| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2013 |
| Session | November |
| Topic | Circles |
| Type | Line-circle intersection points |
| Difficulty | Standard +0.3 Part (i) is routine completing the square (a standard GCSE/AS technique). Part (ii) requires substituting the completed square form into the circle equation and solving a quadratic, which is straightforward once the setup is recognized. This is a standard textbook exercise with clear structure and no novel insight required, making it slightly easier than average for A-level. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02q Use intersection points: of graphs to solve equations1.03d Circles: equation (x-a)^2+(y-b)^2=r^2 |
10 (i) Given that $10 + 4 x - x ^ { 2 } \equiv p - ( x - q ) ^ { 2 }$, show that $q = 2$ and find the value of $p$.\\
(ii) Hence find the coordinates of all the points of intersection of the curve $y = 10 + 4 x - x ^ { 2 }$ and the circle $( x - 2 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 25$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q10}}