4MA0 Foundation January 2014 Paper 1R Q17
17
Diagram NOT accurately drawn
Triangle \(PQR\) is an enlargement, centre \(O\), of triangle \(ABC\).
\(OAP\) and \(OBQ\) are straight lines.
\(OA = 2\) cm.
\(AP = 6\) cm.
\(BQ = 7.2\) cm.
\(AC = 3.7\) cm.
Angle \(C = 36^\circ\)
(a) Find the size of angle \(R\). (1)
(b) Work out the length of \(OB\). (2)
(c) Work out the length of \(PR\). (3)
| Scheme | Marks |
|---|---|
| 36 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| \(\dfrac{7.2 \times 2}{6}\) or \(7.2 \div \dfrac{6}{2}\) | M1 |
| 2.4 | A1 |
| (2) |
Notes
A1: cao
| Scheme | Marks |
|---|---|
| scale factor = \(\dfrac{8}{2}\) or 4 or \(\dfrac{2}{8}\) or \(\dfrac{1}{4}\) | M1 |
| \(3.7 \times 4\) or \(3.7 \div \dfrac{1}{4}\) | M1 |
| 14.8 | A1 |
| (3) | |
| (Total 6 marks) |
Notes
M1: for \(\dfrac{8}{2}\) or 4 or \(\dfrac{2}{8}\) or \(\dfrac{1}{4}\)
M1: Also award for \(3.7 \times 3\) or \(3.7 \div \dfrac{1}{3}\)
May be implied by 11.1
A1: cao