安徽省舒城中学2016-2017学年高一上学期研究性学习材料(三)数学试题

安徽省舒城县2016-2017学年高一数学下学期研究性学习材料试题（二）理（无答案）一、填空题（每小题5分，共60分）1.已知三角形ABC ∆中，30A =︒，105C =︒，4b =，则a =（ ） A.2B.C.D.2.已知实数y x ,满足)10(<<<a a a yx，则下面关系是恒成立的是（ ） A.111122+>+y xB.)1ln()1(ln 22+>+y xC.y x sin sin >D.33y x >3.已知{}n a 是等差数列，公差d 不为零，前n 项和是n S ，若3a ，4a ，8a 成等比数列，则（ ）A.140,0a d dS >>B. 140,0a d dS <<C. 140,0a d dS ><D. 140,0a d dS <>4.若平面区域30,230,230x y x y x y +-≥⎧⎪--≤⎨⎪-+≥⎩夹在两条斜率为1的平行直线之间，则这两条平行直线间的距离的最小值是（ ）5.已知不等式250ax x b -+>的解集为{}32x x -<<，则不等式250bx x a -+>的解集为（ ） A.1132x x x ⎧⎫<>⎨⎬⎩⎭或B.1132x x ⎧⎫-<<⎨⎬⎩⎭C. {}32x x x <->或D.{}32x x -<<6.设{}n a 是等差数列. 下列结论中正确的是（ ）A ．若120a a +>，则230a a +>B ．若130a a +<，则120a a +<C ．若120a a <<，则2a >D ．若10a <，则()()21230a a a a -->7.设0,0x y >>，若lg lg 2x y 成等差数列，则116x y+的最小值为（ ） A.8B.9C.12D.168.在ABC ∆（O 为原点）中，()2cos ,2sin OA αα，()5cos ,5sin OB ββ=，若5OA OB ⋅=-，则OAB △的面积为（ ）C.9.在ABC △中，π4B =，BC 边上的高等于13BC ,则sin A =（ ）（A ）310（B （C （D10.实数,x y 满足01xy x y ≥⎧⎨+≤⎩，使z ax y =+取得最大值的最优解有两个，则1z ax y =++的最小值为（ ）A ．0B ．-2C ．1D ．-111.已知{}n a 满足11a =，*11()()4n n n a a n N ++=∈，21123444n n n S a a a a -=++++，则54nn n S a -=（ ）A ．1n -B ．nC ．2nD ．2n12.在我国古代著名的数学专著《九章算术》里有一段叙述:今有良马与驽马发长安至齐，齐去长安一千一百二十五里，良马初日行一百零三里，日增十三里；驽马初日行九十七里，日减半里；良马先至齐，复还迎驽马，二马相逢，问：几日相逢？（ ）A ．12日 B ．16日 C ．8日D ．9日二、填空题（每小题5分，共20分）13.圆心在直线x y 4-=上，且与直线01=-+y x 相切于点),(23-P 的圆的标准方程为14.设二次函数()()24f x ax x c x R =-+∈的值域为[)0,+∞，则1919c a +++的最大值是 15.已知变量x ，y 满足约束条件⎪⎩⎪⎨⎧≥≤-≤+ax y x y x 11，若212≤-x y 恒成立，则实数a 的取值范围____． 16.已知数列{}n a 的前n 项和为()1211,1,3,432n n n n S a a S S S n +-===-≥，若对于任意*n N ∈，当[]1,1t ∈-时，不等式21211121n x tx a a a ⎛⎫+++<++ ⎪⎝⎭恒成立，则实数x 的取值范围为_______.三、解答题（本大题共70分） 17.（本小题满分10分）已知,,a b c 分别是ABC ∆的三个内角,,A B C 的对边，2cos cosb c Ca A-=. （1）求角A 的大小； （2）求函数sin 6y B C π⎛⎫=+- ⎪⎝⎭的值域.18.（本小题满分12分）n S 为等差数列{}n a 的前n 项和，且17=128.a S =，记[]=lg n n b a ，其中[]x 表示不超过x 的最大整数，如[][]0.9=0lg99=1，． （1）求111101b b b ，，；（2）求数列{}n b 的前1 000项和．19. （本小题满分12分）设函数()()()2230f x ax b x a =+-+≠.（1）若不等式()0f x >的解集为()1,3-，求a ，b 的值；（2）若()12f =， 0a >，0b >，求19a b+的最小值.20. （本小题满分12分）在平面直角坐标系xOy 中，已知圆22:40C x y x +-=及点(1,0)A -，(1,2)B ． （1）若直线l 平行于AB ，与圆C 相交于M ，N 两点，MN AB =，求直线l 的方程； （2）在圆C 上是否存在点P ，使得2212PA PB +=？若存在，求点P 的个数；若不存在，说明理由．21. （本小题满分12分）某企业参加A 项目生产的工人为1000人，平均每人每年创造利润10万元.根据现实的需要，从A 项目中调出x 人参与B 项目的售后服务工作，每人每年可以创造利润⎪⎭⎫ ⎝⎛-500310x a 万元（0>a ），A 项目余下的工人每人每年创造利润需要提高%2.0x（1）若要保证A 项目余下的工人创造的年总利润不低于原来1000名工人创造的年总利润，则最多调出多少人参加B 项目从事售后服务工作？（2）在（1）的条件下，当从A 项目调出的人数不能超过总人数的%40时，才能使得A 项目中留岗工人创造的年总利润始终不低于调出的工人所创造的年总利润，求实数a 的取值范围.22. （本小题满分12分）已知正项数列{}n a 的前n 项和为2)1(41,+=n n n a S S 且有，数列123121,,,,----n n b b b b b b b 是首项为1，公比为21的等比数列.（1）求证：数列{}n a 是等差数列.（2）若}{),2(n n n n c b a c 求数列-⋅=的前n 项和n T . （3）在（2）条件下，是否存在常数λ，使得数列⎪⎪⎭⎫⎝⎛++2n n a T λ为等比数列？若存在，试求出λ；若不存在，说明理由.舒城中学高一研究性学习材料（八）理数答题卷一、填空题（每小题5分，共60分）二、填空题（每小题5分，共20分）13. ； 14. ； 15. ； 16. ；三、解答题（本大题共70分） 17.（本小题满分10分）18.（本小题满分12分）班级： 姓名： 座位号：………………………………… 装 ………………………………… 订 ……………………………… 线 ………………………………………………19. （本小题满分12分）20. （本小题满分12分）舒中高一理数答题卷第2页 (共4页)21. （本小题满分12分）22. （本小题满分12分）舒中高一理数答题卷第3页 (共4页)。

舒城中学高一研究性学习材料（三）英语 2016.11.05第一部分阅读理解（共20小题；每小题2分，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的四个选项中选出最佳选项AOur planet was born some billions of years ago. Ever since this planet has developed, it has surprised us human beings. No matter how much we human beings have developed technologically, we cannot ever create this kind of natural planet. The human race can only discover some amazing facts about it. Let us find out what some of themare.On September 13, 1922 El Azizia, a place in Libya, recorded a temperature of 136 degrees Fahrenheit. This was the highest temperature ever measured (测量) on the planet Earth. The highest waterfall in the world is Angel Falls in Venezuela, which drops from an amazing height of 3,212 feet. The waterfall drops over the edge of Auyantepui in the Canaima National Park. The gravitational pull (万有引力) of the Earth can be escaped if someone moves at a speed of 6.95 miles per second. At such a speed, one could travel from New York to Philadelphia in just 20 s econds. If the entire water in the world’s oceans evaporated, the salt we got from these oceans could cover the entire planet with a 500-foot deep layer of salt. The deepest lake on Earth is Lake Baikal in Russia. Lake Baikal is the largest freshwater lake in t he world, containing about 20% of the world’s unfrozen surface fresh water. The Andes in South America spreads over 4,525 miles. This is the longest mountain range (山脉) in the world.Did you know that the biggest valley in the world is the Grand Valley in Mesa County, Colorado and Grand County, Utah? It is about 30 miles (48 km) long and 5 miles (8 km) wide, along the Colorado River. The amazing facts about the earth are too many to be told completely above.1. The underlined word “evaporated” in Paragraph 2 most probably means“_____”.A. became salt graduallyB. became clear slowlyC. changed into warmer waterD. changed into gas or disappeared2. Where is the longest mountain range in the world?A. In Russia.B. In Libya.C. In South America.D. At the Oregon-Idaho border.3.We can learn from this passage that _____.A. Lake Baikal is the biggest lake in the worldB. the highest temperature ever measured was 136 ℃C. the Angel Falls drops from a height of 3,212 metersD. one end of the Grand Valley is in Colorado and the other in UtahBThis is an open letter to the three people who stole my handbag from the department store where I am employed as a shop assistant.When you took my bag, I don't know what you thought you were going to get. With my wages, there's not much left on a Tuesday. I hope the ￡5 was useful to you . I have informed the social security office so you won't be able to cash the child benefit next week. I hope that won't leave you too short. But if you really need a couple of pounds, I suppose you could always cash one of the two checks left in my check book. Of course,I phoned the bank right away and the check-casing card is no longer valid, so it won’t be much use to you.Actually I don't mind about the money too much. We single parents who work to support our families understand only too well what it means to be short of cash. However, I don’t suppose it went very far among the three of you. Sorry about that!I wish you had left the bag behind and just taken the wallet and check book. There were all kinds of papers in it, and notes and things that I really need. I really think that was very inconsiderate of you. I mean, how would you like something like that to happen to you?Well, perhaps the bag will turn up. It wasn't even an expensive one, just a plain, old brown leather shoulder bag. You probably dumped it in the nearest rubbish bin or threw it into the bushes. We've looked around, of course, but no one saw which way you went after you left the shop.I'm not really angry with you. I know how the pressures of modern living can affect us, but I am sad at the loss of my personal things. I feel violated and helpless. The police were very icy, and they just shruggedtheir shoulders. "It happens all the time," they told me. Some small comfort, I suppose. But I've lost just a little more faith in human nature. And as my young son said when I told him what had happened, "Why? Mummy, why us?" I couldn't answer that question. I wonder if you can.4.In writing Paragraph 2, the writer wants to ．A. describe the contents of the bag in detail．B. give some suggestions to the three thievesC. tell the thieves hardly any money was availableD. state the fact that she was careless with the money5.Which of the following is the most valuable to the writer?A. The cash in her bagB. The papers and notes in the bagC. The handbag itselfD. The check books in the bag6.What can we conclude about the police?A. They have doubts about human natureB. They show sympathy for the woman舒中高一英语第2页(共8页)C. They think the case quite commonD. They are unable to find the thieves7.Why does the author write the letter?A. To give the thieves a serious warningB. To complain about the fall of moralityC. To call people’s attention to their belongingsD. To express her affection for her valuable bagCParents and kids today dress alike, listen to the same music, and are friends. Is this a good thing? Sometimes, when Mr. Ballmer and his 16-year-old daughter, Elizabeth, listen to rock music together and talk about interests they both enjoy, such as pop culture, he remembers his more distant relationship with his parents when he was a teenager.“I would never have said to my mom, ‘Hey, the new Weezer album is really great. How do you like it?’” says Ballmer. “There was just a complete gap in taste.”Music was not the only gulf. From clothing and hairstyles to activities and expectations, earlier generations of parents and children often appeared to move in separate orbits(轨道).Today, the generation gap has not disappeared, but it is getting narrow in many families. And parent—child activities, from shopping to sports, involve a feeling of trust and friendship that can continue into adulthood.But family experts warn that the new equality can also result in less respect for parents. “There’s still a lot of strictness and authority(权威) on the part of parents out there, but there is a change h appening,” says Kerrie, a psychology professor at Lebanon Valley College. “In the middle of that change, there is a lot of confusion among parents.”Family researchers offer a variety of reasons for these changing roles and attitudes. They see the 1960s as a turning point. Great cultural changes led to more open communication and a more democratic(民主的) process that encourages everyone to have a say.“My parents were on the ‘before’ side of that change, but today’s parents, the 40-year-olds, were on the ‘after’ side,” explains Mr. Ballmer. “It’s not something easily achieved by parents these days, because life is more difficult to understand or deal with, but sharing interests does make it more fun to be a parent now.”8. The underlined word “gulf” in Para.3 most probably means _________.A. distanceB. interestC. similarityD. cooperation9. The change in today’s parent-child relationship is _________.A. more confusion among children.B. less respect for parents from children.C. new equality between parents and children.D. more strictness and authority on the part of parents.10. By saying “today’s parents, the 40-year-olds, were on the ‘after’ side.” the author means thattoday’s parents _________.A. can set a limit to the change.B. follow the trend of the change.C. fail to take the change seriously.D. have little difficulty adjusting(适应)to the change.11. The purpose of the passage is to _________.A. describe the difficulties today’s parents have met with.B. discuss the development of the parent—child relationship.C. suggest the ways to handle the parent—child relationship.D. compare today’s parent—child relationship with that in the past.DLONDON: What could possibly be wrong with planting trees? The benefits are obvious; they firm the soil, soak up (摄取) extra water and take carbon dioxide (二氧化碳) our of the atmosphere.However, it now turns out that planting trees could add to global warming.Tree roots do a great job of keeping soil firmly on t he ground and out of the wind’s power. The problem is that some of those dust clouds play an important part in soaking up carbon dioxide.Huge dust storms blow out over the oceans from dry parts of North Africa and central Asia. Tons of dust are lifted and left as a thin film over the ocean surface. The dust fuels oceanic life.Dust from China is carried east and left in the Pacific Ocean. If a tree-planting program there is successful and the dust supply reduced, the net result may be that less carbon dioxide gets locked away in the ocean.Andy Ridgwell, an environmental scientist from the University of East Anglia, has spent the past few years studying dust and says his work “shows clearly the complexity of the system and the importance of not tinkering(粗劣地修补) with it without understanding the results. For this reason the need is to focus(集中) on cutting carbon dioxide giving off rather than monkeying (瞎弄) about with the land surface.”An American scientist, Robert Jackson, has shown that when native grassland areas are invaded(侵入) by trees, carbon is lost from the soil. “We are studying why the soil carbon disappears, but one theory is that trees do a lot more of their growing above ground compared to grasses, so less carbon goes directly into the soil fro m trees, ” says Jackson.In wet areas of the world, the gain from trees absorbing carbon dioxide above ground seems to舒中高一英语第4页(共8页)be outweighed(超过) by the loss of carbon from the soil below ground. Countries that plan to combatglobal warming by planting trees may have to think again.Solutions to environmental problems are often more complex than they first appear, and understanding the Earth’s climate is a very great challenge.12．People usually hold the opinion that .A．huge dust storms can destroy carbon dioxideB．huge dust storms can destroy the oceans on the earthC．huge dust storms can’t do anything beneficial for manD．planting trees is the only way to control huge dust storms13．Andy Ridgwell, the environmental scientist, believes that .A．dust plays a more important part than treesB．trees shouldn’t have been planted in dry placesC．carbon dioxide is harmful to everything on the earthD．environmental problems are more complex than expected14．R obert Jackson’s experiment proves that .A．grassland areas should be covered by forestsB．trees hold more carbon than grassesC．carbon can turn grass into dustD．less carbon can make trees grow faster15．The underlined w ord “combat” in the last paragraph means .A．learn about B．fight against C．live with D．give up第二节（共五小题，每小题2分，共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。

安徽省舒城中学2016-2017学年高一数学上学期研究性学习材料（周考）试题（七）（无答案）（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，只有一项是最符合题目要求的. 1．函数4sin 1)(2xx f +=的最小正周期是( ) A ．2πB ．πC ．π2D ．π42．下列函数中，在区间02π⎛⎫⎪⎝⎭，上为增函数且以π为周期的函数是( ) A ．2sinxy = B ．x y sin = C ．x y tan -= D ． x y 2cos -= 3．已知==-∈x x x 2tan ,54cos ),0,2(则π( ) A ．247B ．－247C ．724D ．－724 4. tan15tan30tan15tan30++等于( )A B ．1CD5．若,5sin 2cos -=+a a 则=a tan（ ） A ．21B ．2C ．21- D ．2- 6.cos251sin 40=-（ ）A ．1B ．2C D7．为得到函数)3cos(π+=x y 的图象，只需将函数x y sin =的图像（ ）A ．向左平移6π个长度单位 B ．向右平移6π个长度单位 C ．向左平移65π个长度单位 D ．向右平移65π个长度单位 8. 已知函数x x x f sin cos )(=)(R x ∈，给出下列四个命题：①若)()(21x f x f -=，则21x x -= ②)(x f 的最小正周期是π2 ③在区间]4,4[ππ-上是增函数． ④)(x f 的图象关于直线43π=x 对称 其中正确的序号是( )A ．①②④B ．①③C ．②③D ．③④9. 已知函数x x x f cos )(2-=，对于⎥⎦⎤⎢⎣⎡-2,2ππ上的任意21,x x ，有如下条件：①21x x >； ②2221x x >；③21x x >．其中能使)()(21x f x f >恒成立的条件序号是（ ） A ．①② B ．②C ．②③D ．③ 10. 已知31)6sin(=+απ，则)232cos(απ-的值等于( )A ．97B ．31C ．97-D ．31-11．偶函数)(x f 在[－1，0]上为减函数，A 、B 为某个锐角三角形的两个内角，则（ ）A ．)B (cos )A (cos f f > B ．)B (sin )A (sin f f >C ．)B (cos )A (sin f f >D ．)B (cos )A (sin f f <12．已知函数22()sincos()336f x x x π=+-，对任意的实数,αβ，当()()f f αβ-最大时，则βα-的最小值是( )A ．3πB ．32πC ．43πD ．53π二.填空题:本大题共4小题，每小题5分，共20分.把答案写在答题卡的相应位置上. 13. 若4sin ,5θ=则cos 2θ=___________． 14.函数sin 2cos2y x x =+的递增区间______________．15. 已知,αβ都是锐角，1sin ),2ααβ=+=则cos β=__________________. 16．已知函数a x x f -=1)(，若存在ϕ)2,4(ππ∈，使0)(co s )(s i n =+ϕϕf f ，则实数a 的取值范围是 .三. 解答题：本大题共6小题，共70分.解答应写出文字说明、证明过程或演算步骤. 17. (本小题满分10分）已知sin()4πα-=tan 7β=，其中,(0,)2παβ∈．（Ⅰ）求sin α的值； （Ⅱ）求αβ+．18．(本小题满分12分）函数R x x x x f ∈-+-=,)2sin()2cos()(π。

舒城中学高一研究性学习材料（一）理 数 2017。

02。

25命题： 审题:（时间：80分钟 满分：100分）一、选择题：本大题共8小题，每小题5分，共40分。

在每小题给出的四个选项中，只有一项是最符合题目要求的.1．已知集合12{|log (2)1}A x R x =∈-≥-，26{|1}3x B x R x+=∈≥-,则AB =（ ）A ．[1,3)-B ．[1,3]-C ．φD ．(2,3) 2．函数)10(1||log)(<<+=a x x f a的图象大致为（ ）3．下列结论中正确结论的个数是（ ）①若向量a,b,c 满足a //b,b //c ,则a //c ；②对任意向量a,b,恒有｜a -b |<|a +b ｜ ; ③=-+-CD BD AC AB 0； ④若OC OB OA 3231+=，则C B A ,,三点共线. A ．4 B ．3 C ． 2 D ．14．若552)4sin(2cos -=+παα，且)2,4(ππα∈，则tan 2α=（ ）A ．43- B ．34-C ．43 D ．345．若1sin()63πα-=，则22cos ()162πα+-=（ ）A ．13B ．13- C ．79 D ．79-6．已知函数),0(cos sin )(R x ab x b x a x f ∈≠-=在4π=x 处取得最大值，则函数)4(x f y -=π是（ ）A 。

偶函数且它的图象关于点)0,(π对称 B. 偶函数且它的图象关于点)0,23(π对称C 。

奇函数且它的图象关于点)0,23(π对称D 。

奇函数且它的图象关于点)0,(π对称 7．在ABC ∆中，已知C B A sin 2tan =+,给出以下四个论断 ①tan 1tan AB= ②2sin sin 0≤+<B A③1cos sin 22=+B A ④C B A 222sin cos cos =+其中正确的是( ）A.①③ B 。