| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Chord length calculation |
| Difficulty | Standard +0.3 Parts (a) and (b) are routine completing-the-square exercises to find centre and radius from circle equation. Part (c) requires applying the cosine rule in triangle PQR after recognizing that PQ=10 (diameter) means angle PRQ=90°, making it a straightforward right-angled triangle calculation. This is a standard C2 circle question with no novel insight required, slightly easier than average due to the helpful hint that PQ equals the diameter. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle1.03f Circle properties: angles, chords, tangents |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | 2.1, 2.2 | 3 |
Question 6:
6 | 2.1, 2.2 | 3 | 2 | 1 | 1 | 7The circle $C$, with centre $A$, has equation
$$x^2 + y^2 - 6x + 4y - 12 = 0.$$
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of $A$. [2]
\item Show that the radius of $C$ is 5. [2]
\end{enumerate}
The points $P$, $Q$ and $R$ lie on $C$. The length of $PQ$ is 10 and the length of $PR$ is 3.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the length of $QR$, giving your answer to 1 decimal place. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q6 [7]}}