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Sample Practice Test Questions
Solve for c:
c2 + 6c - 13 = -c + 5
The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:
c2 + 6c - 13 = -c + 5
c2 + 6c - 13 - 5 = -c
c2 + 6c + c - 18 = 0
c2 + 7c - 18 = 0
Next, factor the quadratic equation:
c2 + 7c - 18 = 0
(c - 2)(c + 9) = 0
For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 2) or (c + 9) must equal zero:
If (c - 2) = 0, c must equal 2
If (c + 9) = 0, c must equal -9
So the solution is that c = 2 or -9
Which of the following is the result of the air-fuel mixture exploding instead of burning?
detonation
Normal combustion in an engine is initiated by a spark plug and results in the complete burning of the air-fuel mixture. If combustion is initiated by a source other than the spark plug, by a hot spot in the cylinder or combustion chamber for example, pre-ignition results. Detonation results if the air-fuel mixture explodes instead of burning. Detonation can cause extremes in pressure in the combustion chamber leading to engine damage.
What prevents blood pumped out of the ventricles from flowing back into the heart?
valves
The heart is the organ that drives the circulatory system. In humans, it consists of four chambers with two that collect blood called atria and two that pump blood called ventricles. The heart's valves prevent blood pumped out of the ventricles from flowing back into the heart.
Friction between two or more solid objects that are not moving relative to each other is called:
static friction
Static friction is friction between two or more solid objects that are not moving relative to each other. An example is the friction that prevents a box on a sloped surface from sliding farther down the surface.
Simplify \( \frac{24}{56} \).
To simplify this fraction, first find the greatest common factor between them. The factors of 24 are [1, 2, 3, 4, 6, 8, 12, 24] and the factors of 56 are [1, 2, 4, 7, 8, 14, 28, 56]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).
Next, divide both numerator and denominator by the GCF:
\( \frac{24}{56} \) = \( \frac{\frac{24}{8}}{\frac{56}{8}} \) = \( \frac{3}{7} \)
According to Boyle's law, for a fixed amount of gas kept at a fixed temperature, which of the following are inversely proportional?
pressure, volume
Boyle's law states that "for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional".
What is the function of the head gasket?
to seal the engine block from the cylinders
A head gasket is a gasket that sits between the engine block and cylinder heads to seal the cylinders to ensure maximum compression and avoid leakage of coolant or engine oil into the cylinders.
Piston rings are responsible for which of the following?
regulating oil distribution inside the cylinder
Cylinders act as a guide for the pistons that translate the heat energy of combustion into the mechanical energy necessary to move a vehicle. Piston rings seal the piston to the cylinder to contain combustion gases and also regulate the oil distribution between the piston and cylinder wall. A cylinder head closes in the top of the cylinder forming the combustion chamber which is sealed by a head gasket (head). The head provides space for air and fuel intake valves, exhaust valves, and mounts for spark plugs and fuel injectors.
The spark plug fires during which engine stoke?
power
During the power stroke, just before the piston reaches top dead center, the spark plug fires and ignites the compressed air-fuel mixture. The resulting expansion due to combustion pushes the piston back down the cylinder toward bottom dead center.