The prefix "poly-" means many and the suffix "-gon" means related to a shape, so a “polygon” is a many-sided shape. 

The prefix "mono­-" means one. A “monopoly” is when one business has exclusive control over a product or market. To provide further help, “inclusive” means comprehensive, including everyone or everything; “anomalous” means irregular, unusual; “suspicious” means doubtful, deserving of distrust. 

The prefix "pseudo-" means pretend or fake and "nym" (more commonly "nom") means related to names, so a “pseudonym” is a fake name or a “nickname.” To provide further help, a “novelty” is something new or different; a “neophyte” is a beginner; “nominate” means to name for a position; a “nihilist” is someone who rejects the idea that life has meaning.

The prefix "hyper-" usually means super, excessive, or a lot of, so “hyperbole” is the literary device of dramatically overstating something. To provide further help, “overwhelming” means overpowering, too much, or extremely large, and “underwhelming” means too little or disappointing. Notice how the prefixes "hyper-" and "over-" are similar to one another, and opposites of the prefix "under-."

The word fragment "morph­" refers to form or shape,and the prefix "a-" means without,so “amorphous” means without form, or formless. To provide further help, “aimless” means without direction or purpose, and “hopeless” means without love. (Observe the meaning of the suffix "-less"—without.) "Converted" means changed from one thing to another; and "solidified" means having attained a solid shape or strengthened.

The word "biological" refers to living things. The best choice is "alive" as it is a part of the definition of "biological." Considering the other choices, "math" refers to mathematical operations, "biology" is a branch of science concerned with living creatures, and "sleepy" means exhausted or tired.

"Apathetic" is an adjective that means "showing or feeling no interest, enthusiasm, or concern," so we need to pick out an answer choice that means something like "unconcerned." "Concerned" cannot be the correct answer, then, because "concerned" is an antonym of "unconcerned." "Indifferent," however, is an adjective that can mean "having no particular interest or sympathy; unconcerned," and because it is the answer choice that is closest in meaning to "apathetic," "indifferent" is the correct answer.

Someone who is “social” is good with people or enjoys talking to people. The prefix "anti­-" is a negation prefix; it causes the new word to have the opposite meaning to the original. So “antisocial” means not social or not considerate, which makes the correct answer “inconsiderate.” Someone who is “inconsiderate” is not kind or not able to think about other people’s feelings. The the prefix "in-" functions similarly to the prefix "anti-" and negates the meaning of the original word. To provide further help, “implacable” means merciless, unstoppable; “parsimonious” means not generous with money; “outlying” means remote or unusual; “extraneous” means not needed. 

You likely know that “enemy” is similar in meaning to “rival,” so the key to answering this question is to understand how the prefix "arch-" changes the meaning of the word “enemy.” In this instance, the meaning is unchanged. "Arch-" means chief or primary, so your “archenemy” is your biggest enemy or rival. To provide further help, “bellow” means to yell; “debris” is the fallen parts of things after they are broken; a “nomad” is someone who wanders from place to place without making a home; “catastrophe” means disaster.

The Greek root "dynam" means energy, so the word “dynamic” means having energy, exciting, or “active.” “Vacant” means unoccupied; “inert” means lifeless and having no energy; "dominant” means in control and in charge; and "despondent" means very sad and pessimistic.