NOCTI - National Occupational Competency Testing Institute Applied Technical Mathematics 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?

Accepted Answer

3.827 inches

Answer

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?

Accepted Answer

11.25 V

Answer

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?

Accepted Answer

14 feet

Answer

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?

Accepted Answer

a² + b² = c²

Answer

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)

Accepted Answer

226.08 cu ft

Answer

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.

NOCTI - National Occupational Competency Testing Institute Practice Test

NOCTI - National Occupational Competency Testing Institute Practice Test

NOCTI - National Occupational Competency Testing Institute Applied Technical Mathematics Questions and Answers