阶段评估检测(四) 必修4

潍坊七中阶段性评估练习题高二数学(文科)本试卷共4页，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，用橡皮擦千净后，再改涂在其它答案标号。

3．参考公式：[]1cos cos cos()cos()2αβαβαβ=++-；sin sin 2sin cos 22x y x y x y +-+=； []1sin sin cos()cos()2αβαβαβ=-+--；sin sin 2cos sin 22x y x y x y +--=； []1sin cos sin()sin()2αβαβαβ=++-；cos cos 2cos cos 22x y x y x y +-+=； []1cos cos sin()sin()2αβαβαβ=+--；cos cos 2sin sin 22x y x y x y +--=-。

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．cos28cos73cos62cos17︒︒+︒︒=（ ）A ．2-BC ．2D ．1± 2．对于向量a ，b ，c 和实数λ，下列叙述正确的是（ ）A ．若0a b ∙=，则0a =或0b =B ．若0a λ=，则0λ=或0a =C ．若22a b =，则a b =或0a = D ．若a b a c ∙=∙，则b c = 3．已知4cos()45πθ+=，则sin 2θ等于（ ） A ．725- B ．725 C ．925 D ．1725 4．已知a ，b 均为单位向量，他们的夹角为60︒，那么a b +等于（ ）A B C D ．45．sin cos θθ+的最大值是（ ）A ．1B ．2 CD6．化简AB BD AC CD−−→+−−→-−−→-−−→等于（ ） A ．AD −−→ B ．0 C ．BC −−→ D ．DA−−→ 7．已知5a =，b 在a 方向上的正射影的数量为6，则a b ∙=（ ）A ．5B ．30C ．6D ．38．在ABC ∆中，若2sin b a B =，则A 等于（ ）A ．30︒或60︒B ．45︒或60︒C ．120︒或60︒D ．30︒或150︒9．函数21sin(2)2cos 2x y x π+-=+的最小正周期是（ ） A ．2π B ．4π C ．2π D ．π 10．在ABC ∆中，角A ，B 均为锐角，且cos sin A B >，则ABC ∆的形状是（ ）A ．直角三角形B ．锐角三角形C ．钝角三角形D ．等腰三角形11．已知A （6，3），B （9，3），C（3,3+，则ABC ∠=（ ）A ．150︒B ．135︒C ．120︒D ．60︒12．已知a b ⊥，2a =，6b =，且32a b +与a b λ-垂直，则实数λ的值为（ ）A ．-6B ．6C ．6±D ．1第II 卷(非选择题 共90分)注意事项：1．第II 卷包括填空题和解答题共两个大题2．第II 卷所有题目的答案考生需用黑色签字笔答在“数学”答题卡指定的位置二、填空题：本大题共4个小题，每小题4分，共16分。

潍坊七中阶段性评估练习题高二数学(理科)本试卷共4页，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，用橡皮擦千净后，再改涂在其它答案标号。

3．参考公式：[]1cos cos cos()cos()2αβαβαβ=++-；sin sin 2sincos 22x y x yx y +-+=； []1sin sin cos()cos()2αβαβαβ=-+--；sin sin 2cos sin22x y x yx y +--=； []1sin cos sin()sin()2αβαβαβ=++-；cos cos 2cos cos22x y x yx y +-+=； []1cos cos sin()sin()2αβαβαβ=+--；cos cos 2sin sin22x y x yx y +--=-。

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．在数列1，1，2，3，5，8，x ，21，34，55中，x 等于（ ） A ．11 B ．12 C ．13 D ．142．对于向量a ，b ，c 和实数λ，下列叙述正确的是（ ）A ．若0a b ∙=，则0a =或0b =B ．若0a λ=，则0λ=或0a =C ．若22a b =，则a b =或0a = D ．若a b a c ∙=∙，则b c =3．已知4cos()45πθ+=，则sin 2θ等于（ ）A ．725-B ．725C ．925D ．17254．已知a ，b 均为单位向量，他们的夹角为60︒，那么a b +等于（ ）A B C D ．4511这两数的等比中项是（ ）A ．1B ．-1C ．1±D ．126．化简AB BD AC CD −−→+−−→-−−→-−−→等于（ ） A ．AD −−→ B ．0 C ．BC −−→ D ．DA−−→ 7．等比数列{}n a 中，2a =9，5a =243，则{}n a 的前4项和为（ ） A ．81 B ．120 C ．168 D ．192 8．在ABC ∆中，若2sin b a B =，则A 等于（ ）A ．30︒或60︒B ．45︒或60︒C ．120︒或60︒D ．30︒或150︒9．函数21sin(2)2cos 2x y x π+-=+的最小正周期是（ ） A ．2π B ．4πC ．2πD ．π10．在ABC ∆中，角A ，B 均为锐角，且cos sin A B >，则ABC ∆的形状是（ ） A ．直角三角形 B ．锐角三角形 C ．钝角三角形 D ．等腰三角形11．已知a b ⊥，2a =，6b =，且32a b +与a b λ-垂直，则实数λ的值为（ ） A ．-6 B ．6 C ．6± D ．112．等差数列{}n a 中，14739a a a ++=，36927a a a ++=，则数列{}n a 前9项的和9S 等于（ ） A ．66 B ．99 C ．144 D ．297 第II 卷(非选择题 共90分) 注意事项：1．第II 卷包括填空题和解答题共两个大题2．第II 卷所有题目的答案考生需用黑色签字笔答在“数学”答题卡指定的位置 二、填空题：本大题共4个小题，每小题4分，共16分。

单元突破：必修4Unit4 单元评估检测第Ⅰ卷第一部分：阅读理解(共两节，满分60分)第一节(共15小题；每小题3分，满分45分)阅读下列短文，从每题所给的四个选项(A、B、C和D)中，选出最佳选项。

ALisa was running late. Lisa，25，had a lot to do at work，plus visitors on the way: her parents were coming in for Thanksgiving from her hometow n. But as she hurried down the subway stairs，she started to feel uncomfortably warm. By the time she got to the platform，Lisa felt weak and tired—maybe it hadn’t been a good idea to give blood the night before，she thought. She rested herself against a post close to the tracks.Several yards away，Frank，43，and his girlfriend，Jennifer，found a spot close to where the front of the train would stop. They were deep in discussion about a house they were thinking of buying.But when he heard the scream，followed by someone yelling，“Oh，my God，she fell in！” Frank didn’t hesitate. He jumped down to the tracks and ran some 40 feet toward the body lying on the rails. “No! Not you！” his girlfriend screamed after him.She was right to be alarmed. By the time Frank reached Lisa，he could feel the tracks shaking and see the light coming. The train was about 20 seconds from the statio n.It was hard to lift her. She was just out. But he managed to raise her the four feet to the platform so that bystanders could hold her by the arms and drag her away from the edge. That was where Lisa briefly regained consciousness，felt herself being pulled along the ground，and saw someone else holding her purse.Lisa thought she’d been robbed. A woman held her hand and a man gave his shirt to help stop the blood pouring from her head. And she tried to talk but shecouldn’t，and that was when she realized how much pain she was i n.Police and fire officials soon arrived，and Frank told the story to an officer. Jennifer said her boyfriend was calm on their 40-minute train ride downtown—just as he had been seconds after the rescue，which made her think about her reaction at the time. “I saw the train coming and I was thinking he was going to die，”she explained.1．What was the most probable cause for Lisa’s weak-ness?A．She had run a long way.B．She felt hot in the subway.C．She had done a lot of work.D．She had donated blood the night before.2．Why did Jennifer try to stop her boyfriend?A．Because they would miss their trai n.B．Because he didn’t see the train coming.C．Because she was sure Lisa was hard to lift.D．Because she was afraid the train would kill him.3．The passage is intended to ________．A．warn us of the danger in the subwayB．show us how to save people in the subwayC．tell us about a subway rescueD．report a traffic accidentBIn China，many people are leaving the countryside to find jobs in the cities，because the countryside is much poorer than the city，and often there isn’t much work there. Services such as hospital and transport are usually much better in the city than in the countryside. They hope that their lives will improve when they move to the city.But in the big cities of Europe like London or Paris，people are moving out ofthe city. These rich families want to live a quieter life. They are tired of the noise and the dirt of the city，and they are tired of the crowded streets，crowded trains and buses. They don’t want to live in the cities any more. They want a house with a garden in the countryside，and breathe the fresh air there.So they move out of the cities. Some don’t go very far，just a little way out of the city，to the towns near the cities. Other people move to the real countryside with sheep，cows and green fields. There，they start new lives and try to make new friends.Not all those who move from the city to the countryside are happy. After two or three years，many people who have done this feel that it was a big mistake. They don’t make so much money and there isn’t much work to do. People in the countryside are very different and aren’t always very friendly.As a result，quite a lot of people who have moved to the countryside move back to the city. “It’s_wonderful_to_see_crowds_in_the_streets_and_cinema_lights，” they say.4．Which is NOT the reason for people moving to the cities in China?A．The countryside is much poorer than the city.B．People in the countryside have nothing to eat.C．People in the countryside don’t have much work to do there.D．Services in cities are usually much better than those in the countryside.5．After moving to the countryside，some people in Europe feel unhappy because ________．A．they can’t make much moneyB．there isn’t much work for them to do in the countrysideC．some people in the countryside aren’t always very friendly to themD．A，B and C6．The underlined sentence in the last paragraph shows ________．A．they are happy to move back to the cityB．they miss their friends in the countrysideC．they still want to move to the countrysideD．they are tired of the noise and the crowded streets in the city7．The best title of thi s passage may be “ ________”．A．A happy life!B．Living in the city!C．Moving out or moving back?D．Living in the countryside!CIn a moment of personal crisis，how much help can you expect from a New York taxi driver？I began studying this question and answers are interesting.One morning I got into three different taxis and announced，“Well，it’s my first day back in New York in seven years. I’ve been in prisons. ” Not a single driver replied，so I tried agai n. “Yeah，I shot a man in Reno. ” I explained，hoping the driver would ask me why，but nobody asked. The only response came from a Ghanaian driver，“Reno？That is in Nevada？”Taxi driver were uniformly sympathetic when I said I’d just been fired. “This is America，” a Haitian driver said. “One door is closed. Another is ope n. ” He argued against my plan to burn down my boss house. A Pakistani driver even turned down a chance to profit from my loss of hope；he refused to take me to the middle of the George Washington Bridge—a $20 trip. “Why you go there？Go home and relax. Don’t worry. Take a new job. ”One very hot weekday in July，while wearing a red ski mask and holding a stuffed pillowcase with the word “BANK” on it，I tried calling a taxi five times outside different banks. The driver picked me up every time. My ride with a Haitian driver was typical of the superb assistance I received.“Let’s go across the park，” I said. “I just robbed the bank there. I got $25，000. ”“$25，000？” he asked.“Yeah，you think it was wrong to take it？”“No，ma n. I work 8 hours and I don’t make almost $70. If I can do that，I do it too. ”As we approached 86th and Lexington，I pointed to the Chemical Bank.“Hey，there is another bank，” I said. “Could you wait here a minute while I go inside？”“No，I can’t wait. Pay me now. ” His unwilling ness may have had something to do with money—taxi drivers think the rate for waiting time is too low—but I think he wanted me to learn that even a bank robber can’t expect unconditional support.8．From the Ghanaian driver’s response，we can infer that ________．A．he was afraid of the authorB．he thought the author was crazyC．he looked down upon the authorD．he was indifferent to the killing9．In the author’s opinion，the driver’s unwillingness “to wait outside the Chemical Bank” indicate ________．A．the driver thought it wrong to support a taxi rider unconditionallyB．the driver was frightened and wanted to leave him as soon as possibleC．the driver did not want to help a suspect to escape from a bank robberyD．the driver thought that the rate for waiting time was too low10．Which of the following statements is TRUE about New York taxi drivers?A．They are ready to help you do whatever you want to.B．They are sympathetic with those who are out of work.C．They refuse to pick up those who would kill themselves.D．They work only for money.11．The passage mainly discusses ________．A．the way to please taxi ridersB．the way to deal with taxi ridersC．taxi driver’s attitude to riders in personal troubleD．taxi driver’s attitude to troublesome taxi ridersDChange is natural part of language development. The words you like to use are probably a little different from those that your grandparents used when they were young. A study carried out by a British company found that the use of e-mail has had a bad influence on the standard of written English.According to the research，computer users today are too busy to hit the “shift” bottoms on their keyboards. E-mails are often written in lower case (小写)，that is to say，with no capital letters for names or the beginning of sentences，spelling mistakes are generally accepted even in formal e-mails. And nouns are often used as verbs (e. g. Please bookmark this site. )．With the development of the Internet，e-mail and mobile phone messages，a new language has developed within just a few years—we call it Weblish. The latest Oxford English Dictionary has included many new words showing the changes in our communication culture.While some language experts are concerned about the future of English and want to do something，John Simpson，chief editor of the dictionary says，“The standards may be different now but it has certainly encouraged writing and communication，which means a faster development of language change. There are a large number of words that either come from the Internet or have been given new meanings by the Internet. ”12．According to the research，people often write e-mails in lower caseto______．A．save time B．show kindnessC．make fun D．be different13．The second paragraph mainly tells ________．A．the mistakes found in English e-mailsB．the side effects of the use of e-mailsC．the changes in English used in e-mailsD．the reason why people use e-mails14．Which of the following is TRUE according to the passage?A．Spelling mistakes are not allowed in today’s e-mails.B．The Internet develops new words as well as new meanings to some old words.C．Weblish is only used in e-mails.D．We cannot find Weblish in a dictionary at present.15．According to the passage，John Simpson probably agrees that ________．A．the use of e-mail stops the development of languageB．mistakes in e-mail are very important to EnglishC．everyone should learn to write e-mails in WeblishD．the Internet has brought great changes to English第二节(共5小题；每小题3分，满分15分)根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。

阶段评估检测（四）必修4(120分钟 150分)第Ⅰ卷第一部分听力(共两节，满分30分)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小题和阅读下一小题。

每段对话仅读一遍。

1. What are they probably talking about?A. An apartment.B. A park.C. Food.2. What is the woman doing?A. Asking for directions.B. Giving directions.C. Shopping.3. What can we know about Jeffrey?A. He is a trouble maker.B. He is talkative.C. He is strict.4. What is the probable relationship between the two?A. Manager and secretary.B. Teacher and student.C. Doctor and patient.5. How would the man describe himself now?A. Fat.B. Slim.C. Wonderful.第二节（共15小题；每小题1．5分，满分22．5分）听下面5段对话或独白。

每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。

听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题给出5秒钟的作答时间。

每段对话或独白读两遍。

听第6段材料，回答第6至8题。

6. What does the man tell the woman about?A. His favorite place in New York.B. His experience of catching a train.C. His favorite movies.7. What is the man’s favorite?A. The clock.B. The ceiling.C. The sky at night.8. What can we infer from what the woman says?A. She likes the stars in New York City.B. New York City is so polluted that you cannot see stars there.C. The stars in New York City are beautiful.听第7段材料，回答第9至11题。

阶段评估检测(四)(必修4)(120分钟150分)第一部分阅读(共两节, 满分50分)第一节(共15小题;每小题2. 5分, 满分37. 5分)阅读下列短文, 从每题所给的A、B、C、D四个选项中选出最佳选项。

ABroken Wings1-4 Aug: Musical adaptation of the poet Kahlil Gibran’s 1912 masterpiece. Set in New York in 1923, it transports you to turn-of-the-century Beirut.7: 30pm (& 2: 30pm 4 Aug). Tickets: ￡10-￡96. www. trh. co. uk. Theatre Royal Haymarket, Haymarket, SWIY 4HT. T: 020-7930 8800. E7. Station: Piccadilly Circus.Chicago the MusicalMartin Kemp stars as Billy in this jazz musical based on real murder cases which shocked Chicago in the 1920s.Mon-Sat 7: 30pm; Wed & Sat 2: 30pm Tickets: ￡25-￡150. www. phoenixtheatrelondon. co. ukPhoenix Theatre, 110 Charing Cross Rd, WC2HOJP. T: 0843-316 1082. E7. Station: Tottenham Court RoadDreamgirlsMusical about a female singing group from Chicago. Classic songs include I Am Telling You I’m Not Going, I Am Changing, and Listen and One Night Only. Join these friends as they go on a musical roller coaster ride through a world of fame, fortune and the ruthless realities of show business, testing their friendships to the very limit.Mon-Sat 7: 30pm; Wed & Sat 2: 30pm Tickets: ￡15-￡75. www. savoytheatre. org. savoy.Strand WC2R OET. T: 0844-871 7687. E8. Station: Covent Garden.Everybody’s Talking about JamieThis feel-good musical is set on a council estate in Sheffield, northern England, and tells the story of 16-year-old Jamie and how he overcomes bullies and prejudice. This is inspired by a true bully story.Mon-Sat 7: 30pm; Wed & Sat 2: 30pm Tickets: ￡20-￡85. www. everybodystalkingaboutjamie. co. ukApollo Theatre, 31 Shaftesbury Ava WID 7ES T: 0330-333 4809. E7. Station: Piccaddly Circus【文章大意】这是一篇广告。

高中英语阶段质量评估（四）外研版必修4(120分钟150分)第Ⅰ卷（选择题）第二部分英语知识运用(共两节，满分35分)第一节语法和词汇知识（共15小题；每小题1分，满分15分）21. —Is my work OK?—_____You are always doing a good job.A. Well done!B. Never mind.C. It depends.D. Good luck!【解析】选A。

上句意为“我的工作还行吗？”根据答语后句“你总是干得很出色！”可知是对对方所做工作表示肯定和鼓励，故选A。

well done意为“干得不错”；never mind意为“别介意”；it depends意为“视情况而定”；good luck意为“祝你好运”。

22. “Listen, there_____. ”“Oh, yes. There_____. ”［2010泰安模拟］A. goes the bell; it goesB. goes the bell; goes itC. the bell goes; it goesD. the bell goes; goes it【解析】选A。

考查倒装。

句意为：——听，铃响了。

——噢，是的，铃响了。

There位于句首引起倒装，若主语为名词，则用倒装；若主语为代词，则不用倒装。

23. Do you think our great ship will_____ the hurricane?A. live withB. go throughC. die fromD. live through【解析】选D。

句意为：你认为我们极好的轮船会挺过这次飓风吗？live through“挺过；活过；度过”，而go through意为“经历”。

24. The police tried to get some clues from the suspect, but he remained_____.A. silentB. quietC. calmD. secret【解析】选A。

阶段评估检测（四）必修4(120分钟 135分)Ⅰ. 语言知识及应用（共两节，满分45分)第一节完形填空(共15小题；每小题2分, 满分30分)阅读下面短文，掌握其大意．然后从1~15各题所给的A、B、C和D项中，选出最佳选项。

Every year on my birthday, a white gardenia (栀子花) was 1 to my house. But no card or note came with it. Calls to the flower shop were always 2 —it was a cash purchase. After a while I stopped trying to discover the sender’s identity and just 3 in the beauty and heady perfume of that one magical, perfect white flower lying in soft pink paper.But I never stopped 4 who the giver might be. My mother 5 to these imaginations. She asked me if there was someone for whom I had done a special kindness who might be showing 6 . I had more fun imagining that it might be a boy I fell in love with or one who had 7 me even though I didn’t know him.One month before my high-school graduation, my father died. My feelings 8 from sorrow to fear and 9 : my dad was missing some of the most important events in my life. I became completely 10 in my coming graduation, the senior-class play and the ball. But my mother would not hear of my losing any of those things. Mother and I had gone shopping and found an impressive dress, but it was the 11 size. When my father died, I forgot about the dress.The day before my ball, I found that dress—in the right size—hanging over the living room sofa. It was 12 to me so lovingly. I didn’t 13 if I had a new dress or not. But my mother did. She wanted her children to feel 14 , filled with a sense that there was a beauty even in the face of 15 .My mother died ten days after I was married. The following year the gardenia stopped coming.1. A. given B. delivered C. taken D. brought2. A. in advance B. in time C. in vain D. in need3. A. delighted B. pleasantC. pleasingD. satisfied4. A. considering B. rememberingC. imaginingD. recalling5. A. referred B. ledC. preferredD. contributed6. A. appreciation B. honorC. kindnessD. respect7. A. observed B. watched C. noticed D. hated8. A. ranged B. differed C. suffered D. judged9. A. shock B. happinessC. depressingD. anger10. A. uninterested B. interestedC. unhappyD. disappointing11. A. wrong B. false C. proper D. right12. A. provided B. presentedC. introducedD. awarded13. A. doubt B. wonder C. desire D. care14. A. loving B. loved C. respected D. honored15. A. trouble B. despair C. problem D. sorrow第二节语法填空(共10小题；每小题1. 5分，满分15分)阅读下面短文，按照句子结构的语法性和上下文连贯的要求，在空格处填入一个适当的词或使用括号中词语的正确形式填空。

阶段评估检测（四）必修4120分钟 150分第一部分听力（共两节，满分30分）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小题和阅读下一小题。

每段对话仅读一遍。

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阶段评估检测（四）必修4120分钟 150分第Ⅰ卷第一部分听力共两节，满分30分第一节（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小题和阅读下一小题。

每段对话仅读一遍。

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阶段质量评估三角函数(A)(本栏目内容，在学生用书中以独立形式分册装订)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．已知1弧度的圆心角所对的弧长为6，则这个圆心角所夹的扇形的面积是( ) A ．3 B ．6 C ．18D ．36解析： ∵l ＝αr ，∴6＝1×r .∴r ＝6. ∴S ＝12lr ＝12×6×6＝18.答案： C2．设α是第三象限角，且⎪⎪⎪⎪cos α2＝－cos α2，则α2的终边所在的象限是( ) A ．第一象限 B ．第二象限 C ．第三象限D ．第四象限 解析： ∵α是第三象限角， ∴π＋2k π＜α＜3π2＋2k π，k ∈Z .∴π2＋k π＜α2＜3π4＋k π，k ∈Z . ∴α2在第二或第四象限． 又∵⎪⎪⎪⎪cos α2＝－cos α2，∴cos α2＜0. ∴α2是第二象限角． 答案： B3．已知角α的终边上一点的坐标为⎝⎛⎭⎫sin 5π6，cos 5π6，则角α的最小正值为( ) A.5π6 B.2π3 C.11π6D.5π3 解析： 因为sin 5π6＝sin ⎝⎛⎭⎫π－π6＝sin π6＝12，cos 5π6＝cos ⎝⎛⎭⎫π－π6＝－cos π6＝－32， 所以点⎝⎛⎭⎫sin 5π6，cos 5π6在第四象限．又因为tan α＝cos5π6sin5π6＝－3＝tan ⎝⎛⎭⎫2π－π3＝tan 5π3，所以角α的最小正值为5π3.故选D.答案： D4．tan ⎝⎛⎭⎫－353π的值是( ) A ．－33B. 3 C ．－ 3D.33解析： tan ⎝⎛⎭⎫－353π ＝－tan ⎝⎛⎭⎫12π－π3 ＝tan π3＝ 3.答案： B5．已知sin θ＋cos θ＝43，θ∈⎝⎛⎭⎫0，π4，则sin θ－cos θ的值为( ) A.23B.13 C ．－23D ．－13解析： ∵已知sin θ＋cos θ＝43⎝⎛⎭⎫cos θ＜π4，∴1＋sin θcos θ＝169， ∴2sin θcos θ＝79，故sin θ－cos θ＝－(sin θ－cos θ)2 ＝1－2sin θ·cos θ ＝－23，故选C. 答案： C6．函数y ＝sin x2是( )A ．周期为4π的奇函数B ．周期为π2的奇函数C ．周期为π的偶函数D ．周期为2π的偶函数解析： ∵y ＝sin x 2，∴T ＝2π12＝4π.∵sin ⎝⎛⎭⎫－x 2＝－sin x 2， ∴y ＝sin x2是奇函数．答案： A7．要得到函数y ＝sin ⎝⎛⎭⎫4x －π3的图象，只需将函数y ＝sin 4x 的图象( ) A ．向左平移π12个单位B ．向右平移π12个单位C ．向左平移π3个单位D ．向右平移π3个单位解析： y ＝sin ⎝⎛⎭⎫4x －π3＝sin ⎣⎡⎦⎤4⎝⎛⎭⎫x －π12，故只需将函数y ＝sin 4x 的图象向右平移π12个单位即可得到y ＝sin ⎝⎛⎭⎫4x －π3的图象，故选B. 答案： B8．将函数y ＝3sin ⎝⎛⎭⎫2x ＋π3的图象向右平移π2个单位长度，所得图象对应的函数( ) A ．在区间⎣⎡⎦⎤π12，7π12上单调递减 B ．在区间⎣⎡⎦⎤π12，7π12上单调递增 C ．在区间⎣⎡⎦⎤－π6，π3上单调递减 D ．在区间⎣⎡⎦⎤－π6，π3上单调递增 解析： y ＝3sin ⎝⎛⎭⎫2x ＋π3向右平移π2个单位长度得到y ＝3sin ⎣⎡⎦⎤2⎝⎛⎭⎫x －π2＋π3＝3sin ⎝⎛⎭⎫2x －2π3的图象.2x －2π3∈⎣⎡⎦⎤－π2，π2，则x ∈⎣⎡⎦⎤π12，712π， ∴y ＝3sin ⎝⎛⎭⎫2x －2π3在⎣⎡⎦⎤π12，7π12上单调递增． 答案： B9．已知函数f (x )＝A sin(ωx ＋θ)(A ＞0，ω＞0)的部分图象如图1所示，则f (x )等于( )图1A.2sin ⎝⎛⎭⎫2x －π3 B.2sin ⎝⎛⎭⎫2x －π6C.2sin ⎝⎛⎭⎫4x ＋π3 D.2sin ⎝⎛⎭⎫4x ＋π6 解析： 由图象知A ＝2， ∵5π12－⎝⎛⎭⎫－π3＝3T 4， ∴T ＝π，∴ω＝2.∵2×5π12＋θ＝π2＋2k π(k ∈Z )，∴可取θ＝－π3，∴f (x )＝2sin ⎝⎛⎭⎫2x －π3. 答案： A10．已知函数f (x )＝2sin ωx (ω＞0)在区间⎣⎡⎦⎤0，π4上单调递增，且在这个区间上的最大值是3，那么ω等于( )A.23 B.43 C ．2D ．4解析： 由函数在区间⎣⎡⎦⎤0，π4上单调递增，且在这个区间上的最大值是3，可得f ⎝⎛⎭⎫π4＝2sin π4ω＝3，代入选项检验可得ω＝43，所以选B.答案： B二、填空题(本大题共4小题，每小题5分，共20分．请把正确答案填在题中横线上) 11．满足sin(3π－x )＝32，x ∈[－2π，2π]的x 的取值集合是________． 解析： sin(3π－x )＝sin(π－x )＝sin x ＝32.当x ∈[0,2π]时，x ＝π3或2π3；当x ∈[－2π，0]时，x ＝－5π3或－4π3.所以x 的取值集合为⎩⎨⎧⎭⎬⎫－5π3，－4π3，π3，2π3.答案： ⎩⎨⎧⎭⎬⎫－5π3，－4π3，π3，2π312．若点P 在角－10π3的终边上，且P 的坐标为(－1，y )，则y ＝________.解析： 由三角函数的定义sin ⎝⎛⎭⎫－10π3＝y (－1)2＋y 2，又sin ⎝⎛⎭⎫－10π3＝sin ⎝⎛⎭⎫－4π＋23π＝sin2π3＝32，所以y (－1)2＋y 2＝32，得y ＝3或y ＝－3(舍去)． 答案：313．已知函数f (x )＝sin π2x ，则f (1)＋f (2)＋f (3)＋…＋f (2 020)＋f (2 021)＝________.解析： 因为f (1)＝1，f (2)＝0，f (3)＝－1，f (4)＝0，所以f (1)＋f (2)＋f (3)＋f (4)＝0，又f (x )以4为周期，所以f (1)＋f (2)＋f (3)＋…＋f (2 020)＋f (2 021)＝505×0＋f (2 021)＝0＋f (1)＝1.答案： 114．已知函数f (x )＝A sin(ωx ＋φ)⎝⎛⎭⎫x ∈R ，A ＞0，ω＞0，|φ|＜π2的部分图象如图2所示，则关于函数f (x )的性质的结论正确的有________(填序号)．①f (x )的图象关于点⎝⎛⎭⎫－16，0对称；②f (x )的图象关于直线x ＝43对称；③f (x )在⎣⎡⎦⎤－12，13上为增函数；④把f (x )的图象向右平移23个单位长度，得到一个偶函数的图象．解析： 由图象得A ＝2，T 4＝56－13＝12，∴T ＝2，则ω＝π.又13ω＋φ＝π2＋2k π(k ∈Z )，且|φ|＜π2，∴φ＝π6，f (x )＝2sin ⎝⎛⎭⎫πx ＋π6.∵f ⎝⎛⎭⎫－16＝0，∴f (x )的图象关于点⎝⎛⎭⎫－16，0对称，①正确；∵f ⎝⎛⎭⎫43＝－2，∴f (x )的图象关于直线x ＝43对称，②正确；由－12≤x ≤13，得－π3≤πx ＋π6≤π2，∴f (x )在⎣⎡⎦⎤－12，13上为增函数，③正确；f ⎝⎛⎭⎫x －23＝2sin ⎣⎡⎦⎤⎝⎛⎭⎫x －23π＋π6＝2sin ⎝⎛⎭⎫πx －π2＝－2cos πx 是偶函数，④正确．答案： ①②③④三、解答题(本大题共4小题，共50分．解答时应写出必要的文字说明、证明过程或演算步骤)15．(本小题满分12分)若sin αcos α＜0，sin αtan α＜0，且 1－sin α1＋sin α＋1＋sin α1－sin α＝22，求tan α.解析： ∵sin αcos α＜0，sin αtan α＜0， ∴α是第二象限角， ∴1－sin α1＋sin α＋1＋sin α1－sin α＝(1－sin α)21－sin 2α＋(1＋sin α)21－sin 2α＝2|cos α|＝2－cos α＝22， ∴cos α＝－22， 则sin α＝22，tan α＝－1. 16．(本小题满分12分)做出下列函数在[－2π，2π]上的图象： (1)y ＝1－13cos x ；(2)y ＝⎪⎪⎪⎪sin ⎝⎛⎭⎫x ＋3π2. 解析： (1)描点⎝⎛⎭⎫0，23，⎝⎛⎭⎫π2，1，⎝⎛⎭⎫π，43，⎝⎛⎭⎫3π2，1，⎝⎛⎭⎫2π，23，连线可得函数在[0,2π]上的图象，关于y 轴作对称图形即得函数在[－2π，2π]上的图象，所得图象如答图1所示．答图1(2)由于y ＝⎪⎪⎪⎪sin ⎝⎛⎭⎫x ＋3π2＝|cos x |，所以只需作出函数y ＝|cos x |，x ∈[－2π，2π]的图象即可．而函数y ＝|cos x |，x ∈[－2π，2π]的图象可采用将函数y ＝cos x ，x ∈[－2π，2π]的图象在x 轴下方的部分翻折到x 轴上方的方法得到，所得图象如答图2实线所示．答图217．(本小题满分12分)函数f (x )＝3sin ⎝⎛⎭⎫2x ＋π6的部分图象如图3所示． (1)写出f (x )的最小正周期及图中x 0，y 0的值； (2)求f (x )在区间⎣⎡⎦⎤－π2，－π12上的最大值和最小值．图3解析： (1)f (x )的最小正周期为π，x 0＝7π6，y 0＝3.(2)因为x ∈⎣⎡⎦⎤－π2，－π12， 所以2x ＋π6∈⎣⎡⎦⎤－5π6，0， 于是当2x ＋π6＝0，即x ＝－π12时，f (x )取得最大值0；当2x ＋π6＝－π2，即x ＝－π3时，f (x )取得最小值－3.18．(本小题满分14分)函数f (x )＝A sin(ωx ＋φ)⎝⎛⎭⎫A ＞0，ω＞0，|φ|＜π2的一段图象如图4所示．(1)求f (x )的解析式；(2)把f (x )的图象向左至少平移多少个单位长度，才能使得到的图象对应的函数为偶函数？图4解析： (1)A ＝3，2πω＝43⎝⎛⎭⎫4π－π4＝5π，ω＝25. 由f (x )＝3sin ⎝⎛⎭⎫25x ＋φ过⎝⎛⎭⎫π4，0， 得sin ⎝⎛⎭⎫π10＋φ＝0，又|φ|＜π2，故φ＝－π10， ∴f (x )＝3sin ⎝⎛⎭⎫25x －π10. (2)由f (x ＋m )＝3sin ⎣⎡⎦⎤25(x ＋m )－π10＝3sin ⎝⎛⎭⎫25x ＋2m 5－π10为偶函数(m ＞0)， 知2m 5－π10＝k π＋π2，即m ＝52k π＋3π2，k ∈Z . ∵m ＞0，∴m min ＝3π2. 故把f (x )的图象向左至少平移3π2个单位长度，才能使得到的图象对应的函数是偶函数．。