Higher November 2021 Paper 2 Q2
2 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 algebraic 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 only)
M1: for expanding 2 sets of brackets correctly (one for each shape)
[allow ×2 or ÷2 for the wrong shape for this mark]
Need not be in an equation at this stage.
M1: for a correct equation with terms in \(x\) on one side and number terms the other side
A1: oe dep on M1