2012年石家庄市高中毕业班第二次模拟考试文科综合能力测试本试卷分为第I卷（选择题）和第II卷（非选择题）两部分。
第I卷l至8页，第II 卷 9至16页，共300分。
考生注意：1. 答题前，考生务必将自己的准考证号、姓名填写在答题卡上。
考生要认真核对答题卡上粘贴的条形码的“准考证号、姓名、考试科目”与考生本人准考证号、姓名是否一致。
2. 每小题选出答案后，用2B铅笔把答题卡上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号。
第∏卷用黑色墨水签字笔在答题卡上书写作答，在试题卷上作答，答案无效。
3. 考试结束，监考人员务必将试题卷、答题卡一并收回。
第I卷(选择题共140分）本卷共35个小题，每小题4分，共140分Q在每小题给出的四个选项中，只有一项是符合题目要求的。
30年前电影《星球大战》中首次描绘了一个有两次日出的世界(如图1所示），如今这一想象被证明是现实。
2011年9 月15日，美国航空航天局用开普勒探测器发现，距地球200光年的地方有颗行星在绕两颗恒星旋转，它和《星战大战》中虚构的星球十分相似，天文学家把它命名为“开普勒一16b”。
这颗行星的体积、密度与土星非常相近，极有可能也是气体巨行星，中心由冰块和岩石组成，与绕转的两颗恒星几乎同处于一个平面。
两颗恒星之间距离很近，比水星和太阳之间的距离更近。
据此回答l〜2题。
1. 下列现象，有可能在该双日行星上出现的是①全球白昼无夜②白天立物双影③双日此升彼落④某天一次日落A.①②B.①③C.②③D.②④2. 该行星下列特征中，不利于其存在生命的是A.体积、密度与土星非常相近B.同时接受两颗恒星照射C.绕转的两颗恒星之间距离很近D.与绕转的两颗恒星几乎在一个平面上入渗率指水分自地表渗入土壤中的强度，以每小时若干毫米表示。
在某种情况下，降雨渗入土壤时的最大入渗率，叫“入渗容量”。
读图2回答3〜4题。
3. 若图中曲线表示干湿状况不同的沙壤土和粘壤土在其他条件相同时的入渗率变化情况，则下列组合正确的是A.①——湿粘壤土B.②——湿沙壤土C.③——干沙壤土D.④——干粘壤土4. 关于入渗率和入渗容量的叙述，正确的是A. 若其他条件相同，降水时间越长，土壤的入渗率越大B. 若其他条件相同，降水量越大，土壤的入渗率越大C. 在降雨量满足时，入渗容量出现在入渗初期D. 在降雨量满足时，入渗容量出现在降雨后期抚养比又称抚养系数，指非劳动人口与劳动人口数量的比率。
高中英语真题:2012届高考模拟（二）本试卷分为四个部分，包括听力、语言知识运用、阅读和书面表达。
时量120分钟。
满分15分。
Part I Listening Comprehension (30 marks)Seetion A (22.5 marks )Directions :In this section, you will hear six conversations betwe en two speakers .For each conversation ,there are several ques tions and each question is followed by three choices marked A , B and C. Listen carefully and then choose the best answer for each question.You will hear each conversation TWICE.Example ：When will the magazine probably arrive ?A．Wednesday . B．Thursday . C．Friday .The answer is B.Conversation 1.1．What’s wrong with woman ?A．She can’t sleep at night ?B．She has a serious headache.C．She hasn’t recovered from her illness.2．What made it difficult for the woman to follow the man’s advi ce ?A．She didn’t want to lose her job.B．She had to look after her children .C．She didn’t want to spend much money .Conversation 23．When did the speakers see each other last time ?A．Last Christmas . B．Two years ago .C．A few weeks ago .4．What do we know abort Joe ?A．He is interested in sports now .B．He broke his leg last week .C．He is learning to play the piano .Conversation 35．Where did kate and Laura meet ?A．At a camp . B．On a train. C．At a concert . 6．What to Laura and Kate have in common ?A．They both know the man .B．They are both interested in dance .C．They both enjoy camping .Conversation 47．Why did the oven stop working ?A．It broke down B．There was a short circuit . C ．The power was cut off.8．When does the conversation most probably take place ? A．In the late afternoon B．At noon C．At night . 9．What will the speakers probably do next ?A．Turn to their neighbor . B．Get a new oven .C．Pay the bill.Conversation 510．What so we learn about the woman ?A．She is a professor.B．She is new to the country.C．She has never had a Western dinner .11．What does the man advise the woman to do?A．Help set the table or serve the food .B．Leave the table when invited to .C．Help wash the dishes after dinner.12.．What day is it today ?A．Thursday. B．Friday. C．Saturday .Conversation 613．Why does the woman want to move ?A．There’s only one room in her present apartment.B．She can’t afford the rent of the present apartment .C．She can’t see a view in her present apartment . 14．How much monthly rent is acceptable ?A．1,000 yuan . B．1,500 yuan .C．2,500 yran.15．What do the speakers agree to do in the end ?A．Have a look at the apartment.B．Walk upstairs every day .C．Wait for a good opportunity.Section B (7.5 marks )Directions : In this section , you will hear a short passage．List en carefully and then fill in the numbered blanks with the inform ation you have heard . Fill in each blank with NO MORE THAN THREE WORDS.You will hear the short passage TWICE.At Dale’s Health FarmⅠ·Diet●Foods :Only fruit ,vegetables ,fish and chicken; no 16.●Drinks ;Only one glass of red wine at lunch time .Ⅱ·Exercise●17. : needed as exercise can be dangerous .●Activities :mostly light exercises and swimming .Ⅲ·18.TV: not availableNewspapers : delivered daily and can be sent 19. on de mand.Books :can be borrowed from the library .20Part ⅡLanguage Knowledge (45 marks)Section A (15 marks )Directions :For each of the following unfinished sentences there are four choices marked A,B ,C and D. Chose the one that bes t completes the sentence.Example:The wild flowers looked like a soft orange blanket thedesert .A．covering B．covered C．coverD．to coverThe answer is A .21．In a study of 43,000 men aged 40or more , diets c ontained the highest amount of sugar were 37 percent more lik ely to develop heart disease .A．those whose B．whose C．which D ．those of which22．You’ll start having positive results you replace negat ive thoughts with positive ones .A．since B．unlessC．until D．once23． ,we can all recycle plastic ,paper and metal as well as drink cans and newspapers.A．To be environmentally friendly B．Being environmental ly friendlyC．It being environmentally D．Be environmentally fri endly .24．Each of us is shaped by our parents .That is the explanatio n for we are different in many ways.A．howB．that C．why D．what25．—How much of the foreign expert’s speech did you understand ?—Next to .I wish I had worked harder at English.A．something B．everythingC．anything D．nothing26． nobody can avoid making mistakes in his life ,why not give him another chance instead of firing him ?A．While B．Though C．Since D．When 27．－France , a cab to school in such thundering weather.—I will, Mom.A．gets B．to get C．get D．getting 28．Don’t you think it is high time you yourself in your bo oks ?A．can bury B．to bury C．buryingD．buried29．You can not feel it but you can taste it .Very often the food tasting sells .A．well ; well B．good ; good C．good ; well D．well ;good30．When you come this time next month ,I an importa nt simulation test .A．take B．have taken C．will be taking D．have been taken31．He was nice than wise , so he could not hide his e mbarrassment.A．more B．or C．but D．worse 32．Be smart about the advertisement there are alread y two knives in the kitchen.A．unless B．or C．but D．and 33．—Where do you think he the computer ?—Sorry ,I have no idea.A．/; bought B．has ; bought C．did ; buy D．had ; bought34．There are eight tips in Dr Roger’s lecture on sleep ,and on e of them is to bed early unless you think it is necessary .A．doesn’t go B．not go C．not goingD．don’t go35．The party they had been looking forward to a disappo intment.A．turn out B．turning out C．turned out D．has turned outSection B(18 marks)Directions : For each blank in the following passage there are fo ur words or phrases marked A,B , C and D. Fill in each blank wi th the word or phrase that best fits the context .Mr ,and Mrs .Brown were going abroad for their holiday .They h ad a dog called Blackie which they were very fond of ,but they c ould not 36 him abroad with them ,so they looked for a good place to 37 him while they were away ,and at last found a pla ce which 38 bogs very well while their owners were away .Th ey took Blackie there just before they left for their holiday ,and 39 said goodbye to him .At the end of their holiday ,they got back to England very late at night ,and as they thought that the place where Blackie was sta ying might be closed at that 40 hour ,they decided to wait unti l the next morning before going to get him.So the next morning Mr .Brown got into his car and drove off ha ppily to 41 Blackie .When he reached home with the dog ,he said to his 42 .“Do you know ,dear ,I don’t think Blackie can have enjoyed his 43 at that place very much .He 44 all the way hone in the c ar as if he wanted to tell me something . ”Mrs .Brown looked at the dog 45 and then answered ,“You ar e quite 46 ,dear .He was certainly trying to tell you 47 .But he wasn’t trying to tell you that he hadn’t enjoyed his stay at th at place .He was only trying to tell you that you were bringing th e wrong dog home .This isn’t Blackie！”36．A．bring B．take C．sendD．carry37．A．leave B．forget C．dropD．deliver38．A．searched for B．looked for C．ran after D．looked after39．A．happily B．desperately C．sadlyD．angrily40．A．early B．late C．properD．delightful41．A．collect B．claim C．layD．return42．A．dog B．customer C．bossD．wife43．A．holiday B．trip C．stayD．meal44．A．talked B．cried C．barkedD．jumped45．A．occasionally B．carefully C．casually D．constantly46．A．serious B．nervous C．excitedD．right47．A．everything B．anything C．something D．nothingSection C (12 marks)Directions: Complete the following passage by filling in each bla nk with one word that best fits the context .Dear boys and girls,It’s a great honor to speak here .I’m really sorry that it will be only ten days 48. you graduate from our school .I have always been feeling honored to have been your English teacher in the 49. three years, during 50 I have been greatly impressed by yo ur 51 qualities such as honesty ,diligence. Cleverness, unself ishness ,co-operation and so on 52 in my teaching career have I met such wonderful students as you .The possibility of enhancing one’s knowledge is limitless .Gradu ation 53 marks a stage of one’s education .Unceasing acq uisition 54 knowledge will unceasingly escalate us to ever hig her and higher attainments.I do believe that your efforts will eventually pay off .I, as well as your other teachers ,am praying that every one of you will be a dmitted to 55 ideal college.Love fromYour English teacherPart Ⅲ Reading Comprehension (30 marks )Directions : Read the following three passages .Each passage is followed by several questions or unfinished statements .For e ach of them there are four choices marked A,B,C and D . Choo se the one that fits best according to the information given in th e passage.ADallas Children’s Theater AcademyShow Biz Sumner 2012Rosewood Center for Family arts5938 Skillman *Dallas ,TX 75231*(214) 978—0110 Important Information* All classes are taught by DCT Theater Professionals !* All Grade Levels indicated are for Fall 2012.* Tuition Deposit required for registration .* Tuition balance due on the first day of class . No tuition re funds ( 退款 ).* DCT reserves the right to cancel any class ;refunds made for canceilation .* Please accompany student to first day of class .* Registration begins one-half hour before class time .* Questions ? Call Nancy Schaeffer at (214)978 -0110 or e-mail nancy@How To RegisterMAIL:Fill out the form in this brochure.* Be sure to list the class and group that you want & the dates.* The registration form may be copied.FAX: Complete the registration form and fax it to DCT at (214)9 78—0118.PHONE: Call (214)978—0110.WEB: Visit , click on Academy Classes Drama Days! —$ 175Entering Grades :Group A :K Group B : lst & 2nd Group C:3rd — 5th .Mon .— Fri .9: 30 a. m.—l p. m. June 2—June 6* Day One —come up with a character ,work with your class to plan the play .* Day Two —create the situations and scenes for your one —of—a—kind show!* Day Three—rehearse ( 排演 )your part .* Day Four —pick a costume, get ready !* Day Five —SHOWTLME－invite family and friends to your Friday Showcase !* Bring a sack lunch and drink each day !Laugh Out Loud —$ 175Entering Grades : 5+Mon .—Fri .1.30 p.m.—5:00 p.m. June 23—June 27 Show Friday. June 27* Do you like comedy ? Try your hand at the world of comedy in the class just for you !* Learn a comedy sketch from the old masters !* Tell a joke ! Learn why old jokes can be the best !* Work with your class to put on a one —of—a—kind Comedy Show for family and friends !Acting —Just Acting—$225Group A: Entering Grades K: Group B: Entering Grades lst —2nd; Group C: Entering Grades 3rd — 4th ; Mon.—Fri.9:30 a.m.—2:30 p.m.; Session I :July 28—Aug .l; Session II :Aug.4-Aug8; Session III: Aug. 11—Aug .15* Are you ready to challenge your acting skills and try somethin g new !* Start with the characters :Who are you ? Be the Star of your D reams .* Become the character you’ve always wanted to be.* Work with your class to create the plot.* Get ready to present your show for family and friends on the fi nal Friday!Summer Scenes —$ 225Entering Grades 5th and 6th ;Mon.—Fri .9: a. m—2:30 p.m.; Session I: July —28—Aug. l; Session II:Aug.4—Aug. 8; Session Ⅲ: Aug .ll —Aug.15* Do you want to be an actor ?* Improve your skills with instruction from professional actors & directors.* Rehearse and perform scenes from your favorite plays .* Develop characters and polish performances ! 56．What is the purpose of the text ?A．To earn money from the text ?B．To attract readers to attend Summer Scenes .C．To persuade readers to attend Show Biz Summer 2012.D．To teach readers how to register for Show Biz Summer 201 2.57．If you want to attend Show Biz Summer 2012,you should b e aware that .A．there’ll be no refunds in any case .B．tuition must be paid at least before June 2.C．registration begins half an hour after class time .D．students had better be accompanied on the first bay . 58．It can be inferred from the text that all the four one -week specials .A．are intended for children aged belowB．are all held at Rosewood Center for Family ArtsC．will take place in June or July and last five daysD．need students to bring a sack lunch and drink each day 59．Which of the following classes suits those who want to beactors ?A．Summer Scenes B．Acting —Just ActingC．Laugh Out Loud . D．Drama Days ! 60．Where is the text most probably from ?A．A newspaper .B．An entertainment magazine.C．A guide book . D．part of a brochure.BThere’s no need to say it ,but there are really more than a few b enefits to educational tours .From the word itself ,an educationa l tour is something bone to gain knowledge while traveling and t ouring to some place .It creates opportunities for people to think out of the box and see things and places that aren’t usually see n in their normal environment..Educational trips aren’t always those that cover far distances .A s already said ,it is done to gain knowledge and you wouldn’t ne ed to go very far to have it .Sometimes , an educational trip coul d be in your hometown .Historic places and museums are always on top of the lists of the places to go in an educational tour .Educational tours like the se would make you know your country better .Your country’s hi story is rich and it is the reason why you came to be .But reme mber that the history of other states ,counties and countries are as important as your own .When you go on a trip to another country ,it is likely that you lea rn their culture first .Different cultures have different understandi ng and perspective of different acts ,and it could be dangerous or offending if you cannot understand a culture .When you go on an educational tour ,it is likely that you would h ave the opportunity to socialize with other people .Students are encouraged to talk to locals and natives and learn from them .b ecause it is with understanding that students gain knowledge . When students talk with local people ,they are gaining insights t o their life and their culture .It is said that when in Rome ,act an d think as the Romans do ,and this is a valuable skill that not all people could do .There are millions of people who want to travel ,and an educati onal tour is the perfect time to do so .Traveling opens new door s and opportunities ; it always makes you want to learn more .Cultures are many and widely different , and it is a very valuable t alent to understand the people of different cultures .Traveling with groups of other students is safer than traveling al one ,and bulk travels like those could also be helpful on the bud get .Group of friends could stay at one place and get discounts on the place that you wouldn’t get if you are traveling alone .Tra veling is fun and moue budget —friendly when with other people on an educational tour .Travel abroad for a month ,Try and see if you wouldn’t miss you r own country. Traveling would let you see your own country in a different way .The benefits of an educational tour are all impor tant，but this one creates patriotism in a person .A school isn’t a place where they teach you to find the answers ; it is a place where one teaches you to find the questions and l earn the answers for yourself .Educational tours are valuable thi s way . They teach you that you are not the only one seeking fo r questions and that there are other people who are willing to he lp you on your way too.61．What are educational tours according to the passage ?A．Something done to gain knowledge while traveling.B．Something done to know more about one’s own country whi le traveling .C．Something done to know more about a foreign country whil e traveling .D．Something done to seek for more friends while traveling. 62．What places are people most likely to go to in an education al tour?A．Schools and churches .B．Government buildings .C．Places of amusement.D．Historical places and museums .63．Which statement is correct according to the passage ?A．Educational trips always cover long distances.B．When on educational trips ,you seldom have the chance to t alk with other people.C．Educational trips are always too short to learn knowledge.D．Learning the culture first is a must before you go on educati onal trips.64．If you want to go on a cheap and safe educational trip ,you’d better .A．go with groups of other students B．avoid the top spotsC．book one in advanceD．learn the culture first65．What does the word “patriotism”in the eighth paragraph me an?A．同情B．爱国心C．羞耻心D．虚荣心CBecause the brain controls just abort everything , when somethi ng goes wrong with it, it’s often serious and can affect many diff erent parts of the body . Inherited diseases, brain disorders ass ociated with mental illness , and head injuries can all affect the way the brain works and upset the daily activities of the rest of t he body .Problems that can affect the brain include:Brain tumors .A tumor is swelling caused by overgrown tissue.A tumor in the brain may grow slowly and produce few sympto ms until it becomes large, or it can grow and spread rapidly ,ca using severe and quickly worsening symptoms . Brain tumors in children can be benign or malignant. Benign tumors usually gro w in one place and may be curable through surgery if they’re lo cated in a place where they can be removed without damaging the normal tissue near the tumor . A malignant tumor is cancero us and more likely to grow rapidly and spread.Headaches. Of the many different types of headaches , the mo st frequently occurring include tension headache (the most com mon type ),caused by muscle tension in the head ,neck , and sh oulders ; migraine , an intense, recurring headache with an uncl ear cause ; and cluster headache , considered by some to be a form of migraine. Migraines occur with or without warning and may last for several hours or days . There seems to be an inher ited predisposition to migraines as well as certain triggers that c an lead to them .People with migraines may experience dizzine ss, numbness, sensitivity to light , and nausea. And may see fla shing zigzag lines before their eyes .Mental illness. Mental illnesses are psychological and behavior al in nature and involve a wide range of problems in thought an d function. Certain mental illnesses are now known to be linked to structural abnormalities or chemical dysfunction of the brain . Some mental illnesses are inherited, but often the cause is unk nown. Injuries to the brain and chronic drug or alcohol abuse al so can trigger some mental illnesses. Signs of chronic mental ill nesses such as bipolar disorder or schizophrenia may first sho w up in childhood . Mental illnesses that can be seen in younge r people include depression , eating disorders such as bulimia o r anorexia nervosa , obsessive-compulsive disorder (OCD ), and phobias.Head injuries. Head injuries fit into two categories; external (usu ally scalp)injuries and internal head injuries. Internal injuries ma y involve the skull, the blood vessels within the skull , or the brai n .Fortunately, most childhood falls or blows to the head result i n injury to the scalp only, which is usually more frightening than threatening .An internal head injury could have more serious im plications because the skull serves as the protective helmet for the delicate brain.66．What will happen if something goes wrong with the brain?A．It’ll affect the function of the brain.B．It’ll cause brain disorders.C．Nothing serious.D．It won’t affect the rest of the body.67．Which of the following statements about the tumor is NOT t rue?A．A brain tumor grow slowly but may produce a few symptom s at the beginning.B．Benign tumors may be curable.C．A child diagnosed with a malignant tumor is likely to face a l ife threat.D．A tumor is caused by overgrown tissue.68．How many types of headaches are mentioned in the passa ge ?A．2. B．3. C．4. D．5.69．According to the passage, chronic drug or alcohol abuse m ay result in .A．brain tumors B．headaches C．mental illness D．head injuries70．It can be inferred from the last paragraph that .A．external injuries are as threatening as internal injuries .B．problem with blood vessels belong to internal injuries.C．external injuries are less serious than internal injuries.D．the skull protects the delicate brain.Part IV Writing (45 marks)Section A (10 marks )Directions : Read the following passage . Fill in the numbered bl anks by using the information from the passage.Write NO MORE THAN THREE WORDS for each answer.Through various methods of research, anthropologists try to fit t ogether the pieces of the human puzzle –to discover how humanity was first achieved , and why separate societies behave similarly in some ways but quite differently in other ways .Anthropology. which emerged as an independent s cience in the late eighteenth century, has two main divisions :ph ysical anthropology and cultural anthropology.Physical anthropologists whose mission is to solve the mystery of how humans came to be human are most concerned with hu man biology . They study the fossils and organic remains of pri mates that once lived . They also study the connections between humans and other primates that are still living. In the lab . ant hropologists investigate the composition of blood chemistry for clues to the relationship of humans to various primates.A well-known family of physical anthropologists , the Leakey ,conducte d research in East Africa indicating that human evolution center ed there rather than Asia . In 1971. Louis Leakey and his wife Mary Leakey discovered stone tools that pushed back the dates for early humans to 3.75 million years ago.Like physical anthropologists, cultural anthropologists study clu es abort human life in the distant past ;however , cultural anthro pologists also look at similar and different things among human communities today. Some cultural anthropologists work in the fi eld , living and working among people in societies that differ fro m their own , producing descriptions of the daily activities of me n ,women that tell the story of the society’s community life as a whole .Some of them working at research universities making e fforts to discover cross-cultural patterns .A cultural anthropologist who achieved worldwide fame was Ma rgaret Mead . In 1923 , Mead went to Samoa to pursue ter first f ieldwork assignment –a study that resulted in her book Coming of Age in Samon bein g sold well .Mead is regarded as a pioneer to develop new tech nologies for research.According to many researchers , both physical anthropologists and cultural anthropologists are believed to have done a lot to p rovide service for society.Section B (10 marks )Directions : Read the following passage. Answer the questions according to the information given in the passage.He seems an unlikely hero,especially one that would save a kid from the jaws of a wild cougar(美洲豹) .Shen Huigang is just now getting recognition for his bravery in fi ghting off a cougar on Vancouver Island . Canada , during a fa mily outing on Aug .30.Shen , also known as Ian , was then an exchange student at K wantlen Polytechnic University enjoying the afternoon on a bea ch near Ucluelet, a small town on the edge of the Pacific Ocean .With him was a friend , Myles Hagar , and Hagar’s two grandchi ldren.Silently and suddenly a cougar appeared out of nowhere.By the time the two adults spotted the cat , believed to be youn g but still weighing 30 to 35 kilograms , it already had the head of 18-month old Julien in its mouth.Instinctively, the young man gestured as if he were ready for a f ight , and tried to scare the beast off with the bag in his hands.On hearing the noise Shen made , the animal dropped the kid a nd Hagar grabbed his grandson from the cougar’s jaws . Shen and Hagar gradually chased the animal back intro the woods.“We also moved slowly to our vehicle , as we waved our fists an d bags , pretending we wanted to fight with it ,”Shen said .“Thevehicle wasn’t far away but it felt like it took us a century to trav el the short journey .”“Any hesitation , at any moment , even a second delay , would have resulted in certain death for Julien. The cougar was just a bout to break his neck and carry him away to be eaten in the for est.”Hagar said. Julien has since made a full recovery .Parks Canada spokeswoman Arlene Armstrong told the Nation al Post newspaper of Canada in an interview in August .“The tw o men acted properly by maintaining eye contact with the big ca t and aggressively scaring it off.”81．How did Ian get recognition on Vancouver Island ?(No mor e than 12 words ). 82．What happened to Julien by the time the two adults saw th e young cougar ?(No more than 10 words )83．Why did the cougar give up eating the kid ?(No more than 8 words )84．What if you are fighting with a wild cougar ?(No more than12 words )Section C (25 marks )Directions :Write an English composition according to the instru ctions given below in Chinese.某英语报向中学生征集关于开展研究性学习的文章，请你根据堤示，用英语写一篇介绍你校和你们小组研究性学习活动的短文。
广东省2012届高三下学期高考模拟仿真试题 (二)理科数学一、选择题(本大题共8小题，每小题5分，满分40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.设M ，P 是两个非空集合，定义M 与P 的差集为M －P ＝{x |x ∈M 且x ∉P }，则M －(M －P )等于( B )A ．PB ．M ∩PC ．M ∪PD ．M 解析：画韦恩图，易选B.2.(1－i 1＋i )2的值等于( C )A ．1B ．iC ．－1D ．－i 解析：(1－i 1＋i )2＝(－i)2＝－1.3.函数y ＝(13)1x 2＋1值域为( C )A ．(－∞，1)B ．(13，1)C ．[13，1)D ．[13，＋∞)解析：x 2＋1≥1,0<1x 2＋1≤1，y ＝(13)1x 2＋1∈[13，1)．4.设等比数列{a n }的前n 项和为S n ，若S 10∶S 5＝1∶2，则S 15∶S 5＝( A )A ．3∶4B ．2∶3C ．1∶2D ．1∶3解析：方法1：因为{a n }是等比数列，故S 5，S 10－S 5，S 15－S 10也构成等比数列， 记S 5＝2k (k ≠0)，则S 10＝k ，所以S 10－S 5＝－k ，进而得S 15－S 10＝12k ，于是S 15＝32k ，所以S 15∶S 5＝32∶2＝3∶4.方法2：由S 10∶S 5＝1∶2，得1－q 101－q 5＝12，可得q 5＝12， 所以S 15S 5＝1－q151－q 5＝1＋q 5＋q 101＝1－12＋141＝34.5.已知命题p ：x >2是x 2>4的充要条件；命题q ：若a c 2>b c 2，则a >b .下列说法正确的是( A )A ．“p 或q ”为真B ．“p 且q ”为真C ．p 真q 假D ．p ，q 均为假命题 解析：p 为假，q 为真，“p 或q ”为真．6.如图，直线P A 垂直于圆O 所在的平面，△ABC 内接于圆O ，且AB 为圆O 的直径，点M 为线段PB 的中点．现有以下命题：①BC ⊥PC ；②OM ∥平面APC ；③点B 到平面P AC 的距离等于线段BC 的长． 其中真命题的个数为( D ) A ．0 B ．1 C ．2 D ．3 解析：①②③都正确．7.从集合{－1，－2，－3，－4,0,1,2,3,4,5}中，选出5个数组成子集，使得这5个数中的任何两个数之和不等于1，则取出这样的子集的概率为( D )A.5126B.55126C.5563D.863解析：能够相加为1的两个数分别为0,1；－1,2；－2,3；－3,4；－4,5，所以两数之和不等于1的5个数可以在这5组数里各选取一个，所以概率为25C 510＝863，所以选D.8.椭圆满足这样的光学性质：从椭圆的一个焦点发射光线，经椭圆反射后，反射光线经过椭圆的另一个焦点．现在设有一个水平放置的椭圆形台球盘，满足方程：x 216＋y 29＝1，点A 、B 是它的两个焦点，当静止的小球放在点A 处，从点A 沿直线出发，经椭圆壁(非椭圆长轴端点)反弹后，再回到点A 时，小球经过的最短路程是( C )A ．20B ．18C ．16D ．以上均有可能解析：由椭圆定义可知小球经过路程为4a ，所以最短路程为16，故选C. 二、填空题(本大题共7小题，考生作答6小题，每小题5分，满分30分．) (一)必做题(9～13题)9.若函数f (x )＝1－2x 1＋2x ，则f －1(35)的值为 －2 . 解析：由1－2x 1＋2x ＝35，解得x ＝－2.10.设m 、n 是两个单位向量，且m 、n 的夹角为60°，则(m －2n )·m ＝ 0 . 解析：利用数量积定义运算性质即可求得．11.函数f (x )＝a sin(x ＋π4)＋3sin(x －π4)是偶函数，则a ＝ －3 .解析：利用f (π4)＝f (－π4)，可求得a ＝－3.12.设不等式组⎩⎪⎨⎪⎧x ≥a y ≥12x ＋3y －35≤0表示的平面区域是W ，若W 中的整点(即横、纵坐标均为整数的点)共有91个，则实数a 的取值范围是 (0,1] .解析：画出可行域，利用数形结合可得a 的取值范围是(0,1]． 13.关于正四棱锥P －ABCD ，给出下列命题： ①异面直线P A 与BD 所成的角为直角； ②侧面为锐角三角形；③侧面与底面所成的二面角大于侧棱与底面所成的角； ④相邻两侧面所成的二面角为钝角． 其中正确命题的序号是 ①②③④ .解析：画好图，利用线线、线面、面面所成角的概念及算法，可知四个命题都正确． (二)选做题(14～15题，考生只能从中选做一题．)14.(几何证明选讲选做题)如图，⊙O 的直径AB ＝6 cm ，P 是AB 延长线上的一点，过P 点作⊙O 的切线，切点为C ，连接AC ，若∠CP A ＝30°，PC ＝ 33 .解析：连接OC ，PC 是⊙O 的切线，所以∠OCP 为直角． 又因为∠CP A ＝30°，OC ＝AB2＝3，所以tan30°＝3PC，即PC ＝3 3. 15.(坐标系与参数方程选做题)极坐标方程分别为ρ＝cos θ与ρ＝sin θ的两个圆的圆心距为22. 解析：圆心的直角坐标分别为(12，0)和(0，12)．三、解答题(本大题共6小题，共80分．解答应写出文字说明、证明过程或演算步骤．)16.(本小题满分12分)已知A 、B 、C 三点的坐标分别为A (3,0)、B (0,3)、C (cos α，sin α)，α∈(π2，3π2)．(1)若|AC →|＝|BC →|，求角α的值；(2)若AC →·BC →＝－1，求2sin 2α＋sin2α1＋tan α的值．解：(1)因为AC →＝(cos α－3，sin α)，BC →＝(cos α，sin α－3)，所以|AC →|＝(cos α－3)2＋sin 2α＝10－6cos α，|BC →|＝10－6sin α.(3分) 由|AC →|＝|BC →|，得sin α＝cos α，又α∈(π2，3π2)，所以α＝5π4.(6分)(2)由AC →·BC →＝－1，得(cos α－3)cos α＋sin α(sin α－3)＝－1， 所以sin α＋cos α＝23，所以2sin αcos α＝－59.(9分)又2sin 2α＋sin2α1＋tan α＝2sin 2α＋2sin αcos α1＋sin αcos α＝2sin αcos α＝－59，所以2sin 2α＋sin2α1＋tan α＝－59.(12分)17.(本小题满分13分)某工厂在试验阶段大量生产一种零件．这种零件有A 、B 两项技术指标需要检测，设各项技术指标达标与否互不影响．若有且仅有一项技术指标达标的概率为512，至少一项技术指标达标的概率为1112.按质量检验规定：两项技术指标都达标的零件为合格品．(1)求一个零件经过检测为合格品的概率是多少？(2)任意依次抽出5个零件进行检测，求其中至多3个零件是合格品的概率是多少？ (3)任意依次抽取该种零件4个，设ξ表示其中合格品的个数，求Eξ与Dξ. 解：(1)设A 、B 两项技术指标达标的概率分别为P 1、P 2.由题意得⎩⎨⎧P 1·(1－P 2)＋(1－P 1)·P 2＝5121－(1－P 1)·(1－P 2)＝1112.(3分)解得⎩⎨⎧ P 1＝34P 2＝23或⎩⎨⎧P 1＝23P 2＝34，则P 1P 2＝12.(5分)即一个零件经过检测为合格品的概率为12.(6分)(2)任意抽出5个零件进行检查，其中至多3个零件是合格品的概率为 1－C 45(12)5－C 55(12)5＝1316.(10分) (3)依题意知E ～B (4，12)，Eξ＝4×12＝2，Dξ＝4×12×12＝1.(13分)18.(本小题满分13分)如图，已知正四棱柱ABCD —A 1B 1C 1D 1中，底面边长AB ＝2，侧棱BB 1的长为4，过点B 作B 1C 的垂线交侧棱CC 1于点E ，交B 1C 于点F .(1)求证：A 1C ⊥平面BDE ；(2)求A 1B 与平面BDE 所成角的正弦值；(3)设G 是线段CC 1上的动点(不包括端点C )，求证：△BDG 是锐角三角形．解：(1)证明：由正四棱柱性质知A 1B 1⊥平面BCC 1B 1，A 1A ⊥平面ABCD ，所以B 1C 、AC 分别是A 1C 在平面CC 1B 1B 、平面ABCD 上的射影， 因为B 1C ⊥BE ，AC ⊥BD ，所以A 1C ⊥BE ，A 1C ⊥BD ，(2分) 所以A 1C ⊥平面BDE .(4分)．(直接指出根据三垂线定理得“A 1C ⊥BE ，A 1C ⊥BD ”而推出结论的不扣分)(2)以DA 、DC 、DD 1所在直线分别为x 、y 、z 轴，建立坐标系， 则A 1(2,0,4)，C (0,2,0)，B (2,2,0)，所以A 1C →＝(－2,2，－4)，A 1B →＝(0,2，－4)，(6分) 所以cos 〈A 1C →，A 1B →〉＝A 1C →·A 1B →|A 1C →||A 1B →|＝306.(7分)设A 1C ∩平面BDE ＝K ，由(1)可知，∠A 1BK 为A 1B 与平面BDE 所成角，(8分) 所以sin ∠A 1BK ＝cos 〈A 1C →，A 1B →〉＝306.(9分)(3)证明：设点G 的坐标为(0,2，z )(0<z ≤4)，则|BG |＝|DG |＝z 2＋22， 又|DB |＝22，故△DBG 是等腰三角形，要证明它为锐角三角形， 只需证明其顶角∠DGB 为锐角则可．(11分)由余弦定理得cos ∠DGB ＝DG 2＋BG 2－DB 22DG ·BG ＝2(z 2＋4)2－(22)22(z 2＋4)2＝2z 22(z 2＋4)>0，所以∠DGB 为锐角，(12分)即不论点G 为线段CC 1上C 点除外的任意一点，△DGB 总是锐角三角形．(13分) 说明：若没有说明三角形为等腰三角形而只证明一个角是锐角，或只证明底角是锐角的“以偏概全”情况应扣2分)19.(本小题满分14分)设F 1、F 2分别是椭圆C ：x 2a 2＋y 2b 2＝1(a >b >0)的左右焦点．(1)设椭圆C 上的点(3，32)到F 1、F 2两点距离之和等于4，写出椭圆C 的方程和焦点坐标；(2)设K 是(1)中所得椭圆上的动点，求线段KF 1的中点B 的轨迹方程；(3)设点P 是椭圆C 上的任意一点，过原点的直线l 与椭圆相交于M ，N 两点，当直线PM ，PN 的斜率都存在，并记为k PM ，k PN ，试探究k PM ·k PN 的值是否与点P 及直线l 有关，并证明你的结论．解：(1)由于点(3，32)在椭圆上，即(3)2a 2＋(32)2b2＝1，(1分)依题意，2a ＝4，(2分)所以椭圆C 的方程为x 24＋y 23＝1.(3分)焦点坐标分别为(－1,0)，(1,0)．(4分)(2)设KF 1的中点为B (x ，y )，则点K (2x ＋1,2y )．(5分) 把K 的坐标代入椭圆x 24＋y 23＝1中，得(2x ＋1)24＋(2y )23＝1.(7分)线段KF 1的中点B 的轨迹方程为(x ＋12)2＋y 234＝1.(8分)(3)过原点的直线l 与椭圆相交的两点M ，N 关于坐标原点对称． 设M (x 0，y 0)，N (－x 0，－y 0)，P (x ，y )．(9分)M 、N 、P 在椭圆上，应满足椭圆方程，得x 20a 2＋y 20b 2＝1，x 2a 2＋y 2b2＝1.(10分)k PM ＝y －y 0x －x 0，k PN ＝y ＋y 0x ＋x 0.(11分) k PM ·k PN ＝y －y 0x －x 0·y ＋y 0x ＋x 0＝y 2－y 20x 2－x 20＝－b 2a 2.(13分)故k PM ·k PN 的值与点P 的位置无关，同时与直线l 无关．(14分)20.(本小题满分14分)已知函数f (x )＝x 2＋b sin x －2(b ∈R )，F (x )＝f (x )＋2，且对于任意实数x ，恒有F (x )－F (－x )＝0.(1)求函数f (x )的解析式；(2)已知函数g (x )＝f (x )＋2(x ＋1)＋a ln x 在区间(0,1)上单调递减，求实数a 的取值范围；(3)函数h (x )＝ln(1＋x 2)－12f (x )－k 有几个零点？解：(1)因为F (x )＝f (x )＋2＝x 2＋b sin x －2＋2＝x 2＋b sin x ， 依题意，对任意实数x ，恒有F (x )－F (－x )＝0，即x 2＋b sin x －(－x )2－b sin(－x )＝0，即2b sin x ＝0，所以b ＝0. 所以f (x )＝x 2－2，(4分)(2)因为g (x )＝x 2－2＋2(x ＋1)＋a ln x ，所以g (x )＝x 2＋2x ＋a ln x ， g ′(x )＝2x ＋2＋ax.(5分)因为函数g (x )在(0,1)上单调递减，所以在区间(0,1)上，g ′(x )＝2x ＋2＋a x ＝2x 2＋2x ＋ax≤0恒成立，(6分)所以a ≤－(2x 2＋2x )在(0,1)上恒成立，而－(2x 2＋2x )在(0,1)上单调递减，所以a ≤－4为所求．(8分)(3)因为h (x )＝ln(1＋x 2)－12f (x )－k ＝ln(1＋x 2)－12x 2＋1－k ，所以h ′(x )＝2x 1＋x 2－x ，令h ′(x )＝2x1＋x 2－x ＝0，解得x ＝0，－1,1. 所以当x <－1时，h ′(x )>0；当－1<x <0时，h ′(x )<0；当0<x <1时，h ′(x )>0；当x >1时，h ′(x )<0，所以h (x )极大值＝h (±1)＝ln2＋12－k .(9分)所以h (x )极小值＝h (0)＝1－k .(10分)所以①当k >ln2＋12时，函数没有零点；(11分)②当1<k <ln2＋12时，函数有四个零点；(12分)③当k <1或k ＝ln2＋12时，函数有两个零点；(13分)④当k ＝1时，函数有三个零点．(14分) 21.(本题满分14分)已知函数y ＝1－1x ＋2的图象按向量m ＝(2,1)平移后便得到函数f (x )的图象，数列{a n }满足a n ＝f (a n －1)(n ≥2，n ∈N *)．(1)若a 1＝35，数列{b n }满足b n ＝1a n －1，求证：数列{b n }是等差数列；(2)若a 1＝35，数列{a n }中是否存在最大项与最小项，若存在，求出最大项与最小项，若不存在，说明理由；(3)若1<a 1<2，试证明：1<a n ＋1<a n <2.解：f (x )＝1－1x －2＋2＋1＝2－1x ，则a n ＝2－1a n －1(n ≥2，n ∈N *)．(1分)(1)b n ＝1a n －1＝12－1a n －1－1＝a n －1a n －1－1，b n －1＝1a n －1－1， 所以b n －b n －1＝a n －1a n －1－1－1a n －1－1＝1(n ≥2，n ∈N *)．所以数列{b n }是等差数列．(4分)(2)由(1)知，数列{b n }是等差数列，首项b 1＝1a 1－1＝－52，公差为1，则其通项公式b n ＝－52＋(n －1)·1＝n －72.(5分)由b n ＝1a n －1，得a n ＝1＋1b n ＝1＋1n －72，故a n ＝1＋22n －7.(6分)构造函数y ＝1＋22x －7，则y ′＝－4(2x －7)2<0，函数y ＝1＋22x －7在区间(－∞，72)，(72，＋∞)上为减函数．(7分)所以当x <72时，y ＝1＋22x －7<1，且在(－∞，72)上递减，故当n ＝3时，b n 取最小值，b 3＝－1.(8分) 当x >72时，y ＝1＋22x －7>1，且在(72，＋∞)上递减，故当n ＝4时，b n 取最大值b 4＝3.故存在最大项与最小项．(9分) (3)先用数学归纳法证明1<a n <2，再证明a n ＋1<a n . ①当n ＝1时，1<a 1<2成立，(10分) ②假设n ＝k 时命题成立，即1<a k <2，则当n ＝k ＋1时，12<1a k <1，a k ＋1＝2－1a k ∈(1，32)，则1<a k ＋1<2，故当n ＝k ＋1时也成立．(11分)综合①②有，命题对任意n ∈N *时成立，即1<a n <2.(12分) 下证a n ＋1<a n .因为a n ＋1－a n ＝2－1a n －a n ＝2－(a n ＋1a n )<2－2a n ·1a n＝0，所以a n ＋1<a n .(13分) 综上所述：1<a n ＋1<a n <2.(14分)。
道真中学2012-2013学年（下）期末复习试题（一）高一化学可能用到的相对原子质量：H－1 C－12 N－14 O－16 Ag－108第Ⅰ卷(选择题)一、选择题：(每小题只有一个正确选项)1．某些建筑材料含有放射性元素氡()，会对人体产生一定危害。
研究表明氡的α射线会致癌，WHO认定的19种致癌因素中，氡为其中之一，仅次于吸烟。
该原子中中子数和质子数之差是（）A．136 B．50 C．86 D．2222．168O、188O、O2-、O2、O3是：( )Ａ．氧的五种同位素Ｂ. 五种氧元素C. 氧的五种同素异形体Ｄ. 氧元素的五种不同微粒3．下列有关化学用语表达不正确的是( )A．氮气的电子式：∶N∶∶∶N∶ B．CO2分子的结构式：O＝C＝OC．Na的原子结构示意图： D．钙的电子式：Ca2+4．下列说法中，正确的是( )A．在周期表中，族序数等于该族元素的最外层电子数B．非金属性最强的元素，其最高价氧化物对应水化物的酸性最强C．卤素单质随原子序数的增大，其熔沸点逐渐降低D．碱金属随原子序数的增大，其熔沸点逐渐降低5．下列说法不正确的是( )A．含有共价键的化合物一定是共价化合物B．在共价化合物中一定含有共价键C．含有离子键的化合物一定是离子化合物D．双原子单质分子中的共价健一定是非极性键6．据报道，氢燃料电池公交汽车已经驶上北京街头，下列说法中，正确的是( ) A．氢气的一极是正极，氧气的的一极是负极B．发展氢燃料电池汽车不需要安全高效的储氢技术C．氢燃料电池汽车的使用可以有效减少城市空气污染D．氢燃料电池把氢气和氧气燃烧放出的热能转化为电能7．日常所用锌－锰干电池的电极分别为锌筒和石墨棒，以糊状NH4Cl作电解质，电极反应为：Zn－2e－＝Zn2＋，2MnO2＋2NH＋2e-＝Mn2O3＋2NH3＋H2O。
4下列有关锌－锰干电池的叙述中，正确的是( )A．干电池中锌筒为正极，石墨棒为负极B．干电池长时间连续工作后，糊状物可能流出，腐蚀用电器C．干电池工作时，电流方向是由锌筒经外电路流向石墨棒D．干电池可实现化学能向电能和电能向化学能的相互转化8．对于反应2HI(g)H2(g)＋I2(g紫色)，下列叙述能够说明已达平衡状态的是( ) A．混合气体的颜色不再变化 B．温度和体积一定时，容器内压强不再变化C．1molH－H键生成的同时有2molH－I键断裂D．各物质的物质的量浓度之比为2∶1∶1 9.高温下，炽热的铁与水蒸气在一个体积可变的密闭容器中进行反应：3Fe（s）＋4H2O（g）＝Fe3O4(s)＋4H2（g），下列条件的改变对其反应速率几乎无影响( ) A．把铁块变成铁粉 B．将容器的体积缩小一半C．压强不变，充入氮气使容器体积增大D．体积不变，充入氮气使容器压强增大10．等物质的量的下列有机物完全燃烧，生成CO2的量最多的是( )A．CH4B．C2H6C．C3H6DC6H6 11．根X、Y、Z均为短周期元素，它们在周期表中相对位置如图所示。
