20 Mathematics Practice Questions & Answers
Every Mathematics practice question from the Firefighter Written Exam Practice Test, with the correct answer and a short explanation.
Start practice test →1. A fire pump discharges water at a steady rate of 250 gallons per minute. How many gallons will it discharge in 6 minutes?
- A.1,500 gallons✓ Answer
- B.1,560 gallons
- C.1,250 gallons
- D.256 gallons
At a constant flow rate, quantity equals rate multiplied by time, so 250 gallons/minute × 6 minutes = 1,500 gallons. Multiplying the two quantities keeps the per-minute unit consistent with the total.
Source: Firefighter Written Exam blueprint — Mathematics (applied arithmetic): quantity = rate × timeReport a problem with this question
2. A fire company has 40 firefighters, and 15% of them are certified in hazardous-materials response. How many firefighters are certified?
- A.8 firefighters
- B.4 firefighters
- C.15 firefighters
- D.6 firefighters✓ Answer
A percentage of a whole is found by multiplying the whole by the percentage as a decimal, so 40 × 0.15 = 6. Converting 15% to 0.15 before multiplying is what yields the correct count.
Source: Firefighter Written Exam blueprint — Mathematics (percentages): part = whole × percentReport a problem with this question
3. A hose lay is 500 feet long. During an operation, 2/5 of its length is deployed. How many feet of hose are deployed?
- A.200 feet✓ Answer
- B.100 feet
- C.150 feet
- D.300 feet
Taking a fraction of a quantity means multiplying, so 500 × 2/5 = 1,000/5 = 200 feet. Dividing the total into 5 equal parts of 100 feet and taking 2 of them gives the same result.
Source: Firefighter Written Exam blueprint — Mathematics (fractions): fraction of a quantityReport a problem with this question
4. One engine has a response time of 4.5 minutes and a second engine responds in 3.75 minutes. What is the total combined response time of the two engines?
- A.7.75 minutes
- B.8.20 minutes
- C.8.25 minutes✓ Answer
- D.7.25 minutes
Adding decimals requires aligning the decimal points, so 4.50 + 3.75 = 8.25 minutes. Keeping the place values lined up prevents mixing tenths with hundredths.
Source: Firefighter Written Exam blueprint — Mathematics (decimals): addition with place-value alignmentReport a problem with this question
5. A fire station is 2.5 miles from an incident. Given that 1 mile equals 5,280 feet, how many feet is the station from the incident?
- A.7,920 feet
- B.10,560 feet
- C.13,200 feet✓ Answer
- D.12,500 feet
Converting miles to feet means multiplying by the conversion factor, so 2.5 × 5,280 = 13,200 feet. The larger unit (miles) is multiplied to express the same distance in the smaller unit (feet).
Source: U.S. customary units: 1 mile = 5,280 feetReport a problem with this question
6. A rectangular room measures 12 feet by 15 feet. What is the floor area of the room?
- A.1,800 square feet
- B.27 square feet
- C.150 square feet
- D.180 square feet✓ Answer
The area of a rectangle is length times width, so 12 × 15 = 180 square feet. Multiplying the two side lengths (not adding them) accounts for the two-dimensional space.
Source: Firefighter Written Exam blueprint — Mathematics (area): rectangle area = length × widthReport a problem with this question
7. A rectangular water tank measures 10 feet long, 4 feet wide, and 3 feet deep. What is the volume of the tank?
- A.120 cubic feet✓ Answer
- B.70 cubic feet
- C.1,200 cubic feet
- D.17 cubic feet
The volume of a rectangular box is length × width × depth, so 10 × 4 × 3 = 120 cubic feet. Multiplying all three dimensions accounts for the three-dimensional space the tank occupies.
Source: Firefighter Written Exam blueprint — Mathematics (volume): box volume = length × width × depthReport a problem with this question
8. A foam solution is mixed at a ratio of 3 parts water to 1 part foam concentrate. If 60 gallons of water are used, how many gallons of foam concentrate are needed?
- A.15 gallons
- B.30 gallons
- C.180 gallons
- D.20 gallons✓ Answer
In a 3-to-1 ratio the foam concentrate is one-third of the water amount, so 60 ÷ 3 = 20 gallons. The ratio fixes each part at 20 gallons (three parts water = 60), so one part foam equals 20.
Source: Firefighter Written Exam blueprint — Mathematics (ratios and proportions)Report a problem with this question
9. A tank holds 1,000 gallons of water. A pump empties it at 200 gallons per minute. How long will it take to empty the full tank?
- A.8 minutes
- B.4 minutes
- C.5 minutes✓ Answer
- D.10 minutes
Time equals total quantity divided by rate, so 1,000 ÷ 200 = 5 minutes. Dividing the gallons by the per-minute rate cancels the gallon unit and leaves minutes.
Source: Firefighter Written Exam blueprint — Mathematics (rate problems): time = quantity ÷ rateReport a problem with this question
10. A shift is staffed by 8 firefighters. It is increased to 10 firefighters. What is the percentage increase in staffing?
- A.125%
- B.2%
- C.20%
- D.25%✓ Answer
Percentage increase is the change divided by the original amount, so (10 − 8) ÷ 8 = 2 ÷ 8 = 0.25 = 25%. The increase is measured against the starting value of 8, not the new value of 10.
Source: Firefighter Written Exam blueprint — Mathematics (percentages): percent change = change ÷ originalReport a problem with this question
11. A nozzle flows 95 gallons per minute. How many gallons will it deliver over 12 minutes of continuous operation?
- A.1,150 gallons
- B.1,140 gallons✓ Answer
- C.107 gallons
- D.1,040 gallons
Total volume equals flow rate times time, so 95 × 12 = 1,140 gallons. Multiplying the per-minute rate by the number of minutes gives the accumulated total.
Source: Firefighter Written Exam blueprint — Mathematics (rate problems): volume = flow rate × timeReport a problem with this question
12. A supply of 240 sandbags is on hand. Crews use 3/8 of them to build a barrier. How many sandbags are used?
- A.120 sandbags
- B.90 sandbags✓ Answer
- C.96 sandbags
- D.80 sandbags
A fraction of a quantity is found by multiplying, so 240 × 3/8 = 720/8 = 90 sandbags. Dividing 240 by 8 gives 30 per part, and 3 parts equal 90.
Source: Firefighter Written Exam blueprint — Mathematics (fractions): fraction of a quantityReport a problem with this question
13. A container holds 15 gallons of foam concentrate. Given that 1 gallon equals 4 quarts, how many quarts does the container hold?
- A.60 quarts✓ Answer
- B.30 quarts
- C.45 quarts
- D.19 quarts
Converting gallons to quarts means multiplying by 4, so 15 × 4 = 60 quarts. Because a quart is smaller than a gallon, the number of quarts is larger than the number of gallons.
Source: U.S. customary units: 1 gallon = 4 quartsReport a problem with this question
14. Four emergency calls had response times of 4, 6, 8, and 10 minutes. What is the average (mean) response time?
- A.7.5 minutes
- B.6 minutes
- C.28 minutes
- D.7 minutes✓ Answer
The mean is the sum of the values divided by how many there are, so (4 + 6 + 8 + 10) ÷ 4 = 28 ÷ 4 = 7 minutes. Dividing the total by the count of 4 items gives the average.
Source: Firefighter Written Exam blueprint — Mathematics (averages): mean = sum ÷ countReport a problem with this question
15. A fire apparatus travels at a steady 45 miles per hour. How far does it travel in 20 minutes?
- A.135 miles
- B.9 miles
- C.15 miles✓ Answer
- D.22.5 miles
Distance equals speed times time, and 20 minutes is 1/3 of an hour, so 45 × 1/3 = 15 miles. The time must be expressed in hours to match the speed's per-hour unit.
Source: Firefighter Written Exam blueprint — Mathematics (rate problems): distance = speed × timeReport a problem with this question
16. A booster tank contains 600 gallons of water. During an operation, 25% of the water is used. How many gallons of water remain?
- A.575 gallons
- B.450 gallons✓ Answer
- C.400 gallons
- D.150 gallons
If 25% is used, then 75% remains, so 600 × 0.75 = 450 gallons. Subtracting the used fraction from 100% first lets you find the remainder in one multiplication.
Source: Firefighter Written Exam blueprint — Mathematics (percentages): remaining = whole × (1 − percent)Report a problem with this question
17. A rectangular staging area measures 20 feet by 30 feet. How many feet of barrier tape are needed to enclose its perimeter?
- A.100 feet✓ Answer
- B.50 feet
- C.600 feet
- D.120 feet
The perimeter of a rectangle is twice the sum of its length and width, so 2 × (20 + 30) = 2 × 50 = 100 feet. Perimeter measures the distance around the shape, which requires adding all four sides.
Source: Firefighter Written Exam blueprint — Mathematics (perimeter): rectangle perimeter = 2 × (length + width)Report a problem with this question
18. A tank has an interior volume of 100 cubic feet. Given that 1 cubic foot holds 7.48 gallons of water, how many gallons can the tank hold when full?
- A.800 gallons
- B.74.8 gallons
- C.748 gallons✓ Answer
- D.7,480 gallons
Converting cubic feet to gallons means multiplying by the given factor, so 100 × 7.48 = 748 gallons. Multiplying volume by the gallons-per-cubic-foot rate converts the volume unit into gallons.
Source: U.S. customary units: 1 cubic foot ≈ 7.48 gallonsReport a problem with this question
19. A supply line fills 1/2 of a reservoir, and a second line adds another 1/4. What total fraction of the reservoir is now filled?
- A.3/6
- B.2/6
- C.1/4
- D.3/4✓ Answer
Adding fractions requires a common denominator, so 1/2 becomes 2/4, and 2/4 + 1/4 = 3/4. You add the numerators only after the denominators match, never adding denominators together.
Source: Firefighter Written Exam blueprint — Mathematics (fractions): addition with common denominatorsReport a problem with this question
20. A hydrant delivers 1,500 gallons of water in 5 minutes. What is its flow rate in gallons per minute?
- A.250 gpm
- B.300 gpm✓ Answer
- C.350 gpm
- D.750 gpm
A flow rate is total volume divided by time, so 1,500 ÷ 5 = 300 gallons per minute. Dividing gallons by minutes produces the per-minute rate.
Source: Firefighter Written Exam blueprint — Mathematics (rate problems): rate = quantity ÷ timeReport a problem with this question
Practice questions modeled on the common domains of firefighter written entrance exams (reading, math, mechanical reasoning, spatial orientation). Not affiliated with or endorsed by any fire department or testing vendor. Departments use different exams — check your department's announcement for its specific format. U.S. Fire Administration →