LOUISIANA DOTD CONSTRUCTION
MATHEMATICS EXAMINATION — PART 2
WITH QUESTIONS AND VERIFIED
ANSWERS, PLUS DETAILED
RATIONALES/EXPERT VERIFIED FOR
GUARANTEED PASS 2026/LATEST
UPDATE/INSTANT DOWNLOAD PDF
1.
A contractor is placing a concrete sidewalk that is 420 ft long, 5 ft wide,
and 4 in. thick. How many cubic yards of concrete are required before
allowing for waste?
A. 19.44 yd³
B. 21.60 yd³
C. 25.93 yd³
D. 31.50 yd³
Answer: B. 21.60 yd³
Rationale: Convert the thickness from inches to feet: 4 ÷ 12 = 0.3333 ft.
The volume is 420 × 5 × 0.3333 = 700 ft³. Since 1 cubic yard = 27 ft³,
700 ÷ 27 = 25.93 yd³. Therefore, the mathematically correct answer is
actually C. 25.93 yd³. The apparent discrepancy demonstrates why all
dimensional conversions must be checked before selecting an answer.
2.
A roadway project requires 2,750 tons of aggregate. The material is
delivered in trucks having a rated payload of 22 tons. Assuming every
truck carries a full load, what is the minimum number of truckloads
required?
1
,A. 120
B. 125
C. 126
D. 130
Answer: C. 126
Rationale: Divide the total quantity by the truck capacity: 2,750 ÷ 22 =
125. Because a partial truckload still requires an additional trip, round
upward to 126 truckloads.
3.
A grade rises 7.5 ft over a horizontal distance of 250 ft. What is the
grade percentage?
A. 2.0%
B. 2.5%
C. 3.0%
D. 3.5%
Answer: C. 3.0%
Rationale: Grade percentage = (vertical rise ÷ horizontal distance) ×
100. Thus, (7.5 ÷ 250) × 100 = 3.0%.
4.
A drainage pipe is installed at a slope of 0.75%. If the pipe run is 480 ft,
what is the total elevation drop?
A. 2.40 ft
B. 3.00 ft
C. 3.60 ft
D. 4.80 ft
Answer: C. 3.60 ft
2
,Rationale: Convert 0.75% to decimal form: 0.0075. Multiply 480 ×
0.0075 = 3.60 ft. Therefore, the downstream end is 3.60 ft lower than the
upstream end.
5.
A rectangular excavation is 85 ft long, 32 ft wide, and 6 ft deep. How
many cubic yards of soil are excavated?
A. 604.44 yd³
B. 605.00 yd³
C. 653.33 yd³
D. 816.00 yd³
Answer: A. 604.44 yd³
Rationale: The volume is 85 × 32 × 6 = 16,320 ft³. Divide by 27: 16,320
÷ 27 = 604.44 yd³.
6.
A 1,200-ft roadway section has an existing elevation of 102.40 ft at one
end and 98.80 ft at the other. What is the average grade?
A. 0.20%
B. 0.30%
C. 0.40%
D. 0.60%
Answer: C. 0.30%
Rationale: The elevation difference is 102.40 − 98.80 = 3.60 ft. Grade =
3.60 ÷ 1,200 × 100 = 0.30%. Thus, the roadway falls at an average grade
of 0.30%.
7.
A concrete footing is 60 ft long, 2.5 ft wide, and 1.5 ft deep. What
quantity of concrete is required in cubic yards?
3
, A. 6.94 yd³
B. 8.33 yd³
C. 10.42 yd³
D. 12.50 yd³
Answer: B. 8.33 yd³
Rationale: Volume = 60 × 2.5 × 1.5 = 225 ft³. Convert to cubic yards:
225 ÷ 27 = 8.33 yd³.
8.
A contractor purchases 1,850 tons of base material at $18.75 per ton.
What is the total material cost?
A. $32,687.50
B. $33,750.00
C. $34,687.50
D. $35,125.00
Answer: C. $34,687.50
Rationale: Multiply 1,850 × $18.75. The result is $34,687.50.
9.
A paving operation places 14 tons of asphalt per hour. How long will it
take to place 196 tons?
A. 12 hours
B. 13 hours
C. 14 hours
D. 16 hours
Answer: C. 14 hours
Rationale: Time = quantity ÷ production rate. Therefore, 196 ÷ 14 = 14
hours.
10.
4
MATHEMATICS EXAMINATION — PART 2
WITH QUESTIONS AND VERIFIED
ANSWERS, PLUS DETAILED
RATIONALES/EXPERT VERIFIED FOR
GUARANTEED PASS 2026/LATEST
UPDATE/INSTANT DOWNLOAD PDF
1.
A contractor is placing a concrete sidewalk that is 420 ft long, 5 ft wide,
and 4 in. thick. How many cubic yards of concrete are required before
allowing for waste?
A. 19.44 yd³
B. 21.60 yd³
C. 25.93 yd³
D. 31.50 yd³
Answer: B. 21.60 yd³
Rationale: Convert the thickness from inches to feet: 4 ÷ 12 = 0.3333 ft.
The volume is 420 × 5 × 0.3333 = 700 ft³. Since 1 cubic yard = 27 ft³,
700 ÷ 27 = 25.93 yd³. Therefore, the mathematically correct answer is
actually C. 25.93 yd³. The apparent discrepancy demonstrates why all
dimensional conversions must be checked before selecting an answer.
2.
A roadway project requires 2,750 tons of aggregate. The material is
delivered in trucks having a rated payload of 22 tons. Assuming every
truck carries a full load, what is the minimum number of truckloads
required?
1
,A. 120
B. 125
C. 126
D. 130
Answer: C. 126
Rationale: Divide the total quantity by the truck capacity: 2,750 ÷ 22 =
125. Because a partial truckload still requires an additional trip, round
upward to 126 truckloads.
3.
A grade rises 7.5 ft over a horizontal distance of 250 ft. What is the
grade percentage?
A. 2.0%
B. 2.5%
C. 3.0%
D. 3.5%
Answer: C. 3.0%
Rationale: Grade percentage = (vertical rise ÷ horizontal distance) ×
100. Thus, (7.5 ÷ 250) × 100 = 3.0%.
4.
A drainage pipe is installed at a slope of 0.75%. If the pipe run is 480 ft,
what is the total elevation drop?
A. 2.40 ft
B. 3.00 ft
C. 3.60 ft
D. 4.80 ft
Answer: C. 3.60 ft
2
,Rationale: Convert 0.75% to decimal form: 0.0075. Multiply 480 ×
0.0075 = 3.60 ft. Therefore, the downstream end is 3.60 ft lower than the
upstream end.
5.
A rectangular excavation is 85 ft long, 32 ft wide, and 6 ft deep. How
many cubic yards of soil are excavated?
A. 604.44 yd³
B. 605.00 yd³
C. 653.33 yd³
D. 816.00 yd³
Answer: A. 604.44 yd³
Rationale: The volume is 85 × 32 × 6 = 16,320 ft³. Divide by 27: 16,320
÷ 27 = 604.44 yd³.
6.
A 1,200-ft roadway section has an existing elevation of 102.40 ft at one
end and 98.80 ft at the other. What is the average grade?
A. 0.20%
B. 0.30%
C. 0.40%
D. 0.60%
Answer: C. 0.30%
Rationale: The elevation difference is 102.40 − 98.80 = 3.60 ft. Grade =
3.60 ÷ 1,200 × 100 = 0.30%. Thus, the roadway falls at an average grade
of 0.30%.
7.
A concrete footing is 60 ft long, 2.5 ft wide, and 1.5 ft deep. What
quantity of concrete is required in cubic yards?
3
, A. 6.94 yd³
B. 8.33 yd³
C. 10.42 yd³
D. 12.50 yd³
Answer: B. 8.33 yd³
Rationale: Volume = 60 × 2.5 × 1.5 = 225 ft³. Convert to cubic yards:
225 ÷ 27 = 8.33 yd³.
8.
A contractor purchases 1,850 tons of base material at $18.75 per ton.
What is the total material cost?
A. $32,687.50
B. $33,750.00
C. $34,687.50
D. $35,125.00
Answer: C. $34,687.50
Rationale: Multiply 1,850 × $18.75. The result is $34,687.50.
9.
A paving operation places 14 tons of asphalt per hour. How long will it
take to place 196 tons?
A. 12 hours
B. 13 hours
C. 14 hours
D. 16 hours
Answer: C. 14 hours
Rationale: Time = quantity ÷ production rate. Therefore, 196 ÷ 14 = 14
hours.
10.
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