Foundation November 2021 Paper 1 Q8
8 A travel company is taking some passengers on a trip.
They can use coaches or minibuses.
Each coach can carry 53 passengers.
Each minibus can carry 12 passengers.
The passengers going on the trip would exactly fill 3 coaches.
If the company uses only minibuses, how many will they need? [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(53 \times 3\) or 159 | M1 | |
| their \(159 \div 12\) | M1dep | oe eg \(53 \div 4\) for build up method allow one error, must get as far as 1 minibus below their total number of passengers |
| 13. or 13.2 or 13.25 or 13 r (3) or \(13\dfrac{3}{12}\) or build up method reaches 156 (for 13 minibuses) with no errors | A1 | may be implied by correct answer oe fraction |
| 14 | A1ft | ft their decimal or remainder value rounded up to the nearest whole number with M2 scored |
| Alternative method 2 | ||
| \(53 \div 12\) or 4.4… or 4 r 5 or \(4\dfrac{5}{12}\) | M1 | |
| their \(4.4\ldots \times 3\) or \(4\dfrac{5}{12} \times 3\) or \(12\dfrac{15}{12}\) | M1dep | oe fraction |
| 13.(2…) or 13 r (3) or \(13\dfrac{3}{12}\) | A1 | may be implied by correct answer oe fraction |
| 14 | A1ft | ft their decimal or remainder value rounded up to the nearest whole number with M2 scored |
Additional guidance
| For answers of 14, please check for incorrect working | |
| eg \(159 \div 12 = 14.1\) and answer 14 | M2A0A0ft |
| \(159 \div 12\) with result 13.8 and answer 14 | M2A0A1ft |
| \(159 \div 12\) with result 13 r 2 and answer 14 | M2A0A1ft |
| 159 with build up to 13 minibuses is 158 and answer 14 | M2A0A1ft |
| \(159 \div 12\) with no decimal or remainder value and answer 14 | M2A2 |
| \(159 \div 12 = 13.\) Answer 13 | M2A1A0 |
| \(159 \div 12 = 13\) Answer 13 | M2A0 |
| 14 with no working | M2A2 |
| \(159 \div 12\) with result 13.3 (bod from 13.25) and answer 14 | M2A2 |
| \(159 \div 12\) with result 13.3 (bod from 13.25) with no final answer | M2A1A0 |
| \(53 \div 12 = 4(.) = 5\), \(5 \times 3 = 15\), so 15 minibuses (conceptually incorrect) | M1M0A0A0ft |
| \(53 \div 12 = 4.7\), \(4.7 \times 3 = 14.1\), so 15 minibuses | M2A0A1ft |
| For build up method | |
| \(53 \times 3 = 159\), \(12 \times 13 = 156\) | M2A1A0 |
| \(53 \times 3 = 159\), \(12 \times 13 = 156\), 15 minibuses | M2A1A0 |
| \(12 \times 13 = 156\), without their 159 (don’t know what they are building up to) | M0A0 |
| Build up method reaches 156 (for 13 minibuses) with no errors and no answer, but says “3 more seats needed” | M2A1A0 |