FCTC MATH 2026 QUESTIONS AND
ANSWERS | A+ GRADED | WITH EXPERT
SOLUTIONS
Question 1 – Hose Removal
A fire engine carries 1,100 ft of 2.5-inch hose, 900 ft of 4-inch hose, and 1,000 ft of
4.5-inch hose. If all the 4-inch hose is removed from the truck, what percentage of
the total hose is removed?
• A) 30%
• B) 33%
• C) 36%
• D) 40%
Correct ,,,answer,,,: A) 30% – The total hose is 1,100 ft + 900 ft + 1,000 ft = 3,000
ft. Divide the 900 ft removed by this total: 900 ÷ 3,000 = 0.30, which equals 30%.
The other options often arise from miscalculating the total hose length or
incorrectly using the removed hose as the total.
Question 2 – Nozzle Pressure
For a fire on the fourth floor, you need 100 psi at the nozzle. You lose 5 psi for each
floor above the first and 15 psi for every 100 ft of hose. If the hose lay is 400 ft long,
what total pressure must the engine pump to reach the nozzle?
• A) 115 psi
• B) 145 psi
• C) 160 psi
• D) 175 psi
,Correct ,,,answer,,,: D) 175 psi – Start with 100 psi. Elevation loss: 3 floors × 5 psi
= 15 psi loss. Friction loss: 400 ft ÷ 100 ft × 15 psi = 4 × 15 = 60 psi loss. Add both
losses: 100 psi + 15 psi + 60 psi = 175 psi. Alternative options often omit one loss
or miscalculate floor elevation.
Question 3 – Structural Hose Failure
A crew has 6 sections of 100 ft wildland hose and 9 sections of 80 ft structural
hose. If 5 sections of the structural hose fail, what is the total footage of structural
hose that has failed?
• A) 400 ft
• B) 500 ft
• C) 720 ft
• D) 800 ft
Correct ,,,answer,,,: A) 400 ft – Multiply the number of failed sections by the
length per section: 5 sections × 80 ft per section = 400 ft. Common errors include
using 100 ft instead of 80 ft (resulting in 500 ft) or incorrectly totaling all structural
hose.
Question 4 – Class President Election
For the class president election, the votes between boys and girls have a 3:2 ratio,
with a total of 60 votes cast. How many votes did the girls receive?
• A) 12 votes
• B) 24 votes
• C) 36 votes
• D) 60 votes
Correct ,,,answer,,,: B) 24 votes – With a total of 60 votes divided into 5 parts (3
parts boys + 2 parts girls), each part equals 12 votes. Girls receive 2 parts: 2 × 12 =
24 votes. The most common trap is ,,,answer,,,ing 36 votes, which represents the
boys' share of the votes, not the girls'.
,Question 5 – Volume of Rectangular Tank
Engine 17's water tank has dimensions: length 7 ft, width 5 ft, depth 3 ft. How many
cubic feet of water can the tank hold?
• A) 105 ft³
• B) 110 ft³
• C) 115 ft³
• D) 120 ft³
Correct ,,,answer,,,: A) 105 ft³ – Multiply length × width × height: 7 ft × 5 ft × 3 ft =
105 cubic feet. A common mistake is to incorrectly add rather than multiply the
dimensions.
Question 6 – Cylinder Volume
A cylindrical water tank has a diameter of 14 ft and a height of 9 ft. How many cubic
feet of water can it hold? (Use π = 3.14)
• A) 1,384 ft³
• B) 1,385 ft³
• C) 1,400 ft³
• D) 1,500 ft³
Correct ,,,answer,,,: B) 1,385 ft³ – Volume = π × r² × h. First find radius: 14 ft ÷ 2 =
7 ft. Then calculate: 3.14 × (7²) = 3.14 × 49 = 153.86. Multiply by height (9 ft):
153.86 × 9 = 1,384.74 ft³, rounded to 1,385 ft³. Errors often come from using
diameter rather than radius in the formula.
Question 7 – Average Dinner Cost
Four firefighters each paid a different amount for dinner: 12.40,14.20, 14.40,12.20.
What is the average amount they spent on dinner?
, • A) $12.80
• B) $13.30
• C) $13.80
• D) $14.00
**Correct ,,,answer,,,: B) 13.30 ∗∗ –𝑆𝑢𝑚:12.40 + 14.20 +14.40 + 12.20 =53.20.
Divide by the number of people (4): 53.20 ÷ 4 =13.30.
Question 8 – Gallons for Given Depth
A tank with a 12 ft diameter holds 864 gallons per foot of depth. How many gallons
will it hold when filled to a depth of 5 ft?
• A) 3,240 gallons
• B) 4,000 gallons
• C) 4,320 gallons
• D) 5,040 gallons
Correct ,,,answer,,,: C) 4,320 gallons – Multiply the per-foot capacity by the
depth: 864 gal/ft × 5 ft = 4,320 gallons. A frequent error is using the diameter (12 ft)
rather than the given per-foot constant.
Question 9 – Burn Percentage
A patient has specific body parts burned: ¼ of her back (20% of total body), ¼ of her
front (20% of total body), ⅓ of her head (15% of total body), and ½ of one arm (15%
of total body). What is the total body surface area percentage burned?
• A) 15.0%
• B) 20.0%
• C) 22.5%
• D) 27.5%
Correct ,,,answer,,,: C) 22.5% – Calculate each part: back: ¼ × 20% = 5%; front: ¼
× 20% = 5%; head: ⅓ × 15% = 5%; arm: ½ × 15% = 7.5%. Sum these: 5% + 5% +
ANSWERS | A+ GRADED | WITH EXPERT
SOLUTIONS
Question 1 – Hose Removal
A fire engine carries 1,100 ft of 2.5-inch hose, 900 ft of 4-inch hose, and 1,000 ft of
4.5-inch hose. If all the 4-inch hose is removed from the truck, what percentage of
the total hose is removed?
• A) 30%
• B) 33%
• C) 36%
• D) 40%
Correct ,,,answer,,,: A) 30% – The total hose is 1,100 ft + 900 ft + 1,000 ft = 3,000
ft. Divide the 900 ft removed by this total: 900 ÷ 3,000 = 0.30, which equals 30%.
The other options often arise from miscalculating the total hose length or
incorrectly using the removed hose as the total.
Question 2 – Nozzle Pressure
For a fire on the fourth floor, you need 100 psi at the nozzle. You lose 5 psi for each
floor above the first and 15 psi for every 100 ft of hose. If the hose lay is 400 ft long,
what total pressure must the engine pump to reach the nozzle?
• A) 115 psi
• B) 145 psi
• C) 160 psi
• D) 175 psi
,Correct ,,,answer,,,: D) 175 psi – Start with 100 psi. Elevation loss: 3 floors × 5 psi
= 15 psi loss. Friction loss: 400 ft ÷ 100 ft × 15 psi = 4 × 15 = 60 psi loss. Add both
losses: 100 psi + 15 psi + 60 psi = 175 psi. Alternative options often omit one loss
or miscalculate floor elevation.
Question 3 – Structural Hose Failure
A crew has 6 sections of 100 ft wildland hose and 9 sections of 80 ft structural
hose. If 5 sections of the structural hose fail, what is the total footage of structural
hose that has failed?
• A) 400 ft
• B) 500 ft
• C) 720 ft
• D) 800 ft
Correct ,,,answer,,,: A) 400 ft – Multiply the number of failed sections by the
length per section: 5 sections × 80 ft per section = 400 ft. Common errors include
using 100 ft instead of 80 ft (resulting in 500 ft) or incorrectly totaling all structural
hose.
Question 4 – Class President Election
For the class president election, the votes between boys and girls have a 3:2 ratio,
with a total of 60 votes cast. How many votes did the girls receive?
• A) 12 votes
• B) 24 votes
• C) 36 votes
• D) 60 votes
Correct ,,,answer,,,: B) 24 votes – With a total of 60 votes divided into 5 parts (3
parts boys + 2 parts girls), each part equals 12 votes. Girls receive 2 parts: 2 × 12 =
24 votes. The most common trap is ,,,answer,,,ing 36 votes, which represents the
boys' share of the votes, not the girls'.
,Question 5 – Volume of Rectangular Tank
Engine 17's water tank has dimensions: length 7 ft, width 5 ft, depth 3 ft. How many
cubic feet of water can the tank hold?
• A) 105 ft³
• B) 110 ft³
• C) 115 ft³
• D) 120 ft³
Correct ,,,answer,,,: A) 105 ft³ – Multiply length × width × height: 7 ft × 5 ft × 3 ft =
105 cubic feet. A common mistake is to incorrectly add rather than multiply the
dimensions.
Question 6 – Cylinder Volume
A cylindrical water tank has a diameter of 14 ft and a height of 9 ft. How many cubic
feet of water can it hold? (Use π = 3.14)
• A) 1,384 ft³
• B) 1,385 ft³
• C) 1,400 ft³
• D) 1,500 ft³
Correct ,,,answer,,,: B) 1,385 ft³ – Volume = π × r² × h. First find radius: 14 ft ÷ 2 =
7 ft. Then calculate: 3.14 × (7²) = 3.14 × 49 = 153.86. Multiply by height (9 ft):
153.86 × 9 = 1,384.74 ft³, rounded to 1,385 ft³. Errors often come from using
diameter rather than radius in the formula.
Question 7 – Average Dinner Cost
Four firefighters each paid a different amount for dinner: 12.40,14.20, 14.40,12.20.
What is the average amount they spent on dinner?
, • A) $12.80
• B) $13.30
• C) $13.80
• D) $14.00
**Correct ,,,answer,,,: B) 13.30 ∗∗ –𝑆𝑢𝑚:12.40 + 14.20 +14.40 + 12.20 =53.20.
Divide by the number of people (4): 53.20 ÷ 4 =13.30.
Question 8 – Gallons for Given Depth
A tank with a 12 ft diameter holds 864 gallons per foot of depth. How many gallons
will it hold when filled to a depth of 5 ft?
• A) 3,240 gallons
• B) 4,000 gallons
• C) 4,320 gallons
• D) 5,040 gallons
Correct ,,,answer,,,: C) 4,320 gallons – Multiply the per-foot capacity by the
depth: 864 gal/ft × 5 ft = 4,320 gallons. A frequent error is using the diameter (12 ft)
rather than the given per-foot constant.
Question 9 – Burn Percentage
A patient has specific body parts burned: ¼ of her back (20% of total body), ¼ of her
front (20% of total body), ⅓ of her head (15% of total body), and ½ of one arm (15%
of total body). What is the total body surface area percentage burned?
• A) 15.0%
• B) 20.0%
• C) 22.5%
• D) 27.5%
Correct ,,,answer,,,: C) 22.5% – Calculate each part: back: ¼ × 20% = 5%; front: ¼
× 20% = 5%; head: ⅓ × 15% = 5%; arm: ½ × 15% = 7.5%. Sum these: 5% + 5% +
