| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Partial fractions then binomial expansion |
| Difficulty | Standard +0.3 This is a straightforward C4 question combining routine partial fractions with repeated linear factors and standard binomial expansion. Part (a) uses the cover-up method or substitution (very mechanical), and part (b) applies the binomial theorem to two simple terms. The algebra is clean, the techniques are standard textbook exercises, and no problem-solving insight is required—slightly easier than average for A-level. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<1 |
2.
$$f ( x ) = \frac { 3 x - 1 } { ( 1 - 2 x ) ^ { 2 } } , \quad | x | < \frac { 1 } { 2 }$$
Given that, for $x \neq \frac { 1 } { 2 } , \quad \frac { 3 x - 1 } { ( 1 - 2 x ) ^ { 2 } } = \frac { A } { ( 1 - 2 x ) } + \frac { B } { ( 1 - 2 x ) ^ { 2 } } , \quad$ where $A$ and $B$ are constants,
\begin{enumerate}[label=(\alph*)]
\item find the values of $A$ and $B$.
\item Hence, or otherwise, find the series expansion of $\mathrm { f } ( x )$, in ascending powers of $x$, up to and including the term in $x ^ { 3 }$, simplifying each term.\\
(6)
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2006 Q2 [9]}}