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Arithmetic Reasoning

Which of the following is not an integer?

\({1 \over 2}\)

An integer is any whole number, including zero. An integer can be either positive or negative. Examples include -77, -1, 0, 55, 119.

Mechanical Comprehension

Which of these will have the most impact on the kinetic energy of an object?

its speed

Kinetic energy is the energy of movement and is a function of the mass of an object and its speed: \(KE = {1 \over 2}mv^2\) where m is mass in kilograms, v is speed in meters per second, and KE is in joules. The most impactful quantity to kinetic energy is velocity as an increase in mass increases KE linearly while an increase in speed increases KE exponentially.

Mechanical Comprehension

Concurrent forces:

pass through a common point

Collinear forces act along the same line of action, concurrent forces pass through a common point and coplanar forces act in a common plane.

General Science

Which of the following is related to the Cambrian Explosion?

fossil record

The Cambrian period is one of the most significant geological time periods. Lasting about 53 million years, it marked a dramatic burst of changes in life on Earth known as the Cambrian Explosion. It is from this period that the majority of the history of life on Earth, as documented by fossils, is found. Called the fossil record, the layering of these mineralized imprints of organisms preserved in sedementary rock have allowed geologists to build a historical record of plant and animal life on Earth.

Mechanical Comprehension

If A = 10 ft., B = 1 ft., C = 9 ft., the green box weighs 50 lbs. and the blue box weighs 60 lbs., what does the orange box have to weigh for this lever to balance?

48.89 lbs.

In order for this lever to balance, the torque acting on each side of the fulrum must be equal. So, the torque produced by A must equal the torque produced by B and C. Torque is weight x distance from the fulcrum which means that the following must be true for the lever to balance:

f_Ad_A = f_Bd_B + f_Cd_C

For this problem, this equation becomes:

50 lbs. x 10 ft. = 60 lbs. x 1 ft. + f_C x 9 ft.

500 ft. lbs. = 60 ft. lbs. + f_C x 9 ft.

f_C = \( \frac{500 ft. lbs. - 60 ft. lbs.}{9 ft.} \) = \( \frac{440 ft. lbs.}{9 ft.} \) = 48.89 lbs.

Math Knowledge

Which of the following expressions contains exactly two terms?

binomial

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

Word Knowledge

Dubious most nearly means:

suspect

Questionable.

General Science

The crust and upper mantle of the earth is called the:

lithosphere

The biosphere is the global ecological system integrating all living beings and their relationships. This includes their interactions with the lithosphere (the rigid outer part of the earth, consisting of the crust and upper mantle), hydrosphere (all surface water), and atmosphere (the envelope of gases surrounding the planet).

General Science

Which of the following members of the food chain are most alike?

scavengers and decomposers

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.

Arithmetic Reasoning

What is the distance in miles of a trip that takes 1 hour at an average speed of 50 miles per hour?

50 miles

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

speed = \( \frac{\text{distance}}{\text{time}} \)

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 50mph \times 1h \)
50 miles