| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find normal equation at point |
| Difficulty | Moderate -0.3 This is a straightforward implicit differentiation question requiring students to differentiate term-by-term, substitute a given point to find the gradient, then find the perpendicular normal. All steps are routine C4 techniques with no conceptual challenges, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
\begin{enumerate}
\item A curve $C$ is described by the equation
\end{enumerate}
$$3 x ^ { 2 } - 2 y ^ { 2 } + 2 x - 3 y + 5 = 0$$
Find an equation of the normal to $C$ at the point ( 0,1 ), giving your answer in the form $a x + b y + c = 0$, where $a , b$ and $c$ are integers.\\
\hfill \mbox{\textit{Edexcel C4 2006 Q1 [7]}}