| Exam Board | OCR |
|---|---|
| Module | H240/03 (Pure Mathematics and Mechanics) |
| Year | 2020 |
| Session | November |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Implicit equations and differentiation |
| Type | Show dy/dx equals given expression |
| Difficulty | Challenging +1.2 This question requires implicit differentiation (standard A-level technique) followed by finding points where tangents are horizontal/vertical and calculating distance. Part (a) is routine differentiation. Part (b) involves solving for specific points and distance calculation, requiring careful algebra across multiple steps but no novel insights. The 8 marks and 'show detailed reasoning' indicate extended working, but the techniques are all standard Core/Pure content. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.07s Parametric and implicit differentiation |
In this question you must show detailed reasoning.
\includegraphics{figure_6}
The diagram shows the curve with equation $4xy = 2(x^2 + 4y^2) - 9x$.
\begin{enumerate}[label=(\alph*)]
\item Show that $\frac{dy}{dx} = \frac{4x - 4y - 9}{4x - 16y}$. [3]
At the point $P$ on the curve the tangent to the curve is parallel to the $y$-axis and at the point $Q$ on the curve the tangent to the curve is parallel to the $x$-axis.
\item Show that the distance $PQ$ is $k\sqrt{5}$, where $k$ is a rational number to be determined. [8]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/03 2020 Q6 [11]}}