Higher June 2019 Paper 2R Q15
15 \(A\), \(B\), \(C\) and \(D\) are points on a circle, centre \(O\).
Diagram NOT accurately drawn
\(AOC\) is a diameter of the circle.
Angle \(AOD = 98°\)
Work out the size of angle \(DBC\).
Give a reason for each stage in your working.
(4)
| Scheme | Marks |
|---|---|
| \(ABD = 98° \div 2\) (= 49°) or \(ABC = 90°\) | M1 |
| Angle at centre / middle is twice angle at circumference | B1 |
| Angle in a semicircle / from a diameter is 90° / right angle | B1 |
| \(DBC = (90 - 49) = 41\) Answer: 41° | A1 |
| (4) | |
| (4 marks) |
Notes
M1: Correct angle stated or seen on diagram
B1: Dep M1
B1: Dep M1
A1: Correct answer + no reasons = M1A1
| Scheme | Marks |
|---|---|
| 180 – 98 (= 82°) \(OAD = 82 \div 2\) (= 41°) | M1 |
| Base / bottom angles in an isosceles triangle are equal | B1 |
| \(DBC = 41°\) Angles in the same segment / from the same chord (\(DC\)) are equal | B1 |
| 41° | A1 |
Notes
M1: Correct angle stated or seen on diagram
B1: Dep M1
B1: Dep M1
A1: Correct answer + no reasons = M1A1
| Scheme | Marks |
|---|---|
| \(DOC = 180 - 98\) (= 82°) | M1 |
| Angles on a straight line = 180° | B1 |
| \(DBC = 41°\) Angle at centre / middle is twice angle at circumference | B1 |
| 41° | A1 |
Notes
M1: Correct angle stated or seen on diagram
B1: Dep M1
B1: Dep M1
A1: Correct answer + no reasons = M1A1