| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2016 |
| Session | Specimen |
| Marks | 4 |
| Topic | Circles |
| Type | Find centre and radius from equation |
| Difficulty | Easy -1.8 Part (i) requires only direct reading of centre and radius from completed square form with no manipulation. Part (ii) 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 |
**Question 1(i)**
- Centre $(4, -7)$ — B1
- Radius $8$ — B1
**Question 1(ii)**
- Attempt to form midpoint — M1
- Obtain $(8, -3)$ — A1
**Total: 4 marks**1 A circle has equation $( x - 4 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 64$.\\
(i) 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.\\
(ii) Find the coordinates of the midpoint of the chord $A B$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2016 Q1 [4]}}