1MA0 Higher June 2014 Paper 2 Q15
15 The diagram shows the positions of three turbines \(A\), \(B\) and \(C\).
Diagram NOT accurately drawn
\(A\) is 6 km due north of turbine \(B\).
\(C\) is 4.5 km due west of turbine \(B\).
(a) Calculate the distance \(AC\). (3)
(b) Calculate the bearing of \(C\) from \(A\).
Give your answer correct to the nearest degree. (4)
Give your answer correct to the nearest degree. (4)
| Answer | Mark | Notes |
|---|---|---|
| 7.5 | 3 | M1 for \(4.5^2 + 6^2\) (=56.25) M1 for \(\sqrt{56.25}\) or \(\sqrt{4.5^2 + 6^2}\) A1 for 7.5 |
| Answer | Mark | Notes |
|---|---|---|
| 217 | 4 | M1 for use of appropriate trig ratio eg \(\tan CAB = \dfrac{4.5}{6}\) (= 0.75), \(\sin CAB = \dfrac{4.5}{\text{``}7.5\text{''}}\) (= 0.6), \(\cos CAB = \dfrac{6}{\text{``}7.5\text{''}}\) (= 0.8) M1 for inverse trig shown correctly eg \(CAB = \tan^{-1} \dfrac{4.5}{6}\) (= 0.75), \(CAB = \sin^{-1} \dfrac{4.5}{\text{``}7.5\text{''}}\) (= 0.6), \(CAB = \cos^{-1} \dfrac{6}{\text{``}7.5\text{''}}\) (= 0.8) A1 for 36.8 to 37 (or 53 to 53.2 if identified as \(ACB\)) B1ft for bearing 180 + “36.8” if “36.8” is not 40-50 eg 216.8 to 217 |