O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2020 · Q97 Marks

A particle travels in a straight line. As it passes through a fixed point O, the particle is travelling at a velocity of 3 ms⁻¹. The particle continues at this velocity for 60 seconds then decelerates at a constant rate for 15 seconds to a velocity of 1.6ms⁻¹. The particle then decelerates again at a constant rate for 5 seconds to reach point A, where it stops.

(a)Sketch the velocity-time graph for this journey on the axes below. [Figure 9.1][3]
(b)Find the distance between O and A.[3]
(c)Find the deceleration in the last 5 seconds.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

[B3] B1 for correct shape with three distinct linear sections
B1 for 3 and 1.6 on vertical axis
B1 for 60, 75, 80 on horizontal axis
[M2] M1 for attempting at least two terms of the sum: 3×60+15 (1.6) + 0.5 (15) (1.4) + 0.5 (5) (1.6) OR 3×60 +0.5 (3 + 1.6) (15) + 0.5 (5) (1.6)
[A1] 218.5 (metres)
[B1] 0.32 (ms⁻²)

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source: O-Level Additional Mathematics, May/June 2020 Paper 2 Variant 1, question 9.

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