Higher June 2023 Paper 2 Q14
14
Diagram NOT accurately drawn
\(P\), \(Q\), \(R\) and \(S\) are points on a circle, centre \(O\)
\(ROP\) is a diameter of the circle.
Angle \(PRQ = 22^\circ\)
(a)
(i) Find the size of angle \(RQP\) (1)
(ii) Give a reason for your answer. (1)
(b)
(i) Find the size of angle \(PSQ\) (1)
(ii) Give a reason for your answer. (1)
| Scheme | Marks |
|---|---|
| (i) Answer: 90 | B1 |
| (ii) Answer: Angle in a semicircle is 90° oe Angle in a semicircle is 90° oe Triangle in semicircle is 90° oe Angle at centre is double (oe eg ×2) angle at circumference oe Angle at circumference is half (oe) angle at centre. oe | B1 |
| (2) |
Notes
B1: dep on B1 in (a)(i)
Valid reason given, underlined words give minimally acceptable answer.
| Scheme | Marks |
|---|---|
| (i) Answer: 22 | B1 |
| (ii) Answer: Angles in the same segment (are equal) or angles at the circumference subtended from the same arc of the circle or angles on the same chord | B1 |
| (2) | |
| (4 marks) |
Notes
B1: dep on B1 in (b)(i)
Valid reason given, underlined words give minimally acceptable answer.