Foundation June 2018 Paper 2 Q9
9 \(R\) and \(S\) are points on a circle with centre \(O\).
(a) On the diagram above, shade a segment of the circle. (1)
(b) Write down the mathematical name of the straight line \(RS\). (1)
In the diagram below, \(P\) and \(Q\) are points on a circle with centre \(O\).
Diagram NOT accurately drawn
\(QT\) is a tangent to the circle.
Angle \(OPQ\) = 18°
(c) Work out the size of angle \(PQT\).
Give a reason for each stage of your working. (3)
Give a reason for each stage of your working. (3)
| Scheme | Marks |
|---|---|
| Segment shaded | B1 |
| (1) |
Notes
B1: Accept minor segment or major segment.
| Scheme | Marks |
|---|---|
| Chord | B1 |
| (1) |
| Scheme | Marks |
|---|---|
| \(\angle OQT = 90^\circ\) and \(\angle OQP = 18^\circ\) or 90 – 18 | M1 |
| 72 | A1 |
| Angle between tangent and radius is 90 degrees | B1 |
| (3) | |
| (5 marks) |
Notes
M1: For 90° and 18° correctly identified in the working or on the diagram or for 90 – 18 or for other fully correct method
B1: Correct reason for 90° angle
[If used alternate segment theorem]
Note: the printed mark scheme gives the second angle as \(\angle OQT = 18^\circ\); it is angle \(OQP\) that is 18°.