云南省民族大学附属中学2020届高考英语第一次仿真模拟试题
云南省民族大学附属中学2020届高考英语第一次仿真模拟试题 （考试时间 100 分钟 ，满分 120 分） 注意事项： 1.答题前，考生务必用黑色碳素笔将自己的考号、姓名、考场、座位号、班级在答题卡上 填写清楚。 2.每小题选出答案后，用 2B 铅笔把答题卡上对应的题目的答案标号涂黑。如需改动，用橡 皮擦干净后，再选涂其他答案标号。在试卷上作答无效。
第一部分 阅读理解（共两节，满分 40 分） 第一节 (共 15 小题；每小题 2 分，满分 30 分) 阅读下列短文，从每题所给的四个选项(A、B、C 和 D)中, 选出最佳选项。并在答题卡上 将该选项涂黑．
A New York's best classes for after-school kids include sports classes, performing arts classes, art classes and language programs. Make sure your kids are ready for new adventures with these super-cool offerings! 92nd Street Y Classes At this institution your musicians can learn how to play instruments. After-school classes examine different musical pieces and encourage teamwork in a group setting. At the end of the program, mini Mozarts can impress their family and friends at open-house concerts. Plus, when they're not jamming, kids can take advantage of homework help in the Clubhouse, where they are divided up by grade level. Ages 5-15. The Cliffs at LIC After a day of fighting academic courses at school, your favorite achievers can reach heights on a rock-climbing wall. The Cliffs' offerings allow developing bodies to build muscle strength. For example, introductory sessions teach climbers how to safely tie knots ( 结 ) as well as other basics,
mastering them with hands-on games and activities. The Cliffs at LIC, Long Island City. Ages 6-18.
Staten Island Skating Pavilion This large area maintains ( 维持) its year-round frosty temperatures for ice-skating fun.
Courses are offered every day for a variety of interests and skill levels, and public and freestyle sessions are available to children who want to spend some afternoons there without instruction. Ages 4-15. West Side YMCA If your children want to learn how to swim, you'd be hard-pressed to find more options than those offered here. Kids are grouped by age and ability. The courses cover personal safety and swimming techniques. If your children prefer dry land ， the West Side YMCA also offers dance, basketball and football. Visit our website for class descriptions and price information. Ages 5-18. 1．Which of the following offers homework help? A．The Cliffs at LIC． B．West Side YMCA． C．92nd Street Y Classes. D．Staten Island Skating Pavilion. 2．What can participants do at Staten Island Skating Pavilion? A．Learn basic climbing skills. B．Enjoy skating all year around. C．Try a variety of outdoor sports. D．Start skating at the age of three. 3．Who is the text intended for? A．Senior high school teachers. B．Children around school age. C．Adults looking for relaxation. D．Parents with children of school age.
B Adventure-seeker Emma broke her ankle when she fell awkwardly while climbing a rock and spent a week in hospital waiting for an operation on her foot. When she was sent home to recover under strict instructions not to bear any weight, she became so fearful of crutches ( 拐 杖 ) that she
didn't move for three weeks. “I tried crutches but I kept falling over and injuring myself. So I literally just stayed on the sofa all day, ” says Emma. She was gutted at the thought of missing the Wolf Run — a quarterly event that she hasn't missed since 2014. “If you complete four Wolf Runs in a year, one in each season, you get Alpha Wolf status,” explains Emma. “This year was going to be my fifth in a row as an Alpha Wolf and I was really upset that I'd lose my status.” So she was willing to try anything to get through the course — even with her injured ankle. “I was telling my friend that I was going to cancel, and he persuaded me to give it a go. Having something to aim for really kept me going." Emma completed the run wearing an iWALK2.0, which is a medically-approved device and it basically functions like a hi-tech artificial leg, allowing users to walk freely. I decided to get one and it completely changed my recovery. I could move around the house and start getting out and about again, which had a real impact on my mental well-being.” On the day of the race, Emma was nervous but the sound of people cheering her on kept her motivated. Emma made it over the finish line in just under six hours and clocked up her 23rd Wolf Run in five years. “It was an incredible day and my determination to finish combined with the support I received along the way kept me going,” says Emma. 4．Why was Emma frightened to use a crutch? A．She was afraid of recovering slowly. B．She was warned not to move around. C．She just had an operation on her
2020-2021学年云南民族中学高三英语模拟试卷及答案解析
2020-2021学年云南民族中学高三英语模拟试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AIt looks like 2017 is shaping up to be a record-breaking year in movie History. Here is a list of some of the year’s biggest blockbusters so far.Kong: Skull IslandA reboot (重启) of King Kong would normally get laughed at in this day and age, but it looks like this modem version of the story will be worth watching. With US actress Brie Larson and UK actor Tom Hiddleston in the mix, this film is set to be this year’s biggest monster tale.Release Date:3/10/17Beauty and the BeastDirector Bill Condon is bringing back a part of our childhood in live action, complete with the songs we all remember and love. With British stars Emma Watson and Dan Stevens leading thecast, the classic Walt Disney story already sounds like it’ll be a delight for both children and adults.Release Date:3/17/17The Fate of the FuriousThere was doubt that we’d even get a Fast 8, especially after the fitting ending US actor Paul Walker’s character was given at the end of Furious 7. Fans thought they’d never see Dom and the rest of the crew back in action, but thankfully, US star Vin Diesel himself confirmed that The Fate of the Furious is fueling up for another go.Release Date:4/14/17Spider-Man: HomecomingSpider Man is heading home to Marvel Studios for the first time. The movie will show us Peter Parker’s high school days, and will continue the threads we saw formed during his initial appearance in Captain America: Civil War. We know that Michael Keaton is playing The Vulture in this story, and that both Happy Hogan and Tony Stark, played by US actors Jon Favreau and Robert Downey Jr., are along for the ride.Release Date:7/7/171.Which of the following movies can’t you see on May Day?A.Kong: Skull Island.B.Beauty and the Beast.C.The Fate of the Furious.D.Spider-Man: Homecoming.2.What can we know about Beauty and the Beast?A.It is fueling up for another go.B.It is produced by Marvel StudiosC.It’ll show us Peter Parker’s school days.D.It’ll be enjoyable for both children and adults.3.What does the underlined word “cast” probably mean?A.Characters.B.Actors.C.Directors.D.Teachers.BA PhD student inMichigandefended her paper while wearing a skirt madeof rejection letters she received while studying. 29-year-old Caitlin Kirby printed out 17 of her rejection letters — from scholarships, academic journals, and conferences — then folded each one into a fan. She connected them in rows, and by the end she designed the item into a skirt and wore it.She said that the idea behind her unique clothing item came out of a desire to normalize rejection and take pride in overcoming it. "The whole process of revisiting those old letters and making that skirt sort of reminded me that you have to apply to a lot of things to succeed," she said. "A natural part of the process is to get rejected along the way."Caitlin's adviser, Julie Libarkin, a professor of earth and environmental science atMichiganStateUniversity, also encourages the acceptance of failure in her students. Libarkin believes it's important for students to get into habit of applying for things, and to get used to the feeling of rejection, so she encourages them to chase after any opportunity that comes their way. If a student doesn't get the grant or the spot in the academic journal, that's okay. They'll still have learned something in the process.As for Caitlin? Her rejections over the years have led to great things: Since her doctorate, she's won a scholarship to do further research on urban agriculture inGermany.Currently, she's a post-doctoral researcher at the University of Nebraska-Lincoln. As for what the future holds? "I'm prepared to receive a few more rejection letters along the way," she joked heartily, "Maybe I'll make a longer skirt."4. What can we learn about Caitlin Kirby's rejection letters?A. She received 17 rejections in total.B. 29 of her rejections were from journals.C. The rejections were connected into a fan.D. She made some rejection letters into a skirt.5. What is Julie Libarkin's attitude towards Caitlin's action?A. Favorable.B. Ambiguous.C. Skeptical.D. Opposed.6. Which of the following words can best describe Catlin?A. Creative and considerate.B. Caring and determined.C. Optimistic and humorous.D. Generous and intelligent.7. Which of the following may Caitlin agree with?A. Hard work pays off.B. Education is the entrance to success.C. Self-respect earns more respect.D. One needs to normalize failures.CDad’s comb was jade green. I heard he bought it when he married Mum, which made the comb two years older than I was. Every night, he wouldsmile, hand me the comb and say, “Be a good girl and help Daddy clean it, OK?”I was more than happy to do it. At age five this mundane task brought me such joy. I would excitedly turn the tap on, then brush the comb with a used toothbrush as hard as I could. Satisfied that I’d done a good job, I would proudly return the comb to Dad. He would smile at me and place the comb on top of his wallet.About two years later, Dad left his sales job and started his own wholesale business. I started primary school. That was when things started to change. He didn’t come home as much as he used to – just a couple of times a week. And when he did come home, it was always late and I’d already be in bed. I started to get mad. I stopped waiting for him to come home, and stopped going downstairs to check on him.Today, I’m no longer a kid. I’ve graduated from college and got a job. Dad’s business has got back on track. Things are better now. Yet the uncomfortable silence between Dad and me persisted.Two days before my birthday last year, Dad came home early. As usual, I helped him carry his bags into his study. When I turned to leave, he said, “Hey, would you like to help me clean my comb?” I looked at him a while,then took the comb and headed to the sink.I passed the clean comb back to Dad. He looked at it and smiled. But this time, I noticed something different. My dad has aged. He has wrinkles next to his eyes when he smiles, yet his smile is still as heartwarming as before. The smile of a father who just wants a good life for his family. Dad carefully placed his comb on top of his wallet.After so many years, he still organizes his personal items in the same meticulous way. I guess some things never change. And for that, I’m glad.8. What caused the uncomfortable silence between Dad and me?A. Generation gap.B. Dad’s failure in business.C. My ignorance of Dad.D. Dad’s absence from the family.9. Which of the following can best describe Dad?A. Gentle but strict.B. Hardworking and caring.C. Cautious and realistic.D. Demanding but patient.10. Why did Dad ask his daughter to clean his comb before her birthday?A. To give her a lesson.B. To follow his old habit.C. To fix their relationship.D. To praise her helpfulness.11. Which saying concludes the text best?A. Yesterday once more.B. Let bygones be bygones.C. Some things never change.D. Like father, like daughter.DScientists have recently discovered thatAndean condors (秀鹫)— some of the world’s largest birds——barely flap their wings at all while flying. Instead, they use rising air currents to remain in the air for hours.The Andean condor is the world’s largest soaring bird. They can weigh up to 15 kilograms. Their wings, when spread out, measure up to three meters. Their main food source is the meat of large animals which have died. Soaring high in the sky allows condors to easily spot possible meals on the ground.Scientists worked together to study the flight patterns of these huge birds and how much effort the birds use when flying. To study the birds while they were in the sky, the researchers attached special devices which could record every beat of their wings.The scientists learned that most of the condors’ flapping— over 75%— came when the birds were taking off. Once in the sky, the birds flew for very long periods of time without flapping at all. In fact, they only flapped their wings for 1% of the time they were in the air. One bird flew for over five hours without flapping, covering nearly117miles.Soaring without flapping is important because birds bum energy every time they flap their wings.The birds’ soaring isn’t magic. They use the fact that hot air rises to keep themselves up. As hot air rises, it often creates “thermals”— currents of warm air moving upward. The condors soar by making use of these thermals. The tricky part is finding thermals and moving between them.When birds are forced to land and take off again often, it costs them a lot of energy. The researchers learned that to avoid having to land, the condors did most of their non-take-off flapping when they were closer to the ground and looking for a new thermal.The scientists reported that even though all of the condors they studied were young, they knew well how to take advantage of the air currents.12. What can we learn about the Andean condor from the text?A. They live mairly on small animals.B. Their wingspan is at least three meters.C. They rely on hot air to remain high in the sky.D. They are the birds with the strongest flying ability.13. Why was the equipment tied to the birds?A. To measure how far they could fly without flapping.B. To keep track of how often they flapped while flying.C. To calculate the energy required for their flight.D. To confirm their flight patterns.14. Which of the following acts consumes the most energy for a condor?A. Hunting for food.B. Flying in the sky.C. Getting off the ground.D. Landing on the ground.15. What can we infer from the text?A. Condors flap the most when looking for a new thermal.B. No condor can fly for more than five hours without flapping.C. Condors don’t need to look for thermals when soaring in the sky.D. Soaring by using thermals is probably a natural ability of condors.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020年云南民族中学高三英语第一次联考试卷及参考答案
2020年云南民族中学高三英语第一次联考试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AGetting your kid to bed at night is seriously one of the most challenging things you'll ever have to do. Most kids are just so full of energy that they'll tire you out before they're halfway through their store of energy. An easy thing to calm down your child to get into bed is giving in and allowing some iPad screen time. However, it's really not a great idea, just like you thought.Researchers at theArizonaStateUniversityconducted a study with 547 kids between the ages of 7 to 9. Their parents tracked how much screen time the kids were allowed along with their sleep patterns. The study found that kids who did not engage in screen time before bed slept for 23 more minutes every week and also went to sleep about 34 minutes earlier than those playing with iPad. Although that might not seem like so much more time, quality of sleep is vastly important in Children's development.The CDC's (美国疾病控制中心)2018 National Youth Risk Survey outlines that good quality sleep can impact a child's life in many ways, including affecting grades and also weight gain. Students with an "A" average slept for 30 or more minutes per night than those with a "D" or"F" average.A 2018PennsylvaniaStateUniversitystudy showed that children with irregular bedtimes had a higher risk of having increased body weight. Those with consistent and age-appropriate bedtimes when they were 9 years old had a healthier BMI (体质指数)at age 15 than those with irregular bedtimes.Hard as it is, it's really important not to give in and hand over an iPad to your child who is about to go to bed. Just like it's important for adults to go to sleep without any distractions, it's even more important for kids.1. What do the findings of the researchers at theArizonaStateUniversitysuggest?A. More sleep is necessary for children's development.B. Enough sleep helps improve academic performances.C. Screen time before bed leads to later and less sleep.D. Children sleeping irregularly are easy to gain weight.2. What is the text mainly about?A. How is screen time affecting teenagers?B. What are negative effects of irregular bedtimes?C. When should you get your kid to bed at night?D. Why is screen time before bed a bad idea for kids?3. Who is the text intended for?A. Parents.B. Children.C. Teachers.D. Researchers.BConducting interviews for news stories is an important skill for any journalist. To start, do as much research as you can and prepare a list of questions to ask. Once the interview starts, try to develop a rapport(融洽的关系) with your "source"—anyone a journalist interviews, but don't waste your time. If your source starts to talk about things that are clearly of no use to you, don't be afraid to gently but firmly turn the conversationback to the topic at hand.It's an old debate among journalists: Which works better when interviewing a source, taking notes (the old-fashioned way) or using a cassette or digital voice recorder? Both have their advantages and disadvantages. A reporter's notebook and a pen or pencil are the easy-to-use, time-honored tools of the interviewing trade, while recorders enable you to get everything someone says word for word. Which works better? It depends on what kind of story you're doing.Many beginning reporters complain that with a notepad and pen, they can never take down everything a source says in an interview. But you don't have to note everything down. Keep in mind that you're probably not going to use everything they say in your story. So don't worry if youlet slipa few things.So you've done a long interview with a source, you have pages of notes, and you're ready to write. But chances are you'll only be able to choose a few quotes from that information collected directly from the source. Which ones should you use? Reporters often talk about using only "good" quotes for their stories, but what does this mean? Broadly speaking, when someone says something interesting, and says it in an interesting way, that can make a good quote.4. What is a journalist advised to do during an interview?A. Be gentle with the source.B. Carry on a long conversation.C. Make the conversation interesting.D. Prevent the conversation being off-topic.5. What do the underlined words "let slip" in Paragraph 3 mean?A. give awayB. leave outC. get rid ofD. take up6. What is considered as a good quote for a reporter?A. A direct quote.B. An important point of view.C. A piece of basic information.D. Something funny a source says interestingly.7. What is the text mainly about?A. The job of a journalist.B. The process of interviewing.C Some facts about interviewing. D. The relationship between a journalist and a source.CThere are many useful things we can do each day to feel better. It may take some efforts and time to make a habit of drinking 8 glasses of water daily or thinking more positively, but it is well worth it. What things do you do every day to feel better?Probably the healthiest thing you can do to feel better each day is to exercise early in the morning. You don't have to run the whole morning or spend a few hours in the gym. Even doing some easy exercise like walking, sit-ups or jumping the rope will help you feel better in no time!Again, due to our busy schedules, we don't get enough sleep each night. If you have trouble falling asleep, avoid watching TV or surfing the Internet right before bed. Also, try to make healthy bedtime snack choices and don't drink tea or coffee too late in the day.If you drink 3 glasses of water, 4 glasses of coffee or tea and a glass of soda each day and think that you drink enough water, think again. Your body needs water (not coffee or soda!) to function properly. Aiming to drink 7-8 glasses of water each day can make you feel better.Being positive is the key to a longer life. Positive thoughts can help improve your overall heath. Life is full of stressful situations and it's hard to stay cheerful when everything goes wrong, but your positive attitude can help you solve any problem and fight any stress faster and easier. Your positive attitude is especially good for your heart health. Smile, stay positive and live a longer life!8. In the author's opinion which can benefit us most in order that we feel better?A. Sleeping enough.B. Drinking enough water.C. Thinking more positively.D. Taking morning exercise.9. Which of the following agrees with what is said in Paragraph 3?A. Drinking tea or coffee makes us sleep less.B. Drinking tea before bed makes it harder to fall asleep.C. Watching TV or surfing the Internet leads to less sleep.D. Our busy schedules cause more difficulty in falling asleep.10. Why is water necessary to our body?A. Because it can make us feel better.B. Because it can have our body work smoothly.C. Because in can do more good to our body thancoffee.D. Because it can hep avoid feeling thirsty.11. What do we need most when everything goes wrong?A. Thinking positively.B. Thinking out wise ways.C. Having a right attitude.D. Staying cheerful.DIf you easily make mistakes when in a hurry, a new study from Michigan State University—the largest of its kind to date-found that meditation (冥想) could help you improve the situation.The research tested how open monitoring meditation (OMM)—or, meditationthat focuses awareness on feelings or thoughts as they unfold in one’s mind and body—alteredbrain activity in a way that suggested increased error recognition.“People’s interest in meditation is outpacing what science can prove in terms of effects and benefits.” said Jeff Lin, MSU psychology doctoral candidate and study co-author. “But it’s amazing to me that we were able to see how one session of a guided meditation could produce changes to brain activity in non-meditators.”“Some forms of meditation have you focus on a single object, commonly your breath, but open monitoring meditation is a bit different,” Lin said, “It has you tune inward and pay attention to everything going on in your mind and body. The goal is to sit quietly and pay close attention to where the mind travels without getting too caught up in the scenery.”Lin and his MSU co-authors—William Eckerle, Ling Peng and Jason Moser—hired more than 200 participants to test how open monitoring meditation affected how people detect and respond toerrors.The participants, who had never meditated before, were taken through a 20-minute open monitoring meditation exercise while the researchers measured brain activity through electroencephalography (脑电图), or EEG. Then, they completed a computerized distraction (分心) test.“The EEG can measure brain activity at the millisecond level, so we got precise measures of brain activity right after mistakes compared to correct responses,” Lin said. “A certain neural signal occurs about half a second after an error called the error positivity, which is linked to conscious error recognition. We found that the strength of this signal is increased in the meditators to controls.”“These findings show what just 20 minutes of open monitoring meditation can do to improve the brain’s ability to detect and pay attention to mistakes,” Moser said.12. What does the underlined word “altered” in paragraph 2 probably mean?A. Changed.B. Prevented.C. Started.D. Recorded.13. Why is open monitoring meditation different?A. It is just aimed at a single object.B. It clears your mind of everything.C. It gets too caught up in the scenery.D. It focuses on where the mind travels.14. What did the researchers do for the studyA. They hired people who had meditated before.B. They measured the participants’ brain activity.C. They reminded the participants to avoid errors.D. They had non-meditators design a distraction test.15. What is the best title for the text?A. Turn to OMM to Avoid Acting in a HurryB. You’re Able to Recognize Errors ConsciouslyC. Meditators’ Brain Proves Much More ActiveD. OMM Can Help You Make Fewer Mistakes第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020届云南民族大学附属中学高三第一次高考仿真模拟数学(理)试题 (解析版)
2020届云南民族大学附属中学高三第一次高考仿真模拟数学（理）试题一、单选题1．设集合{}2,xA yy x R ==∈∣，{}210B x x =-<∣，则A B =（ ）A ．(1,1)-B ．(0,1)C ．(1,)-+∞D ．(0,)+∞【答案】C【解析】根据指数函数的性质化简集合A ，利用一元二次不等式的解法化简集合B ，再求并集即可. 【详解】集合A 表示函数2xy =的值域， 故(0,)A =+∞.由210x -<，得11x -<<， 故(1,1)B =-. 所以(1,)AB =-+∞.故选：C. 【点睛】本题主要考查指数函数的性质、一元二次不等式的解法以及并集的运算，属于基础题. 2．复数z 满足21z i -+=，则||z 的值是（ ）A ．BCD ．【答案】C【解析】结合复数的模长公式求解即可 【详解】由213z i z i z -+=⇒=-⇒=故选：C 【点睛】本题考查复数的模长公式，属于基础题 3．在ABC ∆中，D 在边AC 上满足12AD DC =，E 为BD 的中点，则CE =（）A．51 63BA BC-B．1536BA BC-C．1536BA BC+D．5163BA BC+【答案】B【解析】根据E为中点，首先易得1122CE CB CD=+，再通过向量加法以及向量的减法和12AD DC=即可得到结果.【详解】如图所示：因为E为BD的中点，所以1122CE CB CD=+，又12AD DC=，23CD CA=∴，12CE CB=∴12111115()23232336CA CB CA CB BA BC BA BC+⨯=+=+-=-，故选B．【点睛】本题主要考查平面向量基本定理的应用，对向量加法和减法的运用较为灵活，属于基础题．4．幂函数()f x xα=的图象过点(3,5)，且1aeα⎛⎫= ⎪⎝⎭，3bα=1log4cα=，则a，b，c的大小关系为（）A．c a b<<B．a c b<<C．a b c<<D．c b a<<【答案】A【解析】根据题意求得参数α，根据对数的运算性质，以及对数函数的单调性即可判断. 【详解】解：依题意，得35α=，故3log5(1,2)α=∈，故3log5101ea⎛⎫<=<⎪⎝⎭，33log51b=>，3log51log04c=<，则c a b<<.故选：A.【点睛】本题考查利用对数函数的单调性比较大小，以及根据幂函数的定义求参数值，考查推理论证能力，属于基础题.5．“函数()2()311f x ax a x =--+在区间[)1+∞，上是增函数”是“01a ≤≤”的（ ）A ．充分不必要条件B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件【答案】C【解析】0a <时，“函数()()2311f x ax a x =--+在区间[)1,+∞上不是增函数”，0a =时，()1f x x =+在[)1,+∞上是增函数，0a >时，令3112a a-≤，得01a <≤，∴“()()2311f x ax a x =--+在区间[)1,+∞上是增函数” 的充分必要条件“01a ≤≤”，故选C.6．已知x ，y 满足条件0{20x y xx y k ≥≤++≤(k 为常数)，若目标函数z ＝x ＋3y 的最大值为8，则k ＝( ) A ．－16 B ．－6C ．-83D ．6【答案】B 【解析】【详解】由z ＝x ＋3y 得y ＝－13x ＋3z ，先作出0{x y x ≥≤的图象，如图所示，因为目标函数z ＝x ＋3y 的最大值为8，所以x ＋3y ＝8与直线y ＝x 的交点为C ，解得C (2,2)，代入直线2x ＋y ＋k ＝0，得k ＝－6.7．已知数列{}n a 的前n 项和n S 满足21n n S a =-.若对任意正整数n 都有10n n S S λ+-<恒成立，则实数λ的取值范围为（ ）A ．(),1-∞B ．12⎛⎫-∞ ⎪⎝⎭，C ．13⎛⎫-∞ ⎪⎝⎭，D ．14⎛⎫-∞ ⎪⎝⎭，【答案】C【解析】先利用1,1,2n nn S n a S S n =⎧=⎨-≥⎩求出数列{}n a 的通项公式，于是可求出n S ，再利用参变量分离法得到1n n S S λ+<，利用数列的单调性求出数列1n n S S +⎧⎫⎨⎬⎩⎭的最小项的值，可得出实数λ的取值范围． 【详解】当1n =时，1121S a =-，即1121a a =-，得11a =；当2n ≥时，由21n n S a =-，得1121n n S a --=-，两式相减得122n n n a a a -=-，得12n n a a -=， 12nn a a -∴=，所以，数列{}n a 为等比数列，且首项为1，公比为2，11122n n n a --∴=⨯=. 12122121n n n n S a -∴=-=⨯-=-，由10n n S S λ+-<，得()()11111112121112221212221n nn n n n n S S λ+++++---<===----， 所以，数列1n n S S +⎧⎫⎨⎬⎩⎭单调递增，其最小项为122211213S S -==-，所以，13λ<， 因此，实数λ的取值范围是1,3⎛⎫-∞ ⎪⎝⎭，故选C ． 【点睛】本题考查利用数列前n 项和求数列的通项，其关系式为1,1,2n nn S n a S S n =⎧=⎨-≥⎩，其次考查了数列不等式与参数的取值范围问题，一般利用参变量分离法转化为数列的最值问题来求解，考查化归与转化问题，属于中等题．8．已知直线l 、m 与平面α、β，l α⊂，m β⊂，则下列命题中正确的是（ ） A ．若//l m ，则必有//αβ B ．若l m ⊥，则必有αβ⊥ C ．若l β⊥，则必有αβ⊥D ．若αβ⊥，则必有m α⊥【答案】C【解析】根据空间点、直线、平面之间的位置关系，结合线线、线面平行垂直的判定和性质，对四个选项逐一判断可得答案. 【详解】解：A .如图所示，设⋂=c αβ，//l c ，//m c 满足条件//l m ，但是α与β不平行，故A 不正确；B .假设//αβ，n β⊂，//n l ，n m ⊥，则满足条件l m ⊥，但是α与β不垂直，故B 不正确；C .若l α⊂，l β⊥，根据面面垂直的判定定理可得αβ⊥，故C 正确；D .设⋂=c αβ，若//l c ，//m c ，虽然αβ⊥，但是可有//m α，故D 不正确， 综上可知：只有C 正确. 故选：C.【点睛】本题考查空间点、直线、平面之间的位置关系，以及线线、线面平行垂直的判定和性质，考查对命题的判断和推理证明思想，属于基础题.9．执行如图所示的程序框图，若输出的S 值为127，则判断框中可以填（ ）A ．5k <？B ．k 6<？C ．7k <？D ．8k <？【答案】C【解析】写出每次循环的运行结果，即可求解. 【详解】由题意知，第一次循环，1S =，1k =；第二次循环，3S =，2k =； 第三次循环，7=S ，3k =；第四次循环，15S =，4k =； 第五次循环，31S =，5k =；第六次循环，63S =，6k =； 第七次循环，127S =，7k =；此时应退出循环，故判断框内可以填入的条件是“7k <？”. 故选：C 【点睛】本题考查了根据程序框图的运行结果补充条件，考查了基本运算能力，属于基础题.10．设1F ，2F 分别为椭圆C ：()222210x y a b a b+=>>的左右焦点，点A ，B 分别为椭圆C 的右顶点和下顶点，且点1F 关于直线AB 的对称点为M .若212MF F F ⊥，则椭圆C 的离心率为（ ）A ．12B ．13C D ．2【答案】C【解析】根据已知求出M 坐标，利用1AB F M ⊥，建立,,a b c 关系，结合222a b c =+，即可求解. 【详解】设()0,M c y ，则1MF 的中点为00,2y N ⎛⎫⎪⎝⎭， 即N 在y 轴上，N 又在直线AB 上， 即点N 与B 重合，故1111AB BF b b AB BF k k a c ⎛⎫⊥⇒=-⇒⋅-=- ⎪⎝⎭222b ac a c ac ⇒=⇒-=210e e ⇒+-=，∴12e =. 故选:C. 【点睛】本题考查椭圆的简单几何性质、点关于直线对称的应用，考查计算求解能力，属于中档题.11．已知六人排成一排拍照，其中甲、乙、丙三人两两不相邻，甲、丁两人必须相邻，则满足要求的排队方法数为（ ） A ．72 B ．96 C ．120 D ．288【答案】A【解析】先把除甲、乙、丙三人外的3人先排好队，然后在排甲，再排乙、两. 【详解】解：除甲、乙、丙三人外的3人先排好队，共有33A 种，这3人排好队后有4个空位， 甲只能在丁的左边或右边，有12C 种排法，乙、两的排法有：23A ， 共有：33A ×12C ×23A ＝72种排队方法．故选A. 【点睛】本题考查了排列问题，不相邻一般采用插空法，同时要注意特殊优先原则.12．已知可导函数()f x 的定义域为(,0)-∞，其导函数()'f x 满足()2()0xf x f x '->，则不等式2(2020)(2020)(1)0f x x f +-+-<的解集为（ ） A ．(,2021)-∞- B ．(2021,2020)-- C ．(2021,0)-D ．(2020,0)-【答案】B【解析】由题可得当(,0)x ∈-∞时，()2()0xf x f x '->，进而构造函数2()()f x g x x =，可判断()g x 在(,0)-∞上的单调性，进而可将不等式转化为(2020)(1)g x g +<-，利用()g x 的单调性，可求出不等式的解集． 【详解】解：构造2()()(0)f x g x x x =<，则243()2()()2()()x f x x f x xf x f x g x x x ''⋅-⋅-'==，因为()2()0xf x f x '->，则()0g x '< ∴函数()g x 在(,0)-∞上是减函数，∵不等式2(2020)(2020)(1)0f x x f +-+-<，且()2(1)(1)(1)1f g f --==--，等价于()()()()()2220201120201f x f g x +-<=-+-，即为(2020)(1)g x g +<-，所以2020120200x x +>-⎧⎨+<⎩，解得20212020x -<<-．故选：B 【点睛】本题考查函数单调性的应用，构造函数2()()f x g x x =是解决本题的关键，属于中档题．二、填空题13．已知三棱锥P ABC -的体积为3，4APC π∠=，3BPC π∠=，PA AC ⊥，PB BC ⊥，且平面PAC ⊥平面PBC ，则三棱锥P ABC -外接球的表面积为______.【答案】16π【解析】取PC 中点D ，根据条件证明AD ⊥平面PBC ，即是棱锥的高，设棱长求出体积，然后等体积转化，可求得棱长，再确定球心，求得半径得到答案. 【详解】设2PC a =，因为PA AC ⊥，4APC π∠=，所以APC △为等腰直角三角形，PC 边上的高为a ，作AD PC ⊥，垂足为D ，因为平面PAC ⊥平面PBC ，平面PAC平面PBC PC =，AD ⊂平面PAC ，所以AD ⊥平面PBC ，所以点A 到平面PBC 的距离为a ，因为3BPC π∠=，PB BC ⊥，所以PB a =，BC 3a =，21332PBC S a a ==△， 所以21343323P ABC A PBC V V a a --==⨯⋅=，解得2a =， 因为PA AC ⊥，PB BC ⊥，所以PC 的中点为外接球的球心，外接球的半径为2， 所以三棱锥P ABC -外接球的表面积为24216ππ⨯=. 故答案为：16π. 【点睛】本题主要考查空间几何体与球接、切问题的求解方法.14．检测600个某产品的质量（单位：g ），得到的频率分布直方图中，前三组的长方形的高度成等差数列，后三组所对应的长方形的高度成公比为0.5的等比数列，已知检测的质量在100.5~105.5之间的产品数为150，则质量在115.5~120.5的长方形高度为______.【答案】160【解析】利用公式求得产品质量在100.5～105.5之间的频率为15016004=，根据等差数列的性质，可知前3个矩形的面积和为34，则后两个矩形面积和为14，设中间矩形的面积为x ，根据题意，求得13x =，结合题意，进而求得结果. 【详解】由题意知产品质量在100.5～105.5之间的频率为15016004=， 则前3个矩形的面积和为34，后两个矩形面积和为14.设中间矩形的面积为x ，则后两个矩形的面积为12x ，14x ，则111244x x +=，所以13x =，最后一个矩形的面积为112，所以长方形高度为160. 故答案为：160. 【点睛】该题考查的是有关频率分布直方图的问题，涉及到的知识点有频率分布直方图崔颖长方形的面积和为1，结合数列的有关性质建立等量关系式，求得结果，属于简单题目. 15．在平面直角坐标系中，当P(x ，y)不是原点时，定义P 的“伴随点”为2222(,)y xP x y x y-++'；当P 是原点时，定义P 的“伴随点“为它自身，平面曲线C 上所有点的“伴随点”所构成的曲线C '定义为曲线C 的“伴随曲线”.现有下列命题： ①若点A 的“伴随点”是点A '，则点A '的“伴随点”是点A ②单位圆的“伴随曲线”是它自身；③若曲线C 关于x 轴对称，则其“伴随曲线”C '关于y 轴对称；④一条直线的“伴随曲线”是一条直线.其中的真命题是_____________（写出所有真命题的序列）. 【答案】②③【解析】【详解】试题分析：对于①，若令(1,1)P ，则其伴随点为11(,)22P '-，而11(,)22P '-的伴随点为(1,1)--，而不是P ，故错误；对于②，设曲线0(),f x y =关于x 轴对称，则(,)0f x y -=对曲线0(),f x y =表示同一曲线，其伴随曲线分别为2222(,)0y x f x y x y -=++与2222(,)0y xf x y x y--=++也表示同一曲线，又因为其伴随曲线分别为2222(,)0y x f x y x y -=++与2222(,)0y xf x y x y --=++的图象关于y 轴对称，所以正确；③令单位圆上点的坐标为(cos ,sin )P x x 其伴随点为(sin ,cos )P x x '-仍在单位圆上，故正确；对于④，直线y kx b =+上取点后得其伴随点2222(,)y xx y x y-++消参后轨迹是圆，故错误.所以正确的为序号为②③. 【考点】对新定义的理解、函数的对称性.三、双空题16．“今有女善织，日益功疾，初日织五尺，今一月共织九匹三丈．”其白话意译为：“现有一善织布的女子，从第2天开始，每天比前一天多织相同数量的布，第一天织了5尺布，现在一个月（按30天计算）共织布390尺．”则每天增加的数量为____尺，设该女子一个月中第n 天所织布的尺数为n a ，则14151617+++=a a a a ______． 【答案】162952 【解析】设从第2天开始,每天比前一天多织d 尺布,由等差数列前n 项和公式求出1629d =,由此利用等差数列通项公式能求出14151617a a a a +++. 【详解】设从第2天开始,每天比前一天多织d 尺布, 则3030293053902S d ⨯=⨯+=, 解得1629d =,即每天增加的数量为1629， 14151617111113141516a a a a a d a d a d a d ∴+++=+++++++1458a d =+ 1645585229=⨯+⨯=，故答案为1629，52. 【点睛】本题主要考查等差数列的通项公式、等差数列的求和公式，意在考查利用所学知识解决问题的能力，属于中档题.四、解答题17．已知函数2()sin cos 2f x x x x =+-. （1）求()y f x =的最小正周期，并求其单调递减区间；（2）ABC 的内角A ，B ，C 所对的边分别为a ，b ，c ，若()2f A =-，且A 为钝角，2a =，求ABC 面积的最大值.【答案】（1）()f x 最小正周期T π=；单调递减区间为()7,1212k k k Z ππππ⎡⎤++∈⎢⎥⎣⎦；（2【解析】（1）利用二倍角和辅助角公式可化简函数为()sin 23f x x π⎛⎫=+⎪⎝⎭；利用2T πω=可求得最小正周期；令()3222232k x k k Z πππππ+≤+≤+∈解出x 的范围即可得到单调递减区间；（2）由()f A =sin 23A π⎛⎫+= ⎪⎝⎭，根据A 的范围可求出A 的取值；利用余弦定理和基本不等式可求出bc 的最大值，代入三角形面积公式求得结果. 【详解】（1）()21sin cos sin 2cos 2sin 22223f x x x x x x x π⎛⎫=⋅-=+=+ ⎪⎝⎭ ()f x ∴最小正周期：22T ππ== 令()3222232k x k k Z πππππ+≤+≤+∈得：()71212k x k k Z ππππ+≤≤+∈ ()f x ∴的单调递减区间为：()7,1212k k k Z ππππ⎡⎤++∈⎢⎥⎣⎦单调递减区间7,()1212k k k z ππππ⎡⎤++∈⎢⎥⎣⎦. （2）由()3f A =-得：3sin 23A π⎛⎫+=- ⎪⎝⎭,2A ππ⎛⎫∈ ⎪⎝⎭472,333A πππ⎛⎫∴+∈ ⎪⎝⎭ 5233A ππ∴+=，解得：23A π= 由余弦定理2222cos a b c bc A =+-得：2243b c bc bc =++≥（当且仅当b c =时取等号）43bc ∴≤11423sin sin 2233ABC S bc A π∆∴=≤⨯= 即ABC ∆面积的最大值为：33【点睛】本题考查正弦型函数最小正周期和单调区间的求解、解三角形中三角形面积最值的求解问题；涉及到二倍角公式和辅助角公式的应用、余弦定理和三角形面积公式的应用等知识；求解正弦型函数单调区间的常用解法为整体代入的方式，通过与正弦函数图象的对应关系来进行求解.18．《中华人民共和国道路交通安全法》第47条的相关规定：机动车行经人行横道时，应当减速慢行；遇行人正在通过人行横道，应当停车让行，俗称“礼让斑马线”，《中华人民共和国道路交通安全法》 第90条规定：对不礼让行人的驾驶员处以扣3分，罚款50元的处罚.下表是某市一主干路口监控设备所抓拍的5个月内驾驶员不“礼 让斑马线”行为统计数据：（1）请利用所给数据求违章人数y 与月份x 之间的回归直线方程y bx a =+； （2）预测该路口 9月份的不“礼让斑马线”违章驾驶员人数；（3）若从表中3、4月份分别抽取4人和2人，然后再从中任选2 人进行交规调查，求抽到的两人恰好来自同一月份的概率.参考公式：1221n i ii nii x y nxy b xnx==-=-∑∑()()()121niii nii x x y y x x ==--=-∑∑，a y bx =-.【答案】(1) 8.5125.5y x =-+;(2) 49人;(3) 715P =. 【解析】试题分析：（1）计算x ，y 利用公式解得ˆb，ˆˆa y bx =-，从而得解； （2）将9x =代入回归方程即可；（3）设3月份抽取的4位驾驶员编号分别为1234,,,a a a a ，4月份的驾驶员编号分別为12,b b ，列出所有基本事件，利用古典概型计算公式求解即可.试题解析：（1）由表中数据知，3,100x y ==，∴1221ˆni i i n i i x y nxy bx nx ==-=-∑∑141515008.55545-==--，ˆ125.ˆ5a y bx=-=， ∴所求回归直线方程为8.512.5ˆ5yx =-+. （2）由（1）知，令9x =，则8.591ˆ25.549y=-⨯+=人. （3）设3月份抽取的4位驾驶员编号分别为1234,,,a a a a ，4月份的驾驶员编号分別为12,b b .从这6人中任选两人包含以下基本事件()()()()()()()()()()()1213141112232421223431,,,,,,,,,,,,,,,,,,,,,a a a a a a a b a b a a a a a b a b a a a b ,()()()()32414212,,,,,,,a b a b a b b b ,共15个基本事件；其中两个恰好来自同一月份的包含7个基本事件， ∴所求概率为715P =. 点睛：古典概型中基本事件数的探求方法 (1)列举法.(2)树状图法：适合于较为复杂的问题中的基本事件的探求.对于基本事件有“有序”与“无序”区别的题目，常采用树状图法.(3)列表法：适用于多元素基本事件的求解问题，通过列表把复杂的题目简单化、抽象的题目具体化.(4)排列组合法：适用于限制条件较多且元素数目较多的题目.19．如图，在四棱锥P ABCD -中，PA ⊥底面ABCD ，AD AB ⊥，//DC AB ，1PA =，2AB =，2PD BC ==.（1）求证：CD ⊥平面PAD ；（2）若棱PB 上存在异于P 、B 的一点E ，使得二面角E AC P --的余弦值为33，求AE 与平面ABCD 所成角的正弦值. 【答案】（1）证明见解析；（25. 【解析】（1）由AD AB ⊥，//CD AB ，推出CD AD ⊥，再根据PA ⊥平面ABCD ，推出CD PA ⊥，最后根据线面垂直的判定定理，从而可证CD ⊥平面PAD ； （2）根据题设条件建立以A 为坐标原点，以AD ，AB ，AP 所在射线分别为,,x y z 轴的空间直角坐标系，设(),,E x y z ，由PE PB λ→→=得出()0,2,1E λλ-，分别求出平面PAC 与平面EAC 的一个法向量，再根据二面角E AC P --3求得λ，从而可得AE 与平面ABCD 所成角的正弦值． 【详解】 （1）证明：AD AB ⊥，//CD AB ，CD AD ∴⊥，PA ⊥平面ABCD ,CD ⊂平面ABCD ，CD PA ∴⊥，AD PA A =，且,AD PA ⊂平面PAD ，CD 平面PAD .（2）解: 以A 为坐标原点，以AD ，AB ，AP 所在射线， 分别为,,x y z 轴建立空间直角坐标系A xyz -，如图所示，则221AD PD PA=-=，由点C向AB作垂线CH, 则221BH BC AD=-=，∴1DC AH AB BH==-=，∴()()()()0,0,0,0,0,1,0,2,0,1,1,0A PB C，设(),,E x y z，则()(),,1,0,2,1PE x y z PB→→=-=-，∵E在棱PB上，∴PE PBλ→→=（01λ<<），即()(),,10,2,1x y zλ-=-，解得：21xyzλλ=⎧⎪=⎨⎪=-⎩，∴()0,2,1Eλλ-，设平面PAC的法向量()111,,u x y z→=，()()0,0,1,1,1,0AP AC→→==，∴·0·0u APu AC⎧=⎨=⎩，即()()()()111111,,0,0,10,,1,1,00x y zx y z⎧⋅=⎪⎨⋅=⎪⎩，即111zx y=⎧⎨+=⎩，取11x=，则11y =-，则()1,1,0u→=-，设平面EAC的法向量()222,,v x y z→=，()()0,2,1,1,1,0AE ACλλ→→=-=，∴·0·0v AEv AC⎧=⎨=⎩，即()()()()222222,,0,2,10,,1,1,00x y zx y zλλ⎧⋅-=⎪⎨⋅=⎪⎩，即()22222100y z x y λλ⎧+-=⎨+=⎩，取21,x =则22221,(0)11y z λλλλ=-=>--， ∴21,1,1v λλ→⎛⎫=- ⎪-⎝⎭，∴()21,1,01,1,cos u u vv λθ→→→→⎛⎫-⋅- ⎪⋅====⋅，解得：12λ=， ∴10,1,2⎛⎫ ⎪⎝⎭E ，10,1,2AE →⎛⎫= ⎪⎝⎭，易知平面ABCD 的法向量()0,0,1m →=，所以AE 与平面ABCD所成角的正弦值1sin Em AEm A α→→→→⋅===⋅【点睛】本题考查线面垂直的判定定理，以及利用空间向量求二面角和线面角，空间向量解答立体几何问题的一般步骤是：（1）观察图形，建立恰当的空间直角坐标系；（2）写出相应点的坐标，求出相应直线的方向向量；（3）设出相应平面的法向量，利用两向量垂直数量积为零列出方程组求出法向量；（4）将空间位置关系转化为向量关系；（5）根据定理结论求出相应的角和距离.20．已知椭圆E ：22221x y a b +=（0a b >>，1F ，2F 分别为E 的左、右焦点，过E 的右焦点2F 作x 轴的垂线交E 于A ，B 两点，1F AB． （1）求椭圆E 的方程；（2）是否存在与x 轴不垂直的直线l 与E 交于C ，D 两点，且弦CD 的垂直平分线过E 的右焦点2F ？若存在，求出直线l 的方程；若不存在，请说明理由．【答案】（1）2212x y +=，（2）不存在，理由见解析.【解析】（1）根据离心率得2c a =，根据1F AB ．得21222b c a ⨯⨯=，从而解得221.2b a ==，可得椭圆E 的方程；（2）假设存在与x 轴不垂直的直线l 满足题意，设:(0)=+≠l y kx m k ，代入2212x y +=，设11(,)C x y ，22(,)D x y ，根据判别式可得2212k m +>，根据韦达定理得弦CD 的中点坐标，可求得弦CD 的垂直平分线方程，将2F 代入可得212k m k+=-，将其代入2212k m +>，得210k +<无解，故不存在符合题意的直线l . 【详解】（1）依题意2c a =，22||b AB a =，所以21222b c a ⨯⨯=，即21b =，所以2221a c b -==，所以22112a a -=，所以22a =， 所以椭圆E 的方程为2212x y +=.（2）假设存在与x 轴不垂直的直线l 满足题意，设:(0)=+≠l y kx m k ，将其代入2212x y +=，整理得222(12)4220k x kmx m +++-=， 所以2222164(12)(22)0k m k m ∆=-+->，所以2212k m +>， 设11(,)C x y ，22(,)D x y ，则122412kmx x k +=-+，则1212y y kx m kx m +=+++2122242()221212k m mk x x m m k k =++=-+=++， 所以CD 的中点为M 222(,)1212km mk k -++，所以弦CD 的垂直平分线方程为2212()1212m kmy x k k k-=-+++， 因为弦CD 的垂直平分线过E 的右焦点2F (1,0)， 所以22120(1)1212m kmk k k -=--++，所以212k m k+=-，将其代入2212k m +>，得2222(12)12k k k ++>， 化简得210k +<，此不等式不成立， 所以不存在符合题意的直线l .【点睛】本题考查了求椭圆的标准方程，考查了直线与椭圆的位置关系，考查了运算求解能力，属于中档题.21．已知函数1()(21)ln 2()f x a x ax a R x=---∈ （1）0a =时，求函数()f x 的极值； （2）0a ≠时，讨论函数()f x 的单调区间.【答案】（1）极大值-1，无极小值；（2）答案不唯一，具体见解析. 【解析】（1）0a =时，1()ln f x x x=--，定义域为(0,)+∞，()0f x '=，求出极值点，逐个区间判断导函数正负，即可得解；（2）求导可得：22222112(21)1(1)(21)()2a ax a x x ax f x a x x x x--+-+-++'=+-==，再进行分类讨论即可得解. 【详解】（1）0a =时，1()ln f x x x=--，定义域为(0,)+∞， 22111()xf x x x x-'=-+=，令()0f x '=得1x =，x ，()'f x ，()f x 的变化如下表：所以()f x 只有极大值(1)1f =-，无极小值；（2）由22222112(21)1(1)(21)()2a ax a x x ax f x a x x x x--+-+-++'=+-==， 令()0f x =得11x =，212x a=-，①当12a <-时，1012a<-<，所以()0f x '<解得112x a -<<； ()0f x '>解得102x a <<-或1x >； 此时()f x 的单调递增区间是10,2a ⎛⎫-⎪⎝⎭和(1,)+∞， 单调递减区间是1,12a ⎛⎫-⎪⎝⎭； ②当12a =-时.()0f x '≥恒成立， 此时()f x 的单调递增区间是(0,)+∞，无单调递减区间； ③当102a -<<时，112a ->， 所以()0f x '<解得112x a<<-， ()0f x '>解得12x a>-或01x <<， 此时()f x 的单调递增区间是(0,1)和1,2a ⎛⎫-+∞ ⎪⎝⎭， 单调递减区间是11,2a ⎛⎫-⎪⎝⎭； ④当0a >时，102a-<，所以()0f x '<解得1x >； ()0f x '>解得01x <<，此时()f x 的单调递增区间是(0,1)， 单调递减区间是(1,)+∞. 综上可知：12a <-时， ()f x 的单调递增区间是10,2a ⎛⎫-⎪⎝⎭和(1,)+∞， 单调递减区间是1,12a ⎛⎫-⎪⎝⎭； 12a =时，()f x 的单调递增区间是(0,)+∞，无单调递减区间；102a -<<时，()f x 的单调递增区间是(0,1)和1,2a ⎛⎫-+∞ ⎪⎝⎭， 单调递减区间是11,2a ⎛⎫- ⎪⎝⎭； 0a >时，()f x 的单调递增区间是(0,1)，单调递减区间是(1,)+∞.【点睛】本题考查了利用导数研究函数的单调性，考查了极值点和单调性的关系，同时考查了分类讨论思想，关键点是找到讨论点，计算量相对较大，属于难题.22．在直角坐标系xOy 中，以坐标原点O 为极点，x 轴正半轴为极轴建立极坐标系，曲线1C 的极坐标方程为4sin ρθ=，曲线2C 的极坐标方程为sin 26πρθ⎛⎫+= ⎪⎝⎭. （1）求曲线1C 、2C 的直角坐标方程;（2）设曲线1C 、2C 交于点A 、B ，曲线2C 与x 轴交于点E ，求线段AB 的中点到点E 的距离.【答案】（1）()221:24C x y +-=，2:40C x -=；（2）1.【解析】（1）将曲线1C 的极坐标方程变形为24sin 0ρρθ-=，将曲线2C 的极坐标方程变形为cos sin 40ρθθ+-=，由222cos sin x y x y ρρθρθ⎧=+⎪=⎨⎪=⎩可将曲线1C 、2C 的极坐标方程化为直角坐标方程；（2）可得出点()4,0E 以及直线2C 的倾斜角为56π，写出直线2C 的参数方程，并将直线2C 的参数方程与曲线1C 的直角坐标方程联立，列出韦达定理，可得出线段AB 的中点所对应的参数，进而可求得线段AB 的中点到点E 的距离.【详解】（1）曲线1C 的极坐标方程可以化为24sin 0ρρθ-=，所以曲线1C 的直角坐标方程为2240x y y +-=，即()2224x y +-=. 曲线2C的极坐标方程可以化为1cos sin 2022ρθρθ+-=， 所以曲线2C的直角坐标方程为40x -=；（2）易知点E 的坐标为()4,0，直线2C 的倾斜角为56π， 所以2C的参数方程为412x y t ⎧=⎪⎪⎨⎪=⎪⎩（t 为参数）.将2C 的参数方程代入曲线1C的直角坐标方程得221+2442t ⎝⎛⎪⎫-= ⎪⎝ ⎪⎭⎛⎫-⎭，整理得()22160t t -+=，判别式()2264120∆=-=>， 设A 、B 对应的参数分别为1t 、2t ，则线段AB的中点对应的参数为1212t t +=， 所以线段AB 的中点到点E的距离为1.【点睛】 本题考查极坐标方程与普通方程之间的相互转化，同时也考查了利用直线的参数方程解决实际问题，考查计算能力，属于中等题.23．已知函数2()4f x x ax =-++，()|1||1|g x x x =++-（1）当2a =时，求不等式()()f x g x ≥的解集；（2）若不等式()()f x g x ≥的解集包含11,22⎡⎤-⎢⎥⎣⎦，求a 的取值范围. 【答案】（1）{12}x x -≤≤∣；（2）77,22⎡⎤-⎢⎥⎣⎦. 【解析】（1）分段讨论可求出不等式的解集；（2）不等式()()f x g x ≥的解集包含11,22⎡⎤-⎢⎥⎣⎦等价于当11,22x ⎡⎤∈-⎢⎥⎣⎦时，()2f x ≥，列出不等式求解即可.【详解】（1）当2a =时，不等式()()f x g x ≥等价于224|1||1|0x x x x --+-++≤①， 当1x <-时，①式化为2440x x --≤，无解；当11x -≤≤时，①式化为2220x x --≤，解得11x ≤≤；当1x >时，①式化为240x -≤，解得12x <≤.综上，()()f x g x ≥的解集为{12}x x ≤≤∣.（2）当11,22x ⎡⎤∈-⎢⎥⎣⎦时，()2g x =， 所以()()f x g x ≥的解集包含11,22⎡⎤-⎢⎥⎣⎦， 等价于当11,22x ⎡⎤∈-⎢⎥⎣⎦时，()2f x ≥. 又()f x 在11,22⎡⎤-⎢⎥⎣⎦的最小值必为12f ⎛⎫- ⎪⎝⎭与12f ⎛⎫ ⎪⎝⎭之一， 所以122f ⎛⎫-≥ ⎪⎝⎭且122f ⎛⎫≥ ⎪⎝⎭， 得7722a -≤≤，所以a 的取值范围为77,22⎡⎤-⎢⎥⎣⎦.【点睛】本题考查含有绝对值不等式的解法，属于中档题.。
云南省民族大学附属中学2020届高考文综第一次仿真模拟试题答案
高考仿真模拟卷1 地理答案36.（22分）（1）.河流数量多；向心状水系（河流由四周流向中心）；流程短；流域面积小。
（任答两点，共4分。
其他言之有理，酌情给分；根据试题用途和使用学段，如果要增加难度则每个点1分）（2）. 特征：夏季（7—8月）降水量与蒸发量差值大于0（降水量大于蒸发量）；春秋冬三季（9月到次年6月）降水量与蒸发量差值小于0（蒸发量大于降水量）；差值最大出现在春季（4月）；（任答两点，共4分。
其他言之有理，酌情给分）（3）.流域内降水量偏少且季节变化大，多为季节性河流，入湖水量少；流域内蒸发量远大于降水量，湖泊水亏损严重；湖泊水位大幅下降，低于南部金沙江与程河的分水岭处河床；全球气候变暖，降水减少，蒸发进一步加剧；流域内人口增多，原生植被破坏严重，植被涵养水源能力下降；人口增多，生活用水量剧增，截留入湖河流；耕地增多，引水灌溉；沿岸的螺旋藻生产大量引水。
（任答4点，两个点是自然，两个点是人为，各4分，共8分。
其他言之有理，酌情给分）（4）.科学规划，跨流域调水，实施程海补水工程；因地制宜，在程海流域实施植被恢复工程，逐步恢复上游的水源涵养和水土保持功能；调整农业的种植结构，发展节水农业；控制流域内人口增长，对于生态脆弱区实施人口外迁；加强用水管理，增强节水意识；整合螺旋藻产业，增加科技投入，加强水资源循环利用；提高用水效率，控制需水量的增长；（任答4点，共8分。
其他言之有理，酌情给分）37．（24分）（1）先出口产品，可以了解本土客户的市场需求；提高产品知名度；提高市场占有率；后投资建厂可以合理设计工厂的规模，降低风险。
（任答三点待6分）（2）巴西热带地区面积广，人口众多；经济发展速度快，对空调的市场需求量大；巴西主体位于南半球，发展巴西市场，利于空调销售市场的稳定（调节销售淡旺季）。
（任答三点得6分）（3）巴西土地成本低、劳动力丰富廉价，生产成本降低；规避关税，降低成本；靠近市场，降低运输成本；灵活应对当地帀场变化。
云南民族大学附属中学2020届高三下学期第一次高考仿真模拟考试文综历史答案
绝密★启用前
云南民族大学附属中学
2020届高三毕业班下学期第一次高考仿真模拟考试文综-历史试题参考答案
40．（25分）
（1）相同：政府采取相应措施；关注灾后救济。
（4分）
不同：明朝官方与民间救济相结合；缺乏科学措施，依靠封建迷
信。
（3分）
英国科学防疫，措施详细；关注公共卫生；坚定人的作用。
（5分）
（2）特点：卫生防疫体系起步较晚；防治结合；重城市轻乡村；形成
中央到地方的防疫体系；利用西方相关成果；（任答三点
得6分）
意义：有利于防疫治疫,医疗技术进步；提高民众卫生意识；促进
城市发展；有利于社会稳定、发展；有利于中国的近代化。
（任答四点得7分）
1。
2020年云南民族中学高三英语第一次联考试卷及答案解析
2020年云南民族中学高三英语第一次联考试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项ANothing beats live music, but the venue makes a difference. When you're able to score tickets to an incredible concert in an incredible place, you won't forget the experience. Here are some of the coolest music venues from around the world. If you haven't been to any of these, you've got some traveling to do.Red Rocks, Morrison, the United StatesRed Rocks might be the most beautiful and famous venue in the United States. At 6,450 feet above sea level, Red Rocks is a geologically formed natural stage. Its massive sandstone provides a perfect stage for jam bands. If you're into the blues and jazz, you'll have no trouble finding something in line with your interests.Meet Factory, Prague, Czech RepublicSmallest venues on this list, Meet Factory is an art gallery, theater, and music venue. The venue only accommodates 1,000 people, so you won't see any huge names come through. Still, it's a great place to see up-and-coming local acts, and if you've got an eye for contemporary art, you'll love your time here.Arena of NÎmes, NÎmes, FranceOriginally built around A. D. 70, the Arena of Nimes presents concertgoers with an interesting question: Should they enjoy the music, or marvel at the architecture? The Arena is, after all, one of the world's best-preserved Roman theaters. Many major touring acts plan stops at the Arena of Nimes, especially during the venue's annual festival.Sydney Opera House, Sydney, AustraliaThe Sydney Opera House is one of the world's most famous performing venues. I's also one of the most distinctive buildings in Sydney, thanks to the breathtaking design by Danish architect Utzon. It hosts about 40 events per week, so whether you're into jazz, rock, classical music, or opera, you'll find something to watch.1.Where can you enjoy music in natural beauty?A.At Red Rocks.B.At Meet Factory.C.At Arena of Nimes.D.At Sydney Opera House.2.What is special about Meet Factory?A.It enjoys breathtaking scenery.B.It hosts both musical and artistic events.C.It is the largest venue of all.D.It is famous for contemporary music.3.What do the listed music venues have in common?A.They have a long history.B.They are built near the sea.C.They accommodate thousands of people.D.They are beautiful tourist attractions.BA year ago I received a full scholarship to attend the University of San Francisco. All of my hard work paid off. My mom had spent a lot on my attending a private high school, so I made sure to push myself: I volunteered, took part in various clubs, and graduated with honors. I was so excited to start a new part of my life.Soon enough, the big day came, but it wasn't like what I had thought. The first two weeks were the most difficult days of my entire life. Every night I would cry myself to sleep. I was missing my family, my home and everything in my hometown so much and I didn’t know how to deal with my broken heart.To distract myself, I threw myself into my studies. I also found a ton of jobs. In any free time, I started forcing myself to go to the gym. I wanted to keep every part of my day busy so I wouldn’t think about how lonely I felt. Soon after, I began to control my eating, considering it another solution to my homesickness. But soon there was something wrong with me.Finally, I went to see a doctor. When the doctor told me I had no choice but to take time away from school, I started to fear. How could I stop? School was what I was best at. “I’m not so bad,” I thought in my head. But the result was that I was taken to hospital again a month later and my mother camewoefully. I had to take a semester off from school, and go to the treatment center near my home.If there are girls who are suffering similarly, I hope you know that there is hope and that you should have a positive attitude towards life. Though you may feel alone, there are so many people who can understand your struggle. That’s why I want to share my story.4. Why did the author push herself during high school?A. She wanted to attend the University of San Francisco.B. It cost too much to study in a private school.C. Her parents controlled much of her life.D. Her family put her under pressure,5. What can we know about the author in the first two weeks?A. She couldn't fall asleep because of pressure.B. She couldn't pay attention to her study.C. She couldn't deal with her homesickness.D. She couldn't catch up with others.6. What does the underlined word “woefully” in paragraph 4 mean?A. Sadly.B. Surprisingly.C. Curiously.D. Happily.7. What is the author's purpose in writing this text?A. To look back on her past life.B. To increase her own confidence.C. To express appreciation to her mother.D. To encourage other girls like her to be positive.CIn the Hollywood industry, most of the studios are using AI to make movies for various reasons such as getting the actors out of danger, replacing the actors indifferent scenes, forming appealing atmosphere to enhance（增强）the views, etc.Directors and producers are using VFX (Visual effects), animations and AI to makea model that looks like the actor and replaces the actor's place. In particular, AI is used in scenes where actor shave to produce certain stunts （特技）to develop setups in the studio artificially. VFX is used to later change the internal studio backgroundsto a different place in the movie.There are many movies with two characters of the same actor. When AI was not a part of the film, editors used different methods to show the two aspects of the same actor in one scene, but now AI is being used to form the second character of the same actor and is being performed to the viewers.By a perfect combination of animation, VFX and AI, realistic models are being created. And the most fun part is the fictitious character can hold the face of the actor but the age, hairstyles, and clothing can be changed to create more enhanced looks according to the movie scene and story. With the help of AI, the directors recreating appealing scenes to enhance the thrill and excitement. InJurassic Park,no dinosaurs were running but with the help of AI and visual effects, we could enjoy the scenes and the atmospheres.The directors and the producers direct to form a green screen including the obstacles and those green screens get replaced with the views that are made from AI and VFX, and the actors make the scenes alive and deliver the most suitable action-packed movie scenes. This method also enhances the viewers' experience, which makes the movie a blockbuster（大片）.8. What does the author intend to tell us in paragraph 1?A. How AI helps actors.B. What AI brings to movies.C. Why AI is applied to movies.D. Where AI is made full use of.9. What can we infer from paragraph 3?A. AI can be used as an editor.B. Editors consider AI irreplaceable.C. Editors used many methods to replace AI.D. AI makes what used to be complex scenes easier.10. What's the author's attitude to using VFX, animations and AI in movies?A. Supportive.B. Sceptical.C. Unconcerned.D. Enthusiastic.11. Which of the following could be the best title for thetext?A. What AI Brings Out Hollywood MoviesB. Why AI Is Applied to Hollywood MoviesC. Which Hollywood Movies Make Much Use of AID. How AI Is Being Applied to Hollywood MoviesDAs one of the world’smost popular cultural mediums, cinema is at the leading position at the Taihu World Cultural Forum(论坛), an annual event that aims to improve cultural exchanges. So far this year, Chinese box office has already topped 58 billion yuan, the China Film Administration said. This indicates that China, the world’s second-largest movie market, is closing the gap with the United States, the world’s top cinema market.Cao Yin, director of the program center at China Movie Channel, said that China has 67,000 cinema screens. the most of any country, and the number is expected to increase to 80,000 by the end of next year. Saying that China has signed coproduction agreements with 22 countries (including the United States, Canada, Japan. India etc.) ,Cao added it has deepened cinematic exchanges between Chinese filmmakers and their foreign counterparts (同行).With the country’s huge native market, which produced more than 1,000 films in 2019, Hong Kong director Stanley Tong said he believes foreign filmmakers will increasingly seek cooperation with China. “International coproduction will become an important platform to send Chinese stories oversea and give us a broader vision ofcreation,” Tong said.Recently, over 80 percent of the world’s top 100 highest box-office titles have been action films. Tong said the films, in which plots are basically secondary to shining stunts (特技), is one of the easiest ways to appeal to foreign audiences. But it has been a decades-long struggle for Chinese filmmakers to sell their stories overseas. When asked what kinds of Chinese films would have the most global appeal. Yan Zhaozhu, chairman of the Taihu World Cultural Forum, said stories that address universal issues, such as environmental protection and climate change, are perhaps the best options.12. What is the purpose of the Taihu World Cultural Forum?A. To strengthen cultural exchanges.B. To build more cinemas in China.C. To invite more tourists to Taihu.D. To attract more international investment.13. What can we infer about Cao Yin’s opinion in Paragraph 2?A. Chinese box office has already overtaken the United States so farB. The screens of Chinese cinemas will be world-leading in the futureC. China has signed the most coproduction agreements with other countriesD. There will be more and more cooperations between Chinese filmmakers and other countries.14. How do Chinese filmmakers feel about selling their movies to the world right now?A. Easy.B. Disappointed.C. Challenged.D. Confused.15. What is the best title for the text?A. Box Office: Unclear FutureB. China: Top Second Movie MarketC. Cinema: The Leading Cultural PositionD. Chinese Filmmakers: Severe Competition Situation第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020届云南师大附属中学高三英语模拟试题及答案
2020届云南师大附属中学高三英语模拟试题及答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AIn the age of social distancing, using robots for some health care interactions is a promising way to reduce in-person contact between health care workers and sick patients. However, a key question is how patients will react to a robot entering the room. Researchers from MIT and Brigham and Women’s Hospital recently set out to answer that question.In a study, the team found that a large majority of patients reported that interacting with a health care provider through a video screen fixed on a robot was similar to an in-person interaction with a health care worker.“We’re working on robots that can help provide care to ensure the safety of the patient and the health care workforce. The results of this study give us some confidence that people are ready and willing to join us. In a larger online survey carried out nationwide, we also found that a majority of respondents were open to having robots perform small tasks such as taking a nose swab (拭子).” says Giovanni Traverso, an MIT assistant professor and the senior author of the study.After the COVID-19 pandemic began early last year, Traverso and his colleagues turned their attention toward new strategies to reduce interactions between potentially sick patients and health care workers. To that end, they created a mobile robot that could interact with patients as they waited in the emergency department. The robots were equipped with sensors that allow them to measure vital signs, including skin temperature, breathing rate, and pulse(脉搏) rate. The robots also carried an iPad for remote video communication with a health care provider.The study suggests that it could be worthwhile to develop robots that can perform tasks that currently require a lot of human effort, such as turning a patient over in bed. These days, turning COVID-19 patients onto their stomachs requires several people. Doing Covid-19 tests is another task that takes a lot of time and effort from health care workers, who could be arranged for other tasks if robots could help.1. Why did the researchers from MIT and BWH carry out the studies?A. To shorten the social distance between doctors and patients.B. To figure out the response of patients to robotic doctors.C. To reduce the risk of being infected with coronavirus.D. To ensure the safety of patients during the pandemic.2. What could be learned from the study?A. Robots are not welcomed by patients.B. Robots will soon replace doctors.C. Robots may help to deal with Covid-19 patients.D. Robots can operate on different patients.3. Which of the following is the best title for the text?A. StrengthsAnd Weaknesses In Robot CareB. The Robotic Doctor Will See You NowC. The Robots Speed Up COVID-19 TestingD. The Development Of Robots In HospitalsBAfter finishing his dinner, Lin Xu opened a WeChat mini-program called "Clear Plate" on his phone and took picture of the empty plates. He was then awarded 157 credit points after the image was uploaded and recognized by artificial intelligence.“Users of the app can use their credit to buy gifts, such as books and cellphones to purchase charity meals donated to children in poor rural areas,” Lin said.A nationwide "Clear Your Plate" campaign is gaining steam online. Efforts to stop food waste and promote thrift are also being made by restaurants that have been urged to create an environment in which consumers are reminded not to waste food. They are also encouraged to offer different portion sizes so that customers can have more choices.The “Clear Plate” mini-program has become popular among young Chinese and currently has nearly 1 million users.Liu Jichen, founder of the startup that developed the app, said that the idea popped up at a dinner in 2017, when Liu found that a restaurant would give diners who polished off their food a card and offer small gifts after a certain number of cards had been collected.“Such an idea can be realized online,” Liu said. He formed a team to work on the project.Yet it was quite challenge for the AI system to identify whether the uploaded photos showed empty plates.To make the AI system smarter, Liu and his team, assisted by more than 1,000 others, spent half a year collecting over 100, 000 samples in canteens and restaurants across the country and used the data to train neural network. Dozens of enterprises, institutions and restaurants have contacted the startup to cooperate on theproject.Through the visualized mini-program, people can clearly see the good results of saving food, which will effectively reduce waste, he noted. "We hope our efforts can start a new trend among the younger generation, encouraging them to carry out the virtue of cherishing food and developing the habit of thrift, " Liu said4. What is the main function of the APP "Clear Plate?A. Awarding credit points.B. Giving charity meals.C. Showing the empty plates.D. Encouraging saving food.5. How is the "Clear Your Plate" campaign carried out?A. Customers wasting food are punished.B. People join in it on mini-program.C. Restaurants limit customers' choices.D. People are encouraged to buy gifts.6. What was the most difficult when the app was created?A. Getting other people to cooperate with the team.B. Collecting samples in canteens and restaurants.C. Ensuring the app to recognize empty plates.D. Finding people to fund the app.7. What is the purpose of the writing?A. To introduce an app.B. To promote saving food.C. To praise a startup founder.D. To raise fund for poor children.CWhen I was trying to find a place where to spend my December holidays, I met by chance some cheap flights to Iceland. After checking just a few winter pictures of Iceland, I realized that the country, known as the land of fire and ice, during the cold months of the year could offer me experiences I had never had before.For sure you can’t miss the chance to go to Iceland in winter if your traveling wish list includes at least one of the crazy experiences Iceland can offer. Iceland in the North Atlantic Ocean is a paradise (乐园) for all those who want to see the northern lights, experience cold weather conditions and put themselves in geothermal (地热的) baths while the snow is falling on their head.The best way to move around Iceland is with a rental car. Distances are huge and public transport in winter is not really common out of the major towns. As we wanted to be even more convenient we decided to rent a small camper (野营车). Sleeping and cooking in a camper saved us a lot of driving, money and gave us the chance tobe always in the right place at the right time.There were also no locals and in many cases no tourist facilities (设备). For us, as we slept in a camper, it waseasier. But for tourists traveling by normal cars it is necessary to check the opening times ofhotels and restaurants as many of them run just from June to September.It is amazing to experience how the weather is changing in Iceland. However, Icelanders prefer to stay inside their houses. They have even no time to complain about the weather in December. All they care about is Christmas. They love to decorate their houses, sing Christmas songs and eat typical Christmas food.8. Why is Iceland famous as the land of fire and ice?A. Because tourists would like to play with fire on the ice.B. Because it is too dry to easily cause fire to happen.C. Because it is hot inside a house and cold outside.D. Because there exist hot springs and freezing ice.9. What did the author think of the rented camper?A. It was not only practical but also economical.B. It was convenient but cost them more money.C. It provided the best chance to see the new country.D. It was much faster than other public transport.10. What does the last paragraph imply?A. The Icelanders prefer to live with their family.B. The joy of Christmas drives the freezing weather away.C. December is the coldest month of the year.D. The Icelanders are always positive and stay outside.11. What does this passage most probably come from?A. A textbookB. A scientific reportC. A travel magazineD. A news reportDDogs are often referred to as “man's best friend”. But MacKenzie, a four-pound Chihuahua (奇瓦瓦狗), who was named winner of the 2020 American Hero Dog competition, is making the world a better place for humans and animals alike. Often called the “Oscars for dogs”, the award recognizes dogs who make great contributions to society.This year's competition attracted over 400 competitors from across the country. While all were impressive, it was tiny MacKenzie who won the judges' hearts. Born at a rescue shelter in Hilton, New York, in 2013, she had acleft palate (腭裂) that required her to be tube fed for the first year of her life. A life-saving operation, performed in 2014, gave her the ability to eat and drink independently, enabling the tiny dog to focus on doing what she loved most: taking care of others.The seven-year-old Chihuahua is now gainfully “employed” by the Mid Foundation, a Rochester, New York-based non-profit organization that shelters and cares for animals born with disabilities. MacKenzie's official job is “to provide love and care for baby rescue animals born with birth defects”. The Chihuahua is good at her job and hasnurturedmany different species-from puppies to kittens to turkeys, squirrels, birds and even a goat. She acts as their mother and teaches them how to socialize, play, and have good manners.In addition to her role as an animal caretaker, MacKenzie also has the important job of greeting the foundation's volunteers and friends. The incredible dog, who has lost her ability to bark, also visits area schools to help children understand physical disabilities in both animals and people. Her heart-warming and inspiring story makes MacKenzie worthy of America's top dog honor!12. What made MacKenzie American Hero Dog?A. Being man's best friend.B. Her struggle with disabilities.C. Rescuing animals with disabilities.D. Her contributions to a better world.13. What can we infer about MacKenzie from Paragraph 2?A. Her growth path was not easy.B. She was deserted by her owner.C. She was operated on at two years old.D. She still needs taking care of by others.14. What does the underlined word “nurtured” in Paragraph 3 mean?A. Trained.B. Comforted.C. Tended.D. Abused.15. Which can be a suitable title for the text?A. MacKenzie—The Most Hard-working DogB. MacKenzie—America's “Most Heroic Dog”C. Chihuahua—Inspiration of Positive EnergyD. Chihuahua—Appeal for Animals' Protection第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
云南省民族大学附属中学2020届高三英语第二次仿真模拟试题(含解析)
Honeyball(By Pete Liebengood, www.xlibris。com， ＄19. 99 sc, $3。 99 eb)
A group of women pull together in a dedicated campaign to find success at the box office while their leader finds the love of her life and the persons responsible for the death of her father in a plane Crash.
Walking the Stones of Time（By Oswald Brown, www。， ＄ 18. 99 sc, $3。 99 eb）
It is an extraordinary love story of an awkward young man and an equally awkward young woman who despite their lack of social skills, developed a love that was stronger than all their inadequacies.
2020届云南民族大学附属中学高三第一次高考仿真模拟数学(文)试题(解析版)
2020届云南民族大学附属中学高三第一次高考仿真模拟数学（文）试题一、单选题1．设集合{}2,xA yy x R ==∈∣，{}210B x x =-<∣，则A B =（ ）A ．(1,1)-B ．(0,1)C ．(1,)-+∞D ．(0,)+∞【答案】C【解析】根据指数函数的性质化简集合A ，利用一元二次不等式的解法化简集合B ，再求并集即可. 【详解】集合A 表示函数2xy =的值域， 故(0,)A =+∞.由210x -<，得11x -<<， 故(1,1)B =-. 所以(1,)AB =-+∞.故选：C. 【点睛】本题主要考查指数函数的性质、一元二次不等式的解法以及并集的运算，属于基础题. 2．复数z 满足21z i -+=，则||z 的值是（ ）A ．BCD ．【答案】C【解析】结合复数的模长公式求解即可 【详解】由213z i z i z -+=⇒=-⇒=故选：C 【点睛】本题考查复数的模长公式，属于基础题 3．在ABC ∆中，D 在边AC 上满足12AD DC =，E 为BD 的中点，则CE =（）A．51 63BA BC-B．1536BA BC-C．1536BA BC+D ．5163BA BC+【答案】B【解析】根据E为中点，首先易得1122CE CB CD=+，再通过向量加法以及向量的减法和12AD DC=即可得到结果.【详解】如图所示：因为E为BD的中点，所以1122CE CB CD=+，又12AD DC=，23CD CA=∴，12CE CB=∴12111115()23232336CA CB CA CB BA BC BA BC+⨯=+=+-=-，故选B．【点睛】本题主要考查平面向量基本定理的应用，对向量加法和减法的运用较为灵活，属于基础题．4．幂函数()f x xα=的图象过点(3,5)，且1aeα⎛⎫= ⎪⎝⎭，3bα=1log4cα=，则a，b，c的大小关系为（）A．c a b<<B．a c b<<C．a b c<<D．c b a<<【答案】A【解析】根据题意求得参数α，根据对数的运算性质，以及对数函数的单调性即可判断. 【详解】解：依题意，得35α=，故3log5(1,2)α=∈，故3log5101ea⎛⎫<=<⎪⎝⎭，33log51b=>，3log51log04c=<，则c a b<<.故选：A.【点睛】本题考查利用对数函数的单调性比较大小，以及根据幂函数的定义求参数值，考查推理论证能力，属于基础题.5．“函数()2()311f x ax a x=--+在区间[)1+∞，上是增函数”是“01a≤≤”的（）A．充分不必要条件B．必要不充分条件C．充分必要条件D．既不充分也不必要条件【答案】C【解析】0a<时，“函数()()2311f x ax a x=--+在区间[)1,+∞上不是增函数”，0a=时，()1f x x=+在[)1,+∞上是增函数，0a>时，令3112aa-≤，得01a<≤，∴“()()2311f x ax a x=--+在区间[)1,+∞上是增函数” 的充分必要条件“01a≤≤”，故选C.6．已知x，y满足条件{20xy xx y k≥≤++≤(k为常数)，若目标函数z＝x＋3y的最大值为8，则k＝()A．－16 B．－6 C．-83D．6【答案】B【解析】【详解】由z＝x＋3y得y＝－13x＋3z，先作出{xy x≥≤的图象，如图所示，因为目标函数z＝x＋3y的最大值为8，所以x＋3y＝8与直线y＝x的交点为C，解得C(2,2)，代入直线2x＋y＋k＝0，得k＝－6.7．已知数列{}n a的前n项和n S满足21n nS a=-.若对任意正整数n都有1n nS Sλ+-<恒成立，则实数λ的取值范围为（）A ．(),1-∞B ．12⎛⎫-∞ ⎪⎝⎭，C ．13⎛⎫-∞ ⎪⎝⎭，D ．14⎛⎫-∞ ⎪⎝⎭，【答案】C【解析】先利用1,1,2n nn S n a S S n =⎧=⎨-≥⎩求出数列{}n a 的通项公式，于是可求出n S ，再利用参变量分离法得到1n n S S λ+<，利用数列的单调性求出数列1n n S S +⎧⎫⎨⎬⎩⎭的最小项的值，可得出实数λ的取值范围． 【详解】当1n =时，1121S a =-，即1121a a =-，得11a =；当2n ≥时，由21n n S a =-，得1121n n S a --=-，两式相减得122n n n a a a -=-，得12n n a a -=， 12nn a a -∴=，所以，数列{}n a 为等比数列，且首项为1，公比为2，11122n n n a --∴=⨯=. 12122121n n n n S a -∴=-=⨯-=-，由10n n S S λ+-<，得()()11111112121112221212221n nn n n n n S S λ+++++---<===----， 所以，数列1n n S S +⎧⎫⎨⎬⎩⎭单调递增，其最小项为122211213S S -==-，所以，13λ<， 因此，实数λ的取值范围是1,3⎛⎫-∞ ⎪⎝⎭，故选C ． 【点睛】本题考查利用数列前n 项和求数列的通项，其关系式为1,1,2n nn S n a S S n =⎧=⎨-≥⎩，其次考查了数列不等式与参数的取值范围问题，一般利用参变量分离法转化为数列的最值问题来求解，考查化归与转化问题，属于中等题．8．已知直线l 、m 与平面α、β，l α⊂，m β⊂，则下列命题中正确的是（ ） A ．若//l m ，则必有//αβ B ．若l m ⊥，则必有αβ⊥ C ．若l β⊥，则必有αβ⊥D ．若αβ⊥，则必有m α⊥【答案】C【解析】根据空间点、直线、平面之间的位置关系，结合线线、线面平行垂直的判定和性质，对四个选项逐一判断可得答案. 【详解】解：A .如图所示，设⋂=c αβ，//l c ，//m c 满足条件//l m ，但是α与β不平行，故A 不正确；B .假设//αβ，n β⊂，//n l ，n m ⊥，则满足条件l m ⊥，但是α与β不垂直，故B 不正确；C .若l α⊂，l β⊥，根据面面垂直的判定定理可得αβ⊥，故C 正确；D .设⋂=c αβ，若//l c ，//m c ，虽然αβ⊥，但是可有//m α，故D 不正确， 综上可知：只有C 正确. 故选：C.【点睛】本题考查空间点、直线、平面之间的位置关系，以及线线、线面平行垂直的判定和性质，考查对命题的判断和推理证明思想，属于基础题.9．执行如图所示的程序框图，若输出的S 值为127，则判断框中可以填（ ）A ．5k <？B ．k 6<？C ．7k <？D ．8k <？【答案】C【解析】写出每次循环的运行结果，即可求解. 【详解】由题意知，第一次循环，1S =，1k =；第二次循环，3S =，2k =； 第三次循环，7=S ，3k =；第四次循环，15S =，4k =； 第五次循环，31S =，5k =；第六次循环，63S =，6k =； 第七次循环，127S =，7k =；此时应退出循环，故判断框内可以填入的条件是“7k <？”. 故选：C 【点睛】本题考查了根据程序框图的运行结果补充条件，考查了基本运算能力，属于基础题.10．设1F ，2F 分别为椭圆C ：()222210x y a b a b+=>>的左右焦点，点A ，B 分别为椭圆C 的右顶点和下顶点，且点1F 关于直线AB 的对称点为M .若212MF F F ⊥，则椭圆C 的离心率为（ ）A ．12B ．13C D ．2【答案】C【解析】根据已知求出M 坐标，利用1AB F M ⊥，建立,,a b c 关系，结合222a b c =+，即可求解. 【详解】设()0,M c y ，则1MF 的中点为00,2y N ⎛⎫⎪⎝⎭， 即N 在y 轴上，N 又在直线AB 上， 即点N 与B 重合，故1111AB BF b b AB BF k k a c ⎛⎫⊥⇒=-⇒⋅-=- ⎪⎝⎭222b ac a c ac ⇒=⇒-=210e e ⇒+-=，∴12e =. 故选:C. 【点睛】本题考查椭圆的简单几何性质、点关于直线对称的应用，考查计算求解能力，属于中档题.11．我国古代数学名著《九章算术》有“米谷粒分”题：粮仓开仓收粮，有人送来米1534石，验得米内夹谷，抽样取米一把，数得254粒内夹谷28粒，则这批米内夹谷约为（ ） A ．134石 B ．169石C ．338石D ．1365石【答案】B 【解析】【详解】设夹谷x 石，则281534254x =， 所以153428169.1254x ⨯=≈， 所以这批米内夹谷约为169石，故选B. 【考点】用样本的数据特征估计总体.12．函数22log (2),02()2(),20x x f x f x x --+≤<⎧=⎨---<<⎩，若(1)()f a f a -<，则实数a 的取值范围是（ ） A ．1,12⎡⎫-⎪⎢⎣⎭B ．1,12⎛⎤⎥⎝⎦C ．11,2⎛⎫- ⎪⎝⎭D ．1,22⎛⎫⎪⎝⎭【答案】D【解析】结合复合函数单调性判断分段函数单增，再由函数的增减性解不等式去“f ”即可 【详解】由复合函数的单调性，可知，22log (2)y x =--+在[)0,2上单调递增，()()222()22log 2log 2y f x x x =--=--+=+⎡⎤⎣⎦在(2,0)-上单调递增，且函数()f x 在0x =处连续，所以()f x 在(2,2)-上是增函数，由(1)()f a f a -<，得121222a aa a -<⎧⎪-<-<⎨⎪-<<⎩，解得122a <<，故选：D 【点睛】本题考查复合函数增减性的判断，由函数增减性解不等式，属于中档题二、填空题13．已知三棱锥P ABC -的体积为3，4APC π∠=，3BPC π∠=，PA AC ⊥，PB BC ⊥，且平面PAC ⊥平面PBC ，则三棱锥P ABC -外接球的表面积为______.【答案】16π【解析】取PC 中点D ，根据条件证明AD ⊥平面PBC ，即是棱锥的高，设棱长求出体积，然后等体积转化，可求得棱长，再确定球心，求得半径得到答案. 【详解】设2PC a =，因为PA AC ⊥，4APC π∠=，所以APC △为等腰直角三角形，PC 边上的高为a ，作AD PC ⊥，垂足为D ，因为平面PAC ⊥平面PBC ，平面PAC平面PBC PC =，AD ⊂平面PAC ，所以AD ⊥平面PBC ，所以点A 到平面PBC 的距离为a ，因为3BPC π∠=，PB BC ⊥，所以PB a =，BC 3a =，21332PBC S a a ==△， 所以213433P ABC A PBC V V a --==⋅=，解得2a =， 因为PA AC ⊥，PB BC ⊥，所以PC 的中点为外接球的球心，外接球的半径为2， 所以三棱锥P ABC -外接球的表面积为24216ππ⨯=. 故答案为：16π. 【点睛】本题主要考查空间几何体与球接、切问题的求解方法.14．已知:64p x -≤，:11q a x a -<<+，a R ∈，且p 是q 成立的必要不充分条件，则实数a 的取值范围是__________． 【答案】[]3,9【解析】先解出不等式64x -≤得出解集为[]2,10，由题意得出()[]1,12,10a a -+，列出不等式组解出实数a 的取值范围.【详解】解不等式64x -≤，即464x -≤-≤，得210x ≤≤，:210p x ∴≤≤. 由于p 是q 成立的必要不充分条件，则()[]1,12,10a a -+，所以12110a a -≥⎧⎨+≤⎩，解得39a ≤≤，因此，实数a 的取值范围是[]3,9，故答案为[]3,9. 【点睛】本题考查利用充分必要性求参数的取值范围，涉及绝对值不等式的解法，解题的关键就是利用充分必要性转化为两集合间的包含关系，考查化归与转化思想，属于中等题. 15．在平面直角坐标系中，当P(x ，y)不是原点时，定义P 的“伴随点”为2222(,)y xP x y x y -++'；当P 是原点时，定义P 的“伴随点“为它自身，平面曲线C 上所有点的“伴随点”所构成的曲线C '定义为曲线C 的“伴随曲线”.现有下列命题： ①若点A 的“伴随点”是点A '，则点A '的“伴随点”是点A ②单位圆的“伴随曲线”是它自身；③若曲线C 关于x 轴对称，则其“伴随曲线”C '关于y 轴对称； ④一条直线的“伴随曲线”是一条直线.其中的真命题是_____________（写出所有真命题的序列）. 【答案】②③【解析】【详解】试题分析：对于①，若令(1,1)P ，则其伴随点为11(,)22P '-，而11(,)22P '-的伴随点为(1,1)--，而不是P ，故错误；对于②，设曲线0(),f x y =关于x 轴对称，则(,)0f x y -=对曲线0(),f x y =表示同一曲线，其伴随曲线分别为2222(,)0y x f x y x y -=++与2222(,)0y xf x y x y --=++也表示同一曲线，又因为其伴随曲线分别为2222(,)0y x f x y x y -=++与2222(,)0y xf x y x y--=++的图象关于y 轴对称，所以正确；③令单位圆上点的坐标为(cos ,sin )P x x 其伴随点为(sin ,cos )P x x '-仍在单位圆上，故正确；对于④，直线y kx b =+上取点后得其伴随点2222(,)y xx y x y-++消参后轨迹是圆，故错误.所以正确的为序号为②③. 【考点】对新定义的理解、函数的对称性.三、双空题16．“今有女善织，日益功疾，初日织五尺，今一月共织九匹三丈．”其白话意译为：“现有一善织布的女子，从第2天开始，每天比前一天多织相同数量的布，第一天织了5尺布，现在一个月（按30天计算）共织布390尺．”则每天增加的数量为____尺，设该女子一个月中第n 天所织布的尺数为n a ，则14151617+++=a a a a ______． 【答案】162952 【解析】设从第2天开始,每天比前一天多织d 尺布,由等差数列前n 项和公式求出1629d =,由此利用等差数列通项公式能求出14151617a a a a +++. 【详解】设从第2天开始,每天比前一天多织d 尺布, 则3030293053902S d ⨯=⨯+=, 解得1629d =,即每天增加的数量为1629， 14151617111113141516a a a a a d a d a d a d ∴+++=+++++++ 1458a d =+ 1645585229=⨯+⨯=，故答案为1629，52. 【点睛】本题主要考查等差数列的通项公式、等差数列的求和公式，意在考查利用所学知识解决问题的能力，属于中档题.四、解答题17．已知函数2()sin cos 2f x x x x =+-. （1）求()y f x =的最小正周期，并求其单调递减区间；（2）ABC 的内角A ，B ，C 所对的边分别为a ，b ，c ，若()2f A =-，且A 为钝角，2a =，求ABC 面积的最大值.【答案】（1）()f x 最小正周期T π=；单调递减区间为()7,1212k k k Z ππππ⎡⎤++∈⎢⎥⎣⎦；（2【解析】（1）利用二倍角和辅助角公式可化简函数为()sin 23f x x π⎛⎫=+⎪⎝⎭；利用2T πω=可求得最小正周期；令()3222232k x k k Z πππππ+≤+≤+∈解出x 的范围即可得到单调递减区间；（2）由()2f A =-sin 232A π⎛⎫+=- ⎪⎝⎭，根据A 的范围可求出A 的取值；利用余弦定理和基本不等式可求出bc 的最大值，代入三角形面积公式求得结果. 【详解】（1）()21sin cos sin 22sin 223f x x x x x x x π⎛⎫=⋅=+=+ ⎪⎝⎭ ()f x ∴最小正周期：22T ππ== 令()3222232k x k k Z πππππ+≤+≤+∈得：()71212k x k k Z ππππ+≤≤+∈ ()f x ∴的单调递减区间为：()7,1212k k k Z ππππ⎡⎤++∈⎢⎥⎣⎦单调递减区间7,()1212k k k z ππππ⎡⎤++∈⎢⎥⎣⎦.（2）由()f A =sin 23A π⎛⎫+= ⎪⎝⎭,2A ππ⎛⎫∈ ⎪⎝⎭472,333A πππ⎛⎫∴+∈ ⎪⎝⎭ 5233A ππ∴+=，解得：23A π= 由余弦定理2222cos a b c bc A =+-得：2243b c bc bc =++≥（当且仅当b c =时取等号）43bc ∴≤1142sin sin 22333ABC S bc A π∆∴=≤⨯=即ABC ∆【点睛】本题考查正弦型函数最小正周期和单调区间的求解、解三角形中三角形面积最值的求解问题；涉及到二倍角公式和辅助角公式的应用、余弦定理和三角形面积公式的应用等知识；求解正弦型函数单调区间的常用解法为整体代入的方式，通过与正弦函数图象的对应关系来进行求解.18．某学校高二年级共有1600人，现统计他们某项任务完成时间介于30分钟到90分钟之间，图中是统计结果的频率分布直方图.（1）求平均值、众数、中位数；（2）若学校规定完成时间在[30,50)分钟内的成绩为A 等；完成时间在[50,70)分钟内的成绩为B 等；完成时间在[70,90)分钟内的成绩为C 等，按成绩分层抽样从全校学生中抽取10名学生，则成绩为B 等的学生抽取人数为？（3）在（2）条件下抽取的成绩为B 等的学生中再随机选取两人，求两人中至少有一人完成任务时间在[60,70)分钟的概率.【答案】（1）平均数56.5=，众数为55，中位数为50656+=；（2）B 中抽7人； （3）两人中至少有一人完成任务时间在[60，70）分钟的概率为1121． 【解析】试题分析：（1）应用条形分布直方图求平均数的公式为350.1450.1550.5650.2750.05850.0556.5⨯+⨯+⨯+⨯+⨯+⨯=（2）根据系统抽样，按照比例抽得人数（3）用列举法，将满足条件的例子都写出来，根据离散型随机变量的概率计算公式得到1121． （Ⅰ）平均数为350.1450.1550.5650.2750.05850.0556.5⨯+⨯+⨯+⨯+⨯+⨯=； 众数为55；因为完成时间在[30，50)分钟内的频率为0.2，在[50，60)分钟内的频率为0.5，所以中位数为50656+=．（Ⅱ）因为A ，B ，C 的频率比为2︰7︰1，共抽10人，所以B 中抽7人． （Ⅲ）抽出的成绩为B 等学生中完成任务时间[50，60)分钟的学生有5人，设为a ，b ，c ，d ，e ；在[60，70)分钟的学生人数为2人，设为x ，y ， 则7人中任选两人共有：(a ，b )，(a ，c )，(a ，d )，(a ，e )，(a ，x )，(a ，y )，(b ，c )，(b ，d )，(b ，e )，(b ，x )，(b ，y )，(c ，d )，(c ，e )，(c ，x )，(c ，y )，(d ，e )，(d ，x )，(d ，y )，(e ，x )，(e ，y )，(x ，y )共21种．两人中至少有一人完成任务时间在[60，70）分钟内的有：(a ，x )，(a ，y )，(b ，x )，(b ，y )，(c ，x )，(c ，y )，(d ，x )，(d ，y )，(e ，x )，(e ，y )，(x ，y )共11种．所以两人中至少有一人完成任务时间在[60，70）分钟的概率为1121． 19．如图，在四棱锥P ABCD -中，PA ⊥底面ABCD ，AD AB ⊥，//DC AB ，1PA =，2AB =，2PD BC ==.（1）求证：CD ⊥平面PAD ；（2）若棱PB 上存在异于P 、B 的一点E ，使得二面角E AC P --的余弦值为33，求AE 与平面ABCD 所成角的正弦值. 【答案】（1）证明见解析；（25. 【解析】（1）由AD AB ⊥，//CD AB ，推出CD AD ⊥，再根据PA ⊥平面ABCD ，推出CD PA ⊥，最后根据线面垂直的判定定理，从而可证CD ⊥平面PAD ； （2）根据题设条件建立以A 为坐标原点，以AD ，AB ，AP 所在射线分别为,,x y z 轴的空间直角坐标系，设(),,E x y z ，由PE PB λ→→=得出()0,2,1E λλ-，分别求出平面PAC 与平面EAC 的一个法向量，再根据二面角E AC P --的余弦值为33，即可求得λ，从而可得AE 与平面ABCD 所成角的正弦值． 【详解】 （1）证明：AD AB ⊥，//CD AB ，CD AD ∴⊥，PA ⊥平面ABCD ,CD ⊂平面ABCD ，CD PA ∴⊥，AD PA A =，且,AD PA ⊂平面PAD ，CD平面PAD.（2）解: 以A为坐标原点，以AD，AB，AP所在射线，分别为,,x y z轴建立空间直角坐标系A xyz-，如图所示，则221AD PD PA=-=，由点C向AB作垂线CH, 则221BH BC AD=-=，∴1DC AH AB BH==-=，∴()()()()0,0,0,0,0,1,0,2,0,1,1,0A PB C，设(),,E x y z，则()(),,1,0,2,1PE x y z PB→→=-=-，∵E在棱PB上，∴PE PBλ→→=（01λ<<），即()(),,10,2,1x y zλ-=-，解得：21xyzλλ=⎧⎪=⎨⎪=-⎩，∴()0,2,1Eλλ-，设平面PAC的法向量()111,,u x y z→=，()()0,0,1,1,1,0AP AC→→==，∴·0·0u APu AC⎧=⎨=⎩，即()()()()111111,,0,0,10,,1,1,00x y zx y z⎧⋅=⎪⎨⋅=⎪⎩，即111zx y=⎧⎨+=⎩，取11x=，则11y=-，则()1,1,0u→=-，设平面EAC的法向量()222,,v x y z→=，()()0,2,1,1,1,0AE AC λλ→→=-=，∴ ·0·0v AE v AC ⎧=⎨=⎩，即()()()()222222,,0,2,10,,1,1,00x y z x y z λλ⎧⋅-=⎪⎨⋅=⎪⎩，即()22222100y z x y λλ⎧+-=⎨+=⎩，取21,x =则22221,(0)11y z λλλλ=-=>--， ∴21,1,1v λλ→⎛⎫=- ⎪-⎝⎭，∴()21,1,01,1,cos u u vv λθ→→→→⎛⎫-⋅- ⎪⋅====⋅，解得：12λ=， ∴10,1,2⎛⎫ ⎪⎝⎭E ，10,1,2AE →⎛⎫= ⎪⎝⎭，易知平面ABCD 的法向量()0,0,1m →=，所以AE 与平面ABCD所成角的正弦值1sin Em AEm A α→→→→⋅===⋅【点睛】本题考查线面垂直的判定定理，以及利用空间向量求二面角和线面角，空间向量解答立体几何问题的一般步骤是：（1）观察图形，建立恰当的空间直角坐标系；（2）写出相应点的坐标，求出相应直线的方向向量；（3）设出相应平面的法向量，利用两向量垂直数量积为零列出方程组求出法向量；（4）将空间位置关系转化为向量关系；（5）根据定理结论求出相应的角和距离.20．已知椭圆E ：22221x y a b +=（0a b >>，1F ，2F 分别为E 的左、右焦点，过E 的右焦点2F 作x 轴的垂线交E 于A ，B 两点，1F AB． （1）求椭圆E 的方程；（2）是否存在与x 轴不垂直的直线l 与E 交于C ，D 两点，且弦CD 的垂直平分线过E 的右焦点2F ？若存在，求出直线l 的方程；若不存在，请说明理由．【答案】（1）2212x y +=，（2）不存在，理由见解析.【解析】（1）根据离心率得c a =，根据1F AB ．得21222b c a ⨯⨯=，从而解得221.2b a ==，可得椭圆E 的方程；（2）假设存在与x 轴不垂直的直线l 满足题意，设:(0)=+≠l y kx m k ，代入2212x y +=，设11(,)C x y ，22(,)D x y ，根据判别式可得2212k m +>，根据韦达定理得弦CD 的中点坐标，可求得弦CD 的垂直平分线方程，将2F 代入可得212k m k+=-，将其代入2212k m +>，得210k +<无解，故不存在符合题意的直线l . 【详解】（1）依题意2c a =，22||b AB a =，所以21222b c a ⨯⨯=，即21b =，所以2221a c b -==，所以22112a a -=，所以22a =， 所以椭圆E 的方程为2212x y +=.（2）假设存在与x 轴不垂直的直线l 满足题意，设:(0)=+≠l y kx m k ，将其代入2212x y +=，整理得222(12)4220k x kmx m +++-=， 所以2222164(12)(22)0k m k m ∆=-+->，所以2212k m +>， 设11(,)C x y ，22(,)D x y ，则122412kmx x k +=-+，则1212y y kx m kx m +=+++2122242()221212k m mk x x m m k k =++=-+=++， 所以CD 的中点为M 222(,)1212km mk k -++，所以弦CD 的垂直平分线方程为2212()1212m kmy x k k k -=-+++， 因为弦CD 的垂直平分线过E 的右焦点2F (1,0)， 所以22120(1)1212m kmk k k-=--++， 所以212k m k+=-，将其代入2212k m +>，得2222(12)12k k k ++>，化简得210k +<，此不等式不成立， 所以不存在符合题意的直线l . 【点睛】本题考查了求椭圆的标准方程，考查了直线与椭圆的位置关系，考查了运算求解能力，属于中档题.21．已知函数()21x f x e x =--（1）求曲线()y f x =在(0,(0))f 处的切线方程；（2）设()()(1)xg x af x a e =+-，若()g x 有两个零点，求实数a 的取值范围.【答案】（1）y x =-；（2）2⎛⎫+∞ ⎪⎪⎝⎭. 【解析】（1）求出()f x 的导数，根据切线的斜率即为函数在0x =处的导数值可求出斜率，求出切点坐标，即可写出切线方程；（2）求出()g x 的导数，讨论a 的范围以确定函数的单调性，令min ()0g x <即可求出a 的取值范围. 【详解】（1）由题意知()2x f x e '=-，(0)121k f '==-=-，又0(0)2010f e =-⨯-=，∴()f x 在(0,(0))f 处的切线方程为y x =-.（2）当时()2x g x e ax a =--，()2xg x e a '=-，当0a ≤时，()0g x '>，∴()g x 在R 上单调递增，不符合题意. 当0a >时，令()0g x '=，得ln(2)x a =， 在(,ln(2))a -∞上，()0g x '<， 在(ln(2),)a +∞上，()0g x '>，∴()g x 在(,ln(2))a -∞上单调递减，在(ln(2),)a +∞上单调递增，∴()()()()()min ln 22ln 22ln 2g x g a a a a a a a ==-=-，∵()g x 有两个零点，且当x →-∞时，()()2210xxg x e ax a e a x =--=-+>，当x →+∞时，()g x →+∞，∴min ()0g x <，即2ln(2)0a a a -<， ∵0a >，∴1ln(2)2a >，解得a >， ∴实数a的取值范围为2⎛⎫+∞⎪ ⎪⎝⎭. 【点睛】本题考查利用导数求切线方程，考查利用导数研究函数的零点，属于中档题. 22．在直角坐标系xOy 中，以坐标原点O 为极点，x 轴正半轴为极轴建立极坐标系，曲线1C 的极坐标方程为4sin ρθ=，曲线2C 的极坐标方程为sin 26πρθ⎛⎫+= ⎪⎝⎭. （1）求曲线1C 、2C 的直角坐标方程;（2）设曲线1C 、2C 交于点A 、B ，曲线2C 与x 轴交于点E ，求线段AB 的中点到点E 的距离.【答案】（1）()221:24C x y +-=，2:40C x -=；（2）1.【解析】（1）将曲线1C 的极坐标方程变形为24sin 0ρρθ-=，将曲线2C 的极坐标方程变形为cos sin 40ρθθ+-=，由222cos sin x y x y ρρθρθ⎧=+⎪=⎨⎪=⎩可将曲线1C 、2C 的极坐标方程化为直角坐标方程；（2）可得出点()4,0E 以及直线2C 的倾斜角为56π，写出直线2C 的参数方程，并将直线2C 的参数方程与曲线1C 的直角坐标方程联立，列出韦达定理，可得出线段AB 的中点所对应的参数，进而可求得线段AB 的中点到点E 的距离. 【详解】（1）曲线1C 的极坐标方程可以化为24sin 0ρρθ-=，所以曲线1C 的直角坐标方程为2240x y y +-=，即()2224x y +-=.曲线2C的极坐标方程可以化为1cos sin 2022ρθρθ+-=， 所以曲线2C的直角坐标方程为40x -=； （2）易知点E 的坐标为()4,0，直线2C 的倾斜角为56π， 所以2C的参数方程为412x y t ⎧=⎪⎪⎨⎪=⎪⎩（t 为参数）. 将2C 的参数方程代入曲线1C的直角坐标方程得221+2442t ⎝⎛⎪⎫-= ⎪⎝⎪⎭⎛⎫-⎭，整理得()22160t t -+=，判别式()2264120∆=-=>，设A 、B 对应的参数分别为1t 、2t ，则线段AB的中点对应的参数为1212t t +=， 所以线段AB 的中点到点E的距离为1. 【点睛】本题考查极坐标方程与普通方程之间的相互转化，同时也考查了利用直线的参数方程解决实际问题，考查计算能力，属于中等题.23．已知函数2()4f x x ax =-++，()|1||1|g x x x =++- （1）当2a =时，求不等式()()f x g x ≥的解集； （2）若不等式()()f x g x ≥的解集包含11,22⎡⎤-⎢⎥⎣⎦，求a 的取值范围. 【答案】（1）{12}x x -≤≤∣；（2）77,22⎡⎤-⎢⎥⎣⎦. 【解析】（1）分段讨论可求出不等式的解集； （2）不等式()()f x g x ≥的解集包含11,22⎡⎤-⎢⎥⎣⎦等价于当11,22x ⎡⎤∈-⎢⎥⎣⎦时，()2f x ≥，列出不等式求解即可. 【详解】（1）当2a =时，不等式()()f x g x ≥等价于224|1||1|0x x x x --+-++≤①，当1x <-时，①式化为2440x x --≤，无解；高三质量检测 当11x -≤≤时，①式化为2220x x --≤，解得11x ≤≤； 当1x >时，①式化为240x -≤，解得12x <≤.综上，()()f x g x ≥的解集为{12}x x ≤≤∣.（2）当11,22x ⎡⎤∈-⎢⎥⎣⎦时，()2g x =， 所以()()f x g x ≥的解集包含11,22⎡⎤-⎢⎥⎣⎦， 等价于当11,22x ⎡⎤∈-⎢⎥⎣⎦时，()2f x ≥. 又()f x 在11,22⎡⎤-⎢⎥⎣⎦的最小值必为12f ⎛⎫- ⎪⎝⎭与12f ⎛⎫ ⎪⎝⎭之一， 所以122f ⎛⎫-≥ ⎪⎝⎭且122f ⎛⎫≥ ⎪⎝⎭， 得7722a -≤≤， 所以a 的取值范围为77,22⎡⎤-⎢⎥⎣⎦. 【点睛】本题考查含有绝对值不等式的解法，属于中档题.。
2020-2021学年云南民族中学高三英语一模试卷及参考答案
2020-2021学年云南民族中学高三英语一模试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AA Lifelong Devotion to Keeping People FedYuan Longping is a Chinese agricultural scientist and educator, known for developing the hybrid rice varieties.Yuan graduated from the Southwest Agriculture Institute in 1953 andbegan his teaching career at an agriculture school.In the 1960s, when a serious food shortage sweptChina, Yuan decided to devote himself to studying how to increase the yields of rice. He then began a lifelong connection with rice.Yuan succeeded in growing the world’s first high-yielding hybrid rice varieties in 1973, which could reach a yield of over 500 kg per mu (about 0.067 hectares), rising from the previous yield of only 300 kg per mu. For the next four decades, he continued to work on research and development of hybrid rice, achieving increasingly higher outputs. In 2020, hybrid rice developed by Yuan’s team achieved 1,500 kilograms per mu in two growing seasons, a new world record.InChina, where rice is the main food for the majority of the 1.4 billion people, the planting area of hybrid rice has reached 16 million hectares, or 57 % of the total planting area of rice, helping feed an extra 80 million people a year.Hybrid rice has also been grown in over 40 countries, including theU.S.,Brazil,India,Vietnam, thePhilippinesandMadagascar. The total planting area of the hybrid rice has reached 8 million hectares overseas.Even after a great success, Yuan never held himself back from making new breakthroughs. In 2017, his team started to grow seawater rice inQingdao. The rice was designed to grow in saline-alkaline land and survive even after being completely in seawater. His team planned to develop a type of seawater rice that could be planted in 6.67 million hectares of saline-alkaline land acrossChinato boost the country’s rice harvest by about 20 %. In 2018, Yuan’s team was invited to plant the saline-alkaline tolerant rice in experimental fields inDubai, which achieved huge success. In June 2020, his team started to grow seawater rice on a farm at an altitude of 2,800 meters in northwestChina’sQinghaiProvince. The experiment succeeded.Yuan had two dreams — to “enjoy the cool under the rice crops taller than men” and that hybrid rice could be grown all over the world to help solve the global food shortage.1. What made Yuan Longping decide to study rice?A. A serious food shortage.B. Agriculture development.C. His interest in the rice experiment.D. His wish to plant the tallest rice in the world.2. From the passage, we know that Yuan Longping ________.A. developed a variety of hybrid riceB. worked as a scientist after graduationC. started to grow seawater rice inDubaiin 2017D. grew the first high-yielding hybrid rice varieties in 19533. We can infer from the passage that Yuan Longping’s most outstanding qualities are________.A. modest and outgoingB. honest and creativeC. generous and optimisticD. responsible and devotedBIn 1990, Hal Donaldson was 23 years old, fresh out of college and found himself in Calcutta, India, where he was asked to interview Mother Teresa.Donaldson says about the great woman famed for feeding the hungry, “She wasn't wearing shoes and her ankles were swollen. She sat down with me and was very polite.” After the interview, Mother Teresa asked him, “What are you doing to help the poor?” Donaldson admitted that he was young and wasn't focused on helping others. With a smile on her face, Mother Teresa said, “Everyone can do something.”Those words deeply struck Donaldson and forced him to face some hard truths about himself.Hal Donaldson grew up in the San Francisco Bay area. When he was 12 years old, his parents were hit by a drunk driver; his father died, and his mother was seriously injured. To make ends meet, they went on welfare. Donaldson says, “I had holes in my shoes and clothes. When you're teased at school for that, you just want to escape.”He managed to do just that. Donaldson got into college and turned his focus to making money for himself He says, “I was just trying to find my way out of insignificance. However, it's easy to overlook others along the way. I was the guy that would see a homeless person and cross the street, so I didn'thave to confront (面对) him. My focus was on climbing to the top instead of helping those trying to climb with me.”Donaldson returned home from India with a different thought. He traveled to eight cities in America and stayed on the streets and listened tostories of the homeless. “My heart broke,” he says. “I knew I could no longer just live for myself.”Inspired by Mother Teresa's words and the stories he'd heard across America. Donaldson loaded a pick-up truck with $300 worth of groceries and handed them out to anyone who needed help. In 1994, Donaldson created the nonprofit organization, Convoy for Hope, which works with communities across America and around the world. Their work focuses on feeding children, women's empowerment, helping farmers and disaster services.4. What did 23-year-old Hal Donaldson do in India?A. He attended an interview for a college.B. He fed the hungry with Mother Teresa.C. He interviewed Mother Teresa.D. He did something to help the poor.5. What can we learn about Hal Donaldson from paragraph 4?A. He was born with disability.B. He led a hard life as a child.C. He was well treated at school.D. He survived as a parentless boy.6. How does Hal Donaldson describe himself in college?A. Self-centered.B. Sympathetic.C. Popular.D. Casual.7. How did Hal Donaldson change after he returned home from India?A. He preferred traveling to volunteering.B. He suddenly fell in love with journalism.C. He turned his focus to living for himself.D. He gradually devoted himself to helping others.CThe COVID-19 vaccination（接种疫苗）rate in the US has fallen to newlows in recent weeks, threatening President Joe Biden’s goal of having 70 percent of American adults with at least one shot by July 4.With just less than one month from July 4, the current vaccination rate will put the US at somewhere between 67 percent and 68 percent of the adult population with at least one dose（剂量）by Independence Day. To reach 70 percent by July 4, around 1.6 percent of the population needs to get their first dose per week from now until July 4.The Centers for Disease Control and Prevention（CDC）reported last week that 63 percent of adults hadreceived their first dose of a COVID-19 vaccine. That was up slightly from 62 percent from the report a week before. The additional 1 percent of adults completing their first dose is the lowest since the CDC started tracking the vaccination rate in mid-February.On average, fewer than 1 million shots are given out per day, a decline of more than two-thirds from the peak of 3.4 million in April, The Washington Post reported. In South Carolina, about 71,000 residents got a shot in the week leading up to June 3, compared to a high of nearly 300,000 in one week in early April, according to data from the CDC.The slowdown is moreprominentacross the South and Midwest. Twelve states have seen vaccinations fall to 15 daily shots per 10,000 residents. Less than a quarter of black Americans had received their first COVID-19 shot as of June 7.James Hildreth, CEO of Meharry Medical College, told Politico, “We need to make a stronger effort to bring the vaccine to the communities, rather than relying on the communities to come to vaccination centers.”The sharp decline in vaccination began in mid-April when federal officials temporarily stopped the use of the Johnson＆Johnson vaccine while they investigated rare blood-clotting（凝血）reactions.The “low-hanging fruit—thosepeople who ly want to get vaccinated without you telling them anything” have already been vaccinated, which has led to the slowdown, Dr Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said on a White House-organized call with community leaders last week, according to the Post.8. What can we learn from the text?A. Dr Anthony Fauci is in charge of the Centers for Disease Control and Prevention.B. In South Carolina, about 300,000 residents got a shot in the week leading up to June 3C. In mid-April federal officials temporarily suspended the Johnson＆Johnson vaccine.D. Less than one fourth of Americans had received their first COVID-19 shot by June 7.9. Which of the following can replace the underlined word “prominent” in Para. 5?A. Meaningful.B. Obvious.C. Inspiring.D. Complex.10. How can America increase the COVID-19 vaccination rate according to James Hildreth?A. By giving the vaccine shot at the communities.B. By offering the vaccine to the public for free.C. By frequently informing the public of the vaccine.D. By urging the communities to come to vaccination centers.11. What can be the best title for the text?A. Biden wishes to have 70% of adults with one shot by July 4B. CDC has been trackingthe vaccination rate since mid-FebruaryC. Some Americans need to get vaccinated without telling them toD. Biden’s July 4th vaccine goal may be missedDAfter finishing his dinner, Lin Xu opened a WeChat mini-programcalled "Clear Plate" on his phone and took apicture of the empty plates. He was then awarded 157 credit points after the image was uploaded and recognized by artificial intelligence. The credit points can be used to buy gifts, such as books, cellphones and red wine, or to purchase charity meals donated to children in poor rural areas.The "Clear Plate" mini-program has become popular among young Chinese. Similar campaigns like an "empty plate challenge" are alsoon the horizonin many Chinese universities."Technological innovation is a good way to reduce food waste," said Liu Jichen. Founder of the start-up that developed the app. The idea popped up at a dinner in 2017, when Liu found that the restaurant owner would give diners who polished off their food a card and offer small gifts after a certain number of cards had been collected. "Everyone who values food is bound to enjoy a sense of gain at a lower cost," Liu mentioned this case, noting that such an idea could potentially be realized online.He formeda team to work on the project. Yet it was quite a challenge for the AI system to assess whether the uploaded photos showed empty plates. To make the AI system smarter，Liu and his team, assisted by more than 1, 000 others, spent half a year collecting over100,000 samples from canteens and restaurants across the country and analyzed the data. Dozens of enterprises, institutions and restaurants have contacted the start-up to cooperate on the project. Through the digitalized, visualized mini-program, people can clearly see the good results of saving food, which will effectively reduce food waste. "We hope our efforts can start a new trend among the younger generation, encouraging them to develop the habit of thrift(节约)," Liu said.12. What does the underlined phrase "on the horizon" in paragraph 2 mean?A. Likely to decrease.B. Likely to succeed.C. Likely to change.D. Likely to appear.13. What caused Liu Jichen to develop the "Clear Plate" app?A. Food waste afterdinner.B. The idea of the restaurant owner.C. Small gifts sent by his friends.D. Charity meals donated to children.14. What was difficult for the project Liu's team worked on?A. Making the AI system smarter.B. Assessing the uploaded photos.C. Collecting samples from canteens and restaurants.D. Encouraging people to develop the habit of thrift.15. What is the text mainly about?A. AI programs becoming popular.B. AI programs appearing in many Chinese universities.C. AI programs encouraging diners toclear their plates.D. AI programs collecting pictures of clearing diners' plates.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。