1 . Ariel Procaccia has thought a lot about how to cut a cake over the last 15 years. As the father of three children, he knows how hard it is to divide a birthday cake to everyone’s satisfaction. But it’s also because Procaccia’s work focuses on exploring the mathematical rules for dividing stuff up fairly. One way to do that is to think abstractly about dessert.
For decades, researchers have been asking the seemingly simple question of how to cut a cake fairly. The answer reaches far beyond birthday parties. A mathematical problem at its heart, cake cutting connects strict reasoning to real-world issues of fairness, and so attracts not only mathematicians, but also social scientists, economists and more. “It’s a very elegant model in which you can distill what fairness really is, and reason about it,” Procaccia says.
The simplest approach is called the “divider-chooser” method, where one person cuts the cake into two equal pieces in his view, and the other person picks first. Each receives a piece that they feel is as valuable as the other’s. But when personal preferences are taken into account, even the easiest rule becomes complicated. Suppose Alice and Bob are to divide a cake, and Alice knows Bob prefers chocolate, she may knowingly divide the cake unequally so the smaller piece contains more chocolate. Then Bob will choose according to his preference, and Alice will get the larger piece. Both of them are satisfied with what they get, but the meaning of fairness changes in this situation.
The cake is a symbol for any divisible good. When cake-cutting principles are employed to settle disagreements, they are potentially helping the world find solutions. Procaccia has used fair division algorithms (算法) to model food distribution. Social scientist Haris Aziz is exploring situations ranging from how to divide up daily tasks to how to best schedule doctors’ shifts in hospitals.
Even after decades of investigation, cake cutting isn’t like a simple jigsaw puzzle (拼图) with a well-defined solution. Instead, over time, it has evolved into a kind of mathematical sandbox, a constructive playground that brings together abstract proofs and easy applications. The more researchers explore it, the more there is to explore.
1. What does the underlined word “distill” in paragraph 2 mean?| A．Get the essence of. | B．Find the opposite of. |
| C．Keep the focus on. | D．Reduce the impact on. |
| A．Its standard is stable. | B．It prevents unequal division. |
| C．Its concept is complex. | D．It dominates personal preferences. |
| A．The application of its rules. | B．The details of its process. |
| C．The problems it produces. | D．The harmony it symbolizes. |
| A．Who benefits most from fairness? |
| B．How has fairness changed over time? |
| C．What method works best in cake-cutting? |
| D．Why are researchers so interested in cake-cutting? |
1. 家训对于一个家庭的意义；
2. 你家的一条家训；
3. 该家训对你的影响。
提示词：家训 family motto
注意：1. 词数80左右；
2. 可以适当增加细节，以使行文连贯。
Dear Jim,
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Yours,
Li Hua
3 . Hanfu, the traditional clothing of the Han , has made a comeback in recent years. The hanfu boom has seen an increase in available styles. To satisfy the diverse tastes of today’s youth, sellers are putting a fancy spin on this ancient costume.
Certain hanfu have a colorful reflective effect, as shiny decorative powders are stamped into the cloth. Modern material like chiffon (薄绸) is also widely used in hanfu, while paillettes (亮片) have been added to the surface of the dress.
Although the young fans of hanfu generally agree there’s no need to strictly follow the ancient rules, their opinions differ significantly. Qing Zhi, a university student, said hanfu is only a kind of clothing. She can match hanfu from different dynasties together, or with modern clothing, according to her own preferences. However, the form of each piece of hanfu she wears must be in accordance with history. Dafan, 24, sees it differently. She said clothing with fancy and exaggerated modern decorations can’t be seen as hanfu at all.
Meanwhile, fans disagree on how often one should wear the clothing. Qingzhi wears hanfu every day, while Wu Yue, another hanfu fan, said the clothing should not be worn daily.
In Wu’s view, hanfu should be properly combined with modern living. For example, special occasions like festivals and weddings are good occasions for wearing hanfu. “Only with functions can hanfu really have vitality.” she said.
Han Hua, a fellow from Chongyang Research Institute for Financial Studies at Renmin University of China, views the evolution of hanfu as natural. “I think people dressing in hanfu can have their own choices, whether sticking to the very traditional style, or whether having them modernized,” she said. “Both sides are OK, or there may even be a third side that introduces some modern elements, or some Western elements into hanfu. I’m totally fine with that. I only hope that there won’t be any disputes (争论), and there will be respect toward each party.”
1. What do we know about hanfu from the first two paragraphs?| A．It’s delicate and comfortable. | B．Its production follows strict rules. |
| C．It appeals to people of different ages. | D．It keeps pace with the times. |
| A．The history of hanfu. | B．Rules of matching hanfu. |
| C．The debate over hanfu’s evolution | D．Different views on the popularity of hanfu. |
| A．It doesn’t match modern living. | B．It is sensible for people to wear it daily. |
| C．It is a good choice for important occasions. | D．Modern decorations give it more vitality. |
| A．Diverse forms of hanfu should harmoniously coexist. |
| B．It is hard to predict the evolution of hanfu. |
| C．Hanfu is a mean of passing on traditional Chinese culture. |
| D．Adding Western elements to hanfu can help spread it worldwide. |
Wrinkles of confusion rippled across Holly’s forehead as she opened the gift from her best friend, Susan.
“I...I thought you could use it for something.” Susan’s stammered explanation did nothing to help us understand why a twelve-by-eighteen-inch dark blue carpet remnant(残余物) was being presented as a birthday gift.
Holly, my daughter, tried bravely not to allow her disappointment to show. She laid the carpet on the kitchen counter, and the two girls headed outside to play.
The next morning, I carried a kitchen bag outside. My heart ached as I saw Susan’s carpet lying in the trash can. Hesitating only a moment, I reached in and picked it up. After giving it a light brushing, I brought it into the house and placed it in the hall closet. Occupied with the business of daily living, the carpet was soon forgotten.
Prior to Holly’s birthday, Susan had been a regular visitor in our home. On several occasions, she rode the bus home with Holly and was one of the few friends ever permitted to stay over on a school night. But now I realized it had been nearly three weeks since we’d even heard mention of Susan’s name. I missed her warm smile and eager-to-please ways.
One day, Holly had arrived home from school. “Susan invited me to come over to her house after school tomorrow,” she announced as she took her books down on the kitchen table. Although her voice carried a so-what attitude, I sensed she was pleased by the invitation.
Arrangements were made, and the girls rode home together on the school bus the following day. As I negotiated the winding country road that led to her house, Susan chatted nervously about her foster mom and the seventeen cats she had taken in and cared for. Soon we arrived at Susan’s house.
Paragraph 1:
A woman wearing a shapeless sweater stood in the doorway to greet us as we approached the small shabby farmhouse.
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Paragraph 2:
Hearing my words about everything of Susan, Holly sat silently in the car, with her head stretching forward(前伸) as if willing the car to move faster.
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Grady and his family go camping every summer. As it was becoming hotter, here came the camping time.
Having planned the camp long, the family finally decided the destination --- the Great National Forest. With food, necessity and cookers loaded onto the car, the family squeezed into the car. The car door closed, heat was shut outside.
In the car, Jared, Grady's younger brother was playing with a toy dinosaur, making great noise. Grady's mother talked excitedly with his father. On settling in the car, Grady put on the earphone and turned on the music. He neither wanted to join his brother nor joined any talk. After what seemed to be hours, the car stopped where they headed. Grady threw down his backpack and slammed the car door.
“This will be a lengthy week,“ he said unhappily to no one in particular. He looked around the campground. Hundreds of tall and green fir trees, some as tall as church towers, covered the mountainside like a green carpet. The sun would be setting soon. Grady thought maybe the heat wouldn't be unbearable. But actually now in the mountain, the hot stickiness of July was closely attached to him.
Grady hated camping, but it was something his family stuck to every summer. His father liked cooking over an open air, telling stories about how to survive things like bear attacks and bites of bees. His mother and Jared liked to hike and take pictures of animals. Jared had a collection of bug pictures that he had pinned to the walls in his half of their room. Grady thought they were just scary and proof that Jared was a strange kid.
They set up camp - two tents, one for his parents and one for himself and Jared. While everyone else started preparing dinner, Grady, looking for some place to cool down, set off for the nearby stream, which was deep enough to swim in.
注意：1. 续写词数应为150左右；
2.请按如下格式在答题卡的相应位置作答。
As Grady got close to the stream, an adorable bear cub (幼崽)caught his eye.
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Turning around, he saw an angry bear moving swiftly towards him.
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