| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Find curve equation from derivative (extended problem with normals, stationary points, or further geometry) |
| Difficulty | Moderate -0.3 This is a straightforward integration question requiring standard power rule application and using a point to find the constant of integration, followed by a routine tangent line calculation. While it involves multiple steps (9 marks total), each step uses basic C1 techniques with no problem-solving insight required, making it slightly easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07l Derivative of ln(x): and related functions1.07m Tangents and normals: gradient and equations1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
The curve $C$ has equation $y = f(x)$, $x \neq 0$, and the point $P(2, 1)$ lies on $C$. Given that
$$f'(x) = 3x^2 - 6 - \frac{8}{x^3},$$
\begin{enumerate}[label=(\alph*)]
\item find $f(x)$. [5]
\item Find an equation for the tangent to $C$ at the point $P$, giving your answer in the form $y = mx + c$, where $m$ and $c$ are integers. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [9]}}