| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Taylor series |
| Type | Maclaurin series for ln(exponential expressions) |
| Difficulty | Standard +0.3 This is a straightforward FP2 Maclaurin series question requiring standard techniques: (i) is direct application of the exponential series formula, and (ii) uses substitution into ln(1+u) series after factoring. While it involves multiple steps and series manipulation, the methods are standard textbook exercises for FP2 students with no novel insight required, making it slightly easier than average. |
| Spec | 1.06f Laws of logarithms: addition, subtraction, power rules4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
\begin{enumerate}[label=(\roman*)]
\item Write down and simplify the first three terms of the Maclaurin series for $e^{2x}$. [2]
\item Hence show that the Maclaurin series for
$$\ln(e^{2x} + e^{-2x})$$
begins $\ln a + bx^2$, where $a$ and $b$ are constants to be found. [4]
\end{enumerate}
\hfill \mbox{\textit{OCR FP2 2009 Q1 [6]}}