| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Line-circle intersection points |
| Difficulty | Moderate -0.3 Part (i) is trivial recall of circle equation form. Part (ii) involves standard simultaneous equations (substitution into circle equation gives a quadratic) and distance formula application. While it requires multiple steps and algebraic manipulation, this is a routine textbook exercise with no conceptual challenges beyond basic technique, making it slightly easier than average for A-level. |
| Spec | 1.02c Simultaneous equations: two variables by elimination and substitution1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | ii | (0, 0), √45 isw or 3√5 |
| Answer | Marks |
|---|---|
| (6−−3)2 +(3−−6)2 | 1+1 |
| Answer | Marks |
|---|---|
| M1 | for correct expn of (3 − y)2 |
| Answer | Marks |
|---|---|
| (A.G.) | 2 |
Question 3:
3 | ii | (0, 0), √45 isw or 3√5
x = 3 − y or y = 3 − x seen or
used
subst in eqn of circle to
eliminate variable
9 − 6y + y2 + y2 = 45
2y2 −6y − 36 = 0 or y2 −3y − 18
= 0
(y − 6)(y + 3)= 0
y = 6 or −3
x = −3 or 6
(6−−3)2 +(3−−6)2 | 1+1
M1
M1
M1
M1
M1
A1
A1
M1 | for correct expn of (3 − y)2
seen oe
condone one error if quadratic
or quad. formula attempted
[complete sq attempt earns
last 2 Ms]
or A1 for (6, −3) and A1 for
(−3, 6)
no ft from wrong points
(A.G.) | 2
8A 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 Q3 [10]}}