4MA0 Higher January 2017 Paper 4R Q14
14 \(ABCDE\) and \(AWXYZ\) are two mathematically similar pentagons.
Diagram NOT accurately drawn
\(AE = 4\) cm \(WX = 6\) cm \(DE = 5\) cm \(YZ = 8\) cm
(a) Calculate the length of \(AZ\). (2)
(b) Calculate the length of \(BC\). (2)
The area of pentagon \(AWXYZ\) is 52.48 cm\(^2\)
(c) Calculate the area of the shaded region. (3)
| Scheme | Marks |
|---|---|
e.g. \(\dfrac{8}{5}\) or 1.6 or \(\dfrac{5}{8}\) or 0.625 or e.g. \(4 \times \dfrac{8}{5}\) or \(4 \div \dfrac{5}{8}\) oe or e.g. \(\dfrac{AZ}{4} = \dfrac{8}{5}\) or \(\dfrac{AZ}{8} = \dfrac{4}{5}\) oe | M1 |
| 6.4 | A1 |
| (2) |
Notes
M1: For correct scale factor or correct expression for \(AZ\) or for a correct equation involving \(AZ\) oe
A1: oe e.g. \(\dfrac{32}{5}\)
| Scheme | Marks |
|---|---|
| Eg \(6 \div \dfrac{8}{5}\) or \(6 \times \dfrac{5}{8}\) or \(\dfrac{6 \times 4}{\text{“}6.4\text{”}}\) oe | M1 |
| 3.75 | A1 |
| (2) |
Notes
M1: Correct expression for \(BC\)
A1: oe
| Scheme | Marks |
|---|---|
| \(52.48 - \dfrac{52.48}{1.6^2}\) | M2 |
| 31.98 | A1 |
| (3) | |
| (7 marks) |
Notes
M2: For a fully correct method or
M1 for \(\dfrac{52.48}{1.6^2}\) or 20.5
A1: Accept 32.0 or 32