高三春季招生考试数学.docx

1、高三春季招生考试数学 2019-2020年高三春季招生考试（数学）考生注意：1答卷前，考生务必在答题纸上将姓名、高考准考证号填写清楚，并在规定区域内贴上条形码2本试卷共有23道试题，满分150分考试时间120分钟一、填空题（本大题满分56分）本大题共有14题，考生应在答题纸相应编号的空格内直接填写结果，每题填对得4分，否则一律得零分1函数的定义域为_。2若集合，则=_。3在ABC中，则=_。4若行列式，则=_。5若，则=_。（结果用反三角函数表示）6的二项展开式的常数项为_。7两条直线与的夹角的大小是_。8若为等比数列的前n项的和，则=_。9若椭圆C的焦点和顶点分别是双曲线的顶点和焦点，则椭圆

2、C的方程是_。10若点O和点F分别为椭圆的中心和左焦点，点P为椭圆上的任意一点，则的最小值为_。11根据如图所示的程序框图，输出结果i=_。12xx年上海春季高考有8所高校招生，如果某3位同学恰好被其中2所高校录取，那么录取方法的种数为_。13有一中多面体的饰品，其表面右6个正方形和8各正三角形组成（如图），AB与CD所成的角的大小是_。14为求方程的虚根，可以把原方程变形为，由此可得原方程的一个虚根为_。二、选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得 5分，否则一律得零分15若向量，则谢列结论正确的是（ ）

3、A B C D16的图像关于 （ ） A原点对称 B直线对称 C直线对称 Dy轴对称17直线与圆 的位置关系是 （ ） A相交或相切 B相交或相离 C相切 D相交18若均为单位向量，则是的答 （ ） A充分不必要条件 B必要不充分条件 C充要条件 D既不充分也不必要条件三、解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号规定区域内写出必要的步骤19（本题满分12分）已知向量，设函数，求函数的最小正周期及时的最大值20（本题满分14分） 某甜品店制作蛋筒冰淇淋，其上半部分呈半球形，下半部分呈圆锥形（如图）。现把半径为10cm的圆形蛋皮分成5个扇形，用一个扇形蛋皮围成锥形

4、侧面（蛋皮厚度忽略不计），求该蛋筒冰淇淋的表面积和体积（精确到001）21（本题满分14分）本题公园小题，第1小题满分4分，第2小题满分10分。已知抛物线（1）ABC的三个顶点在抛物线F上，记ABC的三边AB、BC、CA所在的直线的斜率分别为，若A的坐标在原点，求的值；（2）请你给出一个以为顶点、其余各顶点均为抛物线F上的动点的多边形，写出各多边形各边所在的直线斜率之间的关系式，并说明理由。说明：第（2）小题将根据结论的一般性程度给与不同的评分。22（本题满分16分）本题共有3个小题，第1小题满分6分，第2小题满分6分，第3小题满分4分定义域为R，且对任意实数都满足不等式的所有函数组成的集合记

5、为M，例如，函数。（1）已知函数，证明：；（2）写出一个函数，使得，并说明理由；（3）写出一个函数，使得数列极限23（本题满分18分）本题共有3个小题，第1小题满分4分，第2小题满分8分，第3小题满分6分对于给定首项，由递推公式得到数列，对于任意的，都有，用数列可以计算的近似值。（1）取，计算的值（精确到001）；归纳出的大小关系；（2）当时，证明：；（3）当时，用数列计算的近似值，要求，请你估计n，并说明理由。来源： 2019-2020年高三春季招生考试（英语）考生注意：1本试卷分为第I卷和第II卷两部分。全卷满分150分，考试时间120分钟。2答第I卷前，考生务必在答题卡和答题纸上用钢笔或

6、圆珠笔清楚填写姓名、准考证号、校验码，并用铅笔在答题卡上正确涂写准考证号和校验码。3第I卷（第116小题、2580小题）由机器阅卷，答案必须全部涂写在答题卡上。考生应将代表正确答案的小方格用铅笔涂黑，注意试题题号和答题卡编号一一对应，不能错位。答案需要更改时，必须将原选项用橡皮擦去，重新选择。答案不能涂写在试卷上，涂写在试卷上一律不给分。第I卷中的1724小题、8184小题和第II卷的试题，其答案用钢笔或水笔写在答题纸上，如用铅笔答题，或写在试卷上也一律不给分。第I卷（共105分）IListening prehensionSection ADirections: In Section A, y

7、ou will hear ten short conversations between two speakersAt the end of each conversation, a question will be asked about what was saidThe conversations and the questions will be spoken only onceAfter you hear a conversation and the question about it, read the four possible answers on your paper, and

8、 decide which one is the best answer to the question you have heard1AIn a cinema. BIn a library. CIn a restaurant. DIn a grocery store.2ATable-tennis. BSwimming CJogging. DTennis.3ASix hours. BEight hours. CTen hours. DFourteen hours.4AA policeman. BA waiter. CA hotel receptionist. DA shop-assistant

9、.5AShe no longer believes the man BShe will offer him another cigarette. CThe man must give up smoking. DThe man should make a resolution.6AHe hopes to leave before the woman. BHe is certain that the lock works. CHis office is one hours ride from here. DHe will leave the office in about an hour7AHe

10、wont stay on the beach the whole day. BHe thinks its boring being on a beach. CHe totally disagrees with the woman. DHe thinks not all beaches are nice.8AThe cake is unhealthy. BThe cake is sold by weight. CThe woman should go on a diet. DThe woman should have the cake.9AHe was moved by the conducto

11、r. BThe conductor was unsatisfactory CThey both enjoyed the concert. DHe didnt like the choice of music.10AShe has refused the mans request. BShe cant follow his words CShe thinks its a big favour DShell see if she can help.Section B Directions: In Section B, you will hear two short passages, and yo

12、u will be asked three questions on each of the passagesThe passages will be read twice, but the questions will be spoken only onceWhen you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 1

13、3 are based on the following passage.11AThey read and discuss books. BThey prepare for reading contests. CThey exchange experience in writing. DThey explain and revise books.12ABy asking guests to bring snacks. BBy giving tests to group members. CBy listing must-read books alone. DBy engaging everyo

14、ne in the discussion.13AHow to host a book club. BWhen to host a club meeting. CWhere to locate a book club. DWhom to choose as a club member.Questions 14 through 16 are based on the following passage.14AMobiles may cause health problems BMobiles may disturb people around. CFilm watching will be int

15、errupted. DPeople talk too loud on the phone.15AIt is impossible to ban mobiles. BPeople need mobiles in an emergency. CDinning with a different staff member. DHolding various operational meetings.16AEmbarrassing. BNecessary. CSensible. DMeaningless.Section CDirections: In Section C, you will hear t

16、wo longer conversationsThe conversations will be read twiceAfter you hear each conversation, you are required to fill in the numbered blanks with the information you have heardWrite your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.plete the formWrite ONE

17、 WORD for each answer.Survey SheetName:David GorgeOccupation: 17 baseball playerHobby:Reading 18 Recent exciting event:Had the 19 babyThe most admired person:His wifeFuture plan:To have lots of 20 Blanks 21 through 24 are based on the following conversation.plete the formWrite NO MORE THAN THREE WOR

18、DS for each answer.What does the man find especially expensive? 21 .Where does the man buy his clothes?He mainly shops 22 .When does the man go and buy all the low stuff and get low prices?When there are sales going around, especially after 23 What are the mans money saving tips for international st

19、udents in the UK? Rent a house with friends and dont buy things 24 .IIGrammar and VocabularySection ADirections: Beneath each of the following sentences there are four choices marked A, B, C and DChoose the one answer that best pletes the sentence.25Soon after dinner, Wayne drove off _ the direction

20、 of Paris. Ato Bat Cfor Din26They produced two reports, _ of which contained any useful suggestions. Aeither Ball Cnone Dneither27Some young people these days just _ go out of their homes to contact the real world Amustnt Bwont Cmightnt Dshouldnt28Youd be exposed to a lot _ pollution if you moved to

21、 a town with pure water and air. Amore Bmost Cless Dleast 29Im sure you will do better in the test because you _ so hard this year Astudied Bhad studied Cwill study Dhave been studying30The banker was found in a remote village after _ his office last Thursday. Aleave Bbeing left Cleaving Dhaving bee

22、n left31I have no idea _ the journalist could have got his information from. Athat Bwhy Cwhy Dwhere32A lot of people often forget that oral exams _ to test our municative ability Adesign Bare designed Care designing Dare being designed33Viewers continue to watch TV _ they plain about the quality of

23、the programming. Aeven though Bas if Cas long as Dunless34Mike found his missing car in the street outside his house, _ newly cleaned and polished. Alooked Bto look Clooking Dto be looking35There are fewer teaching positions left in big cities, _ at the same time there are shortages of teachers in s

24、mall towns Aor Band Cso Dfor36_ in 1955, Disneyland in California in regarded by any as the original fun park AOpened BHaving opened COpening DBeing opened37Fayes fondest memory is of last year, _ the club gave a tea party for her birthday. Athat Bwhich Cwhere Dwhen38The result of the study indicate

25、d that it was the type of fat _ made the difference Athat Bwhat Cwho Das39_ es will be weled to the open-air concert. AWhatever BWhoever CNo matter what DNo matter who40Harrison Ford is thought to be one of the few movie stars _ as a carpenter before Ato work Bto be working Cto have worked Dto have

26、been workingSection BDirections: plete the following passage by using the words in the boxEach word can only be used onceNote that there is one word more than you need.AprimarilyBsimilarCconsideratelyDconnectionsEinstructedFseriesGpersonalHservedIdefinedJenvironmentIn a study of the university of Mi

27、nnesota, twins (some raised together and others who had grown up apart) were tested for a wide range of personality traits (特征)In terms of happiness 41 as the ability to enjoy lifetwins who are separated soon after birth were much less alike than twins raised togetherBut when it es to unhappiness, t

28、he twins raised apartsome without contact for as long as 64 yearswere as 42 as those who had grown up together.Why is unhappiness less influenced by 43 ? When we are happy, we are more responsive to people and keep up 44 better than when we are feeling sadThis doesnt mean, however, that some people

29、are born to be sad and thats thatUnhappiness may be related to genes, but this inherited trait can be influenced by 45 choiceYou can increase your happiness through your own actions.In a whole 46 of experiments by psychologists John Reich and Alex Zautra at Arizona State University, they asked students to select their favourite activities from a list of everyday pleasuresthings like going to a movie, talking with friends and playing cards.Then the researchers 47 some of the students in the experiment to increase the number of favourite activities