| Exam Board | WJEC |
|---|---|
| Module | Unit 3 (Unit 3) |
| Year | 2018 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Repeated linear factor with distinct linear factor – decompose and integrate |
| Difficulty | Moderate -0.3 This is a standard partial fractions question with a repeated linear factor, followed by routine integration using logarithms and the standard result for 1/(x-a)². The algebraic manipulation is straightforward, and the integration technique is directly taught. It's slightly easier than average because it follows a well-practiced procedure with no conceptual surprises, though the repeated factor adds minor complexity. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
\begin{enumerate}[label=(\alph*)]
\item Show that
$$\frac{3x}{(x-1)(x-4)^2} = \frac{A}{(x-1)} + \frac{B}{(x-4)} + \frac{C}{(x-4)^2},$$
where $A$, $B$ and $C$ are constants to be found. [3]
\item Evaluate $\int_5^7 \frac{3x}{(x-1)(x-4)^2} \, dx$, giving your answer correct to 3 decimal places. [5]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 3 2018 Q5 [8]}}