| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2011 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Tangent equation at a known point on circle |
| Difficulty | Moderate -0.3 This is a straightforward C1 circles question with standard components: identifying centre/radius from equation (trivial), finding x-intercepts (routine quadratic), verifying a point lies on the circle (substitution), and finding parallel tangents (standard perpendicular gradient method). While part (iii) has multiple steps and involves surds, all techniques are routine textbook exercises with no problem-solving insight required. Slightly easier than average due to the scaffolded structure. |
| Spec | 1.02b Surds: manipulation and rationalising denominators1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
\includegraphics{figure_13}
Fig. 13 shows the circle with equation $(x - 4)^2 + (y - 2)^2 = 16$.
\begin{enumerate}[label=(\roman*)]
\item Write down the radius of the circle and the coordinates of its centre. [2]
\item Find the $x$-coordinates of the points where the circle crosses the $x$-axis. Give your answers in surd form. [4]
\item Show that the point A $(4 + 2\sqrt{2}, 2 + 2\sqrt{2})$ lies on the circle and mark point A on the copy of Fig. 13.
Sketch the tangent to the circle at A and the other tangent that is parallel to it.
Find the equations of both these tangents. [7]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2011 Q13 [13]}}