Foundation June 2018 Paper 2 Q19
19 A farmer has a field in the shape of a semicircle of diameter 50 m.
The farmer asks Jim to build a fence around the edge of the field.
Jim tells him how much it will cost.
| Total cost = £29.86 per metre of fence plus £180 for each day’s work |
Jim takes three days to build the fence.
Work out the total cost. (5)
| Answer | Mark | Mark scheme |
|---|---|---|
| 4378.2(0) | P1 | for a process to find the circumference of the circle or the semi circle, eg \(\pi \times 50\ (= 157.0796327)\) or \(0.5 \times \pi \times 50\ (= 78.53981634)\) |
| P1 | for a complete process to find the perimeter of the field, eg \((0.5 \times \pi \times 50) + 50\) (= 128.5...) OR for working with one cost eg \(\text{``}157.07...\text{''} \times 29.86\) (= 4690.11..) or \(\text{``}78.5...\text{''} \times 29.86\) (= 2345.198...) or \(50 \times 29.86\) (=1493) or \(3 \times 180\) (= 540) | |
| P1 | For finding the costs of two different aspects eg 2 of \(\text{``}78.5...\text{''} \times 29.86\) (= 2345.1..) or \(50 \times 29.86\) (= 1493) or \(3 \times 180\) (= 540) | |
| P1 | for a adding at least 2 costs eg \(\text{``}2345.1..\text{''} + \text{``}540\text{''}\) (=2885.1..) or \(\text{``}1493\text{''} + \text{``}540\text{''}\) (=2033) or \(\text{``}128.5...\text{''} \times 29.86\) (= 3838.2..) | |
| A1 | for answer in the range 4377 – 4392 |
Additional guidance
Figures may be truncated or rounded
May use circle at this point, figures imply method
One cost is 1 length or labour
Figures may be truncated or rounded
Two different aspects means arc and straight edge or arc and labour or straight edge and labour
Condone circle and labour or circle and straight edge.
Finding the cost of the perimeter is two costs added and so implies the previous P1
The circle is not allowed to be counted as one of the two costs for this mark