Numeracy Higher November 2023 Unit 1 Q8
8. On average, Hywel’s car travels a distance of 11 miles per litre of petrol used.
The petrol tank in his car can hold 70 pints of petrol.
At Hywel’s local garage, it would cost him £56 to fill the tank from empty.
Hywel’s petrol tank is \(\dfrac{1}{10}\) full.
At his local garage, he spends £28 on petrol.
Calculate the distance Hywel can travel in the car before the tank is empty.
You must show all your working. [6]
Distance Hywel can travel before the tank is empty = …………… miles
| Scheme | Marks | Comments |
|---|---|---|
| 70 × \(\left(\frac{1}{2}+\frac{1}{10}\right)\) or × \(\left(\frac{28}{56}+\frac{1}{10}\right)\) or × 0.6 | M2 | M2 and M1 can be performed in either order, but have to come from starting with 70 May be embedded within incorrect work M1 for:
|
| ÷ 1.75 or × \(\frac{4}{7}\) or equivalent | M1 | Accept use of ÷ (1.748 to 1.76) or × (0.568 to 0.572) |
| × 11 | m1 | FT from at least one M1 previously awarded |
| = 264 (miles) | A2 | CAO A1 for:
e.g. use of × 0.57 for the conversion to litres 42 × 0.57 = 23.94 (possibly rounded to 24) or 42 × 0.57 × 11 = 263.34 (possibly rounded to 263) |
8. Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| 11 ÷ 1.75 or × \(\frac{4}{7}\) or equivalent | M1 | M1 and M2 can be performed in either order, but have to come from starting with 11 Accept use of ÷ (1.748 to 1.76) or × (0.568 to 0.572) |
| × \(\left(\frac{1}{2}+\frac{1}{10}\right)\) or × \(\left(\frac{28}{56}+\frac{1}{10}\right)\) or × 0.6 | M2 | May be embedded within incorrect work M1 for:
|
| × 70 | m1 | FT from at least one M1 previously awarded |
| = 264 (miles) | A2 | CAO A1 for:
e.g. use of × 0.57 for the conversion to litres 11 × 0.57 = 6.27 (truncated/rounded to 6.2 or 6.3, but not 6) or 11 × 0.57 × 0.6 = 3.762 (truncated/rounded to 3.7 or 3.8, but not 4) |