O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2022 · Q45 Marks

Variables x and y are related by the equation y = 1+2/x+1/x² where x > 0. Use differentiation to find the approximate change in x when y increases from 4 by the small amount 0.01.

Variables x and y are related by the equation y = 1+2/x+1/x² where x > 0. Use differentiation to find the approximate change in x when y increases from 4 by the small amount 0.01.[5]

Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[B1] Substitutes y = 4 and rearranges to correct 3-term quadratic 3x² – 2x−1= 0 oe
[M1] Solves their 3-term quadratic in x as far as x = ...
[B1] dy/dx = -2x^-2 - 2x^-3 oe, isw
[M1] δx/0.01 = their (dy/dx)^-1 or better x=their 1 FT their derivative and their x, providing their x > 0 and their x ≠ 4 unless 4 is a genuine solution of their 3-term quadratic; must see a power decrease for attempted differentiation in two out of the three terms
[A1] 1/400 oe as the only solution dep on all previous marks being awarded

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Topic: Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 5 marks.
Source: O-Level Additional Mathematics, May/June 2022 Paper 2 Variant 2, question 4.

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