題目列表(包括答案和解析)
（本題13分）已知函數
（1）已知一直線
經過原點
且與曲線
相切，求的直線方程；
（2）若關于
的方程
有兩個不等的實根，求實數
的取值范圍。
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秒鐘的時間來回答有關小題和閱讀下一小題。每段對話僅讀一遍。
1.What is the weather like?
A. It’s raining. B. It’s cloudy. C. It’s sunny.
2.Who will go to China next month?
A. Lucy. B. Alice. C. Richard.
3.What are the speakers talking about?
A. The man’s sister. B. A film. C. An actor.
4.Where will the speakers meet?
A. In Room 340. B. In Room 314. C. In Room 223.
5.Where does the conversation most probably take place?
A. In a restaurant. B. In an office. C. At home
第二節 （共15小題；每題1分，滿分15分）
聽下面5段對話或獨白。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。聽每段對話或獨白前，你將有時間閱讀各個小題，每小題5秒鐘；聽完后，每小題將給出5秒鐘的作答時間。每段對話或獨白讀兩遍。
聽第6段材料，回答第6、7題。
6.Why did the woman go to New York?
A. To spend some time with the baby.
B. To look after her sister.
C. To find a new job.
7.How old was the baby when the woman left New York?
A. Two months. B. Five months. C. Seven months.
8.What did the woman like doing most with the baby?
A. Holding him. B. Playing with him. C. Feeding him.
聽第7段材料，回答第9至11題。
9.Where are the speakers talking about?
A. A way to improve air quality.
B. A problem with traffic rules.
C. A suggestion for city planning.
10.What does the man suggest?
A. Limiting the use of cars.
B. Encouraging people to walk.
C. Warning drivers of air pollution.
11.What does the woman think about the man’s idea?
A. It’s interesting.
B. It’s worth trying.
C. It’s impractical.
聽第8段材料，回答第12至14題。
12.How long will the man probably stay in New Zealand?
A. One week. B. Two weeks. C. Three weeks.
13.What advice does the woman give to the man?
A. Go to New Zealand after Christmas.
B. Book his flight as soon as possible.
C. Save more money for his trip.
14.What can we learn about flights to New Zealand at Christmas time?
A. They require early booking.
B. They can be twice as expensive.
C. They are on special offer.
聽第9段材料，回答第15至17題。
15.Why did Jane call Mike?
A. To ask him to meet her.
B. To tell him about Tom.
C. To borrow his car.
16.Where will Jane be in about one hour?
A. At Mike’s place. B. At the airport. C. At a garage.
17.What can we infer from the conversation?
A. Jane has just learned to drive.
B. Jane’s car is in bad condition.
C. Mike will go to the airport.
聽第10段材料，回答第18至20題。
18.What did the speaker ask the students to do the week before?
A. Write a short story.
B. Prepare for the lesson.
C. Learn more about the writer
19.Why does the speaker ask the questions?
A. To check the students’ understanding of the story.
B. To draw the students’ attention to reading skills.
C. To let the students discuss father-son relationships.
20.What will the students do in 10 minutes?
A. Ask more questions.
B. Discuss in groups.
C. Give their answers.
做聽力部分時，請先在試題卷上作答。聽力部分結束前，你將有兩分鐘的時間將第1至第17小題的答案轉涂到答題卡上，將第18至第20小題的答案轉寫到答題卡上。
第一節(共5小題；每小題1.5分，滿分7.5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秒鐘的時間來回答有關小題和閱讀下一小題。每段對話僅讀一遍。
1.Who is on duty today?
A.Jane. B.Peter. C.Jack.
2.Where are the speakers most probably going?
A.To the lab. B.To the lecture hall. C.To the cinema.
3.What does the man want to do?
A.Shop in the supermarket. B.Borrow a book from the library.
C.Get his book back.
4.Why did the man buy the hat?
A.His mother liked it. B.It was very beautiful.
C.It was affordable.
5.What are the two speakers talking about?
A.Their dreams. B.Their lessons. C.Their jobs.
第二節(共12小題；每小題1.5分，滿分18分)
聽下面4段對話，每段對話或獨白后有幾個小題，從題中所給的A、B、C三個選項選出最佳選項，并標在試卷的相應位置。聽每段對話前，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，每段對話讀兩遍。
請聽第6段材料，回答第6至8題。
6.Who went to the party held at Tom’s house yesterday?
A.Jane. B.Peter. C.Helen.
7.Where are the two speakers going next?
A.To Tom’s house. B.To Jane’s office. C.To the cinema.
8.What do we learn about the woman?
A.She made a mistake while working. B.She argued with her boss.
C.She refused to work in her spare time.
請聽第7段材料，回答第9至11題。
9.Which film won the Silver Bear at the Berlinale?
A.The Milk of Sorrow. B.About Elly. C.Forever Enthralled.
10.What is The Milk of Sorrow about?
A.A love story. B.A terrible war. C.A strange disease.
11.When was the festival founded?
A.In 1951. B.In 1959. C.In 1978.
請聽第8段材料，回答第12至14題。
12.What are the two speakers talking about?
A.A new teacher. B.A superstar. C.Their English study.
13.Why is the man surprised?
A.He has improved his English. B.No one misbehaves in the English class.
C.Mrs.Smith is a middle-aged woman.
14.Which word can be used to describe Mrs.Smith?
A.Strict. B.Wonderful. C.Careful.
請聽第9段材料，回答第15至17題。
15.What is the woman doing?
A.Cleaning her bedroom. B.Preparing for her maths exam.
C.Writing a report.
16.What does the man want to buy?
A.Eggs. B.A pizza. C.Some ink.
17.How will the man go to the supermarket?
A.By car. B.By bus. C.On foot.
第三節(共3小題；每小題1.5分，滿分4.5分)
聽下面一段材料，將第18至第20三個小題的信息補充完整，每空限填一個詞或一個數。聽材料前，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。本段材料讀兩遍。
聽第10段材料，回答第18至20題。
Characters The speaker and an old woman
Place At the bus station
Time After the speaker finished his classes at 18..
What happened 1.The speaker saw and old woman carrying a big 19..
2.He went up to her and offered to help her.
3.The woman was 20.at first but then she smiled.
第一節 （共5小題；每小題1.5分，滿分7.5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秒鐘的時間來回答有關小題和閱讀下一小題。每段對話僅讀一遍。
1.How much will the woman pay if she buys two skirts ?
A．$18. B．$19. C．$20.
2.What will the speakers discuss ?
A．A report . B．A computer . C．A report on computer .
3.What are the speakers talking about ?
A．A child . B．A room . C．A present .
4.What can we learn from this conversation ?
A．The woman does not get along well with the man .
B．The woman does not get along well with here roommate .
C．The man will talk with the woman’s roommate .
5.Where are the two speakers now ?
A．On the first floor . B．On the fourth floor . C．On the fifth floor.
第二節 （共15小題；每題1.5分，滿分22.5分）
聽下面5段對話或獨白。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。聽每段對話或獨白前，你將有時間閱讀各個小題，每小題5秒鐘；聽完后，每小題將給出5秒鐘的作答時間。每段對話或獨白讀兩遍。
聽第6段材料，回答第6、7題。
6.What was the woman doing before she went home ?
A．Typing a report . B．Rewriting a report . C．Reviewing a report .
7.Where did the woman have her dinner ?
A．In a restaurant . B．In her office . C．At home .
聽第7段材料，回答第8、9題。
8.Why does the man feel surprised ?
A．The woman has found a new job .
B．The woman doesn’t feel like leaving .
C．The woman disagrees with him .
9.What does the woman say abut her department ?
A．thee is a lack of trust .
B．There are serious problems .
C．There is too much pressure .
聽第8段材料，回答第10至12題。
10.What are the speakers talking about ?
A．Popular sports events .
B．TV programs people like best .
C．Things people do after work .
11.How did the woman do the research ?
A．She talked to people .
B．She sent letters to people .
C．She collected information from newspapers .
12.What do most people do in their spare time ?
A．Go to movies . B．Read books . C．Watch TV.
13.Where does this conversation take place ?
A．At the airport . B．In a restaurant . C．On the street .
14.Why does the woman like San Francisco ?
A．It has less traffic .
B．It has the best food and music .
C．People there are friendlier .
15.Where does the woman come from ?
A．Pennsylvania . B．San Francisco . C．China .
16.What does the woman think of the man’s English ?
A．Excellent . B．Acceptable . C．Strange .
聽第10段材料，回答第17至20題。
17.How many people are there in the woman’s family ?
A．Three . B．Four . C．Five .
18.What did the children think about having dinner together at home ?
A．They thought it was funny .
B．They disliked the idea at first .
C．They preferred eating with friends .
19.How often did the family finally decide to have meals together ?
A．Every Sunday . B．Twice a week . C．Three times a week .
20.Who finally set the time for these family dinners ?
A．The children . B．The father . C．The woman speaker .
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的答案第一節（共5小題：每小題1.5分，滿分7.5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秒鐘的時間來回答有關小題和閱讀下一小題。每例：How much is the shirt?
A. £19.15
B. £ 9.15
C. £ 9.18
答案是B。
1.How much will the man pay for the tickets?
A. £7.5 B. £15 C. £50
2.Which is the right gate for the man’s flight?
A. Gate 16. B. Gate 22. C. Gate 25.
3.How does the man feel about going to school by bike?
A. Happy. B. Tired. C. Worried.
4.When can the woman get the computers?
A. On Tuesday. B. On Wednesday. C. On Thursday.
5.What does the woman think of the shirt for the party?
A. The size is not large enough.
B. The material is not good.
C. The color is not suitable.
第二節（共15小題；每小題1.5分，滿分22.5分）
聽下面5段對話。每段對話后有幾個小題，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。每段對話讀兩遍。
聽第6段材料，回答第6、7題。
6.What can we learn about Mr. Brown?
A. He is in his office. B. He is at a meeting. C. He is out for a meal
7.What will the man probably do next?
A. Call back. B. Come again. C. Leave a message.
聽第7段材料，回答第8、9題。
8.What kind of room does the man want to take?
A. A single room. B. A double room. C. A room for three.
9.What does the man need to put in the form?
A. Telephone and student card numbers.
B. student card number and address
C. Address and telephone number.
聽第8段材料，回答第10至12題。
10.What is the relationship between the speakers?
A. Fellow clerks B. Boss and secretary. C. Customer and salesperson.
11.What does the man like about his job?
A. Living close to the office. B. Chances to go abroad. C. Nice people to work with
12.What do we know about the woman?
A. She likes traveling. B. She is new to the company. C. She works in public relations.
聽第9段材料，回答第13至16題。
13.When will the visitors come?
A. In March. B. In April C. In May
14.How many visitors are coming?
A.8. B.10. C. 12.
15.What will the visitors do on the second day?
A. Go to a party. B. Visit schools. C. Attend a lecture.
16.Where will the visitor go on the final day?
A. To London. B. To Scotland. C. To the coast.
聽第10段材料，回答第17至20題。
17.What is the first word the baby tried to say?
A. Truck. B.OK C. Duck.
18.How old was the baby when he learned to say that word correctly?
A. About 18 months. B. About 21 months. C. About 24 months.
19.What did the father do when the baby screamed that word at the airport?
A. He corrected the baby. B. He tired to stop the baby. C. He hid himself somewhere
20.Why did the mother pretend not to know the baby?
A. She got angry with the father.
B. She was frightened by the noise.
C. She felt uneasy about the noisy baby.
1．C 2．A 3．B 4．D 5．C 6．B 7．D 8．C 9．B 10．A
11．120° 12．3x＋y－1＝0 13．
14．10 15．100 16．（1），（4）
17．解：（1）設拋物線
，將（2，2）代入，得p＝1． …………4分
∴y2=2x為所求的拋物線的方程．………………………………………………………5分
（2）聯立
消去y，得到
． ………………………………7分
設AB的中點為
，則
．
∴ 點
到準線l的距離
．…………………………………9分
而
，…………………………11分
，故以AB為直徑的圓與準線l相切．…………………… 12分
（注：本題第（2）也可用拋物線的定義法證明）
18．解：（1）在△ACF中，
，即
．………………………………5分
∴
．又
，∴
．……………………
7分
（2）
． ……………………………14分
（注：用坐標法證明，同樣給分）
19．
解法一：（1）連OM，作OH⊥SM于H．
∵SM為斜高，∴M為BC的中點，∴BC⊥OM．
∵BC⊥SM，∴BC⊥平面SMO．
又OH⊥SM，∴OH⊥平面SBC．……… 2分
由題意，得
．
設SM＝x，
則
，解之
，即
．………………… 5分
（2）設面EBC∩SD＝F，取AD中點N，連SN，設SN∩EF＝Q．
∵AD∥BC，∴AD∥面BEFC．而面SAD∩面BEFC＝EF，∴AD∥EF．
又AD⊥SN，AD⊥NM，AD⊥面SMN．
從而EF⊥面SMN，∴EF⊥QS，且EF⊥QM．
∴∠SQM為所求二面角的平面角，記為α．……… 7分
由平幾知識，得
．
∴
，∴
．
∴
，即所求二面角為
． ……………… 10分
（3）存在一點P，使得OP⊥平面EBC．取SD的中點F，連FC，可得梯形EFCB，
取AD的中點G，連SG，GM，得等腰三角形SGM，O為GM的中點，
設SG∩EF＝H，則H是EF的中點．
連HM，則HM為平面EFCB與平面SGM的交線．
又∵BC⊥SO，BC⊥GM，∴平面EFCB⊥平面SGM． …………… 12分
在平面SGM中，過O作OQ⊥HM，由兩平面垂直的性質，可知OQ⊥平面EFCB．
而OQ
平面SOM，在平面SOM中，延長OQ必與SM相交于一點，
故存在一點P，使得OP⊥平面EBC． ……………………… 14分
，
，
，
． ……………… 1分
，
，
，
．
，
．
＝（0，1，0），由題意，得
．解得
．
． …………………………………………………… 5分
，
． ………………………………6分
，
，得
解得
∴
．………………… 8分
，∴
．…………… 10分
點．證明如下：
． ………………………… 11分
，令
與n2共線，則
． ……………… 13分
．故存在P∈SM，使OP⊥面EBC．………………………
14分
＝
． ………………3分
＝
=
≥
． …………6分
，
，
，∴公比
．……9分
． …………………………………………10分
． ……………12分
…
…
．……15分21．解：（1）∵
，
，∴
，∴
． 1分
，即
，∴
． …3分
，即
時，上式不成立．………………………………………………4分
，即
時，
．由條件
，得到
．
，解得
或
． ……………………………………………5分
，解得
或
．…………………………………………6分
m的取值范圍是
或
． ………………………………………7分
，即
．
，則
．
． ………………………10分
有相異兩實根
．
，∴
顯然
，
，
，∴
，∴
． …………12分
．
為三次函數
的極小值點，故
只有一個實根．…………………………15分