| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2021 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Circle equation from centre and radius |
| Difficulty | Easy -1.2 This is a straightforward conversion from parametric to Cartesian form using the identity cos²θ + sin²θ = 1, followed by reading off the centre from the standard form. Both parts require only direct application of standard techniques with no problem-solving or insight needed, making it easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03g Parametric equations: of curves and conversion to cartesian |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((x-7)^2 + (y+3)^2 = 5^2\cos^2\theta + 5^2\sin^2\theta\) oe | M1 | allow sign error |
| Use of \(\cos^2\theta + \sin^2\theta = 1\) to eliminate \(\theta\) | M1 | |
| *Alternative:* centre is \((7, -3)\) and substituted in correct form of equation | M1 | |
| radius is \(5\) and substituted in correct form of equation | M1 | |
| \((x-7)^2 + (y+3)^2 = 5^2\) oe isw | A1 | if M0M0 allow SC1 for \(y = 5\sin\{\cos^{-1}\left(\frac{x-7}{5}\right)\} - 3\) or \(x = 5\cos\{\sin^{-1}\left(\frac{y+3}{5}\right)\} + 7\) |
| [3] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((7, -3)\) | B1 | FT their \((x-7)^2 + (y+3)^2 = 25\) |
| [1] |
## Question 7(a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(x-7)^2 + (y+3)^2 = 5^2\cos^2\theta + 5^2\sin^2\theta$ **oe** | M1 | allow sign error |
| Use of $\cos^2\theta + \sin^2\theta = 1$ to eliminate $\theta$ | M1 | |
| *Alternative:* centre is $(7, -3)$ and substituted in correct form of equation | M1 | |
| radius is $5$ and substituted in correct form of equation | M1 | |
| $(x-7)^2 + (y+3)^2 = 5^2$ **oe isw** | A1 | if **M0M0** allow **SC1** for $y = 5\sin\{\cos^{-1}\left(\frac{x-7}{5}\right)\} - 3$ or $x = 5\cos\{\sin^{-1}\left(\frac{y+3}{5}\right)\} + 7$ |
| | **[3]** | |
---
## Question 7(b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(7, -3)$ | B1 | FT their $(x-7)^2 + (y+3)^2 = 25$ |
| | **[1]** | |
---7 The parametric equations of a circle are\\
$x = 7 + 5 \cos \theta , \quad y = 5 \sin \theta - 3$, for $0 \leqslant \theta \leqslant 2 \pi$.
\begin{enumerate}[label=(\alph*)]
\item Find a cartesian equation of the circle.
\item State the coordinates of the centre of the circle.
Answer all the questions.\\
Section B (77 marks)
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2021 Q7 [4]}}