Mathematics Standard • Year 11 • Module 2 • Lesson 18

Units of Energy and Mass, Skill Drill

Drill the conversion chains for mass (mg, g, kg, t), energy (J, kJ, MJ, kcal) and electrical energy (E = P × t in kWh), one step at a time.

Build · Skill Drill

1. Quick recall

Answer each question in the space provided. 1 mark each

Q1.1 Complete each mass conversion factor:

1 t = ____ kg = ____ g. 1 g = ____ mg. To go from g to kg: ____________ by 1000.

Q1.2 Complete each energy conversion:

1 kJ = ____ J. 1 MJ = ____ kJ. 1 Cal (kcal) = ____ kJ. 1 kWh = ____ kJ.

Q1.3 Write the electrical energy formula and the units required for each variable.

E ( ____ ) = P ( ____ ) × t ( ____ )

Stuck? Revisit lesson § Formula Panel, Energy and Mass Formulas.

2. Worked example, electricity cost for an appliance

Every line of working has a reason on the right.

Problem. A 1500 W heater runs for 45 minutes. Electricity costs 33 cents per kWh. Find (a) the energy used in kWh and (b) the cost.

Step 1, Convert power to kW.

P = 1500 ÷ 1000 = 1.5 kW

Reason: E = P × t needs P in kW (not W).

Step 2, Convert time to hours.

t = 45 ÷ 60 = 0.75 h

Reason: E = P × t needs t in hours (not minutes).

Step 3, Substitute into E = P × t.

E = 1.5 × 0.75 = 1.125 kWh

Reason: now both inputs are in compatible units (kW and h) the answer is in kWh.

Step 4, Multiply energy by cost per kWh.

Cost = 1.125 × 33 = 37.125 cents ≈ 37.1 cents

Reason: cost (cents) = energy (kWh) × price (cents per kWh).

Conclusion. (a) 1.125 kWh. (b) 37.1 cents (or $0.37 to the nearest cent).

3. Faded example, fill in the missing steps

A 2200 W dishwasher runs for 90 minutes. Electricity costs 36 cents per kWh. Find the cost of one cycle. 4 marks

Step 1, P to kW: P = 2200 ÷ ____ = ____ kW

Step 2, t to hours: t = 90 ÷ ____ = ____ h

Step 3, E = P × t: E = ____ × ____ = ____ kWh

Step 4, Cost: Cost = ____ × 36 = ____________ cents

Conclusion. One dishwasher cycle costs ____________ cents (or $ ____________).

Stuck? Revisit lesson § Worked Example 3, Electricity Cost. Always convert BEFORE substituting.

4. Graduated practice, energy and mass

Show your working. Round monetary answers to the nearest cent or dollar as required.

Foundation, single-step conversions (4 questions)

Q	Problem	Answer
4.1 1	Convert 4.5 kg to grams.
4.2 1	Convert 750 mg to grams.
4.3 1	Convert 6500 J to kilojoules.
4.4 1	Convert 2.3 MJ to kilojoules.

Standard, typical HSC difficulty (6 questions)

Show at least one line of substitution and label units on every answer.

4.5 A 1.8 t truck is loaded with 540 kg of cement. Calculate the total mass in tonnes. 2 marks

4.6 A food label shows the energy content as 1620 kJ per serve. Convert this to Calories (kcal), correct to 1 decimal place. 2 marks

4.7 A 0.8 kW slow cooker runs for 6 hours. Find the energy used in kWh. 2 marks

4.8 A 2000 W kettle is used for 4 minutes. Find the energy used in kWh. 2 marks

4.9 A household uses 28 kWh of electricity in a day. Electricity costs 31 cents per kWh. Find the daily cost in dollars. 2 marks

4.10 A vitamin supplement contains 2.5 mg per tablet. A patient takes 2 tablets per day for 60 days. Find the total mass of supplement taken, in grams. 2 marks

Extension, combine two components (2 questions)

4.11 A 1600 W air conditioner runs for 5 hours a day. Electricity costs 34 cents per kWh. Find (a) daily kWh, (b) daily cost in dollars, and (c) annual cost (365 days), to the nearest dollar. 3 marks

4.12 An adult athlete eats 3 muesli bars (756 kJ each), a sandwich (1800 kJ) and a smoothie (1240 kJ). (a) Find the total energy intake in kJ. (b) Convert this total to Calories (kcal), to 1 d.p. (c) If their daily requirement is 12 500 kJ, by how many kilojoules is the intake short of the requirement? 3 marks

Stuck on 4.11(c)? Multiply your daily cost (in dollars) by 365, keep the same units throughout.

5. Self-check the easy 3

Tick once you've verified each method.

For 4.1 (kg → g) I MULTIPLIED by 1000 because I'm going to a smaller unit.

For 4.3 (J → kJ) I DIVIDED by 1000 because I'm going to a larger unit.

For 4.7 my P was already in kW and t was already in hours, no conversion needed before E = P × t.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers, Do not peek before attempting

Q1.1, Mass conversions

1 t = 1000 kg = 1 000 000 g. 1 g = 1000 mg. g → kg: divide by 1000.

Q1.2, Energy conversions

1 kJ = 1000 J. 1 MJ = 1000 kJ. 1 Cal (kcal) = 4.184 kJ. 1 kWh = 3600 kJ.

Q1.3, Electrical energy formula

E (kWh) = P (kW) × t (hours).

Q3, Faded example (dishwasher)

Step 1: P = 2200 ÷ 1000 = 2.2 kW. Step 2: t = 90 ÷ 60 = 1.5 h. Step 3: E = 2.2 × 1.5 = 3.3 kWh. Step 4: Cost = 3.3 × 36 = 118.8 cents. Conclusion: cost = 118.8 cents (≈ $1.19).

Q4.1-4.5 kg → g

4.5 × 1000 = 4500 g.

Q4.2-750 mg → g

750 ÷ 1000 = 0.75 g.

Q4.3-6500 J → kJ

6500 ÷ 1000 = 6.5 kJ.

Q4.4-2.3 MJ → kJ

2.3 × 1000 = 2300 kJ.

Q4.5, Truck + cement total mass

540 kg = 0.54 t. Total = 1.8 + 0.54 = 2.34 t.

Q4.6-1620 kJ → Cal

1620 ÷ 4.184 ≈ 387.2 Cal.

Q4.7-0.8 kW slow cooker, 6 h

E = 0.8 × 6 = 4.8 kWh.

Q4.8-2000 W kettle, 4 min

P = 2 kW; t = 4 ÷ 60 = 1/15 h ≈ 0.0667 h. E = 2 × (4/60) = 8/60 ≈ 0.13 kWh (or exactly 2/15 kWh).

Q4.9-28 kWh × 31 cents

28 × 31 = 868 cents = $8.68.

Q4.10, Vitamin total

Per day: 2 × 2.5 = 5 mg; 60 days: 5 × 60 = 300 mg. In grams: 300 ÷ 1000 = 0.3 g.

Q4.11, Air conditioner annual cost

(a) P = 1.6 kW; daily E = 1.6 × 5 = 8 kWh. (b) Daily cost = 8 × 34 = 272 cents = $2.72. (c) Annual = 2.72 × 365 = 992.8 ≈ $993.

Q4.12, Athlete energy intake

(a) Total = 3 × 756 + 1800 + 1240 = 2268 + 1800 + 1240 = 5308 kJ.
(b) 5308 ÷ 4.184 ≈ 1268.6 Cal.
(c) Shortfall = 12 500 − 5308 = 7192 kJ below requirement.