| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Partial fractions with algebraic division first |
| Difficulty | Moderate -0.3 This is a standard C4 partial fractions question with routine algebraic division. Part (a) is textbook partial fractions decomposition and integration, while part (b) involves straightforward polynomial division given in a helpful form. All techniques are standard with no novel problem-solving required, making it slightly easier than average but not trivial due to the multi-part structure and potential for algebraic errors. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
1
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Express $\frac { 5 x - 6 } { x ( x - 3 ) }$ in the form $\frac { A } { x } + \frac { B } { x - 3 }$.\\
(2 marks)
\item Find $\int \frac { 5 x - 6 } { x ( x - 3 ) } \mathrm { d } x$.\\
(2 marks)
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item Given that
$$4 x ^ { 3 } + 5 x - 2 = ( 2 x + 1 ) \left( 2 x ^ { 2 } + p x + q \right) + r$$
find the values of the constants $p , q$ and $r$.
\item Find $\int \frac { 4 x ^ { 3 } + 5 x - 2 } { 2 x + 1 } \mathrm {~d} x$.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA C4 2012 Q1 [11]}}