| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Tangent/normal with axis intercepts |
| Difficulty | Standard +0.3 This is a straightforward implicit differentiation question requiring application of the chain rule and product rule, followed by a standard tangent line calculation. While it involves multiple techniques, these are routine C4 procedures with no novel insight required. The algebra is manageable and the question structure is typical for this topic, making it slightly easier than average. |
| Spec | 1.07m Tangents and normals: gradient and equations1.07s Parametric and implicit differentiation |
The curve $C$ has the equation
$$\sin(\pi y) - y - x^2 y = -5, \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item Find $\frac{dy}{dx}$ in terms of $x$ and $y$.
[5]
The point $P$ with coordinates $(2, 1)$ lies on $C$.
The tangent to $C$ at $P$ meets the $x$-axis at the point $A$.
\item Find the exact value of the $x$-coordinate of $A$.
[4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2013 Q5 [9]}}