Numeracy Higher June 2017 Unit 1 Q1
1.
Jasmine entered herself, Sophie and Bryn as a group in a talent contest.
Bryn only had a minor part.
Bryn, Sophie and Jasmine won the contest.
They shared the prize money in the ratio 2 : 6 : 7, with Bryn getting the smallest share.
Jasmine won £560, the largest share.
How much money did Bryn and Sophie each win? [4]
Bryn receives £ ……………………
Sophie receives £ ……………………
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The talent contest is held once a year.
Every year, the cost of putting on the talent contest increases by 10% of the previous year’s cost.
In summer 2014 the cost was £6600.
Calculate the cost of putting on the summer 2017 talent contest.
You must show all your working. [3 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| (£) 560 ÷ 7 (= £ 80) | B1 | |
| 2 × 560 ÷ 7 OR 6 × 560 ÷ 7 OR ⅓ × (560 – 560 ÷ 7) OR 560 – 560 ÷ 7 | M1 | |
| (Bryn) (£) 160 | A1 | CAO |
| (Sophie) (£) 480 | A1 | CAO |
Alternative
| Scheme | Marks | Comments |
|---|---|---|
| (Total prize money) 560 ×15 ÷ 7 (=£1200) | B1 | |
| 2 × 1200 ÷ 15 OR 6 × 1200 ÷ 15 | M1 | FT 'their 560 ×15 ÷ 7' (= 1200) |
| (Bryn) (£) 160 | A1 | CAO |
| (Sophie) (£) 480 | A1 | CAO |
If no marks, award SC1 only for either of the following answers (from initially 560÷15)
- (Bryn) (£)74(.66...) or (£)75
- (Sophie) (£)222 or (£)223(.98) or (£) 224
| Scheme | Marks | Comments |
|---|---|---|
| (2015 cost of hosting:) 6600 + 0.1 × 6600 (£7260) | B1 | |
| (2016 cost of hosting:) 7260 + 0.1 × 7260 (£7986) AND (2017 cost of hosting:) 7986 + 0.1 × 7986 (£8784.60) | M1 | For the appropriate method of repeatedly increasing by 10% from 2015 to 2017 FT ‘their 6600 + 10%' calculation with ‘their 7260’ + 10% calculation with their 7986’ + 10% calculation Allow intention with sight of rounding or truncation within working, e.g. (£)799 as 10% of (£)7986 |
| (2017 cost of hosting is) (£) 8784.6(0) | A1 | CAO Ignore any further working |
| Organisation and communication | OC1 | For OC1, candidates will be expected to: • present their response in a structured way • explain to the reader what they are doing at each step of their response • lay out their explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means |
| Writing | W1 | For W1, candidates will be expected to: • show all their working • make few, if any, errors in spelling, punctuation and grammar • use correct mathematical form in their working • use appropriate terminology, units, etc. |
Alternative
| Scheme | Marks | Comments |
|---|---|---|
| Sight of 6600 × 1.13 | M1 | |
| Full method to calculate 1.13 and multiply by 6600 | m1 | (For method not accuracy, allow arithmetic errors if intention clear.) |
| (£) 8784.6(0) | A1 | CAO |
If no marks, award SC1 for an answer of (£)8580 (from simple interest, as first B mark is embedded)