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A-LevelMathematicsDifferentiation9709/22 · Oct/Nov 2017 · Q710 Marks

The equation of a curve is x² + 4xy + 2y² = 7.

  1. (i)Find the equation of the tangent to the curve at the point (-1, 3). Give your answer in the form ax + by + c = 0 where a, b and c are integers.[6]
  2. (ii)Show that there is no point on the curve at which the gradient is ½.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] Obtain 4y + 4x dy/dx as derivative of 4xy
  2. [B1] Obtain 4y dy/dx as derivative of 2y²
  3. [B1] State 2x + 4y + 4x dy/dx + 4y dy/dx = 0
  4. [*M1] Substitute x = -1, y = 3 to find gradient of line
  5. [DM1] Form equation of tangent through (-1, 3) with numerical gradient
  6. [A1] Obtain 5x + 4y - 7 = 0 or equivalent of required form
  7. [*M1] Substitute dy/dx = ½ to find relation between x and y
  8. [A1] Obtain 4x + 6y = 0 or equivalent
  9. [DM1] Substitute for x or y in equation of curve
  10. [A1] Obtain -4y² = 7 or -3x² = 7 or equivalent and conclude appropriately

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source
A-Level Mathematics, Oct/Nov 2017 Paper 2 Variant 2, question 7.

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