Mathematics Standard • Year 11 • Module 2 • Lesson 18
Units of Energy and Mass — Past-Paper Style
HSC Mathematics Standard 2-style writing: multi-mark short answers and one extended response on electricity cost analysis, with explicit marking criteria.
1. Short-answer questions
1.1 A clothes dryer rated 2500 W is used for 50 minutes. Electricity costs 36 cents per kWh. Calculate the cost of one drying cycle, to the nearest cent. 3 marks Band 3
1.2 A muesli bar shows energy of 720 kJ per 35 g serve.
(a) Convert 720 kJ to Calories (kcal), to 1 d.p.
(b) If a person eats 3 of these bars after a workout, calculate the total energy intake in kJ. 3 marks Band 3–4
1.3 A delivery truck has its own mass of 6.8 t. It is loaded with crates whose total mass is 2450 kg.
(a) Express the total mass in tonnes.
(b) If the legal weight limit for the truck is 9.5 t, by how many kilograms is the truck under (or over) the limit? Clearly state which. 4 marks Band 4
2. Extended response
2.1 A small Sydney household uses the following appliances daily.
Fridge: 200 W, running continuously (24 hours per day).
Kettle: 2400 W, used for a total of 12 minutes per day.
TV + lights: a combined 250 W, used for 5 hours per day.
Hot-water system: 3500 W, running for an average of 2 hours per day.
(a) Calculate the daily energy used by each appliance in kWh.
(b) Calculate the total daily energy use of the household, in kWh.
(c) Electricity costs 35 cents per kWh. Calculate the household's daily cost, then the annual cost (365 days), to the nearest dollar.
(d) If the household replaces the hot-water system with a heat-pump unit using only 800 W for the same 2 hours/day, calculate the new annual cost. By how many dollars per year does the household save? 7 marks Band 5–6
Explicit marking criteria
Part (a) — 2 marks
• 1 mark — correct conversions (W → kW; min → h).
• 1 mark — correct daily kWh for all four appliances using E = P × t.
Part (b) — 1 mark
• 1 mark — correct daily total kWh from the four appliances.
Part (c) — 2 marks
• 1 mark — correct daily cost in dollars (or cents).
• 1 mark — correct annual cost to the nearest dollar.
Part (d) — 2 marks
• 1 mark — correctly recomputes annual cost with the 800 W heat-pump unit (substituted into the daily total).
• 1 mark — correct dollar savings per year, with a clear conclusion sentence.
Your response:
Stuck? Make a 4-row table: appliance | P (kW) | t (h) | kWh. Sum the kWh column for the daily total, then multiply by 35 c and by 365.How did this worksheet feel?
What I'll revisit before next class:
1.1 — Dryer cost (3 marks)
Sample response.
P = 2500 ÷ 1000 = 2.5 kW; t = 50 ÷ 60 = 5/6 h ≈ 0.833 h.
E = 2.5 × (50/60) = 125/60 ≈ 2.083 kWh.
Cost = 2.083 × 36 ≈ 75.0 cents ≈ $0.75.
Marking notes. 1 mark — correct conversions (W → kW, min → h). 1 mark — correct E in kWh. 1 mark — correct cost with units. Common error: forgetting the time conversion gives E = 2.5 × 50 = 125 kWh — a clearly unrealistic answer worth 0/3.
1.2 — Muesli bar conversions (3 marks)
(a) Sample response. 720 ÷ 4.184 ≈ 172.1 Cal.
(b) Sample response. 3 × 720 = 2160 kJ.
Marking notes. (a) 1 mark — uses ÷ 4.184 correctly with the right direction (kJ → Cal). (b) 1 mark — correct multiplication. 1 mark — both answers have correct units.
1.3 — Truck total mass and limit check (4 marks)
(a) Sample response. Truck = 6.8 t = 6800 kg; load = 2450 kg; total = 6800 + 2450 = 9250 kg = 9.25 t.
(b) Sample response. Limit = 9.5 t = 9500 kg; under by 9500 − 9250 = 250 kg under the limit. The truck is legal to drive.
Marking notes. (a) 1 mark — converts to common unit. 1 mark — correct total in tonnes. (b) 1 mark — correct numerical difference in kg. 1 mark — clear statement of "under" (or "over"). A response of just "250 kg" with no direction loses one mark.
2.1 — Household electricity audit, sample Band-6 (7 marks)
Sample Band-6 response.
(a) Daily kWh per appliance.
Fridge: P = 0.2 kW, t = 24 h → E = 0.2 × 24 = 4.8 kWh.
Kettle: P = 2.4 kW, t = 12/60 = 0.2 h → E = 2.4 × 0.2 = 0.48 kWh.
TV + lights: P = 0.25 kW, t = 5 h → E = 0.25 × 5 = 1.25 kWh.
Hot-water: P = 3.5 kW, t = 2 h → E = 3.5 × 2 = 7 kWh. [1 mark — all conversions correct. 1 mark — all four kWh values correct.]
(b) Daily total.
Total = 4.8 + 0.48 + 1.25 + 7 = 13.53 kWh/day. [1 mark — correct sum.]
(c) Daily and annual cost.
Daily cost = 13.53 × 35 = 473.55 cents ≈ $4.74. [1 mark — daily cost.]
Annual cost = 4.7355 × 365 ≈ $1728 (to the nearest dollar). [1 mark — annual cost.]
(d) Heat-pump replacement and savings.
New hot-water: P = 0.8 kW, t = 2 h → E = 0.8 × 2 = 1.6 kWh (was 7 kWh).
New daily total = 13.53 − 7 + 1.6 = 8.13 kWh.
New daily cost = 8.13 × 35 = 284.55 c = $2.8455.
New annual cost = 2.8455 × 365 ≈ $1039. [1 mark — new annual cost.]
Savings = $1728 − $1039 = $689 per year.
Conclusion: replacing the hot-water system saves approximately $689 per year. [1 mark — clear savings sentence with units and time period.]
Total: 7/7.
Band descriptors for marker.
Band 3: Correctly calculates kWh for 2–3 appliances but forgets W→kW or min→h on one; correct daily total only partially. ≈ 3 marks.
Band 4: All four daily kWh correct; correct daily total; correct daily cost; but does not multiply by 365 (skips annual) or gets the annual cost wrong. ≈ 4–5 marks.
Band 5: Full calculation for (a)–(c) including annual; attempts (d) but forgets to subtract the OLD hot-water energy before adding the new one. ≈ 5–6 marks.
Band 6: Complete and correct including a clear savings sentence in (d), with units and a clear "per year" time frame. 7/7.