| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Taylor series |
| Type | Taylor series about π/4 |
| Difficulty | Challenging +1.2 This is a Further Maths FP2 question requiring differentiation of sec²x and Taylor series expansion about a non-zero point. Part (a) involves chain rule and product rule with trig functions (moderately technical but guided). Part (b) requires computing derivatives at x=π/4 and assembling the Taylor series—more demanding than standard calculus but follows a clear algorithmic procedure. The 10 marks and multi-step nature place it above average difficulty, but it's a standard FP2 exercise without requiring novel insight. |
| Spec | 4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
$y = \sec^2 x$
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac{d^2 y}{dx^2} = 6 \sec^4 x - 4 \sec^2 x$. [4]
\item Find a Taylor series expansion of $\sec^2 x$ in ascending powers of $\left(x - \frac{\pi}{4}\right)$, up to and including the term in $\left(x - \frac{\pi}{4}\right)^3$. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q5 [10]}}