FCTC Firefighter Mathematical Problems 2 — Questions and Answers

Question 1: A fire engine pump is operating at 150 psi engine pressure. Friction loss in the 200-foot hose line is 20 psi. What is the nozzle pressure?

120 psi
130 psi (Correct answer)
150 psi
170 psi

Correct answer: 130 psi

Nozzle Pressure = Engine Pressure − Friction Loss = 150 − 20 = 130 psi.

The basic hydraulic formula is: Nozzle Pressure (NP) = Engine Pressure (EP) − Friction Loss (FL). With EP = 150 psi and FL = 20 psi: NP = 150 − 20 = 130 psi. Maintaining correct nozzle pressure is essential for firefighting effectiveness and safety. Too low a pressure produces a weak stream that cannot reach or cool the fire; too high a pressure makes the hose difficult to control and can injure firefighters.

Question 2: A fire extinguisher rated at 2.5 lbs/minute discharges for 45 seconds. How many pounds of agent are discharged?

1.50 lbs
1.75 lbs
1.875 lbs (Correct answer)
2.00 lbs

Correct answer: 1.875 lbs

45 seconds = 0.75 minutes. 2.5 lbs/min × 0.75 min = 1.875 lbs.

Converting the time: 45 seconds ÷ 60 = 0.75 minutes. Agent discharged = Rate × Time = 2.5 lbs/min × 0.75 min = 1.875 lbs. This type of unit conversion (seconds to minutes) combined with rate calculation is a common component of FCTC math tests. Knowing how much agent a portable extinguisher carries and how long it will last is a practical firefighting skill.

Question 3: A structure measures 40 ft × 60 ft × 10 ft. What is the total volume of the structure in cubic feet?

18,000 cu ft
20,000 cu ft
24,000 cu ft (Correct answer)
26,000 cu ft

Correct answer: 24,000 cu ft

Volume = Length × Width × Height = 40 × 60 × 10 = 24,000 cubic feet.

Volume of a rectangular structure = Length × Width × Height = 40 ft × 60 ft × 10 ft = 24,000 cubic feet. Volume calculations are used in ventilation calculations (air changes per hour), smoke filling rates, foam application (for coverage depth), and water supply needs. Understanding three-dimensional measurements is a foundational mathematical skill for firefighters.

Question 4: Station response data shows 120 calls in January, 95 in February, and 110 in March. What is the average monthly call volume for this period?

105
108.3 (Correct answer)
110
112

Correct answer: 108.3

Average = (120 + 95 + 110) ÷ 3 = 325 ÷ 3 = 108.33 ≈ 108.3.

Average monthly calls = Sum ÷ Number of months = (120 + 95 + 110) ÷ 3 = 325 ÷ 3 = 108.33. Rounding to one decimal place gives 108.3. Statistical calculations like averages and trends are used in fire department planning, staffing decisions, budget justifications, and annual reports. Candidates should be comfortable with basic descriptive statistics.

Question 5: A fire hose 50 feet long needs to be replaced. If replacement hose costs $4.50 per foot, what is the total cost?

$200.00
$215.00
$225.00 (Correct answer)
$230.00

Correct answer: $225.00

50 feet × $4.50/foot = $225.00.

Total cost = Quantity × Unit Price = 50 feet × $4.50/foot = $225.00. Budget and procurement calculations are common in fire department administrative work. Firefighters at all levels may be involved in equipment inventory, requisition forms, and budget tracking. The ability to calculate material costs quickly and accurately is a practical mathematical skill tested on the FCTC.

Question 6: A ladder is 35 feet long and must be placed at a 75-degree angle. Using the 1-in-4 rule, how far from the building should the base be placed?

7.0 ft
8.75 ft (Correct answer)
9.5 ft
10.25 ft

Correct answer: 8.75 ft

1-in-4 rule: base distance = ladder length ÷ 4 = 35 ÷ 4 = 8.75 ft.

The 1-in-4 rule states that for every 4 feet of ladder length, the base should be 1 foot away from the structure. For a 35-foot ladder: 35 ÷ 4 = 8.75 feet. This results in approximately a 75-degree climbing angle, which provides the optimal balance of structural stability and safe climbing angle. Placing the ladder too close creates a steep, unstable angle; too far results in a shallow angle that stresses the ladder and reduces reach.

FCTC Firefighter Mathematical Problems 2

A fire engine pump is operating at 150 psi engine pressure.
Friction loss in the 200-foot hose line is 20 psi.
What is the nozzle pressure?