黑龙江理综、数学高考真题及解析.doc

绝密启用前2017年普通高等学校招生全国统一考试理科数学注意事项：1.答题前，考生先将自己的姓名、准考证号填写清楚，将条形码准确粘贴在条形码区域内。2.选择题必须使用2B铅笔填涂；非选择题必须使用0.5毫米黑色字迹的签字笔书写，字体工整，笔迹清楚3.请按照题号顺序在答题卡各题目的答题区域内作答，超出答题区域书写的答案无效；在草稿纸、试卷上答题无效4.作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑。5.保持卡面清洁，不要折叠、不要弄破、弄皱，不准使用涂改液、修正带、刮纸刀一、选择题：本题共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.（ ）A B C D2.设集合，若，则（ ）A B C D3.我国古代数学名著算法统宗中有如下问题：“远望巍巍塔七层，红光点点倍加增，共灯三百八十一，请问尖头几盏灯？”意思是：一座7层塔共挂了381盏灯，且相邻两层中的下一层灯数是上一层灯数的2倍，则塔的顶层共有灯（ ）A1盏 B3盏 C5盏 D9盏4.如图，网格纸上小正方形的边长为1，粗实线画出的是某几何体的三视图，该几何体由一平面将一圆柱截去一部分所得，则该几何体的体积为（ ）A B C D5.设，满足约束条件，则的最小值是（ ）A B C D6.安排3名志愿者完成4项工作，每人至少完成1项，每项工作由1人完成，则不同的安排方式共有（ ）A12种 B18种 C24种 D36种7.甲、乙、丙、丁四位同学一起去向老师询问成语竞赛的成绩老师说：你们四人中有2位优秀，2位良好，我现在给甲看乙、丙的成绩，给乙看丙的成绩，给丁看甲的成绩看后甲对大家说：我还是不知道我的成绩根据以上信息，则（ ）A乙可以知道四人的成绩 B丁可以知道四人的成绩C乙、丁可以知道对方的成绩 D乙、丁可以知道自己的成绩8.执行右面的程序框图，如果输入的，则输出的（ ）A2 B3 C4 D59.若双曲线（，）的一条渐近线被圆所截得的弦长为2，则的离心率为（ ）A2 B C D10.已知直三棱柱中，则异面直线与所成角的余弦值为（ ）A B C D11.若是函数的极值点，则的极小值为（ ）A. B. C. D.112.已知是边长为2的等边三角形，P为平面ABC内一点，则的最小值是（ ）A. B. C. D.二、填空题：本题共4小题，每小题5分，共20分。13.一批产品的二等品率为，从这批产品中每次随机取一件，有放回地抽取次，表示抽到的二等品件数，则 14.函数（）的最大值是 15.等差数列的前项和为，则 16.已知是抛物线的焦点，是上一点，的延长线交轴于点若为的中点，则 三、解答题：共70分。解答应写出文字说明、解答过程或演算步骤。第1721题为必做题，每个试题考生都必须作答。第22、23题为选考题，考生根据要求作答。（一）必考题：共60分。17.（12分）的内角的对边分别为 ,已知(1)求 (2)若 , 面积为2,求 18.（12分）淡水养殖场进行某水产品的新、旧网箱养殖方法的产量对比，收获时各随机抽取了100 个网箱，测量各箱水产品的产量（单位：kg）某频率直方图如下：（1） 设两种养殖方法的箱产量相互独立，记A表示事件：旧养殖法的箱产量低于50kg, 新养殖法的箱产量不低于50kg,估计A的概率；（2） 填写下面列联表，并根据列联表判断是否有99%的把握认为箱产量与养殖方法有关：箱产量50kg箱产量50kg旧养殖法新养殖法（3） 根据箱产量的频率分布直方图，求新养殖法箱产量的中位数的估计值（精确到0.01）P（K2k）0.0500.0100.001k3.8416.63510.828 19.（12分）如图，四棱锥P-ABCD中，侧面PAD为等比三角形且垂直于底面ABCD， E是PD的中点.（1）证明：直线 平面PAB（2）点M在棱PC 上，且直线BM与底面ABCD所成锐角为 ，求二面角M-AB-D的余弦值 20. （12分）设O为坐标原点，动点M在椭圆C：上，过M做x轴的垂线，垂足为N，点P满足.(1) 求点P的轨迹方程；(2) 设点Q在直线x=-3上，且.证明：过点P且垂直于OQ的直线l过C的左焦点F. 21.（12分）已知函数且.（1）求a；（2）证明：存在唯一的极大值点，且.（二）选考题：共10分。请考生在第22、23题中任选一题作答。如果多做，按所做的第一题计分。22.选修4-4：坐标系与参数方程（10分） 在直角坐标系xOy中，以坐标原点为极点，x轴的正半轴为极轴建立极坐标系，曲线的极坐标方程为（1）M为曲线上的动点，点P在线段OM上，且满足,求点P的轨迹的直角坐标方程；（2）设点A的极坐标为，点B在曲线上，求面积的最大值23.选修4-5：不等式选讲（10分）已知，证明：（1）；（2）绝密启用前2017年普通高等学校招生全国统一考试理科数学试题答案一、选择题1.D 2.C 3.B 4.B 5.A 6.D7.D 8.B 9.A 10.C 11.A 12.B二、填空题13. 1.96 14. 1 15. 16. 6三、解答题17.解：（1）由题设及，故上式两边平方，整理得 解得 （2）由，故又由余弦定理及得所以b=218.解：（1）记B表示事件“旧养殖法的箱产量低于” ，表示事件“新养殖法的箱产量不低于” 由题意知 旧养殖法的箱产量低于的频率为故的估计值为0.62新养殖法的箱产量不低于的频率为故的估计值为0.66因此，事件A的概率估计值为（2）根据箱产量的频率分布直方图得列联表箱产量箱产量旧养殖法6238新养殖法3466由于故有的把握认为箱产量与养殖方法有关（3）因为新养殖法的箱产量频率分布直方图中，箱产量低于的直方图面积为，箱产量低于的直方图面积为故新养殖法箱产量的中位数的估计值为19.解：（1）取中点，连结，因为为的中点，所以,由得，又所以四边形为平行四边形， 又，故（2）由已知得,以A为坐标原点，的方向为x轴正方向，为单位长，建立如图所示的空间直角坐标系A-xyz,则则，,则因为BM与底面ABCD所成的角为45，而是底面ABCD的法向量，所以，即（x-1）+y-z=0又M在棱PC上，设由，得所以M，从而设是平面ABM的法向量，则所以可取m=（0，-，2）.于是因此二面角M-AB-D的余弦值为20.解（1）设P（x,y）,M（x0,y0）,设N（x0,0）, 由得因为M（x0,y0）在C上，所以因此点P的轨迹方程为（2）由题意知F（-1,0）.设Q（-3，t）,P(m,n),则，由得，又由（1）知，故3+3m-tn=0所以，即又过点P存在唯一直线垂直于OQ，所以过点P且垂直于OQ的直线l过C的左焦点F.21.解：（1）的定义域为设，则等价于因为若a=1，则.当0x1时，单调递减；当x1时，0，单调递增.所以x=1是的极小值点，故综上，a=1（2）由（1）知设当时，；当时，所以在单调递减，在单调递增又，所以在有唯一零点x0，在有唯一零点1，且当时，；当时，当时，.因为，所以x=x0是f(x)的唯一极大值点由由得因为x=x0是f(x)在（0,1）的最大值点，由得所以22.解：（1）设P的极坐标为，M的极坐标为，由题设知由得的极坐标方程因此的直角坐标方程为（2）设点B的极坐标为,由题设知,于是OAB面积当时，S取得最大值所以OAB面积的最大值为23.解：（1）（2）因为所以，因此a+b2.2017年普通高等学校招生全国统一考试英语试卷II（正式版解析）第二部分 阅读理解（共两节，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A、B、C、D四个选项中，选出最佳答案。AIn the coming months, we are bringing together artists form all over the globe, to enjoy speaking shakespeares plays in their own language, in our globe, within the architecture shakespeare wrote for.please come and join us.National Theatre Of China Beijing|ChineseThis great occasion(盛会) will be the national theatre of chinas first visit to the uk. The companys productions show the new face of 21st century chinese theatre. This production ofShakespeares Richard III will be directed by the Nationals Associate Director,Wang Xiaoying.Date&Time:Saturday 28 April,2.30pm&Sunday 29 April,1.30pm&6.30pmMarjanishvili Theatre Tbilisi l Georgian One of the most famous theatres in Georgia,the Marjanishvili,founded in 1928,appears regularly at theatre festivals all over the world. This new production of As You Like It is helmed（指导）by the companys Artistic Director Levan Tsuladze.Date & Time :Friday 18May,2.30pm&Sunday 19May,7.30pmDeafinitely Theater London l British Sign Language （BSL）By translating the rich and humourous taxt of Loves Labours Lost into the physical language of BSL,Deafinitely Thertre creates a new interpretation of Shakespeares comedy and aims to build a bridge between deaf and hearing worlds by performing to both groups as one audience.Date&Time:Tueaday 22 May,2.30pm&Wednesday 23 May,7.30pmHabima National Theatre Tel Aviv l HebrewThe Habima is the centre of Hebrew-languege theatre worldwide,Founded in Moscow after the 1905 revolution,the company eventually settled in Tel Aviv in the late 1920s,Since 1958,they have been recognized as the national theatre of Israel.This production of Shakespeares The Merchant of Venice marks their first visit to the UK.Date Date&Time:Monday 28May,7.30&Tuesday 29 May,7.30pm21.which play will be performed by the National Theatre of China?A.Richard . B.Lovers Labours LostC.As You Like It D.The merchant of Venice22.What is special about Deafinnitely Theatre?A.Tt has two groups of actors B.It is the leading theatre in LondonC.It performs plays in BSL D.It is good at prducting comedies23.When can you see a play in Hebrew?A.Onsuturday 28Apil. B.On Sunday 29 AprilC.On Tuesday 22 May. D. On Tuesday 29 May21-23 AAD BI first met Paul Newman in 1968, when George Roy Hill, the director of Butch Cassidy and the Sundance Kid, introduced us in New York City. When the studio didnt want me for the film it wanted somebody as well known as Paul he stood up for me. I dont know how many people would have done that; they would have listened to their agents or the studio powers.The friendship that grew out of the experience of making that film and The Sting four years later had its root in the fact that although there was an age difference, we both came from a tradition of theater and live TV. We were respectful of craft（技艺）and focused on digging into the characters we were going to play. Both of us had the qualities and virtues that are typical of American actors: humorous, aggressive, and making fun of each other but always with an underlying affection. Those were also at the core （核心）of our relationship off the screen.We shared the brief that if youre fortunate enough to have success, you should put something back he with his Newmans Own food and his Hole in the Wall camps for kids who are seriously ill, and me with Sundance and the institute and the festival. Paul and I didnt see each other all that regularly, zxx.k but sharing that brought us together. We supported each other financially and by showing up at events.I last saw him a few months ago. Hed been in and out of the hospital.He and I both knew what the deal was,and we didnt talk about it.Ours was a relationship that didnt need a lot of words.24.Why was the studio unwilling to give the role to author at first?A.Paul Newman wanted it.B.The studio powers didnt like his agent.C.He wasnt famous enough.D.The director recommended someone else.25.Why did Paul and the author have a lasting friendship?A.They were of the same dge.B.They worked in the same theater.C.They were both good actors.D.They han similar charactertics.26.What does the underlined word “that” in paragraph 3 refer to?A.Their belief.B.Their care for chileden.C.Their success.D.Their support for each other.27.What is the authors purpose in writing the test?A.To show his love of films.B.To remember a friend.C.To introduce a new movie.D.To share his acting experience.24-27 CDAB21. 细节理解题。根据“When the studio didnt want me for the film it wanted somebody as well known as Paul”制片人不想要我，他想要当时比较出名的演员Paul,因此，可知作者当时还不是很有名。故选C。C Terrafugia Inc .said Monday that its new flying car has completed its first flight,bringing the company closer to its goal of selling the flying car within the next year.The wehicle-named the Transition has two seats wheels and wings that fold up so it can be driven like a car.The Transition,which flew at 1,400 feet for eight minutes last month, can reach around 70 miles per hour on the road and 115 in the flies using a 23-gallon tank of gas and bums 5 gallons per hour in the air. On the ground, it gets 35 miles per gallon.Around 100 people have already put down a $10,000 deposit to get a Transition when they go on sale, and those numbers will likely rise after Terrafugia introduces the Transition to the public later this week at the New York Auto Show. But dont expect it to show up in too many driveways. Its expected to cost $279,000.And it wont help if youre stuck in traffic. The car needs a runway. Inventors have been trying to make flying cars since the 1930s, according to Robert Mann, an airline industry expert. But Mann thinks Terrafugia has come closer than anyone to making the flying car a reality. The govemment has already permitted z&xxkthe company to use special materials to make it easier for the vehicle to fly. The Transition is now going through crash tests to make sure it meets federal safety siandards.Mann said Terrafugia was helped by the Federal Aviation Administrations decision five years ago to create a separate set of standards for light sport aircraft, which are lower than those for pilots of larger planes. Terrafugia says an owner would need to pass a test and complete20hoursofflyingtimetobeabletoflytheTransition,arequirementpilotswouldfindrelativelyeasytomeet.28. What is the first paragraph mainly about?A. The basic data of the Transition. B. The advantages of flying cars.C. The potential market for flying cars. C. The designers of the Transition.29. Why is the Transition unlikely to show up in too many driveways?A. It causers traffic jams. B. It is difficult to operate.C. It is very expensive. D. It bums too much fuel.30. What is the govemments attitude to the development of the flying car?A. Cautious B. Favorable.C. Ambiguous. D. Disapproving.31. What is the best title for the text?A. Flying Car at Auto Show B. The Transitions Fist FlightC.PilotsDream Coming True D. Flying Car Closer to Reality DWhen a leafy plant is under attack ，it doesnt sit quietly. Back in 1983,two scientists,Jack Schultz and Ian Baldwin,reported that young maple trees getting bitten by insects send out a particular smell that neighboring plants can get. These chemicals come from the injured parts of the plant and seem to be an alarm.What the plants pump through the air is a mixture of chemicals known as volatile organic compounds,VOCs for short. Scientists have found that all kinds of plants give out VOCs when being attacked .Its a plants way of crying out.But is anyone listening?Apparently.Because we can watch the neighbours react. Some plants pump out smelly chemicals to keep insects away.But others do double duty .They pump out perfumes designed to attract different insects who are natural enemies to the attackers.Once they arrive,the tables are turned .The attacker who are natural enemies to the attackers . zxx|k Once they arrive,the tables are turned.The attacker who was lunching now becomes lunch. In study after study,it appears that these chemical conversations help the neighbors .The damage is usually more serious on the first plant,but the neighbors ,relatively speaking ,stay safer because they heard the alarm and knew what to do.Doesthismeanthatplantstalktoeachother?Scientistsdontknow.Maybethefirstplantjustmadeacryofpainorwassendingamessagetoitsownbranches,andso,ineffect,wastalkingtoitself.Perhapstheneighborsjusthappenedto“overhear”thecry.Soinformationwasexchanged,butitwasntatrue,intentionalbackandforth. CharlesDarwin,over150yearsago,imaginedaworldfarbusier,noisierandmoreintimate(亲密的)thantheworldwecanseeandhear.Oursensesareweak.Theresawholelotgoingon.32.Whatdoesaplantdowhenitisunderattack?A.Itmakesnoises.B.Itgetshelpfromotherplants.C.ItstandsquietlyD.Itsendsoutcertainchemicals.33.Whatdoestheauthormeanby“thetablesareturned”inparagraph3?A.Theattackersgetattacked.B.Theinsectsgatherunderthetable.C.Theplantsgetreadytofightback.D.Theperfumesattractnaturalenemies.34.Scientists find from their studies that plants can .A.predict natural disasters B.protect themselves against insectsC.talk to one another intentionally D.help their neighbors when necessary35.what can we infer from the last paragraph?A.The word is changing faster than ever.B.People have stronger senses than beforeC.The world is more complex than it seemsD.People in Darwins time were imaginative. 第二节 （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。选项中有两项为多余选项。Interruptions are one of the worst things to deal with while youre trying to get work done. 36 ,there are several ways to handle things.Lets take a look at them now. 37 .Tell the person youre sorry and explain that you have a million things to do and then ask if the of you can talk at a different time.When people try to interrupt you,have set hours planned and let them know to come back during that time or that youll find them then. 38 .It can help to eliminate(消除) future interruptions.When you need to someone,dont do it in your own office. 39 .its much easeier to excuse yourself to get back to your work than if you try to get someone out of your space even after explaining how busy you areIf you have a door to your office,make good use of it. 40 .If someone knocks and its not an important matter. Excuseyourself and let the person know youre busy so they can get the hint(暗示) than when the door is closed,youre not to be disturbed.A.If youre busy, dont feel bad about saying noB. When you want to avoid interruptions at work zxx.kC. Set boundaries for yourselfas your time goesD. If youre in the other persons office or in a public arceaE. Its important that you let them know when youll be availableF.It might seem unkind to cut people shirt when they interrupt youG.Leave it open when youre available to talk and close it when youre not36-40 BAEDG第三部分 语言知识运用（共两节，满分45分）第一节（共20小题：每小题1.5分，满分30分）阅读下面短文，从短文后各题所给的A、B、C和D四个选项中，选出可以填入空白处的最佳选项。In1973,I was teaching elementary school.Each day,27kids 41 “The Thinking Laboratory.”That was the 42 students voted for after deciding that “Room 104” was too 43 .Freddy was an average 44 ,but not an average person .He had the rare balance of fun and compassion（同情）.He would 45 the loudest over fun and be the saddest over anyones 46 .Before the school year 47 ,I gave the kids a special 48 , T-sherts with the words “Verbs Are Your 49 on them. I had advised the kids that while verbs（动词）may seem dull ,most of the 50 things they do throughout their lives will be verbs.Through the years, Id run into former students who would provide 51 on old classmates. Ilearned that Freddy did several jobs after his 52 from high school and remained the same 53 person I met forty years before .Once, while working overnight at a store, he let a homeless man 54 in his truck. Another time ,he 55 a friend money to buy a house .Just last year,I was 56 a workshop when someone knocked at the classroom door. A woman 57 the interruption and handed me an envelope. I stopped teaching and 58 it up. Inside were the “Verbs” shert and a 59 from Freddys monther. “Freddy passed away on Thanksgiving. He wanted you to have this.”I told the story to the class. As sad as it was, I couldnt help smiling . Although Freddy was taken from us,we all 60 something from Freddy.41. A. built B. entered C. decorated D. ran42. A. name B. rule C. brand D. plan43. A. small B. dark C. strange D. dull44. A. scholar B. student C. citizen D. worker45. A. speak B. sing