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Sample Practice Test Questions

Math Knowledge

What is 4a7 - 9a7?

-5a7

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

4a7 - 9a7 = -5a7

General Science

__________ is caused by a lack of iron in the diet.

anemia

Anemia, which may cause weakness, dizziness, and headaches is caused by a lack of iron in the diet.

Electronics Information

Which of the following is not a common type of battery?

power-cycle

Direct current flows in only one direction in a circuit, from the negative terminal of the voltage source to the positive. A common source of direct current (DC) is a battery. The three most common types of batteries are dry cell (used in small devices like TV remotes), wet cell (used for cars), and deep-cycle (storage batteries used primarily for backup and emergency power).

Arithmetic Reasoning

On average, the center for a basketball team hits 50% of his shots while a guard on the same team hits 60% of his shots. If the guard takes 25 shots during a game, how many shots will the center have to take to score as many points as the guard assuming each shot is worth the same number of points?

30
If the guard hits 60% of his shots and takes 25 shots he'll make:

guard shots made = shots taken x \( \frac{\text{% made}}{100} \) = 25 x \( \frac{60}{100} \) = \( \frac{60 x 25}{100} \) = \( \frac{1500}{100} \) = 15 shots

The center makes 50% of his shots so he'll have to take:

shots made = shots taken x \( \frac{\text{% made}}{100} \)
shots taken = \( \frac{\text{shots taken}}{\frac{\text{% made}}{100}} \)

to make as many shots as the guard. Plugging in values for the center gives us:

center shots taken = \( \frac{15}{\frac{50}{100}} \) = 15 x \( \frac{100}{50} \) = \( \frac{15 x 100}{50} \) = \( \frac{1500}{50} \) = 30 shots

to make the same number of shots as the guard and thus score the same number of points.

Automotive Information

Too much air results in a __________ air-fuel mixture that burns more slowly and hotter.

lean

The stoichiometric ratio defines the proper ratio of air to fuel necessary so that an engine burns all fuel with no excess air. For gasoline fuel, the stoichiometric ratio is about 14.7:1 or for every one gram of fuel, 14.7 grams of air are required. Too much air results in a lean air-fuel mixture that burns more slowly and hotter while too much fuel results in a rich mixture that burns quicker and cooler.

Math Knowledge

Solve 3b + 2b = 9b - 9y + 8 for b in terms of y.

1\(\frac{5}{6}\)y - 1\(\frac{1}{3}\)

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

3b + 2y = 9b - 9y + 8
3b = 9b - 9y + 8 - 2y
3b - 9b = -9y + 8 - 2y
-6b = -11y + 8
b = \( \frac{-11y + 8}{-6} \)
b = \( \frac{-11y}{-6} \) + \( \frac{8}{-6} \)
b = 1\(\frac{5}{6}\)y - 1\(\frac{1}{3}\)

Word Knowledge
Dubious most nearly means:
suspect
Questionable.
Math Knowledge

Find the value of c:
5c + x = -1
-2c - 3x = -3

-\(\frac{6}{13}\)

You need to find the value of c so solve the first equation in terms of x:

5c + x = -1
x = -1 - 5c

then substitute the result (-1 - 5c) into the second equation:

-2c - 3(-1 - 5c) = -3
-2c + (-3 x -1) + (-3 x -5c) = -3
-2c + 3 + 15c = -3
-2c + 15c = -3 - 3
13c = -6
c = \( \frac{-6}{13} \)
c = -\(\frac{6}{13}\)

Mechanical Comprehension
2.36 ft. If the green box weighs 55 lbs. and is 3 ft. from the fulcrum, how far from the fulcrum would a 70 lbs. weight need to be placed to balance the lever?
2.36 ft.

To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

Rada = Rbdb

where a represents the left side of the fulcrum and b the right, R is resistance (weight) and d is the distance from the fulcrum.

Solving for db, our missing value, and plugging in our variables yields:

db = \( \frac{R_ad_a}{R_b} \) = \( \frac{55 lbs. \times 3 ft.}{70 lbs.} \) = \( \frac{165 ft⋅lb}{70 lbs.} \) = 2.36 ft.

Electronics Information

Voltage and current are __________ proportional.

directly

Voltage (V) is the electrical potential difference between two points. Electrons will flow as current from areas of high potential (concentration of electrons) to areas of low potential. Voltage and current are directly proportional in that the higher the voltage applied to a conductor the higher the current that will result.