| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2013 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Chord length calculation |
| Difficulty | Moderate -0.8 This is a straightforward C1 circle question requiring only direct application of standard formulas: reading center/radius from equation, solving simultaneous equations for axis intersections, verifying points satisfy the equation, and using midpoint/perpendicular distance formulas. All techniques are routine with no problem-solving insight needed, making it easier than average but not trivial due to the computational steps involved. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.10f Distance between points: using position vectors1.10g Problem solving with vectors: in geometry |
The circle $(x - 3)^2 + (y - 2)^2 = 20$ has centre C.
\begin{enumerate}[label=(\roman*)]
\item Write down the radius of the circle and the coordinates of C. [2]
\item Find the coordinates of the intersections of the circle with the $x$- and $y$-axes. [5]
\item Show that the points A$(1, 6)$ and B$(7, 4)$ lie on the circle. Find the coordinates of the midpoint of AB. Find also the distance of the chord AB from the centre of the circle. [5]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2013 Q10 [12]}}