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O-LevelAdditional MathematicsDifferentiation and integration4037/21 · Oct/Nov 2010 · Q1210 Marks

OR A particle moves in a straight line so that, at time t s after passing a fixed point O, its velocity is v m s⁻¹, where v = 6t + 4 cos 2t. Find

  1. (i)the velocity of the particle at the instant it passes O,[1]
  2. (ii)the acceleration of the particle when t = 5,[4]
  3. (iii)the greatest value of the acceleration,[1]
  4. (iv)the distance travelled in the fifth second.[4]

Mark scheme

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

  1. [B1] (i) 4
  2. [M1] (ii) Differentiate v to find an expression for a
  3. [A1] (ii) 6 – 8 sin 2t
  4. [DM1] (ii) Substitute t=5
  5. [A1] (ii) 10.3 to 10.4
  6. [B1] (iii) 14
  7. [M1] (iv) Integrate v to find an expression for s
  8. [A1] (iv) s = 3t² + 2 sin 2t
  9. [DM1] (iv) Use limits 4 and 5
  10. [A1] (iv) 23.9

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 10 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2010 Paper 2 Variant 1, question 12.

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