绵阳南山中学自主招生模拟试题(含详解)

1、保密启用前绵阳南山中学(实验学校)2012年自主招生考试数 学 试 题本套试卷分试题卷和答题卷两部份,试题卷共6页,答题卷共6页,满分150分,考试时间120分钟.注意事项:1.答卷前,考生务必将自己的姓名、考试号用0.5毫米的黑色墨水签字笔或黑色墨水钢笔填写在答题卷与机读卡对应位置上,并认真核对姓名与考号;2.选择题每小题选出答案后,用2b铅笔将机读卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后,再选涂其它答案标号,答在试题卷上无效;3.非选择题(主观题)用0.5毫米的黑色墨水签字笔或黑色墨水钢笔直接答在答题卷上每题对应的位置上,答在试题卷上无效.作图一律用2b铅笔或0.5毫米黑色签字

2、笔;4.考试结束后,请将本试题卷、答题卷与机读卡一并上交.第卷(选择题,共36分)一.选择题(本大题共12个小题,每小题3分,共36分.每小题给出的四个选项中,只有一个符合题目的要求.)1. |-25|的平方根是( )a.625 b.5 c.-5 d. 52.下列运算正确的是( )a. b. c. d.3.下左图是一个由小立方块所搭的几何体,则从不同的方向看所得到的平面图形中(小正方形中的数字表示在该位置的小立方块的个数),不正确的是( )第3题图4.有两个口袋,其中甲袋中有写着1,2,3,4的四张牌,乙袋中有写着2,3,4的三张牌.从两袋中各取出一张牌,若每张牌被取出的机会相等,则两张牌上数

3、字之和大于6的概率为( )a. b. c. d. 5.已知圆柱的底面半径为r,高为h,若圆柱的体积为1,表面积为12,则等于( )a.2 b.3 c.6 d.126.创办于1908年的四川省绵阳南山中学,2012年3月27日迎来了她104周年的校庆日.在校庆后,学生会记者随机采访了部分观看校庆文艺节目的学生,并把调查结果绘成了下面的统计图:第6题图已知此次被调查的男、女学生人数相同.根据图中信息,有下列判断:在被调查的学生中,持非常满意态度的人数占53%;本次共调查了200名学生;在被调查的学生中,有30%的女生持满意态度;第7题图在我校高一、高二参加各种社团的900名学生中,根据调查结果估计

4、持满意与非常满意态度的人数之和超过了720人.其中,正确的判断有( )a.4个 b.3个 c.2个 d.1个 7.如图:平面上有两个全等的正十边形abcdefghij、a1b1c1d1e1f1g1h1i1j1,其中c点与j1点重合,e点与h1点重合,则dca1的度数是( )a.96 b.108 c.118 d.1268.已知正abc内接于圆o,四边形defg为半圆o的内接正方形(d、e在直径上,f、g在半圆上的正方形),sabc=a,s四边形defg=b,则的值等于( )a.2 b. c. d.9.根据下左图中已填出的“”和“”的排列规律,把、还原为“”或“”且符合左图的排列规律,下面“”中还

5、原正确的是( )a. b. c. d.第9题图10.若方程的两根为c、d,则方程的两根为( )a.a、b b.-a、-b c.c、d d.-c、-d11.如左图:abc是边长3的正三角形,点d在线段bc上,点e在射线ac上,点d沿bc方向从b点以每秒1个单位的速度向终点c运动,点e沿ac方向从a点以每秒2个单位的速度运动,当d点停止时e点也停止运动.设运动时间为t秒,若dec的图形的面积用y来表示(规定:当三点在一条直线上时,三点组成的三角形面积为零),则y关于t的函数图象是( )第12题图12.如右图:过abc的顶点a作对边bc上的中线ae与高ad,e为bc中点,d为垂足.规定,特别地,当d

6、与e重合时,规定.对、作类似的规定.给出下列结论:若c=,a=,则;若,则abc为直角三角形;若,则abc为钝角三角形;若,则abc为锐角三角形;若,则abc为等边三角形.其中,正确结论的个数是( )a.1 b.2 c.3 d.4 第卷(非选择题,共114分)二.填空题(本大题共6个小题,每小题4分,共24分.请将答案填入答题卡相应的横线上.)第14题图成功祝你南山13.函数的自变量x的取值范围是 .14.将如右图所示的正方体的展开图重新折叠成正方体后,和“成”字相对面上的汉字是 .15.下图是由6个正方形构成的长方形,若最小正方形的面积为1,则这个长方形的面积等于_.第17题图第15题图第1

7、6题图cboade16.上图为abc与o的重叠情形,其中bc为o的直径.若,bc2,则图中阴影部份的面积等于_.第18题图17.如上图:在锐角abc中,ab=,bac=,bac的平分线与bc交于点d,m、n分别是ad、ab上的动点,则mb+mn的最小值等于_.18.如右图,a的半径为r,o的半径为4r,a从图中所示位置出发沿o的表面作无滑动的滚动,当公转一周时,自转的转数为_.三.解答题(本大题共7个小题,共90分.解答应写出文字说明、证明过程或演算步骤)19.(本题共2个小题,每小题8分,共16分)(1)计算:; (2)先化简,再求值:,其中.第20题图20.(本小题满分12分)小王从a地前

8、往b地,到达后立刻返回,他与a地的距离y(千米)和所用的时间x(小时)之间的函数关系如图所示.()小王从b地返回a地用了多少小时？()求小王出发6小时后距a地多远？()在a、b之间有一c地,小王两次经过c地的时间差为2小时20分,求a、c两地相距多远？21.(本小题满分12分)某商业集团新进了40台空调机,60台电冰箱,计划调配给下属的甲、乙两个连锁店销售,其中70台给甲连锁店,30台给乙连锁店.两个连锁店销售这两种电器每台的利润(元)如下表:空调机电冰箱甲连锁店200170乙连锁店160150设集团调配给甲连锁店x台空调机,集团卖出这100台电器的总利润为y(元).()求y关于x的函数关系式

9、,并求出x的取值范围;()为了促销,集团决定仅对甲连锁店的空调机每台让利a元销售,其他的销售利润不变,并且让利后每台空调机的利润仍然高于甲连锁店销售的每台电冰箱的利润,问该集团应该如何设计调配方案,使总利润达到最大？22.(本小题满分12分)如图,反比例函数(x0,且k为正常数)的图象经过四边形oabc的顶点a、c,abc90,oc平分oa与x轴正半轴的夹角,abx轴,将abc沿ac翻折后得ab1c,b1点落在oa上.()求四边形oabc的面积;()若以oa为直径的圆经过点c,且四边形oabc的面积为,求直线ob的解析式.第22题图23.(本小题满分12分)如图,ab为o的直径,am和bn是它

10、的两条切线,e为o的半圆弧上一动点(不与a、b重合),过点e的直线分别交射线am、bn于d、c两点,且cbce.第23题图()求证:cd为o的切线;()连结ac与be交于点h,若tanbac,求的值.24.(本小题满分12分)如图,在平面直角坐标系中,点a(-1,0),点b(0,-),点c在x轴上.已知某二次函数的图象经过a、b、c三点,且它的对称轴为x=1,点p是在直线bc下方的二次函数图象上的一个动点(点p与b、c不重合),过点p作y轴的平行线交bc于点f.第24题图()求该二次函数的解析式; ()在对称轴上求一点m,使得ma+mb取到最小值;()若设点p的横坐标为m,用含m的代数式表示线

11、段pf的长并求pbc面积的最大值,及此时点p的坐标. 25.(本小题满分14分)如图,oa=10是半圆c的直径,点b是该半圆周上一动点(点b与点o、点a不重合),连结ob、ab,并延长ab至点d,使db=ab,过点d作直线oa的垂线,分别交直线oa、直线ob于点e、f,点e为垂足,连结cf.第25题图()当aob=30时,求弧ab的长度; ()当de=8时,求线段ef的长;()在点b运动过程中,是否存在以点e、c、f为顶点的三角形与aob相似?若存在,请求出此时oe的长度;若不存在,请说明理由.保密启用前绵阳南山中学(实验学校)2012年自主招生考试英 语 试 卷本试卷分试题卷和答题卷两部分。

12、试题卷共8页，答题卷共1页。满分150分，考试时间100分钟。注意事项：1. 答题前，考生务必将自己的 姓名、考号、用0.5毫米的黑色墨水签字笔填写在答题卷和机读卡上，并认真核对。2. 1-45题使用2b铅笔填涂在机读卡对应题目标号的位置上，46-50题及非选择题用0.5毫米的黑色墨水签字笔书写在答题卷的对应位置。在草稿纸、试题卷上答题无效。3. 考试结束后，将试题卷，答题卷和机读卡一并交回。 第i卷 （选择题，共100分）第一部分：英语知识运用（共两节，满分60分）第一节：单项填空 （共15小题，每小题2分，满分30分）从（a、b、c、d）四个选项中选出可以填入空白处的最佳选项，并在机读卡上

13、将该项涂黑。1.my best friend neil is _ honest boy. you can believe him. a. a b. an c.the d./2.the fire was completely _ shortly afterwards with the help of the firemen. a.cut down b.put out c.give out d.floated away3.-would you like to have _ cake ? -no, thanks. ive had two. thats enough. a.other b.others

14、 c.another d.the other4. linda, together with her parents, _up the mess in the park at the moment. its meaningful to be a volunteer. lets join them.a. is cleaning b. are cleaning c. has cleaned d. have cleaned5. do you want to see the painting exhibition at the weekend? i wont see it unless i _.a. w

15、ill be invited b. am invited c. invite d. will invite 6. did you return from shanghai on time? no. the train_ i took was late because of the bad weather.a. what b. who c. which d. where7. i saw kevin in the supermarket this morning. no, it_ him. he moved to canada last week.a. can be b. must be c. c

16、ant be d. mustnt be8. bob spends a lot of money on books he is not rich. a. if b. though c. when d. because9. _ you _ your brother can join us. we want one of you.a. both; andb. neither; norc. either; ord. not only; but also10. connie arrived _ the village_ a snowy night.a. at; on b. at; in c. in; a

17、t d. in; on11. lady gagas new cd will_ next month. a. come along b. come up c. come over d. come out12. the 2012 olympics _ in london on july 27, 2012. a. holds b. will hold c. was held d. will be held13. the greens will visit nanshan middle school as soon as they_ to mianyang.a. comes b. come c. ca

18、me d. will come14. yesterday i won the first place in the 100- meter race. really ?_! a. congratulations b. never mind c. that is all right d. im sorry to hear that15. the policeman asked the boy_. a. where is his motherb. where his mother is c. where was his mother d. where his mother was第二节：完形填空 （

19、共15小题，每小题2分，满分30分） 阅读下列短文，从短文后各题所给的(a、b、c、d)四个选项中选出能填入相应空白的最佳选项，并在机读卡上将该项涂黑。 ado you give small money to your children? do you teach them 16 to use the small money? i agree with you about teaching and talking to your children about small money. this can help them make good use of it and 17 good habi

20、ts. children of all ages need to know the 18 of saving money. i think parents should give children small money and let them buy something by 19 . in this way, they can learn how to save money, what to spend money on, and how to 20 plan their money. 16. a. how b. what c. who d.why17. a. lose b. borro

21、w c. develop d.buy18. a. importance b. illness c. instruction d.disadvantage19. a. yourself b. itself c. themselves d.ourselves20. a. strongly b. properly c. slowly d.actually bsheepdogs are very important to farmers.sheepdogs help famers to find their 21 and bring them back to the farm.mike,a farme

22、r from a 22 ,has a very clever and honest sheepdog 23 bobby.he has made a little but 24 house for bobby and regards the dog 25 a family member.he often says,“bobby is the best dog in the world.he 26 my sheep very well.”if the dog house is 27,mike kowns bobby is with his sheep.mike 28 with bobby thro

23、ugh whistles. bobby can understand many differrent instructions from those 29.and bobby can also 30 himself by barking or doing other actions,mike loves bobby very much.they are getting on well with each other.21. a. villagers b. dogs c. farmers d. sheep22. a. village b. city c. park d.bank23. a. ag

24、ed b. dressed c. called d. included24. a. comfortable b. expensive c. dangerous d.terrible25. a. by b. on c. of d. as26. a. looks out b.looks after c. takes back d.takes away27. a. full b. clean c. empty d. dirty28. a. communicates b. compares c. catches d.checks29. a. noises b. talks c. whistles d.

25、 conversations30. a. explain b. express c. examine d.excuse第二部分：阅读理解 （共20小题，每小题2分，满分40分）第一节：短文理解 （共15小题，每小题2分，满分30分） 阅读下列短文，从短文后各题所给的(a、b、c、d) 四个选项中选出最佳选项，并在机读卡上将该项涂黑。a31. we can _ in fun french or spanish clubs. a. have a party b. play chess c. make friends d. watch movies32. in lcf clubs, children

26、 can _. a. join fun painting and gym clubs. b. get education at school clubs onlyc. learn with songs, games and cooking d. learn with stories, games and movement33. jazz-mataz is for children who can speak _. a. spanish b. english c. chinese d. french34. if you want to join an lcf club, youd better

27、not _. a. post a letter b. send an email c. go to the local club d. make a phone call35. from the passage above, we can know _. a. lcf is a language and science school in canada b. lcf has language clubs and music & gym clubs c. lcf music & gym clubs can be found just online d. lce provides excellen

28、t training, teachers and doctors. b many of us dont pay much attention to the importance of eye care. it is said that if you take care of your body, then you can surely be healthy. that is why our eyes should be given a lot of care. natural eye care should be put in a number one place. there are sev

29、eral causes leading to poor eyesight like not enough food, genes(基因) and aging(老化). televisions, computers and reading are also the causes of having poor eyesight. if you happen to work in front of the computer, it is best to take a break every once in a while. something dirty can cause redness and

30、they will make you feel uncomfortable. it is bad for your eyes, too. if this happens, the best way is to clean your eyes by using cold water. you must also try your best to protect your eyes from harmful things. for example, sunglasses are not just for fashion but they can also serve as a great way

31、to protect your eyesight from uv rays. eating healthy foods will do good to your eyesight. remember that vitamins a, c and e are good for eyes. try to eat food groups that have these vitamins. and you should do eye exercises because exercise protects your eyesight, too. if a person exercises regular

32、ly(定期地) and eats the right kind of food, his eyes will stay in good condition for a long time. all above are natural ways of eye care that help us keep healthy eyes. being happy all the time can be helpful to a persons eyesight, too. in a word, eye care is very important, no matter how old a person

33、is.36. _ is the most important way to protect our eyes. a. natural eye care b. taking medicine c. seeing the doctor d. being happy all the time37. all the following causes can lead to bad eyesight except _. a. age b. height c. reading d. computers38. what should you do if you have to work in front o

34、f the computer? a. eat healthy foods. b. clean the eyes by using cold water. c. wear a pair of sunglasses. d. have a rest after working for a while.39. what do the underlined words “uv rays” mean? a. 沙尘 b. 闪电 c. 紫外线 d. 超声波40.which is the best title of the passage? a. ways of eye care b. ways of eye

35、exercises c. ways of being happy d. ways of being healthycgloria is a famous hostess of a tv station. when she was 15, she happened to walk into a bookstore in her hometown and began looking at the books on the shelves. the man behind the counter, john smith, asked if shed like a job. she needed to

36、start saving for college, so she said yes.gloria worked after school and during summer vacations, and the job helped pay for her first year of college. during college she would do many other jobs: she served coffee in the student union, was a hotel cleaner and even made maps for the forest service.

37、but selling books was one of the most satisfying jobs.one day a woman came into the bookstore and asked gloria for books on cancer. the woman seemed anxious. gloria showed her practically everything they had and found other books they could order. the woman left the store less worried, and gloria ha

38、s always remembered the pride( 自豪) she felt in having helped her customer( 顾客).years later, as a television hostess, gloria heard about a child who was born with problems with his fingers and hand. his family could not afford an operation, and the boy lived in shame, hiding his hand in his pocket al

39、l the time.gloria persuaded(说服) her boss to agree to let her do the story. after the story was broadcast, some doctors called, offering to perform the operation for free.gloria visited the boy in the hospital after the operation. the first thing he did was to hold up his repaired hand and say, thank

40、 you. what a sweet sense of satisfaction gloria felt!at smiths bookstore, gloria always realized she was working for the customers, not the store. today its the same. the tv station pays her, but she feels that she should work for the people who watch the programmes, helping them understand the worl

41、d better. 41. when did gloria get her first job? a. a few years before college. b.several years after college. c.when she was studying at college. d.when she was working in the tv station.42. in which part-time job did gloria feel the happiest? a.cleaning in the hotel. b.selling books in the booksto

42、re. c.serving coffee in the student union. d.making maps for the forest service.43. what does the word she in the third paragraph refer to( 所指) ? a. the boss. b. the woman. c gloria. d. the doctor.44. how did gloria help the child get the operation he needed? a.her boss agreed to raise money. b.she

43、paid for the operation herself. c.she allowed the boy to show on tv. d.her news report affected some doctors.45. what particularly gives her the feeling of pride? a.helping people through her work. b.reporting interesting stories. c.being able to do different jobs well. d.paying for her college educ

44、ation herself.第二节：补全对话（共5小题，每小题2分，满分10分）根据下面的对话内容，从方框内的选项（a、b、c、d、e、f或g）中选出最佳选项，并将答案写在答题卷上对应题号后面的横线上。选项中有两个为多余选项。a : hello!is that lulu restaurant?b: yes, 46_a: i want to know if you send takeaway food.b: sure.a: 47 b: what would you like to have? a: 48 .b: ok,anything else? a：no,thanks,how can i pa

45、y you?b: 49 by the way,what time do you expect your lunch? and 50 a：around 11:30 a.m. room110,building c.b: oh,yeah.see you then.a.id like to order something for my lunch e.id like to have some beef. b. what can i do for you? f. thats enough.c. how much would you like? g.you can pay us when we send

46、you the food.d.could you leave us your address? 第二卷（非选择题，共50分）第三部分：写作（共两节，满分50分）第一节：选词填空（共10小题，每小题2分，满分20分）阅读下面短文，根据文中意思，从方框中选出恰当的词，并在答题卷上对应题号后面的横线上写出各单词的完整、正确的形式，使短文文理通顺，意义完整。 condident, world, deep, ready, plenty, while, decide, up, modern, welcome the 2012 olympics will open in london on july 27,

47、 2012.london will become the _51_ first city to host the olympics three times, in 1908, in 1948 and in 2012.as is known to all, london is a garden city. when you step into the city, you will find yourself _52_attracted by the beautiful views around. also, there are 53 of nice stadiums and gymnasiums

48、 for olympic games, such as the swimming pools, football playground and basketball gyms. the building of the new stadiums has been completed. london is 54 for the “greatest show on earth”. the all-england club, the site of wimbledon, will host tennis. wembley stadium will be used for football 55 lords cricket(板球)ground will host archery(剑术). london wants to show their historic sites and a few new-classics to the world this summer.mascots(吉祥物) of the london olympic games are wenlo