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Sample Practice Test Questions
A(n) __________ is to a parallelogram as a square is to a rectangle.
rhombus
A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.
Which of the following is not true about both rectangles and squares?
the lengths of all sides are equal
A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s2).
If the radius of the axle is 5 and the radius of the wheel is 6, what is the mechanical advantage of this wheel and axle configuration?
The mechanical advantage of a wheel and axle lies in the difference in radius between the inner (axle) wheel and the outer wheel. But, this mechanical advantage is only realized when the input effort and load are applied to different wheels. Applying both input effort and load to the same wheel results in a mechanical advantage of 1.
A machine in a factory has an error rate of 6 parts per 100. The machine normally runs 24 hours a day and produces 5 parts per hour. Yesterday the machine was shut down for 6 hours for maintenance.
How many error-free parts did the machine produce yesterday?
The hourly error rate for this machine is the error rate in parts per 100 multiplied by the number of parts produced per hour:
\( \frac{6}{100} \) x 5 = \( \frac{6 \times 5}{100} \) = \( \frac{30}{100} \) = 0.3 errors per hour
So, in an average hour, the machine will produce 5 - 0.3 = 4.7 error free parts.
The machine ran for 24 - 6 = 18 hours yesterday so you would expect that 18 x 4.7 = 84.6 error free parts were produced yesterday.
What type of load doesn't create specific stress points or vary with time?
static uniformly distributed load
A concentrated load acts on a relatively small area of a structure, a static uniformly distributed load doesn't create specific stress points or vary with time, a dynamic load varies with time or affects a structure that experiences a high degree of movement, an impact load is sudden and for a relatively short duration and a non-uniformly distributed load creates different stresses at different locations on a structure.
Convert 0.0006095 to scientific notation.
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
0.0006095 in scientific notation is 6.095 x 10-4
If the force applied at the blue arrow over 5 ft. moves the green box 2.5 ft., what is the mechanical advantage of this lever?
Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:
MA = \( \frac{E_d}{R_d} \)
where Ed is the effort distance and Rd is the resistance distance. For this problem, the equation becomes:
MA = \( \frac{5 ft.}{2.5 ft.} \) = 2
You might be wondering how having an effort distance of 2 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 2 times the resistance distance, the effort force must be \( \frac{1}{2} \) the resistance force. You're trading moving 2 times the distance for only having to use \( \frac{1}{2} \) the force.
If there were a total of 350 raffle tickets sold and you bought 24 tickets, what's the probability that you'll win the raffle?
You have 24 out of the total of 350 raffle tickets sold so you have a (\( \frac{24}{350} \)) x 100 = \( \frac{24 \times 100}{350} \) = \( \frac{2400}{350} \) = 7% chance to win the raffle.