| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Taylor series |
| Type | Differential equation given |
| Difficulty | Challenging +1.2 This is a standard Taylor series question requiring differentiation of an implicit differential equation and systematic calculation of derivatives at a point. Part (a) is routine differentiation using the product rule and chain rule. Part (b) involves methodical computation of successive derivatives by substitution—a textbook exercise in FP2 Taylor series technique with no novel insight required. The 8 marks reflect computational length rather than conceptual difficulty. Slightly above average due to the algebraic manipulation involved and being a Further Maths topic. |
| Spec | 1.07s Parametric and implicit differentiation4.08a Maclaurin series: find series for function |
$$x \frac{dy}{dx} = 3x + y^2.$$
\begin{enumerate}[label=(\alph*)]
\item Show that
$$\frac{d^2 y}{dx^2} + (1 - 2y) \frac{dy}{dx} = 3.$$ [2]
\end{enumerate}
Given that $y = 1$ at $x = 1$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find a series solution for $y$ in ascending powers of $(x - 1)$, up to and including the term in $(x - 1)^3$. [8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP2 Q5 [10]}}