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Philosophers believe that mathematics exists outside of us, independent of our minds. But it's (wide) accepted that math is inside us. However, does the truth lie somewhere between the stark choice of being invented or discovered? (understand) the truth better, let's try to understand exactly how old math really is. The tale of mathematics is as old as humanity. It has gradually evolved from simple mathematics, such as (count) cows, to the complex study of an object through the abstract concepts we know today. It was not until 600 BC, when civilizations settled and various occupations began, math began its initial development. It (use) to measure plots, calculate the taxation of individuals, etc. Later, in 500 BC, we saw the development of Roman numerals, which (be) still used to represent numbers today.

Scientists believe that thousands of years ago, basic mathematical functions like addition and subtraction (减法) might have appeared at same time, but in different places, like India, Egypt and Mesopotamia. (advance) math dates back to Greece over 2500 years ago, when mathematician Pythagoras put forward his famous equation. It was about the (side) of a right-angle triangle (直角三角形) , which we now study as the Pythagorean theorem (勾股定理).

then on, more mathematicians started working on expanding their understanding of mathematics. Yet, no one could find the one true answer to the big question.

One evening, near the end of the2, my daughter, the school group and I were on a platform in the London Underground. Just then, a train3 to the platform. Suddenly, Chamber let go of my hand, jumped on the train, and the doors began to4. On the other side of the glass, I could see my daughter's5 face. The last thing I saw before the train pulled out of the station was Chambers crying and pounding her small fists against the glass. Behind her, a bearded man dressed in black leather with a spiked (带钉的) dog collar around his neck rose from his seat and started6 to Chamber. In my opinion, such a person was by no means a good person. Thinking about this, I felt everything went7 before my eyes.

After what seemed centuries, suddenly one of my students appeared at my8, saying, "She's back." I turned and there was my little girl. Beside her stood the bearded man. Immediately, my previous idea that he was9 was destroyed.

He10 in silence without leaving a word as I hugged my daughter and cried. It brought tears to my eyes to think how things could have turned out11.

So I set out on a journey to12 my unsung hero. I posted, "... When I find myself judging people by their13, his image was in my mind. I want him to14 that he saved me from my worst days." The second day I was pleasantly surprised to see a reply that said, "No15 needed. It was a happy day for me."

Research published in the journal Emotion shows that early risers enjoy a more positive mood and better emotional regulation than those who wake up late. The benefits of getting up early are clear.. Here are a few things to keep in mind:

This morning started last night.

Early rising is really the second part of two habits:. This probably seems like the easier habit to keep, but for many people it isn't. For many young adults, the problem is what psychologists call "revenge bedtime procrastination" (报复性熬夜). Or they simply find it hard to turn off their mental machine. For this issue, a consistent bedtime routine and reducing screen time-can help to earlier sleep.

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One reason people struggle to rise early is because they aren't required to do so. When there is no penalty for oversleeping, it is all too easy to hit the snooze button and continue sleeping. Setting a fixed morning commitment, like a workout or an early class, increases the "cost" of staying in bed. Even a trivial task immediately after the alarm can discourage further sleep, gradually transforming a habitual night owl into an early riser.

Make early rising divine (神圣的).

Many religions use the time before dawn for prayer and worship (崇拜), believing the quiet morning brings peace and clear thoughts.. By rising early, you welcome a new day full of energy and hope. This practice not only helps us start the day with a positive spirit but also prepares us to face challenges with calm and strength.

For the early risers among us, this means a before dawn routine will start to become a true part of your life by the end of January; for the late sleepers, it could take until sometime in September. It felt pretty bad to leave our warm bed when it was still dark..

A. Raise the cost of not getting up

B. Lower the difficulty of getting up

C. The first part is going to bed early enough that you get sufficient (足够的) sleep.

D. Even those who do not believe can enjoy these special hours.

E. But it was worth it: the early morning time is now the best time of a day.

F. Quality sleep depends on avoiding late-night snacks and exercise.

G. But what do you need to do to succeed in your resolution and develop this habit?

Research from across the social sciences has consistently shown that social relationships are critical for mental and physical health. However, a paper published in Nature Communications Psychology, based on a series of studies conducted with more than 2,400 participants, discovered that people are surprisingly hesitant to initiate interactions to reconnect. There are various barriers to reaching out, many of which are identified similar to the ones that prevent people from talking to strangers. This similarity made researchers wonder whether the passage of time makes old friends feel like strangers.

In one study, researchers asked 288 people how willing they were to engage in various everyday actions, including picking up garbage, booking a dentist appointment, and critically, talking to a stranger. Sure enough, people were no more willing to reach out to an old friend than the listed things.

Researchers have also worked on an intervention shown to ease anxieties about conversing with strangers. We decided to adapt that approach to the case of reconnecting with old friends. So we asked some of our study participants to complete a three-minute warm-up exercise in which they sent messages to current friends and acquaintances. Meanwhile others-our control group-simply scrolled (滑动) through social media. Afterward every participant was encouraged to contact an old friend. Only about a third of people in the control group sent a message while about half the people in the warm-up group did so. That's because practicing the behavior involved in reaching out to others reminded people of how simple it is to send a message and how enjoyable it can be to connect.

Social relationships are a key source of happiness. Reaching out to old friends is easier after warming up, which benefits mentally and physically. So people could go through the contact list on their phones and message a few folks they talk to often-and then find someone they haven't spoken to in a while and have been missing and try to get hold of them, too.

"We were inspired by the Svalbard Global Seed Vault (库) in Norway, which takes advantage of freezing Arctic temperatures to preserve millions of seeds from around the world. But in 2017, melting permafrost (冻土) flooded the vault and put its precious seeds at risk. That event showed the need for a backup plan," Hagedorn says.

Given the shadowy south pole's low temperatures, Hagedorn says, a vault there could store "one of the most powerful cells that we have today" — fibroblasts. Scientists can transform these animal cells into stem cells, "and then those stem cells can be used for cloning," she says. The cells could be valuable for regenerating populations of threatened or extinct species and for building ecosystems in future human colonies on the moon or Mars.

The new proposal has its share of obstacles, including what to do about radiation and the long-term effects of microgravity on the samples. Hagedorn and colleagues are designing radiation-proof sample storage containers. The next step would be to test out prototypes (原型) on a future moon mission. Some of the moon's permanently dark regions also aren't immune from temperature swings, as more or less reflected light shines into the shadows, Greenhagen says. "They are still cold but perhaps not always cold enough for this project without some level of heat management." By far, the biggest challenge will be getting buy-in from the scientific community and other stakeholders, and to get nations to work together on the plan, Hagedorn says.

Lloyd was recently in town, and on a steamy Sunday night he played a sold-out two-and-a-half-hour show, performing with one of his trios, held in Sony Hall, a Times Square basement space. Lloyd is a young person in an old person's body with a passion for music since his youth.

When he grew up, his mother provided accommodation for performers who were banned from local hotels, Duke Ellington among them. As a boy fond of instrument at the age of three, Lloyd was in heaven. He said, "I would wait for those guys to get up in the morning because I had so many questions." One day, his mother told Ellington that her son wanted to be a musician. But Duke said, "No, he has to be a doctor, lawyer, or Indian chief, because this stuff is too hard — the life. Don't let him do it." But by that time, Lloyd was bit by the cobra, and there was no turning back.

After some apprenticeships, he formed a band in 1965, with Keith Jarrett, then an unknown, on piano. The group had multiple gold records on Atlantic, and even played in San Francisco in 1967. But His career was not all smooth sailing. For much of the seventies and eighties, he holed up for he was exhausted and it seemed that he had run out of his talent because of the hassles of touring and also some unhealthy living habits. After years of struggling, Lloyd eventually managed to set off once more and further his music journey.

"What keeps me younger than springtime is that I'm still learning, I'm still growing," he went on. "I've got experience, but I've got a beginner's mind, and that's a blessing." Still, he admitted, the touring continue to weigh on him and he's thought about slowing down-at some point. "The Creator has a carrot on a stick," he added. "you know, and I'm always falling short and I never got good enough to quit."

Join the "HKU Hands-on Experience: Different Subjects & Community Study" — a 5-day activity run by Simon K. Y. Lee Hall. Students take part in active learning meetings covering Medicine, Dentistry, Law (through mock trials (模拟法庭)), Science, and Engineering, while experiencing HKU's campus life. Accommodation at the hall is included, offering a firsthand experience of university community living.

Highlights:

Academic & Cultural Study: Explore newest fields, join admission talks, and learn from HKU students. Experience Hong Kong's culture through a guided ferry tour of Victoria Harbour, listed by National Geographic as a "place of a lifetime."

Team Activities: Try lacrosse, softball, or hockey, and join cultural activities like drama or band performances to build teamwork and creativity.

Eligibility (合格): Applicants must submit a 4-minute video or 400-word written responses addressing their motivation, expectations, and suitability.

Programme Fee: HKD 23,000 (includes accommodation). Apply by March 31, 2025, for a 20% discount.

Additional discounts (e.g., HKU alumni (校友)) apply but cannot be combined.

Participants must maintain 80% attendance to receive a Certificate of Completion or HKU credits.

This programme offers a unique blend of academic rigor, cultural immersion, and leadership development, equipping students with skills for future success.

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Amanda and Susie, though sisters with a two-year age gap, had never got along. From the minute Susie was born, Amanda knew the baby disliked her.

As Susie grew, she hated Amanda for telling her how to do things. Amanda viewed Susie as spoilt, because she was the youngest in the family. At secondary school, Amanda shone at English; Susie was a maths whizz. Each made the other feel inadequate. When Amanda turned fifteen, Susie was angry when her sister was allowed to go to the youth club disco. Perhaps that was why Susie married so young — anything to beat her sister down the aisle. But Amanda got her revenge. When it was her turn, she chose a bridesmaids clashed with Susie's hair at her wedding.

Now, despite being in their fifties, these grievances (牢骚) were still fresh in the sisters' minds. The only thing they had in common was that they both loved their mother deeply.

Then one day, her father rang with the terrible news that their mother had died suddenly. Both sisters were stricken with grief, but Susie, was also upset that their father hadn't informed her first.

Then their father told them about their mother's will. "She's left you the painting." He said to them both. The painting — a portrait of the sisters by the mother — was the source of one of their biggest childhood arguments. To their surprise, it was bequeathed (遗赠) to both, "Your mom hopes that you each have it for six months and then swap over, for all your rest life." added the father.

"We live miles apart. We could get it delivered." said Susie. "It's against the will," their father replied, "‘I love to look at it, especially now you've both left home.' Your mom used to say. Now it felt like the last link to her."

For the sake of their beloved mother, the two sister began the cyclic keeping of the painting. This time it was Susie's turn to deliver the painting.

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。

Paragraph 1:

When Susie arrived, she found Amanda lying in the bed with her leg broken in an accident.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Paragraph 2:

Silently, they began to admire the painting, and all of a sudden, a line of little words beneath draw Amanda's attention.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

1.你的标语

2.推荐理由

注意：（1）写作词数应为80左右；

（2）请按如下格式在答题纸的相应位置作答。

Dear Mr. Smith,

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Best regards,

Li Hua

An unexpected cultural phenomenon has sparked widespread discussions among netizens recently. Some users shared posts (claim) that while visiting relatives in the UK, they discovered British children using Chinese "Hengshui-style" English writing practice books.

Hengshui Style, also known as "Hengshui Ti", is a standardized English handwriting method popularized by students from Hengshui High School strictness and academic excellence are well known in China. The writing style stands out for its (discipline) structure, neat formatting, and aesthetically pleasing appearance, resembling printed text. Over the years, it has earned a reputation as "secret weapon for exams", which is believed by many educators and students (be) highly beneficial for improving legibility and efficiency during timed tests.

The online buzz triggered nostalgia among Chinese netizens. Many (fond) recalled their own school days, carefully practicing English sentences in "Hengshui-style" workbooks, some even still possessing identical copybooks. Social media platforms (flood) with users sharing their own "Hengshui-style" handwriting samples and offering tutorials and tips for mastering the style. Some shared before-and-after (compare), showcasing dramatic improvements in their penmanship, others humorously debated whether the strict style limited creativity.

This cross-cultural fascination highlights the global reach of educational practices and the enduring legacy of a handwriting method once (confine) to Chinese classrooms.

After becoming a vet in 2015, I witnessed countless pets brought in for euthanasia because their owners no longer wanted them.5 ranged from financial struggles to housing restrictions or behavioral issues. Determined to help, I began taking6 animals home. Word spread, and before long, I'd7 a variety of dogs and cats. Eventually, with the support of friends who also became foster8, I launched a non-profit organization — Celandine Wood Animal Rescue. The cost-of-living crisis saw a (an)9 in animals being given away.

Then came Dave, an eight-month-old Cane Corso. He'd been imported for breeding, but was found out with elbow dysplasia (肘关节发育不良). Considering him10, the owner gave him up. Our11 saved him and found him a wonderful home. Currently, we care for about 50 dogs, 40 cats, and wildlife like birds and foxes.

Stories like this12 our mission, yet countless animals still slip through the cracks.13, we're fundraising to build a larger shelter, providing better resources and space. We never put an animal down unless we've14 all other options.

Every life matters.15 there are animals like Atticus and Dave, we'll keep fighting for them.

In an age dominated by digital media, the question of literature's relevance has never been more pressing. As a novelist and literary critic, I often turn to the insights of great writers who have delved into this question before me.

Toni Morrison once said, "We die. That may be the meaning of life. But we do language. That may be the measure of our lives." For Morrison, literature was not merely a form of entertainment. Through language, we preserve our experiences, our emotions, and our very essence.

James Baldwin, in his essay "The Creative Process", argued that literature serves as a mirror and a map. He wrote, "" Baldwin believed that literature had the power to confront uncomfortable truths and inspire social change. His works demonstrate how stories can simultaneously reflect reality and chart moral progress. The novel Go Tell It on the Mountain, for instance, not only exposed racial injustice in 1950s America but also envisioned paths toward empathy and reconciliation (和解).

Milan Kundera, in "The Art of the Novel", emphasized literature's ability to explore the complexity of human existence. "The novel's wisdom," he claimed, "is different from the wisdom of philosophy. " For Kundera, literature's value lies in its capacity to embrace life's contradictions without seeking simplistic resolutions.

As I reflect on these perspectives, I am reminded of literature's unique role in our lives. By revealing unseen possibilities, it acts as both a time capsule of collective memory and a blueprint for unwritten futures. In a world increasingly driven by binary (二进制) thinking, literature offers a space for subtle difference, empathy, and profound understanding.
 

A. It is an act of resistance against being forgotten.

B. Literature's ability to entertain is its most important function.

C. Literature provides clear answers to life's most difficult questions.

D. Some even argue that literature has lost its place in modern society.

E. It is not just a reflection of who we are but also a vision of who we might become.

F. It is the wisdom of uncertainty, of ambiguity and of questioning rather than answering.

G. It was through literature that we could see ourselves clearly and chart a course for our future.

Traditional conservation methods often risk damaging delicate materials. ARCHiVE's robotic system, equipped with micro-sensors and AI algorithms, can detect cracks invisible to the human eye and predict structural weaknesses before they worsen. "It's like having a doctor for ancient books," explains Dr. Emily Carter, lead conservator. Since its 2022 launch, ARCHiVE has scanned over 8,000 items, from Egyptian papyri to medieval maps, with 99.7% accuracy in damage assessment. Its non-invasive approach has reduced physical handling by 85%, significantly lowering the risk of accidental damage.

The project's digital twin technology creates exact virtual copies, allowing global access to restricted collections. During the 2023 Cairo Museum flood, ARCHiVE's digital models enabled researchers to virtually "restore" water-damaged artifacts within hours. "We're not just saving objects," says Carter, "we're preserving humanity's collective memory." This technology has also democratized access, with over 50,000 digital artifacts now available to researchers and the public worldwide.

However, some scholars argue that over-reliance on technology may distance researchers from hands-on experience. "You can't smell history through a screen," protests Prof. James Whitaker, a traditionalist at Cambridge. Others worry about data ownership, as scanned artifacts become digital assets potentially controlled by tech corporations. A2024 survey revealed that 62% of conservators fear losing control over digitized cultural heritage.

ARCHiVE's next phase involves 4D scanning, capturing how materials change over time. Pilot tests on Viking ship timbers have already revealed previously unknown construction techniques. Meanwhile, UNESCO is developing global standards for digital heritage, ensuring these technological marvels serve humanity rather than corporate interests. As Carter reflects, "Our ancestors left us these treasures; our duty is to pass them forward — both physically and digitally."