2020年2020届四川省成都市实验外国语学校2017级高三高考模拟考试(三)理科数学试卷无答案

2020届成都市实验外国语学校高三英语三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AFine art fairs（艺术博览会）are the trend of the 21st century, with new art and antique（古玩）fairs and festivals springing up in diverse parts of the world. Here is a list of four noteworthy art fairs.Art Basel, Basel, SwitzerlandThe granddaddy of art fairs, Art Basel, was established in 1970 by a group of local art gallerists and is the biggest contemporary art fair in the world. Art Basel takes place over a 5-day period each June in Basel, Switzerland. The high cost of renting space for gallery owners is offset（抵消）by the huge attendance at the fair. For example in 2010, about 60,000 visitors attended Art Basel.Frieze Art Fair, London“Frieze Art Fair was established in 2003 and is one of the few fairs to focus only on contemporary art and living artists.v"Thefair takes place every October in Regent's Park, London. It features over 170 of the most exciting contemporary art galleries in the world. ”In addition to the fair which began in 2003, the fair owners Matthew Slotover and Amanda Sharp publish Frieze, an international art magazine established in 1991 and devoted to contemporary art.TEFAF Maastricht, the NetherlandsEstablished in 1975 as The Pictura Fine Art Fair, and renamed The European Fine Art Foundation（TEFAF）, Maastricht in 1996, the fair includes 260 of the world's most famous art and antique dealers from 16 countries.The 24th edition of the TEFAF fair held March 18 — 27, 2011 featured 260 dealers exhibiting approximately 30, 000 artworks and antiques with an overall value of $ US 1. 4 billion.ARCO, MadridARCO Madrid was established in 1982 and is one of Europe's leading and popular art fairs. In addition to the exhibiting galleries（in 2011, 197 international art galleries participated）, a seriesof lectures and specially focused exhibitions take place.1.How does Art Basel cover the expense of renting space?A.By selling tickets.B.By selling expensive exhibits.C.By donation from dealers.D.By support from the government.2.The owners of Frieze Art Fair are also in charge of____.A.170 living artists.B.An international art magazine.C.30,000 artworks and antiques.D.A series of lectures.3.Which of the following has the longest history?A.Art BaselB.Frieze Art FairC.TEFAFD.ARCOBGray wolves have lived inNorth Americafor at least half a million years. Their living areas once included most of the continentalUnited States. But during the 1800s and early 1900s, wolves were hunted to near extinction(灭绝).By the 1960s, theU. S.wolf population was limited to a handful of creatures in small comers of the northernMidwest.Then, in 1973, a law, the ESA, was passed to protect animals from becoming extinct. Gray wolves were one of the first animals placed on the endangered-species(濒危物种)list. Killing them wasillicit. And theU. ernment worked to promote their protection. In a famous example of this effort, starting in 1995, 31 wolves were moved fromCanadatoYellowstoneNational Park. By 2015, more than 500 gray wolves were living in the Greater Yellowstone Ecosystem(生态系统).Today, the continentalU. S.is home to more than 6,000 gray wolves. On January 4, 2021, theU. ernment removed gray wolves from the endangered-species list.Usually, an animal's removal would be cause for celebration. But some environmental protectors say the wolves still need protection. In some parts of the country, wolves are increasing in numbers. More than a thousand of them can be found just inMichiganandWisconsin. But overall, their range is still a small part of what it was. Wolves used to live across most of the U. S. Now they , are found in fewer than a dozen states. Others argue that as long as a species is not in danger of extinction, it doesn't belong on the endangered-species list. And farmers with land near wolf living areas say that if the wolf's population continues to grow, more of their farm animals will be killed by wolves.But some protection groups worry that without protection, the wolf population will crash again. They hope that no matter what, people and wolves can get along peacefully with each other. They are promoting ways to make that happen.4. What caused gray wolves to be almost extinct?A. Losing their living areas.B. Too many natural enemies.C. The extreme climate changes.D. Being hunted in great numbers.5. What does the underlined word "illicit" in paragraph 2 mean?A. Rather difficult.B. Against the law.C. Totally normal.D. Conditionally allowable.6. Why was the gray wolf removed from the endangered-species list?A. They have a much larger population already.B. They have all been put into the safe natural parks.C. They have been feeding on farmers, farm animals.D. They have grown too strong to be protected by humans.7. What do farmers living near gray wolves' living areas think of the animals?A. The wolves are trouble for them.B. The wolves must be better protected.C. The wolves get along peacefully with them.D. The wolves should live where they belong.CA Bridge Linking Art and the AudienceAccording to a 2018 report, people aged between 16 and 24 make up about 15 percent of the population but only 10 percent of museum-goers. Similarly, people aged over35 go half as much as you would expect from their population size. We have reached the point of recognising the disconnection between art and the audience but haven’t yet determined how to bridge the gap. Two answers to tackling this challenge lie in telling a greater diversity of art histories and communicating these stories in more accessible ways.In 2018, a radio program called Art Matters was started with the aim of discussing art from a pop-culture viewpoint with topics that would engage younger and more diverse audience. It offers an accessible pathway to art history with conversations on different topics. Art history is about storytelling; art content shines when there is an effort to bring audience along for the discussion.More traditional institutions are paying attention. Recently theGettyMuseumissued a social-media challenge for people to recreate paintings using items they had at home. Users displayed incredible creativity, and the museum was flooded with submissions. This reaction proves that there is a potential desire for the audience to engage with art topics if the format is appealing. Since many people feelintimidatedand think that there’s a base level of understanding required to join the conversation, the Getty initiative serves as a reminder that there are many pathways to engaging with it.Another result of the Getty challenge was the exposure given to a diversity of artworks. The famous operasinger Peter Brathwaite, for example, made scores of attractive recreations highlighting centuries of black paintings. His efforts opposed the idea that there were not many historical paintings of black figures. It is extremely important that we do a better job of showing the complex and diverse stories that are represented in art.Social media have offered a platform for people who have not traditionally had a seat at the table. Anyone can recognise a gap in the field and address it. Accounts have gathered tens of thousands of followers. They are the proof that there is hunger to hear these art histories, and these themes work brilliantly for museum programming.But there is only so much that can be done without the museums and galleries changing meaningfully from within. We need to see a better balance of these stories represented in permanent collections. We also need a much wider diversity of people and interests represented on board. Ensuring that art-and writing and talking about art-is able to continue on the rising generation of storytellers, inside and outside of institutions, getting the funding and support they need to paint a brighter picture for the part.8. What challenge is the author trying to tackle?A. People doubt a great diversity of artworks.B. Fewer and fewer young people go to museums.C. Art appears too distant from common audience.D. Adult audience has a different understanding of art.9. What does the underlined word “intimidated” in Paragraph 3 probably mean?A. Tired.B. Worried.C. Annoyed.D. Surprised.10. In the author’s opinion, the museums and galleries should ________.A. make the art history stories accessible in a traditional way.B. change meaningfully for activities like the Getty challenge.C. limit the number of storytellers both in and out of institutions.D. improve the permanent collections by adding famous artworks.11. We can conclude from the passage that common audience ________.A. lacks the channels to understand and talk about art history.B. prefers to view artworks and hear art stories on social media.C. feels satisfied with people and interests represented on board.D. refuses to engage with diverse art topics and art history stories.DThe cumulative rainfall in Henan province during the four days was the highest since the province has records, the provincial meteorological service said. The rain was heaviest in the provincial capital, Zhengzhou, for a short period on Monday and Tuesday. Northern, western and central parts of Henan also experienced downpours, the service said. Zhengzhou's biggest one-hour precipitation (降水量) —201.9 mmbetween 4 and 5 pm on Tuesday—was also the highest on the Chinese mainland. The previous record was 198.5 mmin the village of Linzhuang in Zhumadian in August 1975, the National Meteorological Center said. The city's precipitation duringthe four days exceeded that of its average annual precipitation, the center said.Chen Tao, chief forecaster at the National Meteorological Center, said abundant water vapor (水蒸气) brought by Typhoon In-Fa and the province's special geographical features led to Henan's rain. “Partly affected by the typhoon, large amounts of water vapor have been transported to China's inland areas, including Henan,” he said.From Thursday to Monday, rain was forecast to continue in Henan. However, rainfall will gradually subside in Zhengzhou and the province's northern and central regions, though the storms will increase the risk of mountain torrents and other geological disasters. By Monday, lighter rain is forecast for parts of Henan, the provincial weather service said. However, local authorities are still urged to bevigilantand prepare to prevent or cope with flooding and other possible disasters.Predicting such weather events remains a challenge worldwide because it involves many meteorological phenomena, the center said. “The formation of this kind of extreme weather, including rainstorms and high temperatures, is complex,” Chen said. “We still lack effective solutions and methods for such forecasting”, he said. “We are now putting a lot of effort into tackling the difficulty. We believe that as the technology improves, we can better forecast the events.”12. What message does the author mainly want to convey in the first paragraph?A. heavy rain fell in Zhengzhou.B. The rain in Henan lasted four days.C. Zhumadian also suffered the similar heavy rain.D. Henan experienced the biggest rainfall of all time.13. What can be indicated from Chen Tao's words?A. It is not easy to forecast the extreme weather.B The rain of Henan is mainly caused by Typhoon In-Fa.C. The center hasn't put a lot of effort into solving the problem.D. Rainstorms and high temperatures can account for the heavy rain.14. What does the underlined word “vigilant” probably mean?A. Relaxed.B. Alert.C. Reluctant.D. Communicative.15. Where might the text be most probably taken from?A. history book.B. A novel.C. A news report.D. A science magazine.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届成都市实验外国语学校高三英语模拟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AAmid the coronavirus outbreak, the U. S. Department of Homeland Security recommends having at least a two - week supply of water and food.PotatoesShelf life：2 to 5 weeks if stored in a cool, dry, dark placeYukon Gold, red, and fingerling potatoes will last from two to three weeks. Larger white potatoes can last for three to five weeks. Sweet potatoes have about the same shelf life. Don't store them next to onions, however. The two might go together well in cooking, but raw, each gives off gases and moisture that might cause the other to spoil faster.Tea※Shelf life：6 to 12 months past "sell - by" dateDried tea leaves, whether loose (in a sealed container) or in teabags (in an unopened box) can easily last a year or more if they' re not subjected to damp or humidity. However, the tea does tend to lose flavor over time.Peanuts● Shelf life：1 to 2 monthsPeanuts in their shell, especially when kept cool and dry, are perfectly happy in the cupboard for as long as two months.Canned fruits and vegetables● Shelf life：1 to 2 years past "sell - by” dateCanningis an extremely efficient means of preserving food. Generally speaking, if canned foods aren't subjected to extreme heat, their contents should stay good for two years or more. Be aware, however, of dented cans or those with swollen tops, which may indicate the presence of bacteria inside.1. Which can go bad faster if stored with onions?A. Potatoes.B. Tea.C. Peanuts.D. Canned fruits and vegetables.2. What is special about tea?A. The flavor of tea can always remain the same.B. Tea leaves are better to be preserved in an open jar.C. Tea leaves should be kept away from the state of being wet.D. The maximum length of time that tea can be stored is 6 months.3. What may shorten the "sell - by” date of canned foods ?A. Shapes of cans.B. Categories of foods.C. Decline of the temperature.D. Exposure to high temperature.BWe all use different ways to remember ideas, facts and things we need to store. Remembering is an extremely important part of our learning experience. Information process, storage and recall encourage purposeful learning.But the brain doesn’t store everything we want or need for future use. It makes choices and tends to remember information that forms a memorable pattern. Things you learned recently can be particularly difficult to remember because they haven’t taken root in your mind.“Forgetting allows us to remember what is really important to our survival. We forget much of what we read, watch, and think directly every day.” writes John Medina in his book, Brain Rules.How do you avoid losing 90%of what you’ve learned? An inspiring writer and speaker Zig Ziglar once said: “Repetition is the mother of learning, the father of action, which makes it the architect of accomplishment.”Repetition has been a remembering skill for ages. When you hear or read something once，you don’t really learn it-at least not well enough to store the new information for long. The right kind of repetition can do wonders for your memory. People learn or remember better by repeating things or getting exposed to information many times. Othersrepeat particular steps or processes deliberately a number of times or even years to become better at certain skills.Daniel Coyle explains in his book, The Little Book of Talent:“...closing the book and writing a summary, even short ones, forces you to figure out the key points, process and organize those ideas so they make sense, and write them on the page. When you pick it back up weeks later, reread all of your notes or highlights to strengthen the ideas even further.”People learn by repeating things. Better learning is a repetition process. Every time we repetitively access something we already know, we increase the memory’s stored value.4. Which of the following can be inferred from the passage?A. The brain tends to store 90% of the things we learn.B. The fresher the information isthe easier to remember.C. Thinking is more important than remembering in study.D. The brain tends to choose and keep what it thinks important.5. How does the writer prove his opinion?A.By giving examples.B. By listing numbers.C. By borrowing words of experts.D. By providing scientific finding.6. What does Daniel Coyle want to say in his book?A. You can’t pay too much attention to repetition.B. Summarizing is a very effective learning tool.C. Forgetting forces human brain to make choices.D. Regular repetition helps to form good habits.7. Which do you think is the best title of the passage?A. How the Brain WorksB. Reading for MoreC. Fighting Against ForgettingD. Repeat to RememberCWhile space travel still gets lot of attention, not enough attention has been paid to the exploration of oceans, about which we know much less than the dark side of the moon.Ninety percent of the ocean floor has not even been recorded and while we have been to the moon, the technology to explore the ocean's floors is still being developed. For example, a permanent partially-underwater sea exploration station, called the Sea Orbiter, is currently in development.The oceans play a major role in controlling our climate. But we have not learned yet how to use them to cool us off rather than contribute to our overheating. Ocean organisms are said to hold the promise of cures for a wide of the unique eyes of skate (ray fish) led to advances in conquering blindness, the horseshoe crab was important in developing a test for bacterial pollution, and sea urchins helped in the development of test-tube fertilization(人工授精). The toadfish's' ability to regenerate its central nervous system is of much interest to neuroscientists. A recent Japanese study concluded that the drug Eribulin, which was taken from sea sponges, is effective in fighting with breast, colon, and Urinary cancer.Given the approaching crisis of water insufficiency, we badly need to improve current methods, of desalinating(淡化) ocean water and make them more efficient and less costly. By 2025, 1.8 billion people areexpected to suffer from severe water shortage, with that number jumping to 3. 9 billion by 2050-well over a third of the entire global population.If the oceansdo not make your heart go beating faster, how about engineering a bacterium that eats carbon dioxide — and thus helps protect the world from overheating — and produces fuel which will allow us to drive our cars and machines, without oil? I cannot find any evidence that people young or old, Americans or citizens of other nations would be less impressed or less inspired with such a breakthrough than with one more set of photos of a faraway galaxy or a whole Milky Way full of stars.8. What does the author think about the ocean exploration?A. It is equal to the space exploration.B. It is well developed.C. It deserves more attention and devotion.D. It is beyond our knowledge.9. What technology has been developed to make use of the oceans?A. Curing human diseases with ocean organisms.B. Preventing the world getting warmer.C. Mapping the global ocean floor.D. Removing salt from sea water.10. What does the author imply in the last paragraph?A. The temperature rise will be overcome by a bacterium.B. Solving the existing problems is more significant.C. The space exploration is worth the efforts.D. The ocean exploration is not inspiring.11. What is the best title of the passage?A. Oceans, the Last Hope.B. Oceans, the Hidden Treasure.C. Space, the Final Frontier.D. Space, the Faraway Dream.DAlaska—The American city Anchorage is recovering from a powerful earthquake Friday that damaged public buildings, homes and roads.The 7.0 earthquake caused buildings to slake. But there have been no reports of deaths, serious injuries or damage. Officials say the quake has not affected transportation of food and her supplies. “The ships are coming in on schedule, the supply lines are at this point working well,” the government told reporters Sunday.The Glenn Highway was probably the road hit hardest by the earthquake. It connects the state's largest city toother parts in the north. Traffic has been heavy and slow—moving since the quake. Drivers are being guided. Groups of workers are trying to rebuild areas where the quake left large holes in the road.People who are still nervous after the major quake have been more upset by more than 1, 700 aftershocks. “Anything that moves, you feel terrified”said David, whose home suffered structural(结构)damage, including a sunken foundation(地基). Actually, Alaska came up with strict building rules after a 9. 2 earthquake in 1964. That was the second most powerful earthquake on record.Government officials said a public health center promises that moneyfor medical treatment will continue to come. Mental healthy service(心理健康服务)is also available for people hurt by the disaster.Earthquake experts say there is a 4 percent chance of another 7. 0 earthquake or greater in the following week. "The chance is very small, but its not impossible, ” said the expert, Paul Caruso.12. What was the result of the earthquake?A. Buildings were damaged.B. Food supply was cut off.C. Many people were killedD. The ships could not come in.13. Why is the traffic slow on the Glenn Highway?A. Because small quakes hit the city.B. Because falling rocks are a danger.C. Because the highway is badly damaged.D. Because drivers are misled.14. What can you learn from Paul Caruso?A. Another greater earthquake is on the way.B. Chances still exists of another earthquake.C. It will be safe in the 1th week after the quake.D. There is no possibility for more quakes.15. Where can your possibly read the passage?A. Ina story book.B. In a travel journal.C. In a poster.D. In a newspaper.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。

成都市实验外国语学校高2017级数学模拟（三）文一、选择题（本大题共12小题，每小题5分，共60分）1.已知集合{}|A x y x Z ==∈，{}2|1,B y y x x A ==+∈，则A B 为（ ）A. ∅B. [)0,+∞C. {}1D. (){}0,12.若复数z 满足()1i z i +=，则z 的虚部为（ ） A. 1- B. 2- C. i - D. 2i -3.在平面直角坐标系xOy 中，已知角α的顶点在坐标原点，始边与x 轴正半轴重合，终边经过点P ，则cos2=α（ ）A. 3B. 13C. 13- D. 3- 4.《周易》是我国古代典籍，用“卦”描述了天地世间万象变化．如图是一个八卦图，包含乾、坤、震、巽、坎、离、艮、兑八卦（每一卦由三个爻组成，其中“”表示一个阳爻，“”表示一个阴爻）．若从含有两个及以上阳爻的卦中任取两卦，这两卦的六个爻中都恰有两个阳爻的概率为（ ）A. 13B. 12C. 23D. 345.下列判断正确的是（ ）A. 两圆锥曲线的离心率分别为1e ，2e ，则“121e e <”是“两圆锥曲线均为椭圆”的充要条件B. 命题“若21x =，则1x =.”的否命题为“若21x =，则1x ≠.”C. 若命题“p q ∧”为假命题，则命题“p q ∨”假命题D. 命题“x R ∀∈，22x x ≥."的否定是“0x R ∃∈，0202x x <.”6.函数2()cos ()x x e e x f x x--=的部分图象大致是（ ）A. B.C. D.7.在ABC ∆中，角A ，B ，C 的对边分别是a ，b ，c，且)cos cos 0a C c A --＝，则角A 的大小为（ ） A. 4π B. 3π C. 2π D. 34π 8.设m ，n 是两条不同的直线，α，β是两个不同的平面，则下列命题正确的是( )A. 若//m α，//n α，则//m nB. 若//αβ，m α⊂，n β⊂，则//m nC. 若αβ⊥，m αβ=，n ⊂α，则n β⊥D. 若m α⊥，//m n ，n β⊂，则αβ⊥ 9.若实数x ，y 满足约束条件2040250x y x y x y -+≥⎧⎪+-≥⎨⎪--≤⎩，则11y z x -=+的最大值为（ ） A. 1B. 2C. 3D. 4 10.定义在R 上偶函数()f x 满足()()2f x f x +=，且在[－1，0]上单调递减，设()2.8a f =-，()1.6b f =-，()0.5c f =，则a 、b ，c 大小关系是（）A. a b c >>B. c a b >>C. b c a >>D. a c b >>11.已知双曲线2222:1(0,0)x y E a b a b-=>>的左、右焦点分别为12,F F ,126,F F P =是E 右支上的一点，1PF 与y 轴交于点A ，2PAF ∆的内切圆在边2AF 上的切点为Q ，若AQ =E 的离心率是( )A. B. C. D. 12.已知函数33()1x f x x e =++，其导函数为()f x '，则()()()()2020202020192019f f f f ''+-+-- 的值为（ ）A. 1B. 2C. 3D. 4 二、填空题（本大题共4小题，每小题5分，共20分）13.已知向量()1,3a =，3,1b 则向量a 在向量b 方向上的投影为____________.14.函数f(x)＝x 3＋3ax 2＋3(a ＋2)x ＋1有极大值又有极小值，则a 的范围是 ．15.已知函数()cos (0)f x x x ωωω=+>，其图象与直线2y =的两个相邻交点的距离等于π，则()f x 的单调递增区间为______________．16.已知抛物线方程24y x =，F 为焦点，P 为抛物线准线上一点，Q 为线段PF 与抛物线的交点，定义：||()||PF d P FQ =.已知点(P -，则()d P =______；设点(1,)(0)P t t ->，则2()||d P PF -的值为____. 三、解答题（本大题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤） 17.设等差数列{}n a 的前n 项的和为n S ，且462S =-，675S =-，求：（1）求{}n a 的通项公式n a ；（2）求数列{}n a 的前14项和.18.某网购平台为了解某市居民在该平台的消费情况，从该市使用其平台且每周平均消费额超过100元的人员中随机抽取了100名，并绘制如图所示频率分布直方图，已知中间三组的人数可构成等差数列.（1）求,m n 的值；（2）分析人员对100名调查对象的性别进行统计发现，消费金额不低于300元的男性有20人，低于300元的男性有25人，根据统计数据完成下列22⨯列联表，并判断是否有99%的把握认为消费金额与性别有关？（3）分析人员对抽取对象每周的消费金额y 与年龄x 进一步分析，发现他们线性相关，得到回归方程ˆ5yx b =-+.已知100名使用者的平均年龄为38岁，试判断一名年龄为25岁的年轻人每周的平均消费金额为多少.（同一组数据用该区间的中点值代替）22⨯列联表 300 消费金额300<临界值表：22()()()()()n ad bc K a b c d a c b d -=++++，其中n a b c d =+++19.如图1，在平行四边形ABCD 中，4=AD ，AB =45DAB ∠=︒，E 为边AD中点，以BE 为折痕将ABE △折起，使点A 到达P 的位置，得到图2几何体P EBCD -．（1）证明：PD BE ⊥；（2）当BC ⊥平面PEB 时，求三棱锥C PBD -的体积．20.已知椭圆E的左右焦点分别是1(F、2F，且经过点2M ⎭. （1）求椭圆E 的标准方程：（2）设AC ，BD 是过椭圆E 的中心且相互垂直的椭圆E 的两条弦，问是否存在定圆G ，使得G 为四边形ABCD 的内切圆?若存在，求圆G 的方程，若不存在，请说明理由.21.已知函数2()1xe f x ax bx =++，其中0a >，b R ∈，e 为自然对数的底数. (1)若1b =，且当0x ≥时，()1f x ≥总成立，求实数a 的取值范围；(2)若0b =，且()f x 存在两个极值点1x ，2x ，求证：2121()()2e f x f x ++< 22.己知在平面直角坐标系xOy 中，曲线C 参数方程为222111x t t y t ⎧=-+⎪⎪-⎨⎪=⎪-⎩（t 为参数）.以原点O 为极点，x 轴正半轴为极轴建立极坐标系，直线l 的极坐标方程为cos 3πρθ⎛⎫+= ⎪⎝⎭（1）求曲线C 和直线l 直角坐标方程；（2）若直线l 交曲线C 于A ，B 两点，交x 轴于点P ，求11PA PB+的值. 23.已知a ，b ，c 均为正实数，求证：（1）()2()4a b ab c abc ++≥；的（2）若3a b c ++=.。

2020届成都市实验外国语学校高三英语三模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ASheffieldLincoln College of EnglishClasses for foreign students at all levels.3 months, 6 months, 9 months and one year course.Open all year.Small class (at most 12 students).Library, language laboratory and listening center.Accommodation (住宿)with selected families.25 minutes from London.Course fees for English for one year are￡1,380 with reduction for shorter periods of study.1.This passage is probably taken from _______.A.an advertisementB.a noticeC.a posterD.a piece of news2.Who will be accepted by this college?A.Both foreign and native students.B.Only foreign beginners and the advanced.C.Foreign students from beginners to the advanced.D.Only foreign students advanced.3.While you stay there, who will take care of you?A.Your parents.B.Your classmates.C.The school where you study.D.The family you have chosen.BTrees are “social creature” that communicate with each other in cooperative ways that hold lessons for humans, too, ecologist Suzanne Simard says. Simard grew up in Canadian forests as a child of loggers before becoming an ecologist. She's now a professor of forest ecology at theUniversityofBritish Columbia.Trees are linked to neighboring trees by a network of fungi below the surface of the earth that resembles the nervous networks in the brain, she explains. In one study, Simard watched as a Douglas fir tree that had been injured by insects appeared to send chemical warning signals to a pine nearby. The pine tree then produced defense enzymes to protect against the insect.“This was a breakthrough,” Simard says. The trees were sharing “information that actually is important to the health of the whole forest.”In addition to warning each other of danger, Simard says that trees have been known to share nutrients at critical times to keep each other healthy. She says the trees in a forest are often linked to each other via an older tree she calls a “mother” or “hub” tree.“In connecting with all the trees of different ages, the mother trees can actually ease the growth of these young trees,” she says. “The young trees will link into the network of the old trees and benefit from that huge resource capacity. And the old trees would also pass a little bit of carbon and nutrients and water to the young trees, at crucial times in their lives, that actually help them survive.”The study of trees took on a new resonance for Simard when she suffered from breast cancer. During her treatment, she learned that one of the medicines she relied on was actually obtained from what some trees produce for their own mutual defense. She explains her research on cooperation in the forest, and shares her personal story in the new bookFinding the Mother Tree: Discovering the Wisdom of theForest.4. How could a Douglas fir tree send chemical warning signals to a pine nearby?A. By an underground network of fungi.B. By the nervous networks in the brain.C. By making cooperation with each other.D. By holding lessons to it as human beings.5. According to Simard, what was a breakthrough?A. Simard was-brought up in Canadian forests.B. She became a professor of forest ecology.C. The pine tree produced defense enzymes.D. Vital information was shared among trees.6. What helped Simard understand trees further?A. Her rich knowledge of trees.B. Her childhood in the forest.C. Her medicine gained from trees.D. Her research on cooperation.7. In Simard's book we may discover the wisdom of the forest except .A. communicating cooperativelyB. warning each other of dangerC. sharing nutrientsat critical timesD. sacrificing mother trees for survivalCWhen 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 was easier. 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 reportDI don’t think I can recall a time whenI wasn’t aware of the beauty of the ocean. Growing up inAustralia, I had the good fortune of having the sea at my side. The first time I went toHalfmoonBay,I suddenly had the feeling of not being able to feel the ground with my feet anymore.For my 10th birthday, my sister and I were taken out to theGreat Barrier Reef. There were fish in different color1 s, caves and layers of coral. They made such an impression on me. When I learned that only one percent ofAustralia’sCoral Seawas protected, I was shocked. Australian marine (海洋的) life is particularly important because the reefs have more marine species than any other country on earth. But sadly, only 45% of the world’s reefs are considered healthy.This statistic is depressing, so it’s important for usto do everything to protect them. The hope that theCoral Searemains a complete ecosystem has led me to take action. I’ve become involved with the Protect Our Coral Sea activity, which aims to create the largest marine park in the world. It would serve as a place where the ocean’s species will all have a safe place forever.Together, Angus and I created a little video and we hope it will inspire people to be part of the movement. Angus also shares many beautiful childhood memories of the ocean as a young boy, who grew up sailing, admiring the beauty of the ocean, and trying to find the secrets of ocean species.12. What can we learn about the author from the underlined sentence inPara. 1?A. He seldom went surfing at the sea.B. He forgot his experiences about the ocean.C. He never went back to his hometown.D. He had a wonderful impression ofHalfmoonBay.13. What is Australian marine life like according to the second paragraph?A. It is escaping from theCoral Seagradually.B. It depends on reefs for living greatly.C. It may be faced with danger.D. It is protected better than that in other oceans.14. What’s the purpose of The Protect Our Coral Sea activity?A. It is intended to contribute to a complete ecosystem.B. It is intended to prevent more marine species being endangered.C. It is intended to set up a large nature reserve for reefs.D. It is intended to raise more teenagers’ environmental awareness.15. Why do Angus and the author create a little video?A. To urge more people to take action toprotect the marine species.B. To inspire more people to explore the secret of the ocean.C. To share their childhood experiences about the ocean.D. To bring back to people their memory of ocean species.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年成都市实验外国语学校高三英语三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AConservation Volunteering in New ZealandWhether you are a student, professional or a retiree (退休者), anyone is welcome to make a difference and contribute to protecting some of the most beautiful islands in the world. Choose a suitable city and travelout to your conservation (保护) site to work with local people!Duration: 1-12 weeks Dates: Throughout the yearArrival day: Friday Return day: FridayRequirement: General level of fitness Age: 18+What will I be doing?Volunteer in New Zealand and enjoy conserving the environment through activities such as:·Tree planting·Walking trail construction·Protect native birds, insects, fish and penguins·Seed collection·Weed controlYou, and a group of up to 10 volunteers, will work under the guidance of a conservation team leader. Your team leader will give you regular safety instructions, inform you of the project aims and assist you with working effectively.No previous experience is necessary to join the project. All you need is a love of the environment and a fairly good level of fitness to help out!1.Who can sign up for this conservation volunteering project?A.A retired maths teacher.B.A primary school student.C.A scientist with heart disease.D.A businessman in a wheelchair.2.What can you do on the volunteer trip?A.Protect cultural sites and go shopping.B.Enjoy local sightseeing and go fishing.C.Protect weeds and build roads.D.Collect seeds and plant trees.3.From which is the text probably taken?A.A history book.B.A travel magazine.C.A research paper.D.A novel.BThefirst thing we notice about new people are their faces. The next time we see these people, we remember them because we remember their faces. This seems like a simple process. However, scientists found that it is not such a simple process. The section of the brain that is responsible for face recognition seems to work differently for different people. Some people have great difficulty remembering and recognizing faces, while others almost never forget a face.Normal babies are born with a natural ability to recognize faces. In fact, their face recognition abilities are much better than their parents. Babies are most highly skilled at face recognition at six months. But by nine months, they lose this skill. By nine months, a baby’s face-recognition skills are about the same as an adult’s.Unfortunately, some people are not born with this ability to recognize faces. The part of the brain that is responsible for face recognition doesn’t work for them. This condition is called face blindness. People with very severe face blindness cannot even recognize their own faces. In fact, people with this condition can sometimes be frightened when they look in the mirror. They don’t recognize their own face, so for a second they are startled when they see this unfamiliar face.Face blindness is not always severe. Scientists believe up to 10 percent of the population may be affected by face blindness to some degree, yet many people with mild face blindness might not even know they have it. They have no reason to know they are different from anyone else until someone points it out. This is similar to people with color1 blindness. Colorblind people can’t see the difference between certain color1 s such as red and green, until someone tells them that green and red are two different color1 s.There is no cure for face blindness. So for the time being, people with face blindness need to find simple techniques to compensate for their problem. They can try to recognize people by their hairstyle, their voice, or their glasses. Hopefully, in the future as scientists learn more about this condition, they may find a cure.4. What is the first paragraph mainly about?A. The way to improve one’s face-recognition skills.B. The simple process of the brain to recognize others’ faces.C. The fact that some people have face-recognition problems.D. The importance of face recognition in human communication.5. When do children have the best face-recognition skills?A. At birth.B. Half a year old.C. Nine months old.D. In adolescence.6. What does the underlined word “startled” in the 3rd paragraph probably mean?A. Depressed.B. Confused.C. Embarrassed.D. Surprised.7. What does the author think of the problem of face blindness?A. People need to take it seriously.B. Certain techniques can make up for it.C. It will be cured in the near future.D. It has the same effect with color1 blindness.COne billion people in the world are short of water. How can this problem be solved. Some suggestions have been to desalinate ocean water or to build enormous water pipelines from areas where water is abundant. (Suggestions such as these prove extremely expensive when they are actually used.) One possibility that scientists are considering is pulling icebergs from either the North Pole or the South Pole to parts of the world with a water shortage. Although many questions must be answered before such a project could be tried, moving icebergs seems a reasonable possibility in the future.Engineers, mathematicians, and glaciologists from a dozen countries have been considering the iceberg as a future source of water. Saudi Arabia is particularly interested in this project because it has a great water shortage. Scientists estimate that it would take 128 days to transport a large iceberg (about 1/2 square mile) to Saudi Arabia. Yet the iceberg would be completely melted by the 104th day. Therefore, insulation would be essential, but how to insulate the iceberg remains an unsolved problem.The problems in transporting an iceberg are numerous. The first problem is choosing the iceberg to pull. The icebergs that form in the North Pole are quite difficult to handle because of their shape. Only a small portion extends above the water — most of the iceberg is below the surface, which would make it difficult to pull. South Pole icebergs, on the other hand, are flat and float like table tops. Thus they would be much easier to move.How can a 200-million-ton iceberg be moved. No ship is strong enough to pull such enormous weight throughthe water. Perhaps several ships could be used. Attaching ropes to an iceberg this size is also an enormous problem. Engineers think that large nails or long metal rods could be driven into the ice. What would happen if the iceberg splits into several pieces during the pulling. Even if an iceberg with very few cracks were chosen, how could it be pulled through stormy waters. Furthermore, once the iceberg reached its destination, very few ports would be deep enough to store it.All of these problems must be solved before icebergs can become a reasonable source of water. Yet scientists estimate that it will be possible to transport them in the near future. Each year, enough icebergs form to supply the whole world with fresh water for a full year. In addition, icebergs are free and nonpolluting. As a solution to the world’s water problems, icebergs may be a workable possibility.8. What is a problem in transporting iceberg?A. The size of the iceberg.B. The colour of the iceberg.C. The salt in the iceberg.D. The movement of air and water.9. What is the author’ attitude towards transporting iceberg?A. Pessimistic.B. Objective.C. Optimistic.D. Unconcerned.10. What does the last paragraph mainly tell us?A. It is hard to use iceberg.B. Iceberg are a good choice.C. There are problems with iceberg.D. Man finds no other ways to solve water shortage.11. What can be a suitable title for the text?A. Shortage of water.B. Icebergs for water.C. Scientists and icebergs.D. Iceberg—scientists headache.DPhotographer Rebecca Douglas has always been fascinated by the night sky. Her love for stars has taken theU.K.resident on “star walking” trips toIcelandand into theArctic, where she steps out onto darkened trails to capture twinkling stars and glowing planets in her images.Hiking at night isn’t uncommon. Plenty of people hike after dark to get to campsites or watch the sunrise from a mountaintop. Star walking goes a step further by blending hiking with stargazing. Rather than heading to an observatory or setting up a telescope in your backyard,star walking takes you on a brief journey to look at thestars from different viewpoints.Whether you’re in the mountainside or by the lake with stars reflecting on the water, star walking is often much more dynamic than traditional stargazing.What’s more, star walking is good for you. There are plenty of studies that show the health benefits of being in nature. Spending at least two hours a week outdoors, particularly while engaging in what involves “effortless attention”, can decrease blood pressure, heart rate, and stress levels.So how does an aspiring star walker get started? It doesn’t take much more than a sturdy pair of boots.While telescopes and binoculars obviously have their uses, people are encouraged to start with naked-eye stargazing. Using only the eyes allows one to get lost in the infinite expanse of space and lets the mind go.It is advised that one read up on the night sky before heading out. Free mobile apps, such as Star Walk 2, can help identify celestial bodies（天体）and are easy to use—simply point your phone at the sky to reveal a map. Websites like Sky & Telescope and NASA’s Space Place cover the basics, have in-depth explanations on stars, and offer advice on equipment. Space Place posts monthly skywatching updates, so you can plan outings around events such as meteor showers.In the United States, national parks are great options for inexperienced night hikers. Many offer guided outings that explain the importance of protecting night skies. Those with a good number of walks under their belt may want to try GlacierNational Park in Montana.If national parks and other dark-sky designated areas are out of range, check local astronomy clubs and observatories for guided sessions. Sites like the International Astronomical Union are useful for finding resources by area.At the end of the day, the best advice is to take it slow and enjoy the journey.“With all of the chaos（混乱）that’s happening around us, the one constant has been the night sky,” explains Douglas, who hasbeen exploring popular places nearby, long after the crowds have gone home for the day. “Walking is quite a mindful way of looking up and being reminded that, although everything feels so different, some things are still the same.”12. According to the passage, star walking refers to ________.A. going to an observatoryB. looking at stars in mountainsC. combining hiking and stargazingD. setting up a telescope in the backyard13. One of the reasons why people go on a star walking is that _______.A. it’s easier to identify celestial bodiesB. it is good for physical and mental healthC. they can enjoy the journey without crowdsD. they can raise awareness of protecting night skies14. According to the passage, a star walking beginner is advised to _______.A. prepare a pair of strong bootsB. start by observing with telescopesC. join an astronomy club or an observatoryD. find guided outings with the help of mobile apps15. The main purpose of the passage is to ________.A. excite people’s interest in star walkingB. recommend some places for star walkingC. explain the health benefits of star walkingD. introduce the preparations for star walking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年成都市实验中学高三英语三模试题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ATheatre reflects the values of the civilization out of which it grows. The following are the types of theatre performances an ancient Roman might have witnessed then.Fescennine VerseFescennine Verse was a pioneer of Roman comedy. Ironic and improvisational（即兴的）, it was used mainly at festivals or weddings, and as invective. With early native Italian funny dialogues in Latin verse, it was thought to have combined with a tradition of performances by masked dancers and musicians from Etruria.Fabula AtellanaFabula Atellana relied on common characters, masks, direct humor, and simple plots. They were performed by actors improvising. Fabula Atellana came from the Oscan city of Atella. There were 4 main types of characters: the braggart, the greedy blockhead, the clever hunchback and the stupid old man, like modern Punch and Judy shows.Fabula TogataNamed for the clothing symbolic of the Roman people Fabula Togata had various subtypes. One was the Fabula Tabernaria, named for the tavern（酒馆）where the comedy’s preferred characters, lowlifes, might be found. One describing more middle-class types, and continuing the Roman clothing theme, was the Fabula Trabeata.Fabula PraetextaFabula Praetexta is the name for Roman tragedies on Roman themes, Roman history or current politics. Fabula Praetexta was less popular than tragedies on Greek themes. During the Golden Age of drama in the Middle Republic, there were four great Roman writers of tragedy, Naevius, Ennius, Pacuvius, and Accius. Of their surviving tragedies, 90 titles remain.All the performances above began as a translation of Greek forms, even to the extent of their being performed in Greek costume.1.Where might an ancient Roman witness Fescennine Verse?A.At a party.B.At a funeral.C.At a wedding.D.At a concert.2.Which type of performance describes the middle-class life?A.Fabula Atellana.B.Fabula Tabernaria.C.Fabula Trabeata.D.Fabula Praetexta.3.What do the listed types of performances have in common?A.They copy Latin dramas.B.They take on Greek forms.C.They reflect Roman themes.D.They refer to Italian stories.B“We are running out of space and the only places to go to are other worlds... Spreading out may be the only thing that saves us from ourselves. I am convinced that humans need to leave Earth.” These are the words of the famous scientist Stephen Hawking, spoken at a science festival inNorwayin 2017, a year before his death.Hawking was not alone in this view. Many experts feel that the only way for humanity to last far into the future is to colonize other planets. That way, if an asteroid, a terrible disease, nuclear war, or some other disaster strikes Earth, civilization as we know it would still have a chance. Mars is one of the most tempting destinations. NASA, theUnited Arab Emirates, the private company SpaceX, and the organization Mars One all have plans to send humans there. “Either we spread Earth to other planets, or we risk going extinct, SpaceX founder Elon Musk said at a conference in 2013.But not everyone agrees that colonizing Mars or any other planet is such a great plan. The most common argument against going is that it’s just too expensive or dangerous. It will take huge amounts of money and other resources just to get people there, let alone set up a place for them to live. It’s not even clear if humans could survive on Mars. One of the biggest dangers there is deadly radiation that bombards the planet.Maybe all the time and money people would pour into a Mars mission would be better spent on more urgent projects here on Earth, like dealing with poverty or climate change. Some experts argue that handling a problem like an asteroid strike or disease outbreak while staying here on Earth would be much easier and less expensive than surviving on a new planet.In addition, moving to a new planet could harm or destroy anything that already lives there. Mars seems uninhabited, but it could possibly host microbial life. Human visitors may destroy this life or permanently change or damage the Martian environment. Some feel that’s too much of a risk to take.What do you think? Should humans colonize outer space or stay home?4. What can be inferred from the passage?A. Many experts insist that humans should take the risk.B. Mars is the most attractive destinations for human beings.C. Hawking firmly believes the only way to save humans is moving to Mars.D. All the other experts don’t agree with Hawking’s idea.5. Why do some experts disagree with the plan to colonize Mars?A. It will cost much more money to settle on Mars than on Earth.B. It is too long a distance from the Earth to the Mars.C. Human visitors will bring diseases to Martian environment.D. The deadly radiation that bombards the planet is the biggest danger.6. What’s the writing purpose of the passage?A. To raise people’s awareness of protecting the environment.B. To present different opinions on whether to move to the Mars.C. To arouse readers’ reflection on whether to colonize outer space.D. To inspire people to deal with the environmental problems.7. In which section of a magazine is the passage most likely from?A. Fiction.B. Current affairs.C. Social Studies.D. Science.CCanadaIs Our NeighbourCanada and the United States are neighbours.They are on the same land.They share the same long boundary(国界).These two nations are similar in many ways.Canada buys many goods from the United States.Cars and clothes are two examples.The United States also buys goods from Canada.Much of the paper used in the United States comes from Canada.Some of the oilweuse comes from Canada,too.Americans travel toCanadaon holiday.And Canadians often visit the United States.It is easy for the people of one country to go to the other country.Canadians read about the United States in newspapers and magazines.Many Americans watch Canadian baseball and hockey (曲棍球)matches on Sundays.However,there are important differences between theUnited Statesand Canada.The United States has more people.Because the population is smaller,there are more open places in Canada.There is much unused land.This is another important difference.8.Canadabuys from theUnited States.A.oil and paperB.nothingC.many thingsD.everything9.In the first paragraph “we” means ________.A.CanadiansB.AmericansC.ChineseD.students10.The people in theUnited Stateslike Canadian ________.A.baseballB.basketballC.newspapersD.oil11.Which of the following statements is WRONG?A.Canada has less people than theUSA.B.Canada has not used all the land.C.Canada is connected withAmerica.D.Canadians don’t like hockey.DIn June, 2021, a group of students from eight high schools in Winnipeg, the capital of Canada’s Manitoba province, will begin test-launching (试发射) a satellite the size of a Rubik’s cube.The one-kilogram Win-Cube satellite, named for its home city and its shape, will be put into low orbit. Once in space, it can perform for a few months or up to several years, communicating information that could help find the signs of earthquakes.There are 80 similar satellite projects worldwide, but this is the first high-school based program of its kind in Canada. 30 Manitoba high school students are having a hand in designing and building the satellite, in cooperation with aerospace (航空航天的) experts and 10 students from the University of Manitoba, and with support from two other organizations.The Win-Cube project is not something that goes on a piece of paper; it is real-world engineering, allowing high school students to have an opportunity to learn more about the exciting world of engineering through their participation in this challenging program. It is also taken as a wonderful example of the unique partnerships within Manitoba. Designing, building and launching a satellite with high-school participation will bring this world-class educational project into reality and Manitoba closer to space“These Manitoba high school students deserve congratulations for their enthusiasm, innovation (创新), and a strong love for discovery,” said Education, Citizenship and Youth Minister Peter Bjomson. “We want to make science more relevant, interesting and attractive to high school students by showing them how classroom studies can relate to practical experience in the workplace or, in this case, in space,” Bjomson added.The Win-Cube program is mainly aimed at inspiring a strong desire for discovery on the part of the students. It also shows Manitoba’s devotion to research and innovation and the development of a skilled workforce—all important drivers of knowledge-based economic growth.12. What can we learn from Mr. Bjomson? .A. Those Manitoba high school students are worth praising.B. The study of space can be practically made in classrooms.C. Manitoba high schools are famous for the study of space.D. Scientific research is too far away from high school students.13. What is the primary purpose of the project ? .A. To find the early signs of earthquakes.B. To relate studies to practical.C. To help high school students study real-world engineering.D. To inspire a strong desire for discovery among the students.14. According to the passage, what can we know about the Win-Cube satellite? .A. It is named after Manitoba and its shape.B. It is intended for international communication.C. It is designed like a Rubik’s cube both in shape and size.D. It is challenged by university students around the world.15. What may be the best title for the passage?A. Manitoba SchoolB. Win-Cube ProgramC. Space Co-operationD. Satellite Launching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。

成都市实验外国语学校高2017级数学模拟（三）文一、选择题（本大题共12小题，每小题5分，共60分）1.已知集合{}2|1,A x y x x Z ==-∈，{}2|1,B y y x x A ==+∈，则AB 为（ ）A. ∅B. [)0,+∞C. {}1D.(){}0,1【答案】C 【解析】 【分析】求函数21,y x x Z =-∈的定义域化简集合A 的表示，求函数21,y x x A =+∈的值域化简集合B 的表示，最后利用交集的定义进行求解即可.【详解】因为{}{}2|1,1,0,1A x y x x Z ==-∈=-，{}{}2|1,2,1B y y x x A ==+∈=，所以{}1A B ⋂=. 故选：C【点睛】本题考查了集合的交集运算，考查了求函数的定义域和值域，考查了数学运算能力. 2.若复数z 满足()13i z i +=，则z 的虚部为（ ）A. 1-B. 2-C. i -D. 2i -【答案】A 【解析】 【分析】计算()12i z +=，利用复数除法运算得到答案. 【详解】()13312i z i +==+=，故()()()2121111i z i i i i -===-++-，故虚部为1-. 故选：A.【点睛】本题考查了复数的模，复数的除法，复数的虚部，意在考查学生的计算能力和综合应用能力.3.在平面直角坐标系xOy 中，已知角α的顶点在坐标原点，始边与x 轴正半轴重合，终边经过点(2,1)P ，则cos2=α（ ）A.22B.13C. 13-D. 22-【答案】B 【解析】 【分析】先由角α的终边过点(21)P ，，求出cos α，再由二倍角公式，即可得出结果. 【详解】解：因为角α的顶点在坐标原点，始边与x 轴正半轴重合，终边经过点(21)P ，， 所以26cos 321α==+， 因此21cos 22cos 13=-=αα. 故选：B【点睛】本题主要考查三角函数的定义，以及二倍角公式，熟记三角函数的定义与二倍角公式即可，属于基础题.4.《周易》是我国古代典籍，用“卦”描述了天地世间万象变化．如图是一个八卦图，包含乾、坤、震、巽、坎、离、艮、兑八卦（每一卦由三个爻组成，其中“”表示一个阳爻，“”表示一个阴爻）．若从含有两个及以上阳爻的卦中任取两卦，这两卦的六个爻中都恰有两个阳爻的概率为（ ）A. 13B.12C.23D.34【答案】B 【解析】 【分析】基本事件总数为6个，都恰有两个阳爻包含的基本事件个数为3个，由此求出概率.【详解】解：由图可知，含有两个及以上阳爻的卦有巽、离、兑、乾四卦，取出两卦的基本事件有（巽，离），（巽，兑），（巽，乾），（离，兑），（离，乾），（兑，乾）共6个，其中符合条件的基本事件有（巽，离），（巽，兑），（离，兑）共3个， 所以，所求的概率3162P ==. 故选：B.【点睛】本题渗透传统文化，考查概率、计数原理等基本知识，考查抽象概括能力和应用意识，属于基础题．5.下列判断正确的是（ ）A. 两圆锥曲线的离心率分别为1e ，2e ，则“121e e <”是“两圆锥曲线均为椭圆”的充要条件B. 命题“若21x =，则1x =.”的否命题为“若21x =，则1x ≠.”C. 若命题“p q ∧”为假命题，则命题“p q ∨”是假命题D. 命题“x R ∀∈，22x x ≥."的否定是“0x R ∃∈，0202x x <.”【答案】D 【解析】 【分析】对于A ，取特值：113e =，232e =，可知A 不正确；对于B ，只否定了结论，没有否定条件，故B 不正确；对于C ，命题p 与命题q 一个为真命题、一个为假命题时，可得命题“p q ∨”是真命题，所以C 不正确；对于D ，根据命题的否定的概念，可知D 正确.【详解】对于A ，若两圆锥曲线均为椭圆，则101e <<，201e <<，所以1201e e <<，所以“121e e <”是“两圆锥曲线均为椭圆”的必要条件，取113e =，232e =满足121e e <，此时一个圆锥曲线为椭圆，一个圆锥曲线为双曲线，所以“121e e <”不是“两圆锥曲线均为椭圆”的充分条件，故A 不正确；对于B ，命题“若21x =，则1x =.”的否命题为“若21x ≠，则” 1x ≠，故B 不正确； 对于C ，若命题“p q ∧”为假命题，则p 与q 至少有一个为假命题，当p 为假命题， q 为真命题时，“p q ∨”为真命题，故C 不正确；对于D ，命题“x R ∀∈，22x x ≥."的否定是“0x R ∃∈，0202x x <.”是正确的，故D 正确.故选：D.【点睛】本题考查了充要条件，考查了椭圆和双曲线的离心率，考查了命题的真假判断，考查了否命题和命题的否定，属于基础题.6.函数2()cos ()x x e e xf x x --=的部分图象大致是（ ）A. B.C. D.【答案】B 【解析】 【分析】先判断函数的奇偶性，然后利用特殊点的函数值的符号进行排除即可. 【详解】由题知,函数()f x 的定义域为(,0)(0,)-∞+∞,关于原点对称,且()()22cos()cos ()()()xx xx e e x e e x f x f x x x------==-=--,所以()f x 是奇函数,所以排除C ,D ;又∵()22cos 11()0ee f e e ππππππππ--⎛⎫==-< ⎪⎝⎭,所以排除A , 故选：B .【点睛】本题主要考查函数图像的判断与识别，结合函数的奇偶性与特殊值的符号进行排除即可解决，属于中等题.7.在ABC ∆中，角A ，B ，C 的对边分别是a ，b ，c ，且)cos cos 0a C c A --＝，则角A 的大小为（ ） A.4π B.3π C.2π D.34π 【答案】A 【解析】 【分析】先利用正弦定理化边为角可得sin cos sin cos cos A C C A B A +=，再进一步化简求出cos A =A ．【详解】∵)cos cos 0a C c A --=，由正弦定理可得sin cos sin cos cos A C C A B A +=，即sin cos B B A =.∵sin 0B ≠，∴cos A =0A π<<，∴4A π=.选A ． 【点睛】本题主要考查正弦定理及三角恒等变换，属中等难度题．8.设m ，n 是两条不同的直线，α，β是两个不同的平面，则下列命题正确的是( ) A. 若//m α，//n α，则//m n B. 若//αβ，m α⊂，n β⊂，则//m nC. 若αβ⊥，m αβ=，n ⊂α，则n β⊥D. 若m α⊥，//m n ，n β⊂，则αβ⊥ 【答案】D 【解析】 【分析】利用线面平行的性质，面面垂直的性质与判定，即可得出结论．【详解】解：由m ，n 是两条不同的直线，α，β是两个不同的平面，知： 在A 中，若//m α，//n α，则m 与n 相交、平行或异面，故A 错误； 在B 中，若//αβ，m α⊂，n β⊂，则m 与n 平行或异面，故B 错误； 在C 中，若αβ⊥，m αβ=，n ⊂α，则n 与β相交、平行或n β⊂，故C 错误；在D 中，若m α⊥，//m n ，n β⊂，则由面面垂直的判断定理得αβ⊥，故D 正确． 故选：D ．【点睛】本题考查命题真假的判断，考查空间中线线、线面、面面间的位置关系等基础知识，考查运算求解能力，属于中档题．9.若实数x ，y 满足约束条件2040250x y x y x y -+≥⎧⎪+-≥⎨⎪--≤⎩，则11y z x -=+的最大值为（ ）A. 1B. 2C. 3D. 4【答案】A 【解析】 【分析】作出约束条件所表示的平面区域，结合图象确定目标函数的最优解，即可求得目标函数的最值，得到答案.【详解】由题意，作出约束条件2040250x y x y x y -+≥⎧⎪+-≥⎨⎪--≤⎩所表示的平面区域，如图所示，又由目标函数11y z x -=+表示可行域内点(,)P x y 与定点(1,1)-的连线的斜率， 因为点(1,1)-恰好在直线20x y -+=上，结合图象，可得当点(,)P x y 在线段AB 时，能使得目标函数11y z x -=+取得最大值， 又由直线20x y -+=的斜率为1，所以最大值为max 1z =. 故选：A.【点睛】本题主要考查了线性规划的应用，其中解答中准确作出约束条件所表示的平面区域，结合图象确定目标函数的最优解是解答的关键，着重考查数形结合思想，以及运算能力. 10.定义在R 上的偶函数()f x 满足()()2f x f x +=，且在[－1，0]上单调递减，设()2.8a f =-，()1.6b f =-，()0.5c f =，则a 、b ，c 大小关系是（）A. a b c >>B. c a b >>C. b c a >>D. a c b >>【答案】D 【解析】 【分析】由()()2f x f x +=可求函数周期2，利用周期及偶函数可转化为在[－1，0]上的函数值，利用单调性比较大小.【详解】∵偶函数()f x 满足()()2f x f x +=，∴函数的周期为2. 由于()()2.80.8a f f =-=-，()()()1.60.40.4b f f f =-==-， ()()0.50.5c f f ==-，0.80.50.4-<-<-.且函数()f x 在[－1，0]上单调递减，∴a c b >>.【点睛】本题主要考查了函数的周期性，单调性及偶函数的性质，属于中档题.11.已知双曲线2222:1(0,0)x y E a b a b -=>>的左、右焦点分别为12,F F ,126,F F P =是E 右支上的一点，1PF 与y 轴交于点A ，2PAF ∆的内切圆在边2AF 上的切点为Q ，若AQ =则E 的离心率是( )A.【答案】C 【解析】 【分析】由双曲线的定义和内切圆的切线性质，圆外一点向圆引切线，则切线长相等，结合离心率公式即可得到所求的值【详解】设2PAF ∆的内切圆在边2PF 上的切点为M ，在AP 上的切点为N则PM PN =，AQ AN ==22QF MF =由双曲线的对称性可得：1222AF AF AQ QF QF ==+=由双曲线的定义可得121222PF PF PA AF PM MF QF AN NP PM MF -=+--=++--2a ==解得a =又126F F =，即有3c =则离心率ce a== 故选C【点睛】本题考查了双曲线的离心率，结合了三角形内切球，由切线长定理和双曲线定义求出a 的值是本题的关键，综合性较强 12.已知函数33()1xf x x e =++，其导函数为()f x '，则()()()()2020202020192019f f f f ''+-+-- 的值为（ ）A. 1B. 2C. 3D. 4【答案】C 【解析】 【分析】首先根据题意得到()()3f x f x -+=，()f x '为偶函数，再计算()()()()2020202020192019f f f f ''+-+--即可.【详解】因为33()1x f x x e =++，()333()131x xx f x x e x ee --=+-=-++， 所以()()3f x f x -+=.又因223()3(1)xx e f x x e -'=++， ()222233()33(1)()(1)x x x x e e f x x f x x e e ----'-=+-=+'=++ 所以()f x '为偶函数.所以(2020)(2020)(2019)(2019)3f f f f ''+-+--=. 故选：C【点睛】本题主要考查求导公式，同时考查了函数的奇偶性，属于简单题. 二、填空题（本大题共4小题，每小题5分，共20分） 13.已知向量()1,3a =，3,1b 则向量a 在向量b 方向上的投影为____________.【解析】 【分析】根据||||cos a b a b a ⋅=<，b >，得a 在b 上的投影为||cos a a <，||a bb b ⋅>=，求出a b ⋅，代入投影的公式计算即可．【详解】向量()1,3a =，3,1b，∴3+323a b ⋅==，||2b =，∴a 在b 方向上的投影为||cos a a <，2332||a b b b ⋅>===．故答案为：3．【点睛】本题考查平面向量数量积的坐标运算及几何意义，属于基础题．14.函数f(x)＝x 3＋3ax 2＋3(a ＋2)x ＋1有极大值又有极小值，则a 的范围是 ． 【答案】【解析】 【分析】将原问题转化为二次函数有两个不相等的实数根的问题，然后求解a 的取值范围即可. 【详解】由题意可得：()()2'3632f x x ax a =+++，若函数有极大值又有极小值，则一元二次方程()236320x ax a +++=有两个不同的实数根，即：()()2643320a a ∆=-⨯⨯+>，整理可得：整理可得：()()36120a a +->，据此可知a 的取值范围是2a >或1a <-.【点睛】(1)可导函数y ＝f (x )在点x 0处取得极值的充要条件是f ′(x 0)＝0，且在x 0左侧与右侧f ′(x )的符号不同．(2)若f (x )在(a ，b )内有极值，那么f (x )在(a ，b )内绝不是单调函数，即在某区间上单调增或减的函数没有极值． 15.已知函数()3cos (0)f x x x ωωω=+>，其图象与直线2y =的两个相邻交点的距离等于π，则()f x 的单调递增区间为______________． 【答案】,?36k k ππππ⎡⎤-+⎢⎥⎣⎦【解析】函数()3cos 2sin 6f x x x x πωωω⎛⎫=+=+⎪⎝⎭，因为()y f x =的图象与直线2y =的两个相邻交点的距离等于π，函数的周期T π=，所以2ω=，所以()2sin26f x x π=+（），因为222,262k x k k Z πππππ-≤+≤+∈，解得[]36x k k ππππ∈-+，，k Z ∈，即函数的单调增区间为[]36k k k Z ππππ-+∈，，，故答案为[]36k k k Z ππππ-+∈，，. 16.已知抛物线方程24y x =，F 为焦点，P 为抛物线准线上一点，Q 为线段PF 与抛物线的交点，定义：||()||PF d P FQ =.已知点(P -，则()d P =______；设点(1,)(0)P t t ->，则2()||d P PF -的值为____. 【答案】 (1). 4 (2). 2 【解析】 【分析】（1）根据直线PF的方程1)y x =--，求出点1(2Q ，再利用焦半径公式，即可得答案；（2）根据||2()||22||||PQ d P PF PF FQ -=+-，再利用抛物线的定义，即可得答案； 【详解】（1）(P -，(1,0)F ，∴||6PF =，∴直线PF的方程为1)y x =--，与24y x =联立得：22520x x -+=，解得：12x =或2x =，∴1(2Q ，∴||6()41||12PF d P FQ ===+； （2）设准线与x 轴的交点为M ，QN PM ⊥于N ，∴||||||||2()||2||2||22||||||||PF PQ QF PQ d P PF PF PF PF FQ FQ FQ +-=-=-=+- ||||22||22||22||PQ PF PF PF NQ =+-=+-=， 故答案为：4,2.【点睛】本题考查抛物线中线段比例的新定义题、抛物线的焦半径，考查函数与方程思想、转化与化归思想、数形结合思想，考查逻辑推理能力、运算求解能力.三、解答题（本大题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤） 17.设等差数列{}n a 的前n 项的和为n S ，且462S =-，675S =-，求： （1）求{}n a 的通项公式n a ； （2）求数列{}n a 的前14项和. 【答案】（1）323n a n =-；（2）147. 【解析】 【分析】（1）由已知条件列出关于1,a d 的方程组，求出1,a d 可得到n a ；（2）由通项公式n a 先判断数列{}n a 中项的正负，然后再化简数列{}n a 中的项，即可求出结果.【详解】解：（1）设等差数列{}n a 的公差为d ，依题意得11434622656752a d a d ⨯⎧+=-⎪⎪⎨⨯⎪+=-⎪⎩，解得120,3a d =-=，∴()2013323n a n n =-+-⨯=-； （2）∵323n a n =-，∴由0n a <得8n <，22(20323)3433432222n n n n n S n n -+--===-∴123141278141472a a a a a a a a a S S ++++=----+++=-223433431414772222⎛⎫=⨯-⨯-⨯-⨯ ⎪⎝⎭()()7424372143147=---=.【点睛】此题考查等差数列的基本量计算，考查计算能力，属于基础题.18.某网购平台为了解某市居民在该平台的消费情况，从该市使用其平台且每周平均消费额超过100元的人员中随机抽取了100名，并绘制如图所示频率分布直方图，已知中间三组的人数可构成等差数列.（1）求,m n 的值；（2）分析人员对100名调查对象的性别进行统计发现，消费金额不低于300元的男性有20人，低于300元的男性有25人，根据统计数据完成下列22⨯列联表，并判断是否有99%的把握认为消费金额与性别有关？（3）分析人员对抽取对象每周的消费金额y 与年龄x 进一步分析，发现他们线性相关，得到回归方程ˆ5yx b =-+.已知100名使用者的平均年龄为38岁，试判断一名年龄为25岁的年轻人每周的平均消费金额为多少.（同一组数据用该区间的中点值代替）22⨯列联表男性女性合计300消费金额300<临界值表：22()()()()()n ad bc K a b c d a c b d -=++++，其中n a b c d =+++【答案】（1）0.0035m =，0.0025n =（2）详见解析（3）395元 【解析】 【分析】（1）根据频率分布直方图可得0.006m n +=，结合0.00152m n +=可得,m n 的值. （2）根据表格数据可得28.249K ≈，再根据临界值表可得有99%的把握认为消费金额与性别有关.（3）由频率分布直方图可得调查对象的周平均消费，从而得到520b =，利用线性回归方程可计算年龄为25岁的年轻人每周的平均消费金额.【详解】（1）由频率分布直方图可知，0.010.001520.0010.006m n +=-⨯-=， 由中间三组的人数成等差数列可知0.00152m n +=， 可解得0.0035m =，0.0025n =（2）周平均消费不低于300元的频率为()0.00350.00150.0011000.6++=⨯，因此100人中，周平均消费不低于300元的人数为1000.660⨯=人. 所以22⨯列联表为消费金额30020 40 60 消费金额300<25 15 40 合计455510022100(20152540)8.249 6.63545556040K ⨯-⨯=≈>⨯⨯⨯所以有99%的把握认为消费金额与性别有关. （3）调查对象的周平均消费为0.151500.252500.353500.154500.10550330⨯+⨯+⨯+⨯+⨯=，由题意330538b =-⨯+，∴520b =525520395y =-⨯+=.∴该名年龄为25岁的年轻人每周的平均消费金额为395元.【点睛】（1）频率分布直方图中，各矩形的面积之和为1，注意直方图中，各矩形的高是频率组距； （2）两类变量是否相关，应先计算2K 的值，再与临界值比较后可判断是否相关.（3）线性回归方程对应的直线必经过(),x y .19.如图1，在平行四边形ABCD 中，4=AD ，22AB =，45DAB ∠=︒，E 为边AD 的中点，以BE 为折痕将ABE △折起，使点A 到达P 的位置，得到图2几何体P EBCD -．（1）证明：PD BE ⊥；（2）当BC ⊥平面PEB 时，求三棱锥C PBD -的体积．【答案】（1）证明见解析；（2）83． 【解析】 【分析】（1）由已知条件和勾股定理可得EB AD ⊥，根据折叠的不变性可得EB PE ⊥，EB ED ⊥，由线面垂直的判定和性质可得证；（2）由线面垂直的性质可得出PE ⊥平面BCD ，PE 就是三棱锥P CBD -的高，再运用等体积法可得出三棱锥的体积.【详解】（1）依题意，在ABE △中（图1），2AE =，AB =45EAB ∠=︒，由余弦定理得2222cos 45EB AB AE AB AE =+-⋅⋅︒842242=+-⨯⨯=， ∴222AB AE EB =+，即在平行四边形ABCD 中，EB AD ⊥． 以BE 为折痕将ABE △折起，由翻折不变性得， 在几何体P EBCD -中，EB PE ⊥，EB ED ⊥．又ED PE E =，∴BE ⊥平面PED ，又BE ⊂平面PEB ，∴PD BE ⊥．（2）∵BC ⊥平面PEB ，PE ⊂平面PEB ，∴BC PE ⊥．由（1）得EB PE ⊥，同理可得PE ⊥平面BCE ，即PE ⊥平面BCD ，PE 就是三棱锥P CBD -的高．又45DCB DAB ∠=∠=︒，4BC AD ==，CD AB ==2PE AE ==，∴11sin 454422CBD S BC CD =⨯⨯⨯︒=⨯⨯=△， 11842333C PBD P CBD BCD V V S PE --==⨯=⨯⨯=△，因此，三棱锥C PBD -的体积为83． 【点睛】本题考查由平面图形折叠成空间几何体中的线面关系，以及三棱锥的体积的求解，属于中档题.20.已知椭圆E 的左右焦点分别是1(F 、2F ，且经过点2M ⎭. （1）求椭圆E 的标准方程：（2）设AC ，BD 是过椭圆E 的中心且相互垂直的椭圆E 的两条弦，问是否存在定圆G ，使得G为四边形ABCD 的内切圆?若存在，求圆G 的方程，若不存在，请说明理由.【答案】（1）2214x y +=；（2）存在，2245x y +=. 【解析】 【分析】（1）根据椭圆的定义，求出,,a b c ，得到椭圆的标准方程； （2）先分析BC 与x 轴垂直时，得到圆2245x y +=为四边形ABCD 的内切圆，再当BC 与x 轴不垂直时，设BC 的方程为y kx m =+，与椭圆联立，得到根与系数的关系，再由OB OC ⊥，得到,m k 的关系式，再分析原点O 到BC 的距离d ，再理可得，O 到直线AB ，直线CD ，直线AD ，知存在定圆G ，使得G 为四边形ABCD 的内切圆，并求得内切圆的方程.【详解】（1）设椭圆E 的标准方程是2221(0)x y a b a b+=>>，由椭圆的定义可知，12|2MF MF a +=，所以2a =所以2a =，因为c =，所以1b =，故椭圆E 的标准方程为2214x y +=.（2）若BC 与x 轴垂直，则AB 与x 轴平行，此时四边形ABCD 为正方形，||||5x y ==，所以圆2245x y +=为四边形ABCD 的内切圆.若BC 与x 轴不垂直，则AB 与x 轴不平行，设直线BC 的斜率为k ，直线BC 的方程为y kx m =+，与椭圆E 的交点为()()1122,,,B x y C x y ，由2244y kx mx y =+⎧⎨+=⎩，得222(14)8440k x kmx m +++-=，所以122814km x x k +=-+，21224414m x x k-=+， 因为OB OC ⊥，所以12120x x y y +=， 即()()22121210kx xmk x x m ++++=， ()22222448101414m kmk mk m k k-+-⋅+=++， 所以22544m k =+， 圆心O 到直线BC的距离为d ， 同理可证圆心O 到直线AB ，直线CD ，直线AD， 所以四边形ABCD 的内切圆G 的方程为2245x y +=; 综上所述，存在定圆G ，使得G 为四边形ABCD 的内切圆， 内切圆的方程为2245x y +=. 【点睛】本题考查了椭圆定义求椭圆的标准方程，直线与椭圆的位置关系，点到直线的距离，还考查了设而不解，联立方程组，根与每每的关系等基本技巧，考查了学生的逻辑推理、直观想象与数学运算等数学核心素养，难度较大.21.已知函数2()1xe f x ax bx =++，其中0a >，b R ∈，e 为自然对数的底数.(1)若1b =，且当0x ≥时，()1f x ≥总成立，求实数a 的取值范围；(2)若0b =，且()f x 存在两个极值点1x ，2x ，求证：2121()()2e f x f x ++<【答案】(1) 102a <≤；(2)见解析. 【解析】 【分析】(1)由已知可得2212()()(1)x ae ax x af x ax x -⋅⋅+'=++ ，只需对21a a -与0的大小关系分类讨论，确定函数的单调性，从而确定函数()f x 的最小值，即可求出实数a 的取值范围；(2)根据1x ，2x 是()0f x '=的根，可得1x 与2x 的关系及其范围，进而可将12()()f x f x +用含有1x 的式子表示，构造函数即可证出.【详解】(1)若1b =，则2()1xe f x ax x =++，所以2222222212()(1)(21)[(12)]()(1)(1)(1)x xxxae ax x e ax x e ax e ax a x af x ax x ax x ax x -⋅⋅+++-++-'===++++++， 因为0a >，0x ≥， 所以当120a a-≥，即102a <≤时，()0f x '≥，所以函数()f x 在[0,+)∞上单调递增，所以min ()(0)11f x f ==≥，符合题意；当120a a -<，即12a >时，21(0,)a x a -∈时，()0f x '<；21(,)a x a -∈+∞时，()0f x '>， 所以函数()f x 在21(0,)a a -上单调递减，在21(,)a a-+∞上单调递增， 所以min ()(0)1f x f <=，不符合题意， 综上：实数a 的取值范围为102a <≤. (2) 若0b =，则2()1xe f x ax =+，所以222222(1)2(21)()(1)(1)x x x e ax e ax e ax ax f x ax ax +-⋅-+'==++， 因为()f x 存在两个极值点，所以2440a a ->，所以1a >， 令()0f x '=，得2210ax ax -+=， 所以12,x x 是方程2210ax ax -+=的两个根， 所以122x x +=，121(0,1)x x a=∈，且21112ax ax +=，22212ax ax +=， 不妨设12x x <，则12012x x <<<<，所以12121212221212121()()11222x x x x x x e e e e e e f x f x ax ax ax ax a x x ⎛⎫+=+=+=+ ⎪++⎝⎭121211221211112111()[(2)]222x x x x x x x e x e x e x e x e x e a x x -+=⋅=+=-+， 令2()(2)(01)xxh x x e xex -=-+<<，所以222()(2)(1)()0xxxx x x h x e x e e xe x e e ---'=-+-+-=-+>，所以()h x 在(0,1)上单调递增，所以()(1)2h x h e <=，所以12()()f x f x e +<，又212e e +<，所以2121()()2e f x f x ++<.【点睛】本题主要考查导数的综合应用，考查函数的单调性、最值问题，考查学生分析问题解决问题的能力，属于中档题.22.己知在平面直角坐标系xOy 中，曲线C 的参数方程为222111x t t y t ⎧=-+⎪⎪-⎨⎪=⎪-⎩（t 为参数）.以原点O 为极点，x 轴正半轴为极轴建立极坐标系，直线l的极坐标方程为cos 34πρθ⎛⎫+= ⎪⎝⎭. （1）求曲线C 和直线l 的直角坐标方程；（2）若直线l 交曲线C 于A ，B 两点，交x 轴于点P ，求11PA PB+的值. 【答案】（1）C ：()22411x y x -=≠-；l：12x y -=（2）8. 【解析】 【分析】直接利用转换关系，把参数方程、极坐标方程化为直角坐标方程. 将直线的参数方程与双曲线的方程联立，利用参数的几何意义得出答案.【详解】解：（1）曲线C 的参数方程为222111x t t y t ⎧=-+⎪⎪-⎨⎪=⎪-⎩（t 为参数），转化为直角坐标方程为()22411x y x -=≠-， 直线l的极坐标方程cos 3πρθ⎛⎫+= ⎪⎝⎭直角坐标方程为：12x y -=（2）由于直线与x轴的交点坐标为2⎛⎫ ⎪ ⎪⎝⎭，所以直线的参数方程为12x y t ⎧=+⎪⎪⎨⎪=⎪⎩(t 为参数)， 代入2241x y -=得到：210t --=，所以：12t t +=121t t ⋅=-， 则：1212118t t PA PB t t -+===.【点睛】本题考查参数方程、极坐标方程与直角坐标方程之间的转换，同时考查直线参数的意义，考查了学生的运算能力和转换能力，属于基础题.23.已知a ，b ，c 均为正实数，求证：（1）()2()4a b ab c abc ++≥；（2）若3ab c ++=≤.【答案】证明过程详见解析【解析】【分析】⑴将求证的不等式进行化简，经历移项、提取公因式、配方后，要证明其成立只需要证明化简后的不等式成立 123222a a +++≤=，同理可得另外两个也是成立，结合已知条件即可求证结果【详解】证明：(1)要证()()24a b ab cabc ++≥，可证222240a b ac ab bc abc +++-≥，需证()()2222b 220a c ac a c b bc +-++-≥， 即证()()220b a c a c b -+-≥，当且仅当a b c ==时，取等号，由已知，上式显然成立， 故不等式()()24a b ab c abc ++≥成立．(2)因为,,a b c 均为正实数，123222a a +++≤=，当且仅当12a +=时，取等号， 123222b b +++≤=当且仅当12b +=时 ，取等号，123222c c +++≤=当且仅当12c +=时，取等号，62a b c d +++≤=≤1a b c ===时，取等号．【点睛】本题考查了不等式的证明问题，在求解过程中可以运用基本不等式、对要证明的不等式进行化简等方法来求证，关键是要灵活运用基本不等式等方法求证结果．。

2020年四川省成都市实验外国语学校高考数学模拟（三）试题一、单选题1．已知集合{}1,2,3,4,5A =，集合{}1,2,3B =，则AB =（ ） A ．∅ B ．{}1,2,3C ．{}1,2,3,4,5D ．{}4,5 2．若复z 满足(2)23i z i ⋅+=-+（i 是虚数单位），则z 的虚部为（ ）A ．iB ．2iC ．1D ．23．已知命题p :若>b a 则22b a >；命题q :在ABC ∆中，若A >B 则sinA >sinB ，下列命题为真命题的是( )A ．p q ∧B ．p q ⌝∧C ．p q ∧⌝D ．p q ⌝∧⌝4．已知函数()y f x =在()0+∞，上非负且可导，满足，()()21xf x f x x x +≤-+-',若0a b <<,则下列结论正确的是( )A ．()()af b bf a ≤B ．()()af b bf a ≥C ．()()af a f b ≤D ．()()bf b f a ≤ 5．已知一个射手每次击中目标的概率为35p =，他在四次射击中命中两次的概率为（ ） A ．36625 B ．216625 C ．96625 D ．246256．若双曲线22221(0,0)x y a b a b-=>>与直线y =有交点，则其离心率的取值范围是（ ） A ．()1,2 B ．(]1.2 C ．()2,+∞ D ．[)2,+∞ 7．甲、乙两人准备在一段长为1200 m 的笔直公路上进行跑步，甲、乙跑步的速度分别为4 m/s 和6 m/s ，起跑前乙在起点，甲在乙前面100 m 处，若同时起跑，则两人从起跑至其中一人先到达终点的过程中，甲、乙之间的距离()m y 与时间()s t 的函数图像是（ ）A ．B ．C ．D ．8．8的展开式中常数项为( ) A ．105 B ．358 C ．3516 D ．3549．函数33y x x =-的极大值为m ，极小值为n ，则m n +为( )A ．0B ．1C ．2D ．410．设m ，n 是两条不同的直线，α，β是两个不同的平面，则命题p ：m n ⊥的一个充分条件是（ ）A ．q ：//αβ，m α⊂，n β⊥B ．q ：//αβ，m α⊥，n β⊥C ．q ：αβ⊥，m α⊥，βn//D ．q ：αβ⊥，m α⊂，βn//11．已知β为锐角，角α的终边过点((),2sin αβ+=，则cos β=（ ）A ．12BC D12．已知,,a b c 分别是ABC ∆内角,,A B C 的对边，sin cos a B A =，当4b c +=时，ABC ∆面积的最大值为（ ）A B C D ． 二、填空题13．已知函数()32232x ax f x bx c =+++在区间()0,1内取极大值，在区间()1,2内取极小值，则()223z a b =++的取值范围为______.14．若平面向量1e ，2e 满足11232e e e =+=，则1e 在2e 方向上投影的最大值是________． 15．已知函数()sin()f x A x B ωϕ=++，其中A 、B 、ω、ϕ均为实数，且0A >，0>ω， ||2πϕ<，写出满足(1)2f =，1(2)2f =，(3)1f =-，(4)2f =的一个函数()f x =________（写出一个即可）三、解答题16．设函数21()ln .2f x x ax bx =-- 当3,2a b ==时，求函数()f x 的单调区间；令21()()(03)2a F x f x ax bx x x =+++<≤其图象上任意一点处切线的斜率18≤k 恒成立，求实数a 的取值范围；当0a b 时，令1()(),()H x f x G x mx x=-=若()H x 与()G x 的图象有两个交点1122(,),(,)A x y B x y ,求证：2122x x e >17．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，取与直角坐标系相同的长度单位建立极坐标系.曲线1C 的参数方程为cos sin x a y φφ=⎧⎨=⎩，（φ为参数），曲线2C 的极坐标方程为()04πθρ=≥，且1C 与2C .（1）求曲线1C 的普通方程.（2）设A B ，为曲线1C 与y 轴的两个交点，M 为曲线1C 上不同于A B ，的任意一点，若直线AM 与MB 分别与x 交于P Q ，两点，求证：OP PQ ⋅为定值.18．如图，已知四棱锥P ABCD -的底面是等腰梯形，//AD BC ，2AD =，4BC =，60ABC ∠=︒，PAD △为等边三角形，且点P 在底面ABCD 上的射影为AD 的中点G ，点E 在线段BC 上，且:1:3CE EB =.（1）求证：DE ⊥平面PAD .（2）求二面角A PC D --的余弦值.19．“双十二”是继“双十一”之后的又一个网购狂欢节，为了刺激“双十二”的消费，某电子商务公司决定对“双十一”的网购者发放电子优惠券.为此，公司从“双十一”的网购消费者中用随机抽样的方法抽取了100人，将其购物金额（单位：万元）按照[0.1,0.2)，[0.2,0.3),,[0.9,1]分组，得到如下频率分布直方图：根据调查，该电子商务公司制定了发放电子优惠券的办法如下：（1）求购物者获得电子优惠券金额的平均数；（2）从购物者中随机抽取10人，这10人中获得电子优惠券的人数为X ，求X 的数学期望. 20．已知正数,,a b c 满足3a b c ++=.（Ⅰ）若221a b +=，求c 的取值范围；（Ⅱ）求证：3bc ac ab a b c++≥. 21．已知数列{}n a 中148,2a a ==，且满足212n n n a a a +++=.(1) 求数列{}n a 的通项公式；(2) 设n S是数列{}n a的前n项和，求n S.22．已知以点C为圆心的圆经过点A(－1,0)和B(3,4)，且圆心在直线x＋3y－15＝0上．设点P在圆C上，求△P AB的面积的最大值．四、双空题23．直线l过抛物线C：y2＝4x的焦点F且与C交于A（x1，y1），B（x2，y2）两点，则y1y2＝_____．过A，B两点分别作抛物线C的准线的垂线，垂足分别为P，Q，准线与x轴的交点为M，四边形F APM 的面积记为S1，四边形FBQM的面积记为S2，则S1•S2﹣3|AF|•|BF|＝_____．【答案与解析】1．B直接根据交集的运算得出结果.解：由已知得{}1,2,3AB =， 故选：B.本题考查交集的运算，是基础题.2．D根据复数除法的运算法则，求出z ，即可得出结论.∵223i z i i ⋅+=-+，∴212i z i i-+==+， ∴z 的虚部为2．故选：D .本题考查复数的代数运算及复数的基本概念，属于基础题．3．B举反例得到命题p 为假命题，根据正弦定理得到命题q 为真命题，判断选项得到答案.命题p ：若>b a 则22b a >，取0,2b a ==-，22b a >不成立，故为假命题；命题q ：在ABC ∆中，若A >B ，则a b >，根据正弦定理则：sinA >sinB ，故为真命题；故p q ⌝∧为真命题.故选：B .本题考查了命题的真假判断，意在考查学生的综合应用能力.4．A因为()()21xf x f x x x +≤-+-'()'0,xf x ⎡⎤∴<∴⎣⎦函数()()F x xf x =在()0,∞+上递减，又0a b <<且()f x 非负，于是有()()0af a bf b >≥，① 22110a b >>， ② ①②两式相乘得()()()()0f a f b af b bf a ab >≥→<，根据“或”命题成立的条件可得()()af b bf a ≤成立，故选A. 【方法点睛】本题主要考查抽象函数的单调性以及函数的求导法则，属于难题.求解这类问题一定要耐心读题、读懂题，通过对问题的条件和结论进行类比、联想、抽象、概括，准确构造出符合题意的函数是解题的关键；解这类不等式的关键点也是难点就是构造合适的函数，构造函数时往往从两方面着手：①根据导函数的“形状”变换不等式“形状”；②若是选择题，可根据选项的共性归纳构造恰当的函数.本题通过观察四个选项，联想到函数()()F x xf x =，再结合条件判断出其单调性，进而得出正确结论.5．B命中次数X 服从二项分布34,5B ⎛⎫ ⎪⎝⎭， 所以在四次射击中命中两次的概率为222432216()()55625P C ==.故选B. 点睛：判断一个随机变量是否服从二项分布，要看两点：①是否为n 次独立重复试验，在每次试验中事件A 发生的概率是否均为p ；②随机变量是否为在这n 次独立重复试验中某事件发生的次数，且()()1n k k k n p X k C p p -==-表示在独立重复试验中，事件A 恰好发生k 次的概率．6．C双曲线的焦点在x 轴，一条渐近线方程为b y x a=，只需这条渐近线比直线y =的斜率大，即2b e a >=>，故选C. 7．C设 s t 时，甲、乙两人距离起点分别是1 m s 和2 m s ，得到1s ，2s 的函数关系式，由函数解析式求出甲乙达到终点的时间以及相遇时间，从而判断图像。