Foundation November 2020 Paper 3 Q29
29 A rectangle has length 60 cm and width 40 cm
Not drawn accurately
The length decreases by 15%
The width decreases by 10%
Sue says,
“The perimeter decreases by 25% because 15% + 10% is 25%”
Is she correct?
You must show calculations to support your answer. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(60 \times (1 - 0.15)\) or \(60 \times 0.85\) or 51 or \(40 \times (1 - 0.1)\) or \(40 \times 0.9\) or 36 | M1 | oe \(60 \times 0.15\) or 9 or \(40 \times 0.1\) or 4 |
| \(2 \times\) their \(51 + 2 \times\) their 36 or 174 | M1dep | oe \(2 \times\) their \(9 + 2 \times\) their 4 or 26 their 51, their 36, their 9 and their 4 must come from a correct method |
| \((2 \times 60 + 2 \times 40) \times 0.75\) or \(200 \times 0.75\) or 150 or \((2 \times 60 + 2 \times 40) \times 0.25\) or \(200 \times 0.25\) or 50 | M1 | oe |
| 174 and 150 and No or 224 and 200 and No or 26 and 50 and No | A1 | SC3 176 and 150 and No or 226 and 200 and No or 24 and 50 and No |
| Alternative method 2 | ||
| \(60 \times (1 - 0.15)\) or \(60 \times 0.85\) or 51 or \(40 \times (1 - 0.1)\) or \(40 \times 0.9\) or 36 | M1 | oe \(60 \times 0.15\) or 9 or \(40 \times 0.1\) or 4 |
| \(2 \times\) their \(51 + 2 \times\) their 36 or 174 | M1dep | oe \(2 \times\) their \(9 + 2 \times\) their 4 or 26 their 51, their 36, their 9 and their 4 must come from a correct method |
| \(\dfrac{(2 \times 60 + 2 \times 40) - \text{their } 174}{2 \times 60 + 2 \times 40} \times 100\) or \(\dfrac{200 - \text{their } 174}{200} \times 100\) or 13(%) or \(\dfrac{174}{200} \times 100\) and \(100 - 25\) or 87(%) and 75(%) | M1dep | oe \(\dfrac{2 \times \text{their } 9 + 2 \times \text{their } 4}{200} \times 100\) or \(\dfrac{26}{200} \times 100\) or 13(%) or \(\dfrac{200 - (2 \times \text{their } 9 + 2 \times \text{their } 4)}{200} \times 100\) and \(100(\%) - 25(\%)\) or 87(%) and 75(%) |
| 13% and No or 87% and 75% and No | A1 | oe SC3 12% and No or 88% and 75% and No |
Additional guidance
| Ignore incorrect statements or calculations with full mark response | |
| Consistently working with half of a perimeter can score up to 4 marks | |
| SC3 must come from transposing length and width values | |
| Accept length and width values transposed for up to 3 marks eg \(60 \times 0.9\) with \(40 \times 0.85\) and \(2 \times 54 + 2 \times 34\) eg \(60 \times 0.9\) with \(40 \times 0.9\) and \(2 \times 54 + 2 \times 36\) (not transposed) eg \(60 \times 0.1\) or \(40 \times 0.15\) or 6 | M1M1 M1M0 M1 |