4MA0 Higher January 2013 Paper 3 Q2
2 Rectangle A has a width of \(x\) metres and a height of \((x + 2)\) metres.
Rectangle B has a width of \(2x\) metres and a height of \(4x\) metres.
Diagram NOT accurately drawn
The perimeter of rectangle A is equal to the perimeter of rectangle B.
(i) Use this information to write down an equation in \(x\).
(ii) Find the value of \(x\).
(4)
| Scheme | Marks |
|---|---|
| (i) \(2x + 2(x+2) = 2 \times 2x + 2 \times 4x\) or \(4x + 4 = 12x\) or \(x + (x+2) = 2x + 4x\) or \(2x + 2 = 6x\) | B2 |
| (ii) \(4x + 4 = 12x\) or \(2x + 2 = 6x\) \(4 = 8x\) or \(2 = 4x\) | M1 |
| 0.5 | A1 |
| (4) |
Notes
B2: Must be an equation based on perimeter or semi-perimeter with \(x\)’s on both sides of equation
If not B2 then B1 for \(\{2x + 2(x+2)\}\) or \(\{2 \times 2x + 2 \times 4x\}\) or \(\{4x + 4\}\) or \(12x\) i.e correct perimeter of A or B
or \(\{x + (x+2)\}\) or \(\{2x + 4x\}\) or \(\{2x + 2\}\) or \(6x\) i.e correct semi-perimeter of A or B
M1: One step from correct equation
A1: Allow numerical methods. Correct answer only = M1A1