綿陽南山中學自主招生模擬試題(含詳解)

1、保密啟用前綿陽南山中學(實驗學校)2012年自主招生考試數(shù) 學 試 題本套試卷分試題卷和答題卷兩部份,試題卷共6頁,答題卷共6頁,滿分150分,考試時間120分鐘.注意事項:1.答卷前,考生務(wù)必將自己的姓名、考試號用0.5毫米的黑色墨水簽字筆或黑色墨水鋼筆填寫在答題卷與機讀卡對應(yīng)位置上,并認真核對姓名與考號;2.選擇題每小題選出答案后,用2b鉛筆將機讀卡上對應(yīng)題目的答案標號涂黑,如需改動,用橡皮擦干凈后,再選涂其它答案標號,答在試題卷上無效;3.非選擇題(主觀題)用0.5毫米的黑色墨水簽字筆或黑色墨水鋼筆直接答在答題卷上每題對應(yīng)的位置上,答在試題卷上無效.作圖一律用2b鉛筆或0.5毫米黑色簽字

2、筆;4.考試結(jié)束后,請將本試題卷、答題卷與機讀卡一并上交.第卷(選擇題,共36分)一.選擇題(本大題共12個小題,每小題3分,共36分.每小題給出的四個選項中,只有一個符合題目的要求.)1. |-25|的平方根是( )a.625 b.5 c.-5 d. 52.下列運算正確的是( )a. b. c. d.3.下左圖是一個由小立方塊所搭的幾何體,則從不同的方向看所得到的平面圖形中(小正方形中的數(shù)字表示在該位置的小立方塊的個數(shù)),不正確的是( )第3題圖4.有兩個口袋,其中甲袋中有寫著1,2,3,4的四張牌,乙袋中有寫著2,3,4的三張牌.從兩袋中各取出一張牌,若每張牌被取出的機會相等,則兩張牌上數(shù)

3、字之和大于6的概率為( )a. b. c. d. 5.已知圓柱的底面半徑為r,高為h,若圓柱的體積為1,表面積為12,則等于( )a.2 b.3 c.6 d.126.創(chuàng)辦于1908年的四川省綿陽南山中學,2012年3月27日迎來了她104周年的校慶日.在校慶后,學生會記者隨機采訪了部分觀看校慶文藝節(jié)目的學生,并把調(diào)查結(jié)果繪成了下面的統(tǒng)計圖:第6題圖已知此次被調(diào)查的男、女學生人數(shù)相同.根據(jù)圖中信息,有下列判斷:在被調(diào)查的學生中,持非常滿意態(tài)度的人數(shù)占53%;本次共調(diào)查了200名學生;在被調(diào)查的學生中,有30%的女生持滿意態(tài)度;第7題圖在我校高一、高二參加各種社團的900名學生中,根據(jù)調(diào)查結(jié)果估計

4、持滿意與非常滿意態(tài)度的人數(shù)之和超過了720人.其中,正確的判斷有( )a.4個 b.3個 c.2個 d.1個 7.如圖:平面上有兩個全等的正十邊形abcdefghij、a1b1c1d1e1f1g1h1i1j1,其中c點與j1點重合,e點與h1點重合,則dca1的度數(shù)是( )a.96 b.108 c.118 d.1268.已知正abc內(nèi)接于圓o,四邊形defg為半圓o的內(nèi)接正方形(d、e在直徑上,f、g在半圓上的正方形),sabc=a,s四邊形defg=b,則的值等于( )a.2 b. c. d.9.根據(jù)下左圖中已填出的“”和“”的排列規(guī)律,把、還原為“”或“”且符合左圖的排列規(guī)律,下面“”中還

5、原正確的是( )a. b. c. d.第9題圖10.若方程的兩根為c、d,則方程的兩根為( )a.a、b b.-a、-b c.c、d d.-c、-d11.如左圖:abc是邊長3的正三角形,點d在線段bc上,點e在射線ac上,點d沿bc方向從b點以每秒1個單位的速度向終點c運動,點e沿ac方向從a點以每秒2個單位的速度運動,當d點停止時e點也停止運動.設(shè)運動時間為t秒,若dec的圖形的面積用y來表示(規(guī)定:當三點在一條直線上時,三點組成的三角形面積為零),則y關(guān)于t的函數(shù)圖象是( )第12題圖12.如右圖:過abc的頂點a作對邊bc上的中線ae與高ad,e為bc中點,d為垂足.規(guī)定,特別地,當d

6、與e重合時,規(guī)定.對、作類似的規(guī)定.給出下列結(jié)論:若c=,a=,則;若,則abc為直角三角形;若,則abc為鈍角三角形;若,則abc為銳角三角形;若,則abc為等邊三角形.其中,正確結(jié)論的個數(shù)是( )a.1 b.2 c.3 d.4 第卷(非選擇題,共114分)二.填空題(本大題共6個小題,每小題4分,共24分.請將答案填入答題卡相應(yīng)的橫線上.)第14題圖成功祝你南山13.函數(shù)的自變量x的取值范圍是 .14.將如右圖所示的正方體的展開圖重新折疊成正方體后,和“成”字相對面上的漢字是 .15.下圖是由6個正方形構(gòu)成的長方形,若最小正方形的面積為1,則這個長方形的面積等于_.第17題圖第15題圖第1

7、6題圖cboade16.上圖為abc與o的重疊情形,其中bc為o的直徑.若,bc2,則圖中陰影部份的面積等于_.第18題圖17.如上圖:在銳角abc中,ab=,bac=,bac的平分線與bc交于點d,m、n分別是ad、ab上的動點,則mb+mn的最小值等于_.18.如右圖,a的半徑為r,o的半徑為4r,a從圖中所示位置出發(fā)沿o的表面作無滑動的滾動,當公轉(zhuǎn)一周時,自轉(zhuǎn)的轉(zhuǎn)數(shù)為_.三.解答題(本大題共7個小題,共90分.解答應(yīng)寫出文字說明、證明過程或演算步驟)19.(本題共2個小題,每小題8分,共16分)(1)計算:; (2)先化簡,再求值:,其中.第20題圖20.(本小題滿分12分)小王從a地前

8、往b地,到達后立刻返回,他與a地的距離y(千米)和所用的時間x(小時)之間的函數(shù)關(guān)系如圖所示.()小王從b地返回a地用了多少小時？()求小王出發(fā)6小時后距a地多遠？()在a、b之間有一c地,小王兩次經(jīng)過c地的時間差為2小時20分,求a、c兩地相距多遠？21.(本小題滿分12分)某商業(yè)集團新進了40臺空調(diào)機,60臺電冰箱,計劃調(diào)配給下屬的甲、乙兩個連鎖店銷售,其中70臺給甲連鎖店,30臺給乙連鎖店.兩個連鎖店銷售這兩種電器每臺的利潤(元)如下表:空調(diào)機電冰箱甲連鎖店200170乙連鎖店160150設(shè)集團調(diào)配給甲連鎖店x臺空調(diào)機,集團賣出這100臺電器的總利潤為y(元).()求y關(guān)于x的函數(shù)關(guān)系式

9、,并求出x的取值范圍;()為了促銷,集團決定僅對甲連鎖店的空調(diào)機每臺讓利a元銷售,其他的銷售利潤不變,并且讓利后每臺空調(diào)機的利潤仍然高于甲連鎖店銷售的每臺電冰箱的利潤,問該集團應(yīng)該如何設(shè)計調(diào)配方案,使總利潤達到最大？22.(本小題滿分12分)如圖,反比例函數(shù)(x0,且k為正常數(shù))的圖象經(jīng)過四邊形oabc的頂點a、c,abc90,oc平分oa與x軸正半軸的夾角,abx軸,將abc沿ac翻折后得ab1c,b1點落在oa上.()求四邊形oabc的面積;()若以oa為直徑的圓經(jīng)過點c,且四邊形oabc的面積為,求直線ob的解析式.第22題圖23.(本小題滿分12分)如圖,ab為o的直徑,am和bn是它

10、的兩條切線,e為o的半圓弧上一動點(不與a、b重合),過點e的直線分別交射線am、bn于d、c兩點,且cbce.第23題圖()求證:cd為o的切線;()連結(jié)ac與be交于點h,若tanbac,求的值.24.(本小題滿分12分)如圖,在平面直角坐標系中,點a(-1,0),點b(0,-),點c在x軸上.已知某二次函數(shù)的圖象經(jīng)過a、b、c三點,且它的對稱軸為x=1,點p是在直線bc下方的二次函數(shù)圖象上的一個動點(點p與b、c不重合),過點p作y軸的平行線交bc于點f.第24題圖()求該二次函數(shù)的解析式; ()在對稱軸上求一點m,使得ma+mb取到最小值;()若設(shè)點p的橫坐標為m,用含m的代數(shù)式表示線

11、段pf的長并求pbc面積的最大值,及此時點p的坐標. 25.(本小題滿分14分)如圖,oa=10是半圓c的直徑,點b是該半圓周上一動點(點b與點o、點a不重合),連結(jié)ob、ab,并延長ab至點d,使db=ab,過點d作直線oa的垂線,分別交直線oa、直線ob于點e、f,點e為垂足,連結(jié)cf.第25題圖()當aob=30時,求弧ab的長度; ()當de=8時,求線段ef的長;()在點b運動過程中,是否存在以點e、c、f為頂點的三角形與aob相似?若存在,請求出此時oe的長度;若不存在,請說明理由.保密啟用前綿陽南山中學(實驗學校)2012年自主招生考試英 語 試 卷本試卷分試題卷和答題卷兩部分。

12、試題卷共8頁，答題卷共1頁。滿分150分，考試時間100分鐘。注意事項：1. 答題前，考生務(wù)必將自己的 姓名、考號、用0.5毫米的黑色墨水簽字筆填寫在答題卷和機讀卡上，并認真核對。2. 1-45題使用2b鉛筆填涂在機讀卡對應(yīng)題目標號的位置上，46-50題及非選擇題用0.5毫米的黑色墨水簽字筆書寫在答題卷的對應(yīng)位置。在草稿紙、試題卷上答題無效。3. 考試結(jié)束后，將試題卷，答題卷和機讀卡一并交回。 第i卷 （選擇題，共100分）第一部分：英語知識運用（共兩節(jié)，滿分60分）第一節(jié)：單項填空 （共15小題，每小題2分，滿分30分）從（a、b、c、d）四個選項中選出可以填入空白處的最佳選項，并在機讀卡上

13、將該項涂黑。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第二節(jié)：完形填空 （

19、共15小題，每小題2分，滿分30分） 閱讀下列短文，從短文后各題所給的(a、b、c、d)四個選項中選出能填入相應(yīng)空白的最佳選項，并在機讀卡上將該項涂黑。 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：閱讀理解 （共20小題，每小題2分，滿分40分）第一節(jié)：短文理解 （共15小題，每小題2分，滿分30分） 閱讀下列短文，從短文后各題所給的(a、b、c、d) 四個選項中選出最佳選項，并在機讀卡上將該項涂黑。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. 沙塵 b. 閃電 c. 紫外線 d. 超聲波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( 顧客).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(說服) 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.第二節(jié)：補全對話（共5小題，每小題2分，滿分10分）根據(jù)下面的對話內(nèi)容，從方框內(nèi)的選項（a、b、c、d、e、f或g）中選出最佳選項，并將答案寫在答題卷上對應(yīng)題號后面的橫線上。選項中有兩個為多余選項。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（非選擇題，共50分）第三部分：寫作（共兩節(jié)，滿分50分）第一節(jié)：選詞填空（共10小題，每小題2分，滿分20分）閱讀下面短文，根據(jù)文中意思，從方框中選出恰當?shù)脑~，并在答題卷上對應(yīng)題號后面的橫線上寫出各單詞的完整、正確的形式，使短文文理通順，意義完整。 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(劍術(shù)). 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