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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · May/June 2015 · Q67 Marks

A particle P is projected from the origin O so that it moves in a straight line. At time t seconds after projection, the velocity of the particle, v ms⁻¹, is given by v = 2t² - 14t + 12.

  1. (i)Find the time at which P first comes to instantaneous rest.[2]
  2. (ii)Find an expression for the displacement of P from O at time t seconds.[3]
  3. (iii)Find the acceleration of P when t = 3.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

  1. [M1] 2t² -14t+12 = 0 Can use formula, etc.
  2. [A1] (t=) 1 If t = 1 with no working, then M1A1
  3. [M1] ∫(2t²-14t+12)dt
  4. [A2,1,0] (s=) (2t³/3) - (14t²/2) + 12t -1 for each error or for +c left in or limits introduced
  5. [M1] (a=) dv/dt (4t-14)
  6. [A1] [4(3) - 14 =] -2 cao

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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 2015 Paper 2 Variant 1, question 6.

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