Numeracy Foundation November 2024 Unit 2 Q9
9. 72 000 people were asked to state their main way of travelling to work.
The results are shown accurately in the pie chart.
The people who said ‘Public transport’ travel to work either by bus or by train.
For every person who travels to work by bus, there are 4 people who travel by train.
Calculate the number of people who travel to work by train.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Public transport angle) 150 (°) ± 2° or (72 000 ÷ 360) 200 (people per degree) | B1 | Allow seen or implied by all other angles Percentage of 41.66…± 0.55..% implies 150 (°) ± 2° |
| (Number of people who travel by train) \(\dfrac{4}{5} \times \dfrac{150}{360} \times 72\,000\) or equivalent (= 24 000) | M2 | Or alternative full methods For M2 only FT 150 ± 2° or 41.66…± 0.55..% If B0 previously awarded FT ‘their 72 000 ÷ 360’ (number of people per degree) M1 for any one of the following:
|
| (Number of people who travel by train) 24 000 | A1 | Depends on M2 or an allowed M1 for full method with the angle or percentage within the increased tolerances Must be correct for ‘their 150’ or ‘their 41.66…%’ |
Alternative
The alternative method is printed in italics in the mark scheme.
9. Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Number of people travel by public transport) (72 000 – 72000 ÷ 4 – 72 000 ÷ 6 – 72 000 ÷ 6 =) 30 000 | B2 | B1 for Number of people by: car 72 000 ÷ 4 (= 18 000) AND cycle 72 000 ÷ 6 (= 12 000) AND walk 72 000 ÷ 6 (= 12 000) or equivalent |
| (Number of people who travel by train) \(\dfrac{4}{5}\) × 30 000 24 000 | M1 A1 | FT ‘their 72000 – 72000 ÷ 4 – 72000 ÷ 6 – 72000 ÷ 6’ |