Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

For $(1 + ax)^{-2}$, where $a$ is a positive constant, the expansion in ascending powers of $x$ has matching coefficients for $x$ and $x^3$.
(a(i))[4]

Find $a$ exactly.

(a(ii))[3]

With $a$ equal to this value, write the expansion up to and including the term in $x^2$, simplifying the coefficients.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Unsimplified terms in $x$ and $x^3$ are obtained correctly.” …

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