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Sample Practice Test Questions
Solve for z:
-5z - 3 = \( \frac{z}{-3} \)
To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.
-5z - 3 = \( \frac{z}{-3} \)
-3 x (-5z - 3) = z
(-3 x -5z) + (-3 x -3) = z
15z + 9 = z
15z + 9 - z = 0
15z - z = -9
14z = -9
z = \( \frac{-9}{14} \)
z = -\(\frac{9}{14}\)
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.
Another name for a reciprocating engine is a(n):
piston engine
A reciprocating engine is an engine whose crankshaft is turned by pistons moving up and down in a cylinder.
Which of the following surfaces would have the lowest coefficient of friction?
ice
Coefficient of friction (μ) represents how much two materials resist sliding across each other. Smooth surfaces like ice have low coefficients of friction while rough surfaces like concrete have high μ.
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.
Materials like metals that transfer heat efficiently are called:
conductors
Heat is always transferred from warmer to cooler environments and conduction is the simplest way this transfer can occur. It is accomplished through direct contact between materials and materials like metals that transfer heat efficiently are called conductors while those that conduct heat poorly, such as plastic, are called insulators.
In cell biology, where does DNA replication take place?
nucleus
The cell nucleus contains the genetic material of the cell and is where DNA replication takes place.