4MA0 Higher June 2016 Paper 3R Q17
17
Diagram NOT accurately drawn
Triangle \(ABE\) is similar to triangle \(ACD\).
\(AED\) and \(ABC\) are straight lines.
\(EB\) and \(DC\) are parallel.
\(AE\) = 5 cm, \(BC\) = 4.5 cm, \(BE\) = 4 cm, \(CD\) = 9 cm
(a) Calculate the length of \(AD\). (2)
(b) Calculate the length of \(AB\). (2)
The area of quadrilateral \(BCDE\) is \(x\) cm²
The area of triangle \(ABE\) is \(y\) cm²
(c) Find an expression for \(y\) in terms of \(x\).
Give your answer as simply as possible. (3)
Give your answer as simply as possible. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{9}{4}\) or \(\dfrac{4}{9}\) oe | M1 |
| 11.25 | A1oe |
| (2) |
Notes
M1: For the correct SF seen or used
| Scheme | Marks |
|---|---|
Eg \(\dfrac{5}{\text{"11.25"}} = \dfrac{x}{x + 4.5}\) or \(\dfrac{4}{9} = \dfrac{x}{x + 4.5}\) or \(\dfrac{5}{4} = \dfrac{4.5}{x}\) or \(4.5 \div \dfrac{\text{"11.25"} - 5}{5}\) or \(2.25x = x + 4.5\) oe | M1 |
| 3.6 | A1oe |
| (2) |
Notes
M1: A fully correct equation in \(x\) or a correct calculation for \(x\)
| Scheme | Marks |
|---|---|
\(2.25^2\) or 5.0625 or \(\dfrac{16}{81}\) or \(\dfrac{81}{16}\) or 81 : 16 or 16 : 81 or \(\dfrac{16}{65}\) or \(\dfrac{65}{16}\) or 65 : 16 or 16 : 65 | M1 |
| \(5.0625y - y = x\) or \(\dfrac{65}{16} = \dfrac{x}{y}\) oe | M1 |
| \(\dfrac{16x}{65}\) | A1oe |
| (3) |
Notes
M1: For a fully correct expression in \(x\) and \(y\) that can be rearranged to give \(y\) in terms of \(x\)
A1oe: eg \(\dfrac{x}{4.0625}\)
Accept 0.246(1538....)\(x\) rounded or truncated to at least 3SF