人教版必修五第一章测试题
人教版新课标高中英语 必修五Unit 1 Great scientists 单元测试 含答案详解
Unit 1Great scientists本套试卷分为第Ⅰ卷和第Ⅱ卷两部分。
总分120分。
考试时间100分钟。
第Ⅰ卷Ⅰ.阅读理解(共两节,满分35分)第一节(共10小题;每小题2.5分,满分25分)阅读下列短文,从每题所给的A、B、C和D四个选项中,选出最佳选项。
AMy senior year of high school was a very hectic one, to say the least. If I wasn´t studying or worrying about my grades, I was working on after-class activities. It seemed as if my life had turned into one crazy cloud of confusion and I hoped to find some sort of direction.Finally, I got a part-time job at the local coffee shop. I had thought it would be easy and, for the most part, stress-free. I pictured myself pouring coffee and becoming close friends with my customers.What I hadn´t expected were the people with so many orders. There were moments when I was very angry simply because I couldn´t seem to please anyone. There was always too much sugar, too little ice, or not enough skim milk. However, I kept at it.One day, one of my customers came in, depressed. Before he left, I handed him a bag along with his iced coffee. He looked at me questioningly because he hadn´t ordered anything but the coffee. He opened the bag and saw his favourite doughnut (甜甜圈) I had given him. He smiled and thanked me before heading out into the rain.The next evening, he came. Instead of ordering something, he handed me a single pink rose and a note.“Thanks for being so sweet and thoughtful yesterday. It is so nice to meet someone who´s warm and unselfish. Please don´t change your ways because I truly believe that you will do better. Have a great day!”As time went on, I did come across some customers really particular. But anytime I felt depressed, I thought of that man and his kindness. Then I would smile, hold my head up high, clear my throat and ask politely, “How can I help you?”1.What does the underlined word “hectic” in Paragraph 1 mean?A. Glad.B. Interesting.C. Productive.D. Busy.2.What can we know about the author´s part-time job?A. It is easy and stress-free.B. It is quite busy and challenging.C . It doesn´t need special skills. D. It gives the author a feeling of freshness.3.What´s the message the author wants to convey?A. Kind words are worth much but cost little.B. It is impossible to satisfy everyone in our life.C. A small act of kindness can make a big difference.D. Our attitude determines our suffering or our freedom.BAn idea that started in Seattle´s public library has spread throughout America and beyond. The idea is simple: help to build a sense of community in a city by getting everyone to read the same book at the same time.In addition to encouraging reading as a pursuit(爱好) to be enjoyed by all, theprogramme allows strangers to communicate by discussing the book on the bus, as well as promoting reading as an experience to be shared in families and schools. The idea came from Seattle librarian Nancy Pearl who launched (发起)the “If All of Seattle Read the Same Book” project in 1998. Her original programme used author visits, study guides and book discussion groups to bring people together with a book, but the idea has since expanded to many other American cities, and even to Hong Kong.In Chicago, the mayor appeared on television to announce the choice of To Kill a Mockingbird as the first book in the “One Book, One Chicago” programme. As a result, reading clubs and neighbourhood groups sprang up around the city. Across the US, stories emerged of parents and children reading to each other at night and strangers chatting away on the bus about plot and characters.The only problem arose in New York, where local readers could not decide on one book to represent the huge and diverse population. This may show that the idea works best in medium-sized cities or large towns, where a greater sense of unity(一致)can be achieved.Or it may show that New Yorkers rather missed the point, putting all their energy and passion into the choice of the book rather than discussion about a book itself.As Nancy points out, the level of success is not measured by how many people read a book, but by how many people are enriched by the process or have enjoyed speaking to someone with whom they would not otherwise have shared a word.4.What is the purpose of the project launched by Nancy?A.To invite authors to guide readers.B.To encourage people to read and share.C.To involve people in community services.D.To promote the friendship betweencities.5.Why was it difficult for New Yorkers to carry out the project?A.They had little interest in reading.B.They were too busy to read a book.C.They came from many different backgrounds.D.They lacked support from the local government.6.The underlined words “shared a word” in Paragraph 5 probably mean .A.exchanged ideas with each otherB.discussed the meaning of a wordC.gained life experienceed the same languageCScientific experiments can sometimes go wrong and when they do, the results may range from the disastrous (灾难性的) to the troubling. One such experiment took place in South America about fifty years ago. Whether its final consequences will cause serious damage or nothing more than a small trouble still remains to be seen.The story began in 1956 when an American scientist working in Brazil decided to solve the problem of increasing the productivity of that country´s bees. He imported a very active type of African bee from Tanzania and mated (交配) it with the more easy-going native variety to produce a new kind of bees. The new bees worked harder and produced twice as much honey. It seemed that Professor Kerr, which was the scientist´s name, had a total success on his hands.Then things began to go wrong. For some reason as yet unseen, but perhaps as a result of something in their environment, the new bees began to develop extremely attacking personalities. They became bad-tempered and easy to be angry. They attacked the native bees and drove them from their living places.But worse was to follow. Having taken over the countryside, the new bees, with their dangerous stings (刺), began to attack their neighbours—cats, dogs, horses, chickens and finally man himself. A long period of terror began that has so far killed a great number of animals and about 150 human beings.This would have been bad enough if the bees had stayed in Brazil. But now they are on the move, heading northwards in countless millions towards Central and North America, and moving at the alarming speed of 200 miles a year. The countries that lie in their path are naturally worried because it looks as if nothing can be done to stop them.7. The results of the South American experiment .A.are not importantB.are not yet certainC.have caused a serious troubleD.have proved to be wrong8. The experiment mentioned in this passage was designed to .A.make African bees less activeB.increase the number of bees in BrazilC.make Brazilian bees more easy-goingD.increase the amount of honey in Brazil9. Which of the following may be the cause of the new bees´ attacking personalities?A.Their bad temper.B.Their hard work.C.Their production of honey.D.Their living environment.10. The last paragraph implies that .A.the bees prefer to live in BrazilB.the bees must be stopped from moving northC.the bees may bring about trouble in more countriesD.the bees have been driven to Central and North America第二节阅读七选五(共5小题;每小题2分,满分10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。
人教版高中英语必修五第一单元练习题(含参考答案)
高中英语必修五第一单元练习题一、复习单词：写出下列单词或短语的基本意思。
1.put forward a suggestion__________________2.scientific(adj.)__________________3.conclude(v.)____________________draw a conclusion________________4.defeat(v./n.)____________________5.expert(adj./n.)__________________6.attend(v.)_____________________7.physics(n.)_____________________physician(n.)_________________8.expose to_____________________9.cure(v./n.)_____________________10.challenge(n./v.)_______________11.victim(n.)____________________12.be absorbed in________________13.suspect(n./v.)_________________14.enquiry(n.)___________________15.severe(adj.)___________________16.neighbour(n.)__________________neighbourhood(n.)__________________17.foresee(v.)____________________18.blame________________________19.pollute(v.)_____________________20.link to_________________________21.announce(v.)____________________22.instruct(v.)______________________23.contribute(v.)____________________24.be strict with sb._________________cautious(adj.)________________25.reject(v.)_______________________二、选词填空。
人教A版高中数学必修五第一章 解三角形练习题.doc
第一章 解三角形练习题姓名______学号______ 得分______ 一、选择题（每小题5 分，共70分）1 2 3 4 5 6 7 8 9 10 11 12 13 141．在△ABC 中，若0030,6,90===B a C ，则b c -等于（ ）A ．1B ．1-C ．32D ．32-2．若A 为△ABC 的内角，则下列函数中一定取正值的是（ ）A ．A sinB ．A cosC ．A tanD ．Atan 1 3．等腰三角形一腰上的高是3，这条高与底边的夹角为060，则底边长为（ ）A ．2B ．23 C ．3 D ．32 4．在△ABC 中，若B a b sin 2=，则A 等于（ ）A ．006030或B ．006045或C ．0060120或D ．0015030或5．边长为5,7,8的三角形的最大角与最小角的和是（ ）A ．090B ．0120C ．0135D ．01506．在△ABC 中，::1:2:3A B C =，则::a b c 等于（ ）A ．1:2:3B ．3:2:1C ．1:3:2D ．2:3:17．在△ABC 中，若B A 2=，则a 等于（ ）A ．A b sin 2B ．A b cos 2C ．B b sin 2D ．B b cos 28．在△ABC 中，若2lg sin lg cos lg sin lg =--C B A ，则△ABC 的形状是（ ）A ．直角三角形B ．等边三角形C ．不能确定D ．等腰三角形9．在△ABC 中，若,3))((bc a c b c b a =-+++则A = ( )A ．090B ．060C ．0135D ．015010．在△ABC 中，若1413cos ,8,7===C b a ，则最大角的余弦是（ ） A ．51- B ．61- C ．71- D ．81- 11．A 为△ABC 的内角，则A A cos sin +的取值范围是（ ） A ．)2,2( B ．)2,2(- C ．]2,1(- D ．]2,2[-12．在△ABC 中，若8,3,7===c b a ，则其面积等于（ ）A ．12B ．221 C ．28 D ．36 13．在△ABC 中，090C ∠=，00450<<A ，则下列各式中正确的是（ ）A ．sin cos A A >B ．sin cos B A >C ．sin cos A B >D ．sin cos B B >14．在△ABC 中，若)())((c b b c a c a +=-+，则A ∠=（ ）A ．090B ．060C ．0120D ．0150二、填空题（每小题5分，共30分）1．在△ABC 中，若005,60,15a A C ===，则此三角形的最大边长为_________。
人教A版高中数学必修五第一章测试.doc
高中数学学习材料唐玲出品第一章测试(时间：120分钟满分：150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．在△ABC中，AB＝5，BC＝6，AC＝8，则△ABC的形状是() A．锐角三角形B．直角三角形C．钝角三角形D．非钝角三角形解析最大边AC所对角为B，则cos B＝52＋62－822×5×6＝－320<0，∴B为钝角．答案 C2．在△ABC中，已知a＝1，b＝3，A＝30°，B为锐角，那么A，B，C的大小关系为()A．A>B>C B．B>A>CC．C>B>A D．C>A>B解析由正弦定理asin A＝bsin B，∴sin B＝b sin Aa＝32.∵B为锐角，∴B＝60°，则C＝90°，故C>B>A. 答案 C3．在△ABC 中，已知a ＝8，B ＝60°，C ＝75°，则b 等于( ) A ．4 2 B ．4 3 C ．4 6D.323解析 由A ＋B ＋C ＝180°，可求得A ＝45°，由正弦定理，得b ＝a sin B sin A ＝8×sin60°sin45°＝8×3222＝4 6.答案 C4．在△ABC 中，A ＝60°，a ＝3，则a ＋b ＋csin A ＋sin B ＋sin C 等于( )A.833B.2393C.2633D ．2 3解析 利用正弦定理及比例性质，得 a ＋b ＋c sin A ＋sin B ＋sin C ＝a sin A ＝3sin60°＝332＝2 3.答案 D5．若三角形三边长之比是1:3:2，则其所对角之比是( ) A ．1:2:3 B ．1: 3 :2 C ．1: 2 : 3D. 2 : 3 :2解析 设三边长分别为a ，3a,2a ，设最大角为A ，则cos A ＝a 2＋(3a )2－(2a )22·a ·3a＝0，∴A ＝90°.设最小角为B ，则cos B ＝(2a )2＋(3a )2－a 22·2a ·3a ＝32，∴B ＝30°，∴C ＝60°. 因此三角之比为1:2:3. 答案 A6．在△ABC 中，若a ＝6，b ＝9，A ＝45°，则此三角形有( ) A ．无解 B ．一解C ．两解D ．解的个数不确定解析 由b sin B ＝a sin A ，得sin B ＝b sin A a ＝9×226＝3 24>1. ∴此三角形无解． 答案 A7．已知△ABC 的外接圆半径为R ，且2R (sin 2A －sin 2C )＝(2a －b )sin B (其中a ，b 分别为A ，B 的对边)，那么角C 的大小为( )A ．30°B ．45°C ．60°D ．90°解析 根据正弦定理，原式可化为 2R ⎝ ⎛⎭⎪⎫a 24R 2－c 24R 2＝(2a －b )·b 2R ， ∴a 2－c 2＝(2a －b )b ，∴a 2＋b 2－c 2＝2ab ， ∴cos C ＝a 2＋b 2－c 22ab ＝22，∴C ＝45°. 答案 B8．在△ABC 中，已知sin 2A ＋sin 2B －sin A sin B ＝sin 2C ，且满足ab ＝4，则该三角形的面积为( )A ．1B ．2C. 2D. 3解析 由a sin A ＝b sin B ＝csin C ＝2R ，又sin 2A ＋sin 2B －sin A sin B ＝sin 2C ，可得a 2＋b 2－ab ＝c 2.∴cos C ＝a 2＋b 2－c 22ab ＝12，∴C ＝60°，sin C ＝32. ∴S △ABC ＝12ab sin C ＝ 3. 答案 D9．在△ABC 中，A ＝120°，AB ＝5，BC ＝7，则sin Bsin C 的值为( ) A.85 B.58 C.53D.35解析 由余弦定理，得cos A ＝AB 2＋AC 2－BC 22AB ·AC ，解得AC ＝3. 由正弦定理sin B sin C ＝AC AB ＝35. 答案 D10．在三角形ABC 中，AB ＝5，AC ＝3，BC ＝7，则∠BAC 的大小为( )A.2π3B.5π6C.3π4D.π3 解析 由余弦定理，得cos ∠BAC ＝AB 2＋AC 2－BC 22AB ·AC ＝52＋32－722×5×3＝－12，∴∠BAC ＝2π3.答案 A11．有一长为1 km 的斜坡，它的倾斜角为20°，现要将倾斜角改为10°，则坡底要加长( )A ．0.5 kmB ．1 kmC ．1.5 kmD.32 km解析 如图，AC ＝AB ·sin20°＝sin20°，BC ＝AB ·cos20°＝cos20°，DC ＝AC tan10°＝2cos 210°， ∴DB ＝DC －BC ＝2cos 210°－cos20°＝1.答案 B12．已知△ABC 中，A ，B ，C 的对边分别为a ，b ，c .若a ＝c ＝6＋2，且A ＝75°，则b 为( )A ．2B ．4＋2 3C ．4－2 3D.6－ 2解析 在△ABC 中，由余弦定理，得a 2＝b 2＋c 2－2bc cos A ，∵a ＝c ，∴0＝b 2－2bc cos A ＝b 2－2b (6＋2)cos75°，而cos75°＝cos(30°＋45°)＝cos30°cos45°－sin30°sin45°＝22(32－12)＝14(6－2)，∴b 2－2b (6＋2)cos75°＝b 2－2b (6＋2)·14(6－2)＝b 2－2b ＝0，解得b＝2，或b＝0(舍去)．故选A.答案 A二、填空题(本大题共5小题，每小题4分，共20分．把答案填在题中横线上)13．在△ABC中，A＝60°，C＝45°，b＝4，则此三角形的最小边是____________．解析由A＋B＋C＝180°，得B＝75°，∴c为最小边，由正弦定理，知c＝b sin Csin B＝4sin45°sin75°＝4(3－1)．答案4(3－1)14．在△ABC中，若b＝2a，B＝A＋60°，则A＝________. 解析由B＝A＋60°，得sin B＝sin(A＋60°)＝12sin A＋32cos A.又由b＝2a，知sin B＝2sin A.∴2sin A＝12sin A＋32cos A.即32sin A＝32cos A.∵cos A≠0，∴tan A＝3 3.∵0°<A<180°，∴A＝30°.答案30°15．在△ABC中，A＋C＝2B，BC＝5，且△ABC的面积为103，则B＝________，AB＝________.解析由A＋C＝2B及A＋B＋C＝180°，得B＝60°.又S＝12AB·BC·sin B，∴10 3＝12AB ×5×sin60°，∴AB ＝8. 答案 60° 816．在△ABC 中，已知(b ＋c ) : (c ＋a ) : (a ＋b )＝8:9:10，则sin A :sin B :sin C ＝________.解析设⎩⎪⎨⎪⎧b ＋c ＝8k ，c ＋a ＝9k ，a ＋b ＝10k ，可得a :b :c ＝11:9:7.∴sin A :sin B :sin C ＝11:9:7. 答案 11:9:7三、解答题(本大题共6个小题，共70分．解答应写出必要的文字说明、证明过程或演算步骤)17．(10分)在△ABC 中，若a 2b 2＝sin A cos Bcos A sin B ，判断△ABC 的形状． 解 依据正弦定理，得a 2b 2＝a b ·cos Bcos A ，所以a cos A ＝b cos B .再由正弦定理，得sin A cos A ＝sin B cos B ，即sin2A ＝sin2B ，因为2A,2B ∈(0,2π)，故2A ＝2B ，或2A ＋2B ＝π.从而A ＝B ，或A ＋B ＝π2，即△ABC 为等腰三角形，或直角三角形．18．(12分)锐角三角形ABC 中，边a ，b 是方程x 2－23x ＋2＝0的两根，角A ，B 满足2sin(A ＋B )－3＝0.求：(1)角C 的度数；(2)边c 的长度及△ABC 的面积． 解 (1)由2sin(A ＋B )－3＝0， 得sin(A ＋B )＝32. ∵△ABC 为锐角三角形，∴A ＋B ＝120°，∴∠C ＝60°.(2)∵a ，b 是方程x 2－23x ＋2＝0的两个根， ∴a ＋b ＝23，ab ＝2. ∴c 2＝a 2＋b 2－2ab cos C ＝(a ＋b )2－3ab ＝12－6＝6. ∴c ＝ 6.S △ABC ＝12ab sin C ＝12×2×32＝32.19．(12分)如右图，某货轮在A 处看灯塔B 在货轮的北偏东75°，距离为12 6 nmile ，在A 处看灯塔C 在货轮的北偏西30°，距离为8 3 nmile ，货轮由A 处向正北航行到D 处时，再看灯塔B 在北偏东120°，求：(1)A 处与D 处的距离； (2)灯塔C 与D 处的距离．分析 (1)要求AD 的长，在△ABD 中，AB ＝126，B ＝45°，可由正弦定理求解；(2)要求CD 的长，在△ACD 中，可由余弦定理求解．解 (1)在△ABD 中，∠ADB ＝60°，B ＝45°，AB ＝12 6，由正弦定理，得AD ＝AB sin Bsin ∠ADB ＝126×2232＝24(nmile)．(2)在△ADC 中，由余弦定理，得 CD 2＝AD 2＋AC 2－2AD ·AC ·cos30°. 解得CD ＝83(nmile)．∴A 处与D 处的距离为24 nmile ，灯塔C 与D 处的距离为8 3 nmile.20．(12分)在△ABC 中，角A ，B ，C 所对的边分别为a ，b ，c ，且满足cos A 2＝255，AB →·AC →＝3.(1)求△ABC 的面积； (2)若b ＋c ＝6，求a 的值． 解 (1)∵cos A 2＝255，∴cos A ＝2cos 2A2－1＝35，sin A ＝45. 又由AB →·AC →＝3，得bc cos A ＝3，∴bc ＝5. 因此S △ABC ＝12bc sin A ＝2.(2)由(1)知，bc ＝5，又b ＋c ＝6， ∴b ＝5，c ＝1，或b ＝1，c ＝5.由余弦定理，得a 2＝b 2＋c 2－2bc cos A ＝20. ∴a ＝2 5.21．(12分)在△ABC 中，已知内角A ＝π3，边BC ＝23，设内角B ＝x ，周长为y .(1)求函数y ＝f (x )的解析式和定义域； (2)求y 的最大值．解 (1)△ABC 的内角和A ＋B ＋C ＝π，由A ＝π3，B >0，C >0，得0<B <2π3.应用正弦定理，得AC ＝BC sin A ·sin B ＝23sin π3·sin x ＝4sin x .AB ＝BCsin A sin C ＝4sin ⎝ ⎛⎭⎪⎫2π3－x .∵y ＝AB ＋BC ＋CA ，∴y ＝4sin x ＋4sin ⎝⎛⎭⎪⎫2π3－x ＋23⎝⎛⎭⎪⎫0<x <2π3.(2)y ＝4(sin x ＋32cos x ＋12sin x )＋2 3 ＝43sin(x ＋π6)＋2 3. ∵π6<x ＋π6<5π6，∴当x ＋π6＝π2，即x ＝π3时，y 取得最大值6 3.22．(12分)△ABC 中，A ，B ，C 所对的边分别为a ，b ，c ，tan C ＝sin A ＋sin B cos A ＋cos B，sin(B －A )＝cos C . (1)求A ，C ；(2)若S △ABC ＝3＋3，求a ，c .精心制作仅供参考唐玲出品 解 (1)因为tan C ＝sin A ＋sin B cos A ＋cos B， 即sin C cos C ＝sin A ＋sin B cos A ＋cos B， 所以sin C cos A ＋sin C cos B ＝cos C sin A ＋cos C sin B ，即sin C cos A －cos C sin A ＝cos C sin B －sin C cos B ，得sin(C －A )＝sin(B －C )．所以C －A ＝B －C ，或C －A ＝π－(B －C )(不成立)，即2C ＝A ＋B ，得C ＝π3，所以B ＋A ＝2π3.又因为sin(B －A )＝cos C ＝12，则B －A ＝π6，或B －A ＝5π6(舍去)．得A ＝π4，B ＝5π12.所以A ＝π4，C ＝π3.(2)S △ABC ＝12ac sin B ＝6＋28ac ＝3＋3，又a sin A ＝c sin C ，即a 22＝c 32. 得a ＝22，c ＝2 3.。
高中数学必修5第一章《解三角形》综合测试
第3页 共 4页
● 以下两题任选一题作答 20. （本题满分 14 分） 在锐角 ABC 中，边 a 、 b 是方程 x2 2 3x 2 0 的两根， A 、 B 满足
2sin( A B ) 3 0 ，解答下列问题： （ 1）求 C 的度数； （ 2）求边 c 的长度； （ 3）求 ABC 的面积 .
3 ，则
abc
的值为 _________.
sin A sin B sin C
13. 一蜘蛛沿正北方向爬行 x cm 捉到一只小虫，然后向右转 105o ，爬行 10 cm 捉到另一只小虫，这
时它向右转 135o 爬行回它的出发点，那么 x _________.
14. ABC 的内角 A 、 B 、 C 的对边分别为 a 、 b 、 c ，向量 m ( 3, 1) ， n (cos A,sin A) ，
高中数学必修 5 第一章《解三角形》综合测试
一、选择题 （每小题 5 分，共 40 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. 某三角形的两个内角为 45o 和 60o ，若 45o 角所对的边长是 6 ，则 60o 角所对的边长是【
】
A． 3 6 2. 在 ABC 中，已知 a
且 ABC 最大边是 12，最小角的正弦值是 . 3
（ 1）判断 ABC 的形状； （ 2）求 ABC 的面积 .
必修 5 第一章综合测试题
第2页 共 4页
19. （本题满分
14 分） 海上某货轮在
A 处看灯塔 B 在货轮的北偏东
o
75 ，距离为
12
6 海里；在
A
处看灯塔 C 在货轮的北偏西
o
30 ，距离为
若 m n ，且 a cosB b cos A c sin C ，则 B _________.
高一数学必修5第一章单元测试题及答案
AC2 AB 2 BC 2 2AB BC cos
2
28t
81
2
20t
2 9 20t
(
1 )
，128t
2
60t
27
0 ，（ 4t －3）（32t+9 ） =0，
2
解得 t= 3 ，t= 9 （舍）∴ AC=28× 3 =21 n mile ，BC=20× 3 =15 n mile 。
4
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4
根据正弦定理，得 sin
a、b、c
，边
c= 2
，且
tanA+tanB=
3
33 tanA ·tanB － 3 ，又△ ABC的面积为 S△ = ABC 2 ，求 a+b 的值。
高一数学必修 5 解三角形单元测试题参考答案
一、选择题 题号 1 答案 B
二、填空题
2 3 4 5 6 7 8 9 10 11 12 CB A B DB BB B D D
13. ②④ 三、解答题
14.50, 15.120
0, 16. 45 0
17. 解：（ 1）∵ m n cosC cosC 2cosC 1
1
cosC
∴
2
0 C 180
∴ C 60
…………………………… 2分
a
2
由正弦定理得， sin 45 sin60 ，
………………………………… 4分
a 22 26
1 sin A sin B 1 2
2 sin A
1
2
42
21 2
内切圆半径的取值范围是
21 0,
2
21. 解析：设用 t h ，甲船能追上乙船，且在 C处相遇。 在△ ABC中， AC=28t，BC=20t，AB=9，设∠ ABC=α ，∠ BAC=β。
人教版高中英语必修五 Unit1 Great scientists 单元测试卷(一) (含答案)
2018-2019学年高二上学期训练卷 必修五 Unit1 Great scientists 英 语 （一） 注意事项： 1．答题前，先将自己的姓名、准考证号填写在试题卷和答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。
2．选择题的作答：每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑，写在试题卷、草稿纸和答题卡上的非答题区域均无效。
3．非选择题的作答：用签字笔直接答在答题卡上对应的答题区域内。
写在试题卷、草稿纸和答题卡上的非答题区域均无效。
4．考试结束后，请将本试题卷和答题卡一并上交。
一、单句语法填空 1．The farmers in this area had a good harvest last year thanks to the ________ (science)farming.2．Who is responsible for the ________ (operate) of such vehicles is not clear among car makers, consumers and lawyers.3．Absorbed ________ painting, John didn't notice evening approaching.4．Our appetite for new products also contributes________ the problem.5．That mixture, according to Bernard, sets the elevator ride ________ from just about everyother situation we find ourselves in as we go about our lives.6．It may not be a great suggestion.But before a better one is put ________， we'll make do with it.7．See, your computer has broken down again ！It doesn't make sense ________ buy thecheapest brand of computer just to save a few dollars.8．The term Nigger Jim, for which the novel is often________ (severe) criticized, never appears in it. 9．The Intelligent Transport team at Newcastle University have turned an electric car into a mobile laboratory named “DriveLAB” in order to understand the ________ (challenge) faced by older drivers and to discover where the key stress points are. 10．Only when Lily walked into the office ________ she realize that she had left the contract at home. 二、单句改错 1．Lots of people find it hard to get up in the morning and put a blame on the alarm clock. _______________________________________________________________________ 2．I always have so many things to attend when I come back to the company after a trip abroad. _______________________________________________________________________ 3．Absorbing in the book she was reading, Mary didn't notice me approaching. _______________________________________________________________________ 4．I had an early start at the age of nine with a role in a 1990s TV series, but it wasn't until I finished film studies that I pursued my career as an actress.Like those early days for Dad ，I faced lots of rejection. _______________________________________________________________________ 5．He was struck by the beauty for the first time he visited Guilin. _______________________________________________________________________ 6．The teacher cured him his bad habits and he made great progress in English. _______________________________________________________________________ 7．Young people may risk going deaf if they are exposed very loud music every day. _______________________________________________________________________ 8．In the company, pay increases are linked at performance. _______________________________________________________________________ 此卷只装订不密封班级姓名准考证号考场号座位号9．Before getting into the car, I thought I had learned the instructor's orders, but once I started the car, my mind goes blank._______________________________________________________________________ 10．There is no sense in force yourself to get what you don't want._______________________________________________________________________ 三、完形填空“Mom, you're always on the computer！” Laure complained.“No, I'm not，” I __1__.“Every day I come home from school you're working on the computer.”“Well, at leas t I'm here __2__ you！”My daughter was right.Day after day, in my home office, I would stare into space as my __3__ typed out the thoughts of a speaker or research completed for an article.It seemed that my work as a writer and speaker __4__ my fingers to the keyboard and my mind to valuable ideas.What Laure did not __5__ was that during her day away, I'd also be doing a lot of housework.It was only around three in the afternoon that I'd __6__ seat myself at my desk for a few __7__ moments of deep thought.Then she'd come from school.I was __8__ of myself on being available to my children.After all, I am a speaker on child behavior and parenting.But Laure's observation __9__ my heart.In her eyes, I must have been a mom who was __10__ but unapproachable.I wouldn't make such an image (形象) before her.My relationship with my children is more __11__ than any other work.“Laure，” I called, “come here a minute.”She wandered to my doorway.I had decided to have her __12__ me when I was too devoted to work.I wanted her to have the __13__ to let me know when she thought I was cold.After I explained my __14__ and the fact that I chose home office to be accessible to her and her sister, I offered Laure the following __15__.“Whenever you feel I'm ignoring you or you need my __16__，I want you to __17__ me，” I said.“Just come up and give me a little hug.That'll be our signal that you __18__ me.”Years later we still have that __19__ sign.I've become much more sensitive to my daughters' comings and goings.__20__ she always gives me a little hug to remind me of the real reason why I work at home.1．A.thought B．refused C．defended D．agreed 2．A.for B．over C．against D．after3．A.feet B．hands C．eyes D．ears4．A.connected B．turned C．gave D．added5．A.admit B．realize C．believe D．recognize 6．A.luckily B．gradually C．instantly D．finally 7．A.anxious B．precious C．busy D．rare8．A.proud B．ashamed C．afraid D．scared9．A.filled B．broke C．touched D．mended 10．A.suitable B．available C．acceptable D．reasonable 11．A.important B．funny C．obvious D．wonderful 12．A.warn B．persuade C．encourage D．remind 13．A.patience B．time C．power D．honor 14．A.pattern B．dream C．schedule D．choice 15．A.promise B．chance C．answer D．truth16．A.help B．attention C．decision D．advice 17．A.hug B．shake C．kiss D．kick18．A.miss B．hate C．need D．scold 19．A.unknown B．unexpected C．unfinished D．unspoken20．A.And B．But C．Or D．Yet四、语法填空Observers say Americans want more choices and fresh food when 1.________ (choose)where and what to eat.This trend is one reason why the fast food restaurant McDonald's has struggled financially.McDonald's is one of the best-known 2.________ (restaurant) in the U．S.and even around the world, 3.________ these days the company leaders are seeing numbers they probably do not like.In the last quarter of last year, McDonald's income dropped by about $300 million.The January earnings report brought more bad news.Worldwide sales dropped for the 4.________ (eight) month in a row and even more than expected.McDonald's is 5.________ (work) hard to get their customers back.In January, the company ran an advertisement during the Super Bowl.The football game is the most watched TV event every year in the U．S.McDonald's has wanted 6.________ (reach) those viewers.Shake Shack is 7.________ new kind of restaurant becoming popular in the U．S.The restaurants are not “fast food”．They are known a s “fast casual”．When McDonald's is struggling to get their customers back, Shake Shack is doing well 8.________ (financial)．The New York-based burger chain had a very 9.________ (success) IPO, or Initial Public Offerings, of shares at the end of January.10.________ its first day of trading, Shake Shack went from $21 a share to just under $46 a share.Shake Shack's a quality hamburger.It's fast food, but not “fast food” food.Being part of the “fast casual” trend has helped Shake Shack.五、七选五阅读理解Tips for summer readingSummer holds many of my strongest and most powerful reading memories.I remember sitting under a tree in the backyard as a child, reading Anne of Green Gables as the shadows crossed the grass.I remember sitting in the back seat of the car on a long family road trip, sharing joke books with my brother and sister and laughing until we cried.__1__ I want all kids to enjoy the fun of summer reading, because summer reading has secret power.__2__ Here are some ways to motivate kids for summer reading.Make children the curators(管理人)of their reading lives.Have students set summer reading goals for themselves.__3__ Students can act as “chief curators” of the blog in turn so that over the course of the summer each of them takes on the responsibility of replying to posts and highlighting a popular title.__4__Taking “curiosity walks” is a fantastic way to bring informational text into a child's reading list.These walks also provide opportunities for authentic writing.Have children take an inspiration notebook on a class walk outside and write down anything they see that they would like to learn more about.Make reading more like summer camp.Let's combine reading with hands-on activities and make reading more like summer camp.We can take field trips to the library and search the shelves for books on a topic chosen out of a hat.__5__ Then they can bring that creation to share on the first days of school.A．It will set the stage for academic success.B．Bring the outdoors back into summer reading.C．Select some books and share them with your students.D．Set up a summer blog so you can all share recommendations.E．These memories became important stepping stones in my life.F．It is important to build and shape a strong reading life during school months.G．We can ask our students to create something in response to one of the books they've read.2018-2019学年高二上学期训练卷必修五Unit1 Great scientists英语（一）答案一、单句语法填空1. scientific2. operation3. in4. to5. apart6. forward7. to8. severely9. challenges 10.did二、单句改错1.a→the2.attend后加to3．Absorbing→Absorbed4.rejection→rejections5.去掉for6.him后加of7.exposed后加to8. at→to9.goes→went10.force→forcing三、完形填空1-5 CABAB 6-10 DBACB 11-15 ADCCA 16-20 BACDA四、语法填空1．choosing 2．restaurants3．but 4．eighth 5．working 6．to reach 7．a 8．financially 9．successful 10．On 五、七选五阅读理解1-5 EADBG。
人教A版高中数学必修五上期第一章测试卷.docx
高中数学学习材料鼎尚图文*整理制作广东华侨中学09-10学年上期高中数学必修五第一章测试卷一、选择题：1.在△ABC 中，一定成立的等式是 ( ) A.a sinA=b sinB B.a cosA=b cosB C.a sinB=b sinA D.a cosB=b cosA2. .在△ABC 中，根据下列条件解三角形，则其中有两个解的是A ．b = 10，A = 45°，B = 70° B ．a = 60，c = 48，B = 100° （ ）C ．a = 7，b = 5，A = 80°D ．a = 14，b = 16，A = 45°3. 在ABC ∆中，已知角,334,22,45===b c B则角A 的值是（ ） A ．15° B ．75° C ．105° D ．75°或15° 4．在ABC ∆中，若2=a ，22=b ，26+=c ，则A ∠的度数是（ ）A ．︒30B ．︒45C ．︒60D ．︒755.. 若cCb B a A cos cos sin ==则△ABC 为（ ）A ．等边三角形B ．等腰三角形C ．有一个内角为30°的直角三角形D ．有一个内角为30°的等腰三角形6.在ABC ∆中，已知,,8,45,60D BC AD BC c B 于⊥===则AD 长为（ ）A ．1)34-（B ．1)34+（C ．3)34+（D ．)334-（ 7. 钝角ABC ∆的三边长为连续自然数，则这三边长为（ ）A ．1、2、3、B ．2、3、4C ．3、4、5D ．4、5、68．已知△ABC 中，a ∶b ∶c ＝1∶3∶2，则A ∶B ∶C 等于( ) A ．1∶2∶3B ．2∶3∶1C ．1∶3∶2D ．3∶1∶2二、填空题：1、已知在ABC △中，23,6,30a c A ===，ABC △的面积S .2、设△ABC 的外接圆半径为R ，且已知AB ＝4，∠C ＝45°，则R ＝________．3、在平行四边形ABCD 中，已知310=AB ，︒=∠60B ，30=AC ，则平行四边形ABCD 的面积 。
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第一章测试题一、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. 已知在△ABC 中，a ＝4，b ＝4 ，∠A ＝30°，则∠B 等于 （ ）.A ．30°B ．30°或150°C ．60°D ．60°或120°2. 已知在△ABC 中，AB ＝6，∠A ＝30°，∠B ＝120°，则△ABC 的面积 （ ）.A ．9B ．18C ．93D ．183. 在△ABC 中，若sin :sin :sin C 3:5A B =C =（ ）.A ．30B ．45C ．60D ．1504. 满足条件4a =，5b =，30A =的三角形（ ）.A ．不存在B ．仅有1个C ．有2个D ．有1个或2个5. 在△ABC 中，根据下列条件解三角形，其中有一解的是 （ ）.A ．b ＝7，c ＝3，C ＝30°B ．b ＝5， c ＝4 ，B ＝45°C ．a ＝6，b ＝6 ，B ＝60°D ．a ＝20，b ＝30，A ＝30°6. 在△ABC 中，已知三边a 、b 、c 满足（a ＋b ＋c ）（a ＋b －c ）＝3ab ，则∠C 等于（ ）.A ．15°B ．30°C ．45°D ．60°7.已知在△ABC 中，sin A : sin B : sin C ＝3: 5 :7，那么这个三角形的最大角是（ ）A ．135°B ．90°C ．120°D ．150°8. 海上有A 、B 两个小岛相距10海里，从A 岛望C 岛和B 岛成60°的视角，从B 岛望C 岛和A 岛成75°的视角，则B 、C 间的距离是（ ）A ．10 海里B ．5海里C ．56 海里D ．53 海里9．在△ABC 中，A 为锐角，lg b +lg （c1）=lgsin A =－lg 2， 则△ABC 为（ ）. A. 等腰三角形 B. 等边三角形C. 直角三角形D. 等腰直角三角形10．在三角形ABC 中，已知A 60︒=，b =1，sin sin sin a b c A B c++++为 （ ）A .B . 3C . 3D . 211. 在△ABC 中，若22tan tan b a B A =，则△ABC 的形状是（ ）. A ．直角三角形 B ．等腰或直角三角形 C ．等腰三角形 D ．不能确定12. 已知锐角三角形三边分别为3、4、a ，则a 的取值范围为（ ）A ．15a <<B ．17a <<C 5a <<D 7a <<二、填空题（本大题共4小题，每小题5分，共20分.把答案填在题中横线上）13. 在△ABC 中，cos A ＝135，sin B ＝53，则cos C 的值为______ . 14. 在△ABC 中，若sin A sin B ＝cos 22C ，则△ABC 为_____. 15、某舰艇在A 处测得遇险渔船在北偏东45°距离为10海里的C 处，此时得知，该渔船沿北偏东105°方向，以每小时9海里的速度向一小岛靠近，舰艇时速21海里，则舰艇到达渔船的最短时间是_________________.16.（1）在△ABC 中，若22=b ，2=a ，且三角形有解，则A ∠的取值范围为 .（2）2002年在北京召开的国际数学家大会，会标是以我国古代数学家赵爽的弦图为基础设计的．弦图是由四个全等直角三角形与一个小正方形拼成的一个大正方形（如图）．如果小正方形的面积为1，大正方形的面积为25，直角三角形中较小的锐角为θ，那么cos2θ．三、解答题（本题共6个小题，共70分，解答时应写出必要的文字说明、证明过程或演算步骤）17 . （10分）在△ABC 中，设,2tan tan bb c B A -=求A 的值.18. （10分）在△ABC 中，a 、b 是方程x 2－23x ＋2＝0的两根，且2cos （A ＋B ）＝－1.求（1）角C 的度数；（2）c ；（3）△ABC 的面积.19. （12分）我炮兵阵地位于地面A 处，两观察所分别位于地面点C 和D 处，已知CD =6000m ，∠ACD =45°，∠ADC =75°， 目标出现于地面点B 处时，测得∠BCD =30°， ∠BDC =15°（如图）.求：炮兵阵地到目标的距离.20．（12分） 如图，已知圆O 的半径为1，点C 在直径AB 的延长线上，BC ＝1，点P 是圆O 上半圆上的一个动点，以PC 为边作正三角形PCD ，且点D 与圆心分别在PC 两侧.（1）若POB θ∠=，试将四边形OPDC 的面积y 表示成θ的函数；（2）求四边形OPDC 面积的最大值.21. （12分）在锐角三角形△ABC 中，角A 、B 、C 的对边分别为a 、b 、c ，已知322sin =A . （1）求)2(sin )2(tan 22A C B ++的值；（2）若2,2==∆ABC S a ，求b 的值. 第19题第20题22．（14分）（1）某海上缉私小分队驾驶缉私艇以h km /40的速度从A 处出发沿北偏东︒60的方向航行，进行海面巡逻，当行驶半小时到达B 处，发现在北偏西︒45的方向上有一艘船C ，船C 位于A 处北偏东︒30的方向上，求缉私艇B 与船C 的距离.（2）已知ABC △顶点的直角坐标分别为(34)A ，，(00)B ，，(0)C c ，．①若5c =，求sin A ∠的值；②若A ∠是钝角，求c 的取值范围．参考答案一、选择题1.A2.C3.C4.C5.C6.D7.C8.C9.D 10.B 11.B 12.C二、填空题13. 6516 14. 等腰三角形 15.40分钟 16. （1） π(0,]4；（2） 725三、解答题17. 解：tan 2,tan A c b B b -=根据正弦定理sin sin 2sin sin sin cos sin 得：-=A B C B B A Bsin cos sin cos 2sin cos A B B A C A ∴+=，sin()2sin cos A B C A ∴+=.1sin sin(180())sin()2sin cos cos 602∴=︒-+=+=⇒=⇒=︒C A B A B C A A A . 18. 解：（1）∵2cos （A ＋B ）＝-1，∴cos C ＝21.∴角C 的度数为60°. （2）∵a 、b 是方程x 2－23x ＋2＝0的两根，∴a ＋b ＝23，ab ＝2， c 2＝a 2＋b 2－2ab cos C ＝（a ＋b ）2－2ab （cos C ＋1）＝12－2＝10.∴c ＝ 6 .（3）S ＝21ab sin C ＝23. 19. 解：在△ACD 中，45600060180=∠==∠-∠-=∠ACD ,CD ,ADC ACD CAD .根据正弦定理有:,CD sin sin CD AD 326045== 同理：在△BCD 中，,BDC BCD CBD 135180=∠-∠-=∠306000=∠=BCD ,CD ， 根据正弦定理有：CD sin sin CD BD 2213530== . 在△ABD 中，,BDC ADC ADB90=∠+∠=∠ 根据勾股定理有：421000642213222==+=+=CD CD BD AD AB .所以，炮兵阵地到目标的距离为.20．解：（1）设POB θ∠=且)1800(︒≤≤︒θ在OPC ∆中，1OP =，2OC =，由余弦定理得：2222cos 54cos PC OP OC OP OC θθ=+-⋅=-，所以21sin sin 4cos )2OPDC OPC PDC S S S OP OC PC θθθ∆∆=+=⋅+=+-435)60sin(2435cos 3sin +︒-=+-=θθθ； （2）因为︒≤≤︒1800θ，，所以当1)60sin(=︒-θ，即︒=︒-9060θ，也即︒=150θ时，OPDC S 有最大值且为4352+，故当150POC ∠=︒时，使四边形OPDC 的面积最大.21. 解：（1）因为锐角△ABC 中，A ＋B ＋C ＝π，sin 3A =，所以cos A ＝13，则︒≤︒-≤︒-1206060θ22222sin 2tan sin sin 222cos 21cos 11cos 171cos ;1cos 21cos 33B CB C A A B C B C A A B C A ＋＋＋＝＋＋－（＋）＋＝＋（－）＝＋＝＋（＋）－ （2）ABC ABC 112S sin A 22因为＝，又因为＝＝Sbc bc bc ＝3. 将a ＝2，cos A ＝13，c ＝3b代入余弦定理：2222cos ＝＋－ab c bc A 中，得：42690－＋＝b b ，解得b .22．（1）解：如图，由题意20=AB ，︒=∠30BAC ，︒=∠75ABC . 所以︒=∠75ACB ，由正弦定理得：BACBC ACB AB ∠=∠sin sin .即20sin30sin75BC ︒==︒. 故缉私艇B 与船C 的距离为.（2）解析：① (3,4)AB =--，(3,4)AC c =--，若c =5，则 (2,4)AC =-，∴cos cos ,A AC AB ∠=<>=，∴si②若∠A为钝角，则39160，，-++<⎧⎨≠⎩cc解得253c>，∴c的取值范围是25(,)3+∞.。