SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Measurement, STD2 EQ-Bank 30

A 2500-watt air-conditioning system is turned on for 3 hours each day. Electricity is charged at 27 cents per kWh.

What is the cost of electricity for using the air-conditioning system over a seven-day period?   (2 marks)

Show Answers Only

`$14.18`

Show Worked Solution
`text{Daily usage}`  `=2500 xx 3`
  `= 7500\ text{Wh}`
  `=7.5\ text{kWh  (1000 Wh = 1 kWh)}`

 

`text{Cost}`  `= 7 xx 7.5 xx 0.27` 
  `= 14.175=$14.18\ \ text{(nearest cent)}`

♦♦ Mean mark 39%.

Measurement, STD2 M7 2025 HSC 21

A house has a reverse-cycle air conditioner which uses 2.5 kW of power for cooling and 3.2 kW of power for heating. The cost of electricity is 29 cents per kWh .

  1. Find the cost, in dollars and cents, of cooling the house for 6 hours.   (1 mark)

  2. The cost of operating the air conditioner to heat the house during winter last year was $640. There are 92 days in winter.
  3. Find the number of hours, to 1 decimal place, that the air conditioner was used on average per day.   (2 marks)

Show Answers Only

a.    \(\text{Cooling cost (6 hours )}\ = 6 \times 2.5 \times 0.29 = \$4.35\)

b.    \(7.5\ \text{hours}\)

Show Worked Solution

a.    \(\text{Cooling cost (6 hours )}\ = 6 \times 2.5 \times 0.29 = \$4.35\)
 

b.    \(\text{Let \(h\) = hours used per day}\)

\(\text{Cost per day}\ = h \times 3.2 \times 0.29\)

\(\text{Cost (92 days )}\ = 92 \times h \times 3.2 \times 0.29\)

\(\text{Find \(h\) when cost = \$640:}\)

\(640\) \(=92 \times h \times 3.2 \times 0.29\)  
\(h\) \(=\dfrac{640}{92 \times 3.2 \times 0.29}=7.5\ \text{hours (1 d.p.)}\)  

Measurement, STD2 M7 2025 HSC 10 MC

An electricity company charges customers 37 cents per kWh for electricity used, \( U\), and pays customers 5 cents per kWh for electricity produced, \(P\).

The electricity company also charges customers a fee of 71 cents per day.

Which formula should be used to calculate a customer's daily cost of electricity, \(C\), in cents?

  1. \( C=71+37 U-5 P \)
  2. \( C=71+37 U+5 P \)
  3. \( C=71-37 U-5 P \)
  4. \( C=71-37 U+5 P \)
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Customer pays:}\ 71 + 37 \times U\)

\(\text{Customer receives:}\ 5 \times P\)

\(\text{Daily cost}\ = 71 + 37 \times U-5 \times P\)

\(\Rightarrow A\)

Measurement, STD2 M7 2024 HSC 17

The cost of electricity is 30.13 cents per kWh .

Calculate the cost of using a 650 W air conditioner for 6 hours.   (2 marks)

Show Answers Only

\(\text{Cost} =\$ 1.18\)

Show Worked Solution

\(\text{Usage}=6 \times 650=3900\, \text{Wh}=3.9\, \text{kWh}\)

\(\text{Cost} =3.9 \times 30.13=117.507 \,\text{c}=\$ 1.18 \, \text {(nearest cent)}\)

Measurement, STD2 M7 2021 HSC 27

The price and the power consumption of two different brands of television are shown.

The average cost for electricity is 25c/kWh. A particular family watches an average of 3 hours of television per day.

  1. The annual cost of electricity for Television A for this family is $48.18.
  2. For this family, what is the difference in the annual cost of electricity between Television A and Television B?   (2 marks)

  3. For this family, how many years will it take for the total cost of buying and using Television A to be equal to the cost of buying and using Television B?   (2 marks)

Show Answers Only

a.    `$4.38`

b.    `5\ text(years)`

Show Worked Solution
a.     `text{Annual power usage (B)}` `= 160 xx 3 xx 365`
    `=175\ 200`
    `=175.2\ text(kWh)`

♦ Mean mark part (a) 49%.

`text{Annual cost (B)}= 175.2 xx 0.25=$43.80`

`text{Difference in cost}= 48.18-43.80=$4.38`
  

♦♦ Mean mark part (b) 23%.

b.    `text{Difference in price}= 921.90-900=$21.90`

`text(Years to even out cost)=21.90/4.38=5\ text{years}`

Measurement, STD2 M7 EQ-Bank 28

Francis is buying a fridge. The energy usage of his two choices are below:

Fridge 1 (5 star rating): 227 kWh per year

Fridge 2 (2 star rating): 492 kWh per year

Each fridge has an expected life of 8 years.

If electricity costs 32.4 cents per kWh, how much will Francis save in electricity over the expected life of the more energy efficient fridge, to the nearest dollar?  (2 marks)

Show Answers Only

`$687`

Show Worked Solution

`text(Energy cost of fridge 1)`

`= 227 xx 0.324 xx 8 = $588.38`

`text(Energy cost of fridge 2)`

`= 492 xx 0.324 xx 8 = $1275.26`

`:.\ text(Energy saving)= 1275.26-588.38= 686.88~~ $687`

Measurement, STD2 M7 2018 HSC 28c

Every day, a 1200-watt microwave oven is used for 45 minutes at 40% power. Electricity is charged at $0.25 per kWh.

What is the cost of running this microwave oven for 180 days?   (3 marks)

Show Answers Only

`$16.20`

Show Worked Solution

`text(Daily usage)= 1200 xx 45/60 xx 40text(%)= 360\ text(watts)`

 

`text(180 day usage)` `= 180 xx 360`
  `= 64\ 800\ text(watt hours)= 64.8\ text(kWh)`

  
`:.\ text(C)text(ost over 180 days)= 64.8 xx 0.25= $16.20`

Measurement, STD2 M7 EQ-Bank 32

Bikram runs a hot yoga studio.

If it costs 34 cents for 1-kilowatt (1000 watts) for 1 hour, how much does it cost him to run three 3200-watt heaters from 9:00 am to 12:30 pm on a single day? (Give your answer to the nearest cent)   (2 marks)

Show Answers Only

`$11.42`

Show Worked Solution

`text(Total energy usage)`

`= 3 xx 3200 xx 3.5\ text(hours)= 33\ 600\ text(Wh)=33.6\ text(kWh)`

  `:.\ text(C)text(ost)= (33.6 xx 0.34= 11.424= $11.42\ \ text{(nearest cent)}`

Measurement, STD2 M1 2016 HSC 28b

The cost of buying a new heater is $990. It has an energy consumption of 505 kWh per year.

Energy is charged at the rate of $0.35 kWh.

How much will it cost in total to purchase and then run this heater for five years?   (2 marks)

Show Answers Only

`$1873.75`

Show Worked Solution

`text(C)text(ost to run heater for 5 years)`

`= 5 xx 505 xx 0.35= $883.75`
 

`:.\ text(Total purchase and running cost)`

`= 883.75 + 990= $1873.75`

Measurement, STD2 M1 2015 HSC 30a

The energy consumption of a computer in standby mode is 21 watts. The cost of electricity is 31 cents per kWh.

A school computer room has 20 computers.

How much will the school save by switching off all 20 computers during 11 weeks of school holidays?   (2 marks)

Show Answers Only

`$240.61`

Show Worked Solution

`text(21 watts usage per computer per hour.)`

♦ Mean mark 49%.

`text(Watts used by 20 computers in 11 weeks)`

`= 21 xx 20 xx 24 xx 7 xx 11`

`= 776\ 160\ text(Wh)= 776.16\ text(kWh)` 
  

`:.\ text(C)text(ost of energy)`

`= 776.16 xx $0.31`

`= $240.6096= $240.61\ \ text{(nearest cent)}`
  

`:.\ text(The school will save $240.61 by switching)`

`text(off all the computers.)`

Measurement, STD2 M1 2014 HSC 20 MC

In a household of 4, each member uses an average of 13 minutes of hot water per day.

The household uses a 9 kW hot water unit.

Electricity is charged at 11.97 c/kWh when the hot water unit is being used.

What is the electricity cost for the hot water used by this household in one week?

  1. $1.63
  2. $6.54
  3. $392.14
  4. $653.56
Show Answers Only

`B`

Show Worked Solution

`text(Usage per day) = 4 xx 13 = 52\ text(mins)`

♦ Mean mark 39%.

`text(Usage per week) = 7 xx 52 = 364\ text(mins)`

`text(Converting to kWh)`

`= text{(hours of usage)} xx 9\ text(kW)`

`= 364/60 xx 9 = 54.6\ text(kWh)`
 

`:.\ text(C)text(ost)` `= 54.6 xx 11.97 text(c)`
  `~~ 654 text(c)=$6.54`

`=>  B`

Measurement, STD2 M1 2013 HSC 26d

A section of Jim’s electricity bill is shown.

2013 26d

  1. What is the value of `A`?   (1 mark)

  2. How much will Jim save if he uses 154 kWh of energy at the Off-peak rate rather than at the Peak rate?   (2 marks)

Show Answers Only

a.    `1084.4`

b.    `$ 58.78\ \ \ (text(nearest cent) )`

Show Worked Solution
a.     `A` `=\ text(Last reading + Energy used)`
    `= 560.9 + 523.5= 1084.4`
♦ Mean mark
part (a) 43%
part (b) 46%.

 

b.     `text(C)text(ost at off-peak)` `= 154 xx 9.6`
    `= 1478.4\ text(cents)`

 

`text(C)text(ost at peak)` `=154 xx 47.77`
  `= 7356.58\ text(cents)`

 

`:.\ text(Saving)` `=7356.58-1478.4`
  `=5878.18= $58.78\ text{(nearest cent)}`