2018年南洋模范中学第二学期高三年级3月月考

南模中学高三月考数学试卷2019.03一. 填空题1. 已知全集U =R ，若集合{|0}1xA x x =>-，则U C A = 2. 双曲线2226x y -=的焦距为3. 已知61()ax x+二项展开式中的第五项系数为152，则正实数a = 4. 已知函数31()x f x x a +=+（13a ≠）的图像与它的反函数的图像重合，则实数a 的值为5. 设x 、y 满足约束条件360200,0x y x y x y --≤⎧⎪-+≥⎨⎪≥≥⎩，则目标函数2z x y =+的最大值为6. 从集合{1,1,2}A =-中随机选取一个数记为k ，从集合{2,1,2}B =-中随机选取一个数记为b ，则直线y kx b =+不经过第三象限的概率为7. 设1F 、2F 是双曲线22124y x -=的两个焦点，P 是双曲线上的一点，且123||4||PF PF =， 则△12PF F 的周长为8. 已知四面体ABCD 中，2AB CD ==，E 、F 分别为BC 、AD 的中点，且异面直线AB 与CD 所成的角为3π，则EF = 9. 已知函数()f x 是定义在R 上的奇函数，当0x <时，2()6f x x =-，则0x >时，不等 式()f x x <的解集为10. 关于x 的方程11|sin |||1|1|2x x π=--在[4,4]-上的解的个数是11. 任意实数a 、b ，定义00ab ab a b a ab b≥⎧⎪⊗=⎨<⎪⎩，设函数2()(log )f x x x =⊗，数列{}n a是公比大于0的等比数列，且61a =，1239101()()()()()2f a f a f a f a f a a +++⋅⋅⋅++=，则1a =12. 以正方形的四个顶点分别作为椭圆的两个焦点和短轴的两个端点，A 、B 、M 是椭圆上的任意三点（异于椭圆顶点），若存在锐角θ，使cos sin OM OA OB θθ=⋅+⋅，则直线OA 、OB 的斜率乘积为二. 选择题 13. “112x <<”是“不等式|1|1x -<成立”的（ ） A. 充分条件 B. 必要条件C. 充分必要条件D. 既非充分也不必要条件 14. 给出下列命题，其中正确的命题为（ ）A. 若直线a 和b 共面，直线b 和c 共面，则a 和c 共面B. 直线a 与平面α不垂直，则a 与平面α内的所有直线都不垂直C. 直线a 与平面α不平行，则a 与平面α内的所有直线都不平行D. 异面直线a 、b 不垂直，则过a 的任何平面与b 都不垂直 15. 已知数列{}n a 的通项公式为1(1)n a n n =+（*n ∈N ），其n 前项和910n S =，则双曲线2211x y n n-=+的渐近线方程为（ ） A. 22y = B. 32y = C. 310y x = D. 10y x = 16. 已知平面直角坐标系中两个定点(3,2)E 、(3,2)F -，如果对于常数λ，在函数|2||2|4y x x =++--，[4,4]x ∈-的图像上有且只有6个不同的点，使得PE PF λ⋅=成立，那么λ的取值范围是（ ）A. 9(5,)5-- B. 9(,11)5- C. 9(,1)5-- D. (5,11-）三. 解答题17. 如图，在圆锥SO 中，AB 为底面圆O 的直径，点C 为弧AB 的中点，SO AB =. （1）证明：AB ⊥平面SOC ；（2）若点D 为母线SC 的中点，求AD 与平面SOC 所成的角. （结果用反三角函数表示）18. 已知函数22cos()sin 2()2cos()6x xf x x ππ-=+（x ∈R ）.（1）求()f x 的最小正周期及判断函数()f x 的奇偶性；（2）在△ABC 中，()0f A =，||AC m =，[2,4]m ∈，若任意实数t 恒有||||AB t AC BC -≥，求△ABC面积的最大值.19. 数列{}n a 满足：12a =，12n n n a a λ+=+⋅，且1a 、21a +、3a 成等差数列，其中*n ∈N . （1）求实数λ的值及数列{}n a 的通项公式； （2）若不等式21625np p n a +≤-成立的自然数n 恰有4个，求正整数p 的值.20. 教材曾有介绍：圆222x y r +=上的点00(,)x y 处的切线方程为200x x y y r +=，我们将其结论推广：椭圆22221x y a b+=（0a b >>）上的点00(,)x y 处的切线方程为00221x x y y a b +=，在解本题时可以直接应用.已知：直线30x y -=与椭圆222:1x E y a+=（1a >）有且只有一个公共点.（1）求a 的值；（2）设O 为坐标原点，过椭圆E 上的两点A 、B 分别作该椭圆的两条切线1l 、2l ，且1l 与2l 交于点(2,)M m ，当m 变化时，求△OAB 面积的最大值；（3）在（2）的条件下，经过点(2,)M m 作直线l 与该椭圆E 交于C 、D 两点，在线段CD 上存在点N ，使||||||||CN MC ND MD =成立，试问：点N 是否在直线AB 上，请说明理由.21. 一个三角形数表按如下方式构成（如图：其中项数5n ≥）：第一行是以4为首项，4为公差的等差数列，从第二行起，每一个数是其肩上两个数的和，例如：(2,1)(1,1)(1,2)f f f =+，(,)f i j 为数表中第i 行的第j 个数.（1）求第2行和第3行的通项公式(2,)f j 和(3,)f j ；（2）证明：数表中除最后2行外每一行的数都依次成等差数列，并求(,1)f i 关于i （1,2,,i n =⋅⋅⋅）的表达式；（3）若(,1)(1)(1)i f i i a =+-，11i i i b a a +=，试求一个等比数列()g i （1,2,,i n =⋅⋅⋅），使得 121(1)(2)()3n n S b g b g b g n =++⋅⋅⋅+<，且对于任意的11(,)43m ∈，均存在实数λ，当n λ>时，都有n S m >.(1,1)f (1,2)f ⋅⋅⋅ (1,1)f n - (1,)f n (2,1)f (2,2)f ⋅⋅⋅ (2,1)f n - (3,1)f ⋅⋅⋅ (3,2)f n - ⋅⋅⋅ ⋅⋅⋅ (,1)f n参考答案一. 填空题1. [0,1]2. 63. 24. 3-5. 146.297. 24 8. 19. (2,)+∞ 10. 14 11. 4 12. 12-或2-二. 选择题13. A 14. D 15. C 16. C三. 解答题17.（1）证明略；（2）25ADO ∠=. 18.（1）最小正周期为π，非奇非偶函数；（2）4m =时，△ABC 83. 19.（1）1λ=，2n n a =；（2）3p =.20.（1）2a =（2）当0m =时，S 2（3）点N 在直线AB 上. 21.（1）(2,)84f j j =+（1,2,1j n =⋅⋅⋅-），(3,)1616f j j =+（1,2,2j n =⋅⋅⋅-）；（2）证明略；（3）()2i g i =.。

2018年南洋模范中学第二学期高三年级3月月考I. Listening (略)Ⅱ. Grammar and VocabularySection ADirections: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.An“invisibility cloak”has been developed that makes animals disappear. Created using glass prisms（核柱），the cloak could eventually be used to shield security guards from views.In one demonstration of the system,researchers from China,Singapore and the US made a goldish disappear 21_________ it swam inside a tank of water.In another,the bottom half of a cat vanished as it explored an invisible box.It's one of 22_________(striking)examples yet of a cloaking device,but the science behind it is surprisingly simple.The high-quality glass prisms used to make the cloak 23______(arrange)to form an enclosure.In the fish experiment,six prisms formed a hexagon,while the cat trick used eight prisms to 24_______(form)a square.“The prisms refract（折射）incoming light rays,25__________(bend)them around the enclosure so any object placed inside becomes invisible,"says-Prof. UIf Leonhardt,an expert on invisibility at Israel's Weizmann Institute of Science."It's fun experiment that shows 26________ we can go with simpl e technology”.Previous efforts to create cloaking devices "27________(focus)on meta materials(超材料）-artificial materials with physical properties not 28_______ (find)in nature.Some of these can guide electromagnetic radiation such as infrared radiation and microwave around an object,like water around a rock.However,the material's structure must be finer than the radiation's wavelength for this to work,meaning that a good-sized cloak for visible light-----29_________wavelengths are just a few hundred billionths of a meter-----is still beyond our capabilities.While the new cloak can control visible light, it is not perfect--the glue holding the cloak together is still visible,for instance, and it only works from a small number of 30________(view)angles.Nevertheless,the researchers say that their cloak could be used in surveillance and security - an airport officer might sit inside one,watching obvious passengers as they walk past.Section BDirections: Fill in each blank with a proper word chosen from the box.Each word can be used only once. Note that there is one word more than you need.summer heat has reached its breaking point for a group of high school students in Wales,as the boys decided to protest their school's strict uniform policy 31__________wearing shorts(短裤)no matter what weather,by showing up to school in skirts.After 32________to the bathroom to change into all-black skirts,seventeen White church High School students emerged wearing skirts on campus,and they were 33__________in the campaign to resist the customary uniform trousers.The boys'34________ was less an act of politically urged civil disobedience than it was a way to beat the heat.While none of the boys were punished for their protesting efforts, the movement was short-lived. After proudly 35_______into the headmaster's office sh outing, “We want to wear shorts! "they were quickly ordered to change back into trousers.“We had a 36________ with some boys and they have worn trousers,” said Principal Jones Williams.Protester Tyrone Evelyn,15,told Wales Online that the group would continue 37__________for a change. "It's just appropriate for the weather. Over the last few days I've had a few headaches and skin irritations. Girls can wear skirts, so I don't see why we can't wear shorts. It's a reasonable protest.”The boys agreed to write a letter to their Students’ Union,38________for a rule change by next summer. Heat 39_______ and heat stroke are the two most common illnesses that occur when temperature rises. According to Mayo Clinic, wearing loose-fitting and light-colored clothing helps protect a person from trapping sweat or 40__________ too much heat.III. Reading ComprehensionSection ADirections: For each blank in the following passages there are four words or phrasesmarked A,B,C and D. Fill in each blank with the word or phrase that best fits the context.If you feel your toddler can understand directions and is able to sit still for a time-out, remember to tell him or her why you are giving them the time out. Don't just call a timeout without giving them the 41__________.42________,“When you do not eat your lunch, you cannot have a snack Mommy does not like it when you throw a temper tantrum(发脾气）and that is why you are getting a time-out. You need to sit here and 43_________."Toddlers also don't need to sit for 44_________of time. They only need to sit along enough to calm down and focus their attention on something else. Generally thirty seconds to a minute is plenty of time. Perhaps have them say theirABC's or count to ten.Keep in mind that you are 45_______ a toddler. Toddlers are 46______ in nature and will get into stuff that they are not supposed to and they will also 47_______their limits with mom and dad. With this in mind, use the time-out method when they are acting or behaving in a way that you have told them many times not to do. Don't use the time-out method for the toddler who is 48_______the world and might do something and not know it is wrong. The time-out method may 49_______ work the first or second or even third time you try it, but 50________it will work. Also make sure to 51_______your child for those times that you child does listen to you or does something that you like. This will also help you enforce the good behavior and show that you are 52________of him. Positive reinforcement can consist of things like a hug or a cookie.53__________,let your toddler know that you are not mad or angry at them, but you dislike their behavior. Getting mad at them might scare them and that is not going to get your point 54______.That will just make them afraid of you or not want to be around you. Even when you are putting your children in time-out, let them know that you 55______them.41.A.expectation B. explanation C. opportunity D. punishment42.A.in addition B. Above all C. For example D. On the contrary43.A.make up B.pay back C.stay up D.calm down44. A.long periods B.plenty C.a number D.a short period45.A.caring about B.turning toC.learning fromD.dealing with46.A.smart B.curious C.anxious D.naughty47.A.break B.test C.prove D.enter48.A.inventing B.making C.exploring D.spoiling49.A.only B.not C.just D.well50.A.firstly B.hopefully rgely D.eventually51.A.praise B.remind C.warn D.blame52.A.proud B.tried C.aware D.confident53.A In all B.First of all C.Above all D.Altogether54.A.understand B.across C.hear D.be understood55.A love B.fear C.respect D.needSection BDirections: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.（A）In the early 20th century,the valleys of South Wales boasted more than 600 coal mines，and employed some 200,000 men in a region that ranked as the world's largest coal exporter.But during the period of increasing industry losses,post-war governments first shut down the state-owned mines,and by the end of the 1990s,only a handful remained.To a generation of miners,a way of life seemed over for good.Now,for the first time since the Thatcher era（撒切尔首相时代），British companies are re-opening those old Welsh mines,hoping to supply nearby power plants and steel-works with coal while competing against foreign competitors on prices,Two mines are already back in operation.More may follow,with the promise of a few hundred jobs - welcome news in an area where government attempts to introduce new high-tech industries to replace the dirty old coal business have met with limited success.Unemployment in some of the worst hit mining areas remains continuously high at 10 percent or more,with few jobs for the young in many of the communities.The reopening of Welsh mines reflects the rising global demand for energy,as well as high oil and natural-gas pared with gas or oil,coal,once thought to be out of favor,is plentiful and relatively cheap to find and exploit,and now accounts for 25 percent of the world's energy consumption,up 2 percentage points since 2001.Result:prices are a expected to more than double this year,to more than $300 a ton for the costliest coal.Coal Y ports in Australia and South Africa are facing bottlenecks trying to meet the rising demand from the biggest consumers,China and India.The demand is also reviving(使复苏）the fortunes of other coal businesses worldwide,including larger export mines in the United States.But regulatory procedures(监督程序）and start-up costs are too high for a small businessman to start reopening old mines in Pennsylvania or West Virginia.Not so in Wales,where there is little local opposition and a ready supply of labor in a region that never quite managed to overcome the loss of the industry decades ago.Much of the available work is low-paying,in shopping centers or stores.since the mines there shut down,thousands of young people have left in search of work elsewhere.But Welsh miners can now earn far above the national minimum wage of $12 per hour.Brian Thomas,a skilled worker in coal industry,earns $1,2000 a week——at least double what his salary would be in the supermarket. “If I didn’t have this job I would probably be ranging shelves in the supermarket,” he says.56.The phrase “for good” in the paragraph means.A.temporarilyB.permanentlyC.automaticallyD.definitely57.The main reason of reopening of coal mines in Wales is that .A.the introduction of high-tech industries into the region is unsuccessfulB.Unemployment in the region should be solved as soon as possibleC.The global demand for energy is shooting upD.The present government tries to recover the industry losses58.The word“bottlenecks”in paragraph means .A.traffic jamsB.narrow entrancesC.opponentsD.obstacles59.The direct result of the reopening of coal is that .A.the prices of oil and gas begin to go downB.Many laid-off workers have returned to their original positionsC.The wages in other industries have been raised accordinglyD.Coal mines in some states in the U.S. may be reopened as well（B）Shopping or the gym? If retail therapy(购物疗法) comes top every time, then you might be the ideal candidate for mall-walking it's a fitness trend from the U.S.that now seems to be catching on here. Losing pounds from your thighs(大腿), not your pocket, is the idea behind mallercise.It involves power-walking around shopping centres and marching upstairs and escalators while doing a spot of window-shopping at the same time. So popular have such sessions become in the u.s. and Canada that manufacturers now market specialmall-walker shoes" o give extra fraction(牵引) for smoother mall floors”.Fans say the advantages of mall-walking include the fact that shopping malls are traffic free, weather resistant and safe. It can also get you reasonably fit. A 30-minute speed walk can bum around 200 calories. One of the first mall-walking schemes in the U.K. was at the White Rose shopping centre in Leeds where groups have been meeting every weekday morning since 2003At the University of Calgary in Canada, physiologists looked at the effects of aneight-week mall-walking programme on health and wellbeing. After two months, results showed that the subjects were walking further and weighed less than when they started.Perhaps more significantly, they displayed high self-motivation, with 63% of subjects mall-walking three or more days a week.In the Calgary study, the average age of those taking part was 66, which led the researchers to suggest that it is the perfect activity for"older people looking for a safe, flat place to improve their functional mobility, fitness and improve their sense of independence.”Another Canadian study revealed that shopping malls are the second most popular walking site for people aged 45 and older, with more women likely to choose them as an exercise destination than men. “For exercise to be successful in terms of weight loss and improvements in health, it needs to be done regularly, ”says Dr Beckie Lang of t he Associationfor the Study of Obesity. “It actually doesn’t matter where you walk as long you do it, and for many people this may be more accessible than a class at a gym.”60. Which of the following does NOT relate to"mallercise"?A .Saving money.B .Gym going.C .Losing weightD .window-shopping.61. According to the Calgary study, .A .more women choose mall-walking as a way of exerciseB. mall-walking does more good to people in their 60’sC. shopping malls are the most popular walking site for the elderlyD. mall-walking benefits old people both physically and mentally62. Which of the following is NOT mentioned in the passage?A. The way people do mall-walkingB. The reason why people do mall-walkingC. The benefits of mall-walkingD. The problems with mall-walking.63. The passage is written to .A distinguish between"mallercise"and gym classB. explore the history and development of mall-walkingC. introduce a new trend of exercising -mall-walkingD suggest ways for old people to stay physically young(C)It begins with a sudden feeling of envy. Next comes the anxiety. The self-doubt and the upsetting sense of inadeguacy(不自信). Finally, those feelings fade away, leaving you full of irritation(恼怒).Whether it's triggered by laura's tweet from backstage at that popular band's concert or joe's photos from his tropical island vacation. most regular users of social media will find those feelings all too familiar. They are “symptoms” of FOMO, or “ fear of missing out.”Today we are so concerned with one another through social networking sites that we can't just be alone anymore. The fear of missing out-on something more run, moreexciting or better that's going on without you-is so strong that we can't “log out”.Connected to this fear of missing out are these fake personas(伪装人格) we promote on websites like Facebook. It is"fake"because we often present only the best side of our lives on social networking sites-many (most?) of us censor（检查)what we post to our social media profile these days. The people on Facebook are often simply their idealized selves, with a bit of misery thrown in from time to time to “keep it real”. After all, who wants to be"friends"with someone who’s always posting depressing status updates and who seems to be doing nothing interesting in their lives?How do we react to those feelings caused by FOMO? A New York Times reporter,Jenna Wortham wrote about her friends story. The friend said she felt fine about her life-until she saw other peoples Facebook updates showing their""lives. On those occasions, her knee-jerk(下意识的) reaction was often to post an account of a cool thing she has done, or to upload a particularly fun picture from her weekend. Doing that would make her feel better, but it could trigger FON1 O in another unsuspecting(无戒心的) person.And that's, in fact, how it works. Caterina Fake, co-founder of photo-sharing service Flickr, said “Social software is both the creator and the cure of FOMO. it's cyclical(循环的).”64. The underlined word"triggered"in Paragraph 2 can be replaced byA. concernedB. connected C caused D. put65. According to the passage, a typical FOMO person will probably post something on his Facebook on the following occasions EXCEPT when he .A. has won a big prize in a very important competitionB. is always complaining of his headacheC. is back from a perfect trip to a beautiful tropical islandD. has got his favorite singer's autograph(签名)66. Which of the following statements CANNOT be inferred from the article?A People tend to show their best selves on social networking sitesB. The sudden envious feeling ends in irritation.C. The FOMO phenomenon is a vicious circle(恶性循环).D. Someone who prefers to emphasize his sufferings is unpopular with othersSection CDirections: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there is one sentence more than you need.We all have friends that need a little advice, but one of the problems with those typesof conversations is that it's really easy to come off as a know-it-all when you're offering help. When you do that,nobody's going to listen.67 But it’s not an easy conversation to have someone,especially when y ou know all the extenuating circumstances of the situation.I talked with relationship and family therapist Roger S. Gil to get some advice for dealing with these situations.Obviously not everyone is looking for your advice. Before you go offering up your point of view, make sure they 're interested in hearing it. As Roger Gil points out, often friends aren't looking for you to solve a problem. They just want you to listen and maybe ask some questions. So, ask if they’d like to hear your input or insights o n a problem, but also ask questions about why ey feel a certain way. If they say "no", let them finish their story and listen politely. 68 Just wait for them to finish complaining before offering advice (or asking if they want it ). Sometimes the best way to figure something out is to do it on their own.Speaking of listening. it's also a good idea to figure out right away what your friends want from you. Gil describes this as differentiating between opinions, expert advice, and being a "sounding board" Essentially, don' pretend like you know something you don’t.69Now that you know whether or not your friends or family actually want your advice, it's time to learn how to advise without sounding like a know-it-all. This is a lot harder than you might think. As Gil points out, one way to offer advice without sounding pretentious (自以为是的) is to avoid- You should" statements. 70 By offering up your opinion clearly defined as your opinion, you remove the implication that “you know best”.IV. Summary WritingDirections: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.Online ProfilesSocial networking sites such as Facebook, Myspace and Orkut are now estimated to have more them 00-mittomusers worldwide. As users can create any profile of themselves they choose, you might expect them to portray themselves in the best possible way. When putting up a profile, it would be reasonable for them to present positive images, choose sophisticated interests, and carefully express their thoughts so as to appear more intelligent than in real life. But according to recent research, this is not the case. Far from presenting themselves in a flattering way. most users' profiles reflect their true personalities, and reveal both psychological and natural physical weaknesses.Research was carried out on 250 Facebook users who filled in a. personality questionnaire Results were compared with the same peoples Facebook profiles. The survey set out to assess not only the participants actual personality, but their " ideal" personality in other words, what kind of person they would be if they actually possessed their ideal characteristics. These results were then compared with the participants Facebook profiles. What emerged was astonishing: far from being idealized versions of themselves, people's online profiles roughly resemble what they were really like. Their profiles accurately reflected how agreeable, outgoing, hardworking. and sociable they were in real life Is not entirely clear why online profiles display users personalities so accurately. It could be that users want to portray themselves as they really are, or it could be that people attempt to present an ideal image of themselves but in fact fail to do so. One thing seems clear: social networking sites can in no way be considered a false online world that is idealized and removed om reality rather, they are simply another way in which people choose to interact with each other.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72.携带瓶装液体的旅客不准登机。

上海市南洋模范中学2023届高三下学期3月模拟1数学试题学校:___________姓名：___________班级：___________考号：___________
④若事件A ，B 满足()0P A >，()0P B >，()()|P B A P B =，则有()()|P A B P A =．10．若已知30个数1230,,,x x x 的平均数为6，方差为9；现从原30个数中剔除1210,,,x x x 这10个数，且剔除的这10个数的平均数为8，方差为5，则剩余的20个数111230,,,x x x 的方差为___________.
11．每年的6月6日是全国爱眼日，某位志愿者跟踪调查电子产品对视力的影响，据调查，某高校大约有45%的学生近视，而该校大约有20%的学生每天操作电子产品超过1h ，这些人的近视率约为50%，现从每天操作电子产品不超过1h 的学生中任意调查一名学生，则他近视的概率为__________.
12．已知函数(e 3)()x f x x =-，若经过点()0,a 且与曲线()y f x =相切的直线有三条，则a 的取值范围是_____．
二、单选题
参考答案：
所以3a <-<e ，解得3a -<<故答案为：()3,e --.13．C
【分析】转化((|)(P AB P A B P B =。

2018 上海市南模中学高三月考数学试卷2017.10一. 填空题1. 已知集合2{|0}5x A x x -=<+，2{|230,}B x x x x R =--≥∈，则A B = 2. 已知函数()arcsin(21)f x x =+，则1()6f π-=3. 在(0,2)π内，使sin cos x x ≤成立的x 的取值范围为4. 函数212()log (32)f x x x =-+-的单调递增区间为5. 函数||y x x =的反函数为6. 若对任意x R ∈，不等式2sin 22sin 0x x m +-<恒成立，则m 的取值范围为7. 设数列{}n a 的前n 项和为n S ，若11a =，114n n S a +=（*n N ∈），则n S = 8. 数列{}n x 中，10x =，111n n n x x n n++=+（*n N ∈），则数列的通项公式n x = 9. 设()f x 是定义域为R 的奇函数，()g x 是定义域为R 的偶函数，若函数()()f x g x +的值 域为[1,3)，则函数()()f x g x -的值域为10. 已知()sin()f x A x A ωϕ=++（0ω>），若两个不相等的实数12,{|()}2Ax x x f x ∈=， 且12min ||x x π-=，则()f x 的最小正周期为 11. 函数2()|2|4sin4xf x x x π=-+-（16x ≤≤）的值域为12. 函数()2|}f x x =-，其中min{,}a a ba b b a b ≤⎧=⎨>⎩，若动直线y m =与函数()y f x =的图像有三个不同的交点，它们的横坐标分别为1x 、2x 、3x ，则1x 、2x 、3x 是否存在最大值？若存在，在横线处填写其最大值；若不存在，直接填写“不存在”二. 选择题13. 已知x R ∈，则“1x ≠”是“2430x x -+≠”的（ ） A. 充分不必要条件 B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件14. 若||a c h -<，||b c h -<，则下列不等式一定成立的是（ ）A. ||2a b h -<B. ||2a b h ->C. ||a b h -<D. ||a b h -> 15. 已知ABC ∆内接于单位圆，则长为sin A 、sin B 、sin C 的三条线段（ ） A. 能构成一个三角形，其面积大于ABC ∆面积的一半 B. 能构成一个三角形，其面积等于ABC ∆面积的一半 C. 能构成一个三角形，其面积小于ABC ∆面积的一半 D. 不一定能构成一个三角形16. 已知函数()21x x e mf x +=+，若对任意123,,x x x R ∈，总有1()f x 、2()f x 、3()f x 为某一个三角形的边长，则实数m 的取值范围是（ ）A. 1[,1]2B. [0,1]C. [1,2]D. 1[,2]2三. 解答题17. 已知()2f x kx =+，不等式|()|3f x <的解集为(1,5)-，不等式1()xf x ≥的解集为A ； （1）求集合A ；（2）设22()log (22)g x ax x =-+的定义域为B ，若B A ≠∅，求实数a 的取值范围；18. 右图为函数()sin()f x A x ωϕ=+（0A >，0ω>，02πϕ<<）的部分图像，M 、N是它与x 轴的两个交点，D 、C 分别为它的最高点和最低点，(0,1)E 是线段MD 的中点， 且OME ∆为等腰直角三角形； （1）求()f x 的解析式；（2）将函数()f x 图像上的每个点的横坐标缩短为原来的一半，再向左平移12的单位长度 得到()y g x =的图像，求()g x 的解析式及单调增区间，对称中心；19. 在ABC ∆中，a 、b 、c 分别为内角A 、B 、C 所对的边，且满足(2)cos cos b A C =；（1）求A 的大小；（2）现给出三个条件：（1）2a =；（2）4B π=；（3）c =，试从中选出两个可以确定ABC ∆的条件，写出你的选择，并以此为依据求ABC ∆的面积；（需写出所有可行的方案）20. 对于函数1()f x 、2()f x 、()h x ，如果存在实数a 、b 使得12()()()h x a f x b f x =⋅+⋅， 那么称()h x 为1()f x 、2()f x 的生成函数； （1）若1()sin f x x =，2()cos f x x =，()sin()3h x x π=+，则()h x 是否分别为1()f x 、2()f x的生成函数？并说明理由；（2）设12()log f x x =，212()log f x x =，2a =，1b =，生成函数()h x ，若不等式(4)(2)0h x th x +<在[2,4]x ∈上有解，求实数t 的取值范围；（3）设1()f x x =（0x >），21()f x x=（0x >）取0a >，0b >，生成函数()h x 图象的 最低点坐标为(2,8)，若对于任意正实数1x 、2x 且121x x +=，试问是否存在最大的常数m ，使12()()h x h x m ≥恒成立？如果存在，求出这个m 的值；如果不存在，请说明理由；21. 对于给定的正整数k ，若数列{}n a 满足11(21)n k n k n k n k n a a a a k a --++-+++⋅⋅⋅++=+对任 意正整数n ()n k >恒成立，则称数列{}n a 是()AP k 数列，若正数项数列{}n b ，满足2111()k n k n k n k n k n b b b b b +--++-+⋅⋅⋅=对任意正整数)(k n n >恒成立，则称{}n b 是()GP k 数列；（1）已知正数项数列{}n a 是(3)GP 数列，且前五项分别为4、2a 、2、4a 、1，求4a 的值； （2）若2sin n a n n ω=+（0ω>）为常数，且{}n a 是(2)AP 数列，求ω的最小值； （3）对于下列两种情形，只要选作一种，满分分别是 ① 7分，② 8分，若选择了多于一种情形，则按照序号较小的解答积分；① 证明：数列{}n a 是等差数列的充要条件为“{}n a 既是(2)AP 数列，又是(3)AP 数列”； ② 证明：正数项数列{}n b 是等比数列的充要条件为“数列{}n b 既是(2)GP 数列，又是(3)AP 数列”；参考答案一. 填空题1. (,2)[3,)-∞+∞2. 14-3. 5(0,][,2)44πππ4. 3(,2)25. 10()x f x x -⎧≥⎪=⎨<⎪⎩ 6. 1,)+∞ 7. 15n -（*n N ∈）8. 1n -（*n N ∈） 9. (3,1]-- 10. 3π 11. [3,29] 12. 1二. 选择题13. B 14. A 15. C 16. D三. 解答题17.（1）[1,2)A =；（2）(0,)a ∈+∞； 18.（1）()2sin()44f x x ππ=+；（2）()2cos 2g x x π=；增区间：[42,4]k k -（*n N ∈）； 对称中心：(21,0)k +（k Z ∈）； 19.（1）6A π=；（2）选（1）（3），得S =1）（2），得1S =）；20.（1）是，12a =，b =；（2）4(,)3-∞-；（3）289；21.（1）2±；（2）2ωπ=；（3）略。

2019届上海市南洋模范中学高三下学期3月月考数学试题一、单选题1．“”是“不等式成立”的（）A．充分条件B．必要条件C．充分必要条件D．既非充分也不必要条件【答案】A【解析】解不等式|x﹣1|＜1，再由充分必要条件即可判断出结论．【详解】不等式|x﹣1|＜1成立，化为﹣1＜x﹣1＜1，解得0＜x＜2，∴“”是“不等式|x﹣1|＜1成立”的充分条件．故选：A．【点睛】本题考查了充分必要条件，绝对值不等式的解法、简易逻辑的判定方法，考查了推理能力与计算能力，属于基础题．2．给出下列命题，其中正确的命题为（）A．若直线和共面，直线和共面，则和共面；B．直线与平面不垂直，则与平面内的所有直线都不垂直；C．直线与平面不平行，则与平面内的所有直线都不平行；D．异面直线，不垂直，则过的任何平面与都不垂直.【答案】D【解析】试题分析：A：直线共面不具有传递性，故A错误；B：根据线面垂直的判定可知B错误；C：若直线，满足直线与平面不平行，故C错误；D：假设存在过的平面与垂直，则可知，∴假设不成立，故D正确，故选D．【考点】空间中点、线、面的位置关系及其判定．3．已知数列的通项公式为，其前项和，则双曲线的渐近线方程为（）A．B．C．D．【答案】C【解析】试题分析：根据数列的通项公式为,其前项和，那么可知，可知n=9,那么根据可知a=,b=3,故可知双曲线的渐近线方程为，选C.【考点】数列的求和，双曲线的性质点评：主要是考查了数列的通项公式和双曲线的性质的运用，属于基础题。

4．已知平面直角坐标系中两个定点，，如果对于常数，在函数，的图像上有且只有6个不同的点，使得成立，那么的取值范围是（）A．B．C．D．【答案】C【解析】画出函数y＝|x+2|+|x﹣2|﹣4在[﹣4，4]的图象，讨论若P在AB上，设P（x，﹣2x﹣4）；若P在BC上，设P（x，0）；若P在CD上，设P（x，2x﹣4）．求得向量PE，PF的坐标，求得数量积，由二次函数的最值的求法，求得取值范围，讨论交点个数，即可得到所求范围．【详解】函数y＝|x+2|+|x﹣2|﹣4，（1）若P在AB上，设P（x，﹣2x﹣4），﹣4≤x≤﹣2．∴（3﹣x，6+2x），（﹣3﹣x，6+2x）．∴x2﹣9+（6+2x）2＝5x2+24x+27=，∵x∈[﹣4，﹣2]，∴λ≤11．∴当λ或时有一解，当λ≤9时有两解；（2）若P在BC上，设P（x，0），﹣2＜x≤2．∴（3﹣x，2），（﹣3﹣x，2）．∴x2﹣9+4＝x2﹣5，∵﹣2＜x≤2，∴﹣5≤λ≤﹣1．∴当λ＝﹣5或﹣1时有一解，当﹣5＜λ＜﹣1时有两解；（3）若P在CD上，设P（x，2x﹣4），2＜x≤4．（3﹣x，6﹣2x），（﹣3﹣x，6﹣2x），∴x2﹣9+（6﹣2x）2＝5x2﹣24x+27，∵2＜x≤4，∴λ≤11．∴当λ或时有一解，当λ<9时有两解；综上，可得有且只有6个不同的点P的情况是λ＜﹣1．故选：C．【点睛】本题考查平面向量的数量积的坐标运算，二次函数的根的个数判断，注意运用分类讨论的思想方法，属于中档题．二、填空题5．已知全集，若集合，则_________.【答案】【解析】求出集合A，即可求解∁U A【详解】全集U＝R，集合A＝{x|x＞1或x<0}则＝故答案为【点睛】本题考查集合的基本运算，补集的求法，分式不等式解法，准确计算是关键，是基础题．6．双曲线的焦距为__________.【答案】6【解析】将双曲线的方程化为标准方程，求得a，b，c，可得焦距2c的值．【详解】双曲线2x2﹣y2＝6即为1，可得a，b，c3，即焦距为2c＝6．故答案为：6．【点睛】本题考查双曲线的简单几何性质，焦距的求法，注意将双曲线的方程化为标准方程，运用双曲线的基本量的关系，考查运算能力，属于基础题．7．已知二项展开式中的第五项系数为，则正实数_____.【答案】【解析】由二项式定理的通项公式可得：，解出即可得出．【详解】T5x﹣2，∴，a＞0．解得a．故答案为：．【点睛】本题考查了二项式定理的应用，考查了推理能力与计算能力，准确计算是关键，属于基础题．8．已知函数的图像与它的反函数的图像重合，则实数的值为___.【答案】-3【解析】先求反函数：y，利用函数f（x）（a）图象与它的反函数图象重合，即为同一个函数即可得出．【详解】由y（a），解得x（y≠3），把x与y互换可得：y，∵函数f（x）（a）图象与它的反函数图象重合，∴﹣a＝3，解得a＝﹣3．故答案为：﹣3．【点睛】本题考查了反函数的求法及其性质，考查了推理能力与计算能力，属于中档题．9．设，满足约束条件，则目标函数的最大值为_____.【答案】14【解析】画出可行域，通过向上平移基准直线到可行域边界的位置，由此求得目标函数的最大值.【详解】画出可行域如下图所示，由图可知，目标函数在点处取得最大值，且最大值为.【点睛】本小题主要考查利用线性规划求线性目标函数的最大值.这种类型题目的主要思路是：首先根据题目所给的约束条件，画出可行域；其次是求得线性目标函数的基准函数；接着画出基准函数对应的基准直线；然后通过平移基准直线到可行域边界的位置；最后求出所求的最值.属于基础题.10．从集合中随机选取一个数记为，从集合中随机选取一个数记为，则直线不经过第三象限的概率为_____.【答案】【解析】将试验发生包含的事件（k，b）的所有可能的结果列举，满足条件的事件直线不经过第三象限，符合条件的（k，b）有2种结果，根据古典概型概率公式得到结果．【详解】试验发生包含的事件（k，b）的取值所有可能的结果有：（﹣1，﹣2）；（﹣1，1）；（﹣1，2）；（1，﹣2）；（1，1）；（1，2）；（2，﹣2）；（2，1）；（2，2）共9种结果．而当时，直线不经过第三象限，符合条件的（k，b）有2种结果，∴直线不过第三象限的概率P，故答案为．【点睛】本题考查古典概型，古典概型要求能够列举出所有事件和发生事件的个数，属于基础题．11．设，是双曲线的两个焦点，是双曲线上的一点，且，则的周长为___.【答案】24【解析】先由双曲线的方程求出|F1F2|＝10，再由3|PF1|＝4|PF2|，运用双曲线的定义，求出|PF1|＝8，|PF2|＝6，由此能求出△PF1F2的周长．【详解】双曲线x21的a＝1，c5，两个焦点F1（﹣5，0），F2（5，0），即|F1F2|＝10，由3|PF1|＝4|PF2|，设|PF2|＝x，则|PF1|x，由双曲线的定义知，x﹣x＝2，解得x＝6．∴|PF1|＝8，|PF2|＝6，|F1F2|＝10，则△PF1F2的周长为|PF1|+|PF2|+|F1F2|＝8+6+10＝24．故答案为：24．【点睛】本题考查双曲线的定义和性质的应用，考查三角形周长的计算，熟练运用定义是关键，属于基础题．12．已知四面体中，，，分别为，的中点，且异面直线与所成的角为，则____.【答案】1或【解析】取BD中点O，连结EO、FO，推导出EO＝FO＝1，，或，由此能求出EF．【详解】取BD中点O，连结EO、FO，∵四面体ABCD中，AB＝CD＝2，E、F分别为BC、AD的中点，且异面直线AB与CD所成的角为，∴EO∥CD，且EO，FO∥AB，且FO1，∴∠EOF是异面直线AB与CD所成的角或其补角，∴，或，当∠EOF时，△EOF是等边三角形，∴EF＝1．当时，EF．故答案为：1或．【点睛】本题考查异面直线所成角的应用，注意做平行线找到角是关键，解题时要认真审题，注意空间思维能力的培养，是易错题13．已知函数是定义在上的奇函数，当时，，则时，不等式的解集为____.【答案】【解析】由奇函数的性质可得x＞0时的解析式，再解不等式即可．【详解】∵函数f（x）是定义在R上的奇函数，∴当x＞0时，﹣x＜0，∴f（﹣x）＝x2﹣6，由奇函数可得f（x）＝﹣x2+6，∴不等式f（x）＜x可化为，解得x＞2∴x＞0时，不等式f（x）＜x的解集为：（2，+∞）故答案为：（2，+∞）【点睛】本题考查函数的奇偶性，涉及不等式的解法，熟记奇函数得定义是关键，属基础题．14．关于的方程在上的解的个数是____.【答案】7【解析】化简y=从而作函数的图像，从而可解【详解】化简y=,作函数在上的图像如下：结合图像可知，两个图像共有7 个交点故答案为7【点睛】本题考查函数与方程，函数的性质，三角函数，准确作图是关键，是中档题15．任意实数，，定义，设函数，数列是公比大于0的等比数列，且，，则____.【答案】4【解析】f（x）＝，及其数列{a n}是公比大于0的等比数列，且＝1，对公比q分类讨论，再利用对数的运算性质即可得出．【详解】由题，∵数列{a n}是公比大于0的等比数列，且，①1＜q时，，，…，∈（0，1），，，∈（1，+∞），1．∴，分别为：，，…，，1，q，…，q4．∵∴0++…+＝，∴q4q q2．∴2．左边小于0，右边大于0，不成立，舍去．②0＜q＜1时，1，∴，分别为：，，…，，1，q，…，q4，，，…，∈（1，+∞），，，∈（0，1），∵∴log2q2．∴2．∴4，∴a1＝4．③q＝1时，＝…＝＝…＝＝1，不满足舍去．综上可得：＝4．故答案为：4．【点睛】本题考查了等比数列的通项公式及其性质、对数的运算性质，考查了分类讨论方法、推理能力与计算能力，属于难题．16．以正方形的四个顶点分别作为椭圆的两个焦点和短轴的两个端点，，，是椭圆上的任意三点（异于椭圆顶点），若存在锐角，使，（0为坐标原点）则直线，的斜率乘积为___.【答案】或-2【解析】设椭圆方程为，A（，），B（，），从而得到的坐标表示，然后，再根据M点在该椭圆上，建立关系式，结合A、B点在也该椭圆上，得到，，从而得到相应的结果，同理当椭圆方程为可得答案【详解】由题意可设椭圆方程为，又设A（，），B（，），因为M点在该椭圆上，∴，则又因为A、B点在也该椭圆上，∴，∴，即直线OA、OB的斜率乘积为，同理当椭圆方程为时直线OA、OB的斜率乘积为﹣2．故答案为：或﹣2．【点睛】本题重点考查椭圆综合，平面向量的坐标运算，注意审题仔细，要注意分类讨论椭圆的焦点位置，属于中档题．三、解答题17．如图，在圆锥中，为底面圆的直径，点为弧AB的中点，.（1）证明：平面；（2）若点为母线的中点，求与平面所成的角.（结果用反三角函数表示）【答案】（1）见证明；（2）【解析】（1）由圆的性质得出AB⊥OC，由SO⊥平面ABC得出SO⊥AB，故而AB⊥平面SOC；（2）连结OD，由AB⊥平面SOC可知∠ADO为所求角，设圆锥底面半径为a，求出OD，得出tan∠ADO,得解【详解】（1）证明：在圆锥中，∵点为弧AB的中点，∴∴由平面（2）联结，∵平面∴为与平面所成的角设，则，∴∴在中，∴【点睛】本题考查了线面垂直的判定，线面角的计算，熟记判断定理，准确找到所成角是关键，属于中档题．18．已知函数.（1）求的最小正周期及判断函数的奇偶性；（2）在中，，，，若任意实数恒有，求面积的最大值.【答案】（1），函数是非奇非偶函数;（2）【解析】（1）由化简得则周期可求，计算；，可判奇偶性；（2）由题得将平方，得t的二次不等式，利用，得，进而得由求得最大值【详解】（1）所以，的最小正周期为；，所以，函数是非奇非偶函数.（2）由得因为是的内角，所以0<A<，由，得两边平方，整理得，对任意实数恒成立所以得则有且所以（当且仅当等号成立）所以，当时，面积的最大值为【点睛】本题考查三角恒等变换，向量数量积，三角形面积，熟记三角公式，灵活运用二次不等式转化是关键，是中档题19．数列满足：，，且，，成等差数列，其中.（1）求实数的值及数列的通项公式；（2）若不等式成立的自然数恰有4个，求正整数的值.【答案】（1），（2）【解析】（1）由题意和等差中项的性质列出方程求出λ，再利用累加法求出数列{a n}的通项公式；（2）结合条件对n进行分类讨论，当n≥3时利用分离常数法化简得p，利用取特值和做商法判断出的单调性，再判断出的单调性，根据条件即可求出正整数p的值．【详解】（1）由题意：，∵，，成等差数列，∴，解得：∵，，∴，检验n=1 成立故（2）解：∵，∴∵，∴显然成立当时，，设∴当时，；当时，；又，，，，若还需有2解，则，即，解得，所以正整数【点睛】本题考查了等差中项的性质，累加法求数列的通项公式，以及数列单调性的判断与应用，考查方程思想与分类讨论思想的应用，是难题20．教材曾有介绍：圆上的点处的切线方程为。

南模中学 2018 届高三综合试卷（二）一、积累运用1. 按要求填空（1）无丝竹之乱耳，__________（刘禹锡《陋室铭》）（2）___________ ，栏杆拍遍，无人会、登临意。

（《水龙吟.登建康赏心亭》）（3）“故天将降大任于是人也，必先苦其心志，劳其筋骨，饿其体肤，空乏其身，行拂乱其所为”强调了苦难对于磨砺意志的重要性，欧阳修在《伶官传序》中的“ ____________________________________”两句，则用对比手法说明了这个道理。

【答案】 (1). 无案牍之劳形 (2). 把吴钩看了辛弃疾 (3). 忧劳可以兴国逸豫可以亡身【解析】试题分析：本题考查默写常见的名句名篇的能力。

学生记忆的时候应该结合诗句的意思。

每句1分，句中有误该句不得分。

要求学生养成回头望的习惯，避免笔误。

本题中易错字“牍”“豫”。

2. 按要求选择（1）在下面一段话的空缺处依次填入词语，最恰当的一组是（）又至重阳节，敬老院再度受到社会的关注，有些老人一天有好几拨“接待任务”，一天要被洗好几次脚，这让他们，重阳前后，'“突击敬老”，一哄而上之后的一哄而散，带给老人的心理可想而知。

关爱老人，需要节日前后的参与，更需要 _ 的用心坚持。

A、不胜其烦落差细水长流B、不厌其烦落差滴水穿石C、不胜其烦失落细水长流D、不厌其烦失落滴水穿石（2）阅读下列对联，判断对应正确的一项（）书店住宅A、上联锦绣成文非我有合家欢乐财源进下联琳琅满架待人求内外平安好运来B、上联内外平安好运来锦绣成文非我有下联合家欢乐财源进琳琅满架待人求C、上联琳琅满架待人求内外平安好运来下联锦绣成文非我有合家欢乐财源进D、上联合家欢乐财源进琳琅满架待人求下联内外平安好运来锦绣成文非我有【答案】1. A 2.A【解析】（1）试题分析：本题考查词语成语的运用。

题中，“不胜其烦”与“不厌其烦”外貌十分相似，含义好像也差不多，这就是很多人误用的原因。

2024届上海市徐汇区南洋模范中学高三3月份模拟考试物理试题注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置．3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B 铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效．5．如需作图，须用2B 铅笔绘、写清楚，线条、符号等须加黑、加粗．一、单项选择题：本题共6小题，每小题4分，共24分。

在每小题给出的四个选项中，只有一项是符合题目要求的。

1、如图所示是杂技团表演猴子爬杆的节目，质量为8kg m =的猴子以初速度10.5v =m/s 沿竖直杆从杆底部向上匀加速运动的同时，杂技演员顶着直杆以初速度21m/s v =，加速度22s 2m/a =沿水平方向向左做匀加速直线运动，3st =末猴子到达杆的顶部。

已知竖直杆的长度为6m =L ，重力加速度210m/s g =，将猴子看作一个质点，关于猴子的运动情况，下列说法中正确的是（ ）A ．猴子沿杆运动的加速度大小为20.5m/sB ．猴子相对地面做匀加速的曲线运动C ．猴子运动的轨迹方程12y x =D ．杆给猴子的作用力大小为88N2、如图所示，一倾角为30°的匀质圆盘绕垂直于盘面的固定对称轴以恒定角速度ω转动，盘面上离转轴距离d 处有一带负电的电荷量为q 、质量为m 的小物体与圆盘始终保持相对静止．整个装置放在竖直向上的匀强电场中，电场强度2mg E q=,则物体与盘面间的动摩擦因数至少为（设最大静摩擦力等于滑动摩擦力，g 为重力加速度）( )A ．23(34)9g d g ω+B ．22(31)3d g ω+C ．23(4)3g d g ω+D ．23(2)3g d gω+ 3、如图所示，斜面体ABC 固定在水平地面上，斜面的高AB 为2m ，倾角为θ=37°，且D 是斜面的中点，在A 点和D 点分别以相同的初速度水平抛出一个小球，结果两个小球恰能落在地面上的同一点，则落地点到C 点的水平距离为（ ）A ．42m 3B ．22m 3 C ．32m 4 D ．4m 34、原子核92238U 有天然放射性，能发生一系列衰变，可能的衰变过程如图所示。

2020学年第二学期南模中学高三年级阶段测验化学学科（等级考）一．选择题（本题共40分，每小题2分，只有一个正确选项）1．下列反应不适用于实验室制备氧气的是A ．高锰酸钾受热分解：424222KMnO K MnO +MnO +O ∆−−→↑ B ．双氧水催化分解：2MnO22222H O 2H O+O −−−→↑ C ．过氧化钠中滴加蒸馏水：22222Na O +2H O 4NaOH+O →↑D ．硝酸铵受热分解：Δ432222NH NO O +2N +4H O −−→↑↑ 2．下列实验中，仪器下端必须插入液体以下的是A ．制备CO 2的简易装置中的长颈漏斗B ．制备乙炔时的分液漏斗C ．制取乙酸乙酯时冷凝产物的导管D ．吸收氨气的导管3．实验室制取下列气体时，发生装置和收集装置都相同的是A ．H 2和Cl 2B ．CO 2和H 2SC ．O 2和NH 3D ．C 2H 4和C 2H 24．下列有关实验所选的试剂或方法可以达到目的的是A ．用燃烧法除去CO 2中的COB ．将C 2H 6通入酸性高锰酸钾溶液中可除去其中的C 2H 4C ．用硫酸铜溶液可以去除并证明其中含有的H 2SD ．氯化铵和熟石灰共蒸制得的NH 3可用无水氯化钙干燥5．下列实验方法中采取的措施正确的是A ．制取乙烯时，烧瓶内产生暴沸现象，应立即加入碎瓷片B ．在制备并收集氯气的试验中，为了防止污染空气，尾气可用饱和食盐水吸收C ．实验室制取乙烯时，先用碱石灰吸收产生的酸性气体，然后再收集D ．制备乙炔时，为了减缓反应速率，可用长颈漏斗加入饱和食盐水6．下列关于实验室割取SO 2的实验，其中叙述正确的是A．可用图①中装置和药品制取SO2B．可用图②中装置和药品制取SO2C．可用图③中装置和药品收集二氧化硫并吸收尾气D．可用图④中装置和药品检验铜和浓硫酸反应生成的CuSO47．可用分液漏斗分离的混合物是A．乙醛和水B．甘油和醋酸C．乙酸乙酯和饱和食盐水D．苯和苯甲酸8．关于煤和石油加工的叙述正确的是A．常压干馏可分离得到汽油、煤油和柴油B．重油的碳链较长，适合采用减压分馏进行分离C．煤炭中含有苯，可用四氯化碳溶出D．煤干馏得到的煤焦油，可用分液的方法得到芳香烃9．下列实验装置设计正确、且能达到目的的是A．实验I：可用于吸收氨气并防止倒吸B．实验II：静置一段时间，小试管内有晶体析出C．实验III：配制一定浓度的稀硫酸D．实验IV：海水淡化10．若使含有Ba2+、Al3+和Ag+的溶液中各离子逐一沉淀，下列所选试剂和加入试剂的顺序正确的是A．H2SO4、HCl、NaOH、CO2B．NaCl、Na2SO4、NaOH、HClC．HCl、Na2SO4、NaOH、CO2D．Na2CO3、NaCl、NaOH、HCl11．如图是KNO3和KCl的溶解度曲线，下列说法正确的是A．将等浓度的KNO3和KCl的混合溶液加热蒸发，首先析出的晶体主要是KNO3B．将上述A所得混合物冷却至室温，析出的晶体主要是KClC．将上述B的混合物过滤，并将溶液加热浓缩，析出的晶体主要是KNO3D．将上述A所得混合物趁热过滤，得到的晶体主要是KCl12．气体X可能含有NH3、Cl2、HBr、CO2中的一种或几种。