Foundation June 2017 Paper 2 Q12
12 A farmer has a field that is in the shape of a trapezium.
He measures the field so that he can work out the area.
He puts his measurements on this diagram of the field.
Not to scale
(a) The farmer has rounded his measurements to two significant figures.
Give a reason why he may have done this. [1]
(b) The field produces 6400 kilograms of wheat per hectare.
One hectare is 10 000 m\(^2\).
One hectare is 10 000 m\(^2\).
Work out how many kilograms of wheat the field produces. [5]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Valid reason | 1 | Such as ‘to make it easier to work out the area’ | See Appendix B |
Appendix B
Acceptable answers are likely to include reference to easier, approximate or estimate
Exemplar responses for Q12(a)
| Response | Mark |
|---|---|
| Rounding it to 1 significant figure could be too inaccurate. | 1 |
| To make it easier to find the area | 1 |
| He will be able to work out easier the area of his field with a bit of extra space. | 1 |
| So that the area of his field is a whole number. Implies easier to calculate because of ‘area’ | 1 |
| So the farmer can get an estimate | 1 |
| Easier and more efficient than having measurements with lots of decimal places | 1 |
| As it gives an easier length to have whole numbers rather than a decimal ‘Easier’ is the key word to score | 1 |
| It can give him an approximate idea on the field quicker and easier | 1 |
| It is easier to calculate | 1 |
| It makes it easier for him | 1 |
| So he does not get decimal answers | 0 |
| To make it a whole number. | 0 |
| So he can get a rounded number with no decimals. | 0 |
| So that he gets a whole number instead of a decimal. This could apply to 1sf | 0 |
| because it is difficult to work out the area of the whole field | 0 |
| To give a accurate measurement | 0 |
| He will have just over what he needs for the field | 0 |
| to give him a more accurate and easier figure to use Contradictory | 0 |
| The exact area is quite difficult to measure ‘calculate’ instead of ‘measure’ would score | 0 |
| The measurement of the field was probably not accurate | 0 |
| So the measurements would be more accurate | 0 |
| To get a rough measurement of the field ‘calculation’ instead of ‘measurement’ would score | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 19 000 or 19 200 | 5 | M2 for \(150 \times (180 + 220) \div 2\) soi Or M1 attempt at an area And M1 attempt to convert their area to hectares soi And M1 for \(6400 \times\) their area | Mark answer line first, award 5 for a correct answer. If incorrect, then award M marks for correct steps seen Area of trapezium 30000 Such as \(180 \times 150\) or \(220 \times 150\) Eg their area \(\div\) 10000 oe Their area in m\(^2\) or hectares eg \(180 \times 150 \times 6400\) or \(6400 \times 30000\) or eg \(6400 \times 3\) For the final 2 marks their area may have come from an attempt at perimeter, volume, etc |