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A-LevelFurther MathematicsIntegration9231/12 · Oct/Nov 2014 · Q26 Marks

A curve C has parametric equations x = eᵗ cos t, y = eᵗ sin t, for 0 ≤ t ≤ π. Find the arc length of C.

  1. mainA curve C has parametric equations x = eᵗ cos t, y = eᵗ sin t, for 0 ≤ t ≤ π. Find the arc length of C.[6]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

  1. ẋ = eᵗ cos t - eᵗ sin t
  2. ẏ = eᵗ sin t + eᵗ cos t
  3. [M1A1] ẋ² + ẏ² = e²ᵗ (cos² t + sin² t - 2sin t cos t) + e²ᵗ (sin² t + cos² t + 2sin t cos t) = 2e²ᵗ
  4. [B1] √(ẋ² + ẏ²) = √2eᵗ
  5. [M1] S = ∫₀^π √2eᵗ dt
  6. [A1A1] = [√2eᵗ]₀^π = √2(e^π - 1) (= 5.39)

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About this question

Topic
Integration, A-Level Further Mathematics (syllabus 9231). Structured question, 6 marks.
Source
A-Level Further Mathematics, Oct/Nov 2014 Paper 1 Variant 2, question 2.

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