FCTC Math Actual Exam 2026/2027 |
Verified Questions
Firefighter Candidate Testing Center (FCTC) | Verified Q&A | Firefighter Recruitment
Candidates
Introduction
Welcome to the comprehensive set of original verified questions compiled for the FCTC Math Actual
Exam 2026/2027. This preparation pack contains exactly 20 highly focused and professionally structured
questions designed to mirror the Mathematics portion of the official Firefighter Candidate Testing Center
(FCTC) Written Test blueprint. The questions are evenly distributed across four foundational domains:
Arithmetic and Basic Operations (5 questions), Algebra and Equations (5 questions), Geometry and
Measurement (5 questions), and Word Problems and Proportions (5 questions). Each question is crafted
with professional civil service assessment rigor, providing Firefighter Recruitment Candidates with
realistic scenarios to secure their vocational placement success and demonstrate mathematical readiness
in higher municipal departments.
Domain: Arithmetic and Basic Operations
Question 1: [Fraction Operations]
A firefighter is coupling three segments of fire hose together. The first hose is 15 1/2 feet
long, the second is 22 3/4 feet long, and the third is 18 1/3 feet long. What is the total
combined length of the coupled fire hose?
(A) 55 5/12 feet
(B) 56 7/12 feet
(C) 56 1/2 feet
(D) 55 3/4 feet
Correct Answer: B
Rationale: To find the total length, add the three fractions: 15 1/2 + 22 3/4 + 18 1/3. Find a common
denominator, which is 12: 1/2 = 6/12; 3/4 = 9/12; 1/3 = 4/12. Sum the whole numbers: 15 + 22 + 18 = 55.
Sum the fractions: 6/12 + 9/12 + 4/12 = 19/12 = 1 7/12. Add the whole number and fraction results: 55 +
1 7/12 = 56 7/12 feet. This represents standard arithmetic operations tested in civil service exams.
FCTC Math Actual Exam 2026/2027
, Question 2: [Decimal Operations]
A fire station receives an invoice for safety gear maintenance: $415.50 for SCBA
inspections, $189.75 for turn-out coat repairs, and $250.20 for boot replacements. If the
station has a maintenance budget of $1,000.00, how much money remains in the budget
after paying the invoice?
(A) $144.55
(B) $145.45
(C) $155.45
(D) $134.55
Correct Answer: A
Rationale: First, calculate the total cost of the invoice by summing the decimal values: 415.50 + 189.75
+ 250.20 = $855.45. Next, subtract this total from the initial budget amount: 1,000.00 - 855.45 =
$144.55. This tests basic multi-step decimal arithmetic.
Question 3: [Percentages]
To extinguish a Class B flammable liquid fire, a captain orders a 3.00% Class B foam
solution. If the water tank on the fire engine contains exactly 500 gallons of water, how
many gallons of foam concentrate must be mixed in to create the proper 3.00% solution?
(A) 14.5 gallons
(B) 15.5 gallons
(C) 15.0 gallons
(D) 16.0 gallons
Correct Answer: C
Rationale: A 3% foam solution means that 3% of the total mix is foam concentrate. In practice, the
percentage is applied directly to the water volume: 3% of 500 gallons = 0.03 * 500 = 15.0 gallons.
Therefore, 15 gallons of concentrate are required. This tests real-world vocational firefighter
calculations.
Question 4: [Estimation and Rounding]
A fire hose nozzle discharges water at an average rate of 124.6 gallons per minute. By
rounding the flow rate to the nearest ten gallons, estimate the total volume of water
discharged if the hose is active for exactly 15 minutes.
(A) 1,875 gallons
(B) 1,800 gallons
(C) 1,900 gallons
(D) 1,750 gallons
Correct Answer: B
Rationale: Round the flow rate of 124.6 gallons to the nearest ten: 120 gallons per minute. Next,
multiply this rounded rate by the duration of 15 minutes: 120 * 15 = 1,800 gallons. This tests rounding
and mental estimation procedures.
FCTC Math Actual Exam 2026/2027
Verified Questions
Firefighter Candidate Testing Center (FCTC) | Verified Q&A | Firefighter Recruitment
Candidates
Introduction
Welcome to the comprehensive set of original verified questions compiled for the FCTC Math Actual
Exam 2026/2027. This preparation pack contains exactly 20 highly focused and professionally structured
questions designed to mirror the Mathematics portion of the official Firefighter Candidate Testing Center
(FCTC) Written Test blueprint. The questions are evenly distributed across four foundational domains:
Arithmetic and Basic Operations (5 questions), Algebra and Equations (5 questions), Geometry and
Measurement (5 questions), and Word Problems and Proportions (5 questions). Each question is crafted
with professional civil service assessment rigor, providing Firefighter Recruitment Candidates with
realistic scenarios to secure their vocational placement success and demonstrate mathematical readiness
in higher municipal departments.
Domain: Arithmetic and Basic Operations
Question 1: [Fraction Operations]
A firefighter is coupling three segments of fire hose together. The first hose is 15 1/2 feet
long, the second is 22 3/4 feet long, and the third is 18 1/3 feet long. What is the total
combined length of the coupled fire hose?
(A) 55 5/12 feet
(B) 56 7/12 feet
(C) 56 1/2 feet
(D) 55 3/4 feet
Correct Answer: B
Rationale: To find the total length, add the three fractions: 15 1/2 + 22 3/4 + 18 1/3. Find a common
denominator, which is 12: 1/2 = 6/12; 3/4 = 9/12; 1/3 = 4/12. Sum the whole numbers: 15 + 22 + 18 = 55.
Sum the fractions: 6/12 + 9/12 + 4/12 = 19/12 = 1 7/12. Add the whole number and fraction results: 55 +
1 7/12 = 56 7/12 feet. This represents standard arithmetic operations tested in civil service exams.
FCTC Math Actual Exam 2026/2027
, Question 2: [Decimal Operations]
A fire station receives an invoice for safety gear maintenance: $415.50 for SCBA
inspections, $189.75 for turn-out coat repairs, and $250.20 for boot replacements. If the
station has a maintenance budget of $1,000.00, how much money remains in the budget
after paying the invoice?
(A) $144.55
(B) $145.45
(C) $155.45
(D) $134.55
Correct Answer: A
Rationale: First, calculate the total cost of the invoice by summing the decimal values: 415.50 + 189.75
+ 250.20 = $855.45. Next, subtract this total from the initial budget amount: 1,000.00 - 855.45 =
$144.55. This tests basic multi-step decimal arithmetic.
Question 3: [Percentages]
To extinguish a Class B flammable liquid fire, a captain orders a 3.00% Class B foam
solution. If the water tank on the fire engine contains exactly 500 gallons of water, how
many gallons of foam concentrate must be mixed in to create the proper 3.00% solution?
(A) 14.5 gallons
(B) 15.5 gallons
(C) 15.0 gallons
(D) 16.0 gallons
Correct Answer: C
Rationale: A 3% foam solution means that 3% of the total mix is foam concentrate. In practice, the
percentage is applied directly to the water volume: 3% of 500 gallons = 0.03 * 500 = 15.0 gallons.
Therefore, 15 gallons of concentrate are required. This tests real-world vocational firefighter
calculations.
Question 4: [Estimation and Rounding]
A fire hose nozzle discharges water at an average rate of 124.6 gallons per minute. By
rounding the flow rate to the nearest ten gallons, estimate the total volume of water
discharged if the hose is active for exactly 15 minutes.
(A) 1,875 gallons
(B) 1,800 gallons
(C) 1,900 gallons
(D) 1,750 gallons
Correct Answer: B
Rationale: Round the flow rate of 124.6 gallons to the nearest ten: 120 gallons per minute. Next,
multiply this rounded rate by the duration of 15 minutes: 120 * 15 = 1,800 gallons. This tests rounding
and mental estimation procedures.
FCTC Math Actual Exam 2026/2027
