| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle through three points using right angle in semicircle |
| Difficulty | Moderate -0.8 This is a straightforward coordinate geometry question testing standard C1 techniques: gradient calculation to verify perpendicularity, circle equation from diameter endpoints, and finding the other end of a diameter using the center. All parts follow routine procedures with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature and calculation care needed. |
| Spec | 1.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03f Circle properties: angles, chords, tangents |
| Answer | Marks |
|---|---|
| 2 | ii |
| iii | grad AB = 8/4 or 2 or y = 2x − 10 |
| Answer | Marks |
|---|---|
| = (7, 9) | 1 |
| Answer | Marks |
|---|---|
| A1 | uuur ⎛−2⎞ |
| Answer | Marks |
|---|---|
| allow B3 for (7,9) | 3 |
Question 2:
2 | ii
iii | grad AB = 8/4 or 2 or y = 2x − 10
grad BC = 1/−2 or − ½ or
y = − ½ x + 2.5
product of grads = −1 [so perp]
(allow seen or used)
midpt E of AC = (6, 4.5)
AC2 = (9 − 3)2 + (8 − 1)2 or 85
rad = ½ √85 o.e.
(x − 6)2 + (y − 4.5)2 = 85/4 o.e.
(5−6)2 + (0−4.5)2 = 1 + 81/4 [=
85/4]
uuur uuur ⎛ 1 ⎞
BE = ED=
⎜ ⎟
⎝4.5⎠
D has coords (6 + 1, 4.5 + 4.5) ft
or
(5 + 2, 0 + 9)
= (7, 9) | 1
1
1
1
M1
A1
B2
1
M1
M1
A1 | uuur ⎛−2⎞
oo..e. ft their centre; or f BC = ⎜ ⎟
⎝ 1 ⎠
or (9 − 2, 8 + 1); condone mixtures of
vectors and coords. throughout part iii
allow B3 for (7,9) | 3
6
3A$(9, 8)$, B$(5, 0)$ and C$(3, 1)$ are three points.
\begin{enumerate}[label=(\roman*)]
\item Show that AB and BC are perpendicular. [3]
\item Find the equation of the circle with AC as diameter. You need not simplify your answer.
Show that B lies on this circle. [6]
\item BD is a diameter of the circle. Find the coordinates of D. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C1 Q2 [12]}}