A Top Candidate Guide
The aptitude test is usually the very first real gate in the recruitment process, before a panel ever sees your face, before your resume gets a second look. Departments use it because it's a fast, standardized way to compare hundreds of applicants on skills that actually matter on the job: doing quick math under pressure, reading and following written instructions exactly, reasoning through mechanical systems, and staying observant when it counts.
Here's what candidates consistently underestimate: this test rewards familiarity with the *format* as much as it rewards raw ability. Someone who's mechanically minded but has never seen a gear-ratio question phrased the way a test phrases it will lose time and confidence they didn't need to lose. Someone who's genuinely strong at math can still get tripped up by order-of-operations questions if they haven't drilled the specific trap those questions set. Practice closes that gap, not by making you smarter, but by making the format familiar enough that your actual ability shows through clearly, without the clock and the unfamiliar phrasing working against you.
Treat this guide as exactly that: closing the familiarity gap. Work through a chapter, then go test it in the Aptitude Trainer, then come back here for whatever tripped you up. That loop, practice, test, review, is what actually moves your score.
Exact formats vary by department and by province, but most Canadian fire services lean on one of a small number of established testing approaches:
Whichever specific test your target department uses, the underlying skills being measured are consistent: math, mechanical reasoning, reading comprehension, observation and memory, and situational judgment show up almost everywhere, spatial or map-reading sections appear in some formats. That's exactly why this guide, and the Aptitude Trainer, are organized by skill category rather than by test vendor, master the category, and you're ready regardless of which specific test lands in front of you.
Always confirm the specific test format with your target department directly, requirements and vendors do change, and this guide is a preparation tool, not a guarantee of what any one department will use.
A fraction is a part of a whole, written as a numerator (top number) over a denominator (bottom number). Most aptitude tests ask you to add or multiply fractions.
To add or subtract fractions: the denominators must match first. Find a common denominator (a number both original denominators divide into evenly), convert each fraction to that denominator by multiplying top and bottom by the same number, then add or subtract just the numerators.
To multiply fractions: no common denominator needed, just multiply straight across, numerator times numerator, denominator times denominator, then simplify if possible.
1/3 + 1/4 = ? Common denominator of 3 and 4 is 12. 1/3 becomes 4/12, 1/4 becomes 3/12. Add: 4/12 + 3/12 = 7/12.
2/5 x 3/4 = ? Step 1: multiply the numerators: 2 x 3 = 6. Step 2: multiply the denominators: 5 x 4 = 20. Step 3: you now have 6/20. Step 4: simplify by finding the greatest common factor of 6 and 20, which is 2. Step 5: divide both by 2: 6/20 becomes 3/10. Final answer: 3/10.
5/6 - 1/4 = ? Common denominator of 6 and 4 is 12. 5/6 becomes 10/12, 1/4 becomes 3/12. Subtract: 10/12 - 3/12 = 7/12.
A percentage is a number out of 100. "Percent" literally means "per hundred." Nearly every percentage question comes down to one move: convert the percent to a decimal by dividing by 100, then multiply.
Finding a percentage of a number: decimal form of the percent, times the number. 20% of 150 = 0.20 x 150 = 30.
Percent increase or decrease: find the change amount first (percent times the original number), then add it (increase) or subtract it (decrease) from the original.
Finding what percent one number is of another: divide the part by the whole, then multiply by 100.
A value of 80 is increased by 25%. 25% of 80 = 0.25 x 80 = 20. New value = 80 + 20 = 100.
What is 15% of 60? Step 1: write the percent as a fraction over 100: 15/100. Step 2: convert that to a decimal by dividing 15 by 100: 0.15. Step 3: multiply the decimal by the number: 0.15 x 60. Step 4: break the multiplication down if needed: 0.1 x 60 = 6, and 0.05 x 60 = 3. Step 5: add those two pieces together: 6 + 3 = 9. Final answer: 9.
18 is 30% of what number? Divide the part by the decimal form of the percent: 18 / 0.30 = 60. Check: 30% of 60 = 0.30 x 60 = 18, correct.
Algebra problems ask you to find an unknown value, usually written as x. The goal is always to isolate x on one side of the equation by undoing whatever's been done to it.
The method: undo addition or subtraction first (move the constant to the other side), then undo multiplication or division last. Whatever you do to one side of the equation, you must do to the other.
3x + 5 = 20. Subtract 5 from both sides: 3x = 15. Divide both sides by 3: x = 5.
Solve: 4x - 7 = 21. Step 1: identify the goal, get x alone on one side. Step 2: undo the subtraction first, add 7 to both sides: 4x - 7 + 7 = 21 + 7, which simplifies to 4x = 28. Step 3: undo the multiplication, divide both sides by 4: 4x/4 = 28/4. Step 4: simplify: x = 7. Step 5: check your work by substituting back in: 4(7) - 7 = 28 - 7 = 21, which matches, confirming x = 7 is correct.
Solve: x/3 + 4 = 9. Subtract 4 from both sides: x/3 = 5. Multiply both sides by 3: x = 15. Check: 15/3 + 4 = 5 + 4 = 9, correct.
When an expression has multiple operations, there's a required order: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). PEMDAS is the common way to remember it.
3 + 4 x 2 = ? Multiplication happens before addition: 4 x 2 = 8, then 3 + 8 = 11. Not 7 x 2 = 14.
Solve: 12 - (3 + 2) x 2. Step 1: parentheses first: 3 + 2 = 5, so the expression becomes 12 - 5 x 2. Step 2: multiplication next, before subtraction: 5 x 2 = 10, so the expression becomes 12 - 10. Step 3: subtraction last: 12 - 10 = 2. Final answer: 2. Notice subtracting left to right first (12 - 5 = 7, then 7 x 2 = 14) gives the wrong answer, order matters.
Solve: (10 - 4) x 3 + 2. Parentheses first: 10 - 4 = 6, giving 6 x 3 + 2. Multiplication next: 6 x 3 = 18, giving 18 + 2. Addition last: 18 + 2 = 20.
A ratio compares two quantities. When you're asked to split a total according to a ratio, think of the ratio numbers as "parts" of the whole.
The method: add the ratio numbers together to find the total number of parts, divide the total amount by that to find the value of one part, then multiply by whichever ratio number you need.
Split 25 in a 2:3 ratio. Total parts = 2 + 3 = 5. One part = 25 / 5 = 5. First group = 2 x 5 = 10. Second group = 3 x 5 = 15.
Split 40 in a 3:5 ratio. Step 1: add the ratio numbers to find total parts: 3 + 5 = 8. Step 2: divide the total amount by total parts to find the value of one part: 40 / 8 = 5. Step 3: multiply each ratio number by that value: first group = 3 x 5 = 15, second group = 5 x 5 = 25. Step 4: check your work, 15 + 25 = 40, which matches the original total, confirming the split is correct.
Split 60 among three people in a 2:3:1 ratio. Total parts = 2+3+1 = 6. One part = 60/6 = 10. Shares: 2x10=20, 3x10=30, 1x10=10. Check: 20+30+10=60, correct.
Area measures the space inside a shape. Perimeter measures the distance around its edge. Each shape has its own formula.
Rectangle: Area = length x width. Perimeter = 2 x (length + width).
Triangle: Area = (base x height) / 2.
A rectangle is 8 long and 5 wide. Area = 8 x 5 = 40. Perimeter = 2 x (8 + 5) = 2 x 13 = 26.
Find the area of a triangle with base 14 and height 6. Step 1: write the formula: Area = (base x height) / 2. Step 2: multiply base by height first: 14 x 6 = 84. Step 3: divide that result by 2: 84 / 2 = 42. Final answer: 42. Common trap: dividing the base or height by 2 before multiplying instead of dividing the final product, both approaches happen to give the same answer here, but keeping the order consistent (multiply, then divide) avoids errors on harder numbers.
A rectangular garage floor is 20 ft by 12 ft. What's the area, and how much baseboard (perimeter) is needed? Area = 20 x 12 = 240 sq ft. Perimeter = 2 x (20+12) = 2 x 32 = 64 ft of baseboard needed.
An exponent tells you how many times to multiply a number by itself. In 2^4, the 2 is the base and the 4 is the exponent, meaning 2 x 2 x 2 x 2.
3^3 = 3 x 3 x 3 = 27. Not 3 x 3 = 9, and not 3 x 3 = 9 (a common shortcut error is stopping one multiplication early).
Calculate 4^3. Step 1: an exponent of 3 means multiply the base by itself 3 times: 4 x 4 x 4. Step 2: multiply the first two: 4 x 4 = 16. Step 3: multiply that result by the remaining 4: 16 x 4 = 64. Final answer: 64. Writing out each multiplication step separately, rather than trying to jump to the answer, is the reliable way to avoid stopping one multiplication too early.
Calculate 5^2, then use it in a follow-up: what is 5^2 + 3^2? 5^2 = 5x5 = 25. 3^2 = 3x3 = 9. 25 + 9 = 34.
Average (mean): add every value together, then divide by how many values there are.
Median: put the numbers in order from smallest to largest. If there's an odd count, the median is the middle number. If even, average the two middle numbers.
Set: 6, 8, 5, 7, 9. Ordered: 5, 6, 7, 8, 9. Median = 7 (the middle value). Mean = (5+6+7+8+9)/5 = 35/5 = 7.
Find the mean and median of: 12, 7, 9, 15, 7. Step 1, for the mean: add all values: 12+7+9+15+7 = 50. Step 2: divide by how many values there are: 50 / 5 = 10. Mean = 10. Step 3, for the median: sort the values from smallest to largest: 7, 7, 9, 12, 15. Step 4: with 5 values (an odd count), the median is the middle one, the 3rd value: 9. Median = 9. Notice the mean and median are different numbers here, that's normal and expected.
Find the mode of: 4, 7, 7, 9, 7, 3. The mode is the value that appears most often. 7 appears three times, more than any other value. Mode = 7.
Rate problems connect two quantities over time or distance: gallons per minute, kilometres per hour, work per crew size. Almost all of them reduce to one relationship: rate x time = total, or its rearrangements.
The method: identify the rate (per minute, per hour, per worker), identify what you're solving for, and multiply or divide accordingly, always double-check your units match before you calculate.
A pump delivers 250 GPM. How much in 4 minutes? 250 x 4 = 1,000 gallons. Rate x time = total.
A pump delivers 180 gallons in 3 minutes. What's the rate per minute, and how much in 7 minutes? Step 1: find the rate by dividing total gallons by total minutes: 180 / 3 = 60 gallons per minute. Step 2: to find the amount for a new time, multiply the rate by the new number of minutes: 60 x 7 = 420 gallons. Step 3: sanity check, since 7 minutes is a bit more than double 3 minutes, the answer should be a bit more than double 180 (which is 360), and 420 is indeed a bit more than 360, so the answer is reasonable.
Two pumps working together deliver 90 gallons in 3 minutes. If one pump alone delivers 20 gallons per minute, how much does the second pump alone deliver per minute? Combined rate = 90/3 = 30 gallons per minute. Second pump's rate = 30 - 20 = 10 gallons per minute.
Gears are wheels with teeth that mesh together to transfer motion. Two things to know: direction and ratio.
Direction: two gears touching directly always spin in opposite directions. In a chain of gears, count the reversals, an even number of meshed pairs returns to the original direction, an odd number reverses it.
Ratio: the ratio of teeth counts tells you the ratio of turns. A small gear with fewer teeth turns more times than a large gear with more teeth for the same amount of engagement.
A 10-tooth gear drives a 30-tooth gear. Ratio is 10:30, or 1:3. Every 3 turns of the small gear equals 1 turn of the large gear.
A 12-tooth gear meshes with a 36-tooth gear. What's the ratio, and if the small gear turns 6 times, how many times does the large gear turn? Ratio = 12:36, simplified to 1:3. Every 3 turns of the small gear = 1 turn of the large gear. 6 turns of the small gear ÷ 3 = 2 turns of the large gear.
A gear train has three gears in a row: a 10-tooth drive gear, a 20-tooth idler gear, and a 40-tooth final gear. If the drive gear turns clockwise, which way does the final gear turn, and what's the overall ratio? Each meshed pair reverses direction, two reversals bring the final gear back to clockwise, same as the drive gear. Overall ratio (drive to final) = 10:40, or 1:4, every 4 turns of the drive gear equals 1 turn of the final gear.
Pulleys redirect or reduce the force needed to lift a load.
Fixed pulley: changes direction only. The force needed still equals the full weight of the load.
Movable pulley: roughly halves the force needed, because the load is supported by two rope sections instead of one.
Block and tackle: count how many rope sections actually support the load, then divide the load's weight by that number for an estimate of the force needed.
A block and tackle has 3 supporting strands lifting 300 lb. Force needed ≈ 300 / 3 = 100 lb.
A block and tackle has 4 supporting strands lifting a 400 lb load. Force needed ≈ 400 / 4 = 100 lb. Compare this to a single fixed pulley lifting the same 400 lb load, which would still need the full 400 lb of force, more supporting strands is what actually reduces the effort.
A single movable pulley lifts a 250 lb load. What force is needed, and how does that compare to using two movable pulleys in the same system? One movable pulley: force ≈ 250/2 = 125 lb. Two movable pulleys stacked (4 supporting strands total): force ≈ 250/4 = 62.5 lb, roughly half again.
Levers: balance around a fulcrum. Effort x effort-arm distance = load x load-arm distance. Moving the fulcrum closer to the load, or applying effort farther from the fulcrum, both increase mechanical advantage.
Torque: force x distance from the pivot point. A longer handle produces more torque for the same hand force.
Wheel and axle: mechanical advantage = wheel radius ÷ axle radius. A bigger wheel relative to the axle gives more advantage.
A 100 lb load sits 1 ft from a fulcrum. Effort is applied 4 ft from the fulcrum on the other side. Effort x 4 = 100 x 1, so effort = 25 lb.
A 60 lb load sits 2 ft from a fulcrum. How much effort is needed 6 ft from the fulcrum on the other side? Effort x 6 = 60 x 2, so effort x 6 = 120, so effort = 120 / 6 = 20 lb. Moving the effort point farther out (from 6 ft to 12 ft) would cut that required force in half again.
A torque wrench applies 90 ft-lb of torque using 30 lb of force. How long is the handle? Torque = force x distance, so distance = torque / force = 90 / 30 = 3 ft.
When flow rate is held constant, the size of the opening water passes through controls its speed. A narrower opening speeds the water up, a wider one slows it down, since the same total volume has to pass through either way.
Narrowing a hose nozzle while flow rate stays constant increases the water's exit speed, this is why a narrow nozzle produces a faster, more concentrated stream.
Two hoses carry the same flow rate. Hose A has a wide nozzle, Hose B has a narrow nozzle. Which produces a faster stream? Hose B, the narrow opening, since the same volume of water is forced through a smaller space, increasing its speed.
A fire hose flowing at a constant 200 GPM is fitted with a nozzle that has half the opening area of the standard tip. What happens to the exit velocity? With flow rate held constant, halving the opening area roughly doubles the exit velocity, the same volume has to pass through half the space in the same time.
Buoyancy: an object submerged in water experiences an upward force equal to the weight of the water it displaces (Archimedes' principle), regardless of the object's own weight.
Energy from height: the higher an object falls from, the more energy it builds up along the way, meaning more force at the moment of impact, all else being equal.
Friction resists motion between two surfaces. Rougher surfaces create more friction and require more force to keep something moving. Steeper inclines require more force to move something upward, and shift how weight is distributed, which affects stability, like a ladder set too steep or too shallow against a wall.
Read the passage once for the general idea rather than trying to memorize it. Then, for each question, go back to the specific part of the passage that answers it, don't rely on memory alone.
When a question asks for the "main point" or "main idea," look for what the passage spends the most time on, or what it closes on, rather than just the first sentence, passages often build to their real point.
Watch for questions that ask what the passage does NOT say, or what can't be concluded, these require you to check every option against the text rather than picking the first one that sounds plausible.
During the study window, don't try to memorize word for word, that approach falls apart under time pressure. Instead, build a quick mental picture of the scene and deliberately note the details most likely to be tested: numbers, names, times, locations, and anything unusual or out of place.
A technique worth practicing: scan the scene in a consistent order every time (left to right, or top to bottom), and mentally narrate it as you go ("six bottles, two tagged out of service"). Narrating out loud, even quietly, measurably improves recall for most people.
After the study window closes, resist the urge to guess immediately, take a half-second to actually picture the scene again before answering each question.
Look for the option that's professional, honest, and respects the proper channel, even when it's not the most dramatic or decisive-sounding choice. Panels are testing judgment and professionalism, not boldness.
Eliminate options first that involve dishonesty, going over someone's head without cause, or ignoring a safety concern, those are almost never correct regardless of how the scenario is framed. Between the remaining options, the strongest answer usually balances taking the concern seriously with respecting the chain of command.
These questions reward broad familiarity with fire service terms and concepts more than memorized textbook definitions. When you're unsure, eliminate any option that's clearly about a different topic area first, then compare what's left.
Build familiarity in clusters rather than isolated facts: fire behaviour (triangle, flashover, backdraft) as one group, apparatus and equipment as another, incident command and safety systems as a third. Understanding how the concepts in each cluster relate to each other sticks better than memorizing them one at a time.
Firefighter-knowledge practice is one area where dedicated third-party tools already do excellent, deep work, apps like Essentials of Firefighting offer extensive question banks built directly around standard fire service training material. Rather than duplicate that depth, this guide and the Aptitude Trainer give you a strong working base, and we'd genuinely recommend pairing that with a dedicated firefighter-knowledge app if you want to go deeper on this category specifically, our aptitude trainer's own knowledge questions are here to round out the full test experience, not replace focused study material where it already exists.
These questions test whether you can track direction changes reliably, a genuinely practical skill on scene, where crews give and follow directional instructions constantly (advance to the north side, ventilate the east window).
The method: picture a compass, North at the top, East to the right, South at the bottom, West to the left. A 90° clockwise turn always moves you one position clockwise around that circle (North → East → South → West → North). A 90° counterclockwise turn moves the opposite way. 180° is a straight flip to the opposite direction.
Facing North, turn 90° clockwise: now facing East. Turn another 90° clockwise: now facing South. Two clockwise quarter-turns from North always lands on South.
A crate is dragged first across ice, then across gravel. Which requires more force to keep moving at a steady pace? Gravel, since its rougher surface creates more friction than the smoother ice, requiring more force to overcome that resistance.
A firefighter drags a hose across three different surfaces at the same effort: wet grass, dry pavement, and gravel. Rank them from least to most friction. Wet grass (slickest, least friction), dry pavement (moderate), gravel (roughest, most friction), matching how much resistance each surface creates against the hose sliding across it.
Two identical containers are submerged: Container A is empty (mostly air), Container B is filled with sand. Which experiences more net buoyant lift relative to its own weight? Container A, both displace the same volume of water (so the same buoyant force), but Container A weighs far less, so that buoyant force has a much bigger effect on it relative to its own weight, which is why it floats and the sand-filled one likely sinks.
Object A is dropped from 2 metres, Object B (identical) is dropped from 8 metres. Which hits the ground with more force? Object B, since it builds up more energy over the longer fall, resulting in greater force at impact.
These questions show a shape or arrow in a reference position, then ask which option shows it correctly rotated. The underlying skill is mentally rotating an object without physically moving anything, useful for reading blueprints, apparatus diagrams, or a floor plan handed to you sideways.
The method: the same compass logic from direction questions applies here. Treat the shape's "point" as a direction and rotate it the same way you'd rotate a compass heading.
Map questions test reading a simple grid or street layout and determining direction or distance between two points, directly relevant to navigating a response area or reading a pre-incident plan.
For direction: compare the two points' positions. If the destination is above and to the right of the start, it's Northeast. Directly above is North, directly right is East, and so on around the compass.
For distance along a grid (no diagonal shortcuts): add up the horizontal blocks and the vertical blocks separately, then add those two totals together, this is sometimes called "block" or "taxicab" distance, since you can only travel along the lines, not cut across.
Start at (0,0), destination at (3,2) on the grid. Horizontal distance = 3 blocks, vertical distance = 2 blocks. Total shortest distance = 3 + 2 = 5 blocks.
These questions ask where something is located relative to your position after entering through a specific point, a direct simulation of forming a mental map while entering an unfamiliar structure, which is exactly what search and rescue requires.
The method: fix your orientation the moment you "enter," whatever direction you're facing as you walk in becomes your forward reference. Everything else on the plan is described relative to that: ahead, behind, left, or right of where you're standing, facing that way.