4MA0 Higher January 2018 Paper 4R Q15
15
Diagram NOT accurately drawn
\(B\), \(C\), \(D\) and \(E\) are points on a circle.
\(ABC\) and \(AED\) are straight lines.
\(AB = 8\) cm, \(AE = 6\) cm and \(ED = 5\) cm.
Angle \(BAE = 25^\circ\)
(a) Calculate the length of \(BD\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
(b) Calculate the length of \(AC\). (2)
| Scheme | Marks |
|---|---|
| \((BD^2 =)\;8^2 + (6 + 5)^2 - 2 \times 8 \times (6 + 5) \times \cos 25\) | M1 |
\((BD^2 =)\;64 + 121 - 159(.510...)\) or 25.4(898...) or \((BD =)\sqrt{64 + 121 - 159(.510...)}\) | M1 |
| 5.05 | A1 |
| (3) |
Notes
M1: For the correct use of Cosine rule
M1: For correct order of operations
A1: Accept 5.04(8745...) rounded or truncated to at least 3SF
| Scheme | Marks |
|---|---|
Eg \(AC \times 8 = (6 + 5) \times 6\) or \((AC =)\;\dfrac{(6 + 5) \times 6}{8}\) or \(\dfrac{11 \times 6}{8}\) oe \((8 + BC) \times 8 = (6 + 5) \times 6\) oe | M1 |
| 8.25 oe | A1 |
| (2) | |
| (5 marks) |
Notes
M1: For a correct equation involving \(AC\) or \(BC\)
A1: Eg \(\dfrac{66}{8}\) or \(\dfrac{33}{4}\)