| Exam Board | AQA |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2013 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Taylor series |
| Type | Use binomial with exponential series |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question combining two standard series expansions. Part (a) is direct substitution into the exponential series, and part (b) requires multiplying two series and collecting the x² term—a routine technique practiced extensively in FP3. While it involves Further Maths content, the execution is mechanical with no novel insight required. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<14.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
2
\begin{enumerate}[label=(\alph*)]
\item Write down the expansion of $\mathrm { e } ^ { 3 x }$ in ascending powers of $x$ up to and including the term in $x ^ { 2 }$.
\item Hence, or otherwise, find the term in $x ^ { 2 }$ in the expansion, in ascending powers of $x$, of $\mathrm { e } ^ { 3 x } ( 1 + 2 x ) ^ { - \frac { 3 } { 2 } }$.\\
(4 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA FP3 2013 Q2 [5]}}