| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2003 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Partial fractions with tangent equation |
| Difficulty | Challenging +1.2 This is a multi-part AEA question requiring partial fractions decomposition (with quadratic factor), binomial expansions of multiple terms, and finding a tangent equation. While AEA questions are inherently harder, this is relatively standard: the partial fractions setup is given, the expansions use familiar techniques, and the tangent at x=0 is straightforward. It requires careful algebra across multiple steps but no particularly novel insight. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<1 |
4.
$$f ( x ) = \frac { 1 - 3 x } { \left( 1 + 3 x ^ { 2 } \right) ( 1 - x ) ^ { 2 } } , x \neq 1$$
\begin{enumerate}[label=(\alph*)]
\item Find the constants $A , B , C$ and $D$ such that
$$\mathrm { f } ( x ) \equiv \frac { A x + B } { 1 + 3 x ^ { 2 } } + \frac { C } { 1 - x } + \frac { D } { ( 1 - x ) ^ { 2 } }$$
\item Find a series expansion for $\mathrm { f } ( x )$ in ascending powers of $x$ ,up to and including the term in $x ^ { 4 }$ .
\item Find an equation of the tangent to the curve with equation $y = \mathrm { f } ( x )$ at the point where $x = 0$ .
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2003 Q4 [11]}}