Foundation June 2019 Paper 1 Q10
10 Coaches take people to a festival.
Each coach can take 50 people.
(a) From one city there are 820 people.
How many coaches are needed? [3 marks]
(b) From a different city 13 coaches are needed.
Each coach costs £450 to hire.
Work out the total cost of hiring 13 coaches. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(820 \div 50\) or \(82 \div 5\) | M1 | oe eg \(1640 \div 100\) eg counting up in 50s to at least 800 (allow one error) eg counting down in 50s to less than 50 (allow one error) |
| 16.4 or 16+ or over 16 | A1 | oe eg 16 r 20 or 16 with 20 left allow 16 if 17 is final answer |
| 17 | A1ft | ft rounding up from a decimal, fraction or remainder with M1 awarded |
| Alternative method 2 | ||
| 850 | M1 | |
| \(850 \div 50\) | M1dep | oe eg \(85 \div 5\) eg counting up in 50s to try to achieve 850 (allow one error) eg counting down in 50s to at least 50 (allow one error) |
| 17 | A1 | |
Additional guidance
| Incorrect remainders or decimals or fractions cannot score the second mark eg \(820 \div 50 = 16.2\) answer 17 Remainder or decimal not shown, leading to answer of 17 will score full marks eg \(820 \div 50 = 16.\) \(\quad\) answer 17 | M1A0A1ft M1A1A1ft |
| A1ft cannot be scored if their division does not yield a remainder eg \(820 \div 50 =\) (exactly) 14 answer 14 | M1A0A0ft |
| \(800 \div 50\) or 16 implies M1 from Alt 1 | |
| \(800 \div 50 = 16\) so 17 needed (oe) | M1A1A1 |
| If \(82 \div 5\) is attempted, allow 16 r 2 or 16 with 2 left over for the first A1 |
| Answer | Mark | Comments |
|---|---|---|
| \(13 \times 450\) | M1 | Accept repeated addition of thirteen 450s |
| Correct vertical method of long multiplication with 4500 correct or Correct vertical method of long multiplication with at least one of 650 and 5200 correct or Correct set up of grid method with at least three of the four or six products correct or Correct set up of Gelosia method with at least three of the six products correct or \(10 \times 450 = 4500\) and \(3 \times 450 = 1350\) attempted with at least one correct or \(13 \times 400 = 5200\) and \(13 \times 50 = 650\) attempted with at least one correct | M1dep | oe Allow a placeholder space to be present instead of a physical zero in vertical method |
| 5850 | A1 |
Additional guidance
| For repeated addition method, to score M1dep, answer must end in 50 with a 6 carried into the hundreds column | |
| Students may choose to multiply 13 by 45 using any method, for the method marks. We do not need the zero to be recovered for either method mark, so \(13 \times 45\) scores at least M1 eg \(13 \times 45 = 585\) scores M2 even if answer line gives 585 eg \(13 \times 45\) vertical method with 450 correct or at least one of 65 and 520 correct eg \(13 \times 45\) using grid method with 40 and 5 rather than 400, 50 and 0, with three of the four products correct eg \(13 \times 45\) using Gelosia method with no zero column, with at least three (of the now four) products correct | M2 M2 M2 M2 |