4MA0 Higher June 2012 Paper 3 Q11
11
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.
(a) Work out the length of \(CR\). (2)
(b) Work out the length of \(AC\). (3)
The area of triangle \(ABC\) is 2 cm\(^2\)
(c) Work out the area of triangle \(PQR\). (2)
| 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
Apart from Questions 9, 13, 18, 20 and 21 (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| 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) |
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
| Scheme | Marks |
|---|---|
| “5”\(^2\) or “25” | M1 |
| 50 | A1 |
| (2) | |
| (Total 7 marks) |
Notes
M1: for squaring their scale factor
(must be one of 5, 4, \(\frac{1}{5}\), \(\frac{1}{4}\))
or for \(\left(\dfrac{19}{3.8}\right)^2\) oe
or for complete correct method of finding vert ht (\(h\) cm) of \(\Delta ABC\) and vert ht (\(H\) cm) of \(\Delta PQR\)
eg \(\frac{1}{2} \times \text{“}3.8\text{”} \times h = 2\)
\(h = \dfrac{4}{\text{“}3.8\text{”}}\) (1.0526...)
\(H = \dfrac{4}{\text{“}3.8\text{”}} \times \text{“}5\text{”}\) (5.2631...)
A1: for 50
or for answer which rounds to 50.0
ft only from their scale factor of 4
ie if M1 scored for \(4^2\) or 16, award A1 for an answer of 32