O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2020 · Q1210 Marks
[Figure 12.1] The diagram shows the velocity-time graph of a particle P that travels 2775 m in 90s, reaching a final velocity of V ms⁻¹.
- (a)(i)Find the value of V.[3]
- (a)(ii)Write down the acceleration of P when t = 40.[1]
- (b)(i)The acceleration, a ms⁻², of a particle Q travelling in a straight line, is given by a = 6 cos 2t at time ts. When t = 0 the particle is at point O and is travelling with a velocity of 10ms⁻¹. Find the velocity of Q at time t.[3]
- (b)(ii)Find the displacement of Q from O at time t.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- M1 for attempt to find the area under the graph
- Dep M1 on previous M mark for attempt to equate to 2775 and simplify in order to find V or V - 30
- A1 55
- B1 0
- M1 Must have ±3 sin 2t
- M1 Dep for attempt to find +c,
- A1 v = 3 sin 2t +10
- M1 For attempt to integrate their v, must have ±3/2 cos2t
- M1 Dep on previous M mark for attempt to find d.
- A1 s = -3/2 cos 2t +10t + 3/2
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