Replace the underlined portion with the answer choice that results in a sentence that is clear, precise, and meets the requirements of standard written English.

Due to the elliptical shape of celestial orbits, the distance between the sun and the planets vary over time.

“Mathematics and Learning”

What subject should be learned first? The question rightly troubles anyone who’s interest is in education. Of course, young children often must learn in a very basic and rote fashion, applying their apt memorization skills to simple tasks that will serve them very well in later years when they go one to apply such knowledge to more complex topics. However, when the time comes to designing curricula, an important question must be answered for older students, namely “What is most important first topic in these students’s education?”

An argument can be made for the use of mathematics as a tool for teaching students how to reason more clearly. This is not because mathematics is the basis of all knowledge. Indeed not. There are many important subjects including not only the humanities like poetry and history but sciences like biology and physiology too. These topics are not strictly speaking mathematical in nature, even though mathematics can be used in it in many ways.

Our minds are best geared for learning things that we can sense, things that are visible and tangible. Although mathematics is abstract, it can begin with this kind of sense derived experience. Beginning with simple everyday examples, children can be taught the more abstract and difficult skills that must be learned for the sake of the development of mathematical skills. In the process of learning these topics, the children will begin to learn important rules about reasoning. He or she will learn how several propositions can serve as the basis for conclusions. They will learn how certain properties are related to various geometric figures and arithmetical rules. Although much of this will be memorized at first, with time, they will have the opportunity to see that human reasoning in mathematical subjects is orderly and logical. On the basis of such “logical experience,” young learners can then begin to be taught the rules of logic that they have been using all along. As the medievals used to say, they could go from logica utens, logic used in other subjects, to logica docens logic taught, as a unique, and separate subject.

Choose the answer that best corrects the underlined portion of the sentence. If the underlined portion is correct as written, choose "NO CHANGE."

Adapted from “Puritanism as a Literary Force” in A Book of Prefaces by H.L. Mencken (1917)

Naturally enough, this moral obsession has given a strong color to American literature. It is true that American literature is set off sharply from all other literatures. In none other will you find so wholesale and ecstatic a sacrifice of ideas, of all the fine gusto of passion and beauty, to notions of what is proper and nice. From the books of grisly sermons that were the first American contribution to letters down to that amazing literature of "inspiration" which now exists, one observes no relaxation of the moral pressure.

In the history of every other literature there have been periods of what might be called moral innocence. In such periods a naive “joie de vivre” (joy of living) has broken through all concepts of duty and responsibility, and the wonder and glory of the universe has been hymned with unashamed zest. The age of Shakespeare comes to mind at once. The violence of the Puritan reactions offers a measure of the pendulums’ wild swing. But in America no such general rising of the blood has ever been seen.

The literature of the nation, even the literature of the minority, has been under harsh and uneducated Puritan restraints from the beginning, and despite a few stealthy efforts at revolt, it shows not the slightest sign of emancipating itself today. The American, try as he will, can never imagine any work of the imagination as wholly without moral content. It must either tend toward the promotion of virtue or, otherwise, be questionable.

Which of the following adjectives could be added to the two bolded adjectives “proper and nice”?

Adapted from "The Weakness, Unrest, and Defects of Man," from The Thoughts of Blaise Pascal (ed. 1901)

We care nothing for the present. We anticipate the future as too slow in coming, as if we could make it move faster; or we call back the past, to stop its rapid flight. So imprudent are we that we wander through the times in which we have no part, unthinking of that which alone is ours; so frivolous are we that we dream of the days which are not and pass by without reflection those which alone exist. For the days of the present generally gives us pain; we conceal it from our sight because it afflicts us, and if it be pleasant, we regret to see it vanish away. We endeavor to sustain the present by the future, and think of arranging things not in our power, for a time at which we have no certainty of arriving.

If we examine our thoughts, we shall find them always occupied with the past or the future. We scarcely think of the present, and if we do so, it is only that we may borrow light from it to direct the future. The present is never our end; the past and the present are our means, the future alone is our end. Thus we never live, but hope to live, and while we always lay ourselves out to be happy, it is inevitable that we can never be so.

Which of the following is the best form of the bolded selection, “if it be pleasant . . .”?

“Mathematics and Learning”

What subject should be learned first? The question rightly troubles anyone who’s interest is in education. Of course, young children often must learn in a very basic and rote fashion, applying their apt memorization skills to simple tasks that will serve them very well in later years when they go one to apply such knowledge to more complex topics. However, when the time comes to designing curricula, an important question must be answered for older students, namely “What is most important first topic in these students’s education?”

An argument can be made for the use of mathematics as a tool for teaching students how to reason more clearly. This is not because mathematics is the basis of all knowledge. Indeed not. There are many important subjects including not only the humanities like poetry and history but sciences like biology and physiology too. These topics are not strictly speaking mathematical in nature, even though mathematics can be used in it in many ways.

Our minds are best geared for learning things that we can sense, things that are visible and tangible. Although mathematics is abstract, it can begin with this kind of sense derived experience. Beginning with simple everyday examples, children can be taught the more abstract and difficult skills that must be learned for the sake of the development of mathematical skills. In the process of learning these topics, the children will begin to learn important rules about reasoning. He or she will learn how several propositions can serve as the basis for conclusions. They will learn how certain properties are related to various geometric figures and arithmetical rules. Although much of this will be memorized at first, with time, they will have the opportunity to see that human reasoning in mathematical subjects is orderly and logical. On the basis of such “logical experience,” young learners can then begin to be taught the rules of logic that they have been using all along. As the medievals used to say, they could go from logica utens, logic used in other subjects, to logica docens logic taught, as a unique, and separate subject.

Choose the answer that best corrects the underlined portion of the sentence. If the underlined portion is correct as written, choose "NO CHANGE."

As he stepped into the shower that morning, Ronald wondered whether he would be scalded or frozen. It would happen every morning because his neighbors usually took their showers at the same time as he did, and the water temperature would either dip precariously or rise sharply, depending on the day. About five minutes into his shower, he could hear the telltale sound of his neighbors' turning on their shower, and he braced himself. Sure enough, a jet of steaming hot water was shooting through the shower nozzle, and Ronald darted to the side to wait until it cooled down again. As it was January, he was grateful that it wasnt cold water—if it had been, he might of spent the whole morning frozen in a block of ice. Soon the water returned to normal, and Ronald resumed his shower, cursing himself for ever moving into such an old building in the first place.

Choose the answer that best corrects the bolded portion of the passage. If the bolded portion is correct as written, choose "NO CHANGE."

Choose the answer that best corrects the underlined portion of the sentence. If the underlined portion is correct as written, choose "NO CHANGE."

Billy gone to the ocean once before in his life.

Replace the underlined portion with the answer choice that results in a sentence that is clear, precise, and meets the requirements of standard written English.

The spokesperson noted that over the past year, a new wave of technological advances have increased the company’s profitability.

“Mathematics and Learning”

What subject should be learned first? The question rightly troubles anyone who’s interest is in education. Of course, young children often must learn in a very basic and rote fashion, applying their apt memorization skills to simple tasks that will serve them very well in later years when they go one to apply such knowledge to more complex topics. However, when the time comes to designing curricula, an important question must be answered for older students, namely “What is most important first topic in these students’s education?”

An argument can be made for the use of mathematics as a tool for teaching students how to reason more clearly. This is not because mathematics is the basis of all knowledge. Indeed not. There are many important subjects including not only the humanities like poetry and history but sciences like biology and physiology too. These topics are not strictly speaking mathematical in nature, even though mathematics can be used in it in many ways.

Our minds are best geared for learning things that we can sense, things that are visible and tangible. Although mathematics is abstract, it can begin with this kind of sense derived experience. Beginning with simple everyday examples, children can be taught the more abstract and difficult skills that must be learned for the sake of the development of mathematical skills. In the process of learning these topics, the children will begin to learn important rules about reasoning. He or she will learn how several propositions can serve as the basis for conclusions. They will learn how certain properties are related to various geometric figures and arithmetical rules. Although much of this will be memorized at first, with time, they will have the opportunity to see that human reasoning in mathematical subjects is orderly and logical. On the basis of such “logical experience,” young learners can then begin to be taught the rules of logic that they have been using all along. As the medievals used to say, they could go from logica utens, logic used in other subjects, to logica docens logic taught, as a unique, and separate subject.

Choose the answer that best corrects the underlined portion of the sentence. If the underlined portion is correct as written, choose "NO CHANGE."

Thomas placed his quill on the parchment, looking toward the mantel upon which, earlier that morning, he saw the painting of the old monastic saint, Benedict of Nursia. To his surprise, the mantel was empty, not having any items on it’s narrow flat surface. As the image had been a gift from his old schoolmaster; he was concerned at the absence of the item.

He asked himself “Where could it have went?” Then, he gathered together his work and decided to ask one of his officemates about the cherished image. Leaving the room, he entered the foyer and turning to the secretary asked about the whereabouts of the others’.

The secretary looked at Thomas’ imposing figure and answered, “A group of the professors departed earlier for a University meeting; however, I cant recall exactly when they departed.” Although Thomas was not known for being passionate, the young secretary could see that he was agitated than usual.

The older man did not wish to worry his younger coworker. Smiling slightly, he said, “Don’t worry, Reginald. I seem to have misplaced my image of Benedict, though I know not how.” He continued by telling the younger man the chronology of events. Suddenly, the detailed recounting jogged the latters’ memory. He forgot an obvious detail that he only now remembered.

Looking at Thomas in embarrassment, Reginald, said, “Earlier this afternoon, I came in to your working area take the painting. Bonaventure had come to visit and asked to borrow it. You were so engrossed by you’re work that I did not want to disturb you. He will be stopping by to see you and I later today, so we can ask him to return it.”

Choose the answer that best corrects the bolded portion of the passage. If the bolded portion is correct as written, choose "NO CHANGE."