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Sample Practice Test Questions

Mechanical Comprehension
2 If the force applied at the blue arrow over 5 ft. moves the green box 2.5 ft., what is the mechanical advantage of this lever?
2

Mechanical advantage (MA) can be calculated knowing only the distance the effort (blue arrow) moves and the distance the resistance (green box) moves. The equation is:

MA = \( \frac{E_d}{R_d} \)

where Ed is the effort distance and Rd is the resistance distance. For this problem, the equation becomes:

MA = \( \frac{5 ft.}{2.5 ft.} \) = 2

You might be wondering how having an effort distance of 2 times the resistance distance is an advantage. Remember the principle of moments. For a lever in equilibrium the effort torque equals the resistance torque. Because torque is force x distance, if the effort distance is 2 times the resistance distance, the effort force must be \( \frac{1}{2} \) the resistance force. You're trading moving 2 times the distance for only having to use \( \frac{1}{2} \) the force.

Arithmetic Reasoning

\({b + c \over a} = {b \over a} + {c \over a}\) defines which of the following?

distributive property for division

The distributive property for division helps in solving expressions like \({b + c \over a}\). It specifies that the result of dividing a fraction with multiple terms in the numerator and one term in the denominator can be obtained by dividing each term individually and then totaling the results: \({b + c \over a} = {b \over a} + {c \over a}\). For example, \({a^3 + 6a^2 \over a^2} = {a^3 \over a^2} + {6a^2 \over a^2} = a + 6\).

General Science

Scavengers break down the dead bodies of plants and animals into which of the following?

simple nutrients

Like decomposers, scavengers also break down the dead bodies of plants and animals into simple nutrients. The difference is that scavengers operate on much larger refuse and dead animals (carrion). Decomposers then consume the much smaller particles left over by the scavengers.

Math Knowledge

Factor y2 - 4y - 32

(y - 8)(y + 4)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -32 as well and sum (Inside, Outside) to equal -4. For this problem, those two numbers are -8 and 4. Then, plug these into a set of binomials using the square root of the First variable (y2):

y2 - 4y - 32
y2 + (-8 + 4)y + (-8 x 4)
(y - 8)(y + 4)

Word Knowledge
Each year, the Franklins commemorate their anniversary by visiting the site of their first date.
observe
To mark by a ceremony.
Mechanical Comprehension
17.14 lbs. If 15 lbs. of force is applied 8 ft. from the fulcrum at the blue arrow and the green box is 7 ft. from the fulcrum, how much would the green box have to weigh to balance the lever?
17.14 lbs.

To balance this lever the torques at the green box and the blue arrow must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

Rada = Rbdb

where a represents the green box and b the blue arrow, R is resistance (weight/force) and d is the distance from the fulcrum.

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

Ra = \( \frac{R_bd_b}{d_a} \) = \( \frac{15 lbs. \times 8 ft.}{7 ft.} \) = \( \frac{120 ft⋅lb}{7 ft.} \) = 17.14 lbs.

Arithmetic Reasoning

Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 20 small cakes per hour. The kitchen is available for 2 hours and 26 large cakes and 480 small cakes need to be baked.

How many cooks are required to bake the required number of cakes during the time the kitchen is available?

15

If a single cook can bake 5 large cakes per hour and the kitchen is available for 2 hours, a single cook can bake 5 x 2 = 10 large cakes during that time. 26 large cakes are needed for the party so \( \frac{26}{10} \) = 2\(\frac{3}{5}\) cooks are needed to bake the required number of large cakes.

If a single cook can bake 20 small cakes per hour and the kitchen is available for 2 hours, a single cook can bake 20 x 2 = 40 small cakes during that time. 480 small cakes are needed for the party so \( \frac{480}{40} \) = 12 cooks are needed to bake the required number of small cakes.

Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 3 + 12 = 15 cooks.

Arithmetic Reasoning

In a class of 24 students, 14 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 3 are taking both courses. How many students are not enrolled in either course?

7

The number of students taking German or Spanish is 14 + 6 = 20. Of that group of 20, 3 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 20 - 3 = 17 who are taking at least one language. 24 - 17 = 7 students who are not taking either language.

General Science

What part of the nervous system is responsible for controlling involuntary actions like breathing, swallowing, and heartbeat?

medulla

Part of the brainstem, the medulla is the connection between the brain and the spinal cord. It controls involuntary actions like breathing, swallowing, and heartbeat.

Mechanical Comprehension

An object's resistance to changes in direction is known as:

inertia

The more mass a substance has the more force is required to move it or to change its direction. This resistance to changes in direction is known as inertia.