NOCTI - National Occupational Competency Testing Institute Applied Technical Mathematics Questions and Answers 1 — Questions and Answers
Question 1: A machinist needs to drill a bolt circle with 8 equally spaced holes on a circular plate with a diameter of 10 inches. What is the straight-line distance, to the nearest thousandth of an inch, between the centers of two adjacent holes?
- 4.821 inches
- 3.827 inches (Correct answer)
- 3.927 inches
- 5.000 inches
Correct answer: 3.827 inches
The 8 holes form a regular octagon inscribed in a circle with a radius of 5 inches. The angle between two adjacent holes from the center is 360°/8 = 45°. The distance between two holes can be found using the law of cosines: c² = a² + b² - 2ab*cos(C). Here, a and b are the radius (5 inches) and C is the angle (45°). So, c² = 5² + 5² - 2(5)(5)cos(45°) = 25 + 25 - 50(0.7071) = 50 - 35.355 = 14.645. Taking the square root, c ≈ 3.827 inches.
Question 2: A DC circuit has a total resistance of 45 ohms and draws a current of 0.25 amps. According to Ohm's Law (V = IR), what is the voltage of the circuit?
- 180 V
- 11.25 V (Correct answer)
- 45.25 V
- 0.005 V
Correct answer: 11.25 V
Ohm's Law states that Voltage (V) is equal to Current (I) multiplied by Resistance (R). Given I = 0.25 amps and R = 45 ohms, the calculation is V = 0.25 * 45 = 11.25 Volts.
Question 3: A construction plan is drawn to a scale of 1/4 inch = 1 foot. A wall on the blueprint measures 3 1/2 inches long. What is the actual length of the wall?
- 7 feet
- 12 feet
- 14 feet (Correct answer)
- 8.75 feet
Correct answer: 14 feet
To find the actual length, you can set up a proportion: (1/4 inch / 1 foot) = (3.5 inches / x feet). To solve for x, you can divide 3.5 by 1/4 (or multiply by 4). So, x = 3.5 * 4 = 14 feet.
Question 4: Which of the following equations correctly represents the Pythagorean theorem, used to find the length of the sides of a right triangle?
- a² - b² = c²
- a + b = c
- a² * b² = c²
- a² + b² = c² (Correct answer)
Correct answer: a² + b² = c²
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle, denoted as 'c') is equal to the sum of the squares of the lengths of the other two sides (denoted as 'a' and 'b'). The formula is a² + b² = c².
Question 5: A cylindrical tank has a radius of 3 feet and a height of 8 feet. What is the volume of the tank in cubic feet? (Use V = πr²h and π ≈ 3.14)
- 75.36 cu ft
- 150.72 cu ft
- 226.08 cu ft (Correct answer)
- 24.00 cu ft
Correct answer: 226.08 cu ft
The formula for the volume of a cylinder is V = πr²h. Plugging in the given values: V = 3.14 * (3 ft)² * 8 ft = 3.14 * 9 sq ft * 8 ft = 3.14 * 72 cu ft = 226.08 cubic feet.
Question 6: A steel rod needs to be cut into pieces that are 5 1/8 inches long. If the rod is 48 inches long, how many full pieces can be cut from it, ignoring any material lost from the cuts (kerf)?
- 8
- 10
- 9 (Correct answer)
- 11
Correct answer: 9
First, convert the mixed number to a decimal or an improper fraction. 5 1/8 inches is 5.125 inches. Then, divide the total length of the rod by the length of one piece: 48 inches / 5.125 inches/piece ≈ 9.36 pieces. Since the question asks for the number of *full* pieces, we must round down to the nearest whole number, which is 9.
NOCTI - National Occupational Competency Testing Institute Applied Technical Mathematics Questions and Answers 1
A machinist needs to drill a bolt circle with 8 equally spaced holes on a circular plate with a diameter of 10 inches.
What is the straight-line distance, to the nearest thousandth of an inch, between the centers of two adjacent holes?