| 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 requiring the product rule and algebraic manipulation, followed by finding a normal line equation. While it involves multiple steps, the techniques are routine for C4 students and the question follows a very common template with no novel problem-solving required. |
| Spec | 1.07s Parametric and implicit differentiation |
| Answer | Marks | Guidance |
|---|---|---|
| \(2x + 3y + 3x\frac{dy}{dx} - 4y\frac{dy}{dx} = 0\) | M1 A2 | |
| \(\frac{dy}{dx} = \frac{2x + 3y}{4y - 3x}\) | M1 A1 | |
| \(\text{grad} = \frac{6 - 6}{-8 - 9} = 0\) | M1 | |
| \(\therefore\) normal parallel to \(y\)-axis \(\therefore x = 3\) | M1 A1 | (8 marks) |
$2x + 3y + 3x\frac{dy}{dx} - 4y\frac{dy}{dx} = 0$ | M1 A2 |
$\frac{dy}{dx} = \frac{2x + 3y}{4y - 3x}$ | M1 A1 |
$\text{grad} = \frac{6 - 6}{-8 - 9} = 0$ | M1 |
$\therefore$ normal parallel to $y$-axis $\therefore x = 3$ | M1 A1 | (8 marks)
---A curve has the equation
$$x^2 + 3xy - 2y^2 + 17 = 0.$$
\begin{enumerate}[label=(\alph*)]
\item Find an expression for $\frac{dy}{dx}$ in terms of $x$ and $y$. [5]
\item Find an equation for the normal to the curve at the point $(3, -2)$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q2 [8]}}