Numeracy Intermediate June 2018 Unit 2 Q10
10. 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
What is the total area of grass in the two straight sections of the racetrack?
You must show all your working. [2]
Calculate the area of the grass racetrack.
You must show all your working. [4]
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]
Cost is £ ……………
| Scheme | Marks | Comments |
|---|---|---|
| (2 × ) 65 × 5 | M1 | |
| 650 (m2) | 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 | M1 | FT ‘their area’ from 10(b) |
| £80 | A1 | Must be correct to the nearest £ An answer of 8000 implies M1, A0 |