Higher January 2023 Paper 2R Q13
13 A rectangle has length \(L\) and width \(W\)
\(L\) is increased by 20%
\(W\) is decreased by 35%
Calculate the percentage reduction in the area of the rectangle.
(3)
| Scheme | Marks |
|---|---|
| eg 1.2 × 0.65 (= 0.78) or \(1.2L \times 0.65W\;(= 0.78LW)\) or 1.2 × 0.65 × 100 (= 78) or \(1.2L \times 0.65W \times 100\;(= 78LW)\) | M1 |
| eg \((1 - \text{``}{0.78}\text{''}) \times 100\) or \((LW - \text{``}{0.78LW}\text{''}) \times 100\;(= 22LW)\) or \(100 - \text{``}{78}\text{''}\) or \(100LW - \text{``}{78LW}\text{''}\;(= 22LW)\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 22 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: allow use of other variables to \(L\) and \(W\) as long as clearly labelled as length and width
allow (1 + 0.2) as their 1.2 and (1 – 0.35) as their 0.65
M1: method to find the percentage reduction, allow the subtraction to be written the other way around eg “78” – 100
A1: allow −22
| Scheme | Marks |
|---|---|
| eg \(1.2 \times x\) and \(0.65 \times y\) where \(x\) and \(y\) are positive numbers | M1 |
eg \(\left(1 - \dfrac{1.2x \times 0.65y}{xy}\right) \times 100\) or \(\left(\dfrac{xy - 1.2x \times 0.65y}{xy}\right) \times 100\) | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 22 | A1 |
Notes
M1: accept any positive values for \(x\) and \(y\)
allow (1 + 0.2) as their 1.2 and (1 – 0.35) as their 0.65
M1: method to find the percentage reduction, allow the subtraction to be written the other way around eg \(\left(\dfrac{1.2x \times 0.65y}{xy} - 1\right) \times 100\)
A1: allow −22