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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2011 · Q99 Marks

Given that y = x sin 4x, find dy/dx.

  1. (i)Given that y = x sin 4x, find dy/dx.[3]
  2. (ii)Hence find ∫x cos 4x dx and evaluate ∫₀^(π/8) x cos 4x dx.[6]

Mark scheme

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

  1. [M1] M1 for differentiation of a product
  2. [B1, A1] B1 for 4cos4x , A1 all else correct
  3. [DM1] DM1 for realising integration is form reverse process of (i) – do not need (1/4)
  4. [A1, A1] A1 for xsin4x , A1 for (1/4)cos4x
  5. [B1] B1 for (1/4)cos4x
  6. [M1] M1 for correct application of limits
  7. [A1] A1 for final numerical answer

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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 1 Variant 2, question 9.

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