| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2003 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Parametric integration |
| Type | Parametric area under curve |
| Difficulty | Challenging +1.8 This question requires finding a tangent equation to a parametric curve, determining where it intersects the curve again (solving a cubic), then computing area between curve and tangent using parametric integration. While each step is standard A-level technique, the multi-stage problem-solving and algebraic manipulation (especially solving for the second intersection point) make this significantly harder than typical textbook exercises, though not requiring truly novel insight. |
| Spec | 1.03g Parametric equations: of curves and conversion to cartesian1.07s Parametric and implicit differentiation1.08e Area between curve and x-axis: using definite integrals |
3.
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\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{25f0c7cc-0701-4836-931e-0eff5145e029-2_441_1111_1598_551}
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\end{figure}
Figure 2 shows a sketch of a part of the curve $C$ with parametric equations
$$x = t ^ { 3 } , y = t ^ { 2 } .$$
The tangent at the point $P ( 8,4 )$ cuts $C$ at the point $Q$ .\\
Find the area of the shaded region between $P Q$ and $C$ .\\
\hfill \mbox{\textit{Edexcel AEA 2003 Q3 [11]}}