4MA0 Higher January 2015 Paper 4R Q10
10
Diagram NOT accurately drawn
In the diagram ABC and ADE are straight lines.
BD is parallel to CE.
\(AB = 9\) cm, \(BC = 13.5\) cm, \(AD = 10\) cm, \(BD = 17\) cm
(a) Calculate the length of CE. (2)
(b) Calculate the length of DE. (2)
The area of triangle ABD is 36 cm2
(c) Calculate the area of quadrilateral BDEC. (3)
| Scheme | Marks |
|---|---|
\(\dfrac{CE}{17} = \dfrac{22.5}{9}\) oe or 22.5 ÷ 9 (=2.5) or 9 ÷ 22.5 (=0.4) | M1 |
| 42.5 | A1 |
| (2) |
Notes
M1: for correct scale factor
A1: for 42.5 or \(42\dfrac{1}{2}\)
| Scheme | Marks |
|---|---|
\(\dfrac{AE}{10} = \dfrac{22.5}{9}\) \(DE = 10 \times 2.5 - 10\) or \(10 \times \dfrac{13.5}{9}\) or 10 × 1.5oe | M1 |
| 15 | A1 |
| (2) |
Notes
M1: for a complete method
A1: cao
| Scheme | Marks |
|---|---|
| \(2.5^2 \times 36\) (=225) | M1 |
| “225” – 36 | M1 |
| 189 | A1 |
| (3) | |
| (7 marks) |
Notes
M1: or for a fully correct method to find area of triangle ACE
(height of triangle ABD = 4.2(3…)
height of triangle ACE = 10.5(8…))
M1: (dep)
A1: cao