June 2023 Paper 2 Q21
21 \(A\), \(B\), \(C\), \(D\) and \(E\) are points on a circle, centre \(O\).
Not drawn accurately
Work out the value of \(x\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| angle \(AOD = 12x - (180 - 4x)\) or angle \(AOD = 16x - 180\) or angle \(BOD = 14x - (180 - 4x)\) or angle \(BOD = 18x - 180\) or angle \(AOB = 180 - 4x\) and angle \(BOD = 360 - 12x\) and angle \(AOD = 360 - 14x\) or angle \(AOB = 180 - 4x\) and reflex angle \(BOD = 12x\) and reflex angle \(AOD = 14x\) | B2 | oe B1 angle \(AOB = 180 - 2x - 2x\) or angle \(AOB = 180 - 4x\) or reflex angle \(BOD = 12x\) or angle \(BOD = 360 - 12x\) or reflex angle \(AOD = 14x\) or angle \(AOD = 360 - 14x\) all angles for B2 or B1 may be seen on diagram |
| \(14x + 12x - (180 - 4x) = 360\) or \(14x + 16x - 180 = 360\) or \(12x + 18x - 180 = 360\) | M1 | oe equation eg \(180 - 4x + 16x - 180 + 18x - 180 = 360\) or \(180 - 4x + 360 - 12x + 360 - 14x = 360\) |
| 18 | A1 |
Additional guidance
| Up to B2 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| An equation scoring M1 implies B2 | |
| Incorrect use of obtuse/acute must be recovered | |
| Missing brackets must be recovered | |
| Condone eg angle \(BOD = 12x\) if marked as reflex angle \(BOD = 12x\) on diagram | B1 |
| NOTE 18 may be seen from incorrect working eg (interior angle of regular pentagon =) \(540 \div 5 = 108\) \(108 \div 6 = 18 \qquad\) (no other correct working seen) | B0M0A0 |