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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2013 · Q1211 Marks

A particle P moves in a straight line such that, t s after leaving a point O, its velocity v m s⁻¹ is given by v = 36t –3t² for t ≥ 0.

  1. (i)Find the value of t when the velocity of P stops increasing.[2]
  2. (ii)Find the value of t when P comes to instantaneous rest.[2]
  3. (iii)Find the distance of P from O when P is at instantaneous rest.[3]
  4. (iv)Find the speed of P when P is again at O.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

  1. [1] M1 attempt to differentiate and equate to zero
  2. [1] When dv/dt = 0, t = 6 A1
  3. [1] M1 for equating v to zero and attempt to solve
  4. [1] When v = 0, t = 12 A1
  5. [1] M1 for a correct attempt to integrate at least one term, allow unsimplified
  6. [1] A1 for all correct
  7. [1] When t = 12, s = 864 A1 for s = 864
  8. [1] M1 for substitution of s = 0 into their s equation
  9. [1] √A1 on their s
  10. [1] DM1 for substitution of their t back into v equation
  11. [1] A1 for 324 only

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 11 marks.
Source
O-Level Additional Mathematics, May/June 2013 Paper 1 Variant 2, question 12.

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