| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Taylor series |
| Type | Taylor series about π/4 |
| Difficulty | Standard +0.3 This is a straightforward Taylor series question requiring routine differentiation of tan x (using chain/product rule), substitution into the standard Taylor formula about x=π/4, and a simple numerical application. While it involves Further Maths content, the execution is mechanical with no conceptual challenges—slightly easier than average A-level questions overall. |
| Spec | 1.07i Differentiate x^n: for rational n and sums4.08a Maclaurin series: find series for function |
Given that $y = \tan x$,
\begin{enumerate}[label=(\alph*)]
\item find $\frac{dy}{dx}$, $\frac{d^2 y}{dx^2}$ and $\frac{d^3 y}{dx^3}$. [3]
\item Find the Taylor series expansion of $\tan x$ in ascending powers of $\left(x - \frac{\pi}{4}\right)$ up to and including the term in $\left(x - \frac{\pi}{4}\right)^3$. [3]
\item Hence show that $\tan \frac{3\pi}{10} \approx 1 + \frac{\pi}{10} + \frac{\pi^2}{200} + \frac{\pi^3}{3000}$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q33 [8]}}