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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2016 · Q25 Marks

Variables x and y are related by the equation y = (5x-1) / (3-x).

  1. (i)Find dy/dx, simplifying your answer.[2]
  2. (ii)Hence find the approximate change in x when y increases from 9 by the small amount 0.07.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

  1. [M1] Clear attempt at quotient rule or equivalent product rule
  2. [A1] dy/dx = 14/(3-x)² or dy/dx = 14/(x²-6x+9) cao or correct simplified equivalent
  3. [B1] [y = 9] x = 2
  4. [M1] condone 0.07 ≈ (dy/dx)[x=2] δx oe
  5. [A1] 0.005 oe

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2016 Paper 2 Variant 2, question 2.

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