Numeracy Higher June 2019 Unit 1 Q3
3.
(a) Sam’s Garden Centre buys trees to sell.
Sam bought 200 trees.
Each tree cost Sam £25.
22% of the trees were not sold.
Sam sold all the other trees for £40 each.
How much profit did Sam make?
You must show all your working. [5]
(b) The trees are planted in identical pots. They each have a uniform cross-section in the shape of a regular hexagon.
Show that these pots will tessellate. [1]
| Scheme | Marks | Comments |
|---|---|---|
| (Cost to Sam) 200 × 25 (= £ 5000) | M1 | |
| (Number of trees Sam expects to sell is) 200 – 0.22 × 200 or 200 × 0.78 | M1 | |
| (=) 156 (trees) | A1 | Depends only on previous M1 |
| (Money from sales of trees is 40 × 156 = £) 6240 | B1 | FT the number of trees sold, i.e. 40 × 'their 156' |
| (Expected profit is £6240 - £5000 =) (£) 1240 | B1 | FT ‘their (40 × 'their 156')’ – 5000 correctly evaluated |
3(a) Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| (Number of trees Sam expects to sell is) 200 – 0.22 × 200 or 200 × 0.78 | M1 | |
| (=) 156 (trees) | A1 | |
| (Expected profit) 156 × (40 – 25) - (200 – 156) × 25 | M2 | FT 'their 156' M1 for 156×(40-25) - ..... or .... - (200 – 156) × 25) |
| (£) 1240 | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| A suitable diagram with at least 3 hexagons (or 2 extra hexagons) shown to tessellate OR Sight of 3 × 120° = 360° or equivalent | E1 | ISW A suitable diagram will involve 3 hexagons meeting at a point at least once, the 6 sides of the hexagons must be shown Allow if a correct diagram given with angles unlabelled or incorrectly labelled Do not accept if only the exterior angles (labelled correctly or incorrectly) of the given hexagon shown, need to show further hexagons |