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《高等数学、大学英语》综合模拟题

《高等数学、大学英语》综合模拟题
《高等数学、大学英语》综合模拟题

高等数学部分:

一、选择题: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. 极限()220ln 1lim

x x x →+=( B ) A.1

2 B. 1 C. 2 D. e

2. 若2)(2+=x e x f ,则=)0('f ( C )

A. 1

B. e

C. 2

D. 2e

3. 设函数)3)(2)(1()(---=x x x x x f ,则)0('f 等于( B )

A .0

B .6-

C .1

D .3

4.设,则等于( C )

A. B.

C. D. 5.设,2sin

x e y =则=dy ( B ) A .x d e x 2sin B .x d e x 2sin sin 2 C .x xd e x sin 2sin 2sin D .x d e x sin 2sin

6.若事件A 发生必然导致事件B 发生,则事件A 和B 的关系一定是( A ) A. B. C. 对立事件 D.互不相容事件

7. 极限x

x x x x cos cos lim +-∞→( A ) A .等于1 B .等于0 C .为无穷大 D .不存在

8.设',)(',)()(y x f e e f y x f x 则存在且==( C )

A .)()()()('x f x x f x e e f e e f +

B .)(')(')(x f e e f x f x ?

C .)(')()(')()(x f e e f e e f x f x x f x x ?++

D .)()('x f x e e f

二、填空题:把答案填在题中的横线上.

9.设函数2,

||1(),1,

||1x f x x ≤?=??>则f [f(1)]= . 10.已知33lim 1nk

n e n -→∞??+= ??

?,则k= . 11.曲线y=3x 5-5x 4+4x-1的拐点是 .

12.函数()arctan f x x x =-在闭区间[-1,1]上的最大值是 .

13.设函数,则 . 14. .

15.若则 .

16.已知,则 .

9.1 10.-9 11. (1,1) 12.

13. ; 14. ;

15. 16.1.

三、解答题:解题应写出推理、演算步骤.

17.计算1ln e

x xdx ?. 18.设的一个原函数为,求.

19.设函数,求.

20.设函数z=xy+f(u),u=y 2-x 2,其中f 是可微函数. 证明:22z z y

x x y x y ??+=+??. 21.求nx

mx x sin sin lim π→,其中n m ,为自然数. 22.甲、乙两袋装有大小相同的红球和白球,甲袋装有2个红球,2个白球;乙袋装有2个红球,n 个白球.由甲,乙两袋中各任取2个球.

(Ⅰ)若n=3,求取到的4个球全是红球的概率;(Ⅱ)若取到的4个球中至少有2个红球的概率为4

3,求n.

23.求由曲线及围成的平面图形的面积S 以及此平面图形绕x 轴旋转一周所得旋转体的体积.

参考答案:

17. 解:2111ln ln 2e e

x xdx xdx =??211

ln 122e

e

x x xdx =-?

2

21

124e

e x =-

21

44

e =+ 18.

解:因为,所以

19.

解:因为

所以

20. 解:证明:z

()(2)y f u x x ?'=+-?,

()(2)z x f u y y ?'=+? 2222=2()2()=z

z y x y xyf u x xyf u x

y x y ??''+=-++??=+左边右边

21. 解:令,π-=x t n m n nt m mt nx

mx

n m t x -→→-=++=)1()sin()sin(lim sin sin lim 0πππ

22. 解:(I )记“取到的4个球全是红球”为事件A . 222

22

245111().61060C C P A C C =?=?=

(II )记“取到的4个球至多有1个红球”为事件B ,“取到的4个球只有1个红球”为事件1B ,“取到的4个球全是白球”为事件2B . 由题意,得3

1()1.44P B =-= 2111122222122224242()n n n n C C C C C C P B C C C C ++??=?+?2

2;3(2)(1)n n n =++

22222

242()n n C C P B C C +=?(1);6(2)(1)n n n n -=++

所以, 12()()()P B P B P B =+22(1)

3(2)(1)6(2)(1)n

n n n n n n -=+++++14=,

化简,得271160,n n --=解得2n

=,或37n =-(舍去),

故 2n =. 23.求由曲线及围成的平面图形的面积S 以及此平面图形绕x 轴旋转一周所得旋转体的体积. 解:由已知曲线画出平面图形如图所示的阴影区域.

由,得交点坐标为(1,1),则

大学英语部分:

Ⅰ. Phonetics

Directions: In each of the following groups of words, there are four underlined letters or letter combinations marked A, B, C and D. Compare the underlined parts and identify the one that is different from the others in pronunciation.

Mark your answer by blackening the corresponding letter on the Answer Sheet. l. A .background B .although C .blouse D .amount B

2. A .civil B .curriculum C .crystal D .country A

3. A. ground B. country C. thousand D. found B

4. A. pour B. hour C. course D. four B

Ⅱ. Vocabulary and Structure Directions: There are 10incomplete sentences in this section. For each sentence there are four choices marked A, B, C and D. Choose one answer that best completes the sentence and blacken the corresponding letter on the Answer Sheet.

5. Human beings should find a new _______ of energy . B

A. orient

B. source

C. origin

D. souse

6. The couch is comfortable to _______. D

A. sit

B. be sat

C. sitted

D. sit on

7. So loudly _______ that all the people in the room got a fright. C

A. he shouted

B. shout he

C. did he shout

D. he did shout

8. The mountain is 1,000 feet _______ the sea level. C

A. over

B. higher

C. above

D. high 9. It was a ________ room, with beautiful wall paper, 1 (1,1) -1 1 2 O

x

waxed floor and nice furniture. B

A. pleased

B. pleasant

C. pleasing

D. preasant

10. He regretted _______the decision too hastily. C

A. make

B. to make

C. making

D. have maked

11. The professor insisted that we _______ our homework before next month. C

A. handed in

B. will hand in

C. hand in

D. must hand in

12. When I was a child I used____ swimming in the lake. C

A. to going

B. going

C. to go

D. go

13. Saul’s brother left the matter entirely up to____ and____. D

A. I, he

B. him, I

C. me, he

D. him, me

14. The 19th winter Games, held in Salt Lake City, ____ an Olympic tradition which goes back almost 3 , 000 years . D

A. is the part of

B. are the part of

C. is part of

D. are part of

Ⅲ. Cloze

Directions: For each blank in the following passage , there are four choices marked A , B , C and D . Choose the one that is most suitable and mark your answer by blackening the corresponding letter on the Answer Sheet .

The most extraordinary dream I ever had was one in which I fancied that, as I was going into a theater, the cloak-room attendant__15__Me in the lobby and insisted on my __16__my legs behind. I was not surprised; but I was considerably annoyed. I said I had __17__heard of such a rule at any respectable theater __18__, and that I considered it a most absurd regulation. The man replied that he was very__19__, but that those were his instructions. People complained that they could not get to and from their __20__ comfortably, because other people’s legs were always in the__21__; and it had, therefore, been decided that __22__should leave their leg outside. It seemed to me that the management, in making this order, had gone__23__their legal right; and, under ordinary circumstances, I should have disputed it. However, I didn’t want to__24__a disturbance; and __25__I sat down and meekly prepared to comply with the demand. I had never before__26__that the human leg could be unscrewed. I had always __27__ it was more securely fixed. But the man showed me bow to undo them, and I found that they came off__28__easily.The discovery did not surprise__29__any more than the original request that I should take them off. Nothing does surprise one in a dream.

15. A. called B. helped C. stopped D. met C

16. A. leave B. leaves C. leaving D. left C

17. A. ever B. never C. once D. always B

18. A. before B. after C. during D. behind A

19. A. angry B. sorry C. friendly D. helpful B

20. A. homes B. jobs C. arms D. seats D

21. A. road B. lobby C. theater D. way D

22. A. somebody B. everybody C. anybody D. nobody B

23. A. beyond B. from C. to D. around A

24. A. understand B. make C. have D. learn B

25 . A. as B. because C. while D. so D

26. A. know B. known C. knowing D. knows B

27. A. believe B. considered C. thought D. distrusted C

28. A. quite B. much C. do D. greatly A

29. A. him B. them C. me D. us C

IV . Reading Comprehension

Directions: There are five reading passages in this part. Each passage is followed by four questions. For each question there are four suggested answers marked A, B, C and D. Choose one best answer and blacken the corresponding letter on the Answer Sheet.

Passage One

Are you aware that you actually possess six senses? The sixth is a muscular sense responsible for directing your muscles intelligently to the exact extent necessary for each action you perform.

For example, when you reach for an object, the sensory nerves linking the muscles to the brain stop your hand at the correct spot. This automat is perception of the position of your muscles in relation to the object is your muscular sense in action.

Muscles are strongly bundles of fibers varying from one five-thousandth of an inch to about three inches. They have three unique characteristics, they can become shorter and thicker; they can stretch; and they can retract to their original positions. Under a high-powered microscope, muscle tissue is seen as long, slender cells with a grainy texture like wood.

More than half of a person’s body is composed of muscle fibers, most of which are involuntary—in other words, work without conscious direction. The voluntary muscles, those that we move consciously to perform particular actions, number more than five hundred. Women have only 60 to 70 percent as much muscle as men for their body mass. That is why an average woman can’t lift as much, throw as far, or hit as hard as an average man.

30. According to the selection, the muscular sense is responsible for ______.C

A. the efficiency of our muscles

B. the normal breathing function

C. directing our muscles intelligently

D. the work of only our involuntary muscles

31. Intelligent use of the muscles means that ________.C

A. one always knows what his muscles are doing

B. one performs simple actions without working

C. one’s muscles are used only to the extent necessary for each action they perform

D. one improves muscular action consciously

32. Muscles are unique fibers because, they can ________.D

A. contract

B. stretch

C. retract

D. do all of the above

33. Under a microscope, muscle cells appear to be _______.A

A. textured like wood

B. colored like wood

C. smooth and red

D. short and thick

Passage T wo

“Fingers were made before forks” when a person gives up good manners, puts aside knife and fork, and dives into his food, someone is likely to repeat that saying.

The fork was an ancient agricultural tool, but for centuries no one thought of eating with it. Not until the eleventh century, when a young lady from Constantinople brought her fork to Italy, did the custom reach Europe.

By the fifteenth century the use of the fork was widespread in Italy. The English explanation was that Italians wer e averse to eating food touched with fingers, “Seeing all men’s fingers are not alike clean.” English travelers kept their friends in stitches while describing this ridiculous Italian custom.

Anyone who used a fork to eat with was laughed at in England for the next hundred years. Men who used forks were thought to be sissies, and women who used them were called show-offs and overnice. Not until the late 1600’s did using a fork become a common custom.

34. The custom of eating with a fork w as _______.C

A. brought to Europe from America

B. begun when forks were invented

C. brought to Europe from Asia

D. invented by Italians

35. By the fifteenth century forks were used _______.A

A. all over Italy

B. only in Constantinople

C. widely in Europe

D. In England

36. To English travelers in Italy, the use of forks seemed _______.D

A. clever

B. necessary

C. good manner

D. ridiculous

37. The English thought that Italians used forks in order to ________.B

A. imitate the people of the East

B. keep their food clean

C. impress visitors with their good manners

D. amuse the English

Passage Three

What’s the best way to protect a tender, green seedling from the hungry stomach of deer? Give the seedling bad breath!

The same chemical that gives people bad breath after they have eaten garlic can save small trees from being eaten by animals.

A kind of chemical selenium(硒), which is also found in garlic, is planted in the soil near a young tree. The tree’s roots absorb the selenium which is then c arried to the leaves.

From there the selenium is used to form a chemical called dimethyl selenide (乙烷硒化物)—the same chemical made in the human mouth after eating garlic. As deer wander around looking for food, they smell the seedlings’ leaves and leave the plants alone.

The selenium is important. Why? Because each year deer eat millions of dollars’ worth of trees farm seedlings.

So far, selenium has been tested only on Douglas fir (枞树) seedlings, but researchers think they could protect fruit trees and garden plants, too.

38. When people eat garlic, ________.A

A. they send out a horrible smell

B. they are out of breath

C. they will feel sick

D. it is hard for them to breathe

39 According to this passage the bad smell given off from those leaves is that of ______.B

A. the young trees absorb garlic

B. the roots of the young trees smell like garlic

C. the young trees aren’t fit for the deer to eat

D. the leaves of the young trees smell like garlic

40. Up till the time the news was announced, this kind of chemical was used _______.D

A. all over the world

B. all over the United States

C. on fruit trees and garden trees

D. on Douglas fir young trees

41. The best title of this passage is ________.C

A. Hungry Deer and Y oung Trees

B. Why Don’t Deer Eat Y oung Fruit Trees

C. Plants Saved by “Bad Breath”

D. How to Protect Y oung Trees

Passage Four

I was only eight years old when the Second World War ended, but I can still remember something about the victory celebrations in the small town where I lived on the day when the war in Europe ended. We had not suffered much from the war there. But both at home and at school I had become accustomed to the phrases "before the war" and "when the war’s over". " Before the war " , apparently , things had been better , though I was too young to understand why , except that there had been no bombs then , and people had eaten things like ice-cream and bananas, which I had only heard of . When the war was over we would go back to London, but this meant little to me. I did not remember what London was like.

What I remember now about VE (Victory in Europe) Day was the May evening. After dinner I said I wanted to see the bonfire(大火堆), so when it got dark my father took me to the end of the street. The bonfire was very high, and somehow people had collected some old clothes to dress the unmistakable figure with the moustache(胡子)they had to put on top of it. Just as we arrived, they set light to it. The flames rose and soon swallowed the "guy". Everyone was cheering and shouting, and an old woman came out of her house with two chairs and threw them on the fire to keep it going.

I stood beside my father until the fire started to go down, not knowing what to say. He said

nothing, either. He had fought in the First World War and may have been remembering the end of that. At last he said, " Well, that’s it, son. Let’s hope that this time it really will be

the last one."

42. Where did the author live before the Second World War? A

A. In London.

B. In a small town.

C. In Europe.

D. In the countryside.

43. The unmistakable figure with the moustache most probably represents____. D

A. those who died in the war

B. those who had won

C. an imaginary figure

D. the most hated person in the war-Hitler

44. Which of the following statements is true? B

A. The author's father built a bonfire on VE Day.

B. The author's father had fought in the First World War.

C. The author's father had fought in the Second World War.

D. The author's father threw two chairs on the fire to keep it going.

45. By saying" Let’s hope that this time it really will be the last one", the father meant that____ C

A. he wished people had not built the bonfire

B. he hoped people would not build any more bonfires

C. he hoped there would be no more wars in the world

D. he wished the Second World War had not happened

V. Daily Conversation Directions : Pick out five appropriate expressions from the eight choices below and complete the following dialogue by blackening the corresponding letter on the Answer Sheet ·

A. Maybe I should call a taxi

B. can you help me

C. it’s the second left

D. not really

E. at the traffic lights

F. Not at all

G. Museum Drive H. Thanks again

Tourist: Excuse me, __46_ B _? I’m lost! Person: Certainly, where would you like to go? Tourist: I’d like to go to the museum, but I can’t find it. Is it far? Person: No, __47_D_. It’s about a 5 minute walk. Now, go along this street to the traffic lights.

Do you see them? Tourist: Y es, I can see them. Person: Right, __48_E_, turn left into Queen Mary A venue. Tourist: Queen Mary A venue. Person: Right. Go straight on. Take the second left and enter Museum Drive. Tourist: OK .Queen Mary A venue, straight on and then the second left,__49_G_. Person: Right. Just follow Museum Drive and the museum is at the end of the road.

Tourist: Great. Thanks for your help. Person: __50_F_.

《小学综合素质》模拟试卷及答案(二)

《小学综合素质》模拟试卷及答案(二) 一、单项选择题(共25小题,每小题2分) 1.素质教育与应试教育的区别具体表现在()。 ①对教育目的的认识不同②面向的教育对象不同③选学的教育内容不同④教育评价的标准不同⑤运用的教学方法不同 A.①②④ B.①③⑤ C.②③④ D.①②③④⑤ 2.胡锦涛总书记在对全国广大教师的几点希望中指出:“教师是知识的重要传播者和()者。” A.学习 B.点拨 C.引导 D.创造 3.当一位新手型教师把大量时间都花在如何与学生搞好个人关系时,那么在教师成长过 程中他属于()。 A.关注情境阶段 B.关注生存阶段 C.关注学生阶段 D.关注教学阶段 4.良好的师生关系是教育教学活动顺利进行的()。 A.前提条件 B.基本保证 C.必然要求 D.必然结果 5.男同学小陈平时自由散漫,学习不认真,一天在课堂上用手机给班上的女同学发短信“曾某,我爱你”,被上课的王老师发现。王老师收缴了小陈的手机,并将短信内容向全班 同学宣读,同时指责其“思想堕落,道德败坏”。下课后小陈要求王老师归还手机,王老师说,这是罪证不能归还,要交给学校德育处。校长指出王老师:①未经学生同意翻看短信侵犯了学生的隐私权;②批评的话语侵犯了学生的人格权;③收缴手机侵犯了学生的财产权;④作为老师不能以违法的方式对待学生的违纪行为。你认为校长的说法正确的是()。 A.①②③ B.②③④ C.①②④ D.①②③④

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