A-LevelMathematicsDifferentiation9709/21 · Oct/Nov 2025 · Q86 Marks

The equation of a curve is y = 4e¹⁻²ˣ √(3x-1).

Mark scheme

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

[*M1] Differentiate to obtain the form k₁e¹⁻²ˣ(3x−1)¹/² + k₂e¹⁻²ˣ(3x−1)⁻¹/² [Where k₁k₂ ≠ 0.]
[A1] Obtain correct first term -8e¹⁻²ˣ(3x-1)¹/² [OE. Allow unsimplified]
[A1] Obtain correct second term + 6e¹⁻²ˣ(3x-1)⁻¹/² [OE. Allow unsimplified]
[DM1] Equate first derivative to zero and attempt solution as far as 3x-1=k [OE. Must be in the form k₁e¹⁻²ˣ(3x−1)¹/² + k₂e¹⁻²ˣ(3x−1)⁻¹/²]
[A1] Obtain 3x-1= 3/4 OE, and hence x = 7/12 [Or exact equivalent.]
[A1] Obtain y=2√3e⁻¹/² [Or exact equivalent.]

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Topic: Differentiation, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source: A-Level Mathematics, Oct/Nov 2025 Paper 2 Variant 1, question 8.

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