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Sample Practice Test Questions

Math Knowledge

Simplify (y + 8)(y + 3)

y2 + 11y + 24

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 8)(y + 3)
(y x y) + (y x 3) + (8 x y) + (8 x 3)
y2 + 3y + 8y + 24
y2 + 11y + 24

Word Knowledge
Aerate most nearly means:
oxygenate
To supply with air.
Math Knowledge

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.

Arithmetic Reasoning

If \( \left|x + 9\right| \) - 3 = 7, which of these is a possible value for x?

-19

First, solve for \( \left|x + 9\right| \):

\( \left|x + 9\right| \) - 3 = 7
\( \left|x + 9\right| \) = 7 + 3
\( \left|x + 9\right| \) = 10

The value inside the absolute value brackets can be either positive or negative so (x + 9) must equal + 10 or -10 for \( \left|x + 9\right| \) to equal 10:

x + 9 = 10
x = 10 - 9
x = 1
 x + 9 = -10
x = -10 - 9
x = -19

So, x = -19 or x = 1.

Mechanical Comprehension
If you have a gear train with two gears, the first with 32 teeth and the second with 4 teeth, how many revolutions does the second gear make for each revolution of the first gear?
8

The gear ratio (Vr) of a gear train is the product of the gear ratios between the pairs of meshed gears. Let N represent the number of teeth for each gear:

Vr = \( \frac{N_1}{N_2} \) \( \frac{N_2}{N_3} \) \( \frac{N_3}{N_4} \) ... \( \frac{N_n}{N_{n+1}} \)

In this problem, we have only two gears so the equation becomes:

Vr = \( \frac{N_1}{N_2} \) = \( \frac{32}{4} \) = 8

Shop Information

A joint created by welding is __________ the original metal.

as strong or stronger than

The joint created by welding is as strong or stronger than the original metal.

Word Knowledge
Periodic most nearly means:
repeated
Occurring at regular intervals.
Word Knowledge
Helen will only accept something of comparable value for her ticket to the concert.
akin
Similar, equivalent.
General Science

Which of the following states of matter exists at the highest temperature?

gas

Solids exist at a lower temperature than liquids which exist at a lower temperature than gases.

General Science

Which of the following is the formula for work?

\(W = \vec{F}\vec{d}\)

Work is performed on an object when an applied force causes displacement along the same vector. Measured in joules (J) or newton-meter (Nm), work is calculated by multiplying force times displacement:  \(W = \vec{F}\vec{d}\)