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.