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A-LevelMathematicsDifferentiation9709/31 · Oct/Nov 2025 · Q45 Marks

The diagram shows the graph of y = e^(sin 2x) cos 4x for 0 < x < 1/2π, and its maximum point M. [Figure 4.1]

  1. (a)Find the x-coordinate of M.[5]

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Mark scheme

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

  1. [M1] Use correct product rule: psin 4xesin2x + q cos2x cos4xesin2x
  2. [A1] Obtain derivative -4sin4xesin 2x +2cos2x cos4xesin2x
  3. [M1] Equate derivative to zero and obtain an equation in one trig function
  4. [A1] Obtain 2sin² 2x + 4sin2x -1=0
  5. [A1] Obtain x = 0.113 and no other root

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About this question

Topic
Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2025 Paper 3 Variant 1, question 4.

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