As the student always gets poor grades in math, it stands to reason that his or her “arithmetic” would be rudimentary. “Rudimentary” means not well developed, basic. It also stands to reason that a teacher would advise a student that he or she can do or succeed in anything if the student keeps working at it; this should lead to an answer choice of accomplish.

To provide further help, “theology” is the study of religion; “undermine” means weaken; “hesitate” means delay, wait for something; “geometry” is a type of mathematics concerned with shapes; a “conglomerate” is a large, combined, business; “gratuity” is a tip given to someone who provides good service; “affix” means stick to. 

To finish this sentence you have to know that executing criminals can also be referred to as capital punishment. Many people might have selected “corporal” (which means of the body) punishment, but this does not capture the real meaning of the sentence.

To provide further help, “recreational” means done for the purposes of fun or enjoyment; “credulous” means disbelieving; “rakish” means charming, casual.

As the author of this subject did not wish to be recognized it makes sense that he would go to the party in a disguise, or incognito. The word fragment cogn- refers to knowledge or identity.

To provide further help, “unaccompanied” means alone; “condensed” means thick, reduced together; “afflicted” means suffering with; “forlorn” means sad and feeling hopeless. 

The context of the sentence suggests that we are looking for an answer choice that refers to the condition of buildings, so the correct answer is “infrastructure.” "Setting" is a decent answer choice, but since "infrastructure" specifically refers to buildings and the sentence specifically discusses the state of buildings in the area, "infrastructure" is the best answer. "Hotels" and "mansions" are too specific to be the correct answer since the sentence refers specifically to "buildings," a more general word.

Since Donald has "written many books about Greece," we can infer that he knows a lot about that topic. So, we need to pick out an answer choice that means something like knowledgeable. The word that best fits the sentence's blank is "erudite," which means learned and scholarly. As for the other answer choices, "absent" means not present or missing, "enigmatic" means mysterious, "expansive" means extensive or communicative, and "exultant" means triumphant or delighted.

From the context of the sentence, you know that the blank word must describe the king’s lack of mercy and compassion. The correct answer is therefore “ruthless," which means showing no mercy or violent. To help you, "benevolent" means good-natured, "supple" means flexible, "intelligent" means smart, and "gregarious" means sociable.

The key thing for this sentence is to note the boss' surprise. The word "still" in the second independent clause means nevertheless. This adverb indicates that even though the boss announced the meeting was going to be X, he was surprised that people came to it in such a very casual manner. You are looking for a synonym for "casual." "Informal" works well to this end.

"Radical" opinions are ones that are very daring and bold, often held by very few people. The word literally means cut to the root, as though you were to hold an opinion that is "uprooted" from all that is commonly believed by society. Generally speaking, "radical" implies something very innovative and even bold (for good or ill). In contrast to such opinions, "moderate" ones are "middle of the road" or average. Indeed, in political parties, the "moderates" are precisely those people who are said to avoid radical positions.

The key "trigger" word is "instead." This indicates a contrast between Brandon's preferences and the thing following "instead of." In contrast to "new and bold" solutions, Brandon must like "older, tested solutions." When something is "traditional," it is the sort of thing that has been "handed down" from past generations. It contrasts with the "new and the bold" by being "old and familiar."