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类型绵阳中学自主招生模拟试题.doc

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    1、1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.232()xyxy42()(2)xxC. D.1113aa2、 “已知二次函数 的图像如图所示,试判断2yaxbc与abc0 的大小.”一同学是这样回答的:“由图像可知:当 时1x,y所以 .”他这种说明问题的方式体现的数学思想方法0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( )x214x1xA.-2 B.1 C.-1 或 2 D.-2 或 14、若直线 与反比例函数 的图像交于点 ,则

    2、反比例函数 的图像还必yky(,)Pakyx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 ( )*()mn51*2A. B.5 C.3 D.946、一副三角板,如图所示叠放在一起,则 AOBCD( )A.180 B.150C.160 D.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 4 C.减少 4 D.减少 28、一半径为 8 的圆

    3、中,圆心角 为锐角,且 ,则角 所对的弦长等于( )32A.8 B.10 C. D.16829、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.13cm B. cm C.12cm D. cm410 15310、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 ,12A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 ,21CBC则 翻滚到 位置时共走过的路程为( )AA. cm

    4、 B. cm C. cm D. cm82829411、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

    5、的抛物线可以判断:当 _时, 随 的增大而减小;xyx当 _时, 有最小值。14、函数 中,自变量 的取值范围是_.2y15、如图,在圆 中,直径 是上半圆 上的两个动 O10ABCD, , AB点。弦 与 交于点 ,则 _.ACDEE16、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。317、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

    6、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x 赔偿率0 500 60500 1000 701000 3000 80 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: ,3221054xx其中 .21(tan5cos3)x20、 (10 分)在 中, .以 为底作等腰直角 , 是 的中点,ABC190,2ACB BCDE求证: .E21、(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

    7、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,4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yxayA28yxB轴交于点 , ( 是坐标原点) ,两条直线交于点 .yC:7:8AOP(1)求 的值及点 的坐标;aP(2)求四边形 的面积 .BS23、 (12 分)如图:已知 是圆 的直径, 是圆 的弦,圆

    8、 的割线 垂直于 于点ABCODEFAB,G交 于点BC,.HD(1)求证: 是圆 的切线;O(2)请你再添加一个条件,可使结论 成立,说明理由。2BHG(3)在满足以上所有的条件下, 求 的值。10,8.AEFsinA24、 (12 分)如图,菱形 的边长为 12cm, 60 ,点 从点 出发沿线路ABCDAPA做ABD匀速运动,点 从点 同时出发沿线路 做匀速运动.QCB(1)已知点 运动的速度分别为 2cm/秒和,PQ52.5cm/秒,经过 12 秒后, 分别到达 两点,试判断 的形状,并说明理由;PQ、 MN、 AMN(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

    9、 的速、 、 PQ度改为 cm/秒,经过 3 秒后, 分别到达 两点,若 与题(1)中的v、 EF、 BEF相似,试求 的值.AMNv25、 (14 分)在 中, 的长分别是 ,且 .ABC90,ACB,bacotcsBA(1)求证: ;2ba(2)若 2,抛物线 与直线 交于点 和点 ,且2()ymxba4yx1(,)Mxy2(,)Nxy的面积为 6( 是坐标原点).求 的值;MON(3)若 ,抛物线 与 轴的两个交点中,一个交点在24,30anpqb2(3)npq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.yy英 语 素 质 考 查 卷(120 分钟)I 卷I

    10、.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

    11、 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

    12、 a queue. C.Come back in five minutes.6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 w

    13、ill 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 betw

    14、een 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

    15、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.

    16、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?7A.Meeting with his relatives. B.Being together with his wife and his daughter.C.Visiti

    17、ng 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.

    18、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。

    19、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_

    20、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 _develo

    21、pment.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 chan

    22、ge?A.to try going B.try going C.to try and go D.trying to go829.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

    23、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 thatC.Nothing to wo

    24、rry 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 A

    25、sian 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

    26、 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,the

    27、re 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,farmi

    28、ng 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 diffi

    29、cult 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.houses940.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.

    30、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.foreve

    31、r53.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 fo

    32、od 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

    33、 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 f

    34、ruit 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 plac

    35、es,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

    36、plants and non-flowering plants.B.All fruits have seeds in them.C.Seeds are protected by the fruitsD.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10BIn the United States,most children begin attending school when they are 5 years old.Public e

    37、ducation 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,algeb

    38、ra(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 uni

    39、versity 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

    40、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 carefullyC.reading books in

    41、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.Th

    42、e 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 educationC.to hit the books D.to take many tests62.The students in high school_ .A.have to take the S-A-TB.are free and ha

    43、ppyC.have to hit the books if they want to go on to collegeD.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 bec

    44、ause 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.CAnother ReasonIt 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

    45、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.11Once Mr.White was ill in bed. He couldnt work and a young officer, Mr. Hunt, began to train the new soldie

    46、rs 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 you

    47、ng 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

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