4400 Higher June 2010 Paper 3 Q13
13
Diagram NOT accurately drawn
\(P\), \(Q\), \(R\) and \(S\) are points on a circle, centre \(C\).
\(PCR\) is a straight line.
Angle \(PRS = 36^\circ\).
Calculate the size of angle \(RQS\).
Give a reason for each step in your working.
(4)
There are 4 independent requirements to consider when marking this question but the order in which they are satisfied will vary. Focus on these 4 key points, ignoring irrelevant or incorrect statements.
| Scheme | Marks |
|---|---|
| \(\angle PQS = 36^\circ\) or \(\angle SPR = 54^\circ\) | B1 |
| angles in the same segment | B1 |
| \(\angle PQR = 90^\circ\) or \(\angle PSR = 90^\circ\) and angle in a semicircle is a right angle | B1 |
| 54 | B1 |
| (4) | |
| (4 marks) |
Notes
B1: May be stated or marked on diagram
B1: Award if ‘same segment’, ‘same arc’, or ‘same chord’
B1: Angle may be stated or marked on diagram.
Condone omission of ‘is a right angle’ oe.
B1: cao