4400 Higher November 2007 Paper 4 Q15
15
Diagram NOT accurately drawn
\(AB\) is parallel to \(DE\).
The lines \(AE\) and \(BD\) intersect at the point \(C\).
\(AB = 15\) cm, \(AC = 12.3\) cm, \(CD = 6.8\) cm, \(DE = 10\) cm.
(a) Work out the length of \(BC\). (2)
(b) Work out the length of \(CE\). (2)
(c) \(\dfrac{\text{Area of triangle } ABC}{\text{Area of triangle } CDE} = k\)
Work out the value of \(k\). (2)
Work out the value of \(k\). (2)
| Scheme | Marks |
|---|---|
| \(6.8 \times \dfrac{15}{10}\) | M1 |
| 10.2 | A1 |
| (2) |
Notes
A1: cao
| Scheme | Marks |
|---|---|
| \(12.3 \times \dfrac{10}{15}\) | M1 |
| 8.2 | A1 |
| (2) |
Notes
A1: cao
| Scheme | Marks |
|---|---|
| \(\dfrac{15}{10}\) or 1.5 oe | M1 |
| 2.25 oe | A1 |
| (2) | |
| (6 marks) |
Notes
M1: for \(\dfrac{15}{10}\) or 1.5 oe
or for \(\left(\dfrac{10}{15}\right)^2\) or \(\dfrac{4}{9}\) or \(0.\dot{4}\) oe
or for correct expression which, if accurately evaluated, gives the correct answer
or for the area of one of the triangles evaluated correctly
Area \(\triangle ABC\) rounds to 62.3 (62.2700...) NOT 62.73
Area \(\triangle CDE\) rounds to 27.7 (27.6755...) NOT 27.88
Note: the angles of the triangle are 42.5°, 54.5° and 83.1°.
A1: for 2.25 or \(2\frac{1}{4}\) or \(\frac{9}{4}\)
or for answer rounding to 2.25
Even if M1 awarded, do not award A1 for a correct answer, if there are any errors in the working.