Numeracy Higher June 2018 Unit 2 Q4
4. A grass racetrack is shown in the diagram below.
This is the region shaded in the diagram.
Each end of the grass racetrack is created from semicircles.
The inner semicircles have a radius of 15 m.
The outer semicircles have a radius of 20 m.
Each of the straight sections of the racetrack has a length of 65 metres.
Diagram not drawn to scale
(a) What is the total area of grass in the two straight sections of the racetrack?
You must show all your working. [2]
You must show all your working. [2]
(b) Calculate the area of the grass racetrack.
You must show all your working. [4]
You must show all your working. [4]
(c) The grass is to be treated with a fertiliser.
It costs 20p to treat each 3 m2 of grass.
How much will it cost to treat the grass racetrack?
Give your answer correct to the nearest pound.
You must show all your working. [2]
It costs 20p to treat each 3 m2 of grass.
How much will it cost to treat the grass racetrack?
Give your answer correct to the nearest pound.
You must show all your working. [2]
Cost is £ ……………………
| Scheme | Marks | Comments |
|---|---|---|
| (2 × ) 65 × 5 650 (m2) | M1 A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (Area of both ends) π×202 - π×152 or equivalent (=549.7.....) | M2 | (= 1256.(...) – 706.(...)) M1 for ½ × π × 202 - ½ × π × 152 or 2 × π × 202 - 2 × π × 152 |
| + 650 | m1 | FT adding ‘their (a)’ FT provided at least M1 previously awarded |
| An answer in the range 1199 (m2) to 1200 (m2) | A1 | Accept 175π + 650 (m2) FT from M2, m1 previously awarded |
| Scheme | Marks | Comments |
|---|---|---|
| Area × (0.)20 ÷ 3 £80 | M1 A1 | FT ‘their area’ from 4(b) Must be correct to the nearest £ An answer of 8000 implies M1, A0 |