( Module 00102-15) Introduction to Construction Math Module 2

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In calculating a bid for a roof restoration, a contractor estimates that he will need $847 for lumber, $456 for roofing shingles, and $169 for hardware. What is the total cost for the materials portion of the bid?

$1,472

Sheet piles are being used to keep water out of a marsh area. The length of the site is 345' and each pile protects 18" and are 15' long. The piles cost $6.50 per sq ft. What is the total cost of the sheet piles?

$33,637.50 Solution: 345 / 1.5 = 230 piles are 1.5' x 15' = 22.5 sq. ft. x 230 = 5175 x 6.50 = 33,637.50

Refer to the Diagram; The house shown is 40′ X 20′. What is the total cost of the following items, (1) Floor joist 2″ x 10″$ 14.65 ea. (2) Bridge $ 3.50 ea. (3) Splice $ 1.90 ea. Note the joist are spaced 24″ O.C. and has a double floor joist at each end.

$889.90 Solution: 40 / 24" on center = 20 + 1 starter + 2 for double = 23 x 2 = 46 joist , 40 bridges and 40 splices. LOOK AT THE COST OF ITEMS ON THE EXAM!

Convert 72% to a decimal

0.72

10 inches = ____________ feet?

0.83

Refer to the Diagram; If the finished elevation of the project will be 101', how many cubic yards of earth will need to be removed?

1,185.85 CY

An estimate for a commercial flooring job requires one thousand, six hundred ninety-three square meters of carpet to complete the first floor. How would you write this amount as a whole number?

1,639

c. 5/8

1/4 + 3/8 =_____. Reduce your answer to the lowest term. a. 4/8 b. 1/2 c. 5/8 d. 5/4

You need to build a wall. You must use 2x4s. The wall is to be 1,000' long and 10' tall with studs (verticals) placed at 16" O.C. (On Center, meaning you have to have a stud every 16") What is the lineal footage of 2x4s you will need to build the wall? Please disregard the thickness of the framing members (studs, 2x4s, however you call them). Also, please include single top and single bottom plates in your lineal footage calculation.

10,000sf 3,615ft 3,615sf 9,510ft

Refer to the diagram; The reference stake is at an elevation of 100.00, what is the elevation of the target stake ?

105.3 Solution: Benchmark + back site - front site 100+ 8.7- 3.4= 105.3

benchmark has an elevation of 101.7. A back site to the benchmark reads 4.75. A front site to a corner stake reads 3.90. What is the HI ?

106.45 Solution: BM + BS = HI 101.7 + 4.75 = 106.45

Evaluate 1/16 + 5/8 = _______. Reduce your answer to lowest terms and change improper fractions to mixed numbers.

11/16

Your supervisor sends you to the truck for 180 special fasteners. When you get there, you find that the fasteners come in bags of 15. How many bags of fasteners will you need to bring back?

Refer to the Diagram; If the finished elevation of the project will be 99.5', how many cubic yards of earth will need to be removed?

140 Solution: Add the four corners and find the average elevation. 102 + 103.5 + 102.5 + 104 = 412 / 4 = 103 - 99.5 = 3.5 ft. 45 x 24 x 3.5 / 27 = 140 cy

A home measuring 90' by 120' should be excavated and filled to a depth of 4' below the ground surface. The building perimeter must be a minimum of 5' beyond the building line. If the soil compaction factor is 40% and the swelling factor is 30%, calculate in cubic yards the amount of fill that must be brought to the project site. Note: Compaction factor refers to how much a soil is compressed once installed. In this case it is 40%. Therefore, if you were to dig a full cubic yard of this soil, we would need 1.4 cubic yards.

2,696.29 cy

A road is 1 mile long and measures 36′ wide. You are going to grade the road with a road grader with a 12′ blade. Using the following information, how long will it take to grade the road? In 1st. gear the grader travels 2.5mph @ 83% efficiency, 2nd.gear 5mph @ 87% 3rd. gear 7.5mph @ 87% (See diagram for solution)

2.6 hoursSolution: The diagram will not be shown on the exam, this only to show the solution

Evaluate 3/4 x 7/8 = _______. Reduce your answer to lowest terms and change improper fractions to mixed numbers.

21/32

When reduced to lowest terms, the fraction 12/32 would read as ________?

3/8

What is the excavation volume in cubic yards needed for a site with a perimeter of 10' beyond the construction line and measuring 30' wide by 40' long. The excavation is 3' deep.

333.33 cy

A backhoe has a 1.5 cubic yard bucket with a cycle time of 2 minutes. The efficiency of the machine is 50 minute per hour. How many cubic yards can the backhoe move in 1 hour?

37.5Solution: 50/2 = 25 x 1.5 = 37.5 cubic yards

How many pounds does a 16' length of W18 x 24 structural steel weigh?

384 Solution: W is the type beam; 18 is the distance between flanges; 24 is the lbs. per foot 16' x 24 lbs per foot= 384

An equivalent fraction to 1/4 is _______?

4/16

A 3500' long canal trench is excavated to 7' depth. The trench has a 3'-6" wide base. The sides are scoped at 1:1. Each hoe excavates 27.5 cy/hr., soil expands 20%.What range of hours is estimated to excavate the trench with the power hoe?

410-435Solution: The trench is sloped on a 1:1, the bottom is 3.5' wide so the top is 17.5'. 17.5 + 3.5 = 21 /2 =10.5' average width.3500 x 10.5 x 7 / 27 = 9527.77 cy 9527.77 x 1.2(20%) =11433.33 cy Hoe can dig 27.5 cy/hr. 11433.33 / 27.5 = 415.75hrs rise/run= slope 1.find the top width of trench using slope formula 2. find avg width 3. find cy of entier trench / by 27 4. multiply cy by soil and expansion % 5. divide cy total by 27.5 = hours

Convert 0.475 to a percentage

47.5%

A set of stairs has an over-all height of 8'-10 1/4″. If there are 17 equal risers, the height of an individual riser would equal _____ inches.

6 1/4"Solution: total height in inches divided by risers 8' x 12= 96" + 10 1/4" = 106.25" 106.25" divided by 17 = 6.25 = 6 1/4" use their answers against them and convert fractions to decimals

Ceramic tile weighs 4.75 pounds per square foot. Therefore, 128 square feet of ceramic tile weighs ________.

608 pounds

c. 7/24

7/8 x 3/9 =_____. Reduce your answer to the lowest term. a. 21/72 b. 24/63 c. 7/24 d. 8/21

A collection pond measures 23,000 sq. ft. on the surface, and has a depth of 9 ft. How many cubic yards are in the pond?

7677 Solution: 23,000 x 9 = 207,000 cubic ft. / 27 = 7666.66

How many 7/8 inch long strips can be cut from a single 7 inch long strip of material?

If you saw 12-1/16 inches off of a board that is 20-1/4 inches long, the length of the remaining board will be ______?

8-3/16

d. 1/6

8/12 - 4/8 = _____ . Reduce your answer to the lowest term. a. 4/24 b. 2/14 c. 1/7 d. 1/6

Convert 0.45 into a fraction and reduce the answer to lowest terms if necessary.

9/20

A dozer with a standard blade 2.5cyds is pushing 80' forward at 2.8mph and 90' back at 3.9mph with an efficiency of 80%, a fixed time of .02minutes and a maneuver time of .7 minutes. How many cubic yards can it move in a hour?

92 cyds Solution: 80' / 5,280' = .015 of a mile, 90' / 5,280' = .017 of a mile, .015 / 2.8 mph = .0054 hrs., .017 / 3.9 mph = .0043hrs; .0054 + .0043 = .0097 hrs., .0097 x 60 min = .582 mins .582 + .02 + .7 = 1.302 min per trip, 60 / 1.302 = 46.08 cycles per hour, 46.08 x 2.5 x .8 = 92.16 cyds

a. $1012.50

A carpenter has to build an addition which needs 150 studs. Each stud costs $6.75. What is the total cost of the studs needed? a. $1012.50 b. $1201.50 c. $101.25 d. $2101.25

a. 192

A room measures 12 feet by 16 feet long. What is the square footage of this room? a. 192 b. 180 c. 48 d. 28

d. 3.70

A screw is 3-7/10 inches long. Using decimals, this is written as____inches. a. 3.13 b. 3.30 c. 3.60 d. 3.70

b. $210.00

An electrician earns $25.00 per outlet he installs. The cost of material is $7.50 per outlet. A new addition needs 12 outlets installed. How much money will he earn? a. $300.00 b. $210.00 c. $90.00 d. $390.00

You are contracted to plant small trees along a coastal shoreline. The trees will be placed 20" apart in 1 row that is 3200 feet long. It takes 2 manhours per 100 holes and the cost is $15.00 per manhour. The trees are $0.20 each and you have other costs of $1,500.00. These are the only cost for the project. What is your total cost?

Answer $2464.00 Solution: 3200/1.66(20") = 1928 trees 1928/100 =19.28 x 2 = 38.56 man hr x $15.00 = $578.40 1928 x 0.2 = 385.60 then add $1500.00

Refer to the Diagram; If the pipe shown makes a 75 degree bend, what angle would each miter cut be made?

Answer 15 degrees Solution: Look at the diagram, the pipe has 5 pieces in the bend. 75 / 5 = 15 degrees

A grade stake has an elevation of 23.0. A Shot to the top of the stake reads 4.7. What is the HI?

Answer 27.7Solution: 23 + 4.7 HI = Elevation of the grade stake + Reading on the leveling rod = 23.0 + 4.7 = 27.7 Therefore, the HI is 27.7. To calculate the height of instrument (HI), you add the elevation of the grade stake to the reading taken on the leveling rod.

Refer to the Diagram; A footing will be poured that is 1.6" wide and 2' deep with the exception of the North wall which will be 2' wide and 2' deep. How many cubic yards of concrete will be needed?

Answer 75 Solution: The North wall is 200' x 2' x 2' / 27 = 29.62 cubic yards, All other walls are 400' x 1.5' x 2' /27 = 44.44 cubic yards 75 35 145 24 Let's calculate the volume of concrete for each section using the provided solution: North Wall: Width: 2 feet Depth: 2 feet Length: 200 feet Volume = (200 ft × 2 ft × 2 ft) / 27 = 800 cubic feet / 27 ≈ 29.62 cubic yards Other Walls (West, East, South): Width: 1.6 feet Depth: 2 feet Length: (100 feet + 100 feet + 200 feet) = 400 feet Total volume for all other walls = (400 feet × 1.6 feet × 2 feet) / 27 = 1280 cubic feet / 27 ≈ 47.40 cubic yards Now, summing up the volumes of all sections: Total volume = Volume of North Wall + Total volume of Other Walls ≈ 29.62 cubic yards + 47.40 cubic yards ≈ 77.02 cubic yards

You must build a fence that is 995 meters long. It has one post every meter and each post costs $5.50. Fencing material comes in 100 m rolls that cost $125. each. Fabric netting comes in 100 m rolls that cost $95. each. At every lap there will be a double post. A box of staples costs $22. What is the total materials for the fence?

Answer Solution: Total number of posts = 995 + 1 starter + 9 doubles = 1005 x $5.50 =$5527.50; Rolls of fencing = 10 x $125 + $1250; Rolls of netting = 10 x $95 = $950; staples = $22. Total = $5527.50 + $950. + $22. = $7749.50

Refer to the Diagram; What information does the back of the stake give?

Answer? The stake is 450 feet away from the start point marked 0+00 and the centerline is 55.9' from the hub

d. 75.0 cm

Convert 0.75 meters to centimeters. a. 0.0075 cm b. 0.075 cm c. 7.50 cm d. 75.0 cm

d. 78%

Convert 0.78 into a percentage. a. 0.0078% b. 0.78% c. 7.8% d. 78%

c. 43/50

Convert 0.86 into a fraction. Reduce to lowest terms. a. 86/100 b. 14/100 c. 43/50 d. 7/50

b. 6.12 m

Convert 612 centimeters to meters. a. 0.612 m b. 6.12 m c. 61.2 m d. 612 m

An excavation of 14' depth, 25' width and 45' length is being carried out. What is the volume of the excavation in cubic yards? (Do not take into account the swelling factor)

Excavation Volume = 583.33 cy

For the basement of a building, excavation of 2,480 cy was carried out; in the end, the client made it known that he was no longer interested in having the basement, and it had to be filled. How many cubic yards of fill should be applied to that basement? (keep in mind that the compaction factor is 40%)

Fill = 3.472 cy

A stake is marked 3 + 00 and has an elevation of 61.50. The next stake is marked 3 +50 and has an elevation of 61.00. What is the slope?

Given: Elevation at stake 1 (E1) = 61.50 Elevation at stake 2 (E2) = 61.00 Horizontal distance between the stakes (D) = 50 (since the next stake is marked 3+50 from the initial stake) First, calculate the change in elevation: hange in Elevation} = 61.00 - 61.50 = -0.50 Next, calculate the change in horizontal distance: Change in Horizontal Distance=D Change in Horizontal Distance} = 50 Now, plug these values into the formula for slope: Elevation .5 horizontal 50 = .5/50=.001% more the decimal two-times to the left and you have .1% Since the slope is negative, it indicates a downward slope from stake 1 to stake 2.

How many feet long is a standard yardstick?

5500

If a house measures 110 feet long and 50 feet wide, what is the area in feet?

144

In feet, what is the area of a square driveway measuring 12 feet across?

In the back of storage, you find 265 boxes of nails. You have 5 crews who need them. How many boxes can each crew have?

c. 1/10 of a centimeter

In the metric system, each millimeter increment is a. 1/1000 of a centimeter b. 1/100 of a centimeter c. 1/10 of a centimeter d. 10 centimeters

In your work truck, you find a 12 foot piece of rope that needs to be cut into 3" strands. How many strands will you have when you are finished?

It is necessary to transport the debris from an excavation of 1,200 cy with a swelling factor of 14%. If the equipment that collects the debris can transport 15 cy, how many times will we need the equipment?

Machine Usage = 92 times

a. 31.5

Multiply 4.5 x 7. a. 31.5 b. 315 c. 52 d. 5.2"

One of the guys gives you 260 inch long pipe. You need to cut it into 10 equal pieces. How many inches will each piece be?

b. 2,435.0 pounds

One sheet of drywall weighs 48.7 pounds. You have ordered 50 sheets, so your total order will weigh a. 2,532.0 pounds b. 2,435.0 pounds c. 2,430.0 pounds d. 243.5 pounds

b. out of 100

Percentage means a. out of 50 b. out of 100 c. out of 150 d. out of 1000

If you are told that the soil in a particular excavation requires the embankment to be at a 45 degree angle, what type of soil are you dealing with?

Soil type B

c. 12.25 sq ft

The area of a triangular roof section with a base of 7 feet and a height of 3.5 feet is a. 7 cu ft b. 12 sq ft c. 12.25 sq ft d. 24.5 sq ft

b. 6/8 inch

The equivalent of 3/4 inch is a. 1/2 inch b. 6/8 inch c. 3/8 inch d. 4/3 inch

The logging company sends you 330 poles. You have 11 crews waiting for equal shares of the shipment. How many poles should each site receive?

d. 2.6 cm

The marked measurement in the figure above indicates a. 2-3/10 cm b. 2.35 cm c. 2.5 cm d. 2.6 cm

a. 2-1/8

The marked measurement in the figure above indicates_____inches. a. 2-1/8 b. 2-3/16 c. 2-1/4 d. 2-1/2

b. centimeters and millimeters

The metric ruler is divided into a. inches and half inches b. centimeters and millimeters c. millimeters and decimeters d. eighth inches and sixteenth inches

d. temperature

The metric system is used to measure length, weight, volume, and a. currency b. diameter c. language d. temperature

b. 729 cu in

The volume of a 9-inch cube is a. 243 cu yd b. 729 cu in c. 818 sq in d. 1243 cu in

a. cu m

The volume of a shape in the metric system is stated in terms of a. cu m b. sq m c. cu ft d. sq ft

A home measuring 90' by 120' should be excavated and filled to a depth of 4' below the ground surface. The building perimeter must be a minimum of 5' beyond the building line. If the soil compaction factor is 40% and the swelling factor is 30%, determine the number of 20-cubic-yard capacity trucks required to remove the material from the site.a. Trucks Needed = 126

Trucks Needed = 126

Trucks Required = 270

here's a slightly more challenging problem: A cylindrical tank has a diameter of 10 feet and a height of 15 feet. Calculate the volume of water it can hold in gallons, assuming that one cubic foot is equal to 7.48 gallons. To solve this problem, you'll need to use the formula for the volume of a cylinder, which is:

V=πr(2)h V is the volume, π is a constant (approximately 3.14), r is the radius of the cylinder, h is the height of the cylinder First, calculate the radius (r) using the diameter (d) r= d/2 Of course! The radius (r) of a cylinder is the distance from the center of the circular base to the outer edge. It's equal to half of the diameter of the cylinder. Once you find r you can substitute it and the given height (h) into the formula to find the volume (V) Finally, convert the volume from cubic feet to gallons using the given conversion factor. Let's go through the calculation step by step: Calculate the radius (r) r=d/2 = 10ft/2 = 5 ft Substitute the radius and height into the volume formula: V=πr(2)h = 3.14 x 5ft (2) x 15ft Calculate the volume: V=3.14 x25ft (2) x 15= 1177.5 Convert the volume from cubic feet to gallons using the conversion factor: Volume in gallons =1177.5 cubic feet × 7.48 gallons cubic foot Volume in gallons = 1177.5 cubic feet x 7.48 gallons cubic foot = 88,077 Gallons x cubic foot Volume in gallons = 88,077

a. 33 cents

What is 1/3 of a dollar? a. 33 cents b. 0.067 cents c. 67 cents d. 0.33 cents

.75

What is 3/4 written in decimal form?

.33

What is 3/9 written in decimal form?

.47

What is 7/15 written in decimal form?

360

What is the SUM of ALL triangles?

d. two places to the right

When converting decimals to a percentage, simply move the decimal point a. one place to the left b. one place to the right c. two places to the left d. two places to the right

c. 180

While the measurement of the individual angles in a triangle can vary, their sum is always___degrees. a. 45 b. 90 c. 180 d. 360

A home measuring 90' by 120' should be excavated and filled to a depth of 4' below the ground surface. The building perimeter must be a minimum of 5' beyond the building line. If the factor soil compaction is 40% and the swelling factor is 30%, calculate in cubic yards the amount of material that must be transported. Note: Swell factor refers to how much a soil expands once extracted from the ground. In this case it is 30%. Therefore, if you were to dig a full cubic yard of this soil, the soil you would remove would take up a space equivalent to 1.3 cubic yards.

Withdrawn Material = 2,503.7 cy

You are making 50 pounds of cement that requires 1.5 liters of water for each pound of cement. How many liters of water do you need to add?

125

You are mixing 250 pounds of asphalt, for each pound, you need .5 pounds of tar. How much tar will you need?

You found a box with 164 device boxes. You have 41 guys in the shop that need them. How many will each man get when they are equally divided?

You have 200 feet of 12' gauged wire. It needs to be cut into 40 foot pieces. How many pieces will you get?

c. 215 sections with 9 feet left over

You have 5,814 feet of rope that you need to cut into 27-foot sections. How many sections of rope will you have? a. 215 sections with 3 feet left over b. 215 sections with 8 feet left over c. 215 sections with 9 feet left over d. 218 sections with 3 feet left over

You have a surplus of 56 hammers in your inventory. You want to give each linemen team an equal number of hammers. How many hammers can 8 teams receive?

d. 196.0

You have to lay a floor for a 14-foot-square shed. The area is_____ square feet. a. 19.6 b. 28.0 c. 144.0 d. 196.0

b. 1.3 liters

You need to mix 42 pounds of mortar. Each pound of mortar mix requires 0.03 liters of water. How many liters of water do you need? (Round your answer to the nearest tenth.) a. 1.2 liters b. 1.3 liters c. 12.6 liters d. 13.2 liters

You purchased 112 nail guns, you supervise 56 teams, how many nail guns can you give to each team?

You receive 96 flats of concrete. You need to equally distribute them to 8 job sites. How many flats does each site get?

105

Your boss gives you 525 boxes of bolts. Your job is to equally distribute them to the five job sites. How many boxes does each site get?

a. $698

Your job as a carpenter pays $20/hour and you worked 40 hours last week. The taxes paid from your salary were $83 and $19. How much is your total check? a. $698 b. $720 c. $810 d. $912

Your order of 72 bolts of wire comes in on Tuesday. Your 9 sites need them by Friday. How many bolts should each site expect to receive?

Refer to the diagram; How deep is the North side of the ditch when finished?(or they could say "slope") (3) North Top C-0° North Toe C-8° @11° South Toe C-8° @15° South Top C-0° @239

ask chat gpt to give me harder questions answer 8' Solution: The North top is cut 0 and the North Toe is cut 8' so the ditch is 8' deep To determine the depth of the North side of the ditch when finished, we need to consider the information provided on the stake: North Top C-0° (This indicates that the slope angle is 0 degrees, meaning it's flat) North Toe C-8° (This indicates a slope of 8 degrees downward) The slope of the North side of the ditch is given as 8 degrees downward. This means that for every horizontal distance of 1 unit, the depth increases by the tangent of 8 degrees. Using trigonometry, we can calculate the depth: Depth = Tangent of slope angle × Horizontal distance \text{Depth} = \text{Tangent of slope angle} \times \text{Horizontal distance} Depth=Tangent of slope angle×Horizontal distance Given that the horizontal distance is not provided, we cannot calculate the exact depth without this information. If the horizontal distance is provided, we can use the tangent of 8 degrees to find the depth. Let me know if you have the horizontal distance, and I can assist you further with the calculation.

Refer to the Diagram; This stake means

cut 2' 5" below the line Solution: Grade stakes are in feet and tenth's of a foot, not inches. So 5" / 12 = .41' Let's break down why "cut 2' 5" below the line" is the correct answer given the question and solution provided: Measurement Units: The stake is labeled "C2 4/" which indicates a measurement of 4/10 of a foot or 0.4 feet. Conversion to Inches: The solution converts the measurement from feet to inches since grade stakes typically use feet and tenths of a foot, not inches. To convert 0.4 feet to inches, we use the conversion factor 12 inches/foot.Calculation: 0.4 feet * 12 inches/foot = 4.8 inches Rounding: Since measurements on grade stakes are typically rounded to the nearest tenth of a foot, the 4.8 inches is rounded up to the nearest inch, which is 5 inches. Interpretation: Therefore, the interpretation of "C2 4/" is "cut 2 feet and 5 inches below the line", or more succinctly, "cut 2' 5" below the line". In summary, the correct answer is "cut 2' 5" below the line" because the measurement on the stake, when converted to inches and rounded, corresponds to that interpretation. The solution provided explains the conversion and rounding process to arrive at the correct interpretation of the stake's measurement.

A pool was built 15' wide by 25' long with a depth of 5', the slope on its walls or embankment is 90 degrees, what type of soil or rock was necessary for the construction of the pool?

d. Stable Rock

What is the place value of 5 in the number 25,718?

thousands

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( Module 00102-15) Introduction to Construction Math Module 2

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