Higher November 2021 Unit 2 Q1
1. A rectangle has sides of length \(2(3a - 7)\) cm and \((5a + 4)\) cm.
Diagram not drawn to scale
Form an expression, in terms of \(a\), for the perimeter of this rectangle.
You must simplify your expression. [3]
| Scheme | Marks | Comments |
|---|---|---|
| \(4(3a - 7) + 2(5a + 4)\) or equivalent. | B1 | For a correct expression for the perimeter. |
| \(= 12a - 28 + 10a + 8\) or equivalent. | B1 | For removal of brackets FT only from \(2(3a - 7) + (5a + 4)\) or equivalent OR \(2(3a - 7) + 2(5a + 4)\) or equivalent. |
| \(= 22a - 20\) (cm) or \(2(11a - 10)\) (cm) | B1 | For collection of terms FT if of equivalent difficulty. Mark final answer. |
Alternative approach
| Scheme | Marks | Comments |
|---|---|---|
| \(2[2(3a - 7) + (5a + 4)]\) | B1 | For a correct expression for the perimeter. |
| \(= 12a - 28 + 10a + 8\) or \(2(6a - 14 + 5a + 4)\) | B1 | For removal of brackets (within ‘square brackets’) FT only from \(2[2(3a - 7) + 2(5a + 4)]\) or equivalent. |
| \(= 22a - 20\) (cm) or \(2(11a - 10)\) (cm) | B1 | For collection of terms FT only from \(2[2(3a - 7) + 2(5a + 4)]\) or equivalent. FT if of equivalent difficulty. Mark final answer |