南京市2008―2009學年度第一學期期末調研測試卷
高 一 英 語
本試卷分第一卷(選擇題)和第二卷(非選擇題)兩部分，滿分100分，考試用時100
分鐘。注意事項：
答題前考生務必將學校、姓名、班級、學號寫在答卷紙的密封線內。每題答案均寫在答卷紙上對應題目的答案空格里，不寫在試卷上。考試結束，請將答卷紙交回。
第一卷(三部分，共69分)
第一部分 聽力(共兩節，滿分15分)
做題時，先將答案標在試卷上。錄音內容結束后，你將有兩分鐘的時間將試卷上答案轉涂到答題卡上。
第一節(共5小題；每小題1分，滿分5分)
聽下面5段對話。每段對話后有一個小題，從題中所給的A、B、C三個選項中選出最佳選項，并標在試卷的相應位置。聽完每段對話后，你都有10秒鐘的時問來回答有關小題和閱讀下一小題。每段對話僅讀一遍。
1．What will the woman probably do? ( )
A．Stop talking． B．Turn up the radio． C．Turn down the music．
2．What is the man doing? ( )
A．He is looking for a bus stop．
B．He is selling fruit．
C．He is going to a fruit shop．
3．What does the woman mean? ( )
A．She has already been to the concert．
B．Betty is taking her to the concert．
C．The man could probably go with Betty．
4．Why does the
A．She has a new job． B．She needs help C．She has finished school
5．Where is the woman’s mother now? ( )
A．At home． B．In hospital． C．At work
第二節(共10小題；每小題1分，滿分10分)
聽下面4段對話或獨自。每段對話或獨白后有幾個小題，從題中所給的A、B、C三個選項中選出最佳選項，并標在試卷的相應位置。聽每段對話或獨自前，你將有時間閱讀各個小題，每小題5秒鐘，聽完后，各小題將給出5秒鐘的作答時間。每段對話或獨自讀兩遍。
聽第6段材料，回答6至7題。
6．What does the man need? ( )
A．A taxi． B．A timetable． C．A bag．
7．When will the man leave home? ( )
A．2：30． B．3：00． C．3：30．
聽第7段材料，回答8至l0題。
8．Where will they
stay in
A．At a hotel． B．At a friend’s house． C．In a car．
9．What’s the climate like? ( )
A．Cold and sunny． B．Warm and rainy． C．Cold and rain
10．When will they probably leave? ( )
A．At 8：
聽第8段材料，回答11至12題。
11．How many places has the woman been to? ( )
A．Three． B．Four． C．Five．
12．In which season does the woman go on holiday? ( )
A．In autumn． B．In summer． C．In spring．
聽第9段材料，回答13至15題。
13．What were the family going to do? ( )
A．To spend their holiday．
B．To see their friend．
C．To buy some food
1 4．How would they go to the countryside? ( )
A．By train． B．By car． C．On foot．
15．Why did Mrs. Smith move the clocks and watches ahead? ( )
A．She wanted to surprise her husband．
B．She didn’t want to be late．
C．She always did So．
第二部分英語語言知識運用(共兩節；滿分30分)
第一節單項填空(共15小題；每小題1分，滿分15分)
從A、B、GD四個選項中，選出可以填入空白處的最佳選項，并在答題卡上將該項涂黑。
16．If you don’t like the subjects your teachers suggest, you can some of them．
A．enjoy B．drop C．1eave D．consider
17．―Eric, the money with which you were to buy dog food ．
A．has gone B．has missed C．is missed D．is gone
18．Alice said the aliens took her away so that they could do research her．
A．about B．for C．on D．with
19．You have to wear special clothing，a helmet and a life jacket，just your raft gets upside down or sinks．
A．in case B．so that C．as though D．in order that
20．Then，a few months after Carter had opened the tomb，Lord Carnarvon ill with a fever and died in Egypt．
A．fell B．stayed C．sounded D．seemed
21．That is the most beautiful building I visited 1ast year．
A．where B．不填 C．which D．to which
22．He was educated at a local school, he went on to Cambridge University．
A．from which B．after that C．after which D．form that
23．―Ring me at
―No，not that early! I ．
A．sleep B．will sleep C．am sleeping D．will be sleeping
24．The students busily when Mr. Smith went to get some paper he in the office．
A．had written；left B．were writing；has left
C．had written；had left D．were writing；had left
25．Her health broke down under the of work and she had to stay in hospital for a month．
A．measure B．pressure C．damage D．effect
26．The increasing number of the students makes the limited computers not to each student．
A．useful B．hopeful C．available D．suitable
27．There are two universities for you to choose from．Which one would you like to ?
A．join B．join in C．take part in D．attend
28．―Have they found out the reason that caused the traffic accident the other day?
―No．the police are now it．
A．looking for B．looking into C．looking up D．looking on
29．―You’ve known
,since we were babies．
A．Usually B．Finally C．Actually D．Luckily
30．―Do you mind my taking this seat?
A．No．of course not B．Yes，sit down，please
C．Yes，take it，please D．No，you can’t take it
第二節完形填空(共15小題；每小題1分，滿分15分)
閱讀下面短文，掌握其大意，然后從31―45各題所給的四個選項(A、B、C和D)中，選出最佳選項，并在答題卡上將該項涂黑。
Stephen Hawking was born in Oxford，England on 8th January，1942．He went to school in St Albans―a small city near London． 31 he did well，he was never top of his class．After 32 school，Hawking went first to Oxford University， 33 he studied Physics，and then he went to Cambridge University to study cosmology．As he himself admits，he wasn’t very serious about studying．He was a very 1azv student，and did very little work．However，he still 34 good marks．
It was at the age of twenty 35 Hawking first noticed that something went wrong with him．He started to bump into(碰撞)things，and once or twice 36 over for no reason．When he visited his 37 at Christmas time，his father was so worried that he made him see a doctor．Hawking was sent to hospital for tests.
Finally，the 38 came back．Hawking had motor neuron disease，an illness which 39 the muscles of the body to waste away．Doctors said he would die before he was twenty three．
At first，Hawking became very
depressed(沮喪的)．After a while，though，he began to see
his
Today，Hawking still works at Cambridge University．He strongly believes that his story shows that nobody， 44 had their condition is，should lose 45 ．
“Life is not fair，”he once said，“You just have to do the best you can in your situation．”
31．A．Because B．Although C．As D．Unless
32．A．1eaving B．graduating C．visiting D．going
33．A．which B．where C．that D．there
34．A．forgot B．missed C．achieved D．wanted
35．A．when B．at which C．what D．that
36．A．fell B．came C．got D．took
37．A．friends B．classmates C．teacher D．family
38．A．news B．results C．doctors D．parents
39．A．helped B．made C．caused D．prevented
40．A．1ife B．illness C．study D．work
41．A．bored B．happy C．satisfied D．angry
42．A．doing B．waiting C．getting D．crying
43．A．on B．away C．down D，out
44．A．whatever B．however C．whenever D．wherever
45．A．marks B．games C．hope D．interest
第三部分閱讀理解(共12小題；每小題2分，滿分24分)
第一節閱讀下列短文，從每題所給的四個選項(A、B、c~11D)0p，選出最佳選項，并在答題卡上將該項涂黑。
Travel is fun and exciting，but it’s not if you get sick. You may think，“Not me,1 won’t get sick on my vacation．”But for many people，that is what happens．Of course you don’t want to spend your vacation sick in bed．So what can you do to stay in good health? There are three things you should remember when you travel：relax，sleep，and eat well．
A vacation is supposed to be a time for relaxing．But very often it is not．Think about what you do when you are a tourist．There are so many places to visit：museums，shops，parks，and churches．You may spend most days walking around these places．You may be very tired．Your feet may hurt and you may have a terrible headache after a few hours．If this is the way you feel，you should take a rest．Don’t ask your body to do too much．A tired body means a weak body．And a weak body gets sick easily．So sit down for a few hours in a nice spot．In good weather，look for a quiet park bench or you can stop at a care．You can learn a lot by watching people while you rest．
Sleep is also Important．If you want to stay healthy，you need to get enough sleep．You may have trouble sleeping at night when you travel．Your hotel room may be noisy or the bed may be uncomfortable．If this is true，don't be afraid to change rooms or hotels，or you may not get enough sleep．You may want to stay out late at night．In many cities the nightlife can be very exciting Then you should plan to sleep for an hour during the day．That extra hour can make a big difference．
Finally，if you want to stay healthy，you must eat well．That means eating the right kinds of food．Your body needs fresh fruits and vegetables，and some meat，milk or cheese．When you are in a new country，you may want to try new food but you need to be careful about how much you eat．Lots of rich food is not good for you．
So，remember this：if you want to enjoy your vacation，take good care of yourself．Give your body some rest．Get enough sleep and eat good，healthy food．
46?This passage is mainly about ．
A．what to eat when you travel
B．how exciting travel is
C．relaxing when you travel
D．how to stay healthy when you travel
47．Traveling around can be ．
A．the best way to relax B．very tiring
C．no fun D．unhealthy
48．It’s a good idea to when traveling
A．spend every night in hotels B．change hotels
C．get some rest every day D．try lots of rich food
49Accordding t。the passage，you can get to know the 1ocal people by ．
A．going to the shops B．visiting their homes
C．talking to them D．watching them
Read the following，which is the information about a book that appears on a library computer screen．
50．This book is ．
A．a collection of photos B．a collection of space news
C．written for grown―ups D．written for children
51．This book will most likely tell you ．
A．how astronauts are trained
B．how astronauts travel on a space shuttle
C．what a space shuttle is like
D．about the way a space shuttle is built
52．The book is ．
A．borrowed by someone B．on the bookshelf
C．to be sold D．to be published
53．If you want to find other books by the author，you will look under ．
A．Lothrop，Lee B．Sheppard C C．Ride，Sally D．Challenger
C
To tell you the truth，I used to be a very superstitious(迷信的)person and believe in ghosts There was a list of things that didn’t seem proper for a person of my education to believe in．One day，however, I was totally changed through my personal experience with a‘ghost’．
It was last year that I visited my friends Keith and Alice who had bought an old house in the country．They told me that they bought it because it was haunted(鬧鬼的)．They found some‘ghosts’living there．It sounded SO frightening and exciting that I decided to call on them and have a look at the living‘ghosts’．
It was a good―looking house and didn’t seem much different from the nearby houses．We had a very pleasant meal together．While＼re were sitting around a warm fire in the sitting room，I asked Keith to tell me more about the haunted house．
“Did you ever come across any‘ghosts’yourself?”I asked．
“Oh，yes，”he replied．“I saw one moving about the other day―an old lady．She came down the stairs when I was coming into the hall to make a telephone call．”I felt my heart beating
faster．“It’s quite true，” he went on．“She wore a large hat，so I couldn’t make out her face．But it’s her hands that I remember，anyway．I saw her hands swinging．They were ghostly white!”
We chatted a little longer and after that，at about midnight，1 went up to my room．I searched my room for any traces of ghosts but failed．Then t fell asleep at once．In my dream I saw a lady ‘ghost’moving up to me with her white hands swinging．So I woke up．I 1ooked at my watch―it was 2：00 AM．Out of the window I saw the moon and I heard the clock in the corner of the room ticking away slowly but clearly．
Suddenly I saw it! There，at the bottom of the bed，was a ghostly white hand! Immediately，I caught hold of a heavy lamp from the table near the bed and threw it with a11 my strength at the hand．Then I heard myself screaming with pain．It was not a hand at a11．It was my own foot!
And my old belief has gone with that pain forever !
54．From the first paragraph，we can infer that ．
A．the writer didn’t have any education
B．the writer had good education
C．the writer was 0liCe educated to believe in ghosts
D．the writer taught himself
55．Why did the writer’s friends buy the house． ．
A．Because it was in the country．
B．Because it was good―looking and matched the other houses
C．Because it had‘ghosts’living there．
D．Because they could have pleasant meals there．
56．What was Keith doing when he saw the ghost lady? ．
A．He was making a telephone call．
B．He was walking into the hall．
C．He was moving about in the hall．
D．He was coming down the stairs．
57．According to the writer，where was the‘ghost’? ．
A．At the bottom。f his bed． B．In the corner of his room
C．0n the table near the bed． D．Out of the window?
第二卷(兩部分，共31分)
第四部分任務型閱讀(共10小題；每小題1分，滿分10分)
請認真閱讀下列短文，并根據所讀內容在文章后表格中的空格里填八最恰當的單詞。注意：每空格1個單詞。
Nine-year-old Barrack Obama was looking through a magazine．But the African-American boy was shocked by some photos．The pictures were of black man who destroyed his skin with chemicals that promised to make him white．For the first time，the boy began to doubt(懷疑)who he was．‘I stood in front of the mirror and wondered if something was wrong with me，’Obama said．
However，now，the boy who used to struggle with his identity(身份)doesn't see it as a problem any more，but an advantage for his success．A few weeks ago, Obama made history by being elected as the first black president of the United States．
Obama’s story starts in another corner of the world．His white mother was born in the heartland of the US．His black father grew up in a Village in Kenya．They met during college in Hawaii, but his father left the family when Obama was Just two years old and his mother moved to Indonesia．
At 10，Obama moved back to live with his white grandparents in Hawaii, where his sense that he didn’t belong grew．At his class，a white boy asked Obama if his father ate people．Out of embarrassment，Obama lied to his classmates that he father was a prince(王子)．‘I kept asking who I am and I ended up trying dugs and drinking，’Obama remembered．
Things came to change after the young man made friends
with those who had a similar background at college．Their experiences
back in
African identity．He worked hard to become a star at Harvard Law School and the third black senator(參議員)in US history．
At first，few people supported Obama．Many doubted his unusual background，which left him neither‘black’enough nor‘white’enough．
But Obama’s pains of growing up made Americans believe：‘There is not a black America and a white America…．There is the United States of America．’
History has arrived―A great (58) ▲ has come true
第五部分寫作(共兩節，滿分21分)
第一節單詞填空(共6小題；每小題1分，滿分6分)
根據下列句子及所給的漢語注釋，寫出空缺處各單詞的jE確形式。(每空一詞)
68．New scientific ▲ (發現)are being made every day．
69．The job is ▲ (累人的)，but the pay is good．
70．Police wanted to know if anyone ▲ (目擊)the traffic accident．
71．I wasn’t ▲ (通知)of the decision until too late．
72．We promise not to let anyone who breaks the law go ▲ (免受懲罰的) ．
73．You’d better avoid food ▲ (包含)fat so that you can keep slim．
第二節書面表達(滿分15分)
假設你是李華，學完Amazing people這一單元后，你的英語老師請你寫一篇短文，談談你心目中的偶像。請根據以下內容提示，適當發揮，完成這篇短文，并用email發給他。
內容要點：
1．不同的人心目中有不同的偶像；
2．我認為爸爸是我的偶像；
3．他每天辛勤工作，還要照顧生病的媽媽；
4．他常到敬老院幫助老人；
5．四川地震后，他積極捐款。
注意：文章的開頭與結尾已給出，不記入總詞數。
偶像：idol 敬老院：home for the elderly 詞數：i00詞左右
Dear Sir，
How are you? You asked us to write about our idols．Different people……
So，don’t you think my dad is my idol?
Regards，
Li Hua
南京市2008―2009學年度第一學期期末調研測試卷
高一英語聽力錄音稿 2009．01
第一節(共5小題；每小題1分，滿分5分)
聽下面5段對話。每段對話后有1個小題，從題中所給的A、B、C三個選項中選出最佳選項，并標在試卷的相應位置。聽每段對話后，你都有10秒鐘的時間來回答有關小題和閱讀下一小題。每段對話僅讀一遍。
Text 1
M：Look，I'm sorry to trouble you about this，but that music is realiv loud．
W：I didn’t realize you could hear it．
Text 2
M：Which is the way to the fruit shop，please?
W：Sorry，I don’t know．Please ask the old man Over there．He may know it
Text 3
M：Could I get a ride with you to the concert tonight?
W：I can’t go，but you might ask Betty．I think she’s leaving around 7：30
Text 4
M：Will you please give this note to Mary? She needs help．
W：What’s the matter?
M：Her father’s ill and she wants to leave sch001．
Text 5
M：How is your mother feeling these days?
W：Much better．Thanks．She should he coming home in a few days．The operation was a success and the doctors say she’ll recover in no time．
第二節(共10小題；每小題1分，滿分10分)
聽下面4段對話或獨自。每段對話或獨自后有幾個小題，從題中所給的A、B、C三個選項中選出
最佳選項，并標在試卷的相應位置。聽每段對話或獨自前，你將有時間閱讀各個小題，每小題5秒鐘，聽完后，各小題將給出5秒鐘的作答時間。每段對話或獨自讀兩遍。
聽第六段材料，回答6至7題。
M：Hello．Is this the Green Taxi Service7
W：Yes，it is． 、
M：I need a taxi to the train station，口lease．
W：What time do you need a taxi，sir?
M： My train}eaves at 4：30 this afternoon，but I’d 1ike to arrive at the station no later than 3．30。
How long is the ride from here?
W：From here? Where do you live?
M：Oh，I’m sorry．I live at 447 Mile End Street．
W：Let me see一447 Mile End―I’d say that it would take about 30 minutes．We will pick you up at 3：00．Is it Okay with you?
M：Yes，that’11 be fine．The driver will help me with my bags，won’t he?
W：Yes．the driver is a young man．He’11 help you．
聽第7段材料，回答8至10題。
M：How would you like to come to New York with me over the Spring Break，Julia?
W：I’d love to，John．But where shall we stay?
M：At a friend’s house．I always stay with him and there’s room for you，too．
W：0K．He won’t mind?
M：Of course not．He’s looking forward to meeting you．
W：Will we drive to
M：Yes．It takes about six hours．We can leave at noon and get there by supper time．
W：What’s the climate like?
M：It may be cold and rainy．Better bring a jacket and good walking shoes．
W：Well，when do we leave?
M：How about Thursday? Can you be ready by noon?
W：N0 problem．
聽第8段材料，回答11至12題。
M：Have you ever
been to
W：Oh，yes．
M：Where have you been?
W：Well，and we’ve been to England，Scotland and Ireland．We always go in sulnliler because
the weather is better．
M：Yes，but there are more tourists．
W：Yes，that’s right．But it’s the same in every country．
聽第9段材料，回答13至15題。
Mr. and Mrs. Smith and their children were going to spend their holiday in the country．They
had to be at the railway
station before 11：
ready by 11
南京市2008―2009學年度第一學期期末調研測試卷
理科2009屆高三強化訓練（四）綜合能力測試更正
第30題（20分）
Ⅰ．（11分）下列是有關植物礦質代謝的研究：
（1）將番茄植株培養在完全營養液中一段時間后，發現鎂的濃度有所提高，鈣的濃度有所降低，主要原因是： ；
（2）提供42K及相關的實驗器材，利用溶液培養法證明鉀是植物可以移動（反復利用）的元素，寫出其主要實驗步驟及實驗原理。
實驗步驟：
實驗原理：
Ⅱ．（9分）動物腺體功能的研究---甲狀腺分泌甲狀腺激素能影響代謝、生長發育、神經系統的發育及功能，動物體內促甲狀腺激素與甲狀腺激素之間存在著反饋調節，從而維持血液中的甲狀腺激素含量的相對穩定。
碘是合成甲狀腺激素的原料。正常情況下，動物體吸收的碘（131I）會在甲狀腺中濃集。有人用兔子做實驗記錄結果如下圖所示：
以下為實驗步驟，請補充完整并進行分析：
第一步：
第二步：分別注射等量且適量的含131I的注射液，（過量引起甲亢）
第三步：定時測定每組兔子甲狀腺的放射量。
第四步：4天后第2次進行等量的注射：
A組注射 ,B組注射 , C組注射 ；
（選擇A.生理鹽水、B.促甲狀腺激素、C.無放射性的甲狀腺激素）
第五步：定時測定各組兔子甲狀腺的放射量。
分析：第二次注射后：
A組兔子與C組兔子相比：A組兔子的甲狀腺放射量下降的速率慢，原因
是 ；
該實驗說明： 。
答案及解析30.Ⅰ．（11分）
（1）植物吸收水分和吸收礦質元素是兩個相對獨立的過程，根細胞膜上運載鎂離子和鈣離子的載體數量不同（注：該答案能準確解釋題干中鎂和鈣的濃度升、降的現象，也與教材中有關知識進行了鏈接）；
（2）實驗步驟：第一步：用含42K的完全營養液培養植物；一段時間后，檢測葉片的放射性：老葉、幼葉全部都有；第二步：再用缺K的完全營養液培養上述植物，一段時間后、檢測老葉、幼葉的放射性。
實驗原理：鉀進入植物體后呈離子狀態，因此容易轉移，一旦缺乏，老葉中的K可以轉移到
幼葉，用含42K 營養液培養植物可以追蹤到這一現象。
【解析】Ⅰ．
（1）溶液培養法是鑒別各種礦質元素是否為植物必需元素的主要方法。在完全營養液中，植物既吸收礦質元素，也吸收水，這是兩個相對獨立的過程。如果在單位時間內，植物對礦質元素的吸收量與對水分的吸收量不同，則可能導致某種礦質離子的濃度增加或降低。
（2）溶液培養法可以較好地控制植物根系吸收的物質組分,即對培養液添加或除去某種礦質元素, 培養一段時間后，觀察植物的生長發育變化：成熟葉和幼葉是否表現正常或病態，從而判斷是不是可再度利用元素。本實驗通過對42K 進行追蹤：老葉中的42K 是否轉移到幼葉而得出結論。實驗對照應為自身前后對照，實驗原理應簡要寫出設計的理論依據及通過什么方法和觀測指標達到什么目的。
Ⅱ．（9分）
第1步：選生長發育、體重等方面相同的兔子3只，分為A組、B組、C組；第4步：
A組：C(注射無放射性的甲狀腺激素)，B組：B(注射促甲狀腺激素)，C組：A(注射生理鹽水)；
分析：注射甲狀腺激素后，抑制了促甲狀腺激素的合成和分泌，使甲狀腺細胞利用131I合成和分泌甲狀腺激素量減少，從而使甲狀腺放射量下降的速率慢。
該實驗說明：動物體內促甲狀腺激素與甲狀腺激素之間存在著反饋調節。
【解析】動物體內促甲狀腺激素與甲狀腺激素之間存在著反饋調節。
下丘腦中的一些細胞能合成并分泌促甲狀腺激素釋放激素，進而刺激垂體合成并分泌促甲狀腺激素。促甲狀腺激素又能刺激甲狀腺合成并分泌甲狀腺激素，從而促進新陳代謝。當血液中甲狀腺激素的含量增加到一定程度時，就會抑制下丘腦和垂體的活動，使促甲狀腺激素釋放激素和促甲狀腺激素的合成和分泌減少，從而使血液中甲狀腺激素的含量不會過高。由此可見，甲狀腺激素與促甲狀腺激素釋放激素、促甲狀腺激素之間存在著反饋調節。
本實驗重在分析實驗記錄結果（圖示）：從圖中給的信息進行分組；注意縱坐標是測
定甲狀腺吸收的碘（131I）的濃集量，而不是血液中放射性甲狀腺激素的量。在第一次注射放射性碘后的兩天，圖中曲線上升，是因為碘（131I）是合成甲狀腺激素的原料，甲狀腺細胞主動吸收了放射性碘（131I），故甲狀腺的放射性上升；而2―4天內曲線下降，是因為甲狀腺細胞利用放射性碘合成了甲狀腺激素分泌到血液中，故甲狀腺的放射性下降。第2次3組注射了不同的物質，因而3組甲狀腺的放射性下降出現了差異。
新課程地區高三模擬考試理科綜合（物理部分）（1）
本試題分為第Ⅰ卷（選擇題）和第Ⅱ卷（非選擇題）兩部分，共240分，考試時間150分鐘。考試結束后，只收答題卡和第Ⅱ卷答題紙。答卷前，考生務必將自己的姓名、準考證號、考試科目涂寫在答題卡上和答卷規定的地方。
第Ⅰ卷（必做，共88分）
注意事項：
1．每小題選出答案后，用2B鉛筆把答題卡對應題目的答案標號涂黑。如需改動，用橡 皮擦干凈后，再涂寫其它答案標號。不涂答題卡，只答在試卷上不得分。
2．第Ⅰ卷共22小題，每小題4分，共88分。
本2008―2009學年度第一學期期末調研測試卷
高 一 語 文
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高三數學中檔題專項訓練（2）
1、【江蘇?泰州】已知向量a＝（3sinα，cosα），b＝(2sinα, 5sinα－4cosα)，α∈（
），且a⊥b． （1）求tanα的值；（2）求cos(
)的值．
2、【江蘇?南通】（本小題14分）
如圖，在正三棱柱ABC－A1B
（1）求證：AD⊥平面BC C1 B1；
（2）設E是B
的值為多少時，
A1E∥平面ADC1？請給出證明．
3、(本題滿分16分)有如下結論：“圓
上一點
處
的切線方程為
”，類比也有結論：“橢圓
處的切線方程為
”，過橢圓C：
的右準線l上任意一點M引橢圓C的兩條切線，切點為 A、B.
（1）求證：直線AB恒過一定點；（2）當點M在的縱坐標為1時，求△ABM的面積
4、【江蘇?淮、徐、宿、連】(本題滿分16分)
已知函數f(x)=alnx+x2(a為實常數).(1)若a=－2，求證：函數f(x)在(1，+．∞)上是增函數；
(2)求函數f(x)在[1，e]上的最小值及相應的x值；
(3)若存在x∈[1，e]，使得f(x)≤(a+2)x成立，求實數a的取值范圍.
1、【解】（1）∵a⊥b，∴a?b＝0．而a＝（3sinα，cosα），b＝(2sinα, 5sinα－4cosα)，
故a?b＝6sin2α＋5sinαcosα－4cos2α＝0．……………………………………2分
由于cosα≠0，∴6tan2α＋5tanα－4 ＝0．解之，得tanα＝－
，或tanα＝
．……6分
∵α∈（），tanα＜0，故tanα＝（舍去）．∴tanα＝－．…………7分
（2）∵α∈（），∴
．
由tanα＝－，求得
，
＝2（舍去）．
∴
，………………………………………12分
cos(
)＝
＝
＝
． ………………………14分
2、解: （1）在正三棱柱中，C C1⊥平面ABC，AD
平面ABC，
∴ AD⊥C C1．………………………2分
又AD⊥C1D，C C1交C1D于C1，且C C1和C1D都在面BC C1 B1內，
∴ AD⊥面BC C1 B1． ……………………………………………5分
（2）由（1），得AD⊥BC．在正三角形ABC中，D是BC的中點．…………7分
當
，即E為B
事實上，正三棱柱ABC－A1B
又B1B∥AA1，且B1B=AA1，
∴DE∥AA1，且DE=AA1． …………………………………………12分
所以四邊形ADE A1為平行四邊形，所以E A1∥AD．
而E A1
面AD C1內，故A1E∥平面AD C1． …………………………14分
3、【解】（1）設M
∵點M在MA上∴
①……………………3分
同理可得
②…………………………5分
由①②知AB的方程為
…………6分
易知右焦點F（
）滿足③式，故AB恒過橢圓C的右焦點F（）……8分
（2）把AB的方程
∴
……………………12分
又M到AB的距離
∴△ABM的面積
……………………15分
4、【解】（1）當
時，
，當
，
，
故函數
在
上是增函數．………………………………………………4分
（2）
，當
，
．
若
，
在
上非負（僅當，x=1時，
），故函數在上是增函數，此時
． ……………………………………6分
若
，當
時，；當
時，
，此時
是減函數； 當
時，
，此時是增函數．故
．
若
，在上非正（僅當
，x=e時，），故函數在上是減函數，此時
．…………………………………8分
綜上可知，當時，的最小值為1，相應的x值為1；當時，
的最小值為
，相應的x值為
；當時，的最小值為，
相應的x值為
．…………………………………………………………………10分
（3）不等式
， 可化為
．
∵, ∴
且等號不能同時取，所以
，即
，
因而
（）…………………………………………………………12分
令
（），又
，………………14分
當
時，
，
，
從而
（僅當x=1時取等號），所以
在上為增函數，
故的最小值為
，所以a的取值范圍是
． ……………………16分
江蘇省如皋市2009屆高三第一次統一考試
語 文 試 卷
注意事項：
1．本試卷包括必做題和選做題，其中第六大題為選做題，其它題為必做題。滿分為160分，考試時間為150分鐘。
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