Mathematics Standard • Year 11 • Module 2 • Lesson 18
Units of Energy and Mass, Problem Set
Apply mass, food-energy and electrical-energy conversions to realistic Australian household and nutrition scenarios.
Problem 1, Pool pump annual cost
A household pool pump is rated at 750 W. The owner runs it for 8 hours per day, every day of the year. Electricity costs 32 cents per kWh.
Set up: What are we solving for?
(i) Calculate the daily energy use of the pump in kWh. 2 marks
(ii) Calculate the daily cost in dollars, to the nearest cent. 1 mark
(iii) Calculate the annual cost (365 days), to the nearest dollar. 2 marks
Problem 2, Lunchbox energy audit
A student's lunchbox contains:
1 sandwich (energy = 1850 kJ)
1 apple (energy = 360 kJ)
1 muesli bar (energy = 756 kJ)
1 small drink (energy = 420 Cal, note the food Calorie unit)
Set up: What are we solving for?
(i) Convert the drink's energy from Calories to kilojoules, to 1 d.p. 1 mark
(ii) Calculate the total lunchbox energy in kilojoules. 2 marks
(iii) The student's recommended daily energy intake is 8700 kJ. Express the lunchbox total as a percentage of the daily intake, to 1 d.p. 2 marks
Problem 3, Medication course mass
A doctor prescribes a 250 mg antibiotic capsule three times a day for 7 days, followed by 125 mg twice a day for a further 5 days as a tapering dose.
Set up: What are we solving for?
(i) Calculate the total mass of antibiotic, in milligrams, taken during the 7-day full-dose phase. 1 mark
(ii) Calculate the total mass, in milligrams, during the 5-day tapering phase. 1 mark
(iii) Find the total mass of antibiotic taken across the whole course. Express your answer in grams. 3 marks
Problem 4, Choosing a more efficient heater
A family is choosing between two electric heaters.
Heater A: rated 2400 W; needs to run 4 hours per day to warm the room.
Heater B: rated 1800 W; needs to run 6 hours per day for the same warming effect.
Set up: What are we solving for?
(i) Calculate the daily energy used by each heater in kWh. 2 marks
(ii) If electricity costs 34 cents per kWh, calculate the daily cost of each heater (to the nearest cent). 1 mark
(iii) Over a winter period of 90 days, which heater is cheaper to run, and by how much (to the nearest dollar)? State your conclusion clearly. 2 marks
Problem 5, Calorie tracking and conversion
A fitness app tells a user they have burnt 480 Calories (kcal) in a 45-minute spin class. Their daily energy intake is 9200 kJ.
Set up: What are we solving for?
(i) Convert the 480 Calories burnt to kilojoules. 1 mark
(ii) Express the calories burnt as a percentage of the user's daily intake (in kJ), to 1 d.p. 2 marks
(iii) If the user wanted to burn 2500 kJ in one session at the same rate, how many minutes would they need to spin? (Round to the nearest minute.) 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Problem 1, Pool pump annual cost
Set up. Convert W → kW, find daily kWh, daily cost, then scale to annual.
(i) P = 750 ÷ 1000 = 0.75 kW; daily E = 0.75 × 8 = 6 kWh.
(ii) Daily cost = 6 × 32 = 192 cents = $1.92.
(iii) Annual cost = 1.92 × 365 = 700.8 ≈ $701.
Problem 2, Lunchbox energy audit
Set up. Convert all items to a common unit (kJ), sum the total, then express as a percentage of 8700 kJ.
(i) Drink = 420 × 4.184 = 1757.28 ≈ 1757.3 kJ.
(ii) Total = 1850 + 360 + 756 + 1757.3 = 4723.3 kJ.
(iii) Percentage = 4723.3 ÷ 8700 × 100 ≈ 54.3% of daily intake.
Problem 3, Medication course
Set up. Phase 1 total + Phase 2 total, then convert mg → g.
(i) Full dose: 250 × 3 × 7 = 5250 mg → 5250 mg.
(ii) Taper: 125 × 2 × 5 = 1250 mg → 1250 mg.
(iii) Total = 5250 + 1250 = 6500 mg = 6500 ÷ 1000 = 6.5 g.
Problem 4, Heater comparison
Set up. Both heaters use the same daily energy if P × t is equal; calculate to confirm, then cost it out across the winter period.
(i) Heater A: 2.4 × 4 = 9.6 kWh per day. Heater B: 1.8 × 6 = 10.8 kWh per day.
(ii) A: 9.6 × 34 = 326.4 cents ≈ $3.26. B: 10.8 × 34 = 367.2 cents ≈ $3.67.
(iii) 90-day cost: A = 3.264 × 90 = $293.76; B = 3.672 × 90 = $330.48. Difference = $330.48 − $293.76 = $36.72 ≈ $37. Heater A is cheaper by about $37 over winter. (Common slip: assuming the higher-wattage heater is always more expensive, here it runs fewer hours and wins.)
Problem 5, Calorie tracking
Set up. Convert calories to kJ; compare to daily intake; then derive a burn rate to invert the question.
(i) 480 × 4.184 = 2008.32 kJ (≈ 2008.3 kJ).
(ii) 2008.32 ÷ 9200 × 100 ≈ 21.8% of daily intake.
(iii) Burn rate = 2008.32 ÷ 45 ≈ 44.63 kJ/min. To burn 2500 kJ: 2500 ÷ 44.63 ≈ 56.02 ≈ 56 minutes.