| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Topic | Areas Between Curves |
| Type | Circle or Circular Arc Area |
| Difficulty | Standard +0.3 This is a standard areas-between-curves question with straightforward setup. Part (a) is routine verification by substitution. Part (b) requires finding the intersection points, setting up integrals for both the circular arc and parabola, and subtracting—all standard techniques for this topic. The geometry is clear from the diagram, and while the algebra involves some care with the circular sector formula and integration, no novel insight is required. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.08e Area between curve and x-axis: using definite integrals1.08f Area between two curves: using integration |
5 The diagram shows the circle with centre O and radius 2, and the parabola $y = \frac { 1 } { \sqrt { 3 } } \left( 4 - x ^ { 2 } \right)$.\\
\includegraphics[max width=\textwidth, alt={}, center]{f2f45d6c-cfdc-455b-ab08-597b06a69f36-06_838_970_1059_280}
The circle meets the parabola at points $P$ and $Q$, as shown in the diagram.
\begin{enumerate}[label=(\alph*)]
\item Verify that the coordinates of $Q$ are $( 1 , \sqrt { 3 } )$.
\item Find the exact area of the shaded region enclosed by the $\operatorname { arc } P Q$ of the circle and the parabola.\\[0pt]
[8]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 Q5 [11]}}