Foundation November 2021 Paper 2 Q18
18 Here are two rectangles, rectangle \(A\) and rectangle \(B\).
Diagram NOT accurately drawn
The area of rectangle \(B\) is twice the area of rectangle \(A\).
Work out the value of \(x\).
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| \(4 \times (5 - x)\) or \(5 \times (2x - 1)\) or \(20 - 4x\) or \(10x - 5\) oe | M1 |
| one from: \(4(5 - x) = 20 - 4x\) or \(2 \times 4(5 - x) = 40 - 8x\) or \(0.5 \times 4(5 - x) = 10 - 2x\) oe and one from: \(5(2x - 1) = 10x - 5\) or \(2 \times 5(2x - 1) = 20x - 10\) or \(0.5 \times 5(2x - 1) = 5x - 2.5\) oe | M1 |
| eg \(10x + 8x = 40 + 5\) or \(-5 - 40 = -10x - 8x\) or \(18x = 45\) or \(-45 = -18x\) or \(4x + 5x = 20 + 2.5\) oe | M1 |
| Working required Answer: 2.5 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for setting up a correct expression for area A or area B (could be seen as part of an equation)
(condone lack of brackets for multiplying if meaning is clear for this mark)
M1: for expanding 2 sets of brackets correctly (one for each shape)
[We will allow for ×2 or ÷2 for the wrong shape for this expansion mark]
M1: for a correct equation with terms in \(x\) on one side and number terms the other side
A1: oe dep on M1