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A-LevelMathematicsIntegration9709/22 · Oct/Nov 2024 · Q26 Marks

Let f(x) = 4 sin² 3x.

  1. (a)Find the value of f' (π/4).[3]
  2. (b)Find ∫ f(x)dx.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [M1] (a) Differentiate to obtain form ksin 3x cos3x or ksin 6x
  2. [A1] (a) Obtain correct 24sin3xcos 3x or 12 sin 6x
  3. [A1] (a) Substitute x = π/4 to obtain –12
  4. [M1] (b) Express integrand in form k₁ + k₂ cos 6x
  5. [A1] (b) Obtain 2 – 2 cos 6x
  6. [A1] (b) Integrate to obtain 2x – (1/3)sin6x

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 2 Variant 2, question 2.

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