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A-LevelFurther MathematicsPolar coordinates9231/12 · May/June 2011 · Q58 Marks

The curve C has polar equation r = 2 cos 2θ . Sketch the curve for 0 ≤ θ < 2π .

  1. The curve C has polar equation r = 2 cos 2θ . Sketch the curve for 0 ≤ θ < 2π .[4]
  2. Find the exact area of one loop of the curve.[4]

Mark scheme

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

  1. [B1B1] Right-hand loop Position and through pole and (2, 0).
  2. [B1B1] Left-hand loop Position and through pole and (2, π ).
  3. Deduct 1 mark for extra loops (r < 0).
  4. [M1] Uses A = 1/2 ∫ r² dθ
  5. [M1] Uses double angle formula. = ∫ (cos 4θ+1) dθ (LNR)
  6. [A1] Integrates. = 1/2 [1/4 sin 4θ+θ] (LNR)
  7. [A1] Inserts any appropriate limits which legitimately give the result. e.g. [1/4 sin 4θ+θ]₀^(π/2) = π/2

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About this question

Topic
Polar coordinates, A-Level Further Mathematics (syllabus 9231). Structured question, 8 marks.
Source
A-Level Further Mathematics, May/June 2011 Paper 1 Variant 2, question 5.

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