Higher November 2024 Paper 6 Q21
21 The diagram shows a cuboid ABCDEFGH.
Not to scale
FB = 15 cm, GF = 7 cm and HG = 24 cm.
Calculate the angle BHF.
You must show your working. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 30.9 to 31 with correct working | 5 | M2 for \(\sqrt{(24^2 + 7^2)}\) or M1 for \([\ldots]^2 = 24^2 + 7^2\) and M2 for \(\tan^{-1} \frac{15}{\textit{their } 25}\) oe or M1 for \(\tan(\text{BHF}) = \frac{15}{\textit{their } 25}\) oe | Correct working requires evidence of at least M1M1 Alternative method: M2 for \(\sqrt{(24^2 + 7^2 + 15^2)}\) or M1 for \([\ldots]^2 = 24^2 + 7^2 + 15^2\) and M2 for \(\sin^{-1} \frac{15}{\textit{their } \sqrt{850}}\) oe or M1 for \(\sin(\text{BHF}) = \frac{15}{\textit{their } \sqrt{850}}\) oe Other methods: M2 for a correct expression that would give correct HF or HB or M1 for “one-step away” eg \(\sin\left(\tan^{-1}\left(\frac{7}{24}\right)\right) = \frac{7}{\text{HF}}\) and M2 for correct trig inverse expression with angle BHF or M1 for correct trig expression with angle BHF |
| If 0 or 1 scored, instead award SC2 for answer 30.9 to 31 with no or insufficient working If 0 scored, instead award SC1 for [HF =] 25 or for [HB =] \(\sqrt{850}\) oe or 29.1 to 29.2 | May be on diagram | ||