1MA0 Higher November 2014 Paper 2 Q16
16 The diagram represents a metal frame.
Diagram NOT accurately drawn
The frame is made from four metal bars, \(AB\), \(AC\), \(BC\) and \(BD\).
Angle \(ABC\) = angle \(ADB = 90^\circ\)
\(AB = 5\) m
\(BC = 3\) m
Work out the total length of the four metal bars of the frame.
Give your answer correct to 3 significant figures. (5)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(AC^2 = 5^2 + 3^2\) \(AC = \sqrt{25 + 9}\) (=5.83) \(\dfrac{5}{5.83} = \dfrac{DB}{3}\) \(DB = \dfrac{5}{5.83} \times 3\) (= 2.57) \(5 + 3 + 5.83 + 2.57 =\) OR \(AC = \sqrt{25 + 9}\) (=5.83) \(\tan A = \dfrac{3}{5}\) \(A = 30.96\) \(\sin 30.96 = \dfrac{DB}{5}\) \(DB = 5 \times \sin 30.96\) (= 2.57) \(5 + 3 + 5.83 + 2.57 =\) | 16.4 | 5 | M1 for \((AC^2) = 5^2 + 3^2\) (=34) M1 for \(\sqrt{25 + 9}\) or \(\sqrt{34}\) (=5.83) M1 for \(\dfrac{5}{\text{'}5.83'} = \dfrac{DB}{3}\) or \(DB \times AC = 5 \times 3\) M1 for \((DB =)\ \dfrac{5}{\text{'}5.83'} \times 3\) A1 for 16.4 to 16.41 OR M1 for \((AC^2) = 5^2 + 3^2\) (=34) M1 for \(\sqrt{25 + 9}\) or \(\sqrt{34}\) (=5.83) M1 for using a correct trig ratio in an attempt to find angle \(A\) or angle \(C\), e.g. \(\tan A = \dfrac{3}{5}\), \(\sin A = \dfrac{3}{\text{'}5.83'}\), \(\cos C = \dfrac{3}{\text{'}5.83'}\) M1 for using \(DB\) in a a correct trig ratio, e.g. \(\sin \text{'}30.96\text{'} = \dfrac{DB}{5}\) A1 for 16.4 to 16.41 |