4MA0 Higher June 2011 Paper 3 Q16

EdexcelHigherOld spec3 marksCircle Theorems

Circle centre O through A, B, C and D; angle ADB = 57 degrees and angle BCD = 106 degrees

Diagram NOT accurately drawn

\(A\), \(B\), \(C\) and \(D\) are points on a circle, centre \(O\).
Angle \(ADB = 57^\circ\).
Angle \(BCD = 106^\circ\).

(a)

(i) Calculate the size of angle \(AOB\).

(ii) Give a reason for your answer.

(2)

(b) Calculate the size of angle \(BAD\). (1)

Mark scheme (a)

Scheme	Marks
(i) 114	B1
(ii) eg angle at the centre = 2 × angle at circumference	B1
	(2)

Notes

B1: cao

B1: Three key points must be mentioned
1. Angle at centre/middle/O/origin
2. Twice, double, 2× or half/\(\frac{1}{2}\) as appropriate
3. angle at circumference/edge/perimeter (NOT e.g. angle \(D\), angle \(ADB\), angle at top, angle at outside)

Scheme	Marks
74	B1
	(1)
	(Total 3 marks)