| Exam Board | OCR MEI |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle through three points using right angle in semicircle |
| Difficulty | Standard +0.3 This is a straightforward coordinate geometry question requiring perpendicular gradient verification (routine calculation) and finding a circle centre through three points using perpendicular bisectors. Both parts are standard AS-level techniques with clear methods, making it slightly easier than average but still requiring multiple steps and careful algebra. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03b Straight lines: parallel and perpendicular relationships1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(\frac{5-7}{11--3}\) or \(\frac{-9-5}{9-11}\) soi | M1 | All signs reversed in a fraction is correct |
| \(\frac{-2}{14}\) and \(\frac{14}{2}\) oe | A1 | Fractions may be cancelled |
| \(\frac{-2}{14} \times \frac{14}{2} = -1\) oe so lines are perpendicular | A1 | |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| PR is a diameter by angle in a semi-circle | B1 | Stated. Detailed reasoning required |
| \(\left(\frac{-3+9}{2}, \frac{7-9}{2}\right)\) | M1 | allow one slip e.g. sign error |
| \((3, -1)\) | A1 | |
| [3] |
## Question 10:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $\frac{5-7}{11--3}$ or $\frac{-9-5}{9-11}$ **soi** | M1 | All signs reversed in a fraction is correct |
| $\frac{-2}{14}$ and $\frac{14}{2}$ **oe** | A1 | Fractions may be cancelled |
| $\frac{-2}{14} \times \frac{14}{2} = -1$ **oe** so lines are perpendicular | A1 | |
| **[3]** | | |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| PR is a diameter by angle in a semi-circle | B1 | Stated. Detailed reasoning required |
| $\left(\frac{-3+9}{2}, \frac{7-9}{2}\right)$ | M1 | allow one slip e.g. sign error |
| $(3, -1)$ | A1 | |
| **[3]** | | |
---\begin{enumerate}[label=(\alph*)]
\item Show that PQ is perpendicular to QR .
A circle passes through $\mathrm { P } , \mathrm { Q }$ and R .
\item Determine the coordinates of the centre of the circle.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI AS Paper 2 2021 Q10 [6]}}