Higher November 2023 Paper 1 Q22
22 Here is a cyclic quadrilateral.
\(a : b : c = 9 : 5 : 3\)
Not drawn accurately
Work out the size of angle \(d\). [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{180}{9 + 3}\) or 15 or \(3 \times \dfrac{180}{9 + 3}\) or 45 or \(9 \times \dfrac{180}{9 + 3}\) or 135 | M1 | oe eg \(180 \times \dfrac{1}{3 + 1}\) or \(180 \div 4\) size of angle \(c\) size of angle \(a\) |
| \(5 \times \dfrac{180}{9 + 3}\) or \(5 \times 15\) or 75 or \(7 \times \dfrac{180}{9 + 3}\) or \((3 + 5 + 9) \times \dfrac{180}{9 + 3}\) or 255 | M1dep | oe size of angle \(b\) |
| 105 | A1 | |
| Alternative method 2 | ||
| \(a : b : c : d = 9 : 5 : 3 : 7\) or \(b : d = 5 : 7\) | M1 | oe implied by \(d = 7\) |
| \(\dfrac{7}{9 + 5 + 3 + 7} \times 360\) or \(\dfrac{7}{24} \times 360\) or \(\dfrac{7}{5 + 7} \times 180\) or \(\dfrac{7}{12} \times 180\) or \(7 \times 15\) | M1dep | oe allow numerator to be 5 |
| 105 | A1 | |