| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Easy -1.2 This is a straightforward completing-the-square exercise to convert a circle equation to standard form. It requires only routine algebraic manipulation with no problem-solving or geometric insight, making it easier than average but not trivial since students must correctly complete the square for both variables. |
| Spec | 1.03e Complete the square: find centre and radius of circle |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((x \pm 6)^2\) and \((y \pm 4)^2\) | M1 | completing the square twice soi |
| \(r = 7\) not from wrong working | A1 | NB \((x-6)^2 - 36 + (y+4)^2 - 16 + 3 = 0\) oe; allow B2 for \(r=7\) unsupported |
| *Alternatively:* \(\pm 2a = -12\) oe and \(\pm 2b = 8\) oe | M1 | |
| \(r = 7\) not from wrong working | A1 | NB \(r^2 = 6^2 + 4^2 - 3\) |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((6, -4)\) | B1 | FT \((x \pm 6)^2 + (y \pm 4)^2\); or FT \(\pm 2a = -12\) oe and \(\pm 2b = 8\) oe |
| [1] |
## Question 2(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(x \pm 6)^2$ and $(y \pm 4)^2$ | M1 | completing the square twice soi |
| $r = 7$ not from wrong working | A1 | **NB** $(x-6)^2 - 36 + (y+4)^2 - 16 + 3 = 0$ oe; allow **B2** for $r=7$ unsupported |
| *Alternatively:* $\pm 2a = -12$ oe and $\pm 2b = 8$ oe | M1 | |
| $r = 7$ not from wrong working | A1 | **NB** $r^2 = 6^2 + 4^2 - 3$ |
| **[2]** | | |
---
## Question 2(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(6, -4)$ | B1 | **FT** $(x \pm 6)^2 + (y \pm 4)^2$; or **FT** $\pm 2a = -12$ oe and $\pm 2b = 8$ oe |
| **[1]** | | |
---2 The equation of a circle is\\
$x ^ { 2 } - 12 x + y ^ { 2 } + 8 y + 3 = 0$.
\begin{enumerate}[label=(\alph*)]
\item Find the radius of the circle.
\item State the coordinates of the centre of the circle.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2023 Q2 [3]}}