Numeracy Higher June 2019 Unit 2 Q3
3.
(a) In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
On 1st June, Delyth budgets for her next electricity bill.
This bill will be for the months of June, July and August.
Her bill will have to be paid at the beginning of September.
She knows:
- the standing charge is £8 per month,
- her meter reading on 1st June is 20 150 kWh,
- her estimate for her meter reading on 31st August is 20 950 kWh,
- her agreement states that electricity costs 23p per kWh,
- VAT at 5% is payable on the total of the standing charge and the cost of the electricity used.
Calculate how much she should budget each month so that she is able to pay her next electricity bill. [7 + 2 OCW]
(b) Delyth invested £500 in a saver bank account 20 years ago.
She did not withdraw money or make any other payments into this account.
The bank paid 2·2% compound interest per annum during the first 5 years.
Compound interest at 1·6% per annum was paid for the remaining 15 years.
She did not withdraw money or make any other payments into this account.
The bank paid 2·2% compound interest per annum during the first 5 years.
Compound interest at 1·6% per annum was paid for the remaining 15 years.
Delyth closes the account after 20 years.
How much money should she receive? [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Number of units is) 800 | B1 | |
| (Electricity cost is) 800 × 0.23 or 800 × 23 (£)184 or 18400(p) | M1 A1 | FT ‘their 20950 – 20150’, must be from attempting this subtraction If units are given they must be correct Accept £184.00p, do not accept £184p |
| (Standing charge + electricity) (£) 208 or 20800(p) | B1 | FT 24 + ‘their 184’ provided units are consistent May be implied or embedded in further work, e.g. if 184 × 1.05 + 24 seen and calculated correctly to (£)217.2(0) |
| (Total bill including VAT at 5%) 1.05 × 208 or 1.05 × 20800 or equivalent | M1 | FT ‘their (£)208’ or ‘their 20800(p)’, including if the standing charge is omitted (i.e. (£)184 used) Allow if standing charge is added after adding VAT to the electricity cost |
| (£)218.4(0) or 21840(p) | A1 | CAO |
| (Budget per month £218.40 ÷ 3 =) (£)72.8(0) or 7280(p) | B1 | FT ‘their total bill’ ÷ 3 provided at least 2 marks previously awarded Allow rounded up to the nearest £ On FT allow rounding to 10p, or rounding up to the nearest £ (Note: FT answers from
|
| 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
3(a) Alternative method:
| Scheme | Marks | Comments |
|---|---|---|
| Watch for stages in other orders, check for embedded equivalent stages | ||
| (Number of units is) 800 | B1 | |
| (Electricity cost is) 800 × 0.23 or 800 × 23 (£)184 or 18400(p) | M1 A1 | FT ‘their 20950 – 20150’, must be from attempting this subtraction If units are given they must be correct Accept £184.00p, do not accept £184p |
| (Budget before VAT 184÷3 + 24÷3 =) (£) 69.33(3..) | B1 | FT ‘their 184’+ 8 provided units are consistent May be implied or embedded in further work, e.g. if (184÷3)×1.05 + 8 seen and calculated correctly to (£)72.4(0) |
| (Total bill including VAT at 5%) 1.05 × (184 ÷ 3 + 24 ÷ 3) or equivalent | M2 | FT ‘their 184 ÷ 3 + 24 ÷ 3’ M1 for either of the following:
|
| (Budget per month) (£)72.8(0) or 7280(p) | A1 | FT from M2 or M1 Allow rounded up to the nearest £ On FT allow rounding to 10p, or rounding up to the nearest £ |
Corrected by Westie's Workshop
- The board's mark scheme printed “May be in implied or embedded”. Changed to “May be implied or embedded” because “in” is a stray extra word; the matching line of the scheme says “May be implied or embedded in further work”.
Original: see the board's mark scheme PDF (link above).
| Scheme | Marks | Comments |
|---|---|---|
| 500 × 1.0225 × 1.01615 (500 × 1.0225 = 557.473...) (500 × 1.01615 = 634.418... or 634.42) | M3 | OR equivalent method to increase by 2.2% and to increase by 1.6% on different amounts for appropriate number of years M2 for sight of either ×1.0225 or ×1.01615 or equivalent calculations OR M1 for sight of either ×1.022 or ×1.016 or equivalent calculations |
| (£) 707.34 | A1 | Mark final answer, CAO, accepting answers in the range (£) 707.33 to (£) 707.35 (Note: Sight of (£)511 or (£)555 implies 500 × 1.022, from working with 2.2% of £500, M1 is awarded) |