| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Indices and Surds |
| Type | Differentiate after index conversion |
| Difficulty | Moderate -0.8 This is a straightforward C1 differentiation question requiring algebraic manipulation (expanding and simplifying with negative indices) followed by term-by-term differentiation using the power rule. Part (a) is routine algebra, and part (b) applies a standard technique with no problem-solving required. Easier than average for A-level. |
| Spec | 1.02k Simplify rational expressions: factorising, cancelling, algebraic division1.07i Differentiate x^n: for rational n and sums |
$f(x) = \frac{(x^2 – 3)^2}{x^3}$, $x \neq 0$.
(a) Show that $f(x) \equiv x – 6x^{-1} + 9x^{-3}$.
(2)
(b) Hence, or otherwise, differentiate $f(x)$ with respect to $x$.
(3)
END8.
$$f ( x ) = \frac { \left( x ^ { 2 } - 3 \right) ^ { 2 } } { x ^ { 3 } } , x \neq 0$$
\begin{enumerate}[label=(\alph*)]
\item Show that $\mathrm { f } ( x ) \equiv x - 6 x ^ { - 1 } + 9 x ^ { - 3 }$.
\item Hence, or otherwise, differentiate $\mathrm { f } ( x )$ with respect to $x$.
END
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q8 [5]}}