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100道高中基础词汇题讲解

1. We won't know whether it will be successful. We won't know whether there will be good _____.

A. ends

B. results

C. effects

D. causes

[答案]B. results.

[注释]result意为“由某种活动或某种原因所产生的结果”，如：obtain(=get, attain, gain win, secure)good results（取得好结果），publish the results（公布成绩）。

2. Alice was very sorry to hear that her grandmother had _____ two days before.

A. broken off

B. passed off

C. given away

D. passed away

[答案]D. passed away.

[注释]pass away(=die)死亡，是“死亡”的委婉语。

break off中断；give away给掉；泄露；pass off中止，中断。

3. People cannot but feel _____, for they simply cannot understand how he could have made such a stupid mistake.

A. puzzled

B. delighted

C. moved

D. inspired

[答案]A. puzzled.

[注释]be (feel, get) puzzled感到迷惑、为难。

本题译文：人们不得不感到迷惑，因为他们简直不能理解，他怎么能犯这样愚蠢的错误。

4. Radar enables the pilot of an airliner to take off, fly and land in _____.

A. danger

B. comfort

C. safe

D. safety

[答案]D. safety.

[注释]in safety安全地。从逻辑上看，其他选择均不切题。

5. Our Party has always devoted great attention to raising the living _____ of the working people.

A. cost

B. situation

C. level

D. standard

[答案]D. standard.

[注释]living standard生活水准。

6. It was _____ by the railway board that the cost of rail fares would be increased by ten percent.

A. noticed

B. stated

C. suggested

D. noted

[答案]B. stated.

[注释]state此处意为“（=make sth. know, announce）宣布，通告，声明（口头的或书面的）”，如：It is stated that all the accident were killed.(据宣布，事故中全部人员无一幸免。)suggest

建议，是表示欲望意义的动词，从句中要用虚拟语气（should +动词原形）。Note(=notice)“注意到”，如：It was noted that the temperature rose during this time.

7. The party, which had been greatly _____, was spoiled by the rude behavior of an uninvited guest.

A. looked forward to

B. looked up to

C. called forth

D. called for

[答案]A. looked forward to.

[注释]look forward to 期待，盼望。call forth引起，唤起。call for需要。look up to尊敬。

8. It was clear that the small grocer was _____ people he owed money to.

A. at the expense of

B. at the risk of

C. in the way of

D. at the mercy of

[答案]D. at the mercy of.

[注释]at the mercy of在......支配下：The ship was at the mercy of the waves.(这艘船任凭风浪摆布。)

at the expense of以......为代价，靠牺牲......；in the way of碍......事；at the risk of冒......的危险：1)He devoted his time to football at the expense of his studies.(他牺牲学习把时间都花在足球上。) 2)Her social lift got in the way of her studies.(她的社交生活妨碍了她的学习。) 3)We do this at the risk of our lives and liberties.(我们冒丢掉生命和丧失自由的危险做这件事。)

本题译文：显然，这家小杂铺任凭其债主的摆布。

9. I _____ her not to walk on the thin ice but she would not listen to me.

A. warned

B. persuaded

C. suggested

D. noticed

[答案]A. warned.

[注释]warn sb. (not) to do sth.警告某人（不）做某事。

Suggest不能接sb. to do sth。persuade sb.(not) to do sth.说服、某人（不）做某事；本题中不能选D. persuaded, 因该动词强调行为的结果。从逻辑上讲，既然“说服了”，那么与she wouldn't listen to me就前后矛盾了。如果把句子该为：I tried to persuade her not to walk on the thin ice but she wouldn't listen to me.(我极力劝她不要在薄冰上走，但她不愿听我的话。)，那么就符合逻辑了。

[注意]warn sb. of sth.警告某人有......。

10. When products made in factories _____, they are thrown away as garbage.

A. come to an end

B. are put to use

C. are used up

D. wear out

[答案]D. wear out.

[注释]wear out本题中意指（become useless form continued use of wear）用坏，穿破，如：The machine will soon wear out.(这机器即将用坏。)come to and end(结束)，put ... to

use(投入使用), use up(用完)，come into use(开始投入使用)。

11. The microphone enabled them to keep in touch, in other words, it made it _____ for them to contact each other.

A. likely

B. capable

C. possible

D. probable

[答案]C. possible

[注释]able有才能的，有能力的，指人的才智，而且是受过实际锻炼的才干。Capable“有才能的，能胜任的”(有褒、贬二义)，如：He is capable of anything.(他什么事都干得出来。)此句含有明显得贬义。此外，作表语时，able接不定式，capable接of. capable还有一意思是“有可能的”，例如：The car is capable of being repaired .（这辆汽车是有可能修好的。）用于此义时，be capable of 后常接被动语态动名词或有动作意义的名词：The situation is capable of improvement .possible 强调客观可能性，“可能的”程度比probable"大概的，很可能的低一些。

注意likely与possible在结构搭配上的区别。Likely可用于下列句型中：1)It is likely that...例如：It is highly likely that he will succeed.（很可能他会成功。）2)think(feel, consider)it likely ...例如：I think it likely that we will ultimately get a certain amount of money.3)be likely to do sth.例如：He is likely to see you again .但下面的句型是错误的，It is likely for sb to do sth.所以think it likely for sb. to do sth.也是错误的，故本题不能选likely.

12. They did not find _____ to prepare for the worst conditions they might meet.

A. worth their while

B. it worthwhile

C. it worth

D. it worthy

[答案]B. it worthwhile

[注释]worthwhile值花时间（或精力）干的：1)The visit to Paris was worthwhile .2)He thinks teaching foreign languages is worthwhile.3)She has a very worthwhile job.4)I think it worthwhile to work on my stamp collection.

worthy (of)配得上，值得：1)He is worthy of being praised.(=He is worthy to be praised.)2)He is a worthy winner.3)She is not worthy to talk to man like you.（她配不上与你这样一位男士谈话）。

13. In spite of the thunderstorm, the children slept _____ all night.

A. densely

B. soundly

C. loudly

D. noisily

[答案]B. soundly

[注释]sleep soundly熟睡。也可以说sleep heavily.

14. John _____ knowledge of radio just by staying around the radio station.

A. caught on

B. worked up

C. took up

D. picked up

[答案]D. picked up

[注释]pick up学到，习得。

15. Professor Jordon is well known for his _____ into the habits of the common housefly.

A. examination

B. introduction

C. research

D. expression

[答案]C. research

[注释]research into对...研究：1)(作动词用)He is researching into the reading problems of young school children.2)（作名词用）to carry out a research(=some research)into the causes of brain damage.(对大脑损伤原因进行研究)。

研究可译为make researches into, make a study of 或直接用动词study vt或research into (a problem etc.).

16. He put in a special _____ for an extra day's holiday so that he could attend his daughter's wedding.

A. request

B. demand

C. inquiry

D. proposal

[答案]A. request

[注释]request请求，put in a request for (提出请求)。enquiry询问，demand 需求，需要，proposal建议，均不和题意。

17. Scientists have to work hard to keep _____ with modern discoveries and developments.

A. company

B. track

C. touch

D. pace

[答案]D. pace.

[注释]keep pace with跟上：1)This horse is too weak to keep pace with the others. 2)I can't help pace with your plan.

Keep in touch with与......保持联系；了解（情况）；1)People can keep in touch with each other even when they do leave. 2)I find it very difficult to keep in touch with all the recent developments in my subject.(我觉得很难了解我的科目当前的一切新发展。)

Keep company(with)与......相好：Never keep company with dishonest persons.(千万不要和不诚实的人来往。)

Keep track of通晓事态，了解动向：I find it difficult to keep track of my old friends.(我很难了解我的老朋友的情况。)keep track of的反义结构是lose track of（失去联系）。

以上成语均为考试大纲规定的内容，考生务必熟记。

18. He didn't _____ what I read because his mind was on something else.

A. hold on

B. catch on

C. take in

D. get over

[答案]C. take in

[注释]take in(=understand)理解。hold on(打电话时)不要挂断；catch on明白（作不及物动词用），catch on to懂得，明白（作及物动词用）；get over克服。

19. The government has lost a great deal of _____ because of the large increase in food prices.

A. strength

B. support

C. agreement

D. vote

[答案]B. support.

[注释]lose support失去支持。vote作为“选票”解时，是可数名称，所以不能与a great deal of搭配。

20. He thought this was the first pair of shoes that had fitted him _____.

A. perfectly

B. justly

C. fairly

D. rightly

[答案]A. perfectly.

[注释]perfectly(=quite well, completely)十分，完全地。

justly公正地，正当地，应得地；rightly正确地，恰当地，正直地；fairly公正地，正当地；相当，还算；清楚地。

21. So far as he could, John had always tried to _____ the example he saw in Lincoln.

A. live up to

B. set forth

C. call for

D. cut out

[答案]A. live up to.

[注释]live up to不辜负，作到；set forth阐明，提出，列举；cut out删去；call for需要，要求；本题译文：只要约翰能够，他总是努力做到他在林肯身上所看到的榜样。

22. Children who are over-protected by their parents may become _____.

A. hurt

B. spoiled

C. damaged

D. harmed

[答案]B. spoiled.

[注释]spoil(=make a child selfish from having too much attention or praise)宠坏，惯坏；Spare the rod, spoil the child.(省下了棍子，惯坏了孩子。)这是英国谚语，意为“棒头上出孝子”。

23. Paper making began in China and from there it _____ to North Africa and Europe.

A. sprang

B. spilled

C. carried

D. spread

[答案]D. spread.

[注释]spread vt./vi. 此处意指“传播”，如：1)The news spread quickly. 2)Files spread disease.(苍蝇传播疾病。)carry是及物动词，意为把某人从一处带到他处，故也有“传送”的含义，如：He carried the news to everyone in the village. 当carry vt. 在本句中与句子的语法结构不符。Carry作vi.用时，指“（发射物、声音等）能射到，能传到”，如：His voice carries far. (他的声音能传得很远。)

24. When the entire class worked together they finished the project _____.

A. in no way

B. in no time

C. on no account

D. in no case

[答案]B. in no time.

[注释]in no time (=in a very little time, soon, quickly)立即，马上：The bus filled with students

in no time. (这辆公共汽车很快就被学生挤满了。)

25. The _____ of his clothes indicated too clearly that he had been playing football.

A. state

B. condition

C. occasion

D. situation

[答案]A. state.

[注释]state n. 状况，状态。例如：She is in a poor state of health. Situation处境，形势，局面，情况，工作：He was in a hopeless situation. condition 情况（多用复数）：Economic conditions were bad. occasion 场合，时机。

26. Stressful environments lead to unhealthy behaviors such as poor eating habits, which _____ increase the risk of heart disease.

A. in turn

B. in return

C. by chance

D. by turns

[答案]A. in turn。

[注释]in turn (插入语)转而，依次，而又：We need revision of estimated sales and this, in turn , will mean revision in production schedule. (我们必须修改预计销量，而这反过来又意为这修订生产计划。)in return 作为报答: I wish I could do something for you in return. (我要是能为你做点事作为报案就好了。)I gave him a present but he gave me nothing in return.（我送给他一份礼物，可他却什么也不给我作为答谢。）by chance (=by accident)偶然地；无意中：I meet him by chance on Fifth Avenue.(我偶然在第5大街上遇到他。)by turns 轮流地，依次：There were twelve of us in the boat and we rowed by turns.(船上有12人，我们轮流划船。)

本题译文：紧张的环境会导致诸如不良的饮食习惯等不健康行为，而后者又会增加患心脏病的危险。

27. The patients believe that the doctor knows exactly how to put them _____.

A. correct

B. perfect

C. right

D. well

[答案]C. right。

[注释]put sth. /sb. right 纠正；治好，使恢复健康：Since man has done so much damage, it is up to man to put the matters right. (既然人类已造成了如此巨大的损害，人类又哲人纠正这种状况。)又如：This medicine will soon put you right. (这药很快会使你恢复健康。)其他3个选择均不能与put 构成习语，故不能入选。

本题译文：病人相信医生清楚地知道怎样治好他的病。

28. They decided to leave the waiter a big _____ because the food and service had been excellent.

A. note

B. reward

C. tip

D. gift

[答案]C. tip。

[注释]tip 本题中意为“小费”。

29. There was a good _____ of the countryside from the front of the bus.

A. sight

B. view

C. scene

D. scenery

[答案]B. view。

[注释]view在本句中意指“看，眺望”，如：It is a large room with a view of the doctor's well-kept garden. (这是一间大房间，从房间里能看到医生精心管理的花园。)本题译文：坐在汽车的前排座位可以清楚地看到乡间的景色。

30. In aerospace devices the weight of the necessary power producing equipment is _____.

A. vital

B. possible

C. capable

D. reliable

[答案]A. vital。

[注释]vital 极其重要的。本题译文：在航空航天装置中必要的动力设备的重量问题是至关紧要的。

31. This album is _____ as it was the only one ever signed by the President.

A. unusual

B. unique

C. rare

D. special

[答案]B. unique。

[注释]unique(某一类中)独一无二的。如选unusual(不寻常的，独特的)，虽然也说得过去，但毫无疑问，unique是最佳选择，因为它的后面the only one相呼应。Special专门的，专用的，例如；They went to London on a special train.[他们搭一班专车（或加班车）去伦敦。]rare稀有的，罕见的，如：rare metals(稀有的金属)。Singular单数的。

32. There are usually at least two _____ of looking at every question.

A. ways

B. directions

C. views

D. opinions

[答案]A. ways.

[注释]two ways of looking at every questions意指“观察每个问题的两个方面”。

33. He left in such a hurry that I _____ had time to thank him.

A. almost

B. even

C. nearly

D. scarcely

[答案]D. scarcely.

[注释]scarcely(=hardly, not quite, almost not)几乎没有。Scarcely是否定副词，类似的有：hardly, barely, rarely, seldom, little等。研究生入学考试中经常测试这类否定副词的用法。

34. I could tell he was surprised from the _____ on his face.

A. appearance

B. view

C. sight

D. expression

[答案]D. expression.

[注释]expression此处意指“表情”。Appearance表示人的“仪表，外表”。

35. I'd like to take _____ of this opportunity to thank you all for your cooperation.

A. profit

B. benefit

C. advantage

D. interests

[答案]C. advantage.

[注释]take advantage of(=make use of sth. for one's own benefit)利用：take advantage of my ignorance(利用我的无知)。

36. If you ever have the _____ to go abroad to work, you should take it.

A. possibility

B. offer

C. luck

D. chance

[答案]D. chance.

[注释]chance(偶然的)机会。Have与the(或a) possibility不能搭配；常用There is a possibility for sb. to do sth.表示客观存在的“可能性”。

37. Scientists think they have _____ in their attempt to find the causes of some major diseases.

A. broken through

B. worked out

C. fallen out

D. got round

[答案]A. broken through.

[注释]break through(=be successful after overcoming a difficulty)突破；取得重大成果：Scientists hope to break through soon in their fight against heart disease.(科学家希望在与心脏病斗争中很快取得重大成果。)

本题译文：科学家认为他们在探索某些重要疾病的病因中已取得重大突破。

38. The room was so quiet that she could hear the _____ of her heart.

A. hitting

B. beating

C. tapping

D. knocking

[答案]B. beating.

[注释]beating 此处是动名词，指“（心）跳”：Her heart was beating furiously.

39. During World War II Malta managed to _____ most of Italian and German bombers by throwing up an effective anti-aircraft screen.

A. put out

B. shut out

C. come across

D. get across

[答案]B. shut out.

[注释]shut out(=prevent from coming in; block)排除，排斥：They shut out our dust by having double windows.(他们用双层窗户防尘。)

put out扑灭；get across越过；使人了解；come across偶然遇到。

本题译文：第二次世界大战中，马耳他建立了有效的防空屏障以防止意大利和德国的轰炸机侵入。

40. I think we should let Maria go camping with her boyfriend. _____, she's a big girl now.

A. Above all

B. After all

C. First of all

D. For all

[答案]B. After all.

[注释]after all毕竟。

“for all + 名词”意为“尽管”: For all his wealth, he was unhapp y.(尽管他富有，但他并不幸福。)

41. He has recently _____ chess to provide himself with some relaxation.

A. taken on

B. taken up

C. held on

D. held up

[答案]B. taken up.

[注释]take up开始从事。

42. What a terrible experience! _____ , you are safe, that's the main thing.

A. Somehow

B. Anyhow

C. Somewhat

D. Anywhere

[答案]B. Anyhow.

[注释]anyhow(at= any rate; in any case)无论如何，不管怎样。

43. Although he hasn't any formal qualifications, Betas _____ to do well for himself.

A. managed

B. succeeded

C. arranged

D. convinced

[答案]A. managed.

[注释]manage to do sth.(=succeed in doing sth.)设法做成某事：1)He managed to escape to South America.(他设法逃到了南美。) 2)We managed to get what we wanted, anyhow.(我们反正设法得到了需要的东西。) 3)Do you suppose you can manage to get me a passport?(你能设法给我弄到一份护照吗？)

本题译文：虽然他没有正式的资力，但他收入很多。Do well for oneself吃香，收入多，改善自己的社会地位。

44. After a short holiday, he _____ himself once more to his studies.

A. applied

B. used

C. engaged

D. dipped

[答案]A. applied.

[注释]apply oneself to“致力于”。Apply one's mind to(专心于)。Apply to sb. for aid(向某人求援)。Apply a theory to practice(把理论应用于实践)。

45. She felt _____ of having asked such a silly question when the audience couldn't help laughing.

A. guilty

B. crazy

C. miserable

D. ashamed

[答案]D. ashamed.

[注释] be ashamed of因......感到羞耻，惭愧：1)He is ashamed of what he was done.2)She felt ashamed of having done so little.(=She felt ashamed that she had done so little.) 3)John was ashamed to ask for help.(他不好意思向人求助。) 4)Jim was ashamed to have troubled me with so many questions.

Be guilty of犯有......罪，过失：1)He was found guilty. 2)I am not guilty of this crime.

46. The driver can adjust the heating in winter and the air conditioning in summer to suit his own _____.

A. leisure

B. preference

C. convenience

D. selection

[答案]B. preference.

[注释]preference偏爱，更加喜欢：My preference is for beef rather than for lamb.(我更喜欢牛肉面不是羊肉。)

47. There is not much time left; So I'll tell you about it _____.

A. in detail

B. in brief

C. in short

D. in all

[答案]B. in brief.

[注释]in brief(=in a few words)简短地（作状语）,例如：He told me in brief what had happened.（他简短地向我讲了已发生地事情。）此处in brief等于briefly。此处，in brief(=in a word, in short)简言之（作插入语）1)It is a long letter, but in brief, he says "No".(这是一封长信，但简言之，他说“不”。) 2)John is smart, polite, and well-behaved. In brief, he is admirable.此句中in brief意为in a word 或in short. in short作插入语，其意思是in a word(总之)。In detail详细地。In all总计，总共：There are 20 in all.

48. Magnificent views over the countryside have often _____ people to write poems.

A. convinced

B. inspired

C. induced

D. attracted

[答案]B. inspired.

[注释]inspired鼓舞，激励，产生：1)His speech inspired us to try again. 2)He inspired confidence in me.(他使我产生信心。) 3)The good news inspired us with hope.(这个好消息使我们产生希望。)

49. When the little child caught sight of the young woman _____ in white he started brawling immediately.

A. dressed

B. wearing

C. worn

D. putting on

[答案]A. dressed.

[注释]be dressed in 穿这......衣服。Wear意为“穿着”是及物动词，语法结构上与本题不符。Put on穿上，强调的动作。

50. Some areas, _____ their severe weather conditions, are hardly populated.

A. due to

B. but for

C. in spite of

D. with relation to

[答案]A. due to.

[注释]due to由于。有些语言专家认为due to引导的短语，在句中只能作表语，如：1)His absence was due to the storm. 2)The delay was due to heavy traffic. 3)This accident was due to his carelessness.但现代英语里due to引导的短语可以作状语用，如：He failed due to carelessness. Due to heavy traffic, he was late for an hour or so.

51. Be careful how you _____ that jug, it will break very easily.

A. pour

B. operate

C. handle

D. employ

[答案]C. handle.

[注释]handle意为“用手拿......”:Wash your hands before you handle my books.

52. We suddenly saw the bus about to leave and had to run _____ to catch it.

A. hardly

B. heavily

C. hard

D. strongly

[答案]C hard.

[注释]run hard意为“使劲跑”，句中hard是副词。Hardly“几乎不“，是否定副词，与本题不符。

53. He hated the war so much that he decided to leave the army _____.

A. for long

B. once in a while

C. for good

D. once upon a time

[答案] C. for good.

[注释] for good (=permanently)永久地:He says he's leaving the country

for good. for long 长久地。按本题题意，用for long 不妥。once upon a time 从前。once in a while 偶尔。

54. This year the farmers were just able to gather in the _____ before the fine weather came to an end.

A. collection

B. harvest

C. flower

D. plant

[答案] B. harvest.

[注释] gather in “收获(庄稼)”: The farmers are gathering in the corn.

55. Tell your brother to come _____, because it's going to rain in a minute or two.

A. indoors

B. outdoors

C. outward

D. inwards

[答案] A. indoors

[注释] 按句子的逻辑意思应选indoors adv. 向屋里；在屋里，inwards adv，向

内，向中心，outward 向外。outdoors 是indoors 的反义词。

本文译文: 叫你兄弟进屋来，因为天马上要下雨了.

56. I can't advise you what to do. You must use your own _____.

A. opinion

B. guesswork

C. justice

D. judgment

[答案] D judgement

[注释] judgement 判断。guesswork 猜测，justice 正义，公正，ideal 理想。

57. There is a 20 minute parking _____ here, so we must get back to the car very quickly.

A. freedom

B. limit

C. allowance

D. limitation

[答案] B. limit.

[注释] parking limit 意为在停车场“停车的时间限制”。a 20 minutes parking limit (停车时间限制为20分钟).

58. Having said he would mend the clock, he discovered that he had not brought the _____ tools for the job.

A. real

B. correct

C. right

D. fit

[答案] C. right.

[注释] right 适当的，恰当的:He is the right man to do the job。(他是干这项工作的合适人选) real 真的，correct 正确的；exact 确切的：exact time 确切的时间，exact age 确切的年龄，exact weight 确切的重量；exact weight 确切的重量；exact information 确切的信息；exact cause 确切的原因；exact meaning 确切的意思。

59. It has been laid down that each student must _____ a composition to the teacher once

a week.

A. turn in

B. give up

C. put forward

D. bring out

[答案] A. turn in.

[注释] turn in(=hand in) 上交。

60. You will get to the church more quickly if you take this _____ across the fields.

A. track

B. passage

C. method

D. journey

[答案] A. track.

[注释] track(=path made by frequent use)意指“(常走而踏成的)小径”，如:a track across the moor(越过荒野的小径)。passage“通路”，如:force a passage through a crowd(在人群中挤出的一条通路). 可见此处选passage不妥.

61. Don't go too far into the sea, children, or the waves will _____ you off your feet.

A. flow

B. cut

C. press

D. sweep

[答案] D. sweep.

[注释] sweep sb，off sb's feet 由两层意思，直义为“(浪等)把某人冲倒”，转义是“使产生强烈的好感，使完全信服”，如: His speech swept them off their feet。(他的演说使他们五体投地.)

62. The store had no more red shoes _____, so Mary chose brown ones instead.

A. in demand

B. in store

C. in need

D. in stock

[答案] D. in stock.

[注释] in stock(=having sth. ready to sell or use；in present supply) 有现货供应: The shop has sugar in stock.(这个商店有白糖供应.) in demand(=needed；wanted；) 有需求: The book about dogs was much in demand in the library.(=Many people wanted to read the book about dogs that in the library.) in need(=in poverty，in trouble)在贫困中，在困难中: A friend in need is a friend indeed。(A friend who helps when one is in trouble is a real friend.) in store(=saved up in case of need；ready for use for some purpose) 储备待用:于If the electricity goes off，we have candles in the closet.(=We have candles put away if we need them for light.)(如果电灯灭了，我们壁橱里还备有蜡烛.)

[注意] in stock 强调商店备有现货以供出售，而in store 则指储备物品以供急需使用。此外in store 还可以表示“等待着，必将发生”。例如: I have a surprise in store for you.(我有一个你料想不到的消息要告诉你。)

本题译文: 这家商店没有红鞋供应，所以玛丽买了一双宗色的鞋.

63. The current political _____ of our country is favorable for foreign investments.

A. climate

B. weather

C. state

D. occasion

[答案] A. climate.

[注释] climate 指某一地区的长期气侯，而weather则指某一天的“天气”。本题中

的climate(=the general temper or opinion of a group of the people or period of history) 指“某一团体历史时期的总的状况和民意”。例如: climate of the political unrest 不稳定的政治状况. state(=condition) 状态；be in a state of 处于某种状态. 例如: 1 The room was in a very dirty state. 2 She is in a state of confusion.(她处于慌乱状态.) 由上可见，climate 最合题意.

本题译文: 我国目前的政治气候有利于外国的投资.

64. It was with great delight that I read in your February _____ the letter to the Editor written by Prof. Johnson.

A. issue

B. printing

C. magazine

D. copy

[答案] A. issue.

[注释] 根据题意，此处是指某杂志二月份的那一期，故应选issue。printing 印刷；印刷术。至于copy 与issue 的区别，copy 指书刊的“本，册”；而issue 是指报刊或杂志的“期”.

本题译文: 非常高兴地拜读了贵刊二月的一期中所登载的约翰逊教授致编辑的信.

65. My house is very _____ for getting to work as it is only a few minutes from the station.

A. comfortable

B. suitable

C. convenient

D. available

[答案] C. convenient.

[注释]convenient 方便的。suitable也可接for，但其词义和本题不符，故不能选.

66. She chose curtains of a color which would _____ her carpet.

A. equal

B. agree

C. help

D. match

[答案] D. match.

[注释] match vt. 匹配；相配: 1 You can't match him in his knowledge of wild plants.(在野生植物知识方面，你无阀于他相比.) 2 Her hat does match her dress.(她的帽子与她的衣服不配.)

match vi. 相配: These gloves don't match.

67. I have such a bad cold that I have lost all _____ of smell.

A. degree

B. sense

C. strength

D. ability

[答案] B. sense.

[注释] sense 意为“(五官的)感觉”，如: People have five senses: sight，hearing，smell，taste and touch. scent 气味，香味.

68. She is so _____ that she cried for days when her pet rabbit died.

A. sensitive

B. sensible

C. imaginative

D. impressive

[答案] A. sensitive

[注释] sensitive敏感的(to),易受伤害的,灵敏的。sensible明智的(of),通情达理的。imaginative有想象力。impressive的给人留下印象的,感人的。

69. The lorry driver was badly _____ when his lorry crashed into a wall.

A. damaged

B. hit

C. hurt

D. harmed

[答案] C. hurt

[注释] damage损坏;harm对......有害;hurt(精神上或肉体上)伤害; hit打击;pain(精神上或肉体上)痛苦。

70. I caught a _____ of the car before it disappeared around the bend.

A. glance

B. glimpse

C. glare

D. stare

[答案] B. glimpse

[注释] catch (or get) a glimpse of瞥见(强调行为的结果)。take a glance (or look) at 看一眼(强调行为过程本身)。

71. The rainbow _____ as the sun came fully out from behind the clouds.

A. dissolved

B. removed

C. resigned

D. disappeared

[答案] D. disappeared

[注释]disappear消失。dissolve溶解。remove去除。resign辞去,辞职。retire退休。

72. All too _____ it was time to go back to school after the glorious summer holidays.

A. often

B. fast

C. soon

D. late

[答案] C. soon

[注释]all too实在太......，all too soon意为太快了，带有惋惜的意味，如：Tom had snatched a short holiday from his work to come here. He said it ended all too soon.（汤姆趁工作之暇匆匆来此渡一短假，他说，假期过得太快了。）

73. After dinner the minister made a short _____ to the guests.

A. delivery

B. pronunciation

C. conversation

D. speech

[答案] D. speech

[注释]make a speech to sb.(向某人做演讲)。make conversation with sb.(和某人闲谈conversation常与下列动词搭配:get (enter) into conversation with(和......攀谈起来),have a conversation with(与......谈话),interrupt (break off) conversation(中断谈话),turn the conversation to other matters(把话题转到其他问题上)delivery常指"(演讲等的)说话方式,口才",如: His report was good, but his delivery was poor.( 他的报告内容很好,但他的口才太差)。

74. Busy and successful as he was, the novelist was willing to _____ any promising young man and give him all the help he could.

A. take up

B. pick up

C. make up

D. look up

[答案] A. take up.

[注释]take up把......当作被保护人,关照,提携,列如:This athlete was taken up by several Boston universities.(这个运动员得到波士顿大学的关照。)

本题译文：虽然他是一位繁忙又有成就的小说家,但他愿意提携任何有前途的年轻人并尽力给予帮助。

75. He did not find a job yet because he had no _____ to men who could help him.

A. approach

B. application

C. access

D. approval

[答案] C. access.

[注释]have access to进入的路；能接近，进入,了解或使用(不可数名词)。列如：1)We had access to his private files.(我们能接触他的私人档案。)2)Only a few people have access to the full facts of the ase.(只有几人能了解案件的全部事实。)3)Only high officials had access to the emperor.(只有高级官员才能接近皇帝。)

approach接近,走近,快到;对待处理(事情的)方式;接近(到达)的路:1)He was warned of the enemy.(已警告他敌人已接近。)2)His book represents a new approach to the difficulty.(他的书代表了处理困难的一种新方法。)3)The approach to the house was a narrow path.(通到这幢房子的路是一条小径。)

application申请,申请书。approval赞同。根据题意,此句中不是指身体上的“接近或靠近”,而是指“能接触到”的某人故选access更切题意

76. The old man got into the _____ of storing money under the bed.

A. tradition

B. habit

C. use

D. custom

[答案] B. habit.

[注释]get into the habit of doing sth.意为“养成了做......的习惯"。habit指个人的习惯,而custom则指社会的风俗习惯。tradition“传统"。

77. When the Greeks had _____ the Persians, a soldier ran from Marathon to Athens.

A. won

B. bitten

C. beaten

D. hit

[答案] C. beaten.

[注释]beat sb. 打败某人。beat sb. black and blue(把某人打得鼻青脸肿)。hit,击,击中:hit a man on the head(打在人的头上);hit at sb.(向某人打去)。strike(=hit ,give a blow at blows to)打,击:strike a man on the chin(打在某人的下巴上)。win赢得,用作此义时,后不能接某人;可以说win a match, a victory, the first prize等。

78. There was a large box behind the door and Peter couldn't _____ falling over it in the darkness.

A. help

B. resist

C. avoid

D. prevent

[答案]C. avoid.

[注释]avoid 避免(后接动词或名词): He tried to avoid answering my questions. can't (couldn't) help doing sth. 禁不住做......不由自主地做......。can't (couldn't) resist doing sth.禁不住做......: I couldn't resist laughing.

79. Violent programs on television may have a bad _____ on children.

A. affection

B. pressure

C. influence

D. control

[答案]C. influence.

[注释]have a influence on 对...有影响；

80. If you put too many potatoes in that paper-bag it will _____.

A. fail

B. explode

C. crack

D. burst

[答案]D. burst

[注释] burst vt./vi.涨破，涨裂。Burst one's clothes（撑破衣服）。

81. I'm afraid you have no _____ but to come along with us.

A. possibility

B. permission

C. choice

D. selection

[答案]C. choice.

[注释]have no choice but 除了...没有别的选择；只能...：I have no choice but to obey.(我只能服从)。

82. I shall never beat John at tennis; we are clearly not in the same _____.

A. set

B. band

C. group

D. class

[答案] D. class.

[注释]be in the same class 水平相同。此句中class,意为“(高低、优劣的)等级；种类”。

83. As soon as Charles had _____ a little from his surprise, his one thought was to get away.

A. returned

B. absorbed

C. turned

D. recovered

[答案] D. recovered.

[注释]recover from 从......恢复过来

84. The thieves _____ him _____ in the park, took his wallet and escaped.

A. held .. back

B. held .. up

C. held .. on

D. held .. out

答案] B. held ... up.

[注释]hold up sb. 拦劫。hold up, hold on, hold out 的用法请参阅III.82,83注释.

85. The two dogs started to fight, so we tried to _____ them.

A. split

B. separate

C. tear

D. divide

[答案] B. separate.

[注释]separate 意指将结合的东西“分开，拆散”，divide指把整体“分成”几个部分，split（沿一条线-）裂开，tear撕开，distinguish“区分，区别，辨别”。

86. Carl wanted to play a joke on Bob but gave himself _____ by laughing.

A. away

B. in

C. out

D. up

[答案] A. away.

[注释]give away 暴露，泄露。参阅III.68.注释。

87. Many people complain of the rapid _____ of modern life.

A. rate

B. pace

C. speed

D. growth

[答案] B. pace.

[注释]pace 走或跑的速度；发展或进步速度。

88. She has lost her handbag with the _____ sum of $150 in it.

A. extraordinary

B. important

C. considerable

D. valuable

[答案] C.considerable.

[注释]considerable 相当可观的。[注意]considerate考虑周到的，体谅的，体贴的：1）She is considerate to others. (她能体谅别人。)2）That was very considerate of you.（你真体谅别人。）

89. Russia's withdrawal of its experts from China did not strangle (压垮) the Chinese

people; _____ it stirred up their enthusiasm for greater exertions.

A. on the other hand

B. on the contrary

C. to the contrary

D. in consequence

[答案] B. on the contrary.

[注释]on the contrary相反地：--Have you nearly done?--On the contrary, I have only just begun. Monday unless you write me to the contrary. (我星期一将来，除非你写信告诉我有相反地情况。)

90. At first Bob was puzzled by Virginia s waving, but then it _____ his mind that she was trying to tell him something.

A. crossed

B. passed

C. occurred

D. opened

[答案] A. crossed.

[注释]cross one's mind 想起：1)A sudden thought crossed my mind. 2)It never crossed my mind that he might refuse the request. (我从来没有想到他可能会拒绝这个请求。)

如用pass则应加through, 例如：When Jane did not come home by midnight, many terrible fears passed through Mother's mind. (=Mother thought of many things that might have happened to Jane.)

occur的用法如下：1）That view of the case did not occur to me before. (对这个案件的那种看法以前我没有想到过。)2）It occurred to her that she might adopt a homeless child.(她想到，她可以收养一个无家可归的孩子。)

关于“想起”的以上三种表达法考生务必弄懂熟记。这些词组和句形不仅在词汇测试中经常遇到，而且在短文写作时也可以使用。

本题译文：起初鲍玻对弗吉尼亚的挥手致意感到迷惑，但后来他想到，她想告诉他某事。

91. The lady who had invited us heard me telling my wife that the dinner was terrible so I was _____.

A. confused

B. nervous

C. shameful

D. embarrassed

[答案] D. embarrassed.

[注释]be embarrassed 感到窘迫。

92. I'm sorry but what he thinks is not of the _____ importance to me.

A. merest

B. lowest

C. last

D. least

[答案] D. least.

[注释]least 是little的最高级形式。

93. He offered to _____ her a hand as the suitcase was too heavy for her to carry.

A. lend

B. help

C. show

D. loan

[答案] A. lend.

[注释]lend sb. a hand给某人帮个忙。

94. I have been looking for this book for months, and _____ I have found it.

A. at least

B. in no time

C. at last

D. at present

[答案] C. at last.

[注释]at last (=in the end)最终；at least至少；in no time 立即，马上；at present 目前。

95. The _____ stuck on the outside of the envelope said "By Air".

A. label

B. ticket

C. signal

D. sign

[答案] A. label.

[注释]label 标签，标记。signal信号. sign记号；指示牌：traffic signs (交通版示)。notice 布告。

96. Psychological studies show that some people are quick-tempered _____.

A. at heart

B. on purpose

C. in person

D. by nature

[答案] D. by nature.

[注释]by nature 天生，生来。in person 1）亲自，亲身：I shall be present at the meeting in person.(我将亲自出席会议。)2）身体上，外貌上：In person he was handsome, strong and healthy.(他面目清秀，体格强壮。)

at heart 1)内心里，实质上：His manners are cold, but he is at heart a kind man. (他的言谈举止有些冷淡，但实际上他是一个好心肠的人。)2）考虑的是......：When I say don't eat sweets, I have your health at heart.(我叫你别吃果糖，是考虑到你的健康。)on purpose 故意地。

97. His name was on the _____ of my tongue, but I just couldn't recall it.

A. end

B. point

C. edge

D. tip

[答案] D. tip.

[注释]be on (or at) the tip of one's tongue 就在嘴边，差点被想起，如：The answer was on the tip of my tongue, but I could't think of it.(我差点就想起那答案来，可就是想不起来。) be on the point of 正要（去做某事）：I was just on the point of going when you came in.

98. In my opinion, your work does not _____ what I expected of you.

A. catch up with

B. add up to

C. come up to

D. go in for

[答案] C. come up to.

[注释]come up to 达到，符合：1)He tries his best to come up to the expectations of the people.(他努力达到人民对他的期望。)2)This piece of work does not come up to the required standard.(这件工作没有达到需要的标准。)catch up with 赶上；add up to总计；go in for 从事，致力于，追求，沉溺于。

99. I broke my relationship with John because he always found _____ with me.

A. error

B. mistake

C. fault

D. failure

[答案] C. fault.

[注释]find fault with 挑剔，找......的岔子。例如：1)She tries to please him, but he always finds fault. (=He finds something wrong with everything she does.) 2)They found fault with every box I made. (=They found something wrong or something they did not like in every box I made.)

100. He is the rudest man I have ever met. Jane, his present secretary, is the only person who can _____ him.

A. respect

B. stand

C. support

D. dislike

[答案] B. stand.

[注释]stand (=endure, bear, put up with)忍耐，忍受；1)I can't stand that woman. 2)He cannot stand criticism.

2014年高中数学计算题4

计算题专项练习 1．计算：（1）；（2）． 2．计算：（1）lg1000+log342﹣log314﹣log48；（2）． 3．（1）解方程：lg（x+1）+lg（x﹣2）=lg4；（2）解不等式：21﹣2x＞．4．（1）计算：2××（2）计算：2log510+log50.25． 5．计算：（1）；（2）． 6．求log89×log332﹣log1255的值． 7．（1）计算．

（2）若，求的值． 8．计算下列各式的值（1）0.064﹣（﹣）0+160.75+0.25（2）lg5+（log32）?（log89）+lg2． 9．计算：（1）lg22+lg5?lg20﹣1；（2）． 10．若lga、lgb是方程2x2﹣4x+1=0的两个实根，求的值． 11．计算（Ⅰ）（Ⅱ）． 12．解方程：．

13．计算：（Ⅰ）（Ⅱ）． 14．求值：（log62）2+log63×log612． 15．（1）计算（2）已知，求的值． 16．计算（Ⅰ）；（Ⅱ）0.0081﹣（）+??． 17．（Ⅰ）已知全集U={1，2，3，4，5，6}，A={1，4，5}，B={2，3，5}，记M=（?U A）∩B，求集合M，并写出M的所有子集；（Ⅱ）求值：． 18．解方程：log2（4x﹣4）=x+log2（2x+1﹣5）

20．求值：（1）lg14﹣+lg7﹣lg18 （2）． 21．计算下列各题：（1）（lg5）2+lg2×lg50；（2）已知a﹣a﹣1=1，求的值． 22．（1）计算；（2）关于x的方程3x2﹣10x+k=0有两个同号且不相等的实根，数k的取值围． 23．计算题（1）（2） 24．计算下列各式：（式中字母都是正数）（1）（2）．

高中数学数列压轴题练习(江苏)详解

高中数学数列压轴题练习（江苏）及详解 1.已知数列是公差为正数的等差数列,其前n项和为,且? , (Ⅰ)求数列的通项公式; (Ⅱ)数列满足, ①求数列的通项公式; ②是否存在正整数m,,使得,,成等差数列?若存在,求出m,n的值;若不存在,请说明理由. 解:(I)设数列的公差为d,则由?,,得, 计算得出或(舍去). ; (Ⅱ)①,, , , 即,,, ,

累加得:, 也符合上式. 故,. ②假设存在正整数m、,使得,,成等差数列, 则又,,, ,即, 化简得: 当,即时,,(舍去); 当,即时,,符合题意. 存在正整数,,使得,,成等差数列. 解析 (Ⅰ)直接由已知列关于首项和公差的方程组,求解方程组得首项和公差,代入等差数列的通项公式得答案; (Ⅱ)①把数列的通项公式代入,然后裂项,累加后即可求得数列的通项公式;

②假设存在正整数m、,使得,,成等差数列,则 .由此列关于m的方程,求计算得出答案. 2.在数列中,已知, (1)求证:数列为等比数列; (2)记,且数列的前n项和为,若为数列中的最小项,求的取值范围. 解:(1)证明:, 又, ,, 故, 是以3为首项,公比为3的等比数列 (2)由(1)知道,, 若为数列中的最小项,则对有恒成立, 即对恒成立当时,有; 当时,有?; 当时,恒成立,

对恒成立. 令,则对恒成立, 在时为单调递增数列. ,即综上, 解析 (1)由,整理得:.由, ,可以知道是以3为首项,公比为3的等比数列; (2)由(1)求得数列通项公式及前n项和为,由为数列中的最小项,则对有恒成立,分类分别求得当时和当的取值范围, 当时,,利用做差法,根据函数的单调性,即可求得的取值范围. 3.在数列中,已知,,,设为的前n项和. (1)求证:数列是等差数列; (2)求;

[数学]数学高考压轴题大全

1、（本小题满分14分）已知函数．（1）当时，如果函数仅有一个零点，求实数的取值范围；（2）当时，试比较与的大小；（3）求证：（）． 2、设函数，其中为常数．（Ⅰ）当时，判断函数在定义域上的单调性；（Ⅱ）若函数的有极值点，求的取值范围及的极值点；（Ⅲ）当且时，求证：． 3、在平面直角坐标系中，已知椭圆.如图所示，斜率为且不过原点的直线交椭圆于，两点，线段的中点为，射线交椭圆于点，交直线于点. （Ⅰ）求的最小值；（Ⅱ）若?，（i）求证：直线过定点；

（ii ）试问点，能否关于轴对称？若能，求出此时的外接圆方程；若不能，请说明理由. 二、计算题（每空？分，共？分） 4 、设函数的图象在点处的切线的斜率为，且函数为偶函数．若函数满足下列条件：①；② 对一切实数，不等式恒成立．（Ⅰ）求函数的表达式；（Ⅱ）求证：． 5 、已知函数：（1 ）讨论函数的单调性；（2）若函数的图像在点处的切线的倾斜角为，问：在什么范围取值时，函数在区间上总存在极值？ (3)求证：．

6、已知函数=，. (Ⅰ)求函数在区间上的值域；（Ⅱ）是否存在实数，对任意给定的，在区间上都存在两个不同的，使得成立.若存在，求出的取值范围；若不存在，请说明理由；（Ⅲ）给出如下定义：对于函数图象上任意不同的两点，如果对于函数图象上的点（其中总能使得成立，则称函数具备性质“”，试判断函数是不是具备性质“”，并说明理由. 7、已知函数（Ⅰ）若函数是定义域上的单调函数，求实数的最小值；（Ⅱ）方程有两个不同的实数解，求实数的取值范围；（Ⅲ）在函数的图象上是否存在不同两点，线段的中点的横坐标为，有成立？若存在，请求出的值；若不存在，请说明理由． 8、已知函数： ⑴讨论函数的单调性；

高中数学计算题大全

高中数学计算题大全篇一:2014年高中数学计算题五 2014年高中数学计算题五 2014年高中数学计算题五一(解答题(共30小题) 1((1)已知x+y=12，xy=9，且x,y，求的值( (2) 2(计算下列各题: (1) (2) 3(计算下列各题: (?) (?) 4((1)化简:( ( ,lg25,2lg2; ; ( ，(a,0，b ,0)( (2)已知2lg(x,2y)=lgx+lgy，求 5(解方程 6(求下列各式的值: (1)lg, lg+lg 的值( ( 1

7(求值: 2(1)(lg5)+lg2?lg50; (2)( ( 8(计算 9(计算: (1)已知x,0，化简 (2) 10(计算:(1)(0.001) (2)lg25+lg2,lg 11((1 )求值: (2)解不等式: 12(化简: ( ( +27+(),(),1.5的值( ( ,log29?log32( 13((?) 化简:; (?) 已知2lg(x,2y)=lgx+lgy，求 14(计算: (1)(2的值( ),×e++10 lg2(2)lg5+lg2×lg500,lg 15(化简或求值:(1),log29×log32(

16((1)计算:; 2 (2)已知2a=5b=100，求的值( 17((1)计算 (2)已知log189=a，18b=5，试用a，b表示log365( 18(计算: (1)(lg50)2+lg2×lg(50)2+lg22; (2)2(lg)2+lg?lg5+; (3)lg5(lg8+lg1000)+(lg2)2+lg+lg0.06( 19(化简下列式子: (1); (2)( 20(化简下列式子: (1); (2); (3)( 21(化简求值: 22(化简下列式子: (1);

高中数学压轴题试卷整合

2017届北京市海淀区高三下学期期中考试数学理卷 18.已知函数2()24(1)ln(1)f x x ax a x =-+-+，其中实数3a <．（Ⅰ）判断1x =是否为函数()f x 的极值点，并说明理由；（Ⅱ）若()0f x ≤在区间[]0,1上恒成立，求a 的取值范围． 19.已知椭圆G ：2 212 x y +=，与x 轴不重合的直线l 经过左焦点1F ，且与椭圆G 相交于A ，B 两点，弦AB 的中点为M ，直线OM 与椭圆G 相交于C ，D 两点．（Ⅰ）若直线l 的斜率为1，求直线OM 的斜率；（Ⅱ）是否存在直线l ，使得2||||||AM CM DM =?成立？若存在，求出直线l 的方程；若不存在，请说明理由．西城区高三统一测试 18．（本小题满分13分）已知函数21()e 2 x f x x =-．设l 为曲线()y f x =在点00(,())P x f x 处的切线，其中0[1,1]x ∈-．（Ⅰ）求直线l 的方程（用0x 表示）；（Ⅱ）设O 为原点，直线1x =分别与直线l 和x 轴交于,A B 两点,求△AOB 的面积的最小值． 19．（本小题满分14分）如图，已知椭圆2222:1(0)x y C a b a b +=>>的离心率为12，F 为椭圆C 的右焦点．(,0)A a -，||3AF =．（Ⅰ）求椭圆C 的方程；（Ⅱ）设O 为原点，P 为椭圆上一点，AP 的中点为M ．直线OM 与直线4x =交于点D ，过O 且平行于AP 的直线与直线4x =交于点E ．求证：ODF OEF ∠=∠．

2017年南通市高考数学全真模拟试卷一 13.已知角,αβ满足tan 7tan 13 αβ=，若2sin()3αβ+=，则sin()αβ-的值为． 14.将圆的六个等分点分成相同的两组，它们每组三个点构成的两个正三角形除去内部的六条线段后可以形成一个正六角星.如图所示的正六角星的中心为点O ，其中,x y 分别为点O 到两个顶点的向量.若将点O 到正六角星12个顶点的向量都写成ax by +的形式，则a b +的最大值为． 18.已知椭圆:C 22 31mx my +=(0)m > 的长轴长为，O 为坐标原点. （1）求椭圆C 的方程和离心率. （2）设点(3,0)A ，动点B 在y 轴上，动点P 在椭圆C 上，且点P 在y 轴的右侧.若BA BP =，求四边形OPAB 面积的最小值. 19.已知函数32()f x ax bx cx b a =-++=(0)a >. （1）设0c =. ①若a b =，曲线()y f x =在0x x =处的切线过点(1,0)，求0x 的值； ②若a b >，求()f x 在区间[0,1]上的最大值. （2）设()f x 在1x x =，2x x =两处取得极值，求证：11()f x x =，22()f x x =不同时成立. 13.1 5 -14.5 18.（1）由题意知椭圆:C 22 111 3x y m m +=，所以21a m =，213b m =，

高考数学导数与三角函数压轴题综合归纳总结教师版

导数与三角函数压轴题归纳总结近几年的高考数学试题中频频出现含导数与三角函数零点问题，内容主要包括函数零点个数的确定、根据函数零点个数求参数范围、隐零点问题及零点存在性赋值理论.其形式逐渐多样化、综合化. 一、零点存在定理例1.【2019全国Ⅰ理20】函数,为的导数．证明：（1）在区间存在唯一极大值点；（2）有且仅有2个零点．【解析】（1）设()()g x f x '=,则()()() 2 11 cos ,sin 11g x x g x x x x '=- =-+++. 当1,2x π??∈- ???时,单调递减,而()00,02g g π?? ''>< ??? , 可得在1,2π?? - ?? ?有唯一零点,设为. 则当()1,x α∈-时,()0g x '>；当,2x πα?? ∈ ??? 时,. 所以在()1,α-单调递增,在,2πα?? ???单调递减,故在1,2π?? - ???存在唯一极大值点,即()f x '在1,2π?? - ?? ?存在唯一极大值点. （2）()f x 的定义域为. （i ）由（1）知, ()f x '在()1,0-单调递增,而()00f '=,所以当时, ,故()f x 在单调递减,又,从而是()f x 在的唯一零点. ()sin ln(1)f x x x =-+()f x '()f x ()f x '(1,)2 π-()f x ()g'x ()g'x α()0g'x <()g x ()g x (1,)-+∞(1,0)x ∈-()0f 'x <(1,0)-(0)=0f 0x =(1,0]-

（ii ）当0,2x π?? ∈ ??? 时,由（1）知,在单调递增,在单调递减,而 ,02f π??'< ???,所以存在,2πβα?? ∈ ???,使得,且当时, ；当,2x πβ??∈ ???时,.故在单调递增,在,2πβ?? ???单调递减.又,1ln 1022f ππ???? =-+> ? ???? ?,所以当时,. 从而()f x 在0,2π?? ??? 没有零点. （iii ）当,2x ππ??∈ ???时,()0f x '<,所以()f x 在,2ππ?? ???单调递减.而 ()0,02f f ππ??>< ??? ,所以()f x 在,2ππ?? ??? 有唯一零点. （iv ）当时,()l n 11x +>,所以<0,从而()f x 在没有零点. 综上, ()f x 有且仅有2个零点. 【变式训练1】【2020·天津南开中学月考】已知函数3()sin (),2 f x ax x a R =-∈且在,0,2π?? ????上的最大值为32π-，（1）求函数f (x )的解析式； (2)判断函数f (x )在（0，π）内的零点个数，并加以证明【解析】(1)由已知得()(sin cos )f x a x x x =+对于任意的x∈(0, 2 π)，有sin cos 0x x x +>,当a=0时,f(x)=? 3 2 ，不合题意；当a<0时,x∈(0, 2π),f′(x)<0,从而f(x)在(0, 2 π )单调递减，又函数3 ()sin 2f x ax x =- (a∈R)在[0, 2 π]上图象是连续不断的，故函数在[0, 2 π ]上的最大值为f(0)，不合题意； ()f 'x (0,)α,2απ?? ???(0)=0f '()0f 'β=(0,)x β∈()0f 'x >()0f 'x <()f x (0,)β(0)=0f 0,2x ?π?∈ ???()0f x >(,)x ∈π+∞()f x (,)π+∞

高一数学计算题

指数函数对数函数计算题 1、计算：lg 5·lg 8000＋. 2、解方程：lg 2(x ＋10)－lg(x ＋10)3=4. 3、解方程：2. 4、解方程：9-x －2×31-x =27. 5、解方程：=128. 06.0lg 6 1lg )2 (lg 23++3log 1log 66-=x x )8 1(

6、解方程：5x+1=. 7、计算：· 8、计算：(1)lg 25+lg2·lg50; (2)(log 43+log 83)(log 32+log 92). 9求函数的定义域. 10、已知log 1227=a,求log 616. 12 3-x 10log 5log )5(lg )2(lg 2233++.10log 18121 log 8.0--=x x y

11、已知f(x)=,g(x)=(a＞0且a≠1),确定x的取值范围,使得f(x)＞g(x). 12、已知函数f(x)=. (1)求函数的定义域;(2)讨论f(x)的奇偶性;(3)求证f(x)＞0. 13、求关于x的方程a x＋1=－x2＋2x＋2a(a＞0且a≠1)的实数解的个数. 14、求log 927的值. 1 3 22+ -x x a5 2 2- +x x a 3 2 1 1 2 1 x x ? ? ? ? ? + -

15、设3a =4b =36,求＋的值. 16、解对数方程：log 2(x －1)+log 2x=1 17、解指数方程：4x +4-x －2x+2－2-x+2+6=0 18、解指数方程：24x+1－17×4x +8=0 a 2b 1

2020年高考数学压轴题系列训练含答案及解析详解4

第 1 页共 16 页第 1 页共 2020年高考数学压轴题系列训练含答案及解析详解4 1．（本小题满分14分）已知f(x)= 2 22 +-x a x (x ∈R)在区间[－1，1]上是增函数. （Ⅰ）求实数a 的值组成的集合A ；（Ⅱ）设关于x 的方程f(x)= x 1 的两个非零实根为x 1、x 2.试问：是否存在实数m ，使得不等式m 2+tm+1≥|x 1－x 2|对任意a ∈A 及t ∈[－1，1]恒成立？若存在，求m 的取值范围；若不存在，请说明理由. 本小题主要考查函数的单调性，导数的应用和不等式等有关知识，考查数形结合及分类讨论思想和灵活运用数学知识分析问题和解决问题的能力.满分14分. 解：（Ⅰ）f ＇(x)=222)2(224+-+x x ax = 2 22) 2() 2(2+---x ax x ， ∵f(x)在[－1，1]上是增函数， ∴f ＇(x)≥0对x ∈[－1，1]恒成立，即x 2－ax －2≤0对x ∈[－1，1]恒成立. ① 设?(x)=x 2－ax －2，方法一： ?(1)=1－a －2≤0，

— 2 — ① ? ?－1≤a ≤1， ?(－1)=1+a －2≤0. ∵对x ∈[－1，1]，f(x)是连续函数，且只有当a=1时，f ＇(-1)=0以及当a=－1时，f ＇ (1)=0 ∴A={a|－1≤a ≤1}. 方法二： 2a ≥0， 2 a <0， ①? 或 ?(－1)=1+a －2≤0 ?(1)=1－a －2≤0 ? 0≤a ≤1 或－1≤a ≤0 ? －1≤a ≤1. ∵对x ∈[－1，1]，f(x)是连续函数，且只有当a=1时，f ＇(－1)=0以及当a=-1时，f ＇ (1)=0 ∴A={a|－1≤a ≤1}. （Ⅱ）由 2 22 +-x a x =x 1，得x 2－ax －2=0， ∵△=a 2 +8>0 ∴x 1，x 2是方程x 2－ax －2=0的两非零实根， x 1+x 2=a ，

高一数学基础计算题

1-3 初中计算题(一) 班级________ 姓名__________ 一、填空题: 1、若,13+= x 则代数式 3 41 · 132 +++-+x x x x x 的值等于、 2、如果a,b 就是方程012=-+x x 的两个根,那么代数式a b ab +-的值就是、 3.若1

高中数学100道试题

高中数学新课标人教A 版必修1-5选择题100题 1、若M 、N 是两个集合，则下列关系中成立的是( ) A ．? M B ．M N M ?)( C ．N N M ?)( D ．N )(N M 2、若a>b ，R c ∈，则下列命题中成立的是( ) A ．bc ac > B ． 1>b a C ．2 2 bc ac ≥ D ． b a 11< 3、直线x+2y+3=0的斜率和在y 轴上的截距分别是( ) A ．2 1- 和－3 B ． 2 1和－3 C ．2 1- 和 2 3 D ．2 1-和2 3- 4、不等式21<-x 的解集是( ) A ．x<3 B ．x>－1 C ．x<－1或x>3 D ．－1

高考数学压轴题秒杀

第五章压轴题秒杀很多朋友留言说想掌握秒杀的最后一层。关于秒杀法的最难掌握的一层，便是对于高考数学压轴题的把握。压轴题，各省的难度不一致，但毫无疑问，尤其是理科的，会难倒很多很多很多人。不过，压轴题并不是那般神秘难解，相反，出题人很怕很怕全省没多少做出来的，明白么？他很怕。那种思想，在群里面我也说过，在这里就不多啰嗦了。想领悟、把握压轴题的思路，给大家推荐几道题目。全是数学压轴题，且是理科（09的除山东的外我都没做过，所以不在推荐范围内）。 08全国一，08全国二，07江西，08山东，07全国一一年过去了，很多题目都忘了，但这几道题，做过之后，虽然一年过去了，可脉络依然清晰。都是一些可以秒杀的典型压轴题，望冲击清华北大的同学细细研究。记住，压轴题是出题人在微笑着和你对话。具体的题目的“精”，以及怎么发挥和压榨一道经典题目的最大价值，会在以后的视频里面讲解的很清楚。不过，我还是要说一下数列压轴题这块大家应该会什么（难度以及要求依次增高）\ 1：通项公式的求法（不甚解的去看一下以前的教案，或者问老师，这里必考。尤其推荐我押题的第一道数列解答题。） 2.：裂项相消（各种形式的都要会）、迭加、迭乘、错位相减求和（这几个是最基本和简单的数列考察方式，一般会在第二问考） 3：数学归纳法、不等式缩放基本所有题目都是这几个的组合了，要做到每一类在脑中都至少有一道经典题想对应才行哦。开始解答题了哦，先来一道最简单的。貌似北京的大多挺简单的。这道题意义在什么呢？对于这道题在高考中出现的可能性我不做解释，只能说不大。意义在于，提醒大家四个字，必须必须必须谨记的四个字：分类讨论！！！！！！！下面07年山东高考的这道导数题，对分类讨论的考察尤为经典，很具参考性，类似的题目在08、09、10年高考题中见了很多。 (22)(本小题满分14分) 设函数f(x)=x2+b ln(x+1),其中b≠0. (Ⅰ)当b> 时，判断函数f(x)在定义域上的单调性；（Ⅱ）求函数f(x)的极值点；（Ⅲ）证明对任意的正整数n,不等式ln( )都成立. 这道题我觉得重点在于前两问，最后一问..有点鸡肋了~ 这道题，太明显了对吧？

高中数学计算题专项练习

2019年高中数学计算题专项练习1 一．解答题（共30小题） 1．计算：（1）；（2）． 2．计算：（1）lg1000+log342﹣log314﹣log48；（2）． 3．（1）解方程：lg（x+1）+lg（x﹣2）=lg4；（2）解不等式：21﹣2x＞． 4．（1）计算：2×× （2）计算：2log510+log50.25． 5．计算：（1）；（2）． 6．求log89×log332﹣log1255的值． 7．（1）计算．（2）若，求的值． 8．计算下列各式的值（1）0.064﹣（﹣）0+160.75+0.25 （2）lg5+（log32）?（log89）+lg2． 9．计算：（1）lg22+lg5?lg20﹣1；

（2）． 10．若lga、lgb是方程2x2﹣4x+1=0的两个实根，求的值． 11．计算（Ⅰ）（Ⅱ）． 12．解方程：． 13．计算：（Ⅰ）（Ⅱ）． 14．求值：（log62）2+log63×log612． 15．（1）计算（2）已知，求的值． 16．计算（Ⅰ）；（Ⅱ）0.0081﹣（）+??． 17．（Ⅰ）已知全集U={1，2，3，4，5，6}，A={1，4，5}，B={2，3，5}，记M=（?U A）∩B，求集合M，并写出M的所有子集；（Ⅱ）求值：． 18．解方程：log2（4x﹣4）=x+log2（2x+1﹣5） 19．（Ⅰ）计算（lg2）2+lg2?lg50+lg25；

（Ⅱ）已知a=，求÷． 20．求值：（1）lg14﹣+lg7﹣lg18 （2）． 21．计算下列各题：（1）（lg5）2+lg2×lg50；（2）已知a﹣a﹣1=1，求的值． 22．（1）计算；（2）关于x的方程3x2﹣10x+k=0有两个同号且不相等的实根，求实数k的取值范围．23．计算题（1）（2） 24．计算下列各式：（式中字母都是正数）（1）（2）． 25．计算：（1）；（2）lg25+lg2×lg50+（lg2）2． 26．已知x+y=12，xy=27且x＜y，求的值． 27．（1）计算：；

(完整word版)高中数学压轴题系列——导数专题——双变量问题(2).docx

高中数学压轴题系列——导数专题——双变量问题（ 2） 1.（2010?辽宁）已知函数 f （x ） =（ a+1）lnx+ax 2 +1 （1）讨论函数 f （x ）的单调性；（2）设 a ＜﹣ 1．如果对任意 x 1，x 2∈（ 0，+∞），| f （ x 1）﹣ f （ x 2）| ≥ 4| x 1﹣ x 2 | ，求 a 的取值范围．解：（Ⅰ ）f （x ）的定义域为（ 0，+∞） . ．当 a ≥0 时， f ′（x ）＞ 0，故 f （ x ）在（ 0，+∞）单调递增；当 a ≤﹣ 1 时， f ′（ x ）＜ 0，故 f （ x ）在（ 0， +∞）单调递减；当﹣ 1＜ a ＜0 时，令 f ′（ x ） =0，解得．则当时， f'（ x ）＞ 0；时， f' （ x ）＜ 0．故 f （x ）在单调递增，在单调递减．（Ⅱ）不妨假设 x 1≥ 2，而＜﹣ ，由（ Ⅰ）知在（ 0， ∞）单调递减， x a 1 + 从而 ? x 1， 2∈（， ∞）， | f （ 1）﹣ （ 2） ≥ 4| x 1﹣ 2 | x 0 + x f x | x 等价于 ? x 1， 2∈（， ∞）， f （ 2 ） 2 ≥ （ 1 ） 1 ① x 0 + x +4x f x +4x 令 g （ x ）=f （ x ） +4x ，则 ①等价于 g （x ）在（ 0，+∞）单调递减，即．从而故 a 的取值范围为（﹣∞，﹣ 2] ．（ 12 分） 2．（ 2018?呼和浩特一模）已知函数 f （x ） =lnx ， g （ x ） = ﹣ bx （b 为常数）．（Ⅰ）当 b=4 时，讨论函数 h （x ）=f （x ）+g （x ）的单调性；（Ⅱ） b ≥2 时，如果对于 ? x 1，x 2∈（ 1， 2] ，且 x 1≠ x 2，都有 | f （x 1）﹣ f （ x 2）| ＜| g （x 1）﹣ g （x 2） | 成立，求实数 b 的取值范围．解：（ 1）h （ x ）=lnx+ x 2﹣bx 的定义域为（ 0，+∞），当 b=4 时， h （ x ）=lnx+ x 2 ﹣4x ， h'（x ）= +x ﹣4= ，令 h'（x ） =0，解得 x 1 ﹣ ， 2 ，当 ∈（ ﹣ ， 2+ ）时， ′（）＜， =2 x =2+ x2 h x 0 当 x ∈（ 0， 2﹣ ），或（ 2+ ，+∞）时， h ′（x ）＞ 0，所以， h （x ）在∈（ 0， 2﹣ ），或（ 2+ ，+∞）单调递增；在（ 2﹣ ， 2+ ）单调递减；（Ⅱ）因为 f （ x ）=lnx 在区间（ 1，2] 上单调递增，

(推荐)高中数学计算题专项练习一

高中数学计算题专项练习一

高中数学计算题专项练习一一．解答题（共30小题） 1．（Ⅰ）求值：；（Ⅱ）解关于x的方程． 2．（1）若=3，求的值；（2）计算的值． 3．已知，b=（log43+log83）（log32+log92），求a+2b的值．4．化简或计算：（1）（）﹣[3×（）0]﹣1﹣[81﹣0.25+（3）]﹣10×0.027；（2）． 5．计算的值． 6．求下列各式的值．（1）（2）已知x+x﹣1=3，求式子x2+x﹣2的值． 7．（文）（1）若﹣2x2+5x﹣2＞0，化简：（2）求关于x的不等式（k2﹣2k+）x＜（k2﹣2k+）1ˉx的解集． 8．化简或求值：

（1）3a b（﹣4a b）÷（﹣3a b）；（2）． 9．计算：（1）；（2）（lg8+lg1000）lg5+3（lg2）2+lg6﹣1+lg0.006． 10．计算（1）（2）． 11．计算（1）（2）． 12．解方程：log2（x﹣3）﹣=2． 13．计算下列各式（Ⅰ）lg24﹣（lg3+lg4）+lg5 （Ⅱ）． 14．求下列各式的值：（1）（2）． 15．（1）计算（2）若xlog34=1，求4x+4﹣x的值． 16．求值：． 17．计算下列各式的值

（1）0.064﹣（﹣）0+160.75+0.25 （2）lg25+lg5?lg4+lg22． 18．求值：+．19．（1）已知a＞b＞1且，求log a b﹣log b a的值．（2）求的值． 20．计算（1）（2）（lg5）2+lg2×lg50 21．不用计算器计算：． 22．计算下列各题（1）；（2）． 23．解下列方程：（1）lg（x﹣1）+lg（x﹣2）=lg（x+2）；（2）2?（log3x）2﹣log3x﹣1=0． 24．求值：（1）（2）2log525﹣3log264． 25．化简、求值下列各式：（1）?（﹣3）÷；（2）（注：lg2+lg5=1）． 26．计算下列各式（1）；（2）．

(完整)高中数学选择填空题专项训练

综合小测1 一、选择题 1.函数y =2x +1的图象是 2.△ABC 中，cos A = 135，sin B =53 ,则cos C 的值为 A. 65 56 B.－6556 C.－6516 D. 65 16 3.过点（1，3）作直线l ，若l 经过点（a ,0）和(0,b )，且a ,b ∈N*，则可作出的l 的条数为 A.1 B.2 C.3 D.多于3 4.函数f (x )=log a x (a ＞0且a ≠1)对任意正实数x ,y 都有 A.f (x ·y )=f (x )·f (y ) B.f (x ·y )=f (x )+f (y ) C.f (x +y )=f (x )·f (y ) D.f (x +y )=f (x )+f (y ) 5.已知二面角α—l —β的大小为60°，b 和c 是两条异面直线，则在下列四个条件中，能使b 和c 所成的角为60°的是 A.b ∥α,c ∥β B.b ∥α,c ⊥β C.b ⊥α,c ⊥β D.b ⊥α,c ∥β 6.一个等差数列共n 项，其和为90，这个数列的前10项的和为25，后10项的和为75，则项数n 为（） A.14 B.16 C.18 D.20 7.某城市的街道如图，某人要从A 地前往B 地，则路程最短的走法有 A.8种 B.10种 C.12种 D.32种 8.若a ,b 是异面直线，a ?α,b ?β,α∩β=l ，则下列命题中是真命题的为 A.l 与a 、b 分别相交 B.l 与a 、b 都不相交 C.l 至多与a 、b 中的一条相交 D.l 至少与a 、b 中的一条相交

9.设F 1，F 2是双曲线4 2 x －y 2=1的两个焦点，点P 在双曲线上，且1 PF ·2PF =0，则|1 PF |·|2PF |的值等于 A.2 B.22 C.4 D.8 10.f (x )=(1+2x )m +(1+3x )n (m ,n ∈N*)的展开式中x 的系数为13，则x 2的系数为 A.31 B.40 C.31或40 D.71或80 11.从装有4粒大小、形状相同，颜色不同的玻璃球的瓶中，随意一次倒出若干粒玻璃球（至少一粒），则倒出奇数粒玻璃球的概率比倒出偶数粒玻璃球的概率 A.小 B.大 C.相等 D.大小不能确定 12.如右图，A 、B 、C 、D 是某煤矿的四个采煤点，l 是公路，图中所标线段为道路，ABQP 、BCRQ 、CDSR 近似于正方形.已知A 、B 、C 、D 四个采煤点每天的采煤量之比约为5∶1∶2∶3，运煤的费用与运煤的路程、所运煤的重量都成正比.现要从P 、Q 、R 、S 中选出一处设立一个运煤中转站，使四个采煤点的煤运到中转站的费用最少，则地点应选在 A.P 点 B.Q 点 C.R 点 D.S 点题号 1 2 3 4 5 6 7 8 9 10 11 答案二、填空题 13.抛物线y 2=2x 上到直线x －y +3=0距离最短的点的坐标为_________. 14.一个长方体共一顶点的三个面的面积分别是2，3，6，这个长方体对角线的长是_________. 15.设定义在R 上的偶函数f (x )满足f (x +1)+f (x )=1,且当x ∈［1,2］时，f (x )=2－x ,则f (8.5)=_________.

高考数学压轴题系列训(共六套)(含答案及解析详解)

高考数学压轴题系列训练一（含答案及解析详解） 1．（12分）已知抛物线、椭圆和双曲线都经过点()1,2M ，它们在x 轴上有共同焦点，椭圆和双曲线的对称轴是坐标轴，抛物线的顶点为坐标原点. （Ⅰ）求这三条曲线的方程；（Ⅱ）已知动直线l 过点()3,0P ，交抛物线于,A B 两点，是否存在垂直于x 轴的直线l '被以AP 为直径的圆截得的弦长为定值？若存在，求出l '的方程；若不存在，说明理由. 解：（Ⅰ）设抛物线方程为()220y px p =>，将()1,2M 代入方程得2p = 24y x ∴= 抛物线方程为: ………………………………………………（1分）由题意知椭圆、双曲线的焦点为()()211,0,1,0,F F -∴ c=1…………………（2分）对于椭圆， 1222a MF MF =+ + ( 2 2 2222211321 a a b a c ∴=∴=+=+∴=-=+∴= 椭圆方程为：………………………………（4分）对于双曲线，1222a MF MF '=-= 2222221321 a a b c a '∴=-'∴=-'''∴=-=∴= 双曲线方程为：………………………………（6分）（Ⅱ）设AP 的中点为C ，l '的方程为：x a =，以AP 为直径的圆交l '于,D E 两点，DE 中点为H 令()11113,,,22x y A x y +?? ∴ ?? ? C ………………………………………………（7分） ()111231 23 22 DC AP x CH a x a ∴= =+=-=-+

()()( )22 2 2 2 2111212 1132344-23246222 DH DC CH x y x a a x a a a DH DE DH l x ????∴=-= -+--+??? ?=-+==-+=∴=='= 当时,为定值; 此时的方程为： …………（12分） 2．（14分）已知正项数列{}n a 中，16a = ，点(n n A a 在抛物线21y x =+上；数列{}n b 中，点(),n n B n b 在过点()0,1，以方向向量为()1,2的直线上. （Ⅰ）求数列{}{},n n a b 的通项公式；（Ⅱ）若()()() n n a f n b ??=???, n 为奇数, n 为偶数，问是否存在k N ∈，使()()274f k f k +=成立，若存在，求出k 值；若不存在，说明理由；（Ⅲ）对任意正整数n ，不等式 1 120111111n n n a b b b +≤?????? +++ ? ??????? ?? 成立，求正数a 的取值范围. 解：（Ⅰ）将点(n n A a 代入21y x =+中得 ()11111115:21,21 n n n n n n a a a a d a a n n l y x b n ++=+∴-==∴=+-?=+=+∴=+ 直线 …………………………………………（4分）（Ⅱ）()()()521n f n n ?+?=?+??, n 为奇数, n 为偶数………………………………（5分） ()() ()()()()27274275421,4 2735 227145,2 4k k f k f k k k k k k k k k k ++=∴++=+∴=+∴+ +=+∴==当为偶数时，为奇数，当为奇数时，为偶数，舍去综上，存在唯一的符合条件。 ……………………（8分）（Ⅲ）由 1 120111111n n n a b b b +- ≤?????? +++ ? ??????? ??

必修一函数压轴题

函数压轴题一、函数的性质 1.已知函数)1 ()(x x e e x x f - =，若f (x 1)x 2 B ．x 1＋x 2＝0 C ．x 1