4MA0 Foundation January 2015 Paper 1 Q21
21
Diagram NOT accurately drawn
\(ABC\) is a triangle.
The point \(D\) lies on \(AC\).
Angle \(BDC = 90^\circ\)
\(BD = 10\) cm, \(AB = 15\) cm and \(DC = 12.5\) cm.
(a) Calculate the length of \(AD\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
(b) Calculate the size of angle \(BCD\).
Give your answer correct to 1 decimal place. (3)
Give your answer correct to 1 decimal place. (3)
| Scheme | Marks |
|---|---|
| \(15^2 - 10^2\) or 225 – 100 or 125 | M1 |
| \(\sqrt{\text{“}125\text{”}}\) or \(5\sqrt{5}\) | M1 |
| 11.2 | A1 |
| (3) |
Notes
M1: M2 for any complete and correct method
M1: dep on M1
A1: awrt 11.2
| Scheme | Marks |
|---|---|
| \(\tan C = \dfrac{10}{12.5}\) or \(\tan C = 0.8\) | M1 |
| \(\tan^{-1}\left(\dfrac{10}{12.5}\right)\) oe | M1 |
| 38.7 | A1 |
| (3) | |
| (6 marks) |
Notes
M1: M2 for any complete and correct method
A1: Accept 38.6(5980825.....) rounded or truncated to at least 3 SF.