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O-LevelAdditional MathematicsSimultaneous equations4037/21 · May/June 2013 · Q87 Marks

The line y = 2x - 8 cuts the curve 2x² + y² - 5xy + 32 = 0 at the points A and B. Find the length of the line AB.

  1. (a)The line y = 2x - 8 cuts the curve 2x² + y² - 5xy + 32 = 0 at the points A and B. Find the length of the line AB.[7]

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

  1. [1] Eliminates y (or x) and full attempt at expansion
  2. [1] 4x² - 8x – 96 = 0 or y² + 12y - 64 = 0
  3. [1] Factorise 3 term relevant quadratic
  4. [1] x = -4 and 6
  5. [1] y = -16 and 4
  6. [1] Uses Pythagoras for relevant points
  7. [1] 22.4 or √500 or 10√5

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About this question

Topic
Simultaneous equations, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2013 Paper 2 Variant 1, question 8.

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