Numeracy Higher November 2017 Unit 1 Q8
8. A company produces two similar road signs.
Diagrams not drawn to scale
(a)
The cost of the paint needed for the smaller road sign is £1.60.
Calculate the cost of the paint needed for the larger sign. [4]
(b)
The selling price of the smaller road sign is £12.00.
This selling price was calculated from the cost price by:
- adding a profit of 25%,
- then adding VAT at 20%.
Calculate the cost price of the smaller road sign.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Scale factor =) \(\tfrac{3}{2}\) OR \(\tfrac{2}{3}\) or equivalent | B1 | Sight of (£)2.4(0) implies this B1 |
| Sight of \(\left(\tfrac{3}{2}\right)^2\) OR \(\left(\tfrac{2}{3}\right)^2\) or equivalent | B1 | This implies previous B1 |
| (Cost of paint =) 1.60 × \(\left(\tfrac{3}{2}\right)^2\) or equivalent | M1 | |
| = (£)3.6(0) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| 12 ÷1·2 or ×5/6 OR ÷1·25 or ×4/5 | M1 | |
| = (£) 10 = (£) 9.6(0) | A1 | (£)9.6(0) followed by 0·75 × 9.6(0) = (£)7.2(0) indicates an incorrect method M0A0M0A0 |
| ÷1·25 or ×4/5 OR ÷1·2 or ×5/6 | M1 | FT ‘their 10’ OR ‘their 9.6(0)’ provided previous M1 awarded |
| = (£) 8 | A1 | An intermediate answer of (£)9 followed by 0·8 × 9 = (£)7.2(0) indicates an incorrect method M0A0M0A0 Alternative method: M2 for (12÷1·2)÷1·25 or 12×5/6×4/5 or equivalent A2 for (£)8 A1 for intermediate answers of (£)10 or (£)9.6(0) |