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O-LevelAdditional MathematicsDifferentiation and integration4037/11 · May/June 2023 · Q107 Marks

10 It is given that y = (3x+1)²ln(3x+1).

  1. (a)Find dy/dx.[3]
  2. (b)Hence find ∫ (3x+1)ln(3x+1)dx.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

  1. [3] B1 for 3/(3x+1)
  2. M1 for attempt to differentiate a product
  3. A1 for all terms other than 3/(3x+1) correct.
  4. Allow unsimplified.
  5. [4] B1 k(3x+1)² ln(3x+1) soi
  6. M1 May be a multiple
  7. May be seen as 1/3 x 1/2 (3x+1)²
  8. B2 B1 for two correct algebraic terms
  9. For B2 must have (+ c)
  10. 1/6(3x+1)² ln(3x+1) - 3x²/4 - x/2 + c

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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 2023 Paper 1 Variant 1, question 10.

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