2016年专升本理科试题及答案(大学英语及高等数学)最新

中国地质大学(北京)继续教育学院

《大学英语、高等数学》综合试卷

一、选择题：本大题共5个小题，每小题3分，共15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，把所选项前的字母填在题后的括号内.

1. 已知集合A ＝{x |0

A ．(0,1)

B ．(0,2]

C ．(1,2)

D ．(1,2]

2. “φ＝π”是“曲线y ＝sin(2x ＋φ)过坐标原点”的( )

A ．充分而不必要条件

B ．必要而不充分条件

C ．充分必要条件

D ．既不充分也不必要条件

3. 命题“若x >1，则x >0”的否命题是( )

A ．若x >1，则x ≤0

B ．若x ≤1，则x >0

C ．若x ≤1，则x ≤0

D ．若x <1，则x <0

4. 已知直线l 1：x ＋ay ＋1＝0，直线l 2：ax ＋y ＋2＝0，则命题“若a ＝1或a ＝

－1，则直线l 1与l 2平行”的否命题为( )

A ．若a ≠1且a ≠－1，则直线l 1与l 2不平行

B ．若a ≠1或a ≠－1，则直线l 1与l 2不平行

C ．若a ＝1或a ＝－1，则直线l 1与l 2不平行

D ．若a ≠1或a ≠－1，则直线l 1与l 2平行

5. 函数y ＝x ln(1－x )的定义域为( )

A ．(0,1)

B ．[0,1)

C ．(0,1]

D ．[0,1]

6. 极限ln 1

lim

x e x x e →--的值是( ) A ．1 B ．1e

C ．0

D ．e 7.设函数，则等于（ ） A.

B.

C. D. 8. 设函数)3)(2)(1()(---=x x x x x f ，则)0('f 等于（ ）

A ．0

B ．6-

C ．1

D ．3

9.若，则等于（ ）

A. B. C. D.

10、 444.随意地投掷一均匀的骰子两次,则这两次出现的点数和为8的概率为（ ） A.365

B.364

C.363

D.362

二、填空题：本大题共5个小题，每小题3分，共15分.把答案填在题中的横线上.

11. 对于c ＞0，当非零实数a ，b 满足4a 2－2ab ＋b 2－c ＝0且使|2a ＋b |最大时，1a ＋2b ＋4c

的最小值为 ．-1 12. 已知单位向量e 1，e 2的夹角为α，且cos α＝13

.若向量a ＝3e 1－2e 2，则|a |

14. 若圆C 的半径为1，其圆心与点(1，0)关于直线y ＝x 对称，则圆C 的标准方程为 x^2+(y-1)^2=1

15.设双曲线C 经过点(2，2)，且与y 2

4－x 2＝1具有相同渐近线，则C 的方程为

；渐近线方程为

． 16. 已知直线x ＋y ＝a 与圆x 2＋y 2＝4交于A 、B 两点，且|OA →＋OB →|＝|OA →－OB →|，其中O 为坐标原点，则实数a 的值为 ．

17. 已知两个单位向量a ，b 的夹角为60°，c ＝t a ＋(1－t )b .若b ·c ＝0，则t ＝

18.在△ABC 中，若∠A ＝120°，AB →·AC →＝－1，则|BC →|的最小值是

19. 复数(1－i )(1＋i )i

在复平面内对应的点到原点的距离为

20.等比数列{a n }的前n 项和S n ＝2n －1，则a 2

1＋a 22＋…＋a 2n ＝

三、解答题：本大题共4个小题，共30分.解题应写出推理、演算步骤.

21.（本题满分7分）设函数f (x )＝a e x

ln x ＋b e x －1x ，曲线y ＝f (x )在点(1，f (1))处的切线方程为y ＝e(x －1)＋2.

(1)求a ，b ；

(2)证明：f (x )>1.．

答案：

22.（本题满分7分）已知函数f (x )＝2cos x (sin x ＋cos x )．

(1)求f ? ??

??5π4的值； (2)求函数f (x )的最小正周期及单调递增区间．

答案：

23.（本题满分7分）△ABC中，角A，B，C所对的边分别为a，b，c.已知a＝3，

cos A＝

6

3

，B＝A＋

π

2

.

(1)求b的值； (2)求△ABC的面积．

答案：

24.（本题满分9分）已知椭圆C：x2＋2y2＝4.

(1)求椭圆C的离心率；

(2)设O为原点，若点A在椭圆C上，点B在直线y＝2上，且OA⊥OB，试判断直线AB与圆x2＋y2＝2的位置关系，并证明你的结论．

答案：

25.（本题满分7分）设，求k值.

26.（本题满分7分）设函数，求.

27.（本题满分9分）从某批产品中，有放回地抽取产品二次，每次随机抽取1件，假设事件A：“取出的2件产品中至多有1件是二等品”的概率()0.96

P A ．

（1）求从该批产品中任取1件是二等品的概率p；

（2）若该批产品共100件，从中任意抽取2件，求事件B：“取出的2件产品中

至少有一件二等品”的概率()

P B．

大学英语部分：（60分）

Ⅰ. Phonetics (4 points）

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 unde the one that is different from the others in pronunciation. Mark your answer by blackening the corresponding letter on the Answer Sheet.

1. A. climb B. job C. disturb D. club

2. A. sweater B. meant C. pleasure D. pleased

3. A. drunk B. dusty C. duty D. drug

4. A. breathe B. nothing D. weather

5. A. head B. horizon

6. A. broad B. boast C. coast

7 A .civil B .curriculum D .country

8. A. started C. waited D. needed

Ⅱ. Vocabulary and Structure (10 points)

Directions: There are 10 incomplete 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.

9. We returned school late from a party and found the door of the s tudents’apartment____.

A. had closed

B. close

C. to close

D. closed

10. ---Does the man need operation at once, Doctor Li? ---Yes, only small one. But the sooner, the better.

A. an, a

B. a, a

C. an, the

D. ×, ×

11. ---I hear a traffic accident happened yesterday. Was it terrible?---Yes. A car fell over and all the people in it were badly hurt. But luckily,of them were killed.

A. neither

B. none

C. every

D. both

12. He is expected to make a speech this afternoon, ?

A. is he not

B. isn’t he

C. is not he

D.isn’t it

13. ---You can hardly swim, can you?--- . But my mother says she’ll teach me during my summer holiday.

A. Yes, I can’t

B. No, I can

C. No, I can’t

D. Yes, I can

14. ---Look at ____ animal. It’s interesting.

---Which one do you mean? ____ black one with a long tail?

A. an, The

B. an, An

C. the, The

D. the, An

15. ---What happened to Tom?

---He was crossing the street ____ a motorbike hit him from behind.

A. while

B. when

C. until

D. because

16. ---Dad, what’s the sea like?---Well, it’s large and full of water. It covers about _____ of the earth.

A. one third

B. three quarter

C. three-fourth

D. three quarters

17. ---Go and ask the waiter how much_____.

---Don’t worry. It has been _____.

A. does the meal cost, paid for

B. the meal costs, paid

C. the meal spends, paid

D. the meal costs, paid for

18. ---Does the child need any help?

---No. He is old enough to _____ himself.

A. put on

B. wear

C. dress

D. take care

19. ---There can be no life on the earth without water.

---That’s right. Water _____ everywhere.

A. needs

B. is needing

C. is needed

D. needed

20. ---Were you late ____the meeting?

---No, I arrived there ten minutes______ the meeting started.

A. for, before

B. at, before

C. for, till

D. at, after

21. ---Excuse me, but I don’t think you can take photos here.

---Sorry I ____ this is no-photo zone

A. don’t know

B. didn’t know

C. have no idea

D. haven’t known

22 ---How many English words had you learned _____ the end of last term?---Around 2000, but I’ve forgotten most of them.

A. by

B. at

C. to

D. on

23. ---Are you learning art now during your spare time?

---No. I’ve stopped _____ Chinese medicine instead.

A. to learn

B. learning

C. learn

D. studying

24. The couch is comfortable to _______.

A. sit

B. be sat

C. sitted

D. sit on

25. — Ring me at six tomorrow morning, will you?

— Why that early? I ______.

A. will be sleeping

B. have slept

C. have been sleeping

D. will sleep

26. He is the only one of the sons in the family who ______ received high education.

A. are

B. is

C. have

D. has

27. I am quite ____ her face , but I just cannot recall her name .

A. familiar at

B. familiar with

C. acquainted with

D. acquaintance

28. You’re always moaning about something or other. I wish you ____.

A. shut up

B. were shut up

C. had shut up

D. would shut up

29. Since I won the big prize, my telephone hasn’t stopped ringing. People _______ to ask how I am going to spend the money.

A. are phoning

B. phone

C. will phone

D. had phoned

30. We think of Mr. Li ______ our good friend.

A. is

B. to be

C. as

D. has been

31.—Would you like to join us in playing the game?

—I’m sorry, but my homework ______ by now.

32. The road will be blocked if there _______ another snow.

A. is

B. will be

C. to be

D. will have

Ⅲ. Reading Comprehension (16 points)

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

"The price of books for our students is just getting higher and higher and higher and,

along with the rising cost of tuition (学费), it's killing these students," said Peter Jason, a college professor. "Remember, students are one of the poorest groups of people in America. Almost half of them have at least one part-time job. In fact, one of my students has three jobs. And she still manages to have high scores and go to school full-time."

Textbook prices are usually high. Adding to that problem, many college teachers change textbooks year after year, they either upgrade to a new edition (版本) or change to a different textbook. This further hurts students because if a teacher no longer uses a textbook, that book has no resale value.

Dr. Jason decided to make life a little easier and a lot cheaper for his students by writing his own book on public speaking. "Many books have an increased price because of CD-ROMs, lots of color photographs and pictures. I talked to my students, and many of them, like me, prefer to keep things simple. So, a few years ago, I wrote my own textbook. I made sure that it was simple. Compared to most of other public speaking books, mine is half the number of pages, and one-third the price. That is $30 instead of $90. When I wrote a second edition last year, students only had to buy the 35 new pages. For only $7.00, they had almost a new book."

33. What did Dr. Jason say about students at college?

A. They are short of money.

B. They need simple books.

C. They have no part-time jobs.

D. They are trying to get high scores.

34. What does "that problem" in Paragraph 2 refer to?

A. The high prices of textbooks.

B. The low resale value of books.

C. Too many different new books.

D. No color pictures in textbooks.

35. What did Dr. Jason decide to do to help the students?

A. To choose cheaper textbooks.

B. To write a textbook himself.

C. To speak to his students

D. To use old textbooks.

36. How much does a public speaking book usually cost?

A. About 7 dollars.

B. About 30 dollars.

C. About 37 dollars.

D. About 90 dollars.

Passage Two

The Amish are often called the “Plain People.” Their home have no pictures on the walls, and no soft, comfortable furniture. The men wear dark trousers with white or blue shirts, and the women wear long dresses in dark colors. They ride in carriages pulled by horses.

The Amish have a saying: “The old way is the best way.” Although the Amish accept some new ideas- they use new medicines, for example- their way of life has not changed much in 300 years. They do not use electric lights, telephones or TVs. Almost all Amish live on farms. They do not use modern machinery (机器)，yet their farms are successful because the Amish work hard and take good care of their land and animals. Their farms are always small. The Amish think it is wrong to have more land or more money than they need to live upon. A few years ago some Amish farmers discovered oil on their land. They immediately sold their land moved away, without telling anyone about the oil.

The Amish will not buy insurance (保险) of any kind. When there is trouble, they help one another. If an Amish farmer gets sick, friends and neighbors will milk his cows and plant his fields. If a house burns down, as many as 200 men will come and build a new house in one day.

People are curious about the lives of the Amish. Every year thousands of people visit the part of Pennsylvania where most Amish live. Usually the Amish are not happy about the visitors, but they tolerate(容忍) them. Perhaps the Amish understand that the visitors want to experience, at least for a few days, the quieter, simpler Amish way of life.

37. The Amish are called the “ Plain People” because they _______________.

A. live on plains

B. live a simple life

C. do not like new ideas

D. do not care about their clothes

38. Some Amish farmers left their land after discovering oil on it because they_______.

A. didn’t want to have more money than they needed

B. found the land not suitable for farming any more

C. were afraid of getting into trouble

D. didn’t need oil in their life

39. From the passage we know that the Amish people ______.

A. want to be separated from one another

B. used to take no medicines when they got ill

C. believe in what they have been doing for 300 years

D. keep small farms because they are easier to manage

40. What can be inferred form the passage?

A. The Amish way of life is considered to be the best for Americans

B. The coming of visitors greatly improves the life of the Amish people

C. People wonder at the Amish way of life

D. The Amish people are born to tolerate others.

Three

To find out what the weather is going to be, most people go straight to the radio, television or newspaper to get an expert weather forecast. But if you know what to look for, you can use your own senses to make weather predictions.

There are many signs which can help you. For example, in fair weather the air pressure is generally high. The air is still and often full of dust. Faraway objects may look hazy. But when a storm is brewing, the pressure drops and you are often able to see things more clearly.

Sailors took note of this long ago and came up with a saying "The farther the sight, the nearer the rain."

Your sense of smell can also help you detect weather changes. Just before it rains, odors

become stronger. This is because odors are repressed in a fair, high-pressure center. When a bad weather low moves in, air pressure lessens and odors are released.

You can also hear an approaching storm. Sounds bounce off heavy storm clouds and return to earth with increased force. An old saying describes it this way:" Sounds traveling far and wide, a storm day will betide."

And don’t scoff if your grandmother says she can feel a storm coming. It is commonly known that many people feel pains in their bones or in corns and bunions when the humidity rises, the pressure drops, and bad weather is on the way.

41. According to the passage, as a storm approaches, faraway objects look ____.

A. hazy because of dust in the air

B. clearer because air pressure is high

C. clearer because air pressure is dropping

D. distorted because of storm clouds

42. In the last paragraph, the writer implies that ____.

A. the idea of feeling a coming storm is foolish

B. older people know a lot about weather

C. it is possible , but unlikely , that people feel aches when a storm is coming

D. it is definitely true that some people can feel coming weather changes

43. The underlined word "repressed" in paragraph 3 is close to ____ in meaning.

A. crush

B. restrict

C. lower

D. struggle

Ⅳ. Daily Conversation (15 points)

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 ·

——Sara, I’ve been looking forward to our yearly camp out for 3 weeks.44 F. Camping under the stars. This is the life.

——Yeah. But Paul, 45 B . The weatherman said it was going to rain later tonight. ——Nothing can prevent our adventure. Those weather report are never right. ——46 A.

——Ah. Don’t worry.

——Paul, Paul. Did you remember to bring our raincoats just in case, like I told you. ——Uh…no. I left them at home.

——47 E .

——How about playing a card game ?

——Uhh. I left them next to the picnic table. Hey, you want to me to go out in this rain and get them?

——No. That’s Ok.48 G .

——Well, we could go down the mountain and stay at that hotel we passed on the way up.

V. Writing(15 points)

Directions: For this Part, you are supposed to write a notice in English in 100-120 words based on the following situation . Remember to write it clearly.

49以行政管理部门（Administration Office ）的名义写一份考试延期的通知。其内容如下：（l）原考试日期、地点；（2）延期至何时、何地；

（3）延期的原因；（4）涉及的对象。

50、现在诸多的电子辞典及相关翻译软件被开发出来，人们不再需要翻阅厚重的字典

2）有人认为以后机器翻译会完全取代人工翻译

3）你是否同意这种观点，为什么？