A-LevelMathematicsIntegration9709/31 · May/June 2021 · Q910 Marks

The equation of a curve is y = x⁻² ln x for x > 0. The curve has one stationary point.

Mark scheme

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

[M1] Use correct product rule or correct quotient rule
[A1] Obtain correct derivative in any form
[M1] Equate 2 term derivative to zero and solve for x
[A1] Obtain answer x = e^(1/2)
[A1] Obtain answer y = 1 / (2e)
[*M1] Commence integration and reach -x⁻¹ ln x + ∫x⁻² dx
[A1] Obtain -x⁻¹ ln x + -x⁻¹
[A1 OE] Complete the integration and obtain -x⁻¹ ln x - x⁻¹
[DM1] Use limits correctly in an expression of the form p x⁻¹ ln x + q x⁻¹ (pq ≠ 0)
[A1 AG] Obtain 18 ln 2 – 9 from full and correct working

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Integration, A-Level Mathematics (syllabus 9709). Structured question, 10 marks.
Source: A-Level Mathematics, May/June 2021 Paper 3 Variant 1, question 9.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content