| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 4 |
| Topic | Circles |
| Type | Circle from diameter endpoints |
| Difficulty | Moderate -0.3 This is a straightforward application of the diameter property (angle in semicircle = 90°) requiring students to use perpendicular gradients. The setup is clear, requiring calculation of two gradients and solving a simple equation. While it involves multiple steps, each is routine and the problem type is standard in circle geometry, making it slightly easier than average. |
| Spec | 1.03d Circles: equation (x-a)^2+(y-b)^2=r^21.03f Circle properties: angles, chords, tangents |
13. The point $P ( p , 0 )$, the point $Q ( - 2,10 )$ and the point $R ( 8 , - 14 )$ lie on a circle, $C _ { 2 }$
Given that
\begin{itemize}
\item $p$ is a positive constant
\item $Q R$ is a diameter of $C _ { 2 }$\\
find the exact value of $p$.\\
(4)\\
(Total for Question 13 is 4 marks)
\end{itemize}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q13 [4]}}