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O-LevelAdditional MathematicsSimultaneous equations4037/22 · May/June 2011 · Q67 Marks

The line y = 3x – 9 intersects the curve 49x² – y² + 42x + 8y = 247 at the points A and B. Find the length of the line AB.

  1. The line y = 3x – 9 intersects the curve 49x² – y² + 42x + 8y = 247 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 2011). The mark or mark type is shown in brackets.

  1. [1] Eliminates y (or x)
  2. [1] x²+3x-10 = 0 (or y² + 27y + 72 = 0) oe
  3. [1] Factorises 3 term quadratic or solves using formula
  4. [1] x = -5 and 2 (or y = -24 and -3)
  5. [1] y = -24 and -3 (or x = -5 and 2)
  6. [1] Uses Pythagoras
  7. [1] 22.1 or √490 or 7√10

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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 2011 Paper 2 Variant 2, question 6.

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