| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| 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 -0.8 This is a straightforward C1 integration question requiring standard techniques: integrate term-by-term (including x^{-2}), find the constant using given coordinates, then verify a point and find a tangent equation. All steps are routine applications of basic calculus with no problem-solving insight needed, making it easier than average but not trivial due to the multiple parts and algebraic manipulation required. |
| 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 $C$ with equation $y = f(x)$, $x \neq 0$, passes through the point $(3, 7\frac{1}{2})$.
Given that $f'(x) = 2x + \frac{3}{x^2}$,
\begin{enumerate}[label=(\alph*)]
\item find $f(x)$. [5]
\item Verify that $f(-2) = 5$. [1]
\item Find an equation for the tangent to $C$ at the point $(-2, 5)$, giving your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q10 [10]}}