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O-LevelAdditional MathematicsIndices and surds4037/11 · May/June 2021 · Q88 Marks

DO NOT USE A CALCULATOR IN THIS QUESTION. A curve has equation y = (2-√3)x²+x-1. The x-coordinate of a point A on the curve is (√3+1)/(2-√3)

  1. (a)Show that the coordinates of A can be written in the form (p+q√3, r+s√3), where p, q, r and s are integers.[5]
  2. (b)Find the x-coordinate of the stationary point on the curve, giving your answer in the form a+b√3, where a and b are rational numbers.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

  1. [5] M1 For attempt to rationalise and simplify showing all working
  2. [5] A1
  3. [5] M1 For complete method, showing all steps. Allow one slip in arithmetic
  4. [5] A1 for 18
  5. [5] A1 for 11√3
  6. [3] M1 For attempt at differentiation to obtain form of dy/dx = kx + 1
  7. [3] M1 Dep on previous M for equating to zero, rationalisation and attempt to simplify
  8. [3] A1

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About this question

Topic
Indices and surds, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2021 Paper 1 Variant 1, question 8.

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