Higher November 2021 Unit 1 Q8
8. The diagram below shows an isosceles triangle and a square.
Perimeter of triangle = 19 cm
Diagram not drawn to scale
Use an algebraic method (not trial and improvement) to find the value of \(x\) and the value of \(y\).
You must show all your working. [5]
\(x =\) …………………… \(y =\) ……………………
| Scheme | Marks | Comments |
|---|---|---|
| Showing \(4x + 3y = 19\) or equivalent. Showing \(6x - y = 12\) or equivalent. | B1 B1 | \(2x + 2x + 3y = 19\) is an equivalent answer. |
| A correct method to eliminate one variable e.g. ‘equal coefficients AND appropriate addition or subtraction’. OR ‘ method of substitution’. | M1 | Workings must be shown for M1A1A1. FT to solve for simultaneous equations if of equivalent difficulty. Allow one error in one term (not the term with equal coefficients.) |
| First variable found , \(x = 2\tfrac{1}{2}\) or \(y = 3\). Second variable found | A1 A1 | C.A.O. for ‘their equations’. FT substitution of their ‘1st variable’ if M1 gained. If NO (i.e. none of the five) marks gained, allow SC1 for both answers of \(x = 2\tfrac{1}{2}\) AND \(y = 3\) |