| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Partial Fractions |
| Type | Partial fractions then differentiate |
| Difficulty | Standard +0.3 Part (a) is a standard partial fractions decomposition with distinct linear factors—routine C4 material. Part (b) requires differentiating the partial fractions and showing the derivative is always negative, which involves algebraic manipulation and sign analysis but follows a clear method once the partial fractions are found. This is slightly above average difficulty due to the proof element in part (b), but still a fairly standard C4 question. |
| Spec | 1.02y Partial fractions: decompose rational functions1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates |
The function f is given by
$$f(x) = \frac{3(x + 1)}{(x + 2)(x - 1)}, \quad x \in \mathbb{R}, x \neq -2, x \neq 1.$$
\begin{enumerate}[label=(\alph*)]
\item Express $f(x)$ in partial fractions. [3]
\item Hence, or otherwise, prove that $f'(x) < 0$ for all values of $x$ in the domain. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q28 [6]}}