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A-LevelMathematicsDifferentiation9709/22 · Feb/Mar 2025 · Q87 Marks

A curve has equation 3e^2xy + 4e^3x + y³ = 18.

  1. (a)Show that dy/dx = (-2e^2xy - 4e^3x) / (e^2x + y²).[4]
  2. (b)Show that the curve has no stationary points.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

  1. [M1] Attempt use of product rule for differentiating 3e^2xy
  2. [A1] Obtain 6e^2xy + 3e^2x dy/dx
  3. [B1] Obtain remaining terms 12e^3x + 3y² dy/dx
  4. [A1] Equate sum of correct terms to zero and rearrange to confirm given result AG Necessary detail needed.
  5. [B1] Equate derivative to zero and obtain y = –2e^x or equivalent
  6. [M1] Substitute for y in original equation and attempt appropriate simplification
  7. [A1] Obtain –10e^3x = 18 or equivalent and conclude no possible value of x AG Necessary detail needed.

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, Feb/Mar 2025 Paper 2 Variant 2, question 8.

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