Numeracy Intermediate November 2024 Unit 2 Q7
7.
Steffan uses 654 kWh of electricity in a three-month period.
Electricity costs £0.30 per kWh.
The standing charge for the three-month period is £54.
Steffan has to pay VAT at 5% on the total cost.
Calculate Steffan’s electricity bill.
You must show all your working. [5]
Steffan always leaves his fridge-freezer turned on.
His fridge-freezer uses electricity costing £2.31 per week.
Electricity costs £0.30 per kWh.
Calculate the number of kWh of electricity Steffan’s fridge-freezer uses per day.
You must show all your working. [3]
Steffan is thinking of buying the fridge-freezer shown below.
Diagram not drawn to scale
Steffan needs to check that the freezer compartment of this fridge-freezer has enough room.
The height of the freezer door is \(\dfrac{2}{5}\) of the total height of the fridge-freezer.
Calculate the length of the diagonal of the freezer door.
Give your answer in millimetres.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| Incorrect unit of money is penalised -1 once only on the first occurrence, by withholding an A or B mark | ||
| (Electricity cost is) 654 × (£)0.30 (£)196.2(0) or 19620(p) | M1 A1 | Accept 654 × 30(p) If units are given they must be correct Accept £196.20p |
| (Cost of electricity and standing charge is £196.20 + 54 =) (£) 250.2(0) | B1 | FT provided 654 used in a calculation for ‘their cost of electricity’ Do not accept if embedded with an incorrect interpretation of the standing charge, e.g. 196.20 + 3 × 54 = (£)358.20 is B0 If previous M0 A0 B0 for (654 × (£)0.30 × 3 =) £588.60 AND (588.60 + 54 × 3 = 588.60 + 162 =) £750.60, award SC1 for this consistent misunderstanding and then FT |
| (Total bill including VAT) 1.05 × 250.2(0) or 250.2(0) + 12.51 | M1 | FT from ‘their derived total of electricity’ + ‘their standing charge’, accept rounding or truncation to a penny Allow M1 A0 for 1.05 × ‘their total rounded or truncated to a whole pound’ |
| (£)262.71 | A1 | If M0 A0 for inclusive of VAT cost, allow SC1 for an answer of (£)262.70, provided not from incorrect working (allow from 250.20 + 12.50) If final B0 M0 A0, award SC1 for the correct evaluation of 1.05 × ‘their derived cost of electricity’ having not considered and omitted the standing charge, or previously subtracted the standing charge from ‘their cost of electricity’ |
| Scheme | Marks | Comments |
|---|---|---|
| (2.31 ÷ 7) ÷ 0.30 or (2.31 ÷ 0.30) ÷ 7 or (231 ÷ 7) ÷ 30 or (231 ÷ 30) ÷ 7 or equivalent | M2 | Allow if brackets are implied in further working May be shown in stages M1 for any of the following:
|
| 1.1 (kWh) | A1 | CAO. Ignore incorrect units |
| Scheme | Marks | Comments |
|---|---|---|
| (Height freezer door) 2 × 1800 ÷ 5 or \(\dfrac{2}{5}\) × 1800 or 0.4 × 1800 or equivalent | M1 | |
| 720 (mm) | A1 | |
| ((Diagonal of freezer door)\(^2\) =) 600\(^2\) + 720\(^2\) | M1 | Or alternative full method FT ‘their height of freezer door’ including 1080 or 1800 Accept working in m or cm for possible M1, A1 |
| Diagonal\(^2\) = 878 400 or (Diagonal =) √878 400 | A1 | |
| (Diagonal =) 937(.22... mm) | A1 | Final answer must be given in mm FT from M1 for the correctly evaluated square root of ‘their 878 400’ provided ‘their answer’ > ‘their 720’ for possible A1 If final M0 A0 A0 awarded as a different length, not ‘their 720’, is used to calculate the diagonal, award SC1 for a correct statement of Pythagoras’ Theorem, and SC1 for a correct evaluation of ‘their diagonal’ |