| Exam Board | OCR |
|---|---|
| Module | AS Pure (AS Pure Mathematics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 5 |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.8 This is a straightforward two-part question requiring only standard techniques: midpoint formula for the centre, and perpendicular gradient for the tangent. Both are routine AS-level procedures with no problem-solving or geometric insight required, making it easier than average. |
| Spec | 1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.03d Circles: equation (x-a)^2+(y-b)^2=r^21.07m Tangents and normals: gradient and equations |
2 Points $A$ and $B$ have coordinates $( 3,0 )$ and $( 9,8 )$ respectively. The line $A B$ is a diameter of a circle.
\begin{enumerate}[label=(\alph*)]
\item Find the coordinates of the centre of the circle.
\item Find the equation of the tangent to the circle at the point $B$.
\end{enumerate}
\hfill \mbox{\textit{OCR AS Pure 2017 Q2 [5]}}