4MA0 Higher June 2014 Paper 3R Q12
12 In the diagram, \(DAPS\) and \(CBQR\) are straight lines.
\(AB\) is parallel to \(QP\) and \(DC\) is parallel to \(RS\).
\(AD = 11\) cm, \(BC = 5\) cm, \(PS = 27.5\) cm and \(RS = 42.5\) cm.
Diagram NOT accurately drawn
Quadrilateral \(ABCD\) is similar to quadrilateral \(PQRS\).
(a) Find the ratio of the length of \(AB\) to the length of \(PQ\).
Give your answer in the form \(1 : n\) (2)
Give your answer in the form \(1 : n\) (2)
(b) Work out the length of \(RQ\). (2)
(c) Work out the length of \(CD\). (2)
The area of quadrilateral \(ABCD\) is 54 cm2
(d) Work out the area of quadrilateral \(PQRS\). (2)
| Scheme | Marks |
|---|---|
| \(\frac{27.5}{11}\) or \(\frac{11}{27.5}\) | M1 |
| 2.5 | A1 |
| (2) |
Notes
A1: oe
| Scheme | Marks |
|---|---|
\(5 \times\) “2.5” or \(5 \times \frac{27.5}{11}\) or \(\frac{RQ}{5} = \frac{27.5}{11}\) oe or \(\dfrac{5}{11} = \dfrac{RQ}{27.5}\) oe | M1 |
| 12.5 | A1 |
| (2) |
Notes
M1: Correct expression for \(RQ\) or correct equation to give \(RQ\).
ft their answer to (a)
| Scheme | Marks |
|---|---|
\(42.5 \div\) “2.5” or \(42.5 \times \dfrac{11}{27.5}\) or \(42.5 \times \dfrac{5}{\text{“}12.5\text{”}}\) or \(\dfrac{CD}{42.5} = \dfrac{11}{27.5}\) or \(\dfrac{CD}{42.5} = \dfrac{5}{\text{“}12.5\text{”}}\) oe | M1 |
| 17 | A1 |
| (2) |
Notes
M1: Correct expression for \(CD\) or correct equation to give \(CD\).
ft their \(RQ\), if used.
ft their answer to (a)
| Scheme | Marks |
|---|---|
| \(54 \times (\text{“}2.5\text{”})^2\) oe or \(\dfrac{\text{Area}}{54} = \left(\dfrac{27.5}{11}\right)^2\) oe | M1 |
| 337.5 | A1 |
| (2) | |
| (8 marks) |
Notes
M1: Correct expression for area or correct equation to give area.
ft ratio from (a), if used.