4MA0 Higher January 2014 Paper 3R Q12
12
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.
(a) Work out the length of \(OB\). (2)
(b) Work out the length of \(PR\). (3)
The area of triangle \(PQR\) is 72 cm2
(c) Work out the area of triangle \(ABC\). (2)
| Scheme | Marks |
|---|---|
| \(7.2 \times \dfrac{2}{6}\) 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) |
Notes
M1: for \(\dfrac{8}{2}\) or 4 or \(\dfrac{2}{8}\) or \(\dfrac{1}{4}\)
M1: (dep)
A1: Cao
SC: M1 for answer of 11.1
| Scheme | Marks |
|---|---|
| \(4^2\) or \((8 \div 2)^2\) or \((2 \div 8)^2\) or \((1 \div 4)^2\) | M1 |
| 4.5oe | A1 |
| (2) | |
| (7 marks) |
Notes
M1: or for complete correct method of finding vert ht (\(h\) cm) of \(\Delta PQR\) and vert ht (\(H\) cm) of \(\Delta ABC\)
eg \(\frac{1}{2} \times \text{“}14.8\text{”} \times h = 72\)
\(h = \dfrac{144}{\text{“}14.8\text{”}}\) (9.7297...)
\(H = \dfrac{144}{\text{“}14.8\text{”}} \div \text{“}4\text{”}\) (2.4324...)
A1: SC : M1 for an answer of 8