2-2003年数学高考试题及答案(江苏卷).doc

2003年普通高等学校招生全国统一考试（江苏卷）数 学（理工农医类）本试卷分第卷（选择题）和第卷（非选择题）两部分。第卷1至2页，第卷3至10页。考试结束后，将本试卷和答题卡一并交回。第卷（选择题共60分）一、选择题：本大题共12小题，每小题5分，共60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）如果函数的图象与轴有两个交点，则点平面上的区域（不包含边界）为（ ）（2）抛物线的准线方程是，则a的值为（ ）（A）（B）（C）8（D）8（3）已知（ ）（A）（B）（C）（D）（4）设函数的取值范围是（ ）（A）（1，1）（B）（C）（，2）（0，+）（D）（，1）（1，+）（5）是平面上一定点，是平面上不共线的三个点，动点满足的轨迹一定通过的（A）外心（B）内心（C）重心（D）垂心（6）函数的反函数为（ ）（A）（B）（C）（D）（7）棱长为的正方体中，连结相邻面的中心，以这些线段为棱的八面体的体积为（ ）（A）（B）（C）（D）（8）设，曲线在点处切线的倾斜角的取值范围为到曲线对称轴距离的取值范围为 （ ） （A） （B） （C） （D）（9）已知方程的四个根组成一个首项为的的等差数列，则 （ ） （A）1 （B） （C） （D）（10）已知双曲线中心在原点且一个焦点为F（，0），直线与其相交于M、N两点，MN中点的横坐标为，则此双曲线的方程是 （ ） （A） （B） （C） （D）（11）已知长方形的四个顶点A（0，0），B（2，0），C（2，1）和D（0，1），一质点从AB的中点沿与AB的夹角的方向射到BC上的点后，依次反射到CD、DA和AB上的点、和（入射角等于反射角），设的坐标为（，0），若，则tg的取值范围是 （ ） （A）（，1） （B）（，） （C）（，） （D）（，）（12）一个四面体的所有棱长都为，四个顶点在同一球面上，则此球的表面积为（ ）（真的不掉线吗？、？A）（B）4（C）（D）2003年普通高等学校招生全国统一考试（江苏卷）真的不掉线吗？、？数 学（理工农医类）第卷（非选择题共90分）二.填空题：本大题共4小题，每小题4分，共16分。把答案填在题中横线上。（13）的展开式中系数是 （14）某公司生产三种型号的轿车，产量分别为1200辆，6000辆和2000辆。为检验该公司的产品质量，现用分层抽样的方法抽取46辆进行检验，这三种型号的轿车依次应抽取_，_，_辆。（15）某城市在中心广场建造一个花圃，花圃分为6个部分（如图）。现要栽种4种不同颜色的花，每部分栽种一种且相邻部分不能栽种同样颜色的花，不同的栽种方法有_种。（以数字作答）（16）对于四面体ABCD，给出下列四个命题。其中真命题的序号是_.（写出所有真命题的序号）三、解答题：本大题共6小题，共74分，解答应写出文字说明，证明过程或或演算步骤（17）（本小题满分12分） 有三种产品，合格率分别为0.90,0.95和0.95，各抽取一件进行检验。（）求恰有一件不合格的概率；（）求至少有两件不合格的概率。（精确到0.001（18）（本小题满分12分）已知函数上的偶函数，其图象关于点对称，且在区间上是单调函数。求的值。（19）（本小题满分12分） 如图，在直三棱柱中，底面是等腰直角三角形，侧棱，D、E分别是与的中点，点E在平面ABD上的射影是ABD的重心G（）求与平面ABD所成角的大小（结果用反三角函数值表示）（）求点到平面AED的距离（20）（本小题满分12分）已知常数。经过原点O以为方向向量的直线与经过定点为方向向量的直线相交于P，其中。试问：是否存在两个定点E、F，使得为定值。若存在，求出E、F的坐标；若不存在，说明理由。（21）（本小题满分12分）已知为正整数。（）设，证明；（）设，对任意，证明。（22）（本小题满分14分）设，如图，已知直线及曲线上的点的横坐标为作直线平行于轴，交直线作直线平行于轴，交曲线的横坐标构成数列（）试求的关系，并求的通项公式；（）当时，证明（）当时，证明真的不掉线吗？、？一、 仿照例句用所给的词汇造句。1.Example: I, see him, he, cross the streetI saw him while he was crossing the street. He was crossing the street when I saw him.A.the sun, shine, we, e outB.she, study at college, the war, break outC.she, work in a factory, the city, be liberated (解放)D.he, lose his pen, he, go sightseeing in the city2.Example: I, do my homework, last nightI was doing my homework last night.A.they, have a dress rehearsal, yesterday eveningB.my grandma, visit my family, half an hour agoC.I, travel in the south, at this time last yearD.they, build a power station, at that time3.Example: she, not at home that evening, she, look after her sick child in hospitalShe wasnt at home that evening. She was looking after her sick child in hospital.A.it, rather chilly yesterday, the sun, not shineB.she, ill that day, she, suffer from a severe headacheC.I, not say anything, but a struggle (斗争), go on in my mindD.We, be rather busy then, we, make preparation for the journey4.Example: war, go on, during all those yearsWar was going on during all those years.A.a cold rain, drizzle down, all day yesterdayB.the whole night, the wind, howl like madC.in all those days, they, struggle heroically against the fascists (法西斯主义者)D.for three weeks, our forces, push forward at a great speed真的不掉线吗？、？二、 用动词的适当形式填空。1. While we _ (wait) for the bus, a girl _ (run) up to us.2. I _ (telephone) a friend when Bob _ (e) in.3. Jim _ (jump) on the bus as it _ (move) away.4. We _ (test) the new machine when the electricity _ (go) off.5. She _ (not want) to stay in bed while the others _ (all, work) in the fields.6. While mother _ (put) Cathy to bed, the door bell _ (ring).7. As I _ (walk) in the park, it _ (begin) to rain.8. Even when she _ (be) a child she _ (already, think) of being a ballerina (芭蕾舞演员).9. It was quite late at night. George _ (read) and Amy _ (ply) her needle when they _ (hear) a knock at the door.10. There _ (be) a group round the fire when they _ (reach) it. An old woman _ (sit) on the ground near the kettle; two small children _ (lie) near her; a donkey _ (bend) his head over a tall girl.1. I _ (have) my breakfast at half past six yesterday morning.2. Mary _ (go) over her lessons from six to seven last night. John and peter _(do) the same thing.3. What _ you _ (do) at that time? We _ (watch) TV.4. Was your father at home yesterday evening? Yes ,he was. He _ (listen) to the radio.5. They _(not make) a model ship when I saw him.6. _ they _ (have) a meeting at 4 yesterday afternoon?No, they _. They _ (clean) the classroom.7. _ it _(rain) when you left school? Yes, it _. (No, it _)8. What _ your father _ (do) when he was your age?9. One day, Edison _ (wait) for a train to arrive, and suddenly a little boy ran to the track(轨道) to play.10. He asked me if I _ (go) fishing that afternoon.11. The three of them were in a hurry because their plane _ (leave) in five minutes.12. In a letter, john told us that he _ (e) to china next month.13. When the bell rang, jenny _ (wait) in her seat.14. She _ (make) her dress the whole afternoon.15. While my father _ (look) through the evening paper, he suddenly _ a cry.16. When I _ (e) in the room, he _ (see) me, for he _ (read) something17. When we _ (arrive) at the village, it _ (get) dark and it _ (rain) hard.18. I _ (know) you _(wait) for me here.19. One day a little monkey _(play) in a tall tree. A mother crocodile(鳄鱼) _ (look) for food near the bank.20. What _ your father _ (do) yesterday evening? He _ (study) at the evening school.21. Later his parents found that he _ (sit) on some eggs.真的不掉线吗？、？22. When he knocked at the door, my aunt _ (cook)23. The students _ (sing) and _ (dance) happily on the playground at that time.24. I _ (write) a letter when the door bell rang.25. We had no classed at that time. We _ (plant) trees.三、 选择题。1. I _ cooked a meal when you _ me.a. cooked, were ringing b. was cooking, rangc. was cooking, were ringing d. cooked, rang2. He said he _ to draw a plane on the blackboard at that time.a. tries b. tried c. was trying d. will try3. While she _ TV, she _ a sound outside the room.a. was watching, was hearing b. watched, was hearingc. watched, heard d. was watching, heard4. They _ a football game from 7 to 9 last night.a. were watching b. watch c. watched d. are watching5. What book _ you _ when I _ you at four yesterday afternoon?a. did, read, was seeing b. did, read, sawc. were, reading, saw d. were, reading, was seeing6. It was Friday evening. Mr and Mrs. Green _ ready to fly to England.a. are getting b. get c. were getting d. got7. Lei Feng _ always _ of others when he _ in the army.a. is, thinking, was b. was, thinking, is c. did, think, is d. was, thinking, was8. A girl _ my pen fall off the table when she _ me.a. saw, passed b. was seeing, passed c. was seeing, passed d. was seeing, was passing9. We _ for tom at ten last Sunday. He often kept us _.a. were waiting, waiting b. were waiting, wait c. waited, waiting d. waited, wait10. He _ his father on the farm the whole afternoon last Saturday.a. helps b. would help c. was helping d. is helping11. While mother _ some washing, I _ a kite for Kate.a. did, made b. was doing, made c. was doing, was making d. did, was making12. “_ you angry then?” “they _ too much noise.”a. are, were making b. were, were making c. are, made d. were, made13. He _ some cooking at that time, so _ mea. did, heard b. did, didnt hear c. was doing, heard d. was doing, didnt hear14. This time yesterday jack _ his bike. He _ TVa. repaired, didnt watch b. was repairing, watchedc. repaired, watched d. was repairing, wasnt watching15. His parents wanted to know how he _ on with his new classmates.a. was getting b. gets c. is getting d. will get四、 翻译。真的不掉线吗？、？1 昨天这个时候你们英语老师在做什么？她在和一些家长谈话吗？2 当我离开的时候他正在画一幅世界地图。3 当你看见他们的时候他们在干什么？他们在打扫教室。4 那时二班的学生没在操场上踢足球，他们在打篮球。5 一天，母亲下班回家的时候，约翰在写给一个朋友写信。6 上周五一下午，学生们在干什么？他们一直在往墙上贴海报。7 昨天这个时候，一些学生在植树,一些学生在给小树浇水。8 老师走进教室的时候，学术们正在谈论当天的新闻。9 老虎等猴子的时候，他听到一个声音。10. 今天上午放学的时候在下雨吗？是的，天正下着大雨。过去进行时专项练习（二）一填入以下单词的正确形式。1 It was warm,so I _(take) off my coat.2 Jane _(wait) for me when I _(arrive).3 Sue wasnt hungry, so she _(eat) anything.4 My brother came into the bedroom while I _(dance).5 _ he _(lie) on the ground at nine yesterday evening ?6 What _ Jim _(write) when the teacher came in ?7 Mike and I _(play) baskteball at that time yesterday afternoon.8 My brother _(fall) while he _(ride) his bicycle and hurt himself.9 I first met Lisa three years ago. She _(work) at a radio shop at the time.10.When I arrived at his office , he _ on the phone.(speak)二.按要求进行句型转换。1. We were having a PE class at four yesterday afternoon.(改为否定句)We _ _ a PE class at four yesterday afternoon.2. Kate was reviewing her lessons at eight last night.(改为一般疑问句，做肯，否回答，对划线部分提问)3. He ran in the park .(用at this time yesterday改写)4. They were playing puter games at nine last night.( 划线部分提问)5. I was reading a novel at three yesterday afternoon.( 划线部分提问)三.根据汉语提示完成句子。1 他们那时不在打排球。真的不掉线吗？、？They _ _ volleyball at that time.2 当你回来时，他在看电视吗？_ he _ Tv when you came back?3 昨天中午他在哪里等你？_ _ he _ for you at noon yesterday ?4 当我离开时，他正在做家庭作业。He _ _ his homework when I left.5 正当他们扫地的时候，老师进来了。While they_ _ the floor , the teacher came in.过去进行时专项练习（三）一、动词填空。John_（work） all day yesterday.He _（walk） home when the （rian）_begin.What_you _（do） at ten oclock yesterdayI_（studay） in classWhen Harry _（have） breakfast Lily _（telephone） him When I _ （go） to school this morning I _ （see） a car running into a bus6This time yesterday Jack _ (mend) his bike.7.I _ (write) a letter at ten last night.8.It was six. The Greens _ (have) supper.9.When you _ (knock) at the door yesterday,I _ (do) some washing.10.While my mother _ (watch) TV, I _(make) a kite.单项选择二、选择1.My brother _ while he _ his bicycle and hurt himself. A. fell, was riding B. fell, were ridingC. had fallen, rode D. had fallen, was riding 2. Tom _ into the house when no one _. A. slipped, was looking B. had slipped, lookedC. slipped, had looked D. was slipping, looked 3.The last time I _ Jane she _ cotton in the fields. A. had seen, was picking B. saw, picked C. had seen, picked D. saw, was picking 4.I don t think Jim saw me; he _ into space. A. just stared B. was just staring C. has just stared D. had just stared 5.I first met Lisa three years ago. She _ at a radio shop at the time. A. has worked B. was working C. had been working D. had worked 6.-Hey, look where you are going! -Oh, I m terribly sorry._. A. I m not noticing B. I wasn t noticing C. I haven t noticed D. I don t notice 7. The reporter said that the UFO _ east to west when he saw it. A. was traveling B. Traveled C. had been traveling D. was to travel 8. I _ my breakfast when the morning post came. A. had B. had been having C. have been having D. was having 9.When I arrived at his office, he _ on the phone. 真的不掉线吗？、？A. was speaking B. spoke C. had been speaking D. had spoken 10. “ What s the matter, Ali? You look sad. ” “ Oh, nothing much. As a matter of fact, I _ of my friends back home. ” A. just thought B. have just been thinking C. was just thinking D. have just thought三、句型变换1、I was waiting for a bus at that time.改为否定句 对划线部分提问 2、The boy was playing over there at six yesterday.改为一般疑问句 做出肯定和否定回答 对划线部分提问 3、Lucy was helping her mother this time on Sunday.改为反意疑问句 对划线部分提问 四、英汉互译。1、 昨晚我给你打电话时，你正在干什么？ 2、 上中学时，我住老师家里。3、 他昨天本来要看那场戏的，可是太忙4、 They wanted to know when we were leaving for Shanghai.5、 Soon the whole town was talking about it. 真的不掉线吗？、？选择题。Bcdac,cdaac,cbdda用动词的适当形式填空。1.was having 2.was going,were doing 3.were doing,were watching 4.was listening 5.were not making 6.Were having were cleaning 7.was raining 8.did do(do) 9. was waiting 10.was going/would go 11.was leaving 12.is ing /will e 13 was waiting 14.was making 15. was looking ,heard 16.came ,didnt see , was reading 17.arrived , was getting , was raining 18.didnt know ,are waiting 19. was playing ,was looking 20. was doing , was studying 21.was sitting 22.was cooking 23.were singing dancing 24.was writing 25. were planting 翻译。1 What was you English teacher doing this time yesterday?Was she talking with some parents?2When I left, he was drawing a map of the world.3What were they doing when you saw them?They were cleaning the classroom.4At that time the Class Two students were not playing football in the playground. They were playing basketball.5One day John was writing to one of his friends when his mothers came back from work.6What were the students doing the whole afternoon last Friday?They were putting up the posters on the wall.7This time yesterday some students were planting trees and some were watering the trees.8When the teacher came into the classroom, the students were talking about that days news.9 When the tiger was waiting for the monkey, he heard a sound.10Was it raining when school was over this morning?Yes, it was raining heavily.答案:一. 1. A. The sun was shining when we came out. (While sun was shining, we came out.) B. She was studying at college when the was broke out. (While she was studying at college, the was broke out.) C. She was working in a factory when the city was liberated. (While she was working in a factory, the city was liberated.) D. He lost his pen while he was going sightseeing in the city. (When he lost his pen, he was going sightseeing in the city.)2. A. They were having a dress rehearsal yesterday evening. B. My grandma was visiting my family half an hour ago. C. I was traveling in the south at this time last year. D. They were building a power station at that time.3. A. It was rather chilly yesterday. The sun was not shining. B. She was ill that day. She was suffering from a severe headache. C. I did not say anything, but a struggle was going on in my mind. D. We was rather busy then. We were making preparation for the journey.4. A. A cold rain was drizzling down all day yesterday. B. The whole night the wind was howling like mad. C. In all those days they were struggling heroically against the fascists. D. For three weeks our forces were pushing forward at a great speed.二、1. were waiting; ran2. was telephoning; came3. jumped; was moving4. was testing; went5. didnt want; were all working6. was putting; rang 真的不掉线吗？、？Module5Unit3练习题一 根据汉语提示完成句子。1.No one knows whether Mr Li lives on the _(八)floor of this building.2.They have_ _(谈论)the film many times since they saw it.3.Mr Black_(养)a dog last year.4._ _(随便吃)some fish,children.5.My friends are all invited_(除了)me,so I feel sad.6.李小姐也加入到阅读中了。Miss Li_ _ _reading.7.学生们都通过了这次考试，包括我。The students have passed the exam,_me.8.农民们在春天辛勤地劳动是为了在秋天有一个好的收成。The farmers work hard in spring_ _ _have a good harvest in autumn.9.他能读书吗？ 是的。他在五岁时就能读书了。_he read books?Yes,he_.He_do it at the age of 5.10.他建议每天我们应浇三次花。He suggested that we_ _the flowers three times a day.二 用括号内所给单词的适当形式填空。1.Have you ever_(be)to Beijing?2.I have nothing_(drink0.3.I can see a bird _(fly)in the sky.4.We arent allowed _(smoke) in the school.5.He suggested that the girl_(leave) the room at once.6.Sunday is the_(one)day of a week.7.Im sorry to keep you_(wait)so long.8.The policemen are very_(worry) about this traffic accident.9.Education can help children and young