Foundation November 2018 Paper 1 Q8
8. David is laying a small circle of paving stones in his garden.
The diagram shows the shape of each paving stone.
Diagram not drawn to scale
(a) How many paving stones will David need to make a circle? [1]
(b)
David wants his circle to be at least 1 metre in diameter.
Will David’s circle be the size he wants? [1]
Yes ☐ No ☐
Explain how you decide.
(c)
David is going to fill the space around the paving stones with gravel.
He works out that he needs 18 small bags of gravel.
| Green Garden Centre Offer of the week Any small bag of gravel £7.19 Buy 3 bags for the price of 2 |
(i) Estimate how much David will have to pay in total for his gravel from Green Garden Centre.
You must show all your working. [3]
You must show all your working. [3]
(ii)
Is your answer to part (i) an over-estimate or an under-estimate of the cost of David’s gravel?
Over-estimate ☐ Under-estimate ☐
Give a reason for your decision. [1]
| Scheme | Marks | Comments |
|---|---|---|
| 6 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| Yes with valid explanation e.g. ‘because 52cm × 2 = 104 cm’ or ‘the diameter will be 104 cm = 1.04 m’ or ‘the diameter is more than 100.’ | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (i) Use of 12 or 10 bags | M1 | |
| Suitable calculation e.g. (£)7[.00] × 12 or (£)7.2[0] × 12 or (£)7[.00] × 10 or (£)7.2[0] × 10 or (£)7.19 × 10 | M1 | or equivalent; allow (£)7.5[0] × 12 or (£)7.5[0] × 10 or a less accurate rounding e.g. (£)10 × 12 or (£)10 × 10 |
| Correct evaluation e.g. (£)84[.00] or (£)86.4[0] or (£)70[.00] or (£)72[.00] or (£)71.9[0] | A1 | Method must be shown; allow (£)90[.00] or (£)75.00 If first M0, allow M1 for (£)7[.00] × 18 or (£)7[.00] × 20 or (£)7.2[0] × 18 or (£)7.2[0] × 20 or (£)7.19 × 20 or (£)7.5[0] × 18 or (£)7.5[0] × 20 or equivalent or for a less accurate rounding e.g. 10 × 20 and A1 for correct evaluation e.g. (£)126[.00] or (£)140[.00] or (£)129.6[0] or (£)144[.00] or (£)143.80 or (£)135[.00] or (£)150[.00] If M1 M0, allow SC1 for [12 × 7.19 =] £86.28 rounded to £86[.00] or £90[.00] |
| (ii) Appropriate answer e.g. ‘Under-estimate as I rounded down.’ | E1 | Dependent on their calculation for (c)(i); cannot be awarded if (c)(i) is not attempted. NB compare with £86.28 |
| (6) |