Higher June 2023 Paper 2 Q7
7
Diagram NOT accurately drawn
\(A\) and \(C\) are points on a circle, centre \(O\)
\(DA\) is the tangent to the circle at \(A\) and \(DC\) is the tangent to the circle at \(C\)
Angle \(ADC = 48^\circ\)
Work out the size of reflex angle \(AOC\)
(3)
| Scheme | Marks |
|---|---|
| \(DCO\) = 90 (or right (angle)) or \(DAO\) = 90 (or right (angle)) Could also be awarded for \(CAO + CAD = 90\) or \(DAC + CAO = 90\) | M1 |
| Obtuse \(AOC\) = 360 – 90 – 90 – 48 (= 132)oe or Obtuse \(AOC\) = 2(180 – (0.5 × 48) – 90) (= 132) or Obtuse \(AOC\) = 180 – “24” – “24” or 180 – 48 (if working with \(\triangle DAC\) and \(\triangle OAC\)) or Reflex \(AOC\) = 90 + 90 + 48 | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 228 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: may be marked on diagram – also allow right angle ’square’ symbol on diagram
M1: dep on M1 being awarded may be marked on diagram
A1: SC if no other marks awarded 132 gains B1
M2 implied by 360 – 90 – 90 – 48 or 360 – 228