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O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2021 · Q48 Marks

Find the x-coordinates of the stationary points on the curve y = 3 lnx+x² - 7x, where x > 0.

  1. (a)Find the x-coordinates of the stationary points on the curve y = 3 lnx+x² - 7x, where x > 0.[5]
  2. (b)Determine the nature of each of these stationary points.[3]

Mark scheme

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

  1. [B2] B1 for the first term correct and one other term correct or for all terms correct with extra terms seen
  2. [M1] Equates their dy/dx to zero and rearranges to 3-term quadratic in x
  3. [M1] Dep on previous M1 Solves their 3-term quadratic
  4. [A1] no extra solutions x=0.5, 3 nfww isw
  5. [M1] FT their d²y/dx² providing B1 earned in (a)
  6. [A1] x=0.5, d²y/dx² <0 → max or d²y/dx² = -10 → max
  7. [A1] x=3, d²y/dx² >0 → min or d²y/dx² = 5/3 → min

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2021 Paper 2 Variant 2, question 4.

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