4MA0 Higher January 2012 Paper 3 Q12
12 \(ABCD\) and \(APQR\) are two similar quadrilaterals.
\(PQ\) = 9 cm.
\(BC\) = 6 cm.
\(AD\) = 5 cm.
\(QR\) = 12 cm.
Diagram NOT accurately drawn
(a) Find the length of \(DC\). (2)
(b) Find the length of \(AR\). (2)
The area of the quadrilateral \(ABCD\) is 32 cm\(^2\).
(c) Calculate the area of the shaded region. (3)
| Scheme | Marks |
|---|---|
| 6/9 × 12 oe | M1 |
| 8 | A1 |
| (2) |
Notes
M1: e.g 12 ÷ 1.5
| Scheme | Marks |
|---|---|
| 9/6 (or 12/“8”) × 5 | M1 |
| 7.5 | A1 cao |
| (2) |
| Scheme | Marks |
|---|---|
| \(1.5^2 \times 32\) (=72) oe | M1 |
| “72” − 32 | M1 dep |
| 40 | A1 |
| (3) | |
| (Total 7 marks) |
Notes
M1: M1 for \(1.5^2\) or \((2/3)^2\)