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Sample Practice Test Questions

Math Knowledge

Solve for a:
a2 + 6a - 13 = -a + 5

2 or -9

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:

a2 + 6a - 13 = -a + 5
a2 + 6a - 13 - 5 = -a
a2 + 6a + a - 18 = 0
a2 + 7a - 18 = 0

Next, factor the quadratic equation:

a2 + 7a - 18 = 0
(a - 2)(a + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 2) or (a + 9) must equal zero:

If (a - 2) = 0, a must equal 2
If (a + 9) = 0, a must equal -9

So the solution is that a = 2 or -9

General Science

Which of the following is not a vector quantity?

mass

Velocity and displacement are vector quantities which means each is fully described by both a magnitude and a direction.  In contrast, scalar quantities are quantities that are fully described by a magnitude only.  A variable indicating a vector quantity will often be shown with an arrow symbol:  \(\vec{v}\)

Arithmetic Reasoning

What is the next number in this sequence: 1, 3, 7, 13, 21, __________ ?

31

The equation for this sequence is:

an = an-1 + 2(n - 1)

where n is the term's order in the sequence, an is the value of the term, and an-1 is the value of the term before an. This makes the next number:

a6 = a5 + 2(6 - 1)
a6 = 21 + 2(5)
a6 = 31

Automotive Information

Coolant is circulated through the engine by the:

water pump

The water pump is driven by a belt connected to the crankshaft and ensures that coolant moves through the engine and radiator.

Mechanical Comprehension

The force exerted on an object due to gravity is called:

weight

Mass is an intrinsic property of matter and does not vary. Weight is the force exerted on the mass of an object due to gravity and a specific case of Newton's Second Law of Motion. Replace force with weight and acceleration with acceleration due to gravity on Earth (g) and the result is the formula for weight: W = mg or, substituting for g, weight equals mass multiplied by 9.8 m/s2.

General Science

In cell biology, what part of the cell contains organelles?

cytoplasm

The nucleus of a eukaryotic cell contains the genetic material of the cell and is surrounded by cytoplasm which contains many organelles.

Arithmetic Reasoning

A factor is a positive __________ that divides evenly into a given number.

integer

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

Shop Information

Which of the following is not a common pliers configuration?

wire

Pliers are designed to provide a mechanical advantage, allowing the force of the hand's grip to be amplified and focused with precision. Pliers also allow finer control over objects that are too small to be manipulated by the fingers alone. The standard configuration is combination pliers which provide a fixed maximum jaw width. Other styles include adjustable joint pliers that allow selecting jaw width, needle nose pliers for holding small objects in tight spaces and locking pliers that will lock in place to hold or clamp objects together.

General Science

The coldest point in the Earth's atmosphere is reached in which atmospheric layer?

mesosphere

In the mesosphere, temperature again drops as altitude increases until the coldest point in the Earth's atmosphere, the mesopause, is reached where temperatures fall to −225 °F (−143 °C).

Arithmetic Reasoning

What is \( \frac{-7a^5}{7a^4} \)?

-a

To divide terms with exponents, the base of both exponents must be the same. In this case they are so divide the coefficients and subtract the exponents:

\( \frac{-7a^5}{7a^4} \)
\( \frac{-7}{7} \) a(5 - 4)
-a