| Exam Board | AQA |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Partial fractions with algebraic division first |
| Difficulty | Moderate -0.3 This is a standard C4 partial fractions question requiring algebraic division followed by decomposition and integration. While it involves multiple steps (recognizing improper fraction, dividing, finding constants, integrating), each step follows routine procedures taught explicitly in the syllabus with no novel problem-solving required. Slightly easier than average due to the question explicitly providing the form of the answer. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
3
\begin{enumerate}[label=(\alph*)]
\item Given that $\frac { 9 x ^ { 2 } - 6 x + 5 } { ( 3 x - 1 ) ( x - 1 ) }$ can be written in the form $3 + \frac { A } { 3 x - 1 } + \frac { B } { x - 1 }$, where $A$ and $B$ are integers, find the values of $A$ and $B$.
\item Hence, or otherwise, find $\int \frac { 9 x ^ { 2 } - 6 x + 5 } { ( 3 x - 1 ) ( x - 1 ) } \mathrm { d } x$.
\end{enumerate}
\hfill \mbox{\textit{AQA C4 2006 Q3 [8]}}