Foundation November 2020 Paper 2 Q16
16 The diagram shows a square.
Not to scale
By setting up and solving an equation, show that the perimeter of the square is numerically equal to the area of the square. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(4x - 10 = 11 - 2x\) \(4x + 2x = 11 + 10\) | M1 M1 | or better | Alt method M1 for \((4x - 10)(11 - 2x) = 2(4x - 10) + 2(11 - 2x)\) or better M1 for \(2x^2 - 15x + 28 = 0\) |
| \(x = 3.5\) [Dimension of square =] 4 | A1 B1 | Correct or FT 4 × their x – 10 or 11 – 2 × their x | Dep on use of algebra Identifying 4 as the side of the square may be implied by later calculations |
| One perimeter/area calculation correctly evaluated | B1 | FT 4 × their length of square or (their length)2 | B1FT Dep on previous B. Allow embedded solution |
| Perimeter and area both shown to be 16 | A1 | Dep on all previous marks earned and that only \(x = 3.5\) leads to perimeter = area | |