| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find normal equation at point |
| Difficulty | Standard +0.3 This is a standard implicit differentiation question from C4. Part (a) requires applying the product rule and chain rule to differentiate implicitly, then substituting coordinates to find the gradient - a routine multi-step process. Part (b) is straightforward application of the normal gradient formula. While implicit differentiation is a C4 topic requiring careful algebraic manipulation, this is a textbook-style question with no novel insight required, making it slightly easier than average. |
| Spec | 1.07s Parametric and implicit differentiation |
The curve $C$ has equation $5x^2 + 2xy - 3y^2 + 3 = 0$. The point $P$ on the curve $C$ has coordinates $(1, 2)$.
\begin{enumerate}[label=(\alph*)]
\item Find the gradient of the curve at $P$. [5]
\item Find the equation of the normal to the curve $C$ at $P$, in the form $y = ax + b$, where $a$ and $b$ are constants. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q1 [8]}}