1 620 000
  5. 5d = 20 000

Answer20 000

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Also searched as: 4024/21/M/J/23 · 4024_s23_qp_21 · 4024 s23 21 · question 8.
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