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Sample Practice Test Questions
If all of a roofing company's 6 workers are required to staff 3 roofing crews, how many workers need to be added during the busy season in order to send 7 complete crews out on jobs?
In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 6 workers at the company now and that's enough to staff 3 crews so there are \( \frac{6}{3} \) = 2 workers on a crew. 7 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 7 x 2 = 14 total workers to staff the crews during the busy season. The company already employs 6 workers so they need to add 14 - 6 = 8 new staff for the busy season.
A __________ is the smallest multi-atom particle of an element or compound that can exist and still retain the characteristics of the element or compound.
molecule
A molecule is the smallest multi-atom particle of an element or compound that can exist and still retain the characteristics of the element or compound. The molecules of elements consist of two or more similar atoms, the molecules of compounds consist of two or more different atoms.
Which of the following expressions contains exactly two terms?
binomial
A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.
A capacitor is often used for which of the following purposes?
to maintain power in a circuit when the primary power source is disconnected
Capacitors store electricity and are used in circuits as temporary batteries. Capacitors are charged by DC current (AC current passes through a capacitor) and that stored charge can later be dissipated into the circuit as needed. Capacitors are often used to maintain power within a system when it is disconnected from its primary power source or to smooth out or filter voltage within a circuit.
What is -z2 + 5z2?
To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:
-1z2 + 5z2
(-1 + 5)z2
4z2
If the green box is 8 ft. from the fulcrum and a certain force applied 7 ft. from the fulcrum at the blue arrow balances the lever, what is the mechanical advantage?
Because this lever is in equilibrium, we know that the effort force at the blue arrow is equal to the resistance weight of the green box. For a lever that's in equilibrium, one method of calculating mechanical advantage (MA) is to divide the length of the effort arm (Ea) by the length of the resistance arm (Ra):
MA = \( \frac{E_a}{R_a} \) = \( \frac{7 ft.}{8 ft.} \) = 0.88
When a lever is in equilibrium, the torque from the effort and the resistance are equal. The equation for equilibrium is Rada = Rbdb where a and b are the two points at which effort/resistance is being applied to the lever.
In this problem, Ra and Rb are such that the lever is in equilibrium meaning that some multiple of the weight of the green box is being applied at the blue arrow. For a lever, this multiple is a function of the ratio of the distances of the box and the arrow from the fulcrum. That's why, for a lever in equilibrium, only the distances from the fulcrum are necessary to calculate mechanical advantage.
If the lever were not in equilibrium, you would first have to calculate the forces and distances necessary to put it in equilibrium and then divide Ea by Ra to get the mechanical advantage.
Which of the following is not a characteristic of a ceramic?
low density
Ceramics are mixtures of metallic and nonmetallic elements that withstand exteme thermal, chemical, and pressure environments. They have a high melting point, low corrosive action, and are chemically stable. Examples include rock, sand, clay, glass, brick, and porcelain.