Differentiation: past paper questions

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• Question 3Oct/Nov 2025, paper 22Structured9 marks

  The variables $x$ and $y$ are such that $y=2$ when $x=-1$ and $$x^{2}y+(x+y{)}^3=3.$$ Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{4}$ when $x=-1$.

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• Question 2Oct/Nov 2024, paper 22Structured7 marks

  The curve $C$ has equation $$4y^2+4\ln (xy)=1.$$ Show that, at the point $(2,\frac{1}{2})$ on $C$, $\frac{\mathrm{d}y}{\mathrm{d}x}=-\frac{1}{6}$.

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• Question 1Oct/Nov 2023, paper 22Structured5 marks

  Find the Maclaurin’s series for $\ln (x+2)+\ln (x^2+5)$ up to and including the term in $x^2$.

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• Question 2May/June 2024, paper 21Structured4 marks

  Find the Maclaurin’s series for ${\mathrm{e}}^{1+x^2}+{\mathrm{e}}^{1-x}$ up to and including the term in $x^2$.

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• Question 1May/June 2025, paper 23Structured5 marks

  Find the Maclaurin's series for ${\mathrm{e}}^{\left(\frac{1}{x+2}\right)}$ up to and including the term in $x^2$.

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• Question 2May/June 2024, paper 22Structured4 marks

  Find the Maclaurin's series for ${\mathrm{e}}^{1+x^2}+{\mathrm{e}}^{1-x}$ up to and including the term in $x^2$.

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• Question 1May/June 2023, paper 23Structured6 marks

  Find the Maclaurin series for ${\sin }^{-1}x$ up to and including the term in $x^3$.

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• Question 4May/June 2023, paper 23Structured8 marks

  The curve $C$ has equation $$4y^3+(x+y{)}^6=109.$$ Show that, at the point $(-4,3)$ on $C$, $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{1}{17}$.

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