| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Taylor series |
| Type | Direct multiplication of series |
| Difficulty | Challenging +1.2 This is a standard Further Maths FP2 question combining proof by induction with Taylor series. Part (a) requires a methodical induction proof with trigonometric manipulation but follows a predictable structure. Part (b) is routine application of the result from (a) to find Maclaurin coefficients. While requiring multiple techniques and careful algebra, it's a textbook-style question without novel insight, making it moderately harder than average A-level but standard for Further Maths. |
| Spec | 4.01b Complex proofs: conjecture and demanding proofs4.08a Maclaurin series: find series for function |
\begin{enumerate}[label=(\alph*)]
\item Prove by induction that
$$\frac{d^n}{dx^n}(e^x \cos x) = 2^{\frac{1}{2}n} e^x \cos\left(x + \frac{1}{4}n\pi\right), \quad n \geq 1.$$ [8]
\item Find the Maclaurin series expansion of $e^x \cos x$, in ascending powers of $x$, up to and including the term in $x^4$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q34 [11]}}