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Applied Technical Mathematics Flashcards

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

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  1. If a gear with 40 teeth meshes with a gear with 10 teeth, what is the gear ratio?

    Answer: 4:1

    Gear ratio = driven teeth divided by driving teeth. If the 40-tooth gear drives the 10-tooth gear: 40/10 = 4:1.

  2. What is the Pythagorean theorem used to calculate?

    Answer: The length of the hypotenuse in a right triangle

    The Pythagorean theorem (a squared + b squared = c squared) calculates the length of any side of a right triangle when the other two sides are known.

  3. A motor operates at 1,750 RPM with a 6-inch drive pulley connected to a 12-inch driven pulley. What is the driven pulley speed?

    Answer: 875 RPM

    Pulley speed ratio: RPM2 = RPM1 x (D1/D2) = 1,750 x (6/12) = 1,750 x 0.5 = 875 RPM.

  4. How many board feet are in a piece of lumber that is 2 inches thick, 6 inches wide, and 12 feet long?

    Answer: 12 board feet

    Board feet = (Thickness x Width x Length) / 12 = (2 x 6 x 12) / 12 = 144 / 12 = 12 board feet.

  5. What is the slope of a roof that rises 6 inches for every 12 inches of horizontal run?

    Answer: 6:12 pitch

    Roof slope is expressed as rise over run per 12 inches of horizontal distance. A 6-inch rise over 12 inches of run is a 6:12 pitch.

  6. Convert 2.5 meters to centimeters.

    Answer: 250 centimeters

    There are 100 centimeters in 1 meter, so 2.5 x 100 = 250 centimeters.