4MA0 Foundation June 2012 Paper 1 Q15
15
Diagram NOT accurately drawn
Triangle \(PQR\) is an enlargement, centre \(O\), of triangle \(ABC\).
\(OAP\) and \(OCR\) are straight lines.
\(OA = 3\) cm.
\(AP = 12\) cm.
\(OC = 3.5\) cm.
\(PR = 19\) cm.
Angle \(Q = 125^\circ\)
(a) Find the size of angle \(B\). (1)
(b) Work out the length of \(CR\). (2)
(c) Work out the length of \(AC\). (3)
| Scheme | Marks |
|---|---|
| 125 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| \(\dfrac{12}{3} \times 3.5\) or \(\dfrac{15}{3} \times 3.5 - 3.5\) | M1 |
| 14 | A1 |
| (2) |
Notes
M1: for \(\dfrac{12}{3}\) or 4 or \(\dfrac{15}{3}\) or 5
A1: cao
| Scheme | Marks |
|---|---|
| scale factor = \(\dfrac{15}{3}\) or 5 or \(\dfrac{3}{15}\) or \(\dfrac{1}{5}\) | M1 |
| 19 ÷ 5 or \(19 \times \dfrac{1}{5}\) | M1 |
| 3.8 | A1 |
| (3) | |
| (Total 6 marks) |
Notes
M1: for \(\dfrac{15}{3}\) or 5 or \(\dfrac{3}{15}\) or \(\dfrac{1}{5}\)
M1: Also award for 19 ÷ 4 or \(19 \times \dfrac{1}{4}\)
May be implied by 4.75
A1: cao