绵阳中学自主招生模拟试题.doc

数学素质考查卷一.选择题：（本大题共12个小题，每个4分，共48分，将所选答案填涂在机读卡上）1、下列因式分解中，结果正确的是（）A.B.C.D.2、“已知二次函数的图像如图所示，试判断与0的大小.”一同学是这样回答的：“由图像可知：当时，所以.”他这种说明问题的方式体现的数学思想方法叫做（）A.换元法B.配方法C.数形结合法D.分类讨论法3、已知实数满足，则的值是（）A.-2B.1C.-1或2D.-2或14、若直线与反比例函数的图像交于点，则反比例函数的图像还必过点（）A. (-1,6)B.(1,-6)C.(-2,-3)D.(2,12)5、现规定一种新的运算：“*”：，那么（）A.B.5C.3D.96、一副三角板，如图所示叠放在一起，则（）A.180B.150C.160D.1707、某中学对2005年、2006年、2007年该校住校人数统计时发现，2006年比2005年增加20%，2007年比2006年减少20%，那么2007年比2005年（）A.不增不减B.增加4C.减少4D.减少28、一半径为8的圆中，圆心角为锐角，且，则角所对的弦长等于（）A.8B.10C.D.169、一支长为13cm的金属筷子（粗细忽略不计），放入一个长、宽、高分别是4cm、3cm、16cm的长方体水槽中，那么水槽至少要放进（）深的水才能完全淹没筷子。A.13cmB.cmC.12cmD.cm10、如图，张三同学把一个直角边长分别为3cm,4cm的直角三角形硬纸板，在桌面上翻滚（顺时针方向），顶点A的位置变化为，其中第二次翻滚时被桌面上一小木块挡住，使纸板一边与桌面所成的角恰好等于，则翻滚到位置时共走过的路程为（）A.cmB.cmC.cmD. cm11、一辆汽车从甲地开往乙地，开始以正常速度匀速行驶，但行至途中汽车出了故障，只好停下修车，修好后，为了按时到达乙地，司机加快了行驶速度并匀速行驶。下面是汽车行驶路程S(千米)关于时间t(小时)的函数图象，那么能大致反映汽车行驶情况的图像是（）A B C D12、由绵阳出发到成都的某一次列车，运行途中须停靠的车站依次是：绵阳罗江黄许德阳广汉清白江新都成都.那么要为这次列车制作的车票一共有（）A.7种B.8种C.56种D.28种二. 填空题（共6个小题，每个小题4分，共24分。将你所得答案填在答卷上）13、根据图中的抛物线可以判断：当_时，随的增大而减小；当_时，有最小值。14、函数中，自变量的取值范围是_.15、如图，在圆中，直径是上半圆上的两个动 点。弦与交于点，则_.16、下图是用火柴棍摆放的1个、2个、3个六边形，那么摆100个六边形，需要火柴棍_根。17、在平面直角坐标系中，平行四边形四个顶点中，有三个顶点坐标分别是（-2，5），（-3，-1），（1，-1），若另外一个顶点在第二象限，则另外一个顶点的坐标是_.18、参加保险公司的汽车保险，汽车修理费是按分段赔偿，具体赔偿细则如下表。某人在汽车修理后在保险公司得到的赔偿金额是2000元，那么此人的汽修理费是_元.汽车修理费元赔偿率0500605001000701000300080三.解答题（共7个小题，满分78分，将解题过程写在答卷上）19、（10分）先化简，再求值：，其中.20、（10分）在中，.以为底作等腰直角，是的中点，求证：.21、(10分)绵阳中学为了进一步改善办学条件，决定计划拆除一部分旧校舍，建造新校舍。拆除旧校舍每平方米需80元，建造新校舍每平方米需要800元，计划在年内拆除旧校舍与建造新校舍共9000平方米，在实施中为扩大绿化面积，新建校舍只完成了计划的90而拆除旧校舍则超过了计划的10，结果恰好完成了原计划的拆、建总面积。（1）求原计划拆、建面积各是多少平方米？（2）若绿化1平方米需要200元，那么把在实际的拆、建工程中节余的资金全部用来绿化，可绿化多少平方米？22、（10分）已知直线与轴的负半轴交于点，直线与轴交于点，与轴交于点，（是坐标原点），两条直线交于点.（1）求的值及点的坐标；（2）求四边形的面积.23、（12分）如图：已知是圆的直径，是圆的弦，圆的割线垂直于于点，交于点（1）求证：是圆的切线；（2）请你再添加一个条件，可使结论成立,说明理由。（3）在满足以上所有的条件下，求的值。24、（12分）如图，菱形的边长为12cm，60，点从点出发沿线路做匀速运动，点从点同时出发沿线路做匀速运动.（1）已知点运动的速度分别为2cm/秒和2.5cm/秒，经过12秒后，分别到达两点，试判断的形状，并说明理由；（2）如果（1）中的点有分别从同时沿原路返回，点的速度不变，点的速度改为cm/秒，经过3秒后，分别到达两点，若与题（1）中的相似，试求的值.25、（14分）在中，的长分别是，且.（1）求证：；（2）若2，抛物线与直线交于点和点，且的面积为6（是坐标原点）.求的值；（3）若，抛物线与轴的两个交点中，一个交点在原点的右侧，试判断抛物线与轴的交点是在轴的正半轴还是负半轴，说明理由.英语素质考查卷（120分钟）I卷I.听力（ 共20小题；每小题1.5分，满分30分 )第一节：听下面5段对话。每段对话后有一个小题，从题中所给的A，B，C三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话后， 你都有10秒中的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。1.When should the woman go to the zoo according to the man?A. On Sunday afternoon. B.On Saturday afternoon. C. On a week day.2.Where are the two speakers? A. In a hotel B. At a dinner table C. In the street.3.What are the two speakers? A.A bus driver and a passenger. B.A policeman and a driver.C.A taxi driver and a passenger.4.What will the weather be like on Thursday? A.Rainy. B.Fine. C.Cold.5.What does the man suggest? A.Come back for a later show. B.Wait in a queue. C.Come back in five minutes.第二节：听下面5段对话或独白。每段对话或独白后有几个小题，从每题所给的A，B，C三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话或独白前，你将有时间阅读各小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。每段对话或独白读两遍。听第6段材料，回答第6至8题。6.What does the man first invite the woman to do? A. Go shopping. B. Go swimming. C. Go to the cinema.7.When will the two speakers go out for supper together? A. On Friday evening. B. On Saturday evening. C. On Sunday evening.8.When and where will the man pick up the woman? A. At seven at her house. B. At six at her house. C. At five at her office.听第7段材料，回答第9至11题。9.What is the possible relationship between the two speakers?A. They are friends. B.They are strangers.C.They are workers in the same company.10.Where is Jim going?A.Going to the cinema. B.Going home. C.Going to watch TV.11.What time of the day do you think it is? A.In the morning. B.At noon. C.In the evening.听第8段材料，回答第12至14题。12.Why hasnt Kat seen John recently?A.He went on camping. B.He was visiting his brother. C.Hes been studying.13.Why did Kate suggest John camping?A.John can get in touch with the nature. B.John can have a good rest.C.John can go to many parks.14.What did John think of camping?A.Camping was very expensive. B.They could camp anywhere they wanted.C.Camping was not safe.听第9段材料，回答第15至16题。15.Where did the conversation take place?A.In Italy. B.In America. C.In China.16.What did the man enjoy most during the holiday?A.Meeting with his relatives. B.Being together with his wife and his daughter.C.Visiting friends.听第10段材料，回答第17至20题。17.What is the speaker?A.An assistant to help organize the play. B.The director of the school play.C.Chairman of the students union.18.What will the people be asked to do?A.To act in the school play.B.To help organize the school play.C.To direct the school play.19.What can we learn about the peoples work?A.Maybe they will work at night.B.They will work in the daytime.C.They will work every day.20.What will the speaker do after the speech?A.Answer questions. B.Set up the lights. C.Watch their performance.II.选择填空（共15小题，共15分）从A、B、C、D四个选项中，选出可以填入各题空白处的最佳选项。21.To our great _,the beautiful singer could sing a lot of English songs. A.surprise B.surprised C.surprising D.surprisingly22.Making good use of a tape recorder will help you to _ bad pronunciation. A.give in B.give out C.give away D.get rid of23.What do you think of the place? I didnt care for it at_first,but after_ time I got to like it. A./;the B.the;a C./;a D.a;the24.Shall I sit at this end of the boat or the other end? If you keep still,you can sit at _. A.neither B.either C.all D.any25.At the school meeting,the headmaster suggestes the teachers receive _ education to catch up with the _development. A.farther;late B.farther;latest C.further;late D.further;latest26.Be careful when you get _ or _ the bus? A.on;off B.up;down C.in;out D.over;below27.Susan is out.I wonder how long ago_. A.did she go B.she has left C.she leaves D.she left28.I usually go there by train. Why not _by plane for a change? A.to try going B.try going C.to try and go D.trying to go29.Think hard,_ youll get a good idea. A.but B./ C.and D.yet30.They lost their way in the forest,and _ made matter worse was that night began to fall. A.which B.what C.it D.that31.Have you traveled much?No,Ive done _traveling. A.few B.smalll C.little D.less32.Shall I go home now?No,you_.Your work hasnt been finished yet. A.neednt B.mustnt C.wont D.wouldnt33.Dont do anything unless I ask _. A.you to B.you C.of you D. you to do34.I failed in the English test._.Dont lose heart.Try again. A.Youre too slow B.Im sorry to hear that C.Nothing to worry about D.Im angry with you.35.Who do you think knows the news?Nobody but Tom and Jane _ it. A.know B.knows C.have known D.is knownIII.完形填空（本题有20小题，每小题1.5分，共30分）阅读下面短文，掌握其大意，然后从A、B、C、D四个选项中选出可以填入空白处的最佳答案。All big cities are quite similar. 36 in a modern Asian city is not 37 living in an American city.The same cannot be said about living on farms, 38 .In many parts of the world,farmers and their families live in villages or 39 .In the United States,however,each farm family lives 40 its own fields,often out of the sight of any 41 .Instead of traveling in the morning from their 42 to the field every day,American farmers often 43 on their land throughout the week.They travel to the nearest town on Saturdays for 44 or on Sundays for church.The children 45 on buses to large schools which 46 all of the farm families living in the area.In 47 areas,there are small schools for a few families,and the children 48 to school.But life 49 for everyone,of course,including the farmers. 50 there are cars,good roads,radios,and television sets. 51 of course there are modern machines for farming.All of these have changed farm life.For many years,however,farming in America was 52 a lonely way of living.Farmers had to 53 their own problems all by themselves,instead of getting 54 from others.As time went on they learned to try new ways,and trust their own ideas instead of following 55 ways.36.A.Studying B.Living C.Farming D.Working37.A.as far as B.as difficult as C.very different from D.as easy as38.A.either B.however C.now D.of course39.A.towns B.big cities C.streets D.houses40.A.in B.across C.near D.between41.A.animals B.neighbours C.friends D.cattle42.A.hometown B.farm C.field D.village43.A.eat B.sleep C.stay D.depend 44.A.food B.trip C.dinner D.shopping45.A.take B.ride C.sit D.lie46.A.are run by B.are near C.serve D.work for47.A.other B.these C.most D.some48.A.walk B.go C.come D.run49.A.is not easy B.keeps changing C.is hard D.is funny50.A.Often B.Usually C.Today D.Sometimes51.A.Then B.Therefore C.But D.And52.A.not B.often C.never D.forever53.A.answer B.replies C.deal with D.work out54.A.letters B.replies C.thanks D.help55.A.more B.older C.other D.modernIV. 阅读理解（共20小题，每小题2分,共40分）阅读下面短文，从每题所给的A、B、C、D四个选项中选出最佳选项。aPlants are very important living things.Life could not go if there were no plants.This is because plants can make food from air,water and sunlight.Animals and man cannot make food from air,water and sunlight.Animals get their food by eating plants and other animals.So animals and man need plants in order to live.This is why we find that there are so many plants around us.If you look carefully at the plants around you,you will find that there are two kinds of plants:flowering plants and non-flowering plants.Flowering plants can bear seeds.The seeds are protected by the fruits.Some fruits have one seed,some have two,three or four,and some have many seeds.But a few fruits have no seeds at all.An example of a fruit without seeds is the banana fruit.Most non-flowering plants dont grow from seeds.They grow from spores.Spores are very,very small.Some spores are so small and light that they can float in the air.We may say that spores are quite the same as the seeds.When these spores fall on wet and shady places,they usually grow into new plants.56.The main idea of the passage is that _.A.plants are important for life B.plants cannot grow without airC.there are many plants around us D.we cannot live without water.57.Which of the following is NOT true? A.Plants can be divided into two main types:flowering plants and non-flowering plants. B.All fruits have seeds in them. C.Seeds are protected by the fruits D.Some plants grow from spores.58.The word “non-flowering”in this passage means _. A.开花的 B.有花的 C.多花的 D.不开花的BIn the United States,most children begin attending school when they are 5 years old.Public education is free and most children go to learn to read and write.But they also play games and go on trips.There is no reason at such an early age for them to hit the books. The situation changes as children become older.The subjects become more difficult. Students must learn about world history,algebra(代数),and the life sciences.Tests become more common.Pressure is growing to hit the books,study hard,and advance.However,most serious students only really begin hitting the books for long hours when they reach high school.High school students who hope to continue their education at a college or university must take a special national test called the S-A-T.The test has two parts.The first part tests the students ability with numbers and mathematical skills. The second part tests the students ability in the English language.The S-A-T test is very important.A high school student who gets a high score on the two parts of the test has a good chance to enter a top American college.For this reason,many students hit the books for months to prepare for the S-A-T.59.From the text,we can see “hitting the books” means _. A.working hard for the future B.studying a subject carefully C.reading books in a hurry D.reading books with great effort60.Which of the following statements can best express the main idea of the text? A.The S-A-T is the most important test. B.Education is not easy in the United States. C.“Hitting the books ” is very important for the students who want to have a bright future. D.The more you want to learn,the more tests you have to pass.61.American children dont have _ if they want to study in public school. A.to work hard at their lessons B.to pay for the education C.to hit the books D.to take many tests62.The students in high school_ . A.have to take the S-A-T B.are free and happy C.have to hit the books if they want to go on to college D.dont hit the books until they pass the S-A-T63.Which of the following is NOT true according to the text? A.In America the students have to pass certain tests to continue their education. B.Young children neednt work hard at their lessons because education is free. C.Those who fail in the S-A-T cannot go to college. D.The students must spend a lot of time preparing for the S-A-T.CAnotherReasonIt was a quiet village in which there was a military camp.It was far from the towns and cities and there were some high mountains around.Of course it was a good place for training the new soldiers.But it was difficult for the young men to go outside.Mr.White ,an officer of forty,was strict with them and he hardly let them leave the camp.Once Mr.White was ill in bed. He couldnt work and a young officer, Mr. Hunt, began to train the new soldiers instead of him.He knew the young men well and let nine soldiers go to the nearest town to have a holiday.But night fell and none came back to the camp.He was worried about it and stood at the gate.It was five to twelve when Mr.Hunt decided to go to the town and see what was happening with the young men.He started the car quickly and set off.At that moment the nine soldiers came back.It seemed they were all drunk.Of course they found the officer was angry.“Im sorry, sir” said the first soldier. “I left the town on time,But something was wrong with my bus on my way here.I had to buy a horse and made it run fast.Bad luck!It died and I had to run back.”And the other seven soldiers said they were late for the same reason.It was the last soldiers turn.He said, “Im sorry,sir.I got on a bus on time,but”Having heard this,the officer became even angrier and stopped him at once.He called out, “If you say something was wrong with your bus,Ill punish you at once!”“No,no,sir,”said the young man. “My bus was all right,but the dead horses were in its way!”64.The military camp was built in the village to _. A.stop the soldiers going to towns B.stop the soldiers meeting their friends C.train new soldiers D.make the young men live quietly.65.Mr.Hunt let nine soldiers have a holiday because_. A.he was kind to them B.they felt lonely C.they had something important to do D.they were the best of all66.The nine soldiers returned to the camp late because_. A.something was wrong with their busesB.their horses died on their return way C.it took them much time to run backD.they all had drunk too much in the town67.Which answer do you think is right? A.The officer only believed the last soldier.B.The officer believed the nine soldiers. C.The officer believed none of the soldiers.D.The officer wouldnt punish his soldiers.D“If you want to see a thing well,reach out and touch it!”That may seem a strange thing to say.But touching things can help you to see them better.Your eyes can tell you that glass ball is round.But by holding it in your hands,you can feel how smooth and cool the ball is.You can feel how heavy the glass is.When you feel all these about the ball,you really see it.With your skin,you can feel better.For example,your fingers can tell the difference between two coins in your pocket.You can feel a little drop of water on the back of your hand,too.You can also feel sounds against your skin.Have you ever wanted to know why some people like very loud music?They must like to feel the sounds of music.All children soon learn what “Dont touch!”means.They hear it often.Yet most of us keep on touching things as we grow up.In shops,we touch things we might buy,such as food,clothes and so on.To see something well,we have to touch it.The bottoms of our feet can feel things,too.You know this when you walk on warm sand,cool grass or a bad floor.All feel different under your feet.There are ways of learning to see well by feel