O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2017 · Q129 Marks

A particle moves in a straight line so that, t seconds after passing a fixed point O, its displacement, sm, from O is given by s = 1 + 3t - cos 5t.

(i)Find the distance between the particle's first two positions of instantaneous rest.[7]
(ii)Find the acceleration when t = π.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[B2] v = d(3t - cos 5t + 1)/dt = 3 + 5sin 5t B1 for either with no other terms or for both with 1 extra
[M1] their (3 + 5 sin 5t) = 0 Must be from an attempt to differentiate
[A1] awrt 0.76 0.7570187525
[A1] awrt 1.13 1.12793684
[DM1] substitutes their t values into s (4.07..., 3.58...) must be two values
[A1] 0.48 to 0.49 [m] Final A1 may imply earlier A1s
[M1] 25cos 5t Differentiating their v correctly providing at least 2 terms with one trig function
[A1] -25 Ignore +25 following -25

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source: O-Level Additional Mathematics, May/June 2017 Paper 2 Variant 1, question 12.

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