Foundation June 2022 Paper 1 Q23
23 Four friends are going on holiday together.
They each take a suitcase.
The weight of each suitcase is 25 kg, correct to nearest kilogram.
(a) Complete the error interval for the weight, \(w\) kg, of one suitcase.\[\ldots\ldots\ldots\ldots \leqslant w \lt \ldots\ldots\ldots\ldots\]
[2]
(b) The friends must pay extra if the total weight of their four suitcases is more than 102.4 kg.
Can the friends be certain that they will not have to pay extra?
Show how you decide. [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 24.5 25.5 cao | 2 | B1 for each If 0 scored SC1 for correct but reversed or for 24.50[0] and 25.50[0] | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(4 \times 25.5\) or \(4 \times\) their upper bound in (a) | M1 | M0 if \(w = 25\) used | |
| 102 or correct answer to \(4 \times\) their upper bound | A1 | ||
| Yes and their 102 \(\lt / \leqslant\) 102.4 in symbols or words | 1 dep | Dep on previous 2 marks Conclusion and clear comparison FT their upper bound in (a) | Yes/ no conclusions must be consistent with their working |
| Alternative method 1 | |||
| \(102.4 \div 4\) | M1 | ||
| 25.6 | A1 | ||
| Yes and their 25.5 \(\lt / \leqslant\) 25.6 in symbols or words | 1 dep | Dep on previous 2 marks Conclusion and clear comparison FT their upper bound in (a) | |
| Alternative method 2 | |||
| \(102.4 \div 25.5\) or \(102.4 \div\) their upper bound | M1 | ||
| 4.01(…) or correct answer to \(102.4 \div\) their upper bound | A1 | ||
| Yes and \(4 \lt / \leqslant\) their 4.01(…) | 1 dep | Dep on previous 2 marks Conclusion and clear comparison FT their upper bound in (a) | |