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Construction Math Fundamentals Flashcards

6 cards from real NCCER CORE practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 6 Construction Math Fundamentals flashcards as text

  1. A carpenter needs to cut a piece of wood that is 5 1/8 inches long from a board that is 8 3/4 inches long. After the cut, what is the length of the remaining piece of wood?

    Answer: 3 5/8 inches

    To find the remaining length, subtract the cut length from the original length. First, find a common denominator for the fractions, which is 8. Convert 3/4 to 6/8. The problem becomes 8 6/8 - 5 1/8. Subtract the whole numbers (8 - 5 = 3) and the fractions (6/8 - 1/8 = 5/8). The result is 3 5/8 inches.

  2. A construction plan requires a concrete slab with a volume of 3 cubic yards. If the slab is 12 feet long and 9 feet wide, what must be its thickness in inches? (1 cubic yard = 27 cubic feet)

    Answer: 9 inches

    First, convert the required volume from cubic yards to cubic feet: 3 cubic yards * 27 cubic feet/yard = 81 cubic feet. Next, calculate the area of the slab: 12 feet * 9 feet = 108 square feet. To find the thickness in feet, divide the volume by the area: 81 cubic feet / 108 square feet = 0.75 feet. Finally, convert the thickness to inches: 0.75 feet * 12 inches/foot = 9 inches.

  3. Which of the following is the correct conversion of 6 feet 9 inches to decimal feet?

    Answer: 6.75 feet

    To convert inches to decimal feet, divide the number of inches by 12. In this case, 9 inches / 12 inches = 0.75. Then, add this decimal value to the whole number of feet. So, 6 feet + 0.75 feet = 6.75 feet.

  4. A crew is framing a wall and needs to ensure the corners are perfectly square. They measure 6 feet along one wall from the corner and 8 feet along the adjacent wall from the corner. What should the diagonal measurement between those two points be to confirm a 90-degree angle?

    Answer: 10 feet

    This scenario uses the Pythagorean theorem (a² + b² = c²) to verify a right angle. The two wall measurements are the legs of a right triangle (a and b), and the diagonal is the hypotenuse (c). So, 6² + 8² = c². This becomes 36 + 64 = c², which simplifies to 100 = c². The square root of 100 is 10, so the diagonal measurement should be 10 feet. This is a multiple of the common 3-4-5 rule.

  5. You are ordering lumber for a project. You need 10 boards, each measuring 2 inches thick, 6 inches wide, and 8 feet long. What is the total number of board feet you need to order?

    Answer: 80 board feet

    The formula for board feet is (Thickness in inches × Width in inches × Length in feet) / 12. For one board: (2" × 6" × 8') / 12 = 96 / 12 = 8 board feet. Since you need 10 boards, multiply the board feet per board by the number of boards: 8 board feet/board × 10 boards = 80 board feet.

  6. A cylindrical concrete form for a pillar has a diameter of 2 feet and a height of 10 feet. What is the volume of concrete needed to fill the form, rounded to the nearest cubic foot? (Use π ≈ 3.14)

    Answer: 31 cubic feet

    The formula for the volume of a cylinder is V = πr²h. First, find the radius (r) by dividing the diameter by 2: 2 feet / 2 = 1 foot. Then, apply the formula: V = 3.14 × (1 foot)² × 10 feet = 3.14 × 1 square foot × 10 feet = 31.4 cubic feet. Rounded to the nearest cubic foot, the answer is 31 cubic feet.