| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Straight Lines & Coordinate Geometry |
| Type | Coordinates from geometric constraints |
| Difficulty | Challenging +1.8 This AEA question requires recognizing that D² = x² + y² and substituting the curve equation to eliminate x², then minimizing a transcendental function involving sin y. While it needs insight to set up correctly and careful calculus/analysis for part (b), the algebraic manipulation is straightforward and the optimization technique is standard for A-level, making it challenging but not exceptionally difficult for AEA standard. |
| Spec | 1.07s Parametric and implicit differentiation8.05d Partial differentiation: first and second order, mixed derivatives8.05e Stationary points: where partial derivatives are zero8.05f Nature of stationary points: classify using Hessian matrix |
2.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{a8e9db6b-dfad-4278-82d8-a8fa5ba61008-04_904_826_255_623}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{center}
\end{figure}
Figure 1 shows the curve defined by the equation
$$y ^ { 2 } + 3 y - 6 \sin y = 4 - x ^ { 2 }$$
The point $P ( x , y )$ lies on the curve.\\
The distance from the origin,$O$ ,to $P$ is $D$ .
\begin{enumerate}[label=(\alph*)]
\item Write down an equation for $D ^ { 2 }$ in terms of $y$ only.
\item Hence determine the minimum value of $D$ giving your answer in simplest form.\\
\includegraphics[max width=\textwidth, alt={}, center]{a8e9db6b-dfad-4278-82d8-a8fa5ba61008-04_2266_53_312_1977}
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2024 Q2 [6]}}