| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| 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 standard two-part C4 question combining routine partial fractions with binomial expansion. Part (a) uses the cover-up method or substitution (straightforward algebra), and part (b) requires expanding two simple binomial terms and collecting coefficients—both are textbook procedures with no novel insight required. Slightly easier than average due to the straightforward nature of both techniques. |
| Spec | 1.02y Partial fractions: decompose rational functions |
I don't see any mark scheme content in your message to clean up. You've provided a header "Question 7: 7" but no actual marking points, annotations, guidance notes, or content to process.
Please provide the extracted mark scheme content that needs cleaning, and I'll convert the unicode symbols to LaTeX notation and format it according to your specifications.7. Given that
$$\frac { 10 ( 2 - 3 x ) } { ( 1 - 2 x ) ( 2 + x ) } \equiv \frac { A } { 1 - 2 x } + \frac { B } { 2 + x }$$
\begin{enumerate}[label=(\alph*)]
\item find the values of the constants $A$ and $B$.
\item Hence, or otherwise, find the series expansion in ascending powers of $x$, up to and including the term in $x ^ { 3 }$, of $\frac { 10 ( 2 - 3 x ) } { ( 1 - 2 x ) ( 2 + x ) }$, for $| x | < \frac { 1 } { 2 }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q7 [8]}}