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A-LevelFurther MathematicsDifferentiation9231/12 · May/June 2017 · Q35 Marks

A curve C has equation tan y = x, for x > 0.

  1. (i)Use implicit differentiation to show that d²y/dx² = -2x(dy/dx)³.[3]
  2. (ii)Hence find the value of d²y/dx² at the point (1, ¼π) on C.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

  1. [M1] Using implicit differentiation
  2. [M1 A1] M1 for good attempt at product rule
  3. [M1 A1] M1 for good attempt at implicit differentiation
  4. [B1]
  5. [B1 FT]

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About this question

Topic
Differentiation, A-Level Further Mathematics (syllabus 9231). Structured question, 5 marks.
Source
A-Level Further Mathematics, May/June 2017 Paper 1 Variant 2, question 3.

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