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A-LevelMathematicsLogarithmic and exponential functions9709/31 · May/June 2025 · Q23 Marks

It is given that 2 lnp+ln(p-1)-½ln(q+1) = 3. Find q in terms of p.

  1. It is given that 2 lnp+ln(p-1)-½ln(q+1) = 3. Find q in terms of p.[3]

Mark scheme

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

  1. [M1] Use logarithm of a root or a power E.g. 2 ln p = ln p², ½ ln (q + 1) = ln √q +1 or 3 = ln e³.
  2. [A1] Obtain p² (p-1) = e³√q+1 OE without logs.
  3. [A1] Obtain q = (p²(p-1)/e³)² - 1 OE, ISW

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About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source
A-Level Mathematics, May/June 2025 Paper 3 Variant 1, question 2.

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