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Einstein Circle

ELA Mini Exam #6:

  • 3 Reading Passages (6 questions each)
  • 1 Edit-Revise Passage (8 questions)
  • 4 Stand Alone Edit-Revise Questions

Refer to the passages below the questions.

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(1) Are you ready for your brain to hurt a little bit? (2) If you take a sphere and remove the core from it, you’re left with a shape called a napkin ring – because it looks like a napkin ring. (3) Suppose you first remove the core from a sphere the size of a basketball. (4) Next, suppose you core the earth itself (assuming it is a perfect sphere) to get a napkin ring of the same height. (5) Which napkin ring would have a greater volume? (6) Most students would immediately reply, “The napkin ring from the earth of course!” (7) The diameter of the earth is 12,472 km. (8) Surprisingly, they would not be correct. (9) The two napkins rings of vastly different diameters will have identical volumes.

(10) The mathematics behind the napkin ring problem depends on the Pythagorean Theorem and Cavalieri’s Principle. (11) In order to better understand Cavalieri’s Principle, imagine a vertical stack of 5 quarters and shift the stack to the right until the shape looks slanted. (12) Despite the skew, the stack still has the same height, and every cross section is the same circular quarter. (13) Most importantly, it has the same volume of exactly 5 quarters which has not changed. (14) When computing the cross-sectional area of any napkin ring, the outer and inner circle areas are subtracted and the radius term drops out in the process. (15) The cross-sectional area is the same as that of a sphere of radius h. (16) Also, the volume is the same as that of a sphere of radius h; 4/3πh3. (17) The result seems counterintuitive. (18) Whether the napkin ring of height h is carved from the entire earth or a basketball size sphere, the volume will be the same.


College takes a heavy toll on a student’s mental health. The pressure of graduating on time, studying for exams and ultimately planning for a career can lead to increased anxiety, stress and even depression. But now, there’s a new item to add to the list: student loans.
A new study is one of the first to look at the link between student loans and mental health in young adults. Lead author Katrina Walsemann, an associate professor in the Department of Health
Promotion, Education, and Behavior at the University of South Carolina, and her colleagues analyzed responses from 4,643 Americans born between 1980 and 1984 inclusive. As the researchers suspected, the data show a clear trend: the higher the student’s loans, the poorer his or her mental health.
The respondents’ psychological health was assessed via the Mental Health Inventory, a questionnaire that social scientists often use to
measure a person’s psychological state. It asks how often a person felt nervous, calm and peaceful, downhearted and blue, happy, and down in the dumps over the past month.
The researchers also factored in a number of issues, such as the respondent’s current occupation, household income and highest level of education completed. They found that the only defining factor was the amount of loans in a person’s name; loans with higher amounts took a
higher toll on that person’s mental health.
Surprisingly, student debt affected mental health regardless of a person’s socio-economic situation. So, for instance, if a surgeon and a kindergarten teacher borrowed equal amounts of student loans, they were likely equally as concerned about paying back those loans.
Walsemann and her colleagues found the average amount of student loans across their sample to be roughly $5,500 for students graduating as early as 2002 and as late as 2010.
But, this number has dramatically worsened in recent years. In 2011, for example, 4 out of 10 graduating college seniors were leaving school with student loans averaging $23,300. And by 2013, 7 out of 10 graduating college seniors owed $28,000, on average, according to the Project on Student Debt.

There was one factor, however, that actually caused a reversal in the results. If a student was from a low-income family, his or her mental
health actually improved with higher student loans. It’s likely that the loans helped the student earn a higher social standing, which helped increase that person’s overall happiness, the researchers said.
“If student loans provide a vehicle for people who are coming from disadvantaged families to get a college degree, these student loans would help them become upwardly mobile and that might be important for their mental health,” Walsemann
But Walsemann also warned that the results could be skewed. Perhaps these students have a “personality characteristic that just makes them hardier and less prone to mental health problems in the face of a new disadvantage like debt,” she said.
Still, further research is needed to understand the impact of debt on young adults. After all, tuition prices are soaring. The price of higher education
in the United States has increased by 250 percent, adjusting for inflation, over the last three decades alone, according to the new study.
“I think that what we found in our study is conservative because we are looking at a cohort who didn’t take out as much in student loans as young people today, who are in college [and who] are taking out [money] right now,” said Walsemann.
In future studies, the researchers would like to
look at additional factors, including whether young adults with higher debt choose specific occupations, stay in jobs longer due to security, get married earlier or wait longer to have children.
But despite its high cost, research shows that higher education is still a good investment. Studies have shown that a college degree may be a heavy price to pay for young adults, but in the long run it has a positive influence on income, job
security, employment and even health.


Dogs are more than just man’s best friend. The real life stories of Swansea Jack, Bud Nelson and Pickles testify to the daring, adventure and heroics of our canine friends. Swansea Jack was a black retriever who lived with his owner William Thomas near the River Tawe in Swansea, Wales, during the 1930s. One day, Jack saw a small boy drowning in the river and ran in, pulling the boy to shore by the scruff of his neck. There was no one around to see it, and had circumstances been different,
the boy would probably have spent the rest of his life telling the story to people who would never believe him. But Jack wasn’t done. Within a few weeks, Jack rescued another swimmer, this time with witnesses in attendance. And then another. And another. And so on. Over the course of the next decade, Jack was reported to have saved at least 27 people from presumably the most dangerous river and docks in Wales.
If Jack was heroic, then Bud Nelson was equally adventurous. Just one look at Bud Nelson is enough to tell you that he was the greatest dog who ever lived. He’s an old-timey dog wearing goggles in a scratchy black-and-white photo—if he hadn’t existed, he would have been dreamed up for a steampunk novel or video game. The human in the photo is Bud Nelson’s owner, a doctor called Horatio Nelson. Horatio was the first man to cross America by car in the year 1903,
with his hilariously named co-driver Sewall K. Crocker and, of course, Bud. That made Bud the first dog to cross the United States by car.

At the time, the automobile was still in its infancy, meaning that driving was neither safe nor fun. The car was a roofless monstrosity with little to no suspension to protect them from the mostly unpaved roads, and it would have made a lot of noise while belching out noxious smoke. But Bud Nelson was braver around the thing than some
people would have been back then. He was given the goggles to protect his eyes and sat there looking just as happy as he does in the photo, all the way across the continent of North America.

Perhaps the strangest story of all is that of Pickles who saved the World Cup for England. In 1966, the World Cup was being held in England which, to the English, was kind of a big deal. Maybe the reason they were taking it so seriously was because they had a feeling they might win—which
they did—so you can imagine how bummed they were when the World Cup was stolen just four months before the matches started. There was a frenzy to find the cup and avoid international embarrassment, and it was eventually found by a plucky collie named Pickles. Pickles was being walked by his owner when he sniffed something out in the bushes—what Pickles had found was the missing World Cup.

In the aftermath of Pickles finding the Cup, his
rise to fame can only be described as meteoric. He was lavished with attention from the press as the hero dog who’d saved the nation from international embarrassment. Pickles even attended a banquet in his honor, where he was given a bone and a check for £1,000—archive footage shows the check being shoved into his face, so we hope it was cashed by his master and not chewed to shreds. He later went on to star in
several TV shows and even the movies.


Any young man or woman seeking to understand why Vietnam was our nation’s most unpopular and controversial war need look no further than the United States’ early involvement leading up to escalation of the war in 1964. Based on the fear of communist expansion and a policy of containment, our government undertook some decidedly ‘un-American’ actions including installation and support of unpopular governments, thwarting democratic elections
under the Geneva Conference, and misrepresenting the facts about a military confrontation in the Gulf of Tonkin on August 4, 1964 which directly led to escalation of the U.S. war effort.

       Vietnam has a long history as an independent kingdom, a subjugate of China, a colony of France, and a rebellious state ruled by Japan during World War II. Communist Ho Chi Minh and the Viet Minh, the only Vietnam-wide political
organization capable of effective resistance to the Japanese, helped the U.S. fight Japan during WWII. In the fall of 1945, at the end of WWII, Ho Chi Minh sought independence for Vietnam, viewed the U.S. as a powerful anti-colonial ally and adopted a Declaration of Independence mirroring our own. He wrote to President Truman seeking humanitarian aid after a severe drought and French starvation policies resulted in the death of 2 million Vietnamese in 1945. At the same time,
France desired to recreate its colonial glory in Vietnam after WWII. The U.S. was faced with a decision to support an independent albeit communist government under the populist revolutionary Ho Chi Minh or France. Truman never replied to Ho Chi Minh. America’s communist containment policy did not contemplate a government that could be both ally and communist.

         In October 1946 the French bombed North
Vietnam and began an eight-year war (the First Indochina War) against the Viet Minh for control of Vietnam financed largely by the U.S. government after 1949 including up to 80% of the cost by 1954. Plagued by costly defeats and unable to win popular Vietnamese support, the French withdrew in 1954 and agreed to peace at the International Geneva Conference which split the country temporarily along the 17th parallel and called for free national elections in 1956.

       Fearing a void in pro-Western control, the U.S.
almost immediately placed Ngo Dinh Diem, a Catholic aristocrat who recently had been living in Lakewood Township, NJ to become the new leader of south Vietnam; a largely Buddhist nation. Recognizing Ho Chi Minh would likely win upcoming elections, President Diem refused to permit the free elections called for at the Geneva Accord and began a

campaign to repress pro Viet Minh supporters in the south. The U.S. provided military advisers and
$200 million in annual aid to Diem’s regime thus shifting from indirect support of an unpopular government under France to directly establishing and financing a government that refused free elections and did not represent the vast majority of Vietnamese people.

   On the eve of August 4, 1964 President Lyndon Johnson announced on national television that the North Vietnamese launched “unprovoked” attacks on U.S. destroyer Maddox that directly led
to escalation of the Vietnam war for the next decade. Johnson’s televised message stated to the nation: “The initial attack on the destroyer Maddox, on August 2, was repeated today by a number of hostile vessels attacking two U.S. destroyers with torpedoes.” On August 7 Congress almost unanimously approved the Tonkin Resolution which authorized the president “to take all necessary measures” to prevent further aggression. Johnson interpreted this as an
open ended authorization to wage the Vietnam War.

       In reality, however, no torpedo attacks occurred on August 4. At least one half of the incident that would lead to the president’s authorization to wage war in Vietnam was completely false. In addition, the exchange of fire on August 2 was not entirely unprovoked. The Maddox at the time had been acting as provocateur on a radio intercept mission closely bordering North Vietnam’s
nautical territorial limits. Moreover, on August 2 South Vietnam attacked North Vietnamese territory to the southwest of the USS Maddox’s position on a commando raid at the same time as the Gulf of Tonkin incident. In short, the United States entered into the Vietnam war based on false information and administration officials lied to the public.

       Despite thwarting a free election, installing a puppet government and misleading the public, by
1965 the majority of Americans still believed the message from a 1965 Department of Defense recruiting film titled Why Vietnam? – it stated the U.S. was fighting to defend freedom and stop aggression. That perception changed by the late 1960s. It is up to the current generation to learn the lessons of Vietnam and, like the generation before them, ask hard questions of any current or future administration. For example, do parallels exist between “weapons of mass destruction” in
Iraq and the Gulf of Tonkin in Vietnam? Do the words “War on Terror” today replace “Communism” in the Cold War and will the consequences be similar?

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