| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 7 |
| Topic | Taylor series |
| Type | Maclaurin series for ln(a+bx) |
| Difficulty | Standard +0.3 This is a straightforward Maclaurin series question requiring routine differentiation of ln(2+x) and substitution of x=0. While it's Further Maths content, the mechanics are standard calculus with no problem-solving insight needed—just applying the formula systematically. Slightly above average difficulty due to being FM, but still a textbook exercise. |
| Spec | 1.07l Derivative of ln(x): and related functions4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
You are given that $f(x) = \ln(2 + x)$.
\begin{enumerate}[label=(\alph*)]
\item Determine the exact value of $f'(0)$. [2]
\item Show that $f''(0) = -\frac{1}{4}$. [2]
\item Hence write down the first three terms of the Maclaurin series for $f(x)$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q2 [7]}}