Higher November 2021 Paper 4 Q17
17 The diagram shows triangle ABC.
Not to scale
AC = 48 mm, BC = 85 mm and angle BAC = 53°.
Calculate length AB.
You must show your working. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 105 or 104.7 to 104.82 | 6 | M2 for \(\dfrac{48 \times \sin 53}{85}\) oe implied by 26.8… or M1 for \(\dfrac{\sin 53}{85} = \dfrac{\sin[B]}{48}\) oe M1 for [C=] 180 − 53 − their 26.807… or 100.19[…] M2 for \(\dfrac{85 \times \sin \textit{their} C}{\sin 53}\) oe or M1 for \(\dfrac{[AB]}{\sin \textit{their} C} = \dfrac{85}{\sin 53}\) oe | “Correct working” requires evidence of at least M2 or M1M1 |
| Alternative method cosine rule (AB = \(x\)) M3 for quadratic with coefficients evaluated or M2 for \(x^2 + (-2 \times 48 \times \cos 53)x + (48^2 - 85^2)\) [=0] oe or M1 for \(85^2 = x^2 + 48^2 - 2 \times x \times 48\cos 53\) AND M2 for correct use of quadratic formula or M1 for quadratic formula with at most one error | i.e. \(x^2 - 57.77\ldots x - 4921\) [= 0] oe | ||
| If 0 scored SC2 for 105 or 104.7 to 104.82 with no working or SC1 for 26.8… with no working | |||