Intermediate November 2016 Unit 1 Q15
15. Each side of a square is of length \((2x + 3y)\) cm.
The perimeter of the square is 62 cm.
Each side of a regular octagon is of length \((x + 2y)\) cm.
The perimeter of the octagon is 72 cm.
Use an algebraic method to find the value of \(x\) and the value of \(y\). [5]
\(x =\) ………………………… \(y =\) …………………………
| Scheme | Marks | Comments |
|---|---|---|
| (Perimeter of square =) 4 × (2x + 3y) = 62 | B1 | Sight of 8x + 12y = 62 or equivalent e.g. 2x + 3y = 15·5 |
| (Perimeter of octagon =) 8 × (x + 2y) = 72 | B1 | Sight of 8x + 16y = 72 or equivalent e.g. x + 2y = 9 |
| Correct method to solve simultaneous equations, as far as attempt at subtraction | M1 | F.T. ‘their equations’. Allow 1 ‘slip’, if multiplication used, but not in ‘equated variable’ for M1 only. |
| y = 2·5 | A1 | |
| x = 4 | A1 | F.T. from their 1st variable. (Substitution in any relevant equation.) |