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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2011 · Q89 Marks

A particle travels in a straight line so that, t s after passing through a fixed point O, its velocity, vms⁻¹, is given by v = 12cos (t/3).

  1. (i)Find the value of t when the velocity of the particle first equals 2 ms⁻¹.[2]
  2. (ii)Find the acceleration of the particle when t = 3.[3]
  3. (iii)Find the distance of the particle from O when it first comes to instantaneous rest.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [M1] (i) Solve cos(t/3) = 2/12
  2. [A1] (i) 4.21 or 4.2(0)
  3. [M1] (ii) a = dv/dt = k sin(t/3)
  4. [A1] (ii) k = -4
  5. [A1√] (ii) -3.36 or -3.37
  6. [M1] (iii) Find t when v = 0
  7. [B1] (iii) s = ∫vdt = 36 sin(t/3)
  8. [M1] (iii) Substitute t into 36sin(t/3)
  9. [A1√] (iii) 36

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 9 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 2 Variant 2, question 8.

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