| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Partial fractions with linear factors – decompose and integrate (indefinite) |
| Difficulty | Moderate -0.3 Part (i)(a) is a standard partial fractions decomposition with distinct linear factors requiring routine algebraic manipulation. Part (i)(b) follows immediately by integrating the partial fractions to get logarithms. Part (ii) requires recognizing the substitution u³=x, factoring the denominator, and integrating—more steps but still a textbook application of C4 techniques. Overall slightly easier than average due to straightforward setup and standard methods. |
| Spec | 1.02y Partial fractions: decompose rational functions1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08h Integration by substitution1.08j Integration using partial fractions |
\begin{enumerate}[label=(\roman*)]
\item \begin{enumerate}[label=(\alph*)]
\item Express $\frac{7x}{(x + 3)(2x - 1)}$ in partial fractions.
[3]
\item Given that $x > \frac{1}{2}$, find
$$\int \frac{7x}{(x + 3)(2x - 1)} \, dx$$
[3]
\end{enumerate}
\item Using the substitution $u^3 = x$, or otherwise, find
$$\int \frac{1}{x + x^3} \, dx, \quad x > 0$$
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2013 Q6 [11]}}