Higher June 2025 Paper 2 Q23
23 \(ABCD\) is a quadrilateral.
Find the size of angle \(ABC\).
Give your answer correct to the nearest degree. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 73 | P1 | for process to work with cosine eg \((DB^2 =)\ 12^2 + 9^2 - 2 \times 12 \times 9 \times \cos 60\ (= 117)\) |
| P1 | for a correct order of operations to find DB, eg \(\sqrt{225 - 216 \times \cos 60}\) or \(\sqrt{\text{``}117\text{''}}\ (= 10.8\ldots)\) | |
| P1 | for working with sine rule and \(60^\circ\) eg \(\dfrac{\sin CBD}{9} = \dfrac{\sin 60}{[DB]}\) or \(\sin CBD = 0.720\ldots\) or \(CBD = 46.10\ldots\) | |
| P1 | for working with sine rule and \(125^\circ\) eg \(\dfrac{\sin ABD}{6} = \dfrac{\sin 125}{[DB]}\) or \(\sin ABD = 0.454\ldots\) or \(ABD = 27.02\ldots\) | |
| A1 | for answer within the range 72.5 to 73.5 |
Additional guidance
\(\sqrt{117} = 3\sqrt{13}\)
Can be implied by correct use in subsequent calculations
3rd and 4th P1 can be awarded in any order
[\(DB\)] must be clearly identified but may not be correct, but cannot be 6 or 9 or 12
\(CBD\) and \(ABD\) may be given as a variable, award marks unless contradicted