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1、 (时间：60分钟，满分：80分)一、选择题(共6小题，每小题5分，满分30分)1设a，b，c，则a，b，c的大小顺序是()AabcBbcaCcab Dacb解析：a，b，c.0， .abc.答案：A2设a，b，c(，0)，则a，b，c()A都不大于2 B都不小于2C至少有一个不大于2 D至少有一个不小于2解析：因为abc6，所以三者不能都大于2.答案：C3要证：a2b21a2b20，只要证明()A2ab1a2b20 Ba2b210C.1a2b20 D(a21)(b21)0解析：因为a2b21a2b20(a21)(b21)0. 答案：D4若P，Q(a0)，则P、Q的大小关系是()APQBPQC
2、PQ D由a的取值确定解析：假设PQ，要证PQ，只要证P2Q2，只要证：2a722a72，只要证：a27aa27a12，只要证：012，012成立，Pq D不确定解析：qp，故选B.答案：B6用反证法证明命题：若整系数一元二次方程ax2bxc0(a0)有有理数根，那么a，b，c中至少有一个是偶数时，下列假设中正确的是()A假设a、b、c都是偶数B假设a、b、c都不是偶数C假设a、b、c至多有一个偶数D假设a、b、c至多有两个偶数解析：“至少有一个”的反面是“都不是”答案：B二、填空题(共3小题，每小5分，满分15分)7如果abab，则a、b应满足的条件是_解析：abab()2()0a0，b0且
3、ab.答案：a0，b0且ab8设x0，y0，axy，bxcos2ysin2，则a与b的大小关系为_解析：x0，y0，xxy，yxy，xcos2(xy)cos2，ysin2(xy)sin2，bxcos2ysin2b9设x，y，z是空间的不同直线或不同平面，且直线不在平面内，下列条件中能保证“若xz，且yz，则xy”为真命题的是_(填所有正确条件的代号)x为直线，y，z为平面；x，y，z为平面；x，y为直线，z为平面；x，y为平面，z为直线；x，y，z为直线解析：中x平面z，平面y平面z；x平面y或x平面y.又x平面y，故xy成立中若x，y，z均为平面，则x可能与y相交，故不成立xz，yz，x，y
4、为不同直线，故xy成立zx，zy，z为直线，x，y为平面可得xy，成立x，y，z均为直线，则x，y可平行，可相交，可异面，故不成立答案：三、解答题(共3小题，满分35分)10证明： (abc)证明：20，2.同理，.(abc)11已知，k(kZ)，且sin cos 2sin sin cos sin2求证：.证明：证法一(综合法)sin cos 2sin ，sin cos sin2，12sin cos 4sin2，12sin24sin2，12sin 2(12sin2)，cos2sin2(cos2sin2)，即.证法二(分析法)因为(sin cos )22sin cos 1，所以将代入上式，可得4
5、sin22sin21另一方面，要证，即证，即证cos2sin2(cos2sin2)，即证12sin2(12sin2)，即证4sin22sin21.由于上式与相同，于是问题得证12已知f(x)x2pxq，求证：|f(1)|、|f(2)|、|f(3)|中至少有一个不小于.证明：假设|f(1)|、|f(2)|、|f(3)|都小于，即|f(1)|1pq|，|f(2)|42pq|，|f(3)|93pq|，f(2)，1f(1)f(3)1，3f(1)f(3)21，即f(2)，|f(2)|，这与|f(2)|42pq|矛盾，所以假设不成立，原命题|f(1)|、|f(2)|、|f(3)|中至少有一个不小于正确)来
6、源：高考资源网版权所有：高考资源网(www.k s 5 ) 以下是大学体验英语综合教程2(第三版)课后翻译答案Unit11. 任何年满18岁的人都有资格投票。(be eligible to, vote)Answer:Anyone over the age of 18 is eligible to vote.2. 每学期开学前，这些奖学金的申请表格就会由学校发给每一个学生。(apply for, scholarship)Answer:A form to apply for these scholarships is sent by the university to every student
7、before the start of every semester.3. 遵照医生的建议，我决定戒烟。(on the advice of)Answer:On the advice of my doctor, I decided to give up smoking.4. 公园位于县城的正中央。(be located in)Answer:The park is located right in the center of town.5. 这所大学提供了我们所需的所有材料和设备。(facilities)Answer:The university provides all the material
8、s and facilities we desire.1. 他们花了多年的时间寻找内心的平静，但是收效甚微。(search for)Answer:They spent many years searching for peace of mind, but with little success.2. 这种新药的成功研制已经使许多疾病的治疗发生了根本性的变革。(revolutionize)Answer:The successful development of the new drug has revolutionized the treatment of many diseases.3. 由于
9、这个国家的经济不景气，这家公司濒于破产。(on the edge of)Answer:The company is on the edge of bankruptcy due to the economic depression in the country.4. 大学毕业后他成为了一名护士。他认为护士这一职业可能很有发展前途。(rewarding)Answer:He became a nurse after college. He thought nursing could be a very rewarding career.5. 他像往常一样在文件上签了名。(just as)Answer
10、:He signed his name on the paper just as he has always done it.Unit21. 警察们正忙着填写关于这场事故的各种表格。(fill out)Answer:The policemen are busy fi lling out forms about the accident.2. 我想在还车之前把油箱加满。(fill up, fuel tank)Answer:I want to fi ll up the fuel tank before returning the car.3. 如果你要投诉，最好遵循正确的程序。(follow th
11、e procedure)Answer:If you want to make a complaint, youd better follow the correct procedure.4. 要不是约翰帮忙，我们绝不会这么快就完成实验。(without)Answer:We couldnt have fi nished the experiment so soon without Johns help.5. 暴风雨之后，岸边的人们焦急地搜索湖面以期发现小船的踪迹。(scan for)Answer:After the storm, the people on the shore anxiously
12、 scanned the lake for any sign of the boat.1. 这个国家不大，但是在国际事务中它却发挥着重要作用。(play a role)Answer:This country is not big, but it plays an important role in international affairs.2. 正是在我叔叔的帮助下，我得以克服困难，按时完成了任务。(it is . that)Answer:It was with the help of my uncle that I overcame the difficulty and completed
13、 the assignment in time.3. 毕业时他决定留在北京，而他最好的朋友却选择了去西藏。(while)Answer:While he decided to stay in Beijing upon graduation, his best friend chose to go to Tibet.4. 在这次校园英语演讲比赛中，我们班的玛丽获得了第三名。(come in)Answer:In this Campus English Speaking Contest, Mary from our class came in third.5. 你应该知道学习弹钢琴需要有时间，有金钱，
14、还要有毅力。(as well as)Answer:You should know that it takes time, money as well as perseverance to learn to play the piano.Unit31. 我发现量入为出地过日子越来越难了。(increasingly)Answer:I find it increasingly difficult to live within my income.2. 现代政治家们都试图以电视讲话来影响普通百姓。(reach out)Answer:Modern politicians try to reach out
15、 to ordinary people in their TV speeches.3. 应该帮助学生对人生采取积极的态度。(adopt)Answer:Pupils should be helped to adopt a positive attitude to life.4. 希望全班同学参加这些讨论。(participate in)Answer:Everyone in the class is expected to participate in these discussions.5. 如果你犯了罪就必须受到惩罚。(crime)Answer:If you commit a crime yo
16、u must expect to be punished.1.儿子的死让老妇人变得麻木痴呆了。(numb)Answer:The old woman was numbed by her sons death.2.身处所有这些烦恼之中，他依然能保持乐观。(in the midst)Answer:In the midst of all troubles, he managed to remain cheerful.3. 虽有困难，他们还是设法坚持试验下去。(carry on)Answer:They managed to carry on their experiments in spite of t
17、he difficulties.4.我们必须淘汰不合格的申请人。(weed out)Answer:We have to weed out unqualified applicants.5. 医生要他减少抽烟。(cut down on)Answer:The doctor told him to cut down on smoking.Unit41.她在公共汽车站一直等到末班车进站。(come in)Answer:She waited at the bus stop until the last bus came in.2.如果我们能帮得上忙，尽管和我们联系。(contact)Answer:If
18、there is any way we can be of assistance, please do not hesitate to contact us.3 .他需要多少船务人员才能使他的游艇航行？(crew, yacht)Answer:How many crew does he need to sail his yacht?4 .虽然她的新书没有上一本好，但是我还是喜欢它。(not quite as)Answer:I enjoyed her new book though its not quite as good as her last one.5 .我从未遇到过如此善良的人。(nev
19、er before)Answer:Never before have I met such a kind person.1.公共汽车放慢速度并停下，让那位乘客上车。(slow down)Answer:The bus slowed down and stopped to allow the passenger to get on board.2.许多车子都驶过去了，可是没有一辆愿意让我们搭便车。(roll by)Answer:Many vehicles rolled by, but no one offered us a ride.3 .请勿践踏草地。(get off)Answer:Please
20、 get off the grass.4.他按妻子的吩咐，一下班就去了市场。(make ones way)Answer:He made his way to the marketplace right after work, as his wife had asked him to do.5 .值得庆幸的是，史蒂夫 (Steve) 从自行车上摔下来时没有摔断骨头。(luckily)Answer:Luckily, Steve didnt break any bones when he fell off his bike.Unit51. 我们得把感情放在一边，从专业的角度来对待这件事。(from
21、a professional standpoint)Answer:We have to put aside our emotions and take it from a professional standpoint.2. 这部戏非常精彩，我很快就沉浸于激动人心的剧情之中。(lose oneself in)Answer:The play was so wonderful that I soon lost myself in the excitement of it.3 .她没有什么爱好除非你把看电视也算是一种爱好。(unless)Answer:She hasnt got any hobbie
22、s unless you call watching TV a hobby.4. 他说他是直接从市长本人那里得到这个信息的。(first-hand)Answer:He said that he had got the information first-hand from the Mayor himself.5 .既然你不能回答这个问题，我们最好问问别人。(since)Answer:Since you cant answer the question, perhaps wed better ask someone else.1. 由于公共汽车司机突然刹车，旅客们都不由自主地向前摔倒。(brak
23、e, pitch forward)Answer:All the passengers pitched forward because the bus driver braked sharply.2. 这个协议将冲破对自由贸易设置的障碍。(break through, obstacle)Answer:This agreement will break through the obstacles to free trade.3 .我刚放下叫出租车的电话，车就来了。(soon after)Answer:The taxi arrived soon after I rang for it.4. 在过去，
24、不管我什么时候到家，我父母总会等我。(no matter)Answer:My parents always waited up for me no matter what time I got home.5 .由于没有一方愿意让步，两个公司之间的对话完全破裂了。(break down)Answer:Talks between the two companies completely broke down, because neither of them wanted to give in.Unit61. 那件工作很难做，不过我想试试看。(have a shot)Answer:Its a dif
25、ficult job, but Id like to have a shot.2. 这是一本关于商务实践而非理论的书。(as opposed to)Answer:This is a book about business practice as opposed to theory.3. 社会活动从未耽误她的学习。(in the way)Answer:Social activities never get in the way of her studies.4. 直到1911年人们才发现第一种维生素。(It is not until . that)Answer:It was not until
26、1911 that the first of the vitamins was identified.5. 尽管年事已高，爷爷每天还帮忙做家务。(despite)Answer:Despite advanced years, Grandpa helps do housework every day.1. 我们的婚姻很幸福，但我们也曾经历过许多坎坷。(ups and downs)Answer:Our marriage is happy but weve had many ups and downs.2. 许多外语教师常常在课堂上自顾自地讲得太多。(be inclined to)Answer:Man
27、y teachers of foreign languages are inclined to talk too much themselves in class.3. 那位著名演员每天早晨锻炼一小时以保持健康。(work out)Answer:The famous actor keeps fit by working out for an hour every morning.4. 与他促膝长谈之后，她的怀疑消失了。(melt away)Answer:After a long heart-to-heart talk with him, her suspicion melted away.5.
28、 目前我们没有职位空缺，但我们肯定会记住您的申请。(keep in mind)Answer:We have no vacancies now, but well certainly keep your application in mind.Unit71. 他并不后悔说过的话，只是觉得他完全可以不用这种方式表达。(could have done)Answer:He did not regret what he had said but felt that he could have expressed it differently.2. 我们最好等到12月14日。那时大卫已考完试，就能和我们一
29、起去度假了。(will have done)Answer:Wed better wait till 14 December. David will have had his exam by then, so hell be able to go on holiday with us.3. 他正在做一个新项目，年底前必须完成。(work on)Answer:Hes working on a new project which has to be finished by the end of the year.4. 他们让我们使用他们的实验室，作为回报，我们则让他们分享研究成果。(in retur
30、n)Answer:They are letting us use their lab, and in return, we are sharing with them the results of our research.5. 诸如打电话、听电话一类的事情占用了这位秘书的大部分时间。(take up)Answer:Such things as making and answering telephone calls take up most of the secretarys time.1. 他们把房子卖了后就到加拿大和女儿住在一起。(go off) Answer:They sold the
31、ir house and went off to live in Canada with their daughter.2. 你下星期这个时候会在干什么？还是像平常一样干活。(will be doing)Answer:What will you be doing this time next week?Ill be working as usual.3. 他既聪明又勤奋，不久就接管了杂志的编辑工作。(editing; before long)Answer:He was intelligent and hard-working and before long he took over the editing of the magazine.4. 你话还没说完别人就挂断电话，难道你不恼火吗？(hang up)Answer:Dont you hate it when someone hangs up on you before you finish speaking?5. 让他们感到惊恐的是，他们的房顶着火了。(to ones horror)Answer:To their horror, the roof of their house caught fire.
