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A-LevelMathematicsIntegration9709/22 · Oct/Nov 2021 · Q45 Marks

Given that ∫ (from a to a+14) (1/3x) dx = ln 2, find the value of the positive constant a.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

  1. [M1] Integrate to obtain form k ln x or k ln(3x)
  2. [A1] Apply limits and obtain ⅓ ln(a+14) – ⅓ ln a = ln 2 or ⅓ ln(3a+42) – ⅓ ln(3a) = ln 2 OE
  3. [M1] Use one relevant logarithm property correctly
  4. [M1] Apply correct process to obtain equation without logarithms OE. M0 if incorrect logarithm property used.
  5. [A1] Obtain (a+14)/a = 8 or equivalent and hence a = 2

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About this question

Topic
Integration, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2021 Paper 2 Variant 2, question 4.

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