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O-LevelAdditional MathematicsQuadratic functions4037/12 · May/June 2023 · Q25 Marks

DO NOT USE A CALCULATOR IN THIS QUESTION. Solve the equation (2+√5)x² = 4x+3(2-√5), giving your answers in the form a+b√5 where a and b are integers.

  1. DO NOT USE A CALCULATOR IN THIS QUESTION. Solve the equation (2+√5)x² = 4x+3(2-√5), giving your answers in the form a+b√5 where a and b are integers.[5]

Mark scheme

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

  1. [M1] For attempt to equate to zero and use quadratic formula, must see substitution 4±√16-k / 2(2+√5) and with simplification to 4±√16-k / 2(2+√5)
  2. [A1] for one exact solution (x = 4±2 / 2(2+√5) or exact equivalent)
  3. [M1] For evidence of rationalisation and evaluation
  4. [A1] -6+3√5 and 2 + √5

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About this question

Topic
Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source
O-Level Additional Mathematics, May/June 2023 Paper 1 Variant 2, question 2.

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