| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2019 |
| Session | Specimen |
| Marks | 2 |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Easy -1.8 Part (a) requires only direct reading of centre and radius from completed square form with no manipulation. Part (b) is a straightforward midpoint formula application. Both are routine recall exercises with minimal problem-solving, making this significantly easier than average A-level questions. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03e Complete the square: find centre and radius of circle |
(a) Centre $(4, -7)$ — **B1**
Radius $8$ — **B1**
**Total: 2**
(b) Attempt to form midpoint — **M1**
Obtain $(8, -3)$ — **A1**
**Total: 2**1 A circle has equation $( x - 4 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 64$.
\begin{enumerate}[label=(\alph*)]
\item Write down the coordinates of the centre and the radius of the circle.
Two points, $A$ and $B$, lie on the circle and have coordinates $( 4,1 )$ and $( 12 , - 7 )$ respectively.
\item Find the coordinates of the midpoint of the chord $A B$.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2019 Q1 [2]}}