| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2022 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circles |
| Type | Line-circle intersection points |
| Difficulty | Standard +0.3 This is a standard multi-part circle geometry question requiring completing the square, solving simultaneous equations with a line and circle, finding perpendicular distances, and calculating a segment area. All techniques are routine for AS-level, though the multi-step nature and segment area calculation elevate it slightly above average difficulty. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
A circle $C$ has centre $A$ and equation $x^2 + y^2 - 4x - 6y = 3$.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of $A$ and the radius of $C$. [3]
\end{enumerate}
The line $L$ with equation $y = x + 5$ intersects $C$ at the points $P$ and $Q$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Determine the coordinates of $P$ and $Q$. [4]
\item The point $B$ is on $PQ$ and is such that $AB$ is perpendicular to $PQ$. Find the length of $PB$. [2]
\item Show that the area of the smaller segment enclosed by $C$ and $L$ is $4\pi - 8$. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2022 Q7 [11]}}