| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2012 |
| Session | January |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Partial fractions with algebraic division first |
| Difficulty | Standard +0.3 This is a standard C4 partial fractions question with algebraic division. Part (a) is routine partial fractions decomposition, part (b) requires polynomial long division (a standard technique), and part (c) applies integration using the results from parts (a) and (b). The question is scaffolded across three parts with clear guidance on the required forms, making it slightly easier than average but still requiring multiple techniques. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08d Evaluate definite integrals: between limits1.08j Integration using partial fractions |
1
\begin{enumerate}[label=(\alph*)]
\item Express $\frac { 2 x + 3 } { 4 x ^ { 2 } - 1 }$ in the form $\frac { A } { 2 x - 1 } + \frac { B } { 2 x + 1 }$, where $A$ and $B$ are integers. (3 marks)
\item Express $\frac { 12 x ^ { 3 } - 7 x - 6 } { 4 x ^ { 2 } - 1 }$ in the form $C x + \frac { D ( 2 x + 3 ) } { 4 x ^ { 2 } - 1 }$, where $C$ and $D$ are integers.\\
(3 marks)
\item Evaluate $\int _ { 1 } ^ { 2 } \frac { 12 x ^ { 3 } - 7 x - 6 } { 4 x ^ { 2 } - 1 } \mathrm {~d} x$, giving your answer in the form $p + \ln q$, where $p$ and $q$ are rational numbers.\\
(5 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2012 Q1 [11]}}