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A-LevelMathematicsDifferentiation9709/21 · May/June 2024 · Q25 Marks

A curve has equation x²lny+y² + 4x = 9. Find the gradient of the curve at the point (2, 1).

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [M1] Attempt use of product rule for differentiating x² In y
  2. [A1] Obtain 2x ln y + (x² dy/y dx)
  3. [B1] Obtain (dy/dx) + 2y(dy/dx)
  4. [M1] Substitute x = 2, y = 1 in equation equal to 0 involving at least one dy/dx and solve for dy/dx
  5. [A1] Obtain -2/3

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2024 Paper 2 Variant 1, question 2.

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