FCTC MaTh aCTual ExaM – FirEFighTEr CandidaTE TEsTing CEnTEr
(FCTC) – 2026/2027 aCadEMiC YEar – VEriFiEd QuEsTions and
answErs || VEriFiEd BY ExPErTs.
The following 20 questions are evenly distributed across four foundational domains aligned with
the official Firefighter Candidate Testing Center (FCTC) Written Test mathematics blueprint. Each
question includes four answer choices, the correct answer, and a detailed rationale reinforcing
the mathematical competencies required for firefighter recruitment and civil service placement.
Domain 1: Arithmetic and Basic Operations (Questions 1–5)
Question 1: 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.
Question 2: A fire engine's water tank holds 500 gallons. If the crew uses 3/5 of the water to
fight a fire, how many gallons of water remain in the tank?
• A) 200 gallons
, • B) 250 gallons
• C) 300 gallons
• D) 150 gallons
CorrECT answEr: A
raTionalE: Water used = 3/5 × 500 = 300 gallons. Remaining = 500 − 300 = 200 gallons.
Alternatively, remaining fraction = 1 − 3/5 = 2/5. 2/5 × 500 = 200 gallons. This tests fraction
multiplication and subtraction in a firefighting context.
Question 3: A firefighter works 48 hours in one week. What is the average number of hours
worked per day over a 6-day work week? (Round to the nearest whole hour.)
• A) 7 hours
• B) 8 hours
• C) 9 hours
• D) 6 hours
CorrECT answEr: B
raTionalE: 48 hours ÷ 6 days = 8 hours per day. This tests division in a work scheduling
context.
Question 4: A ladder truck extends to a height of 105 feet. If the ladder is raised in 7 equal
sections, how long is each section?
• A) 12 feet
• B) 15 feet
• C) 14 feet
• D) 18 feet
CorrECT answEr: B
raTionalE: 105 feet ÷ 7 sections = 15 feet per section. This tests division.
Question 5: A fire station receives 3/8 of its annual budget for equipment. If the annual budget
is $240,000, how much is allocated for equipment?
(FCTC) – 2026/2027 aCadEMiC YEar – VEriFiEd QuEsTions and
answErs || VEriFiEd BY ExPErTs.
The following 20 questions are evenly distributed across four foundational domains aligned with
the official Firefighter Candidate Testing Center (FCTC) Written Test mathematics blueprint. Each
question includes four answer choices, the correct answer, and a detailed rationale reinforcing
the mathematical competencies required for firefighter recruitment and civil service placement.
Domain 1: Arithmetic and Basic Operations (Questions 1–5)
Question 1: 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.
Question 2: A fire engine's water tank holds 500 gallons. If the crew uses 3/5 of the water to
fight a fire, how many gallons of water remain in the tank?
• A) 200 gallons
, • B) 250 gallons
• C) 300 gallons
• D) 150 gallons
CorrECT answEr: A
raTionalE: Water used = 3/5 × 500 = 300 gallons. Remaining = 500 − 300 = 200 gallons.
Alternatively, remaining fraction = 1 − 3/5 = 2/5. 2/5 × 500 = 200 gallons. This tests fraction
multiplication and subtraction in a firefighting context.
Question 3: A firefighter works 48 hours in one week. What is the average number of hours
worked per day over a 6-day work week? (Round to the nearest whole hour.)
• A) 7 hours
• B) 8 hours
• C) 9 hours
• D) 6 hours
CorrECT answEr: B
raTionalE: 48 hours ÷ 6 days = 8 hours per day. This tests division in a work scheduling
context.
Question 4: A ladder truck extends to a height of 105 feet. If the ladder is raised in 7 equal
sections, how long is each section?
• A) 12 feet
• B) 15 feet
• C) 14 feet
• D) 18 feet
CorrECT answEr: B
raTionalE: 105 feet ÷ 7 sections = 15 feet per section. This tests division.
Question 5: A fire station receives 3/8 of its annual budget for equipment. If the annual budget
is $240,000, how much is allocated for equipment?
