| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Line-circle intersection points |
| Difficulty | Moderate -0.8 Part (i) is trivial recall of circle equation form. Part (ii) involves standard substitution to find intersection points and distance calculation using Pythagoras—routine algebraic manipulation with no conceptual challenge. This is a straightforward textbook exercise testing basic circle properties and simultaneous equations, significantly easier than average A-level questions. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
A circle has equation $x^2 + y^2 = 45$.
\begin{enumerate}[label=(\roman*)]
\item State the centre and radius of this circle. [2]
\item The circle intersects the line with equation $x + y = 3$ at two points, A and B. Find algebraically the coordinates of A and B.
Show that the distance AB is $\sqrt{162}$. [8]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 2006 Q10 [10]}}