Numeracy Foundation June 2017 Unit 1 Q8
8.
Maes Alun Camping
Charges
Tents covering ground area:
AND
Charge per person: £4 per night
Stay 5 nights and get the next night completely free.
This means no charge for tents or people on every 6th night.
Rhodri and Lars are planning a camping holiday, staying at Maes Alun Camping.
They are going to:
- take only one tent between them,
- take a tent covering a rectangular ground area, measuring 2·5 metres by 4·4 metres,
- both stay for a total of 12 nights.
Their holiday is just 8 weeks away.
They each plan to save £15 per week from now until their holiday in 8 weeks’ time.
Will the amount they save be enough to pay for their holiday?
You must show all your working. [8]
| Scheme | Marks | Comments |
|---|---|---|
| (Tent ground area ) 2.5 × 4.4 | M1 | Allow for sight of 2(.)5(0) × 4(.)4(0) Working of the ground area must be seen, i.e. sight of 2.5 × 4.4 not 2 × 4 or 3 × 4 |
| = 11 (m2) | A1 | CAO, not FT If no area calculation seen award M0, A0 then FT for M and A marks, final mark E0 |
| (Total cost for 12 nights, pay for 10 nights =) 10×14 + 2×10×4 | M2 | FT ‘their ground area >12m2 to calculation 10×16 + 2×10×4 (=£240) for M2 or equivalent M1 (see formula below) If incorrect interpretation of ‘their ground area’, award M1 only for either area ≤12m2 with 10×16 + 2×10×4 (=£240), or area>12m2 with 10×14 + 2×10×4 (=£220), M1 for a sum of two products: (2 x) a × b + (2 ×) 4 × c where a = 10, 11 or 12 b = 14 or 16 c = 10, 11 or 12 The initial (2 ×) is if the error is 2 tents! For example:
Working with the cost of 1 night, e.g. 14 + 2 × 4 or 16 + 2 × 4, ignore errors in calculation and award M2 or M1 as appropriate when attempt to multiply by 10, 11 or 12 is seen, i.e work may be seen in stages |
| (140 + 80 = £) 220 | A1 | CAO If previous M0, A0 for costs, award SC1 for sight of 1 night cost (£)22 or for sight of 10×14 and 2×10×4 without indication of addition |
| (Saving = 2×) 8 × 15 (£) 240 | M1 A1 | Allow M1 only 1 person saving CAO, not FT |
| Conclusion, e.g. ‘planned saving is enough to pay for the holiday’ | E1 | FT comparison for ‘their £240 saved’ with ‘their total cost’, provided at least 2 M marks previously awarded one of which must be for area calculation Allow the conclusion 'yes' |
Alternative
| Scheme | Marks |
|---|---|
| (How many weeks of saving) 220 ÷ (2 × 15) (FT ‘their 220’ for M1 only) | M1 |
| 7⅓ or 7.3(.....)(weeks) | A1 CAO |
If no marks, allow SC1 for 14.6(6... weeks) or 14.7 from 220 ÷ 15
Or equivalent for working with cost per person, i.e. ½ × 10 × 14 + 10 × 4 = £110 and saving 8 × 15 = £120, all previous marks are available
This alternative (printed against the saving marks) was printed in italics in the original.