On the weekends, I enjoy hiking, baking, dancing, and to spend time with my friends. Most of all, however, I love to run. I never thought of myself as a talented runner.  However, when Jenna moved to my neighborhood, she inspired me to join the track team and find my stride. We met when we were both walking to class, and when I asked Jenna about her elective classes, she enthusiastically began talking about the track team. “You should join”! she exclaimed. I told her I’m not a very good runner, and she responded that anybody could be a decent runner with enough practice and the right attitude. 

We started practicing after school and on weekends, and eventually I decided to try out for the team.  To my surprise, I made the cut.  Even though everybody else had a faster finish time than me,  I enjoyed being part of the first race of the semester.

Because she is both dedicated and naturally talented, Jenna is the better runner on the entire team. Despite her success, she is never arrogant and always willing to help others develop their athletic skills. When all of the high schools in the state send they’re top three runners to the championship, everyone on the team travel to support Jenna.

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

“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.

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Over winter break, our AP Spanish class took a trip to South America to practice the language and learn more about different Spanish-speaking cultures.  Before we left, every student had to get their vaccinations for yellow fever and typhoid. Our first stop was Bolivia. When we landed at El Alto airport the highest in the world, we could see the city of La Paz sprawling up the hillsides in the shadow of the Andes.   The first day in La Paz, we went to the Witches’s Market, run by local yatiri. The yatiri are medical practitioners who perform healing rituals in they’re communities. At the market, we saw dried frogs, llama fetuses, herbs, and seeds, used in various rituals. After we visited La Paz, we traveled to Cochabamba.  Cochabamba is Bolivia’s culinary capital, with delicious specialties such as salteñas and rellenos. In Cochabamba, we also climbed 1400 steps to see the Cristo de La Concordia statue, the tallest of it’s kind in South America. Next, we visited the salt flats of Uyuni.  Several lagoons dotted the high desert landscape, some of who were full of flamingos!

On our way out of Bolivia, we stopped at Lake Titicaca on the Peruvian border. Because the lake’s elevation is over 12,000 feet, some of my classmates experienced a bit of altitude sickness.  Despite the altitude sickness, everyone said they loved seeing the beautiful scenery and visiting the mysterious “floating islands” made of reeds.   When we crossed the border into Peru, one of my classmates thought she had lost her passport. I would of had a panic attack! She ended up finding it buried in a pocket of her backpack and we were on our way. 

My favorite part of Peru was our trek to the ancient Incan ruins of Machu Picchu. We spent four days hiking in the Andes on a trail to the ruins. Our guides, whom spoke Spanish, English, and Quechua, were very knowledgeable about the history, flora, and fauna in the region.  Upon waking up the next morning, a beautiful sunrise greeted us and cast the mountains in its soft pink glow. After we explored the ruins, we took a train ride back to Cuzco.  The next day, we flew to Lima and prepared to return home. I was sad to leave, but I know I would be back some day!

Select the answer choice that best corrects the bolded underlined portion of the passage. If the sentence is correct as written, select NO CHANGE.

Which answer choice best replaces the underlined portion of the following sentence, with respect to grammar and logic?

With over 165 wins in 11 seasons, the coaching prowess of Mike Ditka made the Chicago Bears a perpetual threat in the NFL.

Weighing more than 15,000 tons each, workers used massive tunnel boring machines to dig the tunnel. Each one could cut through the earth at a rate of approximately 15 feet per hour. These machines also collected the spoil, or earth removed by the machines, and sent it out of the tunnel via a long conveyer belt. A concrete lining was also added to the tunnel to prevent it from collapsing. To ensure that the French and British teams would eventually meet in the middle, the tunnel boring machines were steered using lasers.

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My childhood was fairly idyllic. I grew up in southern suburbia, we could play outside nearly year round. We almost played outside every day. Our days were filled with bike rides, jumping on the trampoline, playing in the sprinklers, and also imagination games. Countless afternoons were spent in the side yard of our home, where our imaginations were the limit to our fun. One of our favorite games was “Lost Children.” Oddly enough, the parents in the game were always deceased or fighting in a foreign war. The source of this game likely stemmed from the books we read.

My mother’s old, rusty, orange wheelbarrow was perpetually propped up against the fence, to serve as the base for our makeshift range. The metal braces beneath the wheelbarrow bin provided the perfect resting place for a pair of burners, hastily sketched on a flat board. Old paint buckets became a sink and a stained picnic table was scrubbed to a relative state of cleanliness. Our visitors, who were often kings and queens, were served heaping helpings of mud and grass pie, possibly adorned with a side helping of flowers. Household chores were far more fun to do in our imaginary world, and we would eagerly sweep and dust our humble home. Even covered in leaves, we loved our outdoor kitchen.  

Other days, we would scamper around the neighborhood park, sometimes venturing into the woods to go exploring. One time we borrowed my little sister’s wagon and flew down the sides of the ditch. Although we had a grand time my mother was not pleased when she had to replace the broken axle. On adventurous days, we would pretend to be statues on the entrance sign to our neighborhood. But, the most perfect afternoons were spent biking up to the local corner store. With spending money burning a hole in our pockets, we would peruse the convenience store shelves, and after carefully picking our selections, we would pedal home. Our plastic shopping bags hung from the handlebars, rustling in the wind.

The bite of crisp fall evenings would barely phase our childlike fantasies. But, to our dismay, twilight would inevitably seep into our childhood world. Mother would call us in for dinner and a bath, if needed. Tired, beds were welcomed. I would often fall asleep to the gentle rhythm of my mother’s voice.

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When the patent on Alexander Graham Bell’s revolutionary invention, the telephone, expired in 1894 thousands of new firms entered the telecommunication industry. Among them were a collection of profitable companies that merged to form what would later become known as The Bell System. The Bell System had amassed such weight in the industry that in 1933, when Congress passed a law declaring phone service a public utility, the Bell System quickly transformed into a monopoly. Lawmakers enthusiastic supported a series of provisions intended to stimulate competition. Appointed as the nation’s sole provider of telecommunication services, widespread criticism about the Bell System began to surface. 

The Federal Communications Act has so far been highly effective and the industry has grown tremendously as a result. In fact, for the past three years, the profitability of the largest three telecommunication companies has been greater than the largest three automotive companies. The number of calls provided by the top three companies range from five billion to six billion per day. Today, virtually everyone has made a phone call over the course of their lives. Most people do not know, however, that payment for swaths of electromagnetic wavelengths have become commonplace.

One explanation for such high call volume and large profits is that calls are becoming much less expensive for companies to provide, regardless for many large fixed expenses such as communication towers, base stations, and paying for utility poles. Over the last century, telephones had become an important part of modern society. In fact, the cost of delivering one telephone call today is about a thousandth of the cost in the 1950s. The increasing affordability and abundance of phone calls mark the progress made since the time of Alexander Graham Bell and the Bell System.

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Alfred Tarski, born on January 14, 1901, became known during his lifetime as a brilliant mathematician and teacher. He is best known for proving several advanced geometric theorems. By the time Tarski moved to the United States, much of Europe has already fallen into the grips of World War II. Hundreds of mathematical problems were solved by Tarski.

Tarski enrolled in Warsaw University in 1920. Originally wishing to study biology, mathematics was the subject in which Tarski ultimately excelled. He graduated with honors, and began his career as a math teacher. A true mathematical virtuoso, Tarski was concerned with neither the application of his research nor publishing his findings.   

Discoveries made by Tarski influenced the work of one of the world’s greatest physicists, Albert Einstein. Einstein and Tarski had many similar interests in common. Unlike Albert Einstein, however, Tarski was especially fond for pure mathematics. Although Tarski and Einstein were contemporaries, Einstein was the most prolific writer of the two.

In 1929, Tarski married his co-worker, Maria Witkowska. An affinity for mathematics ran in the family. Tarski even admitted that his wife knew more about algebra, geometry and trigonometry than did he. Tarski's two children, Jan, and Ina, grew up to be prominent mathematicians themselves; however, neither Jan nor Ina have received a great deal of international attention.

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As the class entered the museum, Ms. Johnson noticed that two of her students had fallen behind the group. After all of the tickets had been secured, she approached the two girls, saying: “what on Earth is causing you to go so slow?” The taller girl, whose name was Ashley, was the first to respond:

“Veronica and I were just discussing something very private. Nobody can hear what her and I are discussing.”

“Well, Ashley, I think that our tour guide, Dr. Mitchell, will be offended by your behavior. You and Veronica should find separate places in the group and you should pay attention to him and me.”

The two girls reluctantly joined the rest of the class. Ms. Johnson looked to see if another student was out of their place, but everything seemed to be in order. The tour guide, Dr. Mitchell, introduced himself to the class: 

“Hello everyone! My name is Dr. Mitchell. I’m so glad that you have all come to the Museum of Natural History today; I think you’ll really enjoy our exhibits, which have been curated with the utmost care. The museum has three distinct types of exhibitions. Permanent exhibitions, temporary exhibitions, and space shows. The permanent exhibition and the space show is always available for viewing, but the temporary exhibition changes seasonally.“

Having finished his introduction, the permanent exhibition was the first thing that Dr. Mitchell showed to the class.

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The bayou was quiet, except for the sounds of insects, water and the occasional alligator. Jim was cleaning his blade, which he had recently used to dispatch one of the undead. His partner Bill and him had come out to the bayou for their nightly patrol and they had found a nest of the undead by an old abandoned dock.

"Hey, Bill!," he shouted gleefully, mindless of whether the noise would attract more undead. "Where'd you go, man?"

A noise to his left had startled him. He turned quick and saw the man who had been closest to him than a brother for the past six months walking slowly toward him.

"Whew," he said: "there you are." He went back to cleaning his blade. "I thought one of those things had got 'cha."

Standing in the dark, the light of the moon did not reach his partners face. The sudden silence caused Jim to look up again. "What's the matter with you, Bill?"

It was only when the thing that was once Bill stepped into the light and Jim saw the fresh bite on it's newly dead face that he realized what the matter was.

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