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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2023 · Q126 Marks

A curve has equation y = √(5x-2) / (x-3).

  1. (a)Explain why the curve does not exist when x < 2/5.[1]
  2. (b)Show that dy/dx can be written in the form -(Ax+B) / (2(x-3)²√(5x-2)), where A and B are positive integers.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

  1. [1] (a) B1 Must be a correct statement related to the question. Allow a numerical argument.
  2. [5] (b) B1 for 5/2 * (5x-2)^(-1/2) seen
  3. [5] (b) M1 for an attempt to differentiate a quotient or correct product
  4. [5] (b) A1 for all other terms correct.
  5. [5] (b) M1 Dep for an attempt to simplify to the given form, allow a sign error and an arithmetic error (e.g. Omission of a factor of 2 in the linear term).
  6. [5] (b) A1

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2023 Paper 1 Variant 2, question 12.

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