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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2010 · Q98 Marks

A particle starts from rest and moves in a straight line so that, t seconds after leaving a fixed point O, its velocity, v ms⁻¹, is given by v = 4 sin 2t.

  1. (i)Find the distance travelled by the particle before it first comes to instantaneous rest.[5]
  2. (ii)Find the acceleration of the particle when t = 3.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.

  1. [M1] (i) t = π/2
  2. [M1] (i) ∫v dt = k cos 2t + c only
  3. [A1] (i) - 2 cos 2t
  4. [M1] (i) Uses both limits
  5. [A1] (i) 4 m
  6. [M1] (ii) a = dv/dt = k cos 2t only
  7. [A1] (ii) 8 cos 2t
  8. [A1] (ii) 7.68 ms⁻²

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2010 Paper 2 Variant 1, question 9.

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