| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Generalised Binomial Theorem and Partial Fractions |
| Type | Partial fractions then binomial expansion |
| Difficulty | Standard +0.3 This is a standard C4 question combining two routine techniques: partial fractions decomposition (straightforward with linear factors) and binomial expansion of two simple terms. The validity question in (b)(ii) requires only recognizing that x=0.4 exceeds the radius of convergence, which is a common textbook check. Slightly easier than average due to the mechanical nature of all parts. |
| Spec | 1.02y Partial fractions: decompose rational functions1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
2 It is given that $\mathrm { f } ( x ) = \frac { 7 x - 1 } { ( 1 + 3 x ) ( 3 - x ) }$.
\begin{enumerate}[label=(\alph*)]
\item Express $\mathrm { f } ( x )$ in the form $\frac { A } { 3 - x } + \frac { B } { 1 + 3 x }$, where $A$ and $B$ are integers.\\
(3 marks)
\item \begin{enumerate}[label=(\roman*)]
\item Find the first three terms of the binomial expansion of $\mathrm { f } ( x )$ in the form $a + b x + c x ^ { 2 }$, where $a$, $b$ and $c$ are rational numbers.\\
(7 marks)
\item State why the binomial expansion cannot be expected to give a good approximation to $\mathrm { f } ( x )$ at $x = 0.4$.\\
(1 mark)
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C4 2013 Q2 [11]}}