| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Integration with Partial Fractions |
| Type | Improper algebraic form then partial fractions |
| Difficulty | Standard +0.3 This is a standard C4 partial fractions question followed by integration. Part (a) requires routine algebraic manipulation to find constants A, B, C using cover-up method or equating coefficients. Part (b) involves integrating the partial fractions form to find area, which is straightforward once decomposed. The techniques are well-practiced in C4 with no novel insight required, making it slightly easier than average. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08j Integration using partial fractions |
\includegraphics{figure_1}
Figure 1 shows part of the curve with equation $y = f(x)$, where
$$f(x) = \frac{x^2 + 1}{(1 + x)(3 - x)}, \quad 0 \leq x < 3.$$
\begin{enumerate}[label=(\alph*)]
\item Given that $f(x) = A + \frac{B}{1 + x} + \frac{C}{3 - x}$, find the values of the constants $A$, $B$ and $C$. [4]
\end{enumerate}
The finite region $R$, shown in Fig. 1, is bounded by the curve with equation $y = f(x)$, the $x$-axis, the $y$-axis and the line $x = 2$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the area of $R$, giving your answer in the form $p + q \ln r$, where $p$, $q$ and $r$ are rational constants to be found. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q2 [9]}}