| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2007 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Find normal line equation at given point |
| Difficulty | Moderate -0.3 This is a straightforward C1 differentiation question requiring standard techniques: finding coordinates, calculating distance using Pythagoras, differentiating a polynomial with a reciprocal term, and finding normal equations. All parts are routine applications with clear methods, though part (a) requires careful arithmetic and the question has multiple parts worth several marks total. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations |
10. The curve $C$ has equation $y = x ^ { 2 } ( x - 6 ) + \frac { 4 } { x } , x > 0$.
The points $P$ and $Q$ lie on $C$ and have $x$-coordinates 1 and 2 respectively.
\begin{enumerate}[label=(\alph*)]
\item Show that the length of $P Q$ is $\sqrt { 170 }$.
\item Show that the tangents to $C$ at $P$ and $Q$ are parallel.
\item Find an equation for the normal to $C$ at $P$, giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.\\
$\_\_\_\_$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2007 Q10 [13]}}