Higher June 2024 Paper 6 Q18
18 The diagram shows two triangles ABC and ADC.
Not to scale
Angle ABC = 60°, angle ACB = 20° and angle ACD = 55°.
AB = 8 cm and DC = 6 cm.
Calculate length AD.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 17.5 to 17.6 with correct working | 6 | ‘Correct working’ requires evidence of at least M1M1 | |
| M2 for \(AC = \frac{8\sin 60}{\sin 20}\) or M1 for \(\frac{AC}{\sin 60} = \frac{8}{\sin 20}\) oe A1 for 20.2 to 20.3 AND | A1 implies M2 after M1 seen | ||
| M2 for \(\sqrt{\textit{their}20.3^2 + 6^2 - 2 \times \textit{their}20.3 \times 6 \times \cos 55}\) or M1 for \(\textit{their}20.3^2 + 6^2 - 2 \times \textit{their}20.3 \times 6 \times \cos 55\) | Their 20.3 or 20 from use of trig May be performed in stages | ||
| If 0, 1 or 2 scored, instead award SC3 for 17.5 to 17.6 with no working or insufficient working If 0 or 1 scored, instead award SC2 for 306.6 to 308.4 with no working or insufficient working If 0 scored, instead award SC1 for 20.2 to 20.3 with no working or insufficient working | |||