尖子生训练题2(学生版)

AlphaGo (1) (strike) again, defeating Ke Jie, the world’s number one Go(围棋) player, 3-0. After his defeat, the young Chinese prodigy said AlphaGo sees the universe of Go (2) he could only see a small area around him. This win, coupled with last year’s victory over Lee Se-dol(李世石), shines a light on the awe-inspiring advancements of technology and places AlphaGo among the greatest Artificial Intelligence (AI) systems (3) (create) to date.The AI industry is certainly making great advancements, constantly surprising the public with new and interesting tools and making life easier. Twenty years ago, just connecting to the Internet was a headache. Now, we can do just about anything on our phones, (4) online banking to live video-streaming. The shifting sands of technology have placed so many paths in front of humanity (5) it is hard to predict even the immediate future. We may talk about how AI can make our lives better, but we must also consider the risks. Many stories and films revolve around the theme of AI vs. humans. One that comes to my mind now is The Terminator(终结者). The film is about an AI system called Skynet, (6) was developed to protect humans. What the programmers did not expect was that Skynet began to think. It came to the conclusion that humans were a danger to its existence, so it started a global nuclear war and tried to “terminate(使终结)” humanity. AlphaGo’s recent achievements highlight the possibilities (7) technology and AI can bring about. They also serve to remind us of the questions and risks we (8) not have had time to think about. Some of us used to doubt the possibility of creating an actual “thinking” AI system, or (9) (assume) that humans will always be able to outsmart an AI system, but certain facts have now been placed in front of us. (10) that’s left to be done is adapt the actual “thinking” part of advanced AI systems like AlphaGo for more fields. Once that happens, human beings will be pretty much obsolete(被淘汰的). If we do not fully understand the risks of AI systems, we might be flying too close to the “sun,” and like Icarus in Greek mythology, we will fall.A Special Menu for KidsJapan is a food heaven which has a unique food culture. You can find food from different countries worldwide in this island nation, and it is also very good at (1) (combine) foreign food with its own traditional food. You may even find some food which (2) only be found in Japan. One of them (3) (call) “Okosama Lunch,” or “Kids’ Lunch.”In majordepartment stores in Japan, there usually are many restaurants on the top floor of the building. No matter what kind of food they serve, they usually have a menu for “Okosama Lunch.” Although called a lunch, it is served at suppertime in most cases. It is said that “Okosama Lunch,” a kids’ menu, was invented in 1930 by Taro Ando, a chief manager of Mitsukoshi Department Store, the most prestigious department store in Japan founded in 1673. Ando came up with an idea to have a variety of food which kids like on one plate and decorate (4) nicely. The plate usually has molded rice with a tiny national flag chosen from one of many countries on top. Since it was during the Depression (经济大萧条), Ando thought it would be nice (5) (have) something looking good for kids to enjoy. Besides a small portion of rice, an “Okosama Lunch” usually contains kids’ favorite food, such as hamburger steak, deep-fried chicken, red Vienna sausages, Spaghetti Neapolitan, fried shrimp and pudding. The details of this special menu are different from restaurant to restaurant, resulting (6) different types of “Okosama Lunch” across the country. They (7) (design) to attract kids with popular comic characters on the plate.Now you can find “Okosama Lunch” anywhere in Japan. At some restaurants, they have (8) age limit for this fun menu and usually serve the menu only for kids under ten years old. But it really depends on your luck (9) you can enjoy this fun food or not. Next time you (10) (visit) Japan, you should try this special menu to have a good time with food and enjoy the diversity of Japanese food culture.A Star That Will Never FallRobin Williams and Christopher Reeve had been friends since they were both students at a school of performing arts. As young actors, they (1) (promise) each other that if one of them became successful, then he would help the other one. Little (2) they realize that they would both become famous, and that the promise would mean so much to Reeve one day. Williams didn’t only offer the emotional support of a genuine and close friend, but he also volunteered to pay the medical bills after Reeve was thrown from a horse during an equestrian competition (骑术竞赛). Reeve, though declining the financial offer, was touched by (3) lay behind it: the love and friendship of a precious friend. (4) (determine) to maintain a positive attitude toward his life after the accident, Reeve went through months of therapy and trained himself to breathe without the assistance of a machine. Even though his doctors said that he would never move again, Reeve continued to work hard and believe in (5) All of his efforts paid off and he was able to move his forefinger. Reeve (6) (encourage) by this exciting progress and decided to “go forward,” as he once said. His goal was to walk again. “I refuse to allow a disability to determine (7) I live my life,” Reeve once said. “I don’t mean to bereckless (不顾后果的), but (8) (set) a goal that seems a bit discouraging is actually very helpful toward recovery.” (9) Reeve passed away in 2004, he once said, “I think a hero is an ordinary individual who finds strength to persevere (10) enormous obstacles.” Living up to his own definition of a hero, Reeve lived a life of extraordinary perseverance and refused to give up on himself.Can Computer Programs Help Students, Teachers?Junior Alvarado was worried when he began his first year at a publiccharterhigh school in Washington, DC (1) he often struggled in his math classes and earned poor grades in middle school. But the teachers at the Washington Leadership Academy used computer programs to identify the areas he was weak (2) and design a learning plan just for him. "For mepersonalized learning is having classes set at your level," the 15-year-old said, in between lessons.Many schools in the United States struggle (3) (raise) the highschoolgraduationrate. They also have difficulty helping many minority and low-incomestudents perform at the same level as (4) So many educators seedigitaltechnology as a way of solving these problems.The use of technology in schools is part of a larger idea of personalized learning, which (5) (gain) popularity in recent years.Personalized learning is a way of teaching (6) (center) around the interests and needs of individual students (7) (此题两空)entire classes as a whole. It includesflexiblelearning environments, specially-designed education plans, and (8) (let) students help decide what and how they learn. Supporters say traditional methods, (9) teachers just speak in the front of the class and test students all at once, do notmatchthe modern world. The economy needs kids who are creative problem solvers, whosynthesize information, form and express a point of view."At Washington Leadership Academy, educators use computer programs to collect information on students' performance. This information helps teachers follow their students' progress and make changes to lessons that meet students' individual needs. That way students are able to master subjects at their own speed.(10) personalized learning works better than traditional teaching remains to be seen.Living among trees, plants and flowers can fill your life with beauty. And if you are a woman, it can also help you live longer. Researchers found that women who live in homes (1) (surround) by plants appear to have lower death rates than women who live in areas with (2) (little) greenery. Researchers at Harvard University's T.H. Chan School of Public Health reported the finding. Flowers, trees and other plant life (3) help women live longer. Peter James is a research associate in the school's Department of Epidemiology. An epidemiologist is an expert in how disease spreads and how it can be controlled. James and his team looked at information from one of the largest and oldest investigations of women's health: the Nurse's Health Study. The Nurse's Health Study began 40 years ago and expanded in 1989. It now has information on nearly 200,000 women .For the new study, the Harvard team looked at the mortality rates of more than 100,000 women between the years 2000 and 2008. Then the researchers compared the mortality rates of (4) women to the greenery around their homes. (5) (determine) the amount of trees and other vegetation, researchers examined satellite images. Satellite images are a great help to scientists as they study Earth. This October 2015 image of a storm (6) (release) by the National Oceanic and Atmospheric Administration. The researchers considered other risk factors – things (7) the age of the women, their economic status, race and ethnicity. They also looked at whether or not the women smoked. The study found that the mortality rate among women who lived in the greenest spaces was 12 percent lower than those from the least green areas. Peter James said he and his team were surprised to find such a strong link (8) high vegetation levels and low mortality rates. He adds they were also surprised to find how high levels of plant life can affect a woman's mental health. The study suggests that living among vegetation -- trees, flower and other plants -- lowered levels of depression. Researchers say women in greener areas spent more time with other people, exercised more and were less exposed to air pollution. One of the biggest effects of greenery appeared to be a lowered risk of respiratory disease and cancer. Here are some numbers. The study found that women (9) (live) in areas with the most greenery had a 34 percent lower rate of dying from a respiratory disease and a 13 percent lower rate of dying from cancer. James says that it is common knowledge (10) vegetation helps the environment in many ways. But, he adds, the new findings suggest ways for city planners, landscape architects and policymakers to grow even healthier living areas.One of the most (1) (captivate) natural events of the year in many areas throughout North America is the turning of the leaves in the fall. The colours are magnificent, but the question of exactly (2) some trees turn yellow or orange, and others red or purple, is something which has long puzzled scientists. Summer leaves are green because they are full of chlorophyll(叶绿素), the molecule that captures sunlight and (3) (convert) that energy into new building materials for the tree. As fall approaches in the northern hemisphere, the amount of solar energy available (4) (decline) considerably. For many trees----evergreen conifers(针叶树) (5) (be) an exception----the best strategy is to abandon photosynthesis until the spring. So rather than maintaining the now redundant leaves throughout the winter, the tree saves its precious resources and discards them. But (6) letting its leaves go, the tree dismantles their chlorophyll molecules and ships their valuable nitrogen back into the twigs(细枝). As chlorophyll is depleted, other colours that have been dominated by it throughout the summer begin to be revealed. This (7) (unmask) explains the autumn colours of yellow and orange, but not the brilliant reds and purples of trees such as the maple or sumac(漆树).The source of the red is widely known: it is created by anthocyanins(花青素), water-soluble plant pigments reflecting the red to blue range of the visible spectrum. They belong to a class of sugar-based chemical compounds also known as flavonoids (类黄酮). What’s puzzling is that anthocyanins are actually newly minted, (8) (make) in the leaves at the same time as the tree is preparing to drop them. But it is hard to make sense of the manufacture of anthocyanins----why should a tree bother making new chemicals in its leaves when it’s already scrambling to withdraw and preserve the ones already there?Some theories about anthocyanins have argued that they (9) act as a chemical defence against attacks by insects or fungi(真菌), or that they might attract fruit-eating birds or increase a leaf’s tolerance to freezing. However there are problems with each of these theories, including the fact that leaves are red for such a relatively short period (10) the expense of energy needed to manufacture the anthocyanins would outweigh any anti-fungal or anti-herbivore activity achieved.Can Better Clothes Make You More Money?After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank. American English has many expressions related to clothes. Two of the more common ones are: "Dress for the job you want, not for the job you have"; and, simply, "Dress for success." A professionalstylisttakes these ideas a bit (1) (far). She says that our clothes can influence how we feel, our confidence, even our ability to do a job. And new research supports her claim.Tara Luizzi is a personal stylist in Washington, D.C. Through her company, Tara Styles DC, she teaches her clients to find the clothingstylesthat work best their (2) bodies, careers and lifestyles. Luizzi says that, like it or not, other peoplesize us upby the way we look. In other words, they make a judgment about us (3) we even speak. And part of what they are considering is what we choose to wear. "My feeling is you don't have a second chance (4) (make) a great firstimpression. So, I think it is very important to have a look that's pulled-together andconveyswho you are and yourstatusof life, I guess."Here, "pulled-together" means that someone's appearance is well-thought out. Luizi says she feels this is very important. She notes that clothes are especially important in (5) (create) the professional image you want toconvey."No matter what, you (6) try to always walk out the door looking pulled-together – if it be on the weekend or if it be during the work week. People take you more seriously when you are pulled-together and dress to a certain level."But choosing the right clothes is not just aboutimpressingothers. A recent study suggests that people who are dressed moreformallyperform better at some work tasks. The co-authors of the study are psychologists Michael Kraus of the University of Illinois, Urbana-Champaign and Wendy Berry Mendes of the University of California, San Francisco. Kraus and Mendes compared more than 100 men fromdiverseeconomic and racial backgrounds. They asked some to dress in business suits. They asked (7) to wear sweatpants, t-shirts and flip-flops. Then the researchers asked the participants to do several work tasks. One task involved making a business deal. Those wearing suits demanded more in their business deal. The participants (8) (dress) morecasuallywere more willing toconcede, or give up. The other task was to use big picture thinking to solve a problem. The men in suits were more able to think about the big picture, the way a boss would. Those in casual clothes focused more on smaller details of the problem. This type of thinking is what you would expect from someone in a lower position. Stylist Tara Luizzi says, to her, the study makes sense. She compares clothing toarmor, what a warrior puts on for protection in battle. "When you feel confident in yourself, I think you have a better day. So, I use clothing as the armor to the world. So, let's say you're having a horrible day or you're nervous about your presentation or maybe the big meeting, if you dress in something you love or you feel great in, you're going to walk in with more confidence."In her job, Luizzi sees (9) the right outfit can change the waya person feels. When she chooses clothing for her clients that good great on them, their backs straighten. They stand taller. And they start smiling. "They just feel so much better about themselves. So, my goal with every client is to try to get that out of a person. I don't want anything in your wardrobe that makes you not happy. It should be happiness."Luizzi says that, in general, people have a powerful emotional connection to their clothes. The intensity of people's feelings about clothes and their appearance has surprised Luizzi."Many people have an emotional connection to their clothing. You know, for a lot of my clients, there's an emotional level to it in that maybe they had a bad experience when they were younger shopping. Maybe they were overweight and they (10) (lose) weight. Or maybe when they were young they couldn't afford the clothes they can afford now. I've been in dressing rooms and closets and tears have been shed because it does bring up an emotional thing. And it was something I wasn't expecting when I first started this business."Scientists have been experimenting with four-legged robots for years, (1) (try) to see if they could be used as pack animals for carrying heavy loads over a difficult terrain. But the machine's power requirements limited their potential. That's changed, with a running robot designed by a group of engineers at Massachusetts Institute of Technology (2) operates on batteries rather than heavy gasoline-powered engines. Scientists say their robots will soon be able to run like cheetahs. But for now, the different technologies that will bring them (3) (close) to everyday life are still being tested. One of the obstacles continues to be power consumption. These complicated machines are still relatively heavy and their numerous motors require a lot of energy to run. The (4) (powerful) among them are either tethered to a power source (5) have a gasoline-powered generator onboard. But engineers at the Massachusetts Institute of Technology (6) (design) a 30-kilogram cheetah-like robot that is light enough to run on batteries. “This robot can actually jump 40 centimeters high and it can land very safely and then it can run, sprint, (7) (此题2空)the special, motor technology we developed,” said Sangbae Kim, director of MIT Biomimetics Robotic Lab. Kim says the robot needs only about 700 watts of power. Its limbs and (8) parts were made in a 3-D printer and reinforced with the strong, light-weight plastic called Kevlar, used for modern military helmets and bodysuits. “The frame has to be very light and very stiff, so we designed this frame to handle these high forces and the high shock,” he said.But the development of MIT's robot is not without setbacks. Its limbs (9) sustain tremendous force and sometimes they break. Kim says another special feature is the custom-made motor controller. “It is also designed by us because none of the commercially available products can handle this kind of power,” he said. Researchers say the new technologies (10) (use) on this robot may find their way toartificial limbs as well as other high-tech machines being developed to replace humans at back-breaking jobs.Cricket FloursAmericans are generally unwilling to eat bugs, (1) for at least two billion people worldwide, bugs or insects are a normal part of the diet. Now, a business (2) (name) Cricket Flours in the U.S. state of Oregon (3) (sell) finely-ground crickets (蟋蟀)as human food. Charles Wilson is the founder and CEO. He says he became (4) (interest) in crickets when he learned he could not eat some common foods, including a protein powder he used to build muscle." So it struck me (5) I could look for alternative proteins. Finally, I stumbled across cricket flour."Wilson says he recognized crickets could be more than a substitute (6) protein. He sensed a business opportunity. At the time, Wilson was attending the University of Oregon's law school. He mentioned the idea to his friend, Omar Ellis, (7) was studying at the business school. At last, Ellis (8) (convince) to become a co-founder and leader of Cricket Flours .Cricket Flours is one of more than a dozen new U.S businesses in the food insects industry. Other businesses focus on cricket farming or snacks made from cricket powder."Why crickets? (9) they're very sustainable. They take one-tenth the feed and one-sixth the water to get the same amount of protein that you would get from beef. It's got more iron than spinach, more calcium than milk, (10) is quite amazing..." Mr. Wilson says cricket flour does not have a strong taste. Maybe, he says, it tastes a little like nuts.A “Robber” in Your PocketAfter school, many students walking out of the school gate tend to read a screen, with their heads bowed. Over the past decade, such scenes have become the norm. Research reveals that American teenagers look at their phones 150 times a day (1) average. Meanwhile, the number of American teenagers reporting feelings of depression has grown significantly. (2) some people blame the increase on the Great Recession following 2008 and other social changes, a big new study suggests a different explanation --- the rise of social media. Jean Twenge, a psychologyprofessor at San Diego State University, led the study. By taking (3) close look at national surveys, with data (4) （collect）from more than 500,000 American teenagers, she found that those (5) spent lots of time on social media were more likely to agree with remarks such as “the future often seems hopeless.” Those who used screens less, spending time socializing with friends in person, were (6) （likely）to report feelings of depression. This, in fact, is not the first time scientists (7) （find）that social media can rob people of their happiness. One study published in 2016 asked a group of adults to quit Face book for a week. A control group continued (8) （use）the social networking site as usual. Those who gave up Face book reported feeling less depressed at the end of the week than those who continued using it. Some research, however, suggests that social-networking sites (9) promote happiness if used to engage directly with other users. This provides a reminder that it is users’ attitudes (10) shape their experiences on social media.Health Benefits of the Lotus RootHealth Benefits of the Lotus RootDo you know that lotus root can be eaten? Well, don’t be surprised because lotus root is considered not only to be very delicious but (1) （be）very important for its health benefits as well. For those (2) suffer from low blood flow or even anemia(贫血), they know how these diseases can be very harmful. However, (3) you include lotus root to your diet, it will be guaranteed that you will do away with such problems. Lotus root stimulates the blood circulation in the body and also helps the blood (4) （flow）smoothly in the body at all times. Sometimes we may suffer from high blood pressure because we are stressed out, anxious or even sometimes depressed. Thankfully, lotus root helps to lower the blood pressure of one’s body. Lotus root is very rich (5) potassium(钾)which helps to keep the blood vessels (6) （relax）at all times. And that means the pressure or the chances of having high blood pressure are eliminated. For proper bone and muscle growth, the presence of Vitamin C is very important.(7) has been confirmed about lotus root is that it is 73% full of Vitamin C. Vitamin C can help to fight against cancer and any heart diseases because it can help to eliminate many harmful free radicals(自由基团)from the body. Moreover, heart attacks closely (8) （connect）with homocysteine(半胱氨酸)levels can to a great extent be prevented by eating lotus. In the growing process, it is also important to have the healthy skin and hair. For this to be effective, the presence of Vitamin A (9) be present in your body at all times. Thankfully, the lotus root (10) vitamin A can be richly found also helps to keep the skin smooth and healthy.If your skin is damaged or inflamed, eating lotus roots can help with its fast repair.How “Power Poses” Can Help Your CareerCan how you stand or sit affect your success? New research shows posture has a bigger impact (1) body and mind than previously believed. Merely (2) (practise) a “power pose” for a few minutes in private—such as standing tall and leaning slightly forward with hands at one's side, or leaning forward over a desk with hands planted firmly on its surface—led to physiological changes in study participants, (3) are linked to more confident behavior and better performance. Katy Kei m, a marketing executive, (4) (use) to step back from listeners during presentations or conversations. She was often surprised when people asked if she was nervous. After (5) (work) with a coach to improve her skills and saw herself on video, she realized her posture didn't look strong. Then she began adjusting her posture, getting up from the table and leaning slightly forward when speaking at meetings. “It is a big change for me, sending a message (6) I want you to get off your smart phones and listen to what I have to say.” she says. During a three-hour meeting last week where she made a presentation, she noticed no one picked up a smart phone. Power posing is also connected with improved performance. In another study (7) (publish) last year, led by Amy J.C. Cuddy, an associate professor of business administration at Harvard Business School, participants (8) struck power poses for several minutes before beginning a mock job interview received better reviews and were more likely (9) (hire).Most speakers aren't aware of the signals they send through body language, says Kelly Decker, president of Decker Communications, a San Francisco coaching, training and consulting firm. Striking a powerful and expansive pose actually (10) (change) a person's hormones and behavior, just as if he or she had real power.Start Eating Purple for Your HealthA. lowerB. globallyC. filledD. unsurprisingE. benefitsF. regularlyG. healthierH. industryI. linkedJ. mineralsK. riskIt is strongly suggested that you should often eat a rainbow of colors. Eating a variety of colorfulfood provides vitamins and (1) that can’t be replaced with supplements(养生片剂)to nourish your body. According to experts who examined consumer behavior (2) across 465 stores, our plates look very colorful this year, with purple foods particularly popular. Walk through any supermarket and you will find richly-colored purple foods are popping upon the shelves: purple cauliflower, black rice, blue berries, black berries, purple sweet potatoes, purple corn and purple cab bage. The purple food trend in the market is (3) given how health-conscious people are becoming in recent years. People have long known that the darker the color of a food, the higher the contents of antioxidants(抗氧化剂) and nutrient t s will be, and the (4) the food. In fact, they are inspired to eat more purple foods after a health and nutrition study found that those who ate purple fruits and vegetables (5) had low cholesterol(胆固醇)and a reduced (6) of getting high blood pressure. Research shows that these foods get their purple color from anthocyanins(花青素), which have been (7) with antioxidants and anti-aging propertiesin the body. Purple foods help promote bone health, and have also been shown to (8) the risk of some cancers and improve memory. Take purple sweet potatoes for example. While the standard sweet potato is packed with health benefits of its own, the purple sweet potato is even better for us. These brightly colored potatoes share the same taste as the orange ones, but are also (9) with anthocyanins, which aid digestion and have anti-inflammatory(抗炎的) properties.Nutrition adviser Matthew Plowman agrees that purple foods are full of natural health (10) “The benefits of antioxidants have long been discussed, but they are also known to fight disease, keep you looking younger and reduce inflammation and are good for your heart — so, why wouldn’t you eat them?”Platform Nine and Three-QuartersSection AThey reached King’s Cross at half past ten. Uncle Vernon Dursley threw Harry’s trunk (大箱子) onto a cart and wheeled it into the station for him. Harry thought this was strangely kind until Uncle Vernon stopped dead, (1) (face) the platforms with an unpleasant grin on his face.“Well, there you are, boy. Platform Nine-Platform Ten. Your platform should be somewhere in the middle, but they don’t seem (2) (build) it yet, do they?”He was quite right, of course. There was a big plastic number nine over one platform and a big plastic number ten over the one next to it, and in the middle, (3) at all.“Have a good term,” said Uncle Vernon with an even more unpleasant smile. He left (4) another word. Harry turned and saw (5) Dursleys drive away. All three of them were laughing. Harry’s mouth went rather dry. What on earth was he going to do? He was starting to attract a lot of funny looks, because of Hedwig, his。

2020-2021学年七年级数学上册尖子生同步培优题典【人教版】专题3.14 第3章一元一次方程单元测试(基础卷)姓名：__________________ 班级：______________ 得分：_________________注意事项：本试卷满分120分，试题共26题．答卷前，考生务必用0.5毫米黑色签字笔将自己的姓名、班级等信息填写在试卷规定的位置．一、选择题(本大题共10小题，每小题3分，共30分)在每小题所给出的四个选项中，只有一项是符合题目要求的．1．(2019秋•田家庵区期末)下列等式变形错误的是( ) A ．若a ＝b ，则3a ﹣1＝3b ﹣1 B ．若a ＝b ，则ac 2＝bc 2 C ．若a c 2=b c2，则a ＝b D ．若ac 2＝bc 2，则a ＝b2．(2020•安徽一模)若x ＝2是关于x 的一元一次方程ax ﹣2＝b 的解，则3b ﹣6a +2的值是( ) A ．﹣8B ．﹣4C ．8D ．43．(2020春•蓬溪县期末)下列方程：①y ＝x ﹣7；②2x 2﹣x ＝6；③23m ﹣5＝m ；④2x−1=1；⑤x−32=1，⑥6x ＝0，其中是一元一次方程的有( ) A ．2个B ．3个C ．4个D ．5个4．解一元一次方程12(x +1)＝1−13x 时，去分母正确的是( ) A ．3(x +1)＝1﹣2x B ．2(x +1)＝1﹣3xC ．2(x +1)＝6﹣3xD ．3(x +1)＝6﹣2x5．(2019秋•滦南县期末)小明在做解方程作业时，不小心将方程中的一个常数污染，被污染的方程是2y +1=12y ﹣□，小明想了想后翻看了书后的答案，此方程的解是y =−53，然后小明很快补好了这个常数，这个常数应是( ) A ．−32B ．32C ．52D ．26．(2019秋•德州期末)解方程2x−13−3x−44=1时，去分母正确的是( )A ．4(2x ﹣1)﹣9x ﹣12＝1B ．8x ﹣4﹣3(3x ﹣4)＝12C ．4(2x ﹣1)﹣9x +12＝1D ．8x ﹣4+3(3x ﹣4)＝127．(2019秋•商河县期末)下列解方程去分母正确的是( ) A ．由x3−1=1−x 2，得2x ﹣1＝3﹣3xB ．由x−22−x 4=−1，得 2x ﹣2﹣x ＝﹣4C ．由y3−1=y 5，得 2 y ﹣15＝3yD ．由y+12=y 3+1，得 3( y +1)＝2 y +68．(2019秋•长清区期末)甲车队有汽车100辆，乙车队有汽车68辆，根据情况需要甲车队的汽车是乙车队的汽车的两倍，则需要从乙队调x 辆汽车到甲队，由此可列方程为( ) A ．100﹣x ＝2(68+x ) B ．2(100﹣x )＝68+x C ．100+x ＝2(68﹣x )D ．2(100+x )＝68﹣x9．(2020春•辉县市期末)我国元朝朱世杰所著的《算学启蒙》中有个问题：良马日行二百四十里，驽马日行一百五十里，驽马先行一十二日，问良马几何追及之．这道题的意思是：跑得快的马每天走240里，跑得慢的马每天走150里，慢马先走12天，快马几天可以追上慢马？如果我们设快马x 天可以追上慢马，则可列方程( ) A ．240x ＝150x +12 B ．240x ＝150x ﹣12 C ．240x ＝150(x +12)D ．240x ＝150(x ﹣12)10．(2020春•叙州区期末)为了提倡节约用水，采用“阶梯水价”收费办法：每户用水不超过5方，每方水费x 元，超过5方，每方加收2元，小张家今年3月份用水11方共交水费56元，根据题意列出关于x 的方程，正确的是( ) A ．5x +6(x ﹣2)＝56 B ．5x +6(x +2)＝56 C ．11(x +2)＝56D ．11(x +2)﹣6×2＝56二、填空题(本大题共8小题，每小题3分，共24分)请把答案直接填写在横线上11．(2019秋•盘龙区期末)若3x 2m ﹣1+6＝0是关于x 的一元一次方程，则m 的值为 ．12．(2019秋•道里区期末)比a 的2倍大5的数等于a 的8倍，列等式表示为 ．13．(2019秋•舞钢市期末)已知关于x 的方程mx ﹣5＝x ﹣3m 的解是x ＝2，则m 的值为 ． 14．(2019秋•宁德期末)由3x ＝2x ﹣1得3x ﹣2x ＝﹣1，在此变形中，方程两边同时 ．15．(2019春•青浦区期末)周末小明在家做功课、做家务和户外活动的时间之比是3：1：4，总共花了8小时．设他做家务的时间是x 小时，则可列方程 ．16．(2020•禅城区模拟)五一期间，青年旅行社组织一个团；老师和学生共50人组成的旅行团到凤凰古城旅游，景区门票售票标准是：成人门票50元/张，学生门票20元/张，该旅行团购买门票共花费1800元，若设该团购买成人门票x 张，则可列方程为： ．17．(2019秋•双清区期末)为节约用电，长沙市实“阶梯电价”具体收费方法是第一档每户用电不超过240度，每度电价0.6元；第二档用电超过240度，但不超过400度，则超过部分每度提价0.05元；第三档用电超过400度，超过部分每度提高0.3元，某居民家12月份交电费222元，则该居民家12月份用电 度．18．(2018秋•宣城期末)定义运算a ⊗b ＝a (1﹣b )，下面给出了关于这种运算的四个结论： ①2⊗(﹣2)＝6②a ⊗b ＝b ⊗a③a ⊗1＝0 ④若2⊗a ＝0，则a ＝0其中正确结论的序号是 (填上你认为所有正确结论的序号)．三、解答题(本大题共8小题，共66分．解答时应写出文字说明、证明过程或演算步骤) 19．(2019秋•罗湖区校级期末)解方程： (1)4x ﹣3(20﹣x )＝3 (2)3x−14−1=5x−7620．(2019秋•沙坪坝区校级期末)解方程： (1)2x ﹣1＝3(x ﹣1)； (2)0.4x+30.2−x−0.10.3=2．21．(2019秋•榆次区期末)下面是小明同学解方程的过程，请仔细阅读，并解答所提出的问题．3x+12=1−2x−23解：去分母，得3(3x +1)＝1﹣2(2x ﹣2)，①去括号，得9x +3＝1﹣4x +4，② 移项，得9x +4x ＝1+4﹣3，③ 合并同类项，得13x ＝2，④ 系数化为1，得x =213．⑤(1)聪明的你知道小明的解答过程在 (填序号)处出现了错误，出现错误的原因是违背了 ． A ．等式的基本性质1；B ．等式的基本性质2：C ．去括号法则：D 加法交换律． (2)请你写出正确的解答过程22．(2019秋•崂山区期末)某人乘船由A 地顺流而下到达B 地，然后又逆流而上到C 地，共用了3小时．已知船在静水中速度为每小时8千米，水流速度是每小时2千米．已知A 、B 、C 三地在一条直线上，若AC两地距离是2千米，则AB两地距离多少千米？(C在A、B之间)23．(2019秋•慈利县期末)列方程解应用题：如图，现有两条乡村公路AB、BC，AB长为1200米，BC长为1600，一个人骑摩托车从A处以20m/s的速度匀速沿公路AB、BC向C处行驶；另一人骑自行车从B处以5m/s的速度从B向C行驶，并且两人同时出发．(1)求经过多少秒摩托车追上自行车？(2)求两人均在行驶途中时，经过多少秒两人在行进路线上相距150米？24．(2019秋•张店区期末)华联超市第一次用7000元购进甲、乙两种商品，其中甲商品的件数是乙商品件数的2倍，甲、乙两种商品的进价和售价如表：(注：获利＝售价﹣进价)甲乙进价(元/件)2030售价(元/件)2540(1)该超市购进甲、乙两种商品各多少件？(2)该超市将第一次购进的甲、乙两种商品全部卖完后一共可获得多少利润？(3)该超市第二次以第一次的进价又购进甲、乙两种商品，其中甲商品的件数不变，乙商品的件数是第一次的3倍：甲商品按原价销售，乙商品打折销售，第二次两种商品都售完以后获得的总利润比第一次获得的总利润多800元，求第二次乙商品是按原价打几折销售？25．(2020春•丽水期末)某班级想购买若干个篮球和排球，某文具店篮球和排球的单价之和为35元，篮球的单价比排球的单价的2倍少10元．(1)求篮球和排球的单价各是多少元；(2)该文具店有两种让利活动，购买时只能选择其中一种方案．方案一：所有商品打7.5折销售；方案二：全场购物每满100元，返购物券30元(不足100元不返券)，购物券全场通用，若该班级需要购买15个篮球和10个排球，则哪一种方案更省钱，并说明理由．26．(2019秋•武汉期末)武汉大洋百货经销甲、乙两种服装，甲种服装每件进价500元，售价800元；乙种服装商品每件售价1200元，可盈利50%．(1)每件甲种服装利润率为，乙种服装每件进价为元；(2)若该商场同时购进甲、乙两种服装共40件，恰好总进价用去27500元，求商场销售完这批服装，共盈利多少？(3)在元旦当天，武汉大洋百货实行“满1000元减500元的优惠”(比如：某顾客购物1200元，他只需付款700元)．到了晚上八点后，又推出“先打折”，再参与“满1000元减500元”的活动．张先生买了一件标价为3200元的羽绒服，张先生发现竟然比没打折前多付了20元钱问大洋百货商场晚上八点后推出的活动是先打多少折之后再参加活动？。

2020-2021学年七年级数学上册尖子生同步培优题典【人教版】专题1.1有理数姓名：__________________ 班级：______________ 得分：_________________注意事项：本试卷满分100分，试题共24题．答卷前，考生务必用0.5毫米黑色签字笔将自己的姓名、班级等信息填写在试卷规定的位置．一、选择题(本大题共10小题，每小题3分，共30分)在每小题所给出的四个选项中，只有一项是符合题目要求的．1．(2019秋•商河县期末)现实生话中，如果收人100元记作+100元，那么﹣800表示( ) A ．支出800元B ．收入800元C ．支出200元D ．收入200元2．(2018秋•广西期中)如果向北走5米记作“+5米”，那么向南走8米记作( ) A ．+8米B ．﹣8米C ．+13米D ．﹣3米3．(2019秋•南宁期末)一种巧克力的质量标识为“100±0.5克”，则下列质量合格的是( ) A ．95克B ．99.8克C ．100.6克D ．101克4．(2019秋•南京月考)在下列各组中，表示互为相反意义的量的是( ) A ．下降的反义词是上升B ．羽毛球比赛胜3场与负3场C ．增产5吨粮食与减产﹣5吨粮食D ．向北走15km 和向西走15km5．(2019秋•石景山区期末)在五个数：①﹣5 ②227③1.3 ④0 ⑤−23中属于分数的是( )A ．②⑤B ．②③C ．②③⑤D ．①⑤6．(2019秋•云冈区期末)下列各数：﹣5，1.1010010001…，3.14，227，20%，π3，有理数的个数有( )A ．3个B ．4个C ．5个D ．6个7．(2019秋•铁锋区期末)下列说法错误的是( ) A ．负整数和负分数统称负有理数 B ．正整数，0，负整数统称为整数C ．正有理数与负有理数组成全体有理数D ．3.14是小数，也是分数8．(2019秋•历下区期中)下列各数中，是负整数的是( ) A ．−25B ．0C ．3D ．﹣69．(2019秋•南开区期末)下列语句正确的是( ) A ．“+15米”表示向东走15米 B ．0℃表示没有温度 C ．﹣a 可以表示正数D ．0既是正数也是负数10．(2019秋•渝中区校级月考)在下列六个数中：0，π2，−227，0.101001，﹣10%，5213，分数的个数是( ) A ．2个 B ．3个 C ．4个 D ．5个二、填空题(本大题共8小题，每小题3分，共24分)请把答案直接填写在横线上11．(2019秋•皇姑区校级月考)在有理数1.7，﹣17，0，﹣527，﹣0.001，92，2003，3.14，π，﹣1中负分数有 ；自然数有 ；整数有 ．12．(2013秋•赛罕区校级月考)有理数中，是整数而不是正数的数是 ，是负数而不是分数的是 ． 13．(2019秋•长汀县校级月考)﹣1，0，0.2，17，3，π中正数一共有 个．14．(2019秋•南山区期末)通常在生产图纸上，对每个产品的合格范围有明确的规定．例如，图纸上注明一个零件的直径是φ30±0.020.03，φ30±0.020.03表示这个零件直径的标准尺寸是30mm ，实际产品的直径最大可以是30.03mm ，最小可以是 ．15．(2020•云南模拟)若零上8℃记作+8℃，则零下5℃记作 ℃．16．(2020春•甘南县期中)只要是向相反的方向运动，就一定用负数表示． (判断对错)17．(2019秋•宜宾期末)如果上升5m 记作+5m ，那么下降7m ，记作 m ，不升也不降记作 m ． 18．(2019秋•西宁期末)最大的负整数是 ．三、解答题(本大题共6小题，共46分．解答时应写出文字说明、证明过程或演算步骤) 19．(2019秋•孝义市期中)把下列各数填入表示它所在的数集的集合里： 3，﹣0.2，0，0.12，−23，﹣500，112，﹣3.1415926，﹣15，0.320．(2019秋•江阴市校级月考)把下列各数填入相应的集合中： ﹣3.14，2π，−13，0.618，227，0，﹣1，6%，+3，3.010010001…(每相邻两个1之间依次多一个0)正数集合{ ……}； 分数集合{ ……}； 有理数集合{ ……}； 非负整数集合{ ……}．21．(2019秋•临洮县期中)把下列各数填在相应的括号内： ﹣19，2.3，﹣12，﹣0.92，35，0，−14，0.563，π正数集合{ …}； 负数集合{ …}； 负分数集合{ …}； 非正整数集合{ …}．22．(2019秋•崇川区校级月考)把下列各数填在相应的大括号内 15，−12，0.81，﹣3，14，﹣3.1，﹣4，171，0，3.14正整数集合{ …} 负整数集合{ …} 整数集合{ …} 分数集合{ …}．23．(2019秋•博白县期中)(1)将下列各数填入相应的圈内：212，5，0，1.5，+2，﹣3．(2)说出这两个圈的重叠部分表示的是什么数的集合： ．24．(2019秋•惠安县校级月考)把下列各数填入相应的大括号内： ﹣13.5，2，0，0.128，﹣2.236，3.14，+27，﹣15%，﹣1，227，2613负数集合{ …} 整数集合{ …} 分数集合{ …}。

Language often seems so skillfully...Language often seems so skillfully (1) （draft) that one can hardly imagine it as anything (2) （此题2空）the perfected handiwork of a master craftsman. How else could this instrument make so much out of barely three dozen measly morsels of sound? In themselves, these configurations (构造) of mouth----p,f,b,v,t,d,k,g,sh, a,e and so on---- (3) (amount) to nothing more than a few haphazard(随意的) spits and splutters, random noises with no meaning, no ability to express, no power to explain. But run them through the cogs and wheels of the language machine, and (4) ( let) it arrange them in some very special orders, and there is nothing (5) these meaningless streams of air cannot do: from sighing the interminable boredom of existence to (6) ( unravel) the fundamental order of the universe. (7) ( extraordinary) thing about language, however, is that one doesn’t have to be a genius to set its wheels in motion. The language machine allows just about everybody----from pre-modern foragers(搜寻食物的人) in the subtropical savannah, to post-modern philosophers in the suburban sprawl---- (8) ( tie) these meaningless sounds together into an infinite variety of subtle senses, and all apparently without the slightest exertion. Yet it is precisely this deceptive ease which makes language a victim of its own success, since in everyday life its triumphs are usually taken for granted. The wheels of language run so smoothly that one rarely bothers (9) ( stop) and think about all the resourcefulness and expertise that must (10) ( go) into making it tick. Language conceals art.Changxing IslandWhat is the closest island to Shanghai? If you answer “ Chongming Island”, then you are wrong. It should be Changxing Island, (1) is located between Congming Island and Pudong New District. As to administration(行政管理), it (2) （belong）to Baoshan District. With a large area of forests and fresh air, this island enjoys reputations of “Clean Island” and “Longevity Island”. Its unique natural environment and rich natural resources make Changxing Island’s tourism industry fully (3) （develop）.There are many places of interest there, such as Shanghai Orange Grove, Mongolian Village Race Track, Hanging Beads Park (Chuizhu Y uan), Shanghai Stunt Center, Xianfeng Resort, and etc. Travelers can take bus No.5, 51, 116, 522, 728, 848 and 849 to Wusong dock (4) you can take a ship to Changxing Island. Travelers can also take Shenchong (Line 2) Shuttle Bus, (5) o perating hour is from 6:00 a.m. to 7:00 p.m. to Changxing Island. If travelers prefer toreach the island with their own cars, ferries which can carry cars should be a great choice. Changxing Island, also known as “the Hometown of Oranges” is a great place for vacation. Once you and your family members or friends reach the island, you can drive to the Orange Grove Resort to enjoy (6) The oranges grown in the grove looks bright and smooth, and they are very juicy and sweet. Once in late autumn season, golden oranges hanging on the branches look very tempting. The thousand acres of oranges there (7) give a total production of 1.75 million kilograms annually. Another place famous for oranges is Shanghai Orangerie Resort located in Qianwei Farm, in the central part of Changxing Island. (8) the 1980s, the Orange Art Festival has been held on this farm each autumn, attracting tens of thousands of admiring visitors.(9) being the famous “orange town”, Changxing Island is a great place for visitors to enjoy rafting or going to the riverside to enjoy the wonderful scene written in a poem by Wang Bo, (10) famous poet in Tang Dynasty.Hot Drinks Linked to CancerNext time you make yourself a hot cup of tea or coffee, you might want to let it cool down a bit before drinking. Researchers say letting your hot drinks cool off (1) help you avoid some kinds of cancer. In fact, the United Nations' cancer research agency decided (2) （list) hot drinks with lead, gasoline and exhaust fumes as "possibly carcinogenic." In other words, each one could cause cancer. The International Agency for Research on Cancer (IARC) is part of the World Health Organization (WHO). The IARC published the findings in the medical journal Lancet Oncology. Researchers at IARC found evidence that drinks at temperatures above 65 degrees Celsius, when (3) (swallow), can cause cancer of the esophagus.The researchers examined findings from other studies (4) t ea and coffee were often served at 70 degrees Celsius or above. Those studies were completed in Iran, China and South America. In developed countries, health experts (5) (link) esophageal cancer to smoking and alcoholic drinks in many studies. However, this form of cancer is (6) ( common) in areas where people drink beverages at very high temperatures.In Europe and the United States, many people drink coffee and tea at temperatures around 60 degrees Celsius. And they often add milk which lowers the temperature considerably. (7) tea-drinkers in Iran and maté-drinkers in South America often enjoy their beverages at closer to 70 degrees Celsius. Maté is a tea-like brew made by (8) (steep) the leaves of the yerba mate plant in near-boiling water.The researchers note that South Americans not only drink their maté very hot, they also drink it through a metal straw. This sends the scalding liquid directly (9) the throat. The findings, however, are good news for coffee drinkers.In 1991, the World Health Organization listed coffee as "possibly carcinogenic." WHO officials have since changed their position on that listing. They now suggest that the temperature of your hot drink is a greater risk factor than the actual drink itself.Christopher Wild is the director of the IARC. When he spoke with the AFP news agency, he said the results "suggest that drinking very hot beverages is one probable cause of esophageal cancer and that it is the temperature, (10) (此题2空) the drinks themselves, that appears to be responsible." The National Coffee Association called the change "great news for coffee drinkers." But how common is esophageal cancer? Worldwide, it is the eighth most common cancer. Cancer of the esophagus killed about 400,000 people in 2012.McDonald’s Szechuan Sauce Will Return This WinterLate Sunday, McDonald’s released a statement promising to bring back the limited-edition sauce again at a date to be determined.“Yesterday, we were truly surprised at the (1) （amaze）curiosity and passion that the community showed to welcome back Szechuan Sauce, (2) （此题两空）it was just for one day.” the company said in a statement. “And our super-limited batch(批次), though well-intentioned, clearly was far from enough (3) (meet) customers’ demands.” (4) （announce）that it was going to “make this right”, McDonald’s promised that this dipping sauce would return in a great quantity in the near future. “We’re bringing more, a lot more, (5) （此题两空）Szechuan Sauce(四川辣酱)will be available to any fan at a nearby McDonald’s,” the company said.McDonald’s Szechuan sauce, (6) was a limited edition condiment tied to the release of Disney’s famous cartoon Mulan in 1998, has seen its profile rise thanks to Rick & Morty, a cartoon sci-fi sitcoms(情景剧) made by The Adult Swim series (7) the main character complaint about the unavailability of Szechuan Sauce. That led (8) McDonald’s later promise to bring back this weekend. The only problem was (9) demand exceeded(超过)supply, which made many Rick & Morty fans angry.“I personally thought it was a sauce that was trying too hard in a world where with McNuggets sauce you just want something to taste like honey or like a BBQ sauce,” co-creator Dan Harmon told about the sauce. “It was (10) sauce that was trying to prove it was different and it tasted much better than an ordinary sauce should be.”Overweight Asian-Americans Seen More AmericanWhat does an American look like? Nearly 1,300 Americans, mostly college students, were asked that question for a recent study in Psychological Science. They were shown pictures of people and asked by University of Washington researchers who looked American to them. (1) Over-weight Asian-Americans were more likely to be seen as Americans than normal weight Asian-Americans, the researchers said. Researchers who worked on the study believe this all fits into common stereotypes. (2) And one common stereotype is that Asians are thin and most Americans are heavy, the researchers said. Sapna Cheryan is a co-author of the study. She also teaches psychology at the University of Washington. She said the findings show an unusual benefit for overweight Asian-Americans. She noted that overweight people often face discrimination. But Cheryan said that being overweight makes Asian-Americans seen more American. That makes them less likely to face discrimination directed at those believed to be foreign, she said. Cheryan said her interest in ethnic and racial stereotypes goes back to her youth in Urbana, Illinois. She is Indian-American and remembers people would praise her mother because she "spoke English so well." It was as if they did not expect a woman who appeared to come from a foreign country to speak English, she said. Cheryan also remembers worrying when friends would come over to her house. She was embarrassed that her family served Indian food. The food seemed "different" compared to American favorites such as pizza and Doritos.The research on how people see Asian-Americans is a follow-up of her 2011 research. It found Asian-Americans were three times as likely to order American food after being asked if they spoke English than if they had not been asked that question. " (3) " Cheryan said. This is not always a good thing for Asian-Americans. She notes that traditional American food often contains more calories and fat than many Asian dishes.The Centers for Disease Control and Prevention estimates that 34.5 percent of white Americans are considered obese, or very overweight. For Asian-Americans, the percentage is 11.7 percent. For African-Americans, the percentage of obesity is 48 percent and for Latino Americans, the percentage is 42.5 percent. The new University of Washington study showed people photos of people from different racial and ethnic groups to see if weight influenced their opinions. Among the questions asked: "How likely is this person to have been born outside the U.S? Another, "How likely is it that this person's native language is English?"Weight did make a difference in how people decided whether Asian-Americans were Americans. Those questioned by the University of Washington researchers also looked at pictures of Latinos, whites and African-Americans.(4) This supported their opinion that people believed to be from foreign countries where people are believed to be mostly thin are considered more likely to be American if they are overweight.The researchers noted that many Americans believe Latinos are overweight. As a result, overweight Latinos are not seen as more likely to be Americans -- as was the case with Asian-Americans.A. A stereotype is a belief, often untrue, that many have about a group of peopleB. The suggestion is that maybe people avoid foods that are stereotypical of their ethnic group so that they would fit in betterC. The researchers found that weight did not influence whether they saw whites, African-Americans and Latinos as being AmericansD. The most surprising answer was how people saw Asian-AmericansE. Most Asian-Americans answer the question without hesitationF. Some stereotypes derive from discrimination against certain groupRunning in Cold Weather Improves PerformanceCold weather during winter months may keep many people from leaving home and running in the open air. However, a new study shows that the drop in temperature is a good reason to run. In fact, researchers say, running in cold weather helps improve one's performance.Many people say running in the winter can be difficult. Two reasons are the low temperatures and bitter winds. Yet many runners might find it easier than running in hot weather. That could be (1) lower temperature reduce stress on the body. When you run in cold weather, your heart rate and the body's dehydration levels are lower than in warmer conditions. The body needs less water on a cold day than in warm weather.This information comes from sports scientists at St. Mary's University in London. John Brewer is a professor of (2) (apply) sport science at St. Mary's. For this study, he and other researchers put a group of people into a room they called an "environmental chamber." The researchers then recreated summer and winter weather conditions in the room. The test subjects (3) （ask) to run 10,000 meters under both conditions. Brewer says he and his team recorded biological measurements of the runners. "We've got a group of subjects into the environmental chamber, we've changed the conditions (4) （replicate) the summer or winter and we've got them to run a 10k under both of those conditions and taken various measurements on each runner whilst they've been completing their 10k."Brewer says every movement runners make produces heat. He explains that one way in which we lose heat is by sweating. "That heat builds up in the body and can be really damaging (5) you can lose that heat. One of the mechanisms by which we lose heat is through sweating, but we also lose heat by transporting the blood to the surface of the skin (6) it can lose heat out into the external environment. Now, that puts more strain on the heart, particularly in hot conditions because it's much harder to lose heat when the external environment is warm as well."And that increased strain, adds Brewer, can be considerable. Running in higher temperatures results in faster heart rates."We found, for example, that heart rates were about 6 percent higher in the hotter conditions.We found that the runners dehydrated by around 30, 38 percent more in (7) hotter conditions. And they found it about 30 percent easier -- the test of their thermal regulation, how they felt, (and) their perception of heat -- was around a third lower when they were running in cold conditions."The body does not have to work as hard to pump blood to the skin's surface. Brewer says that means running in cooler temperatures requires less energy. He adds that serious runners could cut valuable seconds (8) their personal best times by choosing to run in the winter."If you look at top-level sports, if you look at the likes of Mo Farah running 10Ks and winning world and Olympic championships; the difference between success and failure is seconds, and it's certainly not minutes. We can be very confident that in cooler conditions you can certainly slice a decent percentage of time off your personal best."Several websites note that (9) (important) thing for people who run in cold conditions is to wear the right clothing. Keeping as dry as possible is the key issue when exercising in low temperatures. Wear mittens on your hands (10)（此题2空)gloves. Wear shoes that will keep you from falling. And especially, wear more than one layer of clothing to keep sweat away from your skin. So, if you are a runner, don't let winter weather keep you indoors. Simply get ready for the low temperatures and start running.Fruits, Vegetables Can Lower Blood PressureWe may not need another study telling us that fruits and vegetables are good for our bodies. But research and studies can help us to understand how foods affect our bodies in good ways and bad.Researchers at the University of Southern California's Keck School have found (1) great reason to eat more fruits and vegetables. They say that potassium-rich foods like sweet potatoes, avocados, spinach and bananas could help to lower your blood pressure. High blood pressure, (2) hypertension, is an international problem. Experts at the World Health Organization say more than one billion people suffer from high blood pressure. The condition causes 51 percent of deaths (3) stroke and 45 percent of deaths due to heart disease. Health officials in the U.S. say heart disease and stroke together kill more Americans each year than any other cause. Years of research (4) (link) sodium, or salt,intaketo increased blood pressure. So, officials advise people to use salt in moderation. Experts at the United States Centers for Disease Control and Prevention say Americans get most of their sodium -- about 75 % -- from processed foods and eating at restaurants.This is a good reason to eat fresh food (5) (prepare) at home. Alicia McDonough is a professor of cell andneurobiologyat the Keck School of Medicine. She led this recent study. McDonough says that eating less sodium is a well-known way to lower blood pressure. But she also says evidence suggests that eating more potassium may have an equally important effect on hypertension.For her research, she examined studies that looked atthe link between potassium and sodium.McDonough found that people who ate more potassium generally had lower blood pressure unconnected to how much sodium they ate. Her research suggests that the body does creates a balance, using sodium to control potassium levels in the blood. "When dietary potassium is high," she says, "kidneysexcretemore salt and water, (6) increases potassium excretion." This process cleans the kidneys. She explains that as humans evolved, they ate a diet rich in potassium, but low in sodium. This has lead us tocravesodium, not potassium." (7) you eat a typical Western diet," she says, "your sodiumintakeis high and your potassium intake is low." She adds that this greatly "increases your chances of (8) (develop) high blood pressure."McDonough published her study in the April 2017 issue of theAmerican Journal ofPhysiology-EndocrinologyandMetabolism. Health experts at the CDC agree that "eating enough potassium each day can help balance out some of the harmful effects that high sodium intake can have on blood pressure." (9) they also say that eating less sodium is important as well. On its website, the CDC lists these fruits and vegetables -- and other foods -- as being good sources of potassium. But how much potassium should we eat each day? A 2004 study by the Institute of Medicine shows adults (10) eat about 4.7 grams of potassium a day to lower blood pressure. McDonough says eating about 60 grams of beans would provide 50 percent of that.What you can learn from Einstein’s quirky habitsLike it or not, our daily habits have a powerful impact on our brains. Many of the world’s most brilliant scientific minds were also fantastically weird. From Pythagoras’ outright ban on beans to Benjamin Franklin’s naked ‘air baths’, the path to greatness is paved with some truly peculiar habits. But what if these are more than superficial facts? Scientists are increasingly realizing that intelligence is less about sheer genetic luck than we tend to think. According to the (1) (late) review of the evidence, around 40% of what distinguishes the brainiacs from the blockheads in adulthood is environmental. Like it or not, our daily habits have a powerful impact on our brains, shaping their structure and changing the way we think.Of all history’s great minds, arguably the master of combining genius with unusual habits was Albert Einstein – so what better person to study for clues to mind – enhancing behaviors to try ourselves? He taught us how to squeeze energy out of atoms, so maybe, just maybe, he might be able to teach us a thing or two about how to squeeze the most out of our tiny mortal brains. Could there be any benefits in (2)（follow) Einstein’s sleep, diet, and even fashion choices?GOOD SLEEPIt’s common knowledge that sleep is good for your brain – and Einstein took this advice (3)（seriously) than most. He reportedly slept for at least 10 hours per day – nearly one and a half times as much as the average American today (6.8 hours). But can you really slumber your way to a sharper mind? The author John Steinbeck once said: “It is a common experience that a problem difficult at night is resolved in the morning (4) the committee of sleep has worked on it.” Many of the most radical breakthroughs in human history, including the periodic table, the structure of DNA and Einstein’s theory of special relativity, have supposedly occurred while their discoverer was unconscious. The latter came to Einstein while he was dreaming about cows being electrocuted. But is this really true?DAIL Y WALKBesides, Einstein’s daily walk was sacred to him. While he was working at Princeton University, New Jersey, he’d walk the mile and a half journey there and back. He followed in the footsteps of (5) diligent walkers, including Darwin who went for three 45minute walks every day. These constitutionals weren’t just for fitness – there’s mountains of evidence that walking (6) boost memory, creativity and problem-solving.EATING SPAGHETTISo what do geniuses eat? Alas, it’s not clear what fuelled Einstein’s extraordinary mind,(7) the internet somewhat dubiously claims it was spaghetti. He did once joke that his favorite things about Italy were “spaghetti and [mathematician] Levi-Civita”, so we’ll go with that.It’s well known that the brain is a food-guzzling greedy guts, consuming 20% of the body’s energy though it only accounts for 2% of its weight. Just like the rest of the body, the brain prefers to snack on simple sugars, such as glucose, which (8) (break) down from carbohydrates. Sugars can give the brain a valuable boost, but unfortunately this doesn’t mean binging on spaghetti is a good idea. SMOKING A PIPEToday, the many health risks of smoking are widely known, so this is not a habit that it would be wise to follow. But Einstein was a (9) (harden) pipe smoker, known as much around campus for the cloud of smoke which followed him as for his theories. He famously loved to smoke, believing it “contributes to a somewhat calm and objective judgment in all human affairs.” He’d even pick cigarette butts off the street and stuff the remaining tobacco into his pipe.NO SOCKSNo list of Einstein’s eccentricities would be complete (10) a mention of his passionate aversion to socks. “When I was young,” he wrote in a letter to his cousin – and later, wife – Elsa, “I found out that the big toe always ends up making a hole in a sock. So I stopped wearing socks.”Zimbabwe's “Friendship Bench” a Possible Model for Mental Health TreatmentHealth workers in Zimbabwe are helping people with mental health problems through a new program. Experts say the treatment could serve as a model for other countries in Africa. Doctors estimate that about one quarter of Zimbabweans suffer (1) depression or anxiety. But there are only 12 psychiatrists in the country of 14 million people. Psychiatrists are doctors who treat mental or emotional problems.The University of Zimbabwe, the London School of Hygiene and Tropical Medicine and King's College London worked together (2) (create) a new kind of treatment. Dr. Victoria Simms works at the London School of Hygiene and Tropical Medicine. "We can't possibly go the route of training psychiatrists and psychologists (3) it would take 15 years. How are we going to provide treatment?" So, doctors created a simple but effective program. They placed wooden seats – which they call "Friendship Benches" -- outside several health clinics in the city of Harare. Dr. Simms says people (4) the chance to meet on the benches for six sessions with health workers. They call these workers "grandmother health providers." "So the patient explains (5) all their problems are and its opening up the mind in the sense of (6) (allow) the patient to see that they can do something about their problems." The Friendship Bench study involved more than 550 patients. After six months, only 14 percent of the patients in the Friendship Bench group said they were still (7) (depress). That compares to 50 percent of those who did not receive treatment. Those who received the treatment were also five times (8) (likely) to have suicidal thoughts.Dr. Dixon Chibanda is with the University of Zimbabwe. He is one of the founders of the Friendship Bench program. He said that the program has many benefits. "Not only a mental health sort of package, but a package (9) actually improved outcomes of things like hypertension, diabetes and, and adherence to medication for people living with HIV."Friendship Benches are now placed in 60 clinics in Harare and two other cities. The Canadian government is helping to pay for the program's expansion through its Grand Challenges Canada aid program. Researchers say the program could be a model for mental health efforts in poor areas (10) in wealthier countries.Take steps now to set yourself up for financial success. If you make these smart money moves now, you’ll be (1) （likely) to have remorse about not taking control of your finances sooner. Create a budget you can stick to“ Having the discipline to budget every month will ensure your finances (2) （tune) finely and that you are in control of your money,” said Jamie Pomeroy, a Minnesota financial advisor and founder of . (3) trick, he said, is to find a method of budgeting that you like and stick with it.Pomeroy recommends that you give every dollar a home in the budget---- (4) it’s for necessary expenses, savings or incidentals. You could also consider using a 50-30-20 budget, which allots 50 percent of yourincome for needs, 30 percent for wants and 20 percent for savings and debt.Improve your creditBuilding good credit will likely pay off down the line. “ A good credit score is important for obtaining lower rates on large purchases, such as a car or a home,” said Shannon McLay, a financial planner and founder of The Financial Gym. “ Even though you might not be ready to make these purchases, you should work on your credit score now (5) when you are, you will obtain the attractive interest rates you want.”Build an emergency fundYou need a reserve of cash that’s easily accessible (6) (cover) unexpected expenses and help you get through financial emergencies without having to rack up debt, ask friends and family for money or tap your retirement account .Get a handle on your debtFocus on paying off your highest-rate debts first----likely credit card debt----so you’ll pay less in interest over time. Before you start paying down debt, understand (7) you have accumulated it, Kay said. Was it (8) you had a major medical expense or borrowed heavily to cover the cost of college?” If this is your normal way of living, it’s time to take stock and think about why,” Kay said.Plan for the “ (9) - ifs” You can alleviate some of your financial worries by identifying your worst-case money scenarios, and (10) (prepare) for them, Kay said. Creating an emergency fund to cover expenses if you’re out of work is a good place to start.What is Sustainable Agriculture?The goal of sustainable(可持续发展的)agriculture is to meet society’s food needs without compromising(危及)the ability of future generations (1) (meet) their own needs. People (2) (devote) to sustainable agriculture try to accomplish three main goals in their work: a healthy environment, economic profitability, and social and economic equality. Every person involved in the food system — growers, food processors, sellers, consumers, and waste managers — (3) play a role in ensuring a sustainable agricultural system. There are many practices commonly used by people working in sustainable food systems. Growers use methods to promote soil health, reduce water use, and lower pollution levels on the farm. Sellers and consumers look for environmentally friendly foods (4) are good for farm workers’ health and strengthen the local economy. Researchers in sustainable agriculture combine biology, economics, engineering, chemistry, community development, and many other subjects. However, sustainable agriculture is not only (5) collection of subjects, but also a process of negotiation(协商): a push and pull between the interests of an individual farmer and (6) of people in a community as they work to solve complex problems about how we grow our food. Agriculture has changed greatly, especially (7) the end of World War II. Food productivity has greatly increased (8) (此题2空)new technologies,。

三单元---分数除法91.已知a*8/7=b*7/8=2/2*c，并且a,b,c都不等于零。

把a,b,c这三个数按从大到小顺序排列。

2.一个数与它的倒数之差是255/16，求这个数。

3.一个分数的分子是互为倒数的两个数的积，分母是20以内最大的质数，这个分数是多少？4.小强是一个小马虎，在计算时，他把一个数除以4看成了乘4，结果他算出的答案是8/9.问正确答案应该是多少？5.有两摞书，第一摞有40本，如果从第二摞中拿出1/10放入第一摞中，两摞书同样多。

第二摞原来有多少本书？6.在一条长80米的路上插小红旗，每隔4/5米插一面，从头开始共需要插多少面？7.一件上衣比一条裤子贵45元，这个钱数相当于一条裤子的1/3，这套衣服共多少钱？8.校园里栽的杨树是松树的3/4，栽的松树是柳树的4/5，已知栽了120棵杨树，校园里栽了多少棵柳树？9.某小学在全国绘画书法比赛中有24人获得奖牌，相当于参赛学生人数的3/5，这个小学参赛的学生中没有获奖的又有多少人？10.一个人用3天走完全程，第一天走了全程的1/5，第二天走了剩下路程的1/2，第三天走了10千米，全程有多少千米？11.学校美术组有男生、女生若干名，已知女生人数的1/2和男生人数的1/4是12人，女生人数的1/3和男生人数的1/4是9人，女生有多少人？12.小红以每分钟60米的速度从家去学校，她走了1/12小时，正好走了全程的一半，她家距学校多远？13.用一个分数分别去除25/12、5/12、15/7，所得的商都是整数，这个数最大是多少？想一想是否有最小的。

14.一条铁路，修完900千米后，剩余部分比全长的3/4少300千米，这条铁路长多少千米？15.三只猴子吃篮子里的桃子，第一只猴子吃了1/3，第二只猴子吃了剩下的1/3，第三只猴子吃了剩下的1/4，最后篮子里还剩下6个桃子。

篮子里原有桃子多少个？16.有一堆苹果，吃了1/4后又买来324个，这时这堆苹果个数比原来多了1/5。

整理与复习（尖子生学案）2023-2024学年四年级上册数学【拔尖特训】北师大版一、前言数学作为基础学科，对于培养学生的逻辑思维、空间想象能力和解决问题的能力具有重要作用。

为了提高学生的数学素养，培养他们的创新精神和实践能力，我们特编写了本套《整理与复习（尖子生学案）2023-2024学年四年级上册数学【拔尖特训】北师大版》教材。

本教材以北师大版四年级上册数学教材为依据，结合我国教育实际，针对尖子生的学习需求，注重知识体系的完整性、系统性和逻辑性，旨在帮助学生在整理与复习过程中，巩固基础知识，提高解题技巧，培养拔尖创新能力。

二、教材特点1. 知识点全面：本教材涵盖了北师大版四年级上册数学教材的全部知识点，包括数的认识、计算、图形与几何、量的计量、数据的整理与表示等，为学生提供了一个全面的学习框架。

2. 解题方法多样：本教材针对各类题型，总结出多种解题方法，如画图法、列表法、假设法、倒推法等，帮助学生掌握解题技巧，提高解题能力。

3. 拔尖特训：针对尖子生的学习需求，本教材设置了一定数量的拔尖特训题目，旨在培养学生的创新思维和解决问题的能力。

4. 知识体系完整：本教材注重知识体系的完整性，每个章节都按照“知识梳理-典型例题-巩固练习-拓展提高”的结构进行编排，帮助学生系统掌握知识。

5. 实践活动丰富：本教材结合学生的生活实际，设置了丰富多样的实践活动，让学生在实际操作中感受数学的魅力，提高实践能力。

三、使用方法1. 学生在使用本教材时，应先对所学知识进行梳理，了解各个章节的主要内容和知识点。

2. 针对每个章节的典型例题，学生要认真分析解题思路和方法，学会运用多种解题技巧。

3. 在巩固练习环节，学生要独立完成练习题，检验自己的学习效果，并对错题进行总结和反思。

4. 参与拓展提高环节，学生要积极思考，勇于挑战，培养自己的创新精神和实践能力。

5. 家长和教师应关注学生的学习进度，适时给予指导和鼓励，帮助学生克服学习中的困难。

2020-2021学年九年级数学上册尖子生同步培优题典【人教版】专题1.13第1章有理数单元测试(培优卷)姓名：__________________ 班级：______________ 得分：_________________注意事项：本试卷满分120分，试题共26题．答卷前，考生务必用0.5毫米黑色签字笔将自己的姓名、班级等信息填写在试卷规定的位置．一、选择题(本大题共10小题，每小题3分，共30分)在每小题所给出的四个选项中，只有一项是符合题目要求的．1．(2019秋•官渡区期末)在﹣6，|﹣4|，﹣(+3)，0，﹣(﹣2)中，负数共有( ) A ．1个B ．2个C ．3个D ．4个【分析】首先把|﹣4|，﹣(﹣3)，﹣(﹣2)化简，然后再确定负数的个数． 【解析】|﹣4|＝4，﹣(﹣3)＝3，﹣|﹣2|＝﹣2，负数有﹣6，﹣2，共2个， 故选：B ．2．(2020•重庆)下列各数中，最小的数是( ) A ．﹣3B ．0C ．1D ．2【分析】根据正数大于0，0大于负数，正数大于负数，可得答案． 【解析】∵﹣3＜0＜1＜2， ∴这四个数中最小的数是﹣3． 故选：A ．3．(2019秋•新都区期末)﹣(−13)的相反数是( ) A ．3B ．﹣3C ．13D ．−13【分析】直接利用互为相反数的定义得出答案． 【解析】﹣(−13)=13的相反数是：−13． 故选：D ．4．(2020•雁塔区校级三模)在227，π3，1.62，0四个数中，有理数的个数为( )A ．4B ．3C ．2D ．1【分析】根据有理数的定义，即可解答． 【解析】在227，π3，1.62，0四个数中，有理数为227，1.62，0，共3个，故选：B ．5．(2020•广东模拟)据统计，2019年杭州市区初中毕业生为25000余人，25000用科学记数法表示为() A．25×103B．2.5×103C．2.5×104D．0.25×105【分析】科学记数法的表示形式为a×10n的形式，其中1≤|a|＜10，n为整数．确定n的值是易错点，由于25000有5位，所以可以确定n＝5﹣1＝4．【解析】25000＝2.5×104．故选：C．6．(2019秋•南召县期末)若|m|＝5，|n|＝7，m+n＜0，则m﹣n的值是()A．﹣12或﹣2B．﹣2或12C．12或2D．2或﹣12【分析】根据题意，利用绝对值的代数意义求出m与n的值，再代入所求式子计算即可．【解析】∵|m|＝5，|n|＝7，且m+n＜0，∴m＝5，n＝﹣7；m＝﹣5，n＝﹣7，可得m﹣n＝12或2，则m﹣n的值是12或2．故选：C．7．(2019秋•弥勒市期末)如图所示，a、b是有理数，则式子|a|﹣|b|+|b﹣a|化简的结果为()A．﹣2a B．﹣2b C．0D．2a﹣2b【分析】由数轴可知a＜0＜b，则由数的范围可化简式子为|a|﹣|b|+|b﹣a|＝﹣a﹣b+b﹣a＝﹣2a．【解析】由图可知﹣1＜a＜0＜1＜b，∴|a|﹣|b|+|b﹣a|＝﹣a﹣b+b﹣a＝﹣2a，故选：A．8．(2019秋•长安区校级月考)如图是小明同学完成的作业，他做对的题数是()A．1B．2C．3D．4【分析】各式利用有理数的除法，减法法则，相反数，绝对值，以及倒数的性质判断即可． 【解析】−25的相反数是25，﹣1的倒数是﹣1，绝对值等于它本身的数是非负数， ( )﹣7＝﹣3，则括号内的数为4， (﹣3)÷(−13)＝9，则判断错误的个数为3，做对的是2， 故选：B ．9．(2019秋•莒县期中)下列说法： ①若|a |＝a ，则a 为正数；②若a ，b 互为相反数，且ab ≠0，则ba =−1；③若a 2＝b 2则a ＝b ；④若a ＜0，b ＜0，则|ab ﹣a |＝ab ﹣a ． 其中正确的个数有( )个． A ．1B ．2C ．3D ．4【分析】利用相反数，绝对值的性质，以及有理数的除法法则判断即可． 【解析】①若|a |＝a ，则a 为非负数，不符合题意； ②若a ，b 互为相反数，且ab ≠0，则ba =−1，符合题意；③若a 2＝b 2则a ＝b 或a ＝﹣b ，不符合题意； ④若a ＜0，b ＜0，则|ab ﹣a |＝ab ﹣a ，符合题意． 故选：B ．10．(2017秋•硚口区期中)下列结论：①若a 为有理数，则a 2＞0；②若a 2+b 2＝0，则a +b ＝0；③若a +b ＝0，则ab =−1；④若ab ＞0，则a |a|+b |b|+c |c|=−3，则其中正确的结论的个数是( )A ．3个B ．2个C ．1个D ．0个【分析】①根据平方的意义，a 取0时，结论不成立； ②根据非负数的意义即可判断；③由条件得到a ，b 为互为相反数，即可判断结论正确；④当a ，b 同正时，结论错误．【解析】①若a ＝0时，则a 2＝0，故①错误；②∵a 2≥0，b 2≥0，若a 2+b 2＝0，则a ＝b ＝0，∴a +b ＝0，故②正确； ③若a +b ＝0，a ，b 同时为零，则ab =−1不存在，故③错误；④若ab ＞0，则a ，b 同号，当a ＞0，b ＞0时，a|a|+b |b|=2，c ＞0时，a|a|+b |b|+c |c|=3，c ＜0时，a|a|+b |b|+c |c|=1，c ＝0时，a|a|+b |b|+c |c|=2，故④错误，故选：C ．二、填空题(本大题共8小题，每小题3分，共24分)请把答案直接填写在横线上 11．(2020春•普陀区期末)比较大小：﹣2 ＞ ﹣312．(填“＜”或“＞”)【分析】先进行绝对值的化简，然后通分，根据两个负数，绝对值大的其值反而小即可进行判断． 【解析】∵|﹣2|＜|﹣312|，∴﹣2＞−312． 故答案为：＞．12．(2019秋•宾县期末)在数轴上与﹣4相距3个单位长度的点有 2 个，它们分别是 ﹣1 和 ﹣7 ． 【分析】根据题意画出数轴，进而得出符合题意的答案． 【解析】如图所示：在数轴上与﹣4相距3个单位长度的点有2个，它们分别是﹣1和﹣7． 故答案为：2，﹣1，﹣7．13．(2019秋•海淀区校级期中)在下列各数中：12，﹣3，0，﹣0.7，5，其中是非负整数的是 0，5 ．【分析】非负整数包括正整数和0，据此可以得到答案． 【解析】非负整数的有：0，5． 故答案为：0，5．14．(2019秋•绵阳期末)在数轴上点A 对应的数为﹣2，点B 是数轴上的一个动点，当动点B 到原点的距离与到点A 的距离之和为6时，则点B 对应的数为 ﹣4或2 ． 【分析】分情况分别求出AB 、OB ，利用方程求解即可．【解析】设点B表示的数为b，①当点B在点A的左侧时，则有﹣2﹣b﹣b＝6，解得，b＝﹣4，②当点B在OA之间时，AB+AO＝2≠6，因此此时不存在，③当点B在原点的右侧时，则有b+2+b＝6，解得，b＝2，故答案为：﹣4或2．15．(2019秋•绵阳期末)计算：﹣32×16−(﹣4)÷|﹣2|3＝﹣1．【分析】根据有理数的乘方、有理数的乘除法和减法可以解答本题．【解析】﹣32×16−(﹣4)÷|﹣2|3＝﹣9×16+4÷8=−32+12＝﹣1，故答案为：﹣1．16．(2019秋•邹城市期中)若0＜x＜1，则x，x2，1x 的大小关系是x2＜x＜1x．【分析】已知x的取值范围，可运用取特殊值的方法，选取一个符合条件的实数代入选项求得答案．【解析】∵0＜x＜1，∴假设x＝0.1，则x2＝(0.1)2＝0.01，1x =10.1=10，∵0.01＜0.1＜10，∴x2＜x＜1 x．故答案为：x2＜x＜1 x．17．(2019秋•宿豫区期中)规定a⊕b＝a﹣b+1，则(3⊕2)⊕5＝﹣2．【分析】根据a⊕b＝a﹣b+1，可以求得所求式子的值．【解析】∵a⊕b＝a﹣b+1，∴(3⊕2)⊕5＝(3﹣2+1)⊕5＝2⊕5＝2﹣5+1 ＝﹣2， 故答案为：﹣2．18．(2018秋•路南区校级月考)符号“f ”，“g ”分别表示一种运算，它对一些数的运算结果如下： (1)f (1)＝0，f (2)＝1，f (3)＝2，f (4)＝3，…，f (10)＝9，… (2)g (12)＝2，g (13)＝3，g (14)＝4，g (15)＝5，…，g (111)＝11，…利用以上规律计算：f (2018)﹣g (12018)＝ ﹣1 ．【分析】根据题目中的式子，可以得到f (n )和g (1n)，从而可以求得所求式子的值．【解析】由题意可得， f (n )＝n ﹣1，g (1n )＝n ，则f (2018)﹣g (12018)＝2018﹣1﹣2018 ＝﹣1， 故答案为：﹣1．三、解答题(本大题共8小题，共66分．解答时应写出文字说明、证明过程或演算步骤) 19．(2019秋•茂名期中)计算 (1)(﹣4)+9(2)13+(﹣12)+17+(﹣18)【分析】(1)直接利用有理数的加法运算法则得出答案； (2)直接利用有理数的加法运算法则得出答案． 【解析】(1)(﹣4)+9 ＝5；(2)13+(﹣12)+17+(﹣18) ＝13+17+(﹣12)+(﹣18) ＝30+(﹣30) ＝0．20．(2019秋•长汀县校级月考)把下列各数分别填入相应的大括号内：−7，3.5，−3.1415，π，0，1317，0.03，−312，10，−0.2⋅3⋅，−42自然数集合{ 0，10… }； 整数集合{ ﹣7，0，10，−42⋯ }； 正分数集合{ 3.5，1317，0.03… }；非正数集合{ ﹣7，﹣3.1415，0，﹣312，﹣0.23⋅⋅，−42⋯ }； 有理数集合{ ﹣7，﹣3.5，﹣3.1415，0，1317，0.03，﹣312，10，﹣0.23⋅⋅，−42⋯ }．【分析】掌握各自的定义：自然数(大于零的整数)；整数(正整数、零和负整数)；有理数(整数和分数的统称)【解析】自然数集合：{0，10…}； 整数集合：{﹣7，0，10，−42⋯}； 正分数集合：{3.5，1317，0.03…}；非正数集合：{﹣7，﹣3.1415，0，﹣312，﹣0.23⋅⋅，−42⋯}； 有理数集合：{﹣7，﹣3.15，﹣3.1415，0，1317，0.03，﹣312，10，﹣0.2⋅3⋅，−42⋯}．21．(2019秋•和平区期末)计算： (1)12÷(﹣3)﹣(﹣8)×(−34)+12 (2)313−22÷{[(−12)3−38+13]×12}【分析】(1)根据有理数的乘除法和加减法可以解答本题； (2)根据有理数的乘方、有理数的乘除法和加减法可以解答本题． 【解析】(1)12÷(﹣3)﹣(﹣8)×(−34)+12 ＝﹣4﹣6+12 =−192；(2)313−22÷{[(−12)3−38+13]×12}＝313−4÷[(−18−38+13)×12]＝313−4÷(−32−92+4)＝313−4÷(﹣2) ＝313−4×(−12) ＝313+2 ＝513．22．(2018秋•丰城市期末)下列有理数：﹣1，2，5，﹣112(1)将上列各数在如上图的数轴上表示出来； (2)将上列各数从小到大排列，并用“＜”符号连接． 【分析】(1)将各数表示在数轴上，如图所示；(2)根据数轴上点的位置将各数按照从小到大顺序排列即可． 【解析】(1)将各数表示在数轴上，如图所示：(2)根据题意得：﹣112＜−1＜2＜5．23．(2020春•浦东新区期末)一名足球守门员练习折返跑，从球门线出发，向前记作正数，返回记作负数，他的记录为：+6，﹣5，+9，﹣10，+13，﹣9，﹣4(单位：米)． (1)守门员最后是否回到了球门线的位置？(2)在练习过程中，守门员离开球门线最远的距离是多少米？ (3)守门员全部练习结束后一共跑了多少米？【分析】(1)计算这些数的和，根据和的符号、绝对值得出是否回到原来的位置， (2)计算出每一次离开球门的距离，比较得出答案， (3)计算这些数的绝对值的和即可．【解析】(1)(+6)+(﹣5)+9+(﹣10)+13+(﹣9)+(﹣4)＝0， 答：守门员回到了球门线的位置；(2)守门员每次离开球门的距离为：6，1，10，0，13，4，0，答：守门员离开球门的位置最远是13米； (3)6+5+9+10+13+9+4＝56(米) 答：守门员一共走了56米．24．(2019秋•南岸区期末)有个填写运算符号的游戏：“2_3_5_9”，在每个“____”上，填入+，﹣，×，÷中的某一个(可重复使用)，然后计算结果． (1)计算：2+3﹣5﹣9；(2)若2÷3×5 × 9＝30，请推算横线上的符号；(3)在“2 ﹣ 3 × 5+9”的横线上填入符号后，使计算所得数最小，直接写出填上符号后的算式及算式的计算结果的最小值．【分析】(1)根据计算法则进行计算即可； (2)根据运算顺序得出103___9＝30，因此横线上应是乘号；(3)要使结果最小，其中必有负号，即减号，然后使负数的绝对值最大，因此考虑用乘法，从而得出答案． 【解析】(1)原式＝5﹣5﹣9＝﹣9；(2)若2÷3×5×9＝30，因此“空格”上的符号为“×”； (3)2﹣3×5+9＝﹣4， 故答案为：﹣×．25．(2020春•兴化市期中)(1)计算：0×1×2×3+1＝( 1 )2； 1×2×3×4+1＝( 5 )2； 2×3×4×5+1＝( 11 )2； 3×4×5×6+1＝( 19 )2； ……(2)根据以上规律填空：4×5×6×7+1＝( 29 )2； 6 × 7 × 8 × 9 +1＝(55)2．(3)小明说：“任意四个连续自然数的积与1的和都是某个奇数的平方”．你认为他的说法正确吗？请说明理由．【分析】(1)通过有理数的运算便可得结果；(2)由已知等式得到规律：任意四个连续自然数的积与1的和等于较小数与比它大3的数的积与1的和的平方．按此规律解答便可；(3)根据题意可得第n 个等式应是n (n +1)(n +2)(n +3)+1＝[n (n +3)+1]2＝(n 2+3n +1)2，再证明n 2+3n +1是否为奇数便可．【解析】(1)0×1×2×3+1＝0+1＝1＝12；1×2×3×4+1＝24+1＝25＝52；2×3×4×5+1＝120+1＝121＝112；3×4×5×6+1＝360+1＝361＝192，故答案为：1；5；11；19；(2)由已知等式知，任意四个连续自然数的积与1的和等于较小数与比它大3的数的积与1的和的平方．∴4×5×6×7+1＝(4×7+1 )2＝292；∵55＝6×9+1，∴6×7×8×9+1＝552；故答案为：29；6；7；8；9；(3)正确．证明：设四个自然数分别为n，n+1，n+2，n+3，则有n(n+1)(n+2)(n+3)+1＝[n(n+3)][(n+1)(n+2)]+1＝(n2+3n)(n2+3n+2)+1＝(n2+3n)2+2(n2+3n)+1＝(n2+3n+1)2＝[n(n+1)+2n+1]2，∵n为自然数，∴n(n+1)为偶数，2n+1为奇数，∴n(n+1)+2n+1必为奇数，故(n2+3n+1)2是一个奇数的平方，即任意四个连续自然数的积与1的和都是某个奇数的平方．26．(2019秋•崇川区校级期中)已知b是最小的正整数，且a，b满足(c﹣5)2+|a+b|＝0，请回答：(1)请直接写出a，b，c的值：a＝﹣1，b＝1，c＝5；(2)在(1)的条件下，若点P为一动点，其对应的数为x，点P在0到2之间运动，即0≤x≤2时，化简：|x+1|﹣|x﹣1|+3|x﹣2|；(3)在(1)(2)的条件下，a，b，c分别对应的点A、B、C开始在数轴上运动，若点A以每秒1个单位长度的速度向左运动，同时，点B和点C分别以每秒2个单位长度和5个单位长度的速度向右运动，假设t 秒钟过后，若点B与点C之间的距离表示为BC，点A与点B之间的距离表示为AB．请问：BC﹣AB的值是否随着时间t的变化而改变？若变化，请说明理由；若不变，请求其值．【分析】(1)根据b是最小的正整数，即可确定b的值，然后根据非负数的性质，几个非负数的和是0，则每个数是0，即可求得a，b，c的值；(2)根据x的范围，确定x+1，x﹣3，5﹣x的符号，然后根据绝对值的意义即可化简；(3)先求出BC＝3t+4，AB＝3t+2，从而得出BC﹣AB＝2．【解析】(1)∵b是最小的正整数，∴b＝1．根据题意得：c﹣5＝0且a+b＝0，∴a＝﹣1，b＝1，c＝5．故答案是：﹣1；1；5；(2)当0≤x≤1时，x+1＞0，x﹣1≤0，x﹣2＜0，则：|x+1|﹣|x﹣1|+3|x﹣2|＝x+1﹣(1﹣x)+2(2﹣x)＝x+1﹣1+x+4﹣2x＝4；当1＜x≤2时，x+1＞0，x﹣1＞0，x﹣2≤0．|x+1|﹣|x﹣1|+3|x﹣2|＝x+1﹣(x﹣1)+2(2﹣x)＝x+1﹣x+1+4﹣2x＝﹣2x+6；(3)不变．理由如下：t秒时，点A对应的数为﹣1﹣t，点B对应的数为2t+1，点C对应的数为5t+5．∴BC＝(5t+5)﹣(2t+1)＝3t+4，AB＝(2t+1)﹣(﹣1﹣t)＝3t+2，∴BC﹣AB＝(3t+4)﹣(3t+2)＝2，即BC﹣AB值的不随着时间t的变化而改变．(另解)∵点A以每秒1个单位长度的速度向左运动，点B每秒2个单位长度向右运动，∴A、B之间的距离每秒钟增加3个单位长度；∵点B和点C分别以每秒2个单位长度和5个单位长度的速度向右运动，∴B、C之间的距离每秒钟增加3个单位长度．又∵BC﹣AB＝2，∴BC﹣AB的值不随着时间t的变化而改变解．。

浙教版7年级下册尖子生通关重难点集训09 第二章综合测试一、单选题（共20题；共60分）1.（2019七下·江干期中）“孤帆远影碧空尽，唯见长江天际流”为什么远去的帆船会越来越小，直至消失呢？以下对其原因的分析中错误的是()A.看远处的帆船时，睫状肌处于舒张的状态B.看远处的帆船时，晶状体曲度变小C.帆船离晶状体越远，视网膜上成的像越小D.近处的帆船在视网膜上成放大的像，远处的帆船在视网膜上成缩小的像2.（2018七下·柯桥期中）如图所示，不同碗中盛不同的水，然后演奏者可以通过敲击不同的碗，可以演奏出美妙的乐曲，下列说法不正确的是()A.敲击不同的碗，音调不一样B.不同力度敲击相同的碗，音调是一样的C.若碗的材质不同，则敲击时音色将不同D.敲击时美妙的声音是通过空气震动发声的3.将一物体放在凸透镜前，使物体距依次为6厘米、18厘米和24厘米，分别得到放大的虚像、放大的实像和缩小的实像，则凸透镜的焦距f满足关系式（）A.f＜6厘米B.6厘米＜f＜18厘米C.9厘米＜f＜12厘米D.18厘米＜f＜24厘米4.声音在水中传播的过程中，下列说法中正确的是（）A.声音的音调保持不变B.声音的响度保持不变C.声音的传播速度逐渐减小D.以上说法都不对5.如图所示，水平桌面上斜放着一个平面镜M ，桌面上的小球按图示方向滚动，要使小球在平面镜中所成的像沿竖直方向下落，则镜面与桌面间的夹角α应为（）A.90°B.60°C.45°D.30°6.如图，点燃的蜡烛放在距小孔a处，它成像在距小孔b的半透明纸上，且a大于b．则半透明纸上的像是（）A.倒立、放大的虚像B.正立、缩小的虚像C.倒立、缩小的实像D.正立、放大的实像7.甲在足够长的有水自来水管一端打击一次，乙在另一端用耳朵伏管听，能听到（）A.一声B.最多2声C.3声D.4声8.雨后晴朗的夜晚为了不踩到地面的积水，下列判断中正确的是()A.迎着月光走，地上发亮处是水；背着月光走，地上暗处是水B.迎着月光走，地上暗处是水；背着月光走，地上发亮处是水C.无论迎着月光走还是背着月光走，地上发亮处都应是水D.无论迎着月光走还是背着月光走，地上暗处都应是水9.手指不小心被刀片划破后感到疼痛，其感受器和痛觉形成的部位是( )A.均在手指伤处B.在手指伤处和大脑皮层C.在手指伤处的真皮和表皮D.分别在手指伤处和伤处附近10.下列光现象与日食的形成原因不同的是()A.小孔成像B.雨后彩虹C.手影游戏D.树下彩虹11.绝大多数鱼类的体温与周围水温相同，然而，生活在海水中的月鱼，其体温比周围水温高。

编者小k 君小注：本专辑专为2022年初中沪教版数学第二学期研发，供中等及以上学生使用。

思路设计：重在培优训练，分选择、填空、解答三种类型题，知识难度层层递进，由中等到压轴，基础差的学生选做每种类型题的前4题；基础中等的学生必做前4题、选做5-8题；尖子生全部题型必做，冲刺压轴题。

专题04 数形结合之一次函数与二元一次方程组（学生版）错误率：___________易错题号：___________一、单选题1．如图所示，一次函数3y kx =-（k 是常数，0k ≠）与一次函数y x b =-+（b 是常数）的图象相交于点()2,1A ，下列判断错误的是（ ）A ．关于x 的方程3kx x b -=-+的解是2x =B ．关于x 的不等式3x b kx -+>-的解集是2x >C ．当0x <时，函数3y kx =-的值比函数y x b =-+的值小D ．关于x ，y 的方程组3kx y x y b -=⎧⎨+=⎩的解是21x y =⎧⎨=⎩2．对于实数a ，b ，我们定义符号max {a ，b }的意义为：当a ≥b 时，max {a ，b }＝a ；当a ＜b 时，max {a ，b }＝b ；如：max {4，﹣2}＝4，max {3，3}＝3，若关于x 的函数为y ＝max （2x ﹣1，﹣x +2}，则该函数的最小值是（ ）A ．2B ．1C ．0D ．﹣13．如图，在平面直角坐标系中，点A ，B 分别在x 轴和y 轴上，2OB OA =，AOB ∠的角平分线与OA 的垂直平分线交于点C ，与AB 交于点D ，反比例函数k y x=的图象过点C ，当ACD △面积为1时，k 的值为（ ）A ．1B ．2C ．3D ．44．若直线y x m =-+与直线24y x =+的交点在第一象限，则m 的取值范围是（ ）．A ．4m ≥B ．1m ≥-C ．4m >D ．1m >-5．已知两直线()0y kx k k =+≠与36y x =-相交于第四象限，则k 的取值范围是（ ）A ．60k -<<B ．30k -<<C ．3k <-D ．6k <-6．如图，在平面直角坐标系中，点()()()()1,5,4,1,,,3,4A B C m m D m m ---+，当四边形 ABCD 的周长最小时，则 m 的值为（ ）．A B ．32 C ．2 D ．37．如图，等腰Rt△ABC 中，BC ＝AC 为斜边向右做等腰Rt△ACD ，点E 是线段CD 的中点，连接 AE ．作线段CE 关于直线AC 的对称线段CF ，连接BF ，并延长BF 交线段AE 于点G ，则线段BG 长为（ ）A ．B ．C ．D ．8．已知直线l 1：y ＝kx+b 与直线l 2：y ＝﹣12x+m 都经过C （﹣65，85），直线l 1交y 轴于点B （0，4），交x 轴于点A ，直线l 2交y 轴于点D ，P 为y 轴上任意一点，连接PA 、PC ，有以下说法：△方程组12y kx b y x m =+⎧⎪⎨=-+⎪⎩的解为6585x y ⎧=-⎪⎪⎨⎪=⎪⎩；△△BCD 为直角三角形；△S △ABD ＝6；△当PA+PC 的值最小时，点P 的坐标为（0，1）．其中正确的说法是（ ）A ．△△△B ．△△△C ．△△△D ．△△△△9．在平面直角坐标系中，将函数3y x =的图象向上平移m 个单位长度，使其与36y x =-+的交点在位于第二象限，则m 的取值范围为（ ）A ．6m <B ．6m >C ．2m <D ．2m >10．已知函数222y kx k =++（k 为常数，0k >）的图象经过点(),a b ，且实数a ，b ，k 满足等式：()2224212a k b b bk +++=+，则一次函数()2220y kx k k =++>与y 轴的交点坐标为（ ）A ．()0,2B．()1 C．(0,6- D ．()0,4二、填空题 11．如图，根据函数图象回答问题：方程组3y kx y ax b=+⎧⎨=+⎩的解为_________．12．如图，点A 是一次函数21y x =+图象上的动点，作AC △x 轴与C ，交一次函数4y x =-+的图象于B ．设点A的横坐标为m，当m=____________时，AB=1．13．在平面直角坐标系xOy中，直线y＝﹣x+1与直线y＝﹣2x交于点A，点B（m，0）是x轴上的一个动点，过点B作y轴的平行线分别交直线y＝﹣x+1、直线y＝﹣2x于C、D两点，若5ACDS=，则m的值为____________．14．若函数y＝2x+b的图象与两坐标轴围成的三角形面积为4，那么b＝_______．15．如图，已知一次函数y＝－53x＋6的图像与x轴，y轴分别相交于点A、B，与一次函数y＝13x的图像相交于点C，若点Q在直线AB上，且△OCQ的面积等于12，则点Q的坐标为__________________．16．已知平面直角坐标系中，O为坐标原点，点A坐标为（0，8），点B坐标为（4，0），点E是直线y=x+4上的一个动点，若△EAB=△ABO，则点E的坐标为_____________．17．如图，在平面直角坐标系xOy 中，直线y ＝﹣x ﹣2与x 轴，y 轴分别交于点D ，C ．点G ，H 是线段CD 上的两个动点，且△GOH ＝45°，过点G 作GA△x 轴于A ，过点H 作HB△y 轴于B ，延长AG ，BH 交于点E ，则过点E 的反比例函数y ＝k x的解析式为_____．18．已知直线11y k x b =+与直线22y k x b =+的交点坐标为()2,3-，则直线11y k x b =-与直线22y k x b =-的交点坐标为____________．19．对于实数a ，b ，我们定义符号max{a ，b}的意义为：当a≥b 时，max{a ，b}＝a ；当a ＜b 时，max{a ，b]＝b ；如：max{4，﹣2}＝4，max{3，3}＝3，若关于x 的函数为y ＝max{x+3，﹣x+1}，则该函数的最小值是_____．20．若直线112y x =-与直线31y kx k =++交于点(,)P m n ，且函数31y kx k =++的值随x 值的增大而减小，则m 的取值范围是______．三、解答题21．如图1，直线AB 的解析式为6y kx =+，D 点坐标为()8,0，O 点关于直线AB 的对称点C 点在直线AD 上．（1）求直线AD 、AB 的解析式；（2）如图2，若OC 交AB 于点E ，在线段AD 上是否存在一点F ，使ABC ∆与AEF ∆的面积相等，若存在求出F 点坐标，若不存在，请说明理由；（3）如图3，过点D 的直线:l y mx b =+.当它与直线AB 夹角等于45︒时，求出相应m 的值．22．定义：图象与x 轴有两个交点的函数y ＝24(),24()x x m x x m -+≥⎧⎨+<⎩．叫做关于m 的对称函数，它与x 轴负半轴交点记为A ，与x 轴正半轴交点记为B ，（1）关于l 的对称函数y ＝24(1),24(1)x x x x -+≥⎧⎨+<⎩．与直线x ＝1交于点C ，如图． △直接写出点的坐标：A （ ，0）；B （ ，0）；C （1， ）；△P 为关于l 的对称函数图象上一点（点P 不与点C 重合），当=ABC ABP S S 时，求点P 的坐标； （2）当直线y ＝x 与关于m 的对称函数有两个交点时，求m 的取值范围．23．如图1，直线11:32l y x =-+与坐标轴分别交于点A 、B ，与直线2:l y x =交于点C ．（1）求A 、C 两点的坐标；（2）如图2，若有一条垂直于x 轴的直线l 以每秒1个单位的速度从点A 出发沿射线AO 方向作匀速滑动，分别交直线1l 、2l 及x 轴于点M 、N 和Q ．设运动时间为()s t ，连接CQ ．△当2OA MN =时，求t 的值．△若四边形CMEN 为平行四边形，试求出E 点的坐标；（3）试探究在坐标平面内是否存在点P ，使得以O 、Q 、C 、P 为顶点的四边形构成菱形？若存在，请直．接写出．．．t 的值；若不存在，请说明理由．24．在平面直角坐标系中，点A 坐标为(0,)n ， 点B 坐标为(,0)m -，点C 坐标为(,0)m ，且m 、n 满足方程组32120m n m n +=⎧⎨-=⎩． （1）如图1，直接写出点A 和点B 的坐标；（2）如图2，在线段AB 上有一点D （点D 不与A 、B 重合），过点D 作AB 的垂线，分别交y 轴和线段AC 于点E 和点F ，连接DO ，若2AFD AOD ∠=∠，求BDO ∠的度数；（3）如图3，在（2）的条件下，延长DF 交x 轴于点G ，若EO CG =，连接BF 交AO 于点K ，求点K 的坐标．25．如图，在平面直角坐标系中，点O 为坐标原点．△ABO 的顶点A 在y 轴的正半轴上，且OA =16，顶点B 在x 轴正半轴上，且B （12，0），BE 是△ABO 的角平分线，且AB =20．（1）直接写出E 点坐标；（2）点D 是射线BO 上的一个动点（点D 不与点B 、点O 重合），连接DE ，设D 点的横坐标为t ，△BDE 的面积为S ，求S 与t 的关系式，并直接写出t 的取值范围；（3）在（2）的条件下，如图3，当点D 在线段OB 上，连接AD ，AD 、BE 相交于点F ，过点F 作FM △AD 交AB 于点M ，FN △BE 交AB 于点N ，当S =20时，求线段MN 的长度．26．定义：如果一条直线把一个平面图形的面积分成相等的两部分，我们把这条直线称为平面图形的一条面积等分线．（1）如图1，已知ABC ，请用尺规作出ABC 的一条面积等分线．（2）已知：如图2，在平面直角坐标系xOy 中，矩形OABC 的边OA 在x 轴的正半轴上、OC 在y 轴的正半轴上，6,4OA OC ==．△请判断直线4833y x =-是否为矩形OABC 的面积等分线，并说明理由； △若矩形OABC 的面积等分线与坐标轴所围成的三角形面积为4，请直接写出此面积等分线的函数表达式． （3）如图3，在ABC 中，点A 的坐标为()2,0-，点B 的坐标为()4,3，点C 的坐标为()2,0，点D 的坐标()0,2-，求过点D 的一条ABC 的面积等分线的解析式．（4）在ABC 中点A 的坐标为()1,0-，点B 的坐标为()1,0，点C 的坐标为()0,1，直线()0y ax b a =+>是ABC 的一条面积等分线，请直接写出b 的取值范围．27．平面直角坐标系中，直线11:32l y x =-+与x 轴交于点A ，与y 轴交于点B ，直线2:2l y kx k =+与x 轴交于点C ，与直线1l 交于点P ．（1）当1k =时，求点P 的坐标；（2）如图1，点D 为PA 的中点，过点D 作DE x ⊥轴于E ，交直线2l 于点F ，若2DF DE =，求k 的值； （3）如图2，点P 在第二象限内，PM x ⊥轴于M ，以PM 为边向左作正方形PMNQ ，NQ 的延长线交直线1l 于点R ，若PR PC =，求点P 的坐标．28．已知：在平面直角坐标系中，直线4x =与直线(1)2y m x m =+-交于点A ．（1）请证明：无论m 为何值，直线(1)2y m x m =+-，总经过点()2,2．（2）当12m =-时，求点A 的坐标． （3）函数1(04)y x x=<≤的图像与直线4x =、直线(1)2y m x m =+-围成的封闭区域（不含边界）为W ，横纵坐标都为整数的点叫做整点．△当12m =-时，画出函数图像，并直接写出区域W 内整点的个数． △当区域W 内恰好有三个整点时，直接写出m 的取值范围．29．如图，在平面直角坐标系中，直线y ＝﹣0.5x ＋2与x 轴，y 轴分别交于点A 和点B ，与直线y ＝x 交于点C 、P （m ，0）为x 轴上一动点（P 不与原点重合），过P 作x 轴垂线与直线y ＝x 和y ＝﹣0.5x ＋2分别交于点M 和点N ，过N 作x 轴的平行线交直线y ＝x 于D ．（1）求C 点坐标；（2）求当MN ＝OB 时，m 的值；并直接写出此时四边形COPN 的面积＝ ；（3）直接写出当DN ＝2NP 时，m 的值＝ ；（4）过D 作y 轴平行线交直线AB 于点E ，P 点在运动过程中，MN DE的值＝ ．x+3，与x轴、y轴30．如图，在平面直角坐标系中，直线l1的解析式为y＝x，直线l2的解析式为y＝﹣12分别交于点A、点B，直线l1与l2交于点C．（1）求出点A、点B的坐标；（2）求△COB的面积；（3）在y轴上是否存在一点P，使得△PBC为等腰三角形？若存在，请直接写出点P坐标，若不存在，请说明理由．。

小学四年级尖子生语文辅导拔高训练第10讲分析人物形象【学生版】细节描写：写人起特殊作用的细小情节，生活小事、动作、语言、神态等。

品味细节，会感到人物思想品质更鲜明，人物形象更生动、富有生活气息。

外貌（肖像）：容貌、神情、姿态、服饰等方面的描绘。

人物的外貌往往反映人物的个性与内心，以塑造栩栩如生的人物形象、内心变化、个性特点。

语言：人物的语言，往往能反映人物一定的思想、个性和心理特点，读书时分析揣摩人物的语言有助于我们加深对人物的理解。

动作：动作同样能反映个性。

多在动作描写上注意，琢磨其特别的地方，即不同职业和性格的人物。

一些与众不同的动作，又会深化人物的性格特点。

心理活动：对思想活动的描写。

直接反映内心世界，鲜活、生动的人物个性往往是靠许多心理描写。

深刻表现人物特点。

会给读者留下极深刻的印象。

神态：通过对人物的面部神情表现，写出人物的心理或对某件事物的反应。

要求抓住人物面部最具表现力的神情，比如说眼睛、脸色、嘴巴等，来表现人物。

1、学会分析刻画人物的技巧。

2、学会用细节描写的方法分析文章中的人物形象。

地震中的父与子1989年发生在美国洛杉矶一带的大地震，在不到4分钟的时间里，使30万人受到伤害。

在混乱和废墟中，一个年轻的父亲安顿好受伤的妻子，便冲向他7岁的儿子上学的学校。

他眼前，昔日充满孩子们欢声笑语的漂亮的三层教室楼，已变成一片废墟。

他顿时感到眼前一片漆黑，大喊：“阿曼达，我的儿子！”跪在地上大哭了一阵后，他猛地想起自己常对儿子说的一句话：“不论发生什么，我总会跟你在一起！”他坚定地站起身，向那片废墟走去。

他知道儿子的教室在楼的—层左后角处。

他疾步走到那里，开始动手。

在他清理挖掘时，不断地有孩子的父母急匆匆地赶来，看到这片废墟，他们痛哭并大喊：“我的儿子！”“我的女儿！”喊过后，他们绝望地离开了。

有些人上来拉住这位父亲：“太晚了，他们已经死了。

”这位父亲双眼直直地看着好心人，问道：“谁愿意来帮助我?”没人给他肯定的回答，他便埋头接着挖。