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A-LevelMathematicsDifferentiation9709/12 · Oct/Nov 2013 · Q37 Marks

The equation of a curve is y = 2 / √(5x-6)

  1. (i)Find the gradient of the curve at the point where x = 2.[3]
  2. (ii)Find ∫ (2 / √(5x-6)) dx and hence evaluate ∫[2 to 3] (2 / √(5x-6)) dx.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

  1. [1] dy/dx = 2 × −½ × (5x−6)^(−3/2)
  2. [1] Multiplied by 5 (chain rule)
  3. [1] Value at x=2 is −5/8.
  4. [1] Integral of 2(5x-6)^(-1/2) is 2(5x-6)^(1/2) / (1/2)
  5. [1] Divided by 5 (for chain rule in reverse)
  6. [1] Use of limits in an integral.
  7. [1] Value is 0.8.

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Oct/Nov 2013 Paper 1 Variant 2, question 3.

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