Higher November 2024 Paper 2 Q23
23
(a) 
Not drawn accurately
Line \(DAE\) is a tangent at \(A\) to the circle with centre \(O\).
Work out the size of angle \(x\). [2 marks]
(b) Here is a cyclic quadrilateral.
Not drawn accurately
\(f : g = 2 : 3\)
Work out \(\quad f : h\)
Give your answer in its simplest form. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| angle \(ACB = 53\) | M1 | may be seen on diagram |
| 106 | A1 | |
| Alternative method 2 | ||
| angle \(OAB = 90 - 53\) or 37 or angle \(OBA = 90 - 53\) or 37 | M1 | may be seen on diagram |
| 106 | A1 | |
Additional guidance
Accept eg \(\widehat{ACB}\) for angle \(ACB\)
Accept (angle) \(C\) for angle \(ACB\)
Do not accept eg (angle) \(A\) for angle \(OAB\) unless shown on the diagram
Ignore reasons
| Answer | Mark | Comments |
|---|---|---|
| \(g = 180 - 63\) or 117 | M1 | may be seen on diagram |
| \(f =\) their \(117 \div 3 \times 2\) or 78 | M1dep | oe may be seen on diagram |
| \(h = 180 -\) their 78 or 102 | M1dep | may be seen on diagram equivalent ratios to 13 : 17 implies M3 |
| 13 : 17 | A1 | accept \(1 : \dfrac{17}{13}\) or \(\dfrac{13}{17} : 1\) |
Additional guidance
Up to M3 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts
Ignore reasons