| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2014 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Find tangent equation at point |
| Difficulty | Standard +0.3 This is a standard implicit differentiation question requiring systematic application of the product rule and chain rule, followed by algebraic rearrangement to isolate dy/dx. Part (b) is routine substitution into the tangent formula. While it requires careful bookkeeping across multiple terms, it follows a well-practiced procedure with no novel insight needed, making it slightly easier than the average A-level question. |
| Spec | 1.07s Parametric and implicit differentiation |
A curve $C$ has the equation
$$x^3 + 2xy - x - y^3 - 20 = 0$$
\begin{enumerate}
\item[(a)] Find $\frac{dy}{dx}$ in terms of $x$ and $y$. \hfill [5]
\item[(b)] Find an equation of the tangent to $C$ at the point $(3, -2)$, giving your answer in the form $ax + by + c = 0$, where $a$, $b$ and $c$ are integers. \hfill [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 2014 Q1 [7]}}