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A-LevelMathematicsIntegration9709/12 · Oct/Nov 2011 · Q88 Marks

The equation of a curve is y = √(8x – x²). Find

  1. (i)an expression for dy/dx, and the coordinates of the stationary point on the curve,[4]
  2. (ii)the volume obtained when the region bounded by the curve and the x-axis is rotated through 360° about the x-axis.[4]

Mark scheme

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

  1. [4] dy/dx = ½(8x – x²)⁻¹/² × (8 – 2x)
  2. [4] = 0 when x = 4.
  3. [4] → (4,4)
  4. [4] y = 0 when x = 0 or 8
  5. [4] Vol = π ∫(8x - x²) dx
  6. [4] = π [4x² - x³/3]
  7. [4] 256π/3

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, Oct/Nov 2011 Paper 1 Variant 2, question 8.

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