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A-LevelMathematicsDifferentiation9709/32 · Feb/Mar 2022 · Q45 Marks

The parametric equations of a curve are x = 1 – cos θ, y = cos θ – ½ cos 2θ.

  1. (a)Show that dy/dx = –2 sin²(½θ).[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

  1. [1] State dx/dθ = sinθ or dy/dθ = -sinθ + ½ sin 2θ
  2. [1] Use dy/dx = (dy/dθ) / (dx/dθ)
  3. [1] Obtain correct answer in any form e.g. (-sinθ + ½ sin 2θ) / sinθ
  4. [1] Use double angle correctly to obtain dy/dx in terms of θ
  5. [1] Obtain the given answer with no errors seen – 2sin²(½θ)

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Feb/Mar 2022 Paper 3 Variant 2, question 4.

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