O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2023 · Q86 Marks

Maya leaves the office for a factory visit. The distance-time graph shows her journey from the office to the factory. [Figure 8.1] Maya stays at the factory for 1½ hours. She then returns to the office at an average speed of 35 km/h. Complete the distance-time graph to show this information.

(a)(i)Maya leaves the office for a factory visit. The distance-time graph shows her journey from the office to the factory. [Figure 8.1] Maya stays at the factory for 1½ hours. She then returns to the office at an average speed of 35 km/h. Complete the distance-time graph to show this information.[2]
(a)(ii)Use your graph to find the time Maya arrives back at the office.[1]
(b)The diagram shows the distance-time graph for the journey of a cyclist. The cyclist travels d metres from home to a lake and then returns home. [Figure 8.2] At 08 36 the cyclist is (d – 7200) metres from home. The average speed of the cyclist between 0800 and 0836 is 4/5 of the average speed of the cyclist between 09 10 and 09 55. Calculate the value of d.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[2] (a)(i) Line from (1100, 42) to (1230, 42) Line from (1230, 42) to (1342, 0) B1 for line from (1100, 42) to (1230, 42) or B1 for line with gradient –35 km/h
[1] (a)(ii) 13 42 or [0]1 42 pm FT their graph
[3] (b) 20 000 M2 for (d-7200)/36 = (4/5) × (d/45) oe or M1 for use of distance/time for first or third part of journey

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