Type on any line or blank, or switch Draw on to write with a finger, stylus or mouse. Your work is saved in this browser on this device only. Nothing is sent anywhere. The answer key after page 2 stays covered until you open it, and it never prints with your work: it has its own print button.

Practice sheet · Energy Path · Lens 1: Math

Power & percent

Practice for The Math of Energy: kW and kWh, barrels, capacity factors, prices, emissions, efficiency and demand (pp.8–15), plus Algebra A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Energy (kWh) = power (kW) × hours. 1,000 W = 1 kW; 1 MWh = 1,000 kWh. 1 barrel = 159 L. A year has 8,760 hours.

Capacity factor = actual output ÷ (capacity × hours). Efficiency = useful out ÷ energy in. Percent change = change ÷ start.

Warm-up

One step

Watts, barrels and bills.
1

Hair dryer

A 1,200 W hair dryer runs for 30 minutes. How many kWh? What does it cost at $0.15 per kWh?

2

Barrels

How many litres are in 500 barrels? About how many barrels are in 1 m³ (1,000 L)?

3

LED year

A 10 W LED bulb is on 6 hours a day for a year. How many kWh is that?

4

Price units

Electricity sells for $43.68 per MWh. What is that in cents per kWh?

Core

Two or three steps

Keep W, kW, kWh and MWh labelled.
5

Capacity factor

A 300 MW wind farm made 788,400 MWh in a year. What was its average output, and its capacity factor?

6

Price drop

Alberta’s average pool price fell from $133.63/MWh (2023) to $62.78 (2024). What percent change is that?

Energy Practice · Energy Path · Unizon1/2
Energy Path · Unizon · PracticePower, percent & efficiency
7

Share of emissions

Canada emitted about 685 Mt CO₂e; Alberta about 260 Mt, of which oil sands about 92 Mt. What percent of Canada is Alberta? What percent of Alberta is oil sands?

8

Efficiency

A power plant is 40% efficient. How much fuel energy makes 200 units of electricity? A heat pump with COP 2.5 uses 10 kWh: how much heat does it deliver?

9

Demand data

A made-up town peaks at 50 MW and averages 35 MW. What is its load factor? How much more than average must the grid supply at peak?

10

Pipeline flow

A pipeline carries 890,000 barrels a day. About how many barrels a second is that? How many days would it take to move 10 million barrels?

Level Up

Equations

A1–A2 (pp.17–18).
11

Solve the bill

A made-up bill is $18 a month plus $0.15 per kWh: C = 18 + 0.15k. How many kWh make a $141 bill?

12

Two plans

Plan B is $6 plus $0.17 per kWh. When do the plans cost the same? Which is cheaper at 800 kWh?

13

Squares

Wire heat loss is P = I²R. With R = 2 Ω and P = 450 W, find the current I.

14

Cubes

A small turbine makes P = 0.5v³ (made-up units). Find P at v = 4 and v = 8. If P = 108, find v.

Make your own problem

Your turn to be the energy analyst

  1. Find the wattage on one device at home.
  2. Write a question about its kWh, cost or efficiency over a week or a year.
  3. Solve it, and ask what data you would need to check it.

My problem, and my worked answer:

Energy Practice · Energy Path · Unizon2/2
Energy Path · Unizon · PracticePower, percent & efficiency

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Bills, plans and the town are made-up; Alberta prices and emissions are rounded public figures (pp.12–13).

Warm-up
1
0.6 kWh · 9¢ 1.2 kW × 0.5 h = 0.6 kWh. 0.6 × $0.15 = $0.09.
2
79,500 L · ≈ 6.29 barrels 500 × 159 = 79,500. 1,000 ÷ 159 ≈ 6.29.
3
21.9 kWh 10 × 6 × 365 = 21,900 Wh = 21.9 kWh.
4
≈ 4.4¢ per kWh $43.68 ÷ 1,000 = $0.04368 per kWh.
Core
5
90 MW · 30% 788,400 ÷ 8,760 = 90. 90 ÷ 300 = 0.30. Wind doesn’t blow at full speed all the time.
6
≈ −53.0% (62.78 − 133.63) ÷ 133.63 ≈ −0.530.
7
≈ 38.0% · ≈ 35.4% 260 ÷ 685 ≈ 0.380. 92 ÷ 260 ≈ 0.354. Numbers rounded (p.13).
8
500 units · 25 kWh 200 ÷ 0.40 = 500. 2.5 × 10 = 25: a heat pump moves heat, so it can deliver more than it uses.
9
70% · 15 MW 35 ÷ 50 = 0.70. 50 − 35 = 15 MW of extra capacity for the peak.
10
≈ 10.3 barrels/s · ≈ 11.2 days A day has 24 × 3,600 = 86,400 s: 890,000 ÷ 86,400 ≈ 10.3. 10,000,000 ÷ 890,000 ≈ 11.2 days.
Level Up
11
820 kWh 0.15k = 123 → k = 820.
12
600 kWh · Plan A ($138 vs $142) 18 + 0.15k = 6 + 0.17k → 0.02k = 12 → k = 600. At 800: 18 + 120 = 138; 6 + 136 = 142.
13
15 A I² = 450 ÷ 2 = 225 → I = 15.
14
32 · 256 (8×) · v = 6 0.5 × 64 = 32; 0.5 × 512 = 256. v³ = 216 → v = 6. Double the wind, 8 times the power.
Make your own: convert to kW and hours first, keep units on every line, and say which number is “start” in a percent change.
Energy Practice · Energy Path · UnizonAnswer key