Higher June 2018 Unit 2 Q8
8. A rectangle of length 12 cm and width \((2x - y)\) cm has an area of 72 cm2.
Diagram not drawn to scale
KLMN is a kite where KL = \(3x\) cm and LM = \(y\) cm.
Diagram not drawn to scale
The perimeter of the kite KLMN = 33 cm.
Calculate the values of \(x\) and \(y\).
You must show all your working.
Do not use a trial and improvement method. [5]
| Scheme | Marks | Comments |
|---|---|---|
| 2x – y = 6 or equivalent e.g. 12(2x – y) = 72 | B1 | B1 for sight of correct equation. |
| 3x + y = 16·5 or equivalent e.g. 3x + y + 3x + y = 33 | B1 | B1 for sight of correct equation. FT ‘their two simultaneous equations’. |
| Correct method to solve simultaneous equations. | M1 | Equating a variable (if necessary) AND adding or subtracting as appropriate. Allow one slip. |
| x = 4·5 | A1 | C.A.O. from ‘their equations’ for 1st variable. |
| y = 3 | A1 | F.T. from substituting ‘their 1st variable’ if M1 gained. SC1 if x = 4·5 AND y = 3 given without using simultaneous equations method. This could happen after a B1 (or B1B1) gained or just appear with no equations shown. |