Numeracy Higher June 2017 Unit 2 Q12
12. A plan view of Lowri’s garden is shown below.
Diagram not drawn to scale
All the measurements are correct to the nearest 10 cm.
(a) Calculate the greatest possible area of Lowri’s garden. [4]
(b) Lowri plans to spread grass seed over her garden using a spreading tool.
Over each square metre, the spreading tool spreads 30 g of grass seed, correct to the nearest 5 g.
Over each square metre, the spreading tool spreads 30 g of grass seed, correct to the nearest 5 g.
Lowri has exactly 1·5 kg of grass seed.
Can she be certain that she has enough grass seed?
You must show all your calculations. [3]
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 805 (cm) or 405 (cm) | B1 | Do not accept 804∙9 or 404∙9, but allow 804∙9 recurring or 404∙9 recurring |
| (805 × 405) + (405 × 400) OR a consistent attempt at converting these into metres | M2 | FT their upper bounds M1 for 805×405 + (400<n≤405 × 405) (Note: use of 805×405 + 405×405 leads to 490 050) |
| = 488 025 (cm2) | A1 | OR 48∙8(025) m2. Allow 488 000 (cm2) CAO. Ignore attempts to convert into m2. Alternative method: M2 for 8052 − 4002 Allow M1 for 8052 – (395≤n<400)2 A1 for 488 025 (cm2) CAO. Ignore attempts to convert into m2. |
| Scheme | Marks | Comments |
|---|---|---|
| Conversion 48∙8(025) (m2) OR 0∙00325 (g/cm2) | B1 | FT ‘their 488 025’ OR ‘their 32∙5’ (805 × 405 + 405 × 405 = 490 050 (cm2) or 49(∙0050) m2) |
| 32∙5 × 48∙8(025) OR 0∙00325 × 488 025 | M1 | FT ‘their 32∙5’ provided it is greater than 30 and ≤35, and FT their area provided an attempt made at converting into g/cm2 or m2 |
| = 1586(∙08125) (g) AND Statement e.g. ‘No, more than 1∙5 kg (could be) needed’ | A1 | Accept 1∙6 kg from correct working FT 32∙5 × ‘their area’ correctly converted into m2 Alternative method: M1 for 0∙0325×48∙8(025) OR 3∙25×10-6×488 025 (kg/m2 × m2) (kg/cm2 × cm2) FT ‘their 32∙5’ provided it is greater than 30 and ≤35, and FT their area A1 for 1∙58(60…) or 1∙6 (kg) AND Statement e.g. ‘No, more than 1∙5 kg (could be) needed’ FT 32∙5 × ‘their area’ correctly converted into m2 OR For candidates clearly considering the smallest area that could be seeded B1 for 1500 (g) OR 0∙0325 (kg) FT ‘their 32∙5’ M1 for 1500 ÷ 32∙5 OR 1∙5 ÷ 0∙0325 FT ‘their 32∙5’ provided it is greater than 30 and ≤35 for M1 only A1 for 46(∙15…) (m2) AND Statement e.g. ‘No, more than 1∙5 kg (could be) needed’ FT their area, Only award A1 if their area has been correctly converted into m2 for comparison |