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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2018 · Q107 Marks

A particle moves in a straight line such that its displacement, s metres, from a fixed point O at time t seconds, is given by s = 4 + cos3t, where t≥ 0. The particle is initially at rest.

  1. (i)Find the exact value of t when the particle is next at rest.[2]
  2. (ii)Find the distance travelled by the particle between t = π/4 and t = π/2 seconds.[3]
  3. (iii)Find the greatest acceleration of the particle.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

  1. [1] (i) v = ds/dt = -3 sin 3t
  2. [1] (i) When v = 0, t = π/3
  3. [1] (ii) Finding s when t = π/4 and t = π/2
  4. [1] (ii) Finding s when t = their π/3 and correct plan
  5. [1] (ii) Using their (i) correctly
  6. [1] (ii) 1.29 nfww
  7. [1] (iii) a = dv/dt = -9 cos 3t
  8. [1] (iii) 9
  9. [1] (iii) FT their k cos3t

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2018 Paper 2 Variant 1, question 10.

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