If something is pivotal, it means that it is important.  For example, the last regular football game of a season is pivotal in determining whether the team will play in the semifinals.

Something that is “eminent” is well-known or important. This is opposed to something that is "imminent," which means about to happen. To provide further guidance, "futile" means pointless; "worthless" means not worth anything; "morose" means miserable and glum; "novelty" means innovation, something original.

"Tangential" is an adjective that means either "diverging from a previous course or line; erratic," or "hardly touching a matter; peripheral." So, we need to pick out an answer choice that means something like "erratic" or "peripheral." "Essential" cannot be the correct answer, then, because "essential" means "absolutely necessary; extremely important," making it an antonym of "tangential," not a synonym. "Nonessential," however, is an adjective that means "not absolutely necessary," and because "nonessential" is the answer choice closest in meaning to "tangential," "nonessential" is the correct answer.

"Petty" is and adjective that means relatively unimportant, so the answer choice closest in meaning to "petty" is "insignificant," an adjective meaning of no significance, unimportant, or irrelevant. None of the other answer are close in meaning to "petty": "lucrative" is an adjective meaning profitable; "important" is an antonym of "petty" meaning of great significance; and "dark" is an adjective meaning having little light by which to see or closer to black than to white in shade.

"Substantial" means of great weight or significance. Therefore, "significant" is the correct synonym. 

Something that is "imperative" is crucial or essential, so "essential" is the correct answer choice. As for the other answer choices, "somber" means sad and serious; "abrupt" means sudden; and "optional" means not necessary.

“Pertinent” means relevant or able to be applied and is therefore most similar in meaning to “applicable.” To provide further help, “irrelevant” means not related to the subject; “extraneous” means not needed, additional, and wasted; “intravenous” means injected into the veins; and “immaterial” means not related to the subject, irrelevant, or not pertinent.

When something is described as "staged" it can mean simply put on, held, performed. But, it can also mean faked. As in "some people believe that the moon landing was staged." To provide further help, "arranged" means set up; "assaulted" means attacked. 

"Metaphorical" means figurative, not literal, a figure of speech not meant to be taken literally. To provide further help, "literal" means taken at face value, not meant to be deeply analyzed, (of a phrase) not metaphorical. Additionally, "outstanding" means amazing, fantastic; "immaculate" means clean or perfect or miraculous; "unconscionable" means not morally right, unreasonably excessive in nature. 

Whenever we want to "persuade" someone of something, we wish to convince him or her of our viewpoint. We do not have to do this in an intelligent or an honest way. (Of course, that can help.) Still, the general idea of being "persuasive" is that of "carrying force"—in the sense of forcing someone to change his or her mind to come to your side of an argument or topic. Thus, the best option for this question is actually "forceful." This sense of the word comes out if you think of an opposite word, namely "unpersuasive." Sometimes, this means weak—in the sense of not being able to force someone to change his or her viewpoint.