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怀化市2008届高三第一次模拟考试试卷
英 语
命题: 宫可成 审题: 佘长保、禹细保、邓全生、彭小华
本试题卷分四个部分， 共10页。 时量120分钟。满分150分。
第一部分 听力(共三节，满分30分)
做听力部分时，请先在试卷上作答。听力部分结束前，你将有两分钟的时间将第1至第16小题的答案转涂到答题卡上，将第17至第20小题的答案转写到答题卡上。
第一节(共5小题，每小题1.5分，满分7.5分)
听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试题卷的相应位置。听完每段对话后，你都有10秒钟的时间来回答有关问题和阅读下一小题。每段对话仅读一遍。
例：How much is the shirt?
A.￡19.15. B.￡9.15. C.￡9.18.
答案是B．
1. How will the two people go to
A. By bus. B. By car. C. By air.
2. Where does the conversation take place?
A. In a hospital. B. In a library. C. In a museum.
3. What does the man suggest the woman do?
A. Go on a diet. B. Eat more fruit and vegetables. C. Take enough exercise.
4. How much will the woman pay?
A. 36 dollars. B. 32 dollars. C. 40 dollars.
5. Why does nothing appear on the screen?
A. There’s something wrong with the screen. B. The woman forgot to turn on the power.
C. There’s something wrong with the button.
第二节(共12小题；每小题1.5分，满分18分)
听下面4段对话。每段对话后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试题卷的相应位置。听每段对话前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出5秒钟的作答时间。每段对话读两遍。
听下面一段对话，回答第6和第8三个小题
6. What’s the probable relationship between the two speakers?
A. Mother and son. B. Doctor and patient. C. Teacher and student.
7.When did Mrs Smith see Jack’s parents?
A. Yesterday. B. This morning. C. The day before yesterday.
8. What can we know from the dialogue?
A.
Jack is telling the truth. B.
Jack is lying. C.
Jack is in
听下面一段对话，回答第9至第11三个小题
9. Why does the woman want to see her boss?
A. To ask him to take her husband to hospital. B. To ask him to look after her baby.
C. To ask him to allow her a few days off.
10. What is the woman going to do?
A. To look after her son. B. To see a doctor.. C. To go to hospital.
11. Where does the conversation take place?
A. In the street. B. At the man’s office. C. At a hospital.
听下面一段对话，回答第12至第14三个小题
12.What will they put on a show for?
A. For money. B. For others. C. For fun.
13. How many people will appear in the play?
A. Three. B. Four. C. Five.
14.What can we learn about the man?
A. He’ll sing and dance in the show. B. He sings pop songs for money. C. He once got up a stage.
听下面一段对话，回答第15至第17三个小题
15.What are they doing?
A. They are watching TV at home. B. They’re talking about a match.
C. They’re watching a match on the playground.
16.How does the woman find the match?
A. It’s very rough. B. It’s very interesting. C. It’s very exciting.
17.Why does the woman want to go home early?
A. Because she isn’t interested in American football.
B. Because she doesn’t like a soccer game.
C. Because she can’t wait for so long.
第三节 （共3小题，每小题1.5分，满分4.5分）
听下面一段材料，将第18至第20三个小题的信息补充完整，每个小题不超过三个单词，听材料前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题将给出15秒钟的作答时间。本段材料读两遍。
The Evening News
What
18._____________people were badly hurt in the accident this morning.
Why
Because a fast-moving truck hit 19.________________.
When
There are two accidents 20._______________.
第二部分 英语知识运用（共两节，满分45分）
第一节 单项填空(共15小题；每小题1分，满分15分)
从A、B、C、D四个选项中，选出可以填人空白处的最佳选项。
例： It is generally considered unwise to give a child _____ he or she wants.
A. however B. whatever C. whichever D. whenever
答案是B。
21.―It’s
time to tidy your room, Mike！
―See the tidy room, Mum! ____ is
where it should be.
A. Something B. Anything C. Everything D. Nothing
22.－Has John arrived yet?
－No, she
_____ an hour ago.
A. was supposed to come B. must have come
C. should come D. ought to have come
23.They suggest __________ to a lawyer before I do anything.
A. me talk B. me to talk C. my talking D. I will talk
24.It was ________ World War II _______ the importance of Fleming’s discovery was fully recognized.
A. not until; that B. not until; when C. until; that D. until; when
25.Everyone was on time for the
meeting ―______Chris, who's is usually ten
minutes late for everything.
A. but B.
only C.
even D.
yet
26.Ten
dollars____ a big sum for a small child, and they will go a long way.
A .are B.
being C.
have D.
is
27.How many years will have to pass ______ scientists succeed in providing a
treatment for cancer?
A. when B. before C. since D. until
28.－What’s Shanghai like?
－Oh, it is
____ New York of China.
A. a B.
the C.
an D.
/
29.－Sorry, Joe. I didn’t mean to…
－Don’t call me “Joe”. I am Mr Parker to you, and ____ you forget it！
A. do B. didn’t C. did D. don’t
30. ______, I have never seen anyone who’s as wise as John.
A. As long as I have traveled B. Now that I have traveled so much
C. As I have traveled so much D. Much as I have traveled
31. If we have illegal immigrants _____ in, many local workers will lose their jobs.
A. came B. coming C. to come D. having come
32. Villagers here depend on the fishing industry, _____ there won’t be much work.
A. where B. that C. by which D. without which
33. Officials say that few patients _____ with the virus owing to the effective prevention.
A. infected B. are infected C. have infected D. be infected
34.The melon served by the Smiths at dinner would have tasted _____if it had been put in the fridge for a
little while.
A. tasty B. tastier C. tastiest D. the tastiest
35.The coal mine accident, which we are eager to see _______, should have attracted the government’s
attention.
A . solved B. solving C. solve D. to solve
第二节 完形填空(共20小题；每小题1.5分，满分30分)
阅读下面短文，掌握其大意，然后从36～55各题所给的四个选项(A、B、C和D)中，选出最佳选项。
Homebuyers nationwide are watching housing prices go up, up, and up. “How high can they go?” is the question on everyone’s lips. “It’s 36 ,” said Tim, who is looking for a house near the beach. “In 1993, I 37 my first place, a two-bedroom condominium(公寓)in Venice, for $70,000. My friends thought 38 that I was overpaying. Five years later, I had to move. I sold it for $230,000, which was a nice 39 . Last year, while visiting friends here, I saw in the local paper that the exact same condominium was 40 for $510,000!”
It is a
seller’s market. Homebuyers feel like they have to 41 at least 10 percent more than the
asking 42 . Donna, a new
owner of a one-bedroom condominium in
Tim says he
hopes he doesn’t get 45 desperate(绝望的). “Whether
you decide to buy or not, you still feel like you made the wrong 46 . If you buy, you feel like you 47 . If you don’t buy, you want to kick
yourself for
Everyone says
the bubble(泡沫)has to 49 sometime, but everyone hopes it will
burst the day 50 they sell
their house. Even government officials have no idea what the 51 will bring. “What goes up must come
down,” said the state director of housing. “ 52 , as we all know, housing prices
always
36. A. unfair B. reasonable C. crazy D. suitable
37. A. bought B. prepared C. hired D. sold
38. A. afterwards B. finally C. firstly D. then
39. A. profit B. action C. challenge D. chance
40. A. no longer B. for sale C. once again D. up to
41. A. demand B. charge C. earn D. offer
42. A. wealth B. price C. content D. debt
43. A. which B. when C. where D. what
44. A. ashamed of B. pleased with C. tired of D. puzzled about
45. A. always B. that C. still D. almost
46. A. explanation B. decision C. comparison D. suggestion
47. A. failed B. corrected C. overpaid D. misunderstood
48. A. grasping B. accepting C. refusing D. demanding
49. A. burst B. appear C. continue D. exist
50. A. before B. when C. until D. after
51. A. future B. hope C. market D. worry
52. A. Yet B. But C. Therefore D. Besides
53. A. go up B. look away C. turn back D. stay up
54. A. lose B. start C. move D. perform
55. A. hunted for B. competed for C. paid for D. went for
第三部分：阅读理解（共20小题；每小题2分，满分40分）
第一节：选择题（共17小题：每小题2分，满分34分））
阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项。
A
It was Thanksgiving morning and in the crowded kitchen of my small home I was busy preparing the traditional Thanksgiving turkey when the doorbell rang. I opened the front door and saw two small children in rags huddling(拥挤)together inside the storm door on the top step.
“Any old papers, lady?” asked one of them.
I was busy. I wanted to say “no” until I looked down at their feet. They were wearing thin?little sandals(便鞋), wet with heavy snow.
“Come in and I’ll make you a cup of hot cocoa.”
They walked over and sat down at the table. Their wet sandals left marks upon the floor. I served them cocoa and bread with jam to fight against the cold outside. Then I went back to the kitchen and started again on my household budget.
The silence in the front room struck me. I looked in. The girl held the empty cup in her hands, looking at it. The boy asked in a flat voice, “Lady, are you rich?”
I looked at my shabby slipcovers(沙发套). The girl put her cup back in its saucer(茶碟)carefully and said, “Your cups match your saucers.” Her voice was hungry with a need that no amount of food could supply. They left after that, holding their bundles of papers against the wind. They hadn’t said “Thank you.” They didn’t need to. They had reminded me that I had so much for which to be grateful. Plain blue china cups and saucers were only worth five pence. But they matched.
I tasted the potatoes and stirred the meat soup. Potatoes and brown meat soup, a roof over our heads, my man with a good steady job ? these matched, too.
I moved the chairs back from the fire and cleaned the living room. The muddy prints of small sandals were still wet upon my floor. Let them be for a while, I thought, just in case I should begin to forget how rich I am.
56. Two children came to the writer’s front door because .
A. it was Thanksgiving Day. B. they were beggars
C. they wanted old papers D. they wanted a cup of cocoa
57. Why did the writer let the children in?
A. She showed great pity on them. B. She had old papers to sell.
C. She wanted to invite them to dinner. D. She wanted them to see how rich she was.
58. From the passage, we can infer that whether you are rich depends on .
A. how much money you have had B. how you feel about your life
C. how you have helped others D. what job your husband is doing
59. The writer left the muddy prints of small sandals on the floor for a while to .
A. show her husband that someone had come B. remind her that she had helped two children
C. remind her that she was very once rich D. remind her how life should be
B
Small discoveries in
Clues that the little people may have lived long ago
were first revealed last year in the scientific journal Nature. Scientists said that they had found the bones of a
three-foot-tall female on the
Now the team is saying it has unearthed even more pieces of the puzzle, including a jawbone and parts of arms, legs and hands from several individuals, as well as stone tools. They reported their find in Nature this month. “The new evidence makes it very clear that these people are a new species, distinct from modern humans,” Peter Brown, a scientist on the team, said. They named these ancient humans Homo floresiensis.
Brown says that these little people lived as recently as 12,000
years ago. If Homo floresiensis was a
different species from modern humans, that would make our family tree bigger
than we knew. It means, says Brown, that “until recently, a relative shared the
planet with us.”
Many scientists think a new species is unlikely. Some argue that the bones must have belonged to modern humans whose small size was the result of a genetic problem.
Daniel E. Lieberman, a scientist at
60. Researchers name the skeleton Hobbit because _____.
A. it is a figure described in the Lord of the Rings B. it resembles the tiny heroes in a set of books
C. it proves to be a full-grown adult D. it belongs to an ancient human species
61. Small discoveries in
A. are revealed in the scientific journal Nature B. are made by Peter Brown, a famous scientist
C. are about ancestors of modern humans D. might provide new evidence for human study
62. According to Daniel E. Lieberman, _____.
A. Homo floresiensis doesn’t exist B. disagreement leads to further research
C. the investigation hasn’t begun yet D. our family tree is bigger than we knew
63. Which of the following might be the best title of the passage?
A. Comparison between Different Peoples B. Arguments over Human Origin
C. Discovery of a Possible New Human Species D. History of Indonesian People
C
 |
 |
64. What does Passage ① tell us about the boy?
A. He was injured in the head when he was 14.
B. He has waited for the payout for a long time.
C. He has lived in the same place since the accident.
D. He was run over by a taxi when riding on the pavement.
65. What can we learn about Lee and Collier counties from Passage②?
A. They both became safe places. B. They won the same place in a race.
C. They had the same number of accidents. D. They joined hands in reducing accidents.
66. What is SB 36?
A. An agreement. B. A law. C. A result of the accidents D. Traffic rules.
67. Which passage would give more information on the prevention of road accidents?
A. ① B. ② C. ③ D. ④
D
Every year, the American Library
Association honors artists and writers of books for children. One of these
honors is the Newbery Award. It is named after a book seller in
The Newbery Medal winner for 2006 is Lynne Rae Perkins for writing Criss Cross. Her book is about four teenagers in a small town. They are trying to find the meaning of life and love. They are fourteen years old. Criss Cross is written in several different ways. Sometimes it is like a song. Sometimes it is like a poem. Lynne Rae Perkins is a writer and artist. Criss Cross is her sixth book.
Another
award, the Caldecott, honors the best American picture book of the year. It is
named after an artist from
In the book, a little girl tells about visiting the home of her grandparents. The committee that chose Chris Raschka for the award praised how he captures the natural way children draw. It says the pictures express the emotional warmth of connections between older family members and children, Chris Raschka also won the award in 1994. In addition to the winners, four Caldecott Honor Books and four Newbery Honor Books were named last month.
Another honor from the American Library Association is the Margaret L. Batchelder Award. It goes to the company that publishes the best translation of a children’s book into English. The winner for 2006 is Arthur A. Levine Books for the book An Innocent Soldier written by Josef Holub. Michael Hoffman translated it from German.
Awards
are chosen by committees of people who work with children’s books. But in some
schools, children vote unofficially for their own Newbery and Caldecott
winners. This year, schoolchildren could watch the award ceremony live on the
Internet. A teacher in
68. The passage is probably about ______.
A. the American Library Association
B. the Newbery Award
C. Children’s Book Awards and the winners in 2006
D. the Margaret L. Batchelder Award
69. According to the text, Chris Raschka ______.
A. was an artist B. was a writer
C. was an artist and writer D. got the Caldecott Medal for the first time
70. Who got the Mararet L. Batchelder Award?
A. The author of the honored book.
B. The translator of the honored book.
C. The library which collects the honored book.
D. The company that brings out the honored book.
71. The book An Innocent Soldier was _______.
A. awarded with the Margaret L. Batchelder Award
B. translated from German into English
C. put into German from English
D. written by Michael Hoffman
72. We may infer from the text _____.
A. the honored books are really popular among children
B. the two awards are named after famous English writers
C. Lynne Rae Perkin’s six books are all awarded with the Newbery Award
D. the children vote together with those working with children’s books
第二节 简答题（共3小题， 满分6分）
阅读下面短文，根据第73至第75小题的具体要求，简要回答问题。
Ballroom dancing
Ballroom dancing(交际舞)in the UK used to be seen as something rather unpopular that old people might do. For the past five years though, the popularity of ballroom dancing has soared(高涨)thanks to a reality TV show. Every Saturday night millions of people watch the show which airs from September right up to Christmas. In the show a number of professional ballroom dancers each partner a celebrity(名流). Every week they have to learn a different ballroom dance and perform it live on TV on the Saturday night.
Four judges, all of whom have a background in professional dance, give the celebrities scores and comments about their dances. It is then up to the public to call in and vote for their favorite couple. The two least favorite then have to dance again and the judges decide who stays in the competition and who leaves. The celebrities get to wear colorful dresses to dance in, and it looks like a lot of fun.
The TV program also shows what good exercise
it can be to ballroom dance and what hard work is involved(涉及)in learning the dances and performing them
properly. Dance schools around the country have seen an increase in the number of people wanting to learn how to dance.
And it’s not only older people who are interested. Lots of children and young
people in their 20s are eager to
learn.
The show demonstrates how glamorous(富有魅力的)ballroom dancing is. The format(形式)for the show has been copied in lots of
countries around the world. In
73. Find in the passage a word closest in meaning to the underlined word “demonstrates”.
74. Why are so many people interested in ballroom dancing in the
75. How does the TV show make so many people enjoy the TV program?（回答词数不超过8个）
题 号
第一部分
第二部分
第三部分
第四部分
总 分
第一节
第二节
第一节
第二节
得 分
怀化市2008届高三第一次模拟考试英语答题卷
第一卷答题卡（供不使用正式答题卡学校用）
题 号
1
2
3
4
5
6
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8
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10
11
12
13
14
15
16
17
答 案
18. __________________ 19. _________________ 20. ____________________
题 号
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
答 案
题 号
36
37
38
39
40
41
42
43
44
45
46
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48
49
50
51
52
53
54
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答 案
题 号
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
答 案
73.
74.
75.
第四部分 书面表达（共两节，满分35分）
第一节 填空（共10小题上，每小题1分，满分10分）
阅读短文，根据所读内容在文后第76至第85小题的空格里填上适当的单词或短语。
注意：每空不超过3个单词。
The US Department of Labor statistics show that there is an oversupply of college trained workers and that this oversupply is increasing. Already there have been more than enough teachers, engineers, physicists, aerospace experts and other specialists. Yet colleges and graduate schools continue every year to turn out highly-trained people to compete for jobs that aren’t there. The result is that graduates cannot enter the professions for which they were trained and must take temporary jobs which don’t require a college degree.
On the other hand, there is a great need for skilled workers of all sorts. These people have more work than they can deal with, and their annual incomes are often higher than those of college graduates. The old gap that white-collar workers make a better living than blue-collar workers no longer holds true. The law of supply and demand now favors the skilled workmen.
The reason for this situation is the traditional myth that college degree is a passport to a prosperous future. A large part of American society matches success in life equally with a college degree. Parents begin indoctrinating(灌输) their children with this myth before they are out of grade school. High school teachers play their part by acting as if high school education were a preparation for college rather than for life. Under this pressure the kids fall in line. Whether they want to go to college or not doesn’t matter. Everybody should go to college, so of course they must go. And every year college enrollments go up and up, more and more graduates are overeducated for the kind of jobs available to them.
The development of our society is made by all kinds of workers. Only when the need of them is balanced can our nation process healthily. So parents and teachers are wished to pay more attention to the children’s choices.
Title: 76______________________________
Situation
Labors
77_________________
College trained workers
78_________________: not enough professions for which they trained
79________________________
In great need: more work to deal with
80____________
81________________________ : college degree a
passport to a prosperous future
Parents: 82________________ their children with this myth
Teachers: regard high school education as a 83________________________
Kids: have to go to college only because 84 _______________ should go there
85____________
To pay more attention to the children’s choices
第二节 写作（满分25分）
某校报为配合学校创建“节约型校园”工作，开展了“创建节约型校园英语征文活动”。请根据以下提示所列举的现象用英文写一篇120词左右的征文稿，表达自己的看法和建议。
校园内存在的现象：
1. 浪费水电；2. 可回收的饮料瓶、旧书本被扔掉；3. 餐厅饭菜浪费严重。
注意：标题和首句已给出，不计入词数。
Set up a Saving?oriented Campus
It seems that wasting things in today’s campus is a common phenomenon. ___________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
怀化市2008届高三第一次模拟测试卷
怀化市2008年高三第一次模拟考试统一检测试卷
数 学（文科）
命题人：怀铁一中 袁莉忠 审题人：市教科院 唐振球
李 辛 怀化三中 胡 斌
怀化一中 张登科
沅陵一中 张清锋
说明：本卷满分150分，考试时间120分钟。
怀化市2008年高三第一次模拟考试统一检测试卷
数 学（理科）
命题人：怀铁一中 向重新 审题人：市教科院 唐振球
怀化三中 周 睿
怀化一中 禹平宇
沅陵一中 沈清臣
一、选择题：（本大题共10小题，每小题5分，共50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．若
其中
都是实数，i是虚数单位，则
=
A．1+2i B．1－2 i C．2+ i D．2－i
2. 设p：log2 x<0，q：
，则p是┲q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．若
, 则直线
=1必不经过
A. 第一象限 B. 第二象限 C. 第三象限 D. 第四象限
4．设函数
是连续函数，则不等式
的解集为
A．
B．
C．
D．
5．边长为1的正方形ABCD上有一动点P，则向量
・
的范围是
A．[0，1]
B．[0，
] C．[1，] D．{1}
6．已知等差数列
的前n项和为Sn，且S2 =10，S5 = 55，则过点P(n，
)和
Q(n+2，
) (n∈N *)的直线的一个方向向量的坐标可以是
A． （2，
） B．
C.
D. 
7．设
是
展开式中x的系数，则
的值为
A．16
B．
8．已知方程
的两个根都大于2，则实数m取值范围是
A．
B．
C．
D．
9. 如图1，在正方体ABCD－A1B
A．
B．
C．
D．
10．已知函数
，则函数
（其中0<a<1）的单调递减区间是
A、
B、
C、
D、
山东省潍坊市2008年2月高三教学质量检测
政 治 试 题
本试卷分第Ⅰ卷和第Ⅱ卷两部分。第Ⅰ卷为选择题，将答案直接涂在答题卡上；第Ⅱ卷为非选择题，用钢笔或圆珠笔直接答在试卷上。全卷满分100分，考试时间90分钟。
第Ⅰ卷（选择题，共50分）
山东省潍坊市2008年2月高三教学质量检测
语 文 试 题
注意事项：
1．本试题分为选择题和非选择题两部分，时间150分钟，满分150分。
2．答卷前，务必将自己的班级、姓名、座号、考号分别填涂在答题卡及答题纸的相应位置。
第Ⅰ卷（共36分）
山东省潍坊市2008年高三教学质量检测
物 理 试 题
本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，全卷满分100分，考试时间90分钟。
第Ⅰ卷（选择题，共40分）
注意事项：
1．答第Ⅰ卷前，考生务必将自己的姓名、考号、考试科目、试卷类型（A或B）涂写在答题卡上。
2．每小题选出答案后，用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。
山东省潍坊市2008年高三教学质量检测
数学试题（文科）
本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分．共150分．考试时间120分钟．
第Ⅰ卷（选择题 共60分）
注意事项：
1．答第Ⅰ卷前，考生务必将自己的姓名、准考证号、考试科目用铅笔涂写在答题卡上．
2．每题选出答案后，用2B铅笔把答题卡对应题目的答案标号涂黑．（特别强调：为方便本次阅卷，每位考生在认真填涂“数学”答题卡的前提下，再将Ⅰ卷选择题答案重涂在另一答题卡上．）如需改动，用橡皮擦干净后，再改图其他答案标号．
2007年高考数学试题分类汇编（导数）
(18) (安徽理 本小题满分14分)
设a≥0，f (x)=x－1－ln2 x＋
（Ⅰ）令F（x）＝xf＇（x），讨论F（x）在（0.＋∞）内的单调性并求极值；
（Ⅱ）求证：当x>1时，恒有x>ln2x－
(20)(安徽文 本小题满分14分)
设函数
f（x）=-cos2x-4tsin
cos+4t2+t2-3t+4,x∈R,
其中
≤1，将f(x)的最小值记为g(t).
(Ⅰ)求g(t)的表达式；
(Ⅱ)诗论g(t)在区间（-1,1）内的单调性并求极值.
19．（北京理 本小题共13分）
如图，有一块半椭圆形钢板，其半轴长为
，短半轴长为
，计划将此钢板切割成等腰梯形的形状，下底
是半椭圆的短轴，上底
的端点在椭圆上，记
，梯形面积为
．
（I）求面积以
为自变量的函数式，并写出其定义域；
（II）求面积的最大值．
19．（共13分）
解：（I）依题意，以的中点
为原点建立直角坐标系
（如图），则点
的横坐标为．
点的纵坐标
满足方程
，
解得
，
其定义域为
．
（II）记
，
则
．
令
，得
．
因为当
时，
；当
时，
，所以
是
的最大值．
因此，当时，也取得最大值，最大值为
．
即梯形面积的最大值为
．
9．(北京文)
是
的导函数，则
的值是 3 ．
11．（福建理、文）已知对任意实数，有
，且
时，
，则
时（ B
）
A． B．
C．
D．
22．（福建理 本小题满分14分）
已知函数
（Ⅰ）若
，试确定函数的单调区间；
（Ⅱ）若
，且对于任意
，
恒成立，试确定实数
的取值范围；
（Ⅲ）设函数
，求证：
．
22．本小题主要考查函数的单调性、极值、导数、不等式等基本知识，考查运用导数研究函数性质的方法，考查分类讨论、化归以及数形结合等数学思想方法，考查分析问题、解决问题的能力．满分14分．
解：（Ⅰ）由得
，所以
．
由得
，故的单调递增区间是
，
由得
，故的单调递减区间是
．
（Ⅱ）由
可知
是偶函数．
于是对任意成立等价于
对任意
成立．
由
得
．
①当
时，
．
此时在
上单调递增．
故
，符合题意．
②当
时，
．
当变化时
的变化情况如下表：
单调递减
极小值
单调递增
由此可得，在上，
．
依题意，
，又
．
综合①，②得，实数的取值范围是
．
（Ⅲ）
，
，
，
由此得，
故
．
20．（福建文 本小题满分12分）
设函数
．
（Ⅰ）求的最小值
；
（Ⅱ）若
对
恒成立，求实数
的取值范围．
20．本题主要考查函数的单调性、极值以及函数导数的应用，考查运用数学知识分析问题解决问题的能力．满分12分．
解：（Ⅰ）
，
当
时，取最小值
，
即
．
（Ⅱ）令
，
由
得
，
（不合题意，舍去）．
当
变化时
，
的变化情况如下表：
递增
极大值
递减
在
内有最大值
．
在内恒成立等价于
在内恒成立，
即等价于
，
所以的取值范围为
．
20．(广东理、文 本小题满分14分)
已知
是实数，函数
．如果函数
在区间
上有
零点，求的取值范围．
20解: 若
, 
,显然在上没有零点, 所以 
令 
得 
当 
时, 
恰有一个零点在
上;
当 
即 
时, 也恰有一个零点在上;
当 在上有两个零点时, 则
或
解得
或
因此的取值范围是 
或 
;
12．（广东文）函数
的单调递增区间是
．
12. 
10．（海南理）曲线
在点
处的切线与坐标轴所围三角形的面积为（ ）
Ａ．
Ｂ．
Ｃ．
Ｄ．
21．（海南理 本小题满分12分）
设函数
（I）若当
时，取得极值，求的值，并讨论的单调性；
（II）若存在极值，求的取值范围，并证明所有极值之和大于
．
21．解：
（Ⅰ）
，
依题意有
，故
．
从而
．
的定义域为
，当
时，；
当
时，；
当
时，．
从而，分别在区间
单调增加，在区间
单调减少．
（Ⅱ）的定义域为
，
．
方程
的判别式
．
（?）若
，即
，在的定义域内，故的极值．
（?）若
，则
或
．
若
，
，
．
当
时，，当
时，，所以无极值．
若，
，
，也无极值．
（?）若
，即
或
，则有两个不同的实根
，
．
当时，
，从而有的定义域内没有零点，故无极值．
当时，
，
，在的定义域内有两个不同的零点，由根值判别方法知在
取得极值．
综上，存在极值时，的取值范围为
．
的极值之和为
．
10．（海南文）曲线
在点
处的切线与坐标轴所围三角形的面积为（ ）
Ａ．
Ｂ．
Ｃ．
Ｄ．
19．（海南文 本小题满分12分）
设函数
（Ⅰ）讨论的单调性；
（Ⅱ）求在区间
的最大值和最小值．
19．解：的定义域为．
（Ⅰ）
．
当时，；当时，；当时，．
从而，分别在区间
，
单调增加，在区间单调减少．
（Ⅱ）由（Ⅰ）知在区间的最小值为
．
又
．
所以在区间的最大值为
．
20．（湖北理 本小题满分13分）
已知定义在正实数集上的函数
，
，其中
．设两曲线，
有公共点，且在该点处的切线相同．
（I）用表示
，并求的最大值；
（II）求证：
（）．
20．本小题主要考查函数、不等式和导数的应用等知识，考查综合运用数学知识解决问题的能力．
解：（Ⅰ）设与
在公共点
处的切线相同．
，
，由题意
，
．
即
由
得：
，或
（舍去）．
即有
．
令
，则
．于是
当
，即
时，
；
当
，即
时，
．
故在
为增函数，在
为减函数，
于是在
的最大值为
．
（Ⅱ）设
，
则
．
故
在
为减函数，在
为增函数，
于是函数在上的最小值是
．
故当时，有
，即当时，
．
13．（湖北文）已知函数的图象在点
处的切线方程是
，则
＿＿＿＿．
19．（湖北文 本小题满分12分）
设二次函数
，方程
的两根
和
满足
．
（I）求实数的取值范围；
（II）试比较
与
的大小．并说明理由．
19．本小题主要考查二次函数、二次方程的基本性质及二次不等式的解法，考查推理和运算能力．
解法1：（Ⅰ）令
，
则由题意可得
．
故所求实数的取值范围是
．
（II）
，令
．
当时，
单调增加，当
时，
，即
．
解法2：（I）同解法1．
（II）
，由（I）知，
．又
于是
，
即
，故
．
解法3：（I）方程
，由韦达定理得
，
，于是
．
故所求实数的取值范围是．
（II）依题意可设
，则由，得
，故．
13．（湖南理）函数
在区间
上的最小值是 ．
19．（湖南理 本小题满分12分）
如图4，某地为了开发旅游资源，欲修建一条连接风景点
和居民区的公路，
2007年高考数学试题分类汇编（不等式）
1（全国2理科）.不等式:
>0的解集为（C）
(A)( -2, 1) (B) ( 2, +∞)
(C) ( -2, 1)∪ ( 2, +∞) (D) ( -∞, -2)∪ ( 1, +∞)
2．（北京理科6）若不等式组
表示的平面区域是一个三角形，则
的取值范围是（ D ）
Ａ．
Ｂ．
Ｃ．
Ｄ．或
3．（北京理科7）如果正数
满足
，那么（ A ）
Ａ．
，且等号成立时的取值唯一
Ｂ．
，且等号成立时的取值唯一
Ｃ．，且等号成立时的取值不唯一
Ｄ．，且等号成立时的取值不唯一
4．（北京理科12）已知集合
，
．若
，则实数的取值范围是 （2，3） ．
5（上海理科6）已知
，且
，则
的最大值为
6．(上海理科13)已知
为非零实数，且
，则下列命题成立的是(C)
A、
B、
C、
D、
7．(上海理科15)已知
是定义域为正整数集的函数，对于定义域内任意的
，若
成立，则
成立，下列命题成立的是（D）
A、若
成立，则对于任意
，均有成立
B、若
成立，则对于任意的
，均有
成立
C、若
成立，则对于任意的
，均有成立
D、若
成立，则对于任意的，均有成立
8（天津理科2）设变量
满足约束条件
则目标函数
的最大值为（ B ）
Ａ．4 Ｂ．11 Ｃ．12 Ｄ．14
9（天津理科9）设
均为正数，且
，
，
．则（ A ）
Ａ．
Ｂ．
Ｃ．
Ｄ．
10．（浙江理科1）“
”是“
”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
11．（浙江理科13）不等式
的解集是_____________。
12．（浙江理科17）设
为实数，若
，则的取值范围是_____________。
13．（湖北理科3）3.设P和Q是两个集合，定义集合P-Q=
，如果P={x|log2x<1},Q={x||x-2|<1},那么P-Q等于（B）
A．{x|0<x<1} B.{x|0<x≤1} C.{x|1≤x<2} D.{x|2≤x<3}
14．（湖北理科21）（本小题满分14分）
已知m，n为正整数.
（Ⅰ）用数学归纳法证明：当x>-1时，(1+x)m≥1+mx；
（Ⅱ）对于n≥6，已知
，求证
，m=1,1,2…，n；
（Ⅲ）求出满足等式3n+
解：（Ⅰ）证：当x=0或m=1时，原不等式中等号显然成立，下用数学归纳法证明：
当x>-1，且x≠0时，m≥2,(1+x)m>1+mx. 1
(i)当m=2时，左边＝1+2x+x2,右边＝1+2x，因为x≠0,所以x2>0，即左边>右边，不等式①成立；
（ii）假设当m=k(k≥2)时，不等式①成立，即（1+x）k>1+kx,则当m=k+1时，因为x>-1,所以1+x>0.又因为x≠0,k≥2,所以kx2>0.
于是在不等式（1+x）k>1+kx两边同乘以1+x得
（1+x）k・(1+x)>(1+kx)(1+x)=1+(k+1)x+kx2>1+(k+1)x,
所以（1+x）k+1>1+(k+1)x,即当m＝k+1时，不等式①也成立.
综上所述，所证不等式成立.
(Ⅱ)证：当
而由（Ⅰ），
（Ⅲ）解：假设存在正整数
成立，
即有（
）+
＝1. ②
又由（Ⅱ）可得
（）+
+
与②式矛盾，
故当n≥6时，不存在满足该等式的正整数n.
故只需要讨论n=1,2,3,4,5的情形；
当n=1时，3≠4，等式不成立；
当n=2时，32+42＝52，等式成立；
当n=3时，33+43+53＝63，等式成立；
当n=4时，34+44+54+64为偶数，而74为奇数，故34+44+54+64≠74,等式不成立；
当n=5时，同n=4的情形可分析出，等式不成立.
综上，所求的n只有n=2,3.
15（湖南理科2）．不等式
的解集是（ D
）
A．
B．
C．
D．
16（湖南理科14）．设集合
，
，，
（1）
的取值范围是 ；
（2）若
，且
的最大值为9，则的值是
．
（1）
（2）
17．（福建理科3）已知集合A＝
，B＝
，且
，则实数的取值范围是（C）
A．
B． a<
D．a>2
18．（福建理科7）已知
为R上的减函数，则满足
的实数
的取值范围是（C）
A．（－1，1） B．（0，1）
C．（－1，0）
（0，1） D．（－
，－1）（1，＋）
19．（福建理科13）已知实数x、y满足
，则
的取值范围是___
_______；
20．（重庆理科2）命题“若
，则
”的逆否命题是（ ）
A．若
，则
或
B.若，则
C.若
或
，则
D.若或，则
21．（重庆理科13）若函数f(x) = 
的定义域为R，则a的取值范围为_______.
22．(江西理科17)．（本小题满分12分）
已知函数
在区间(0，1)内连续，且
．
（1）求实数k和c的值；
（2）解不等式
23．（山东理科2）．已知集合
，
则
（B）
(A) 
(B) 
(C)
(D)
24．(山东理科16)函数y=loga(x+3)-1(a>0,a
1)的图象恒过定点A，若点A在直线mx+ny+1=0上，其中mn>0,则
的最小值为
.
25．(安徽理科3)若对任意
R,不等式
≥ax恒成立，则实数a的取值范围是
(A)a＜-1
(B)
≤1
(C) ＜1
（D）a≥1
26．（安徽理科5）若
，
，则
的元素个数为
（A）0 （B）1 （C）2 （D）3
27．（江苏6）设函数定义在实数集上，它的图像关于直线
对称，且当
时，
，则有
A．
B．
C．
D．
28．（陕西理科9）给出如下三个命题：ZXXK.COM
①四个非零实数a、b、c、d依次成等比数列的充要条件是ad=bc;ZXXK.COM
②设a,b∈R，则ab≠0若
＜1，则
＞1；ZXXK.COM
③若f(x)=log
2x=x,则f（|x|）是偶函数.ZXXK.COM
其中不正确命题的序号是ZXXK.COM
A.①②③ B.①② C.②③ D.①③ZX
29（全国1文科1）设
，
，则
A．
B．
C．
D．
30．（北京文科15）（本小题共12分）
记关于的不等式
的解集为
，不等式
的解集为
．
（I）若
，求；
（II）若
，求正数的取值范围．
解：（I）由
，得
．
（II）
．
由
，得
，又，所以
，
即的取值范围是
．
31．（天津文科1）（1）已知集合
，
，则（ B ）
A．
B．
C．
D．
32．(浙江文科3)“x＞
(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
33．湖南文科1．不等式的解集是（ D
）
A．
B．
C．
D．
34．湖南文科14．设集合，，，（1）的取值范围是 ；（2）若，且的最大值为9，则的值是
．
（1）
（2）
35．福建文科4．“
”是“
”的什么条件……（A ）
A．充分而不必要 B．必要而不充分 C．充要 D．既不充分也不必要
36．福建文科7．已知是R上的减函数，则满足
的实数x的取值范围是（D ）
A．
B．
C．
D．
37．（重庆文科5）“-1＜x＜
（A）充分必要条件 （B）充分但不必要条件
（C）必要但不充分条件 （D）既不充分也不必要条件
38．（安徽文科16）（本小题满分10分）
解不等式
＞0.
39．（广东文科1）．已知集合M={x|1+x>0}，N={x|
>0}，则M∩N=（C）
A．{x|-1≤x＜1 B．{x|x>1} C．{x|-1＜x＜1} D．{x|x≥-1}
