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A-LevelFurther MathematicsComplex numbers9231/12 · May/June 2017 · Q89 Marks

Let z = cos θ + i sin θ.

  1. (i)Show that z - 1/z = 2i sin θ and hence express 16 sin⁵θ in the form sin 5θ + p sin 3θ + q sin θ, where p and q are integers to be determined.[6]
  2. (ii)Hence find the exact value of ∫ (from 0 to ½π) 16 sin⁵θ dθ.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [B1]
  2. [M1A1]
  3. [M1A1] Grouping not required at this stage.
  4. [A1] M1 for grouping and applying initial result
  5. [M1A1FT]
  6. [A1]

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About this question

Topic
Complex numbers, A-Level Further Mathematics (syllabus 9231). Structured question, 9 marks.
Source
A-Level Further Mathematics, May/June 2017 Paper 1 Variant 2, question 8.

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