Numeracy Higher November 2020 Unit 1 Q8
8. On a building site, 4 bricklayers were able to lay 2000 bricks in 8 hours.
To complete the work on time, bricklayers will need to lay 9000 bricks in 10 hours.
(a) Calculate how many bricklayers would be needed to lay 9000 bricks in 10 hours.
You must show all your working. [4]
You must show all your working. [4]
(b) Give one assumption that you made in answering part (a). [1]
A table method altering all 3 in the same manner at the same time is M0
| Scheme | Marks | Comments | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 × \(\dfrac{8}{10}\) × \(\dfrac{9000}{2000}\) or 4 × 0.8 × 4.5 or equivalent | M2 | M1 for correct use of 4 with either 8/10 or 9000/2000 e.g.
| |||||||||
| = 14.4 or equivalent | A1 | Must be from M2 Allow sight of 14.(…) or 14 with a remainder May not be seen | |||||||||
| = 15 (needed) | A1 | FT provided at least M1 awarded, a second step attempted to find the number of bricklayers needed for 9000 bricks in 10 hours AND rounding up required Accept an answer of 14 provided their assumption in (b) states that some bricklayers can work at a quicker rate than others |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{2000}{8\times 4}\) (=62.5 (bricks per hour per bricklayer)) | M1 | |
| \(\dfrac{9000}{2000\div(8\times 4)\times 10}\) | m1 | Accept multiples of 2000÷(8×4)×10 (= 625) in order to reach 9000 |
| = 14.4 or equivalent | A1 | Must be from M2 Allow sight of 14.(…) or 14 with a remainder May not be seen Or 14 bricklayers can lay 8750 bricks, or 15 bricklayers can lay 9375 bricks |
| = 15 (needed) | A1 | FT provided at least M1 awarded, a second step attempted to find the number of bricklayers needed for 9000 bricks in 10 hours AND rounding required Accept an answer of 14 provided their assumption in (b) states that some bricklayers can work at a quicker rate than others |
| Scheme | Marks | Comments |
|---|---|---|
| Valid assumption e.g. ’All bricklayers work at the same rate’, or ‘All bricklayers took no breaks (or took breaks as often as before)’, or ‘The weather did not affect the work’, or ‘All the bricks are the same size’, or ‘All conditions remain the same’, or ‘Bricklayers work at the same constant rate’ | E1 | Accept an assumption that some bricklayers can work at a quicker rate than others provided a final answer of 14 given in (a) Do not accept an assumption based on the need to round 14.4 |