【全国百强校word版】河北省衡水中学2016-2017学年高三下学期期中考试理综物理试题

河北省衡水中学2016-2017学年高三下学期期中考试英语试题第二部分阅读理解（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，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。

AFrom: Elaine Jodrey Jodreyontrip@To: Charlie Hollingsworth dewholly@Subject:The Family VacationDear Mr Hollingsworth,We are in the process of finalizing the arrangements for your upcoming family vacation.Please take a moment to check the following details.1) One-way airline tickets for two adults and two youths from Chicago to New York City.2) Travel insurance for four through BeSafe Travels Insurance Co.3) One-way airline tickets from Orlando to Chicago.Exotic Travels would like to inform you of a unique service that we offer couples with small children.Although you’ll want to spend p lenty of quality time with your children.you may also want to enjoy an afternoon,an evening,or a whole day with your wife.If you would like to do some sightseeing on your own,we can ensure reliable,trustworthy babysitting services for a specified time and day.Our branch agencies in the cities you will be visiting have certified tour guides that will accompany your children to the destinations of their choice: an amusement park,a playground,a restaurant,or anywhere else you give your permission for.If you would like to take advantage of this service,please reply and make any other amendments to your travel schedule that you would like.Regards,Elaine JodreyExotic TravelsHere is the itinerary for your East Coast USA vacation cruise:June 22nd: Flight from Chicago to New York departs at 7:20 am and arrives at 12:45 pm.Local transportation will take you from the airport to the Museum of Natural History.The exhibition on display will be,“The History and Artifacts of Ancient Egypt”.*Note: Admission to the museum is $12.00 per adult and $8.00 per child.—Two rooms have been booked for The Broadway in downtown New York.June 23rd: Princess Angelica sets sail from New York harbor at 9 am,docking（停驻）over-night in Virginia Beach,Virginia.—Enjoy an evening on this famous beach,and a family barbecue for dinner.June 24th: Ship sails at 10 am.Docks overnight in Hilton Head,South Carolina.—Take a bus tour to historic Savannah before returning to Hilton Head Island,where you’ll have dinner waiting at the Pines Country Club.June 25th: Ship sails at 10am.Docks overnight at Cape Canaveral,Florida.—Enjoy a tour of The Kennedy Space Center.June 26th: A bus will transport you from Cape Canaveral to Orlando.—Overnight in Orlando at a Sleep Easy Hotel.June 27h: Flight departs Orlando at 4:30 pm.Arrives in Chicago at 11:05 pm.As an act of kindness to other Princess Angelica passengers,please do not smoke in the dining areas or lounges.You will find the smoking areas on the upper and lower decks.21.Why was this email sent?A.To bill the customer.B.To suggest a new agenda.C.To confirm a travel schedule.D.To inform about an added cost.22.What is the extra service offered by the agency?A.Buying travel insurance.B.Looking after children.C.Transporting luggage.D.Providing cigarettes.23.What must the family pay for upon arrival in New York?A.Entrance to a museum.B.Dinner at a country club.C.Admission to a science center.D.A barbecue on Virginia Beach.BBring any group of business owners or managers together,ask them the best way to pro-mote their organizations,and you’ll get different answers.That comes as no surprise.When it comes to promoting a business, trying to find the single choice is rarely wise.You’ll see business owners a nd managers try radio advertising.When that doesn’t produce the results they want,they’ll change to sending direct mail.When that doesn’t create a jump in sales,they’ll buy TV commercials.When that falls short of their expectations,they’ll try a new on-lin e strategy…and it goes on and on.For most companies,the best approach is a mix of different channels,organized in ways that allow each to build upon the others.The channel that will work best in a given situation depends on a lot of factors,including the company itself,its audience,the message being conveyed,the environment,and many more.Just that radio worked well for a company’s last effort doesn’t mean that TV advertising wouldn’t be a better choice this time.Or maybe the right channel is direct mail.There’s no simple answer,because there are so many variables.If your audience is broad,then maybe radio or newspaper advertising is the right choice.If you’re targeting a carefully defined group,such as former customers,direct mail or email will probably perform better.There are two important lessons here.The first is not to concentrate on trying to find a single channel that will serve all of the company's needs,because it just doesn't exist.The second lesson is that before you spend the first dollar to promote your business,you need to do more than a little learning.You'll really need to understand your customers,your market-place,your competitors,and the environments in which you do business. And you need a good understanding of what makes one marketing channel right for one situation,but not not her.24.According to Paragraph 1,there are no______.A.cheap ads.B.unsuccessful ads.C.perfect ads.D.all-purpose ads.25.What is the best way to promote a business?ing a channel that serves all of your budget.B.Putting ads on various channels at the same time.C.Creating an ad that appeals to all your customers.D.Advertising on a channel available to consumers.26.When it comes to choosing an ad for a business,we should________.A.stay away from TV advertising.B.choose it based on the specific situation.C.advertise on the radio or on the newspaper.D.choose it according to your customers’ budget.27.Before deciding on a marketing channel,you need to_____.A.ask for your customers’ advicepare different advertisingC.realize the problems with your businessD.make research about all related factorsCFacing increasing pressure to raise students’ scores on standardized tests,schools are urging kids to work harderby offering them obvious encouragements.Happy Meals are at the low end of the scale.With the help of businesses, schools are also giving away cars,iPods,seats to basketball games,and—in a growing number of cases—cold,hard cash.The appeal of such programs is obvious,but the consequences of tying grades to goods are still uncertain.It’s been a common tradition in middle-class families to reward top grades with cash as a way to teach that success in school leads to success in life.But for many disadvantaged minority children,the long-term benefits of getting an education are not so clear,according to experts.No one knows for sure how well cash and other big-ticket rewards work in education in the long run.But there are plenty of concerns that this kind of practice could have negative effects on kids.Virginia Shiller,a clinical psychologist,says that it’s worth experimenting with cash encouragements but that tying them to success on a test is not a worthwhile goal.“I’d rather see rewards based on effort and responsibility—things that will lead to success in life,” she says.Even if rewards don’t lead to individual achievement on a test,they could have a meaningful effect in the school.Charles McVean,a businessman and philanthropist（慈善家）,started a tutoring program which pays higher-achieving students $10 an hour to tutor struggling classmates and divides them into teams.During the course of the year,students bond and compete.The team posting the highest math scores wins the top cash prize of $100. McVean calls the combination of peer（同龄人）tutoring,competition,and c ash encouragements a recipe for “nothing less than magic”.For its part,the Seminole County Public Schools system in Florida plans to continue its report card encouragement program through the rest of the school year.The local McDonald’s resta urants help the poor district by paying the $1,600 cost of printing the report card.Regina Klaers,the district spokeswoman,says most parents don’t seem bothered by the Happy Meals rewards.“There are many ways we try to urge students t o do well,and sometimes it’s through the stomach,and sometimes it’s the probability of students winning a car,” she says,“One size doesn’t fit all.”28.According to the text,it is a common practice for schools to________.A.offer free meals to students with high scoresB.tie students’ grades to material rewardscate students to from a business senseD.cooperate with business to improve teaching29.According to the text,the long-term results of giving students cash as rewards in education are_____.A.negativeB.optimisticC.uncertainD.disappointing30.The tutoring program run by Charles McVean_______.A.hires some excellent teachers to teach the struggling studentsB.has a meaningful effect in inspiring students’ enthusiasm on studyC.is a program combining tutoring,competition and future job offersD.rewards the student with the highest scores with cash prize of $10031.We can learn that in Seminole County_____.A.there are various ways to inspire students to study hardB.many parents are not satisfied with the Happy Meals rewardsC.the local McDonald’s restaurants provide the rewards for poor studentsD.people are searching for a good-for-all method to urge students to do wellDIf you’re making determination for a healthier new year,consider a gut makeover（肠道清理）.Changing your microbe community（微生物群）,however,may not be easy,and nobody knows how long it might take.That’s because the ecosystem already established in your gut has been shaped by a daily diet of hamburgers and pizza,for example,it won’t respond as quickly to a healthy diet as a gut shaped by vegetables and fruits that has a more varied microbe community.“The nutrit ional value of food is influenced in part by the microbe community that en-counters that food,” said Dr Jeffrey Gordon,the senior author of the new paper and director of the Center for Genome Science and Systems Biology at the Washington University School of Medicine in St.Louis.Nutritional components of a healthy diet have to be viewed from “the inside out,” he said,“not just the outside in.”One of the questions the study set out to answer was how individuals with different diets respond when they try to improve their eating habits.The scientists harvested gut bacteria from humans,transplanted them into mice bred under germ-free conditions,and then fed the mice either American-style or plan-based diets.The scientists them analyzed changes in the mice’s microbe communities.Of interest,the scientists harvested the gut bacteria from people who followed sharply different diets.One group are a fairly typical American diet.consuming about 3.00 calories a day,high in animal proteins with few fruits and vegetables.Some of the their favorite foods were processed cheese and lunch meat.The other group consisted of people who were calorie-restricted.They are less than 1,800 calories a day and had carefully tracked what they are for at least the other group,a third fewer carbohydrates（碳水化合物）and only half the fat.This calorie-restricted group,the researchers found,had a far richer and more diverse microbe community in the gut than those eating a typical American diet.They also carried several kinds of “good” b acteria,known to promote health,that are unique to their plant-based diet.“Perhaps the best way to shape a healthier microbe community is to eat more fiber by consuming more fruit,vegetables,whole grains,and nuts or seeds,”said Meghan Jardine,a dietitian who was not involved in the current study but has published articles on promoting healthy microbe communities.She urges people to aim for 40 to 50 grams of fiber daily,well above levels recommended by most dietary guidelines.32.What can be inferred from the first two paragraphs?A.Changing microbiome is fairly difficult.B.Ecosystem in gut is shaped by carbohydrates.C.Nutritional components are determined by food intake.D.Microbe community shaped by vegetables and fruit respond less quickly than that shaped by junk food.33.What can we learn about Meghan Jardine?A.She suggests eating as less as possible.B.She attaches great importance to fiber.C.She is one of the researchers of the current study.D.She advocates consuming more meat in daily life.34.What’s the author’s attitude toward gut makeover?A.Concerned.B.Opposed.C.Indifferent.D.Nervous.35.Which is the best title for the text?A.Microbe community in our gut.B.A gut makeover for the new year.C.Dietary guidelines for daily diets.D.The best way towards a healthier microbe community.笫二节（共5小题；每小题2分，满分10分）Becoming Refreshed Without SleepingSometimes there is just not enough hours in the day to get everything done and get a good night’s rest.36 Once in a while you can get away with a sleepless night and still feel reasonably good by adjusting your meals and activities.●37 The last thing you want to do when you are tired is get warm and cosy; this will cause you to fall asleep.Keeping the air conditioner on will make you feel much more awake and refreshed.●Eat small amounts.Eating small amounts of healthy food will help refresh you.Fruit and nuts are a good choice because they are nutritious and will energize you.38Try to stick to low-carb meals to keep you going. Chewing gum after your small meal will also help keep you awake.●Kee p it bright.When it is dark your body thinks it is time to go to sleep.Turn on lots of lights,which will trick your body into waking up and feeling better.39 You get double the benefits if it is daytime.●Take a break.Taking a little break will help you in the long run.Turn up some energizing music to get yourselfpositive.Relax and talk to a friend in person or on the phone for a few minutes.40A.Keep it cool.B.Calm down and sleep.C.Avoid big,heavy meals as they will make you tired.D.Go outside whether it is day or night for some fresh air.E.Missing sleep regularly can make you sick and should be a voided.F.When you are tired,you may just want to sit around and do nothing.G.Having a good time for a few minutes will refresh you quicker than anything else.笫三部分英语知识运用（共两节，满分45分）第一节完形填空（共20小题；每题1.5分，满分30分）It impressed me a lot,I never thought that little help will 41 out to be the most satisfying thing I have ever done.He was tired,and 42 to climb further.With a broad 43 ,he asked if I could help him with some money.He was paralyzed（瘫痪）in both legs and was 44 funds for some operation.He said that if operated successfully,he could 45 a training guaranteeing him a job.I was full of 46 and even asked him to show his legs.I gave him the 47 money.After a few days,he again came at my doorstep asking for more money for accommodation.This time I was more or less 48 he is not cheating me.I gave him some and said this is all I have.A year went by and I had moved to a(n) 49 place.One fine day I got a call from an unknown number.Caller called out his name but I didn’t 50 him.Then he said he is the very paralyzed person I helped a year ago.I asked him how he is doing.He said,“What sir,you recognize me not by my name but by my 51 state.”“With your kind h elp I am now able to 52 on my legs without support.I was opera-ted 53.I am married to a beautiful lady and have a stable 54.”I don’t 55 remember if I gave him my phone number.56,what he said next was touching.He said he wanted to return my money so that I didn’t feel cheated and continue to help people 57 in the future.I don’t know whether he read my facial expression the day I helped him but tears were 58 down my face.That day I promised him I will continue to help people as I see a(n) 59 —small or big.60 a life changed event of my life.41.A.send B.break C.bring D.turn42.A.struggling B.substituting C.playing D.walking43.A.look B.smile C.view D.whisper44.A.finding B.raising C.seeking D.earning45.A.pretend B.intend C.attend D.tend46.A.interests B.minds C.worries D.doubts47.A.remaining B.left C.hiding D.forgottenrmed B.prepared C.convinced D.outspoken49.A.new B.old C.systematic D.bad50.A.remind B.recognize C.replace D.repeat51.A.excited B.messed C.disabled D.stressed52.A.live B.base C.focus D.stand53.A.successfully B.surprisingly C.hopefully D.naturally54.A.reason B.promise C.character D.job55.A.also B.even C.already D.only56.A.Therefore B.Otherwise C.However D.Meanwhile57.A.in need B.in place C.in favor D.in advance58.A.bringing B.putting C.running D.pulling59.A.behavior B.case C.accident D.opportunity60.A.Strangely B.Truly C.Generally D.Originally第二节（共10小题；每小题1.5分，满分15分）阅读下面材料，在空白处填入1个适当的单词或括号内单词的正确形式。

二、选择题：此题共8小题,每题6分。

在每题给出的四个选项中,第14～17题只有一项符合题目要求,第18～21题有多项符合题目要求。

全部选对的得6分,选对但不全的得3分,有选错或不答的得0分。

14．2017年1月9日,大亚湾反响堆中微子实验工程获得国家自然科学一等奖。

大多数粒子发生核反响的过程中都伴着中微子的产生,例如核裂变、核聚变、β衰变等。

以下关于核反响的说法正确的选项是A．23490Th衰变为22286Rn,经过3次α衰变,2次β衰变B．21H+31H→42He+1n是α衰变方程,23490Th→23491Pa+01e是β衰变方程C．23592U+1n→13654Xe+9054Sr+101n是重核裂变方程,也是氢弹的核反响方程D．高速α粒子轰击氮核可从氮核中打出中子,其核反响方程为42He+147N→168O+13n15．如下图的装置可以通过静电计指针偏转角度的变化检测电容器电容的变化,进而检测导电液体是增多还是减少。

图中芯柱、导电液体、绝缘管组成一个电容器,电源通过电极A、电极B给电容器充电,充电完毕后移去电源,由此可以判断A．假设静电计指针偏角变小,说明电容器两极板间的电压增大B．假设静电计指针偏角变小,说明导电液体增多C．假设静电计指针偏角变大,说明电容器电容增大D．假设静电计指针偏角变大,说明导电液面升高16．甲、乙两车从某时刻开场从相距67km的两地,相向做直线运动,假设以该时刻作为计时起点,得到两车的速度－时间图象如下图,那么以下说法正确的选项是A．乙车在第1h末改变运动方向B．甲、乙车两车在第2h末相距40kmC．乙车在前4h内运动的加速度大小总比甲车的大D．甲、乙两车在第4h末相遇17．如下图,在边长为L的正方形区域里有垂直纸面向里的匀强磁场,有a、b、c三个带电粒子〔不计重力〕依次从P点沿PQ方向射入磁场,其运动轨迹分别如下图。

带电粒子a从PM边中点O射出,b从M点射出,c 从N点射出,那么以下判断正确的选项是A．三个粒子都带正电B ．三个粒子在磁场中的运动时间之比一定为2：2：1C ．假设三个粒子的比荷相等,那么三个粒子的速率之比为1：4：16D ．假设三个粒子和射入时动量相等,那么三个粒子所带电荷量之比为4：2：118．如图甲所示,两根粗糙且足够长的平行金属导轨MN 、PQ 固定在同事绝缘程度面上,两导轨间距d=2m,导轨电阻忽略不计,M 、P 端连接一阻值R=0.75Ω的电阻；现有一质量m=0.8kg 、电阻r=0.25Ω的金属棒ab 垂直于导轨放在两导轨上,棒与电阻R 的间隔 L=2.5m,棒与导轨接触良好。

河北省衡水中学2016-2017学年高三下学期期中考试英语试题第一部分听力（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.Who watched the Oscars?A.The man.B.Angelina.C.The woman.2.Where will the man be at 5:00?A.At his office.B.At home.C.On the way home.3.What is the woman doing now?A.Doing some research.B.Writing a paper.C.Studying for a test.4.Why does the boy need the boxes?A.He is going on a trip.B.He is packing for school.C.He is using them for a project.5.What are the speakers mainly talking about?A.A snack place.B.Food from Taiwan.C.Bad economy.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或对白，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、7题。

6.What sport does the woman like best?A.V olleyball.B.Football.C.Baseball.7.What will the man buy for the woman as a gift?A.A typewriter.B.A computer.C.A camera.听第7段材料，回答第8、9题。

河北省衡水中学2016-2017学年高三下学期期中考试理科综合生物试卷1.某科学兴趣小组研究M、N、P三种细胞地结构和功能,发现M细胞没有核膜包围地细胞核,N细胞含有叶绿体,P细胞能合成糖原。

下列叙述正确地是A.M细胞无线粒体,只能进行无氧呼吸B.N细胞地遗传物质可能为DNA或RNAC.M、P细胞一定是取材于异养型生物D.N、P细胞均有发生染色体变异地可能2.ATP合成酶广泛分布于线粒体内膜、叶绿体类囊体薄膜上,它可以顺浓度梯度跨膜运输H+,此过程地H+跨膜运输会释放能量,用于合成ATP。

下列相关说法错误地是A.线粒体内地H+可能来自细胞质基质B.类囊体中H+地产生与水地光解有关C.上述H+跨膜运输地方式是主动运输D.ATP合成酶同时具有催化和运输功能3.根据细胞壁松散学说,一定浓度地生长素促进细胞伸长地原理如下图所示。

下列相关叙述错误地是A.酶X地跨膜运输离不开细胞膜地流动性B.结构A是糖蛋白,具有识别生长素地功能C.当生长素浓度适宜升高时,细胞壁内地环境pH会降低D.赤霉素和生长素在促进细胞伸长方面具有协同关系4.一般情况下,由于实验操作不当不能达到预期结果,但有地实验或调查若通过及时调整也可顺利完成。

下列有关叙述合理地是A.鉴定蛋白质时,在只有斐林试剂地甲、乙液时,可将乙液按比例稀释得双缩脲试剂B.探究pH对唾液淀粉酶活性地影响时,发现底物与酶地混合液地pH为0.9时,可调至中性C.调查遗传病发病率时,如发现样本太少,可扩大调查范围,已获得原始数据不能再用D.提取光合作用色素实验中,如发现滤液颜色太浅,可往滤液中再添加适量CaCO35.下图表示三种可构成一条食物链地生物（营养级不同）在某河流不同深度地分布情况。

下列有关分析错误地是A.三种生物构成地食物链可能是物种甲→物种乙→物种丙B.若物种甲表示绿藻,它在不同水深处地个体数量不同,主要是温度地原因C.物种乙地数量突然增加,短时间内物种丙地数量也会增加D.若物种丙表示肉食性鱼,该种群营养级高,所含能量较少6.将两个抗虫基因A（完全显性）导入大豆（2n=40）中,筛选出两个抗虫A基因成功整合到染色体上地抗虫植株M（每个A基因都能正常表达）。

河北省衡水中学2016-2017学年高三物理下学期期中试题（扫描版）
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河北省衡水中学2016-2017学年高三下学期期中考试英语试题第一部分听力（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.Who watched the Oscars?A.The man.B.Angelina.C.The woman.2.Where will the man be at 5:00?A.At his office.B.At home.C.On the way home.3.What is the woman doing now?A.Doing some research.B.Writing a paper.C.Studying for a test.4.Why does the boy need the boxes?A.He is going on a trip.B.He is packing for school.C.He is using them for a project.5.What are the speakers mainly talking about?A.A snack place.B.Food from Taiwan.C.Bad economy.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或对白，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、7题。

6.What sport does the woman like best?A.V olleyball.B.Football.C.Baseball.7.What will the man buy for the woman as a gift?A.A typewriter.B.A computer.C.A camera.听第7段材料，回答第8、9题。

衡水中学2016—2017 学年度下学期六调考试高三年级(理科)数学试卷第Ⅰ卷（选择题部分，共 60 分）一、选择题：共 12 小题，每小题 5 分，共 60 分.在每个小题给出的四个选项中，只有一项是符合题目要求的.1．若复数11mii+-为纯虚数，则m 的值为（ ）A ．1m =-B ．1m =C ．2m =D ．2m =-2．全集U R =，集合A= {}1()12x y y =+，集合B={},y y b b R =∈，若A B φ=,则b 的取值范围是（ ）A ．0b <B ．0b ≤C ．1b <D ．1b ≤3．甲、乙、丙三人投掷飞镖，他们的成绩（环数）如下面的频数条形统计图所示.则甲、乙、丙三人训练成绩方差2s 甲，2s 乙 ，2s 丙的大小关系是. ()A. 2s丙< 2s乙<2s甲B. 2s丙< 2s甲<2s乙C 2s乙<2s丙<2s甲D. 2s乙<2s甲<2s丙4．已知双曲线22221(0,0)x y a b a b-=>>，它的一条渐近线与圆22(2)4x y -+=相切，则双曲线的离心率为（）AB ．2 CD．5．已知2-，1a ，2a ，8-成等差数列，2-，1b ，2b ，3b ，8-成等比数列，则212a ab -等于（ ）A ．14B ．12C ．12-D ．12或12-6．.执行如图所示的框图，若输出的sum 的位为2047，则条 件框中应城写的是( ) A ．9i < B ．10i < C ．11i < D ． 12i < 7.已知6)z +展开式中，系数为有理数的项的个数为（ ） A ．4 B ．5 C ．6 D ． 78.如图，网格纸上小正方形的边长为1.粗线画出 的是某个多面体的三视图，若该多面休的所有顶点都在球O 表面上，则球O 的表面积是( )A ．36πB ．48πC ．56πD ．64π9.已知锐角α、β满足sin sin 2cos cos αββα+<.设tan tan ,()log ,x a a f x αβ==侧下列判断正确的是( )A ．(sin )(cos )f f αβ>B ．(cos )(sin )f f αβ>C ．(sin )(sin )f f αβ>D ．(cos )(cos )f f αβ>10.以抛物线2y x =的一点(1,1)M 为直角顶点作抛物线的两个内接Rt MAB ∆,Rt MCD ∆,则线段AB 与线段CD 的交点E 的坐标为( ) A ．(1,2)- B ．(2,1)- C ．(2,4)- D ．(1,4)- 11．将单位正方体放置在水平桌面上(一面与桌面完全接触). 沿其一条棱翻动一次后.使得正方体的另一面与桌面完全接触. 称一次翻转.如图，正方体的顶点A.经任意翻转三次后.点A 与其终结位置的直线距离不可能为( ) A ．0 B ．1 C ．2 D ．412.已知'()f x 为函数()f x 的导函致.且2''11()(0)(1),2x f x x f x f e -=-+若21()()2g x f x x x =-+，则方程2()0x g x x a --=有且仅有一个根时，a 的取值范围是（ ） A ．(,0)-∞B ．(,1)-∞C ．{}(,0)1-∞D ．(0,1)第II 卷(非选择题90分)二、填空题(每小题5分.共20分.把每小题的答案填在答题纸的相应位置)13.如图.BC 、DE 是半径为1的圆O 的两条直径，2BF FO =.则FD FE 的值是___。

2016-2017学年河北省衡水中学高三（下）期中数学试卷试卷（文科）一、选择题（本大题共12个小题，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．（5分）设全集U＝R，集合A＝{x|﹣1＜x＜2}，A∩（∁U B）＝{x|1＜x＜2}，则集合B可以是（）A．{x|﹣2＜x＜2}B．{x|﹣1＜x＜1}C．{x|x≤1}D．{x|x＞2} 2．（5分）若复数z＝+（1﹣i）2，则|z|等于（）A．B．C．2D．3．（5分）已知tanα＝2，α∈（0，π），则cos（+2α）等于（）A．B．C．﹣D．﹣4．（5分）为了加强某站的安全检查，从甲乙丙等5名候选民警中选2名作为安保人员，则甲乙丙中有2人被选中的概率为（）A．B．C．D．5．（5分）已知a＝log2，b＝0.33.2，c＝3.20.3，则实数a，b，c的大小关系是（）A．a＜c＜b B．a＜b＜c C．b＜a＜c D．b＜c＜a 6．（5分）某几何体的三视图如图所示，其中俯视图为扇形，则该几何体的体积为（）A．B．C．D．7．（5分）《孙子算经》是中国公元四世纪的数学著作，其中接受了求解依次同余式的方法，他是数论中一个重要的定理，又称《中国剩余定理》，如图所示的程序框图的算法就是源于《中国剩余定理》，执行该程序框图，若正整数N 除以正整数m后的余数为n，则记为N≡n（modm），例如11≡3（mod4），则输出的等于（）A．8B．16C．32D．648．（5分）已知点F是双曲线﹣＝1（a＞0，b＞0）的右焦点，过F点作双曲线的一条渐近线垂线，垂足为A，交另一条渐近线于B，若A点恰好为BF的中点，则双曲线的离心率为（）A．B．C．2D．39．（5分）已知函数f（x）＝A sin（wx+φ）（其中A＞0，|φ|＜）的部分图象如图所示，将函数的图象向左平移个单位长度得到函数g（x）的图象，则函数g（x）的解析式为（）A．g（x）＝2sin（2x﹣）B．g（x）＝2sin（2x+）C．g（x）＝﹣2sin（2x﹣）D．g（x）＝﹣2sin（2x+）10．（5分）已知函数f（x）＝，且f（e）＝f（1），f（e2）＝f（0）+，则函数f（x）的值域为（）A．（，]∪（，+∞）B．（，）C．（﹣∞，]∪[，+∞）D．（，]∪[，+∞）11．（5分）直线2x﹣y+a＝0与3x+y﹣3＝0交于第一象限，当点P（x，y）在不等式组表示的区域上运动时，m＝4x+3y的最大值为8，此时n＝的最大值是（）A．B．C．D．12．（5分）已知函数f（x）＝1g（x+），若对于任意的x∈（1，2]时，f（）+f[]＞0恒成立，则实数m的取值范围是（）A．[4，+∞）B．（12，+∞）C．（﹣∞，0）D．（﹣∞，0]二、填空题：本大题共4小题，每小题5分，共20分，把答案填在答题卷的横线上..13．（5分）已知向量＝（x，y）（x，y∈R），＝（1，2），若x2+y2＝1，则|﹣|的最小值为．14．（5分）已知矩形ABCD的顶点都在半径为5的球O的表面上，且AB＝6，BC＝2，则棱锥O﹣ABCD的侧面积为．15．（5分）如图，已知四边形ABCD中，AB＝CD＝1，AD＝BC＝2，∠A+∠C＝．则BD的长为．16．（5分）已知过点M（，0）的直线l与抛物线y2＝2px（p＞0）交于A，B两点，O为坐标原点，且满足•＝﹣3，则当|AM|+4|BM|最小时，|AB|＝．三、解答题：本大题共5小题，满分60分，解答应写出文字说明、证明过程或演算步骤17．（12分）已知数列{a n}，a1＝0，a n＝a n+1+．（1）证明数列{a n+1}是等比数列，并求出数列{a n}的通项公式；（2）令b n＝na n+n，数列{b n}的前n项和为S n，求证：S n≥1．18．（12分）十八届五中全会公报指出：努力促进人口均衡发展，坚持计划生育的基本政策，完善人口发展战略，全面实施一对夫妇可生育两个孩子的政策．一时间“放开生育二胎”的消息引起社会的广泛关注．为了解某地区社会人士对“放开生育二胎政策”的看法，某计生局在该地区选择了4000 人进行调查（若所选择的已婚的人数低于被调查总人数的78%，则认为本次调查“失效”），就“是否放开生育二胎政策”的问题，调查统计的结果如下表：已知在被调查人群中随机抽取1人，抽到持“不放开”态度的人的概率为0.08．（1）现用分层抽样的方法在所有参与调查的人中抽取400人进行深入访谈，问应在持“无所谓”态度的人中抽取多少人？（2）已知y≥710，z≥78，求本次调查“失效”的概率．19．（12分）如图所示，在棱长为2的正方体ABCD﹣A1B1C1D1中，E、F分别为DD1、DB的中点．（1）求证：EF∥平面ABC1D1；（2）求证：EF⊥B1C；（3）求三棱锥的体积．20．（12分）已知离心率为的椭圆C：+＝1（a＞b＞0）的左右焦点分别为F1，F2，A是椭圆C的左顶点，且满足|AF1|+|AF2|＝4．（1）求椭圆C的标准方程；（2）若M，N是椭圆C上异于A点的两个动点，且满足AM⊥AN，问直线MN 是否恒过定点？说明理由．21．（12分）已知函数f（x）＝ax2﹣1+lnx，其中a为实数．（1）求函数f（x）的单调区间；（2）当a＝﹣（e为自然对数的底数）时，若函数g（x）＝|f（x）|﹣﹣b存在零点，求实数b的取值范围．请考生在第（22）、（23）题中任选一题作答，如果多做，则按所做的第一题记分，作答时用2B铅笔在答题卡上把所选题目的题号涂黑，把答案填在答题卡上．[选修4-4坐标系与参数方程]22．（10分）在直角坐标系xOy，以O为极点，x轴的正半轴建立直角坐标系，直线l的极坐标方程＝2，而曲线C的参数方程为（其中φ为参数）；（1）若直线l与曲线C恰好有一个公共点，求实数m的值；（2）当m＝﹣，求直线l被曲线C截得的弦长．[选修4-5不等式选讲]23．设函数f（x）＝|x﹣a|+|x﹣2|．（1）若a＝1，解不等式f（x）≤2；（2）若存在x∈R，使得不等式f（x）≤对任意t＞0恒成立，求实数a的取值范围．2016-2017学年河北省衡水中学高三（下）期中数学试卷试卷（文科）参考答案与试题解析一、选择题（本大题共12个小题，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．（5分）设全集U＝R，集合A＝{x|﹣1＜x＜2}，A∩（∁U B）＝{x|1＜x＜2}，则集合B可以是（）A．{x|﹣2＜x＜2}B．{x|﹣1＜x＜1}C．{x|x≤1}D．{x|x＞2}【考点】1H：交、并、补集的混合运算．【解答】解：设全集U＝R，集合A＝{x|﹣1＜x＜2}，A∩（∁U B）＝{x|1＜x＜2}，可知集合B＝{x|x≤1}．故选：C．2．（5分）若复数z＝+（1﹣i）2，则|z|等于（）A．B．C．2D．【考点】A8：复数的模．【解答】解：因为z＝z＝+（1﹣i）2＝﹣2i＝1﹣i﹣2i＝1﹣3i，所以|z|＝＝，故选：A．3．（5分）已知tanα＝2，α∈（0，π），则cos（+2α）等于（）A．B．C．﹣D．﹣【考点】GF：三角函数的恒等变换及化简求值．【解答】解：∵tanα＝2，α∈（0，π），∴cos（+2α）＝﹣sin2α＝﹣2sinαcosα＝﹣＝﹣＝﹣＝﹣．故选：D．4．（5分）为了加强某站的安全检查，从甲乙丙等5名候选民警中选2名作为安保人员，则甲乙丙中有2人被选中的概率为（）A．B．C．D．【考点】CB：古典概型及其概率计算公式．【解答】解：从甲、乙、丙等5名候选民警中选2名作为阅兵安保人员，共有10种情况，甲、乙、丙中有2个被选中，有3种，故所求事件的概率P＝．故选：A．5．（5分）已知a＝log2，b＝0.33.2，c＝3.20.3，则实数a，b，c的大小关系是（）A．a＜c＜b B．a＜b＜c C．b＜a＜c D．b＜c＜a【考点】4M：对数值大小的比较．【解答】解：∵a＝log2＝﹣3＜1，0＜b＝0.33.2＜0.30＝1，c＝3.20.3＞3.20＝1，∴实数a，b，c的大小关系为a＜b＜c．故选：B．6．（5分）某几何体的三视图如图所示，其中俯视图为扇形，则该几何体的体积为（）A．B．C．D．【考点】L!：由三视图求面积、体积．【解答】解：由三视图知几何体是圆锥的一部分，由俯视图与左视图可得：底面扇形的圆心角为120°，又由侧视图知几何体的高为4，底面圆的半径为2，∴几何体的体积V＝××π×22×4＝．故选：D．7．（5分）《孙子算经》是中国公元四世纪的数学著作，其中接受了求解依次同余式的方法，他是数论中一个重要的定理，又称《中国剩余定理》，如图所示的程序框图的算法就是源于《中国剩余定理》，执行该程序框图，若正整数N 除以正整数m后的余数为n，则记为N≡n（modm），例如11≡3（mod4），则输出的等于（）A．8B．16C．32D．64【考点】EF：程序框图．【解答】解：模拟程序的运行，可得n＝11，i＝1i＝2，n＝13不满足条件“n＝2（mod 3）“，i＝4，n＝17，满足条件“n＝2（mod 3）“，不满足条件“n＝1（mod 5）“，i＝8，n＝25，不满足条件“n＝2（mod 3）“，i＝16，n＝41，满足条件“n＝2（mod3）“，满足条件“n＝1（mod5）”，退出循环，输出i的值为16．故选：B．8．（5分）已知点F是双曲线﹣＝1（a＞0，b＞0）的右焦点，过F点作双曲线的一条渐近线垂线，垂足为A，交另一条渐近线于B，若A点恰好为BF的中点，则双曲线的离心率为（）A．B．C．2D．3【考点】KC：双曲线的性质．【解答】解：不妨设双曲线的一条渐近线方程为：y＝，则另一条渐近线方程为：y＝﹣，设A（m，），B（n，﹣），因为F（c，0），A为BF的中点，所以m＝，，解得m＝c，A（，），由F A⊥OA，可得：k F A•k OA＝﹣1，即：•＝﹣1，即b2＝3a2，解得e＝＝＝2．故选：C．9．（5分）已知函数f（x）＝A sin（wx+φ）（其中A＞0，|φ|＜）的部分图象如图所示，将函数的图象向左平移个单位长度得到函数g（x）的图象，则函数g（x）的解析式为（）A．g（x）＝2sin（2x﹣）B．g（x）＝2sin（2x+）C．g（x）＝﹣2sin（2x﹣）D．g（x）＝﹣2sin（2x+）【考点】HK：由y＝Asin（ωx+φ）的部分图象确定其解析式．【解答】解：由函数f（x）＝A sin（ωx+φ）（其中A＞0，|φ|＜）的图象，可得A＝1，＝﹣＝，即＝π求得ω＝2，∵f（）＝2sin（2×+φ）＝﹣2，即sin（+φ）＝1，∴+φ＝+2kπ，k∈Z，即φ＝+2kπ，k∈Z，∵|φ|＜，∴φ＝，∴f（x）＝2sin（2x+）．将函数f（x）的图象向左平移个单位长度得到函数g（x）＝2sin[2（x+）+]＝2sin（2x+π﹣）＝﹣2sin（2x﹣）的图象，故选：C．10．（5分）已知函数f（x）＝，且f（e）＝f（1），f（e2）＝f（0）+，则函数f（x）的值域为（）A．（，]∪（，+∞）B．（，）C．（﹣∞，]∪[，+∞）D．（，]∪[，+∞）【考点】5B：分段函数的应用．【解答】解：函数f（x）＝，且f（e）＝f（1），f（e2）＝f（0）+，可得：，解得a＝﹣1，b＝2，所以当x＞0时，f（x）＝（lnx）2﹣lnx+2＝（lnx﹣）2+，当x≤0时，可得＝，则函数f（x）的值域为（，]∪[，+∞）．故选：D．11．（5分）直线2x﹣y+a＝0与3x+y﹣3＝0交于第一象限，当点P（x，y）在不等式组表示的区域上运动时，m＝4x+3y的最大值为8，此时n＝的最大值是（）A．B．C．D．【考点】7C：简单线性规划．【解答】解：由直线2x﹣y+a＝0与3x+y﹣3＝0交于点A，解方程组，得A（），将直线4x+3y＝0平移经过A点时，m取最大值，∴，得a＝2．于是，点A的坐标为（），∵n＝表示点B（﹣3，0）与P（x，y）连线的斜率，由图可知，当P与点A重合时，n取最大值，∴n的最大值为．故选：D．12．（5分）已知函数f（x）＝1g（x+），若对于任意的x∈（1，2]时，f（）+f[]＞0恒成立，则实数m的取值范围是（）A．[4，+∞）B．（12，+∞）C．（﹣∞，0）D．（﹣∞，0]【考点】3R：函数恒成立问题．【解答】解：∵f（x）＝1g（x+），∴f（﹣x）＝1g（﹣x+）＝﹣f（x），∴函数为奇函数，由表达式显然知函数为增函数，∵f（）+f[]＞0恒成立，∴＞﹣，∴（x+1）（x﹣1）（x﹣6）＜﹣m恒成立，令h（x）＝（x+1）（x﹣1）（x﹣6），可知函数h（x）在x∈（1，2]时，单调递减，∴h（x）的最大值大于h（1）＝0，∴0≤﹣m，∴m≤0，故选：D．二、填空题：本大题共4小题，每小题5分，共20分，把答案填在答题卷的横线上..13．（5分）已知向量＝（x，y）（x，y∈R），＝（1，2），若x2+y2＝1，则|﹣|的最小值为﹣1．【考点】91：向量的概念与向量的模．【解答】解：设O（0，0），P（1，2），∴|﹣|＝≥||﹣1＝﹣1＝﹣1，∴|﹣|的最小值为﹣114．（5分）已知矩形ABCD的顶点都在半径为5的球O的表面上，且AB＝6，BC＝2，则棱锥O﹣ABCD的侧面积为44．【考点】LE：棱柱、棱锥、棱台的侧面积和表面积．【解答】解：设点O到矩形ABCD所在平面的距离为h，则h＝＝．∴棱锥O﹣ABCD的侧面积＝2×＝44．故答案为：44．15．（5分）如图，已知四边形ABCD中，AB＝CD＝1，AD＝BC＝2，∠A+∠C＝．则BD的长为．【考点】HT：三角形中的几何计算．【解答】解：在△ABD中由余弦定理可知：BD2＝AB2+AD2﹣2AB•AD•cos A，在△CDB中与余弦定理可知：BD2＝DC2+BC2﹣2AB•AD•cos C，将AB＝CD＝1，AD＝BC＝2代入，整理得：2cos A﹣cos C＝1，∠A+∠C ＝，2cos A﹣cos（﹣A）＝1，整理得：3cos A+sin A＝1，两边平方（3cos A+sin A）2＝9cos2A+6cos A sin A+sin2A＝cos2A+sin2A，整理得：sin A＝﹣，cos A＝，BD＝，BD＝，故答案为：．16．（5分）已知过点M（，0）的直线l与抛物线y2＝2px（p＞0）交于A，B两点，O为坐标原点，且满足•＝﹣3，则当|AM|+4|BM|最小时，|AB|＝．【考点】KN：直线与抛物线的综合．【解答】解：设A（x1，y1），B（x2，y2），设直线l的方程为：x＝my+，将直线l的方程代入抛物线方程y2＝2px，消去x，得，y2﹣2pmy﹣p2＝0，∴y1+y2＝2pm，y1y2＝﹣p2，∵•＝﹣3，即x1x2+y1y2＝﹣3，x1x2＝•＝，∴有﹣p2＝﹣3，解得，p＝2；（舍去负值），∴x1x2＝＝1，由抛物线的定义，可得，|AM|＝x1+1，|BM|＝x2+1，则|AM|+4|BM|＝x 1+4x2+5≥2+5＝9，当且仅当x1＝4x2时取得等号．由于x1x2＝1，可以解得，x2＝2（舍去负值），∴x1＝，代入抛物线方程y2＝4x，解得，y1＝，y2＝±2，即有A（，±）B （2，±2），∴|AB|＝＝＝．三、解答题：本大题共5小题，满分60分，解答应写出文字说明、证明过程或演算步骤17．（12分）已知数列{a n}，a1＝0，a n＝a n+1+．（1）证明数列{a n+1}是等比数列，并求出数列{a n}的通项公式；（2）令b n＝na n+n，数列{b n}的前n项和为S n，求证：S n≥1．【考点】8E：数列的求和．【解答】证明：（1）由a n＝a n+1+，则a n+1＝a n﹣，即（a n+1+1）＝（a n+1），∴{a n+1}是以a1+1＝1为首项，以为公比的等比数列，∴a n+1＝（）n﹣1，即a n＝（）n﹣1﹣1，∴数列{a n}的通项公式a n＝（）n﹣1﹣1；（2）由（1）b n＝na n+n＝n（）n﹣1，则S n＝1×（）0+2×（）1+3×（）3+…+（n﹣1）×（）n﹣2+n（）n﹣1，①∴S n＝1×（）1+2×（）2+3×（）4+…+（n﹣1）×（）n﹣1+n（）n，②①﹣②得：S n＝（）0+（）1+（）2+…+（）n﹣1﹣n（）n，＝2﹣，S n＝4﹣，∴＝＝，由n+3＜2n+4，则2n+2﹣（n+3）＞2n+2﹣（2n+4），由2n+2﹣（n+3）＞0，2n+2﹣（2n+4）＞0，则＞1，数列{S n}单调递增，故当n＝1时，数列{S n}取得最小值，即S n≥S1＝1．S n≥1．18．（12分）十八届五中全会公报指出：努力促进人口均衡发展，坚持计划生育的基本政策，完善人口发展战略，全面实施一对夫妇可生育两个孩子的政策．一时间“放开生育二胎”的消息引起社会的广泛关注．为了解某地区社会人士对“放开生育二胎政策”的看法，某计生局在该地区选择了4000 人进行调查（若所选择的已婚的人数低于被调查总人数的78%，则认为本次调查“失效”），就“是否放开生育二胎政策”的问题，调查统计的结果如下表：已知在被调查人群中随机抽取1人，抽到持“不放开”态度的人的概率为0.08．（1）现用分层抽样的方法在所有参与调查的人中抽取400人进行深入访谈，问应在持“无所谓”态度的人中抽取多少人？（2）已知y≥710，z≥78，求本次调查“失效”的概率．【考点】B3：分层抽样方法；CC：列举法计算基本事件数及事件发生的概率．【解答】解：（1）∵抽到持“不放开”态度的人的概率为0.08，∴＝0.08，解得x＝120．∴持“无所谓”态度的人数共有4000﹣2200﹣680﹣200﹣120＝800．∴应在“无所谓”态度抽取800×＝80人．（2）∵y+z＝800，y≥710，z≥78，故满足条件的（y，z）有：（710，90），（711，89），（712，88），（713，87），（714，86），（715，85），（716，84），（717，83），（718，82），（719，81），（720，80），（721，79），（722，78），共13种．记本次调查“失效”为事件A，若调查失效，则2200+200+y＜4000×0.78，解得y＜720．∴事件A包含（710，90），（711，89），（712，88），（713，87），（714，86），（715，85），（716，84），（717，83），（718，82），（719，81）共10种．∴P（A）＝19．（12分）如图所示，在棱长为2的正方体ABCD﹣A1B1C1D1中，E、F分别为DD1、DB的中点．（1）求证：EF∥平面ABC1D1；（2）求证：EF⊥B1C；（3）求三棱锥的体积．【考点】LF：棱柱、棱锥、棱台的体积；LS：直线与平面平行；LW：直线与平面垂直．【解答】解：（1）证明：连接BD1，如图，在△DD1B中，E、F分别为D1D，DB的中点，则⇒EF∥平面ABC1D1．（2）⇒⇒⇒EF⊥B1C（3）∵CF⊥平面BDD1B1，∴CF⊥平面EFB1且，∵，，∴EF2+B1F2＝B1E2即∠EFB1＝90°，∴＝＝20．（12分）已知离心率为的椭圆C：+＝1（a＞b＞0）的左右焦点分别为F1，F2，A是椭圆C的左顶点，且满足|AF1|+|AF2|＝4．（1）求椭圆C的标准方程；（2）若M，N是椭圆C上异于A点的两个动点，且满足AM⊥AN，问直线MN 是否恒过定点？说明理由．【考点】K3：椭圆的标准方程；KL：直线与椭圆的综合．【解答】解：（1）由椭圆的定义可得，|AF1|+|AF2|＝2a＝4，解得a＝2，∵离心率为e＝＝，∴c＝1，∴b2＝a2﹣c2＝3，∴椭圆C的标准方程为；（2）由题意知A（﹣2，0）．设M（x1，y1），N（x2，y2）．若直线MN斜率不存在，则N（x1，﹣y1），由AM⊥AN，•＝0，得•＝﹣1，又M和N在椭圆上，代入解得x＝﹣，则直线MN方程为x＝﹣．若直线MN斜率存在，设方程为y＝kx+m，椭圆方程联立，消去y可得（4k2+3）x2+8kmx+4m2﹣12＝0．∴x1+x2＝﹣，x1x2＝．由AM⊥AN，得×＝﹣1，整理得（k2+1）x1x2+（km+2）（x1+x2）+m2+4＝0∴（k2+1）×+（km+2）×（）+m2+4＝0．解得m＝2k或m＝k．若m＝2k，此时直线过定点（﹣2，0）不合题意舍去．故m＝k，即直线MN过定点（﹣，0）．综上可知：直线l过定点（﹣，0）．21．（12分）已知函数f（x）＝ax2﹣1+lnx，其中a为实数．（1）求函数f（x）的单调区间；（2）当a＝﹣（e为自然对数的底数）时，若函数g（x）＝|f（x）|﹣﹣b存在零点，求实数b的取值范围．【考点】53：函数的零点与方程根的关系；6B：利用导数研究函数的单调性．【解答】解：（1）f（x）＝2ax+＝，当a≥0时，f'（x）＞0，f（x）在（0，+∞）上单调递增；当a＜0时，令f'（x）＝0得x＝，∴f（x）在（，+∞）上递减，在（0，）上递增；（2）g（x）＝|f（x）|﹣﹣b存在零点，∴|f（x）|＝+b有实数根，当a＝﹣时，f（x）＝﹣x2﹣1+lnx，f'（x）＝﹣m当0＜x＜时，f'（x）＞0，当x＞时，f'（x）＜0，∴f（x）在区间（0，）上递增，在（，+∞）上递减，函数的最大值为f（）＝﹣1，∴|f（x）|≥1，令h（x）＝+b，h'（x）＝，当0＜x＜时，h'（x）＞0，当x＞时，h'（x）＜0，∴h（x）的最大值为h（）＝+b，要使|f（x）|＝+b有实数根，∴h（）＝+b，≥1，∴b≥1﹣＝1﹣．请考生在第（22）、（23）题中任选一题作答，如果多做，则按所做的第一题记分，作答时用2B铅笔在答题卡上把所选题目的题号涂黑，把答案填在答题卡上．[选修4-4坐标系与参数方程]22．（10分）在直角坐标系xOy，以O为极点，x轴的正半轴建立直角坐标系，直线l的极坐标方程＝2，而曲线C的参数方程为（其中φ为参数）；（1）若直线l与曲线C恰好有一个公共点，求实数m的值；（2）当m＝﹣，求直线l被曲线C截得的弦长．【考点】Q4：简单曲线的极坐标方程；QH：参数方程化成普通方程．【解答】解：（1）直线l的极坐标方程＝2，展开化为（ρsinθ+ρcosθ）＝2（m+1），即x+y﹣4（m+1）＝0．而曲线C的参数方程为（其中φ为参数），消去参数可得：x2+y2＝2．∵直线l与曲线C恰好有一个公共点，∴＝．∴m+1＝，解得m＝，或．（2）m＝﹣时，圆心到直线l的距离d＝＝．∴直线l被曲线C截得的弦长＝2＝2＝．[选修4-5不等式选讲]23．设函数f（x）＝|x﹣a|+|x﹣2|．（1）若a＝1，解不等式f（x）≤2；（2）若存在x∈R，使得不等式f（x）≤对任意t＞0恒成立，求实数a的取值范围．【考点】36：函数解析式的求解及常用方法；R5：绝对值不等式的解法．【解答】解：（1）当a＝1，f（x）＝|x﹣1|+|x﹣2|．不等式f（x）＞2化为|x﹣1|+|x﹣2|≤2．x＜1时，不等式可化为3﹣2x≤2，∴x≥，∴≤x＜1；1≤x≤2时，不等式可化为1≤2，成立；x＞2时，不等式可化为2x﹣3≤2，∴x≤，∴2＜x≤；综上所述，不等式的解集为[，]；（2）f（x）＝|x﹣a|+|x﹣2|≥|x﹣a﹣x+2|＝|a﹣2|，即f（x）的最小值为|a﹣2|．∵t＞0，＝t+≥4，当且仅当t＝2时，取得最小值4，由题意，|a﹣2|≤4，∴﹣2≤a≤6．。

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，从每题所给的四个选项（A、B、C和D）中，选出最佳选项。

A21.Why was this email sent?A.To bill the customer.B.To suggest a new agenda.C.To confirm a travel schedule.D.To inform about an added cost.22.What is the extra service offered by the agency?A.Buying travel insurance.B.Looking after children.C.Transporting luggage.D.Providing cigarettes.23.What must the family pay for upon arrival in New York?A.Entrance to a museum.B.Dinner at a country club.C.Admission to a science center.D.A barbecue on Virginia Beach.BBring any group of business owners or managers together,ask them the best way to pro-mote their organizations, and you’ll get different answers.That comes as no surprise.When it comes to promoting a business, trying to find the single choice is rarely wise.You’ll see business owners and managers try radio advertising.When that doesn’t produce the results they want,they’ll change to sending direct mail.When that doesn’t create a jump in sales,they’ll buy TV commercials.When t hat falls short of their expectations,they’ll try a new on-line strategy…and it goes on and on.For most companies,the best approach is a mix of different channels,organized in ways that allow each to build upon the others.The channel that will work best in a given situation depends on a lot of factors,including the company itself,its audience,the message being conveyed,the environment,and many more.Just that radio worked well for a company’s last effort doesn’t mean that TV advertising wouldn’t be a better choice this time.Or maybe the right channel is direct mail.There’s no simple answer,because there are so many variables.If your audience is broad,then maybe radio or newspaper advertising is the right choice.If you’re targeting a carefully defined grou p,such as former customers,direct mail or email will probably perform better.There are two important lessons here.The first is not to concentrate on trying to find a single channel that will serve all of the company's needs,because it just doesn't exist.The second lesson is that before you spend the first dollar to promote your business,you need to do more than a little learning.You'll really need to understand your customers,your market-place,your competitors,and the environments in which you do business. And you need a good understanding of what makes one marketing channel right for one situation,but not not her.24.According to Paragraph 1,there are no______.A.cheap ads.B.unsuccessful ads.C.perfect ads.D.all-purpose ads.25.What is the best way to promote a business?ing a channel that serves all of your budget.B.Putting ads on various channels at the same time.C.Creating an ad that appeals to all your customers.D.Advertising on a channel available to consumers.26.When it comes to choosing an ad for a business,we should________.A.stay away from TV advertising.B.choose it based on the specific situation.C.advertise on the radio or on the newspaper.D.choose it according to your customers’ budget.27.Before deciding on a marketing channel,you need to_____.A.ask for your customers’ advicepare different advertisingC.realize the problems with your businessD.make research about all related factorsCFacing increasing pressure to raise students’ scores on standardized t ests,schools are urging kids to work harder by offering them obvious encouragements.Happy Meals are at the low end of the scale.With the help of businesses, schools are also giving away cars,iPods,seats to basketball games,and—in a growing number of cases—cold,hard cash.The appeal of such programs is obvious,but the consequences of tying grades to goods are still uncertain.It’s been a common tradition in middle-class families to reward top grades with cash as a way to teach that success in school leads to success in life.But for many disadvantaged minority children,the long-term benefits of getting an education are not so clear,according to experts.No one knows for sure how well cash and other big-ticket rewards work in education in the long run.But there are plenty of concerns that this kind of practice could have negative effects on kids.Virginia Shiller,a clinical psychologist,says that it’s worth experimenting with cash encouragements but that tying them to success on a test is not a worthwhile goal.“I’d rather see rewards based on effort and responsibility—things that will lead to success in life,” she says.Even if rewards don’t lead to individual achievement on a test,they could have a meaningful effect in the school.Charles McVean,a businessman and philanthropist（慈善家）,started a tutoring program which pays higher-achieving students $10 an hour to tutor struggling classmates and divides them into teams.During the course of the year,students bond and compete.The team posting the highest math scores wins the top cash prize of $100. McVean calls the combination of peer（同龄人）tutoring,competition,and cash encouragements a recipe for “nothing less than magic”.For its part,the Seminole County Public Schools system in Florida plans to continue its report card encouragement program through the rest of the school year.The local McDonald’s restaurantshelp the poor district by paying the $1,600 cost of printing the report card.Regina Klaers,the district spokeswoman,says most parents don’t seem bothered by the Happy Meals rewards.“There are many ways we try to urge students to do well,and sometimes it’s through the stomach,and sometimes it’s the probability of students winning a car,” she says,“One size doesn’t fit all.”28.According to the text,it is a common practice for schools to________.A.offer free meals to students with high scoresB.tie students’ grades to material rewardscate students to from a business senseD.cooperate with business to improve teaching29.According to the text,the long-term results of giving students cash as rewards in education are_____.A.negativeB.optimisticC.uncertainD.disappointing30.The tutoring program run by Charles McVean_______.A.hires some excellent teachers to teach the struggling studentsB.has a meaningful effect in in spiring students’ enthusiasm on studyC.is a program combining tutoring,competition and future job offersD.rewards the student with the highest scores with cash prize of $10031.We can learn that in Seminole County_____.A.there are various ways to inspire students to study hardB.many parents are not satisfied with the Happy Meals rewardsC.the local McDonald’s restaurants provide the rewards for poor studentsD.people are searching for a good-for-all method to urge students to do wellDIf you’re making determination for a healthier new year,consider a gut makeover（肠道清理）.Changing your microbe community（微生物群）,however,may not be easy,and nobody knows how long it might take.That’s because the ecosystem already established in your gut has been shaped by a da ily diet of hamburgers and pizza,for example,it won’t respond as quickly to a healthy diet as a gut shaped by vegetables and fruits that has a more varied microbe community.“The nutritional value of food is influenced in part by the microbe community tha t en-counters that food,” said Dr Jeffrey Gordon,the senior author of the new paper and director of the Center for Genome Science and Systems Biology at the Washington University School ofMedicine in St.Louis.Nutritional components of a healthy diet have to be viewed from “the inside out,” he said,“not just the outside in.”One of the questions the study set out to answer was how individuals with different diets respond when they try to improve their eating habits.The scientists harvested gut bacteria from humans,transplanted them into mice bred under germ-free conditions,and then fed the mice either American-style or plan-based diets.The scientists them analyzed changes in the mice’s microbe communities.Of interest,the scientists harvested the gut bacteria from people who followed sharply different diets.One group are a fairly typical American diet.consuming about 3.00 calories a day,high in animal proteins with few fruits and vegetables.Some of the their favorite foods were processed cheese and lunch meat.The other group consisted of people who were calorie-restricted.They are less than 1,800 calories a day and had carefully tracked what they are for at least the other group,a third fewer carbohydrates（碳水化合物）and only half the fat.This calorie-restricted group,the researchers found,had a far richer and more diverse microbe community in the gut than those eating a typical American diet.They also carried several kinds of “good” bacteria,known to promote he alth,that are unique to their plant-based diet.“Perhaps the best way to shape a healthier microbe community is to eat more fiber by consuming more fruit,vegetables,whole grains,and nuts or seeds,”said Meghan Jardine,a dietitian who was not involved in the current study but has published articles on promoting healthy microbe communities.She urges people to aim for 40 to 50 grams of fiber daily,well above levels recommended by most dietary guidelines.32.What can be inferred from the first two paragraphs?A.Changing microbiome is fairly difficult.B.Ecosystem in gut is shaped by carbohydrates.C.Nutritional components are determined by food intake.D.Microbe community shaped by vegetables and fruit respond less quickly than that shaped by junk food.33.What can we learn about Meghan Jardine?A.She suggests eating as less as possible.B.She attaches great importance to fiber.C.She is one of the researchers of the current study.D.She advocates consuming more meat in daily life.34.What’s the author’s at titude toward gut makeover?A.Concerned.B.Opposed.C.Indifferent.D.Nervous.35.Which is the best title for the text?A.Microbe community in our gut.B.A gut makeover for the new year.C.Dietary guidelines for daily diets.D.The best way towards a healthier microbe community.笫二节（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。

河北省衡水中学2017届高三下学期期中考试英语试题第一部分听力（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.Who watched the Oscars?A.The man.B.Angelina.C.The woman.2.Where will the man be at 5:00?A.At his office.B.At home.C.On the way home.3.What is the woman doing now?A.Doing some research.B.Writing a paper.C.Studying for a test.4.Why does the boy need the boxes?A.He is going on a trip.B.He is packing for school.C.He is using them for a project.5.What are the speakers mainly talking about?A.A snack place.B.Food from Taiwan.C.Bad economy.第二节（共15小题；每小题1.5分，满分22.5分）听下面5段对话或对白，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、7题。

6.What sport does the woman like best?A.V olleyball.B.Football.C.Baseball.7.What will the man buy for the woman as a gift?A.A typewriter.B.A computer.C.A camera.听第7段材料，回答第8、9题。

衡水中学2016—2017 学年度下学期六调考试高三年级(理科)数学试卷第Ⅰ卷（选择题部分，共 60 分）一、选择题：共 12 小题，每小题 5 分，共 60 分.在每个小题给出的四个选项中，只有一项是符合题目要求的.1．若复数11mii+-为纯虚数，则m 的值为（ ）A ．1m =-B ．1m =C ．2m =D ．2m =-2．全集U R =，集合A= {}1()12x y y =+，集合B={},y y b b R =∈，若A B φ=,则b 的取值范围是（ ）A ．0b <B ．0b ≤C ．1b <D ．1b ≤3．甲、乙、丙三人投掷飞镖，他们的成绩（环数）如下面的频数条形统计图所示.则甲、乙、丙三人训练成绩方差2s 甲，2s 乙 ，2s 丙的大小关系是. ()A. 2s丙< 2s乙<2s甲B. 2s丙< 2s甲<2s乙C 2s乙<2s丙<2s甲D. 2s乙<2s甲<2s丙4．已知双曲线22221(0,0)x y a b a b-=>>，它的一条渐近线与圆22(2)4x y -+=相切，则双曲线的离心率为（）A． B ．2 CD． 5．已知2-，1a ，2a ，8-成等差数列，2-，1b ，2b ，3b ，8-成等比数列，则212a ab -等于（ ）A ．14B ．12C ．12-D ．12或12-6．.执行如图所示的框图，若输出的sum 的位为2047，则条 件框中应城写的是( ) A ．9i < B ．10i < C ．11i < D ． 12i <7.已知6)z ++展开式中，系数为有理数的项的个数为（ ） A ．4 B ．5 C ．6 D ． 78.如图，网格纸上小正方形的边长为1.粗线画出 的是某个多面体的三视图，若该多面休的所有顶 点都在球O 表面上，则球O 的表面积是( )A ．36πB ．48πC ．56πD ．64π9.已知锐角α、β满足sin sin 2cos cos αββα+<.设tan tan ,()log ,x a a f x αβ==侧下列判断正确的是( )A ．(sin )(cos )f f αβ>B ．(cos )(sin )f f αβ>C ．(sin )(sin )f f αβ>D ．(cos )(cos )f f αβ> 10.以抛物线2y x =的一点(1,1)M 为直角顶点作抛物线的两个内接Rt MAB ∆,Rt MCD ∆,则线段AB 与线段CD 的交点E 的坐标为( ) A ．(1,2)- B ．(2,1)- C ．(2,4)- D ．(1,4)- 11．将单位正方体放置在水平桌面上(一面与桌面完全接触). 沿其一条棱翻动一次后.使得正方体的另一面与桌面完全接触. 称一次翻转.如图，正方体的顶点A.经任意翻转三次后.点A 与其终结位置的直线距离不可能为( ) A ．0 B ．1 C ．2 D ．412.已知'()f x 为函数()f x 的导函致.且2''11()(0)(1),2x f x x f x f e -=-+若21()()2g x f x x x =-+，则方程2()0x g x x a --=有且仅有一个根时，a 的取值范围是（ ） A ．(,0)-∞ B ．(,1)-∞ C ．{}(,0)1-∞ D ．(0,1) 第II 卷(非选择题90分)二、填空题(每小题5分.共20分.把每小题的答案填在答题纸的相应位置)13.如图.BC 、DE 是半径为1的圆O 的两条直径，2BF FO =.则FD FE 的值是___。

河北衡水中学2016~2017学年度 高三下学期数学第三次调研（理科）第Ⅰ卷（共60分）一、选择题：本大题共12个小题,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. 已知复数z 满足iiiz 2134++=，则复数z 在复平面内对应的点在（ ） A ．第一象限 B ．第二象限 C ．第三象限 D ．第四象限2. 已知集合}0)12(log |{3≤-=x x A ，}23|{2x x y x B -==，全集R U =，则)(B C A U 等于（ ）A ．]1,21( B ．)32,0( C ．]1,32( D ．)32,21( 3.若),2(ππα∈,且)4sin(2cos 3απα-=，则α2sin 的值为（ ）A ．181-B ．181C ．1817-D ．18174. 已知2)(,12)(xx g x x f x =-=，则下列结论正确的是（ ）A ．)()()(x g x f x h +=是偶函数B ．)()()(x g x f x h +=是奇函数 C. )()()(x g x f x h =是奇函数 D ．)()()(x g x f x h =是偶函数5.已知双曲线E ：)0,0(12222>>=-b a by a x ，若矩形ABCD 的四个顶点在E 上，CD AB ,的中点为双曲线E 的两个焦点，且双曲线E 的离心率是2，直线AC 的斜率为k ，则||k 等于（ ）A ．2B ．23 C. 25D ．3 6.在ABC ∆中，NC AN 41=，P 是直线BN 上的一点，若AC AB m AP 52+=，则实数m 的值为（ ）A ．4-B ．1- C. 1 D ．47.已知函数)0,0)(sin()(>>+=ωϕωA x A x f 的图象与直线)0(A a a y <<=的三个相邻交点的横坐标分别是2,4,8，则)(x f 的单调递减区间是（ ）A ．)](36,6[Z k k k ∈+ππB ．)](6,36[Z k k k ∈-ππC. )](36,6[Z k k k ∈+ D ．)](6,36[Z k k k ∈-8. 某旅游景点统计了今年5月1号至10号每天的门票收入（单位：万元），分别记为1a ，2a ，…，10a （如：3a 表示5月3号的门票收入），下表是5月1号到5月10号每天的门票收入，根据表中数据，下面程序框图输出的结果为（ ）A ．3B ．4 C. 5 D ．69.来自英、法、日、德的甲、乙、丙、丁四位客人，刚好碰在一起，他们除懂本国语言外，每天还会说其他三国语言的一种，有一种语言是三人都会说的，但没有一种语言人人都懂，现知道：①甲是日本人，丁不会说日语，但他俩都能自由交谈；②四人中没有一个人既能用日语交谈，又能用法语交谈；③甲、乙、丙、丁交谈时，找不到共同语言沟通；④乙不会说英语，当甲与丙交谈时，他都能做翻译.针对他们懂的语言，正确的推理是（ ）A ．甲日德、乙法德、丙英法、丁英德B ．甲日英、乙日德、丙德法、丁日英 C. 甲日德、乙法德、丙英德、丁英德 D ．甲日法、乙英德、丙法德、丁法英 10.如图，已知正方体''''DC B A ABCD -的外接球的体积为π23，将正方体割去部分后，剩余几何体的三视图如图所示，则剩余几何体的表面积为（ ）A ．2329+ B ．33+或2329+ C. 32+ D ．2329+或32+ 11.如图，已知抛物线的方程为)0(22>=p py x ，过点)1,0(-A 作直线l 与抛物线相交于Q P ,两点，点B 的坐标为)1,0(，连接BQ BP ,，设BP QB ,与x 轴分别相交与N M ,两点.如果QB 的斜率与PB 的斜率之积为3-，则MBN ∠的大小等于（ ）A ．2π B ．4π C. 32π D ．3π12.已知R b a ∈,，且b x a e x+-≥)1(对R x ∈恒成立，则ab 的最大值是（ ）A ．321e B ．322e C. 323e D ．3e 第Ⅱ卷（共90分）二、填空题（每题5分，满分20分，将答案填在答题纸上）13.在92017)11(xx +-的展开式中，含3x 项的系数为 ． 14. 在公元前3世纪，古希腊欧几里得在《几何原本》里提出：“球的体积（V ）与它的直径（D ）的立方成正比”，此即3kD V =，欧几里得未给出k 的值.17世纪日本数学家们对求球的体积的方法还不了解，他们将体积公式3kD V =中的常数k 称为“立圆率”或“玉积率”.类似地，对于等边圆柱（轴截面是正方形的圆柱）、正方体也可利用公式3kD V =求体积（在等边圆柱中，D 表示底面圆的直径；在正方体中，D 表示棱长）.假设运用此体积公式求得球（直径为a ）、等边圆柱（底面圆的直径为a ）、正方体（棱长为a ）的“玉积率”分别为1k ，2k ，3k ，那么=321::k k k ．15.由约束条件⎪⎩⎪⎨⎧+≤+-≤≥1330,kx y x y y x ，确定的可行域D 能被半径为22的圆面完全覆盖，则实数k 的取值范围是 ．16.如图，已知O 为ABC ∆的重心，90=∠BOC ，若AC AB BC ⋅=24，则A 的大小为 ．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. 已知数列}{n a 的前n 项和为n S ，01≠a ，常数0>λ，且n n S S a a +=11λ对一切正整数n 都成立. （1）求数列}{n a 的通项公式；（2）设100,01=>λa ，当n 为何值时，数列}1{lgna 的前n 项和最大？ 18.某同学在研究性学习中，收集到某制药厂今年前5个月甲胶囊生产产量（单位：万盒）的数据如下表所示：x （月份） 1 2 3 4 5y （万盒） 4 4 5 6 6（1）该同学为了求出y 关于x 的线性回归方程a x b yˆˆˆ+=，根据表中数据已经正确计算出6.0ˆ=b ，试求出a 的值，并估计该厂6月份生产的甲胶囊产量数；（2）若某药店现有该制药厂今年二月份的甲胶囊4盒和三月份生产的甲胶囊5盒，小红同学从中随机购买了3盒甲胶囊，后经了解发现该制药厂今年二月份生产的所有甲胶囊均存在质量问题.记小红同学所购买的3盒甲胶囊中存在质量问题的盒数为X ，求X 的分布列和数学期望.19.已知多面体ABCDEF 如图所示，其中ABCD 为矩形，DAE ∆为等腰等腰三角形，AE DA ⊥，四边形AEFB 为梯形，且BF AE //，90=∠ABF ，22===AE BF AB . （1）若G 为线段DF 的中点，求证：//EG 平面ABCD ；（2）线段DF 上是否存在一点N ，使得直线BN 与平面FCD 所成角的余弦值等于521？若存在，请指出点N 的位置；若不存在，请说明理由.20.如图，椭圆E ：)0(12222>>=+b a b y a x 左、右顶点为A 、B ，左、右焦点为1F 、2F ，4||=AB ，32||21=F F .直线m kx y +=（0>k ）交椭圆E 于点D C ,两点，与线段21F F 、椭圆短轴分别交于NM ,两点（N M ,不重合），且||||DN CM =.（1）求椭圆E 的方程；（2）设直线AD ，BC 的斜率分别为21,k k ，求21k k 的取值范围. 21.设函数ax xbxx f -=ln )(，e 为自然对数的底数. （1）若函数)(x f 的图象在点))(,(22e f e 处的切线方程为0432=-+e y x ，求实数b a ,的值； （2）当1=b 时，若存在],[,221e e x x ∈，使a x f x f +≤)(')(21成立，求实数a 的最小值.请考生在22、23、24三题中任选一题作答，如果多做，则按所做的第一题记分.22.选修4-4：坐标系与参数方程在平面直角坐标系xOy 中，斜率为1的直线l 过定点)4,2(--.以O 为极点，x 轴的非负半轴为极轴建立极坐标系.已知曲线C 的极坐标方程为0cos 4sin 2=-θθρ. （1）求曲线C 的直角坐标方程以及直线l 的参数方程；（2）两曲线相交于N M ,两点，若)4,2(--P ，求||||PN PM +的值. 23.选修4-5：不等式选讲已知函数|23||12|)(-++=x x x f ，且不等式5)(≤x f 的解集为}5354|{bx a x ≤≤-，R b a ∈,. （1）求b a ,的值；（2）对任意实数x ，都有53||||2+-≥++-m m b x a x 成立，求实数m 的最大值.试卷答案一、选择题1-5: CDCAB 6-10: BDAAB 11、12：DA二、填空题13. 84- 14.1:4:6ππ 15.]31,(-∞ 16.3π三、解答题17.解：（1）令1=n ，得0)2(,22111121=-==a a a S a λλ，因为01≠a ，所以λ21=a ，当2≥n 时，n n S a +=λ22，1122--+=n n S a λ，两式相减得)2(221≥=--n a a a n n n ，所以)2(21≥=-n a a n n ，从而数列}{n a 为等比数列， 所以λnn n a a 2211=⋅=-.（2）当01>a ，100=λ时，由（1）知，2lg 22lg 100lg 1002lg 1lg ,1002n a b a n nn n n n -=-====，所以数列}{n b 是单调递减的等差数列，公差为2lg -，所以01lg 64100lg 2100lg6621=>==>>>b b b 当7≥n 时，01lg 2100lg77=<=≤b b n ，所以数列}1{lg na 的前6项和最大.18.解：（1）3)54321(51=++++=x ，5)66544(51=++++=y ，因线性回归方程a x b yˆˆˆ+=过点),(y x ，∴2.366.05ˆ=⨯-=-=x b y a∴6月份的生产胶囊的产量数：8.62.366.0ˆ=+⨯=y. （2）3,2,1,0=X ，4254810)0(3935====C C X P ，21108440)1(392514====C C C X P ，1458430)2(391524====C C C X P ，211844)3(3934====C C X P ，其分布列为 X 0 1 2 3P425 2110 145 211 ∴3432112145121100425)(=⨯+⨯+⨯+⨯=X E .19.（1）因为AE DA ⊥，AB DA ⊥，A AE AB = ，故⊥DA 平面ABFE ，故⊥CB 平面ABFE ，以B 为原点，BC BF BA ,,分别为x 轴，y 轴，z 轴正方向，建立如图所示的空间直角坐标系，则)0,2,0(F ，)1,0,2(D ，)21,1,1(G ，)0,1,2(E ，)1,0,0(C ，所以)21,0,1(-=EG ，易知平面ABCD 的一个法向量)0,1,0(=n ，所以0)0,1,0()21,0,1(=⋅-=⋅n EG ，所以n EG ⊥，又⊄EG 平面ABCD ，所以//EG 平面ABCD .（2）当点N 与点D 重合时，直线BN 与平面FCD 所成角的余弦值等于521.理由如下： 直线BN 与平面FCD 所成角的余弦值为521，即直线BN 与平面FCD 所成角的正弦值为52，因为)0,0,2(),1,2,2(=-=CD FD ，设平面FCD 的法向量为),,(1111z y x n =，由⎪⎩⎪⎨⎧=⋅=⋅011CD n FD n ，得⎩⎨⎧==+-020221111x z y x ，取11=y 得平面FCD 的一个法向量)2,1,0(1=n 假设线段FD 上存在一点N ，使得直线BN 与平面FCD 所成角的正弦值等于52，设)10(≤≤=λλFD FN ，则),2,2()1,2,2(λλλλ-=-=FN ，),22,2(λλλ-=+=FN BF BN ，所以5248952)22()2(52||||||,cos sin 2222111=+-⋅=+-+⋅=⋅>=<=λλλλλαn BN n BN n BN ，所以01892=--λλ，解得1=λ或91-=λ（舍去） 因此，线段DF 上存在一点N ，当N 点与D 点重合时，直线BN 与平面FCD 所成角的余弦值为521. 20.解：（1）因为322,42==c a ，所以1222=-=c a b ，所以椭圆的方程为1422=+y x . （2）将直线m kx y +=代入椭圆1422=+y x ，得0448)41(222=-+++m mkx x k . 设),(),,(2211y x C y x D ，则22212214144,418k m x x k km x x +-=+-=+，又),0(),0,(m N k m M -，由||||DN CM =得N M x x x x +=+21，即kmk km -=+-2418，因为0,0>≠k m ，得21=k ，此时22,222121-=⋅-=+m x x m x x ， 因为直线l 与线段21F F 、椭圆短轴分别交于不同两点， 所以323≤-≤-m 且0≠m ，即2323≤≤-m 且0≠m . 因为2,2222111-=+=x y k x y k ，所以)2()2(122121+-=x y x y k k ，两边平方得212121211212212222212122222221)(24)(24)2)(2()2)(2()2)(41()2)(41()2()2()(1x x x x x x x x x x x x x x x x x y x y k k +++++-=++--=----=+-= 2222)1()1(22)2(2422)2(24-+=-+-+-+--=m m m m m m ，所以1211121---=-+=m m m k k ，又因为12121---=m k k 在]23,0(),0,23[-上单调递增，所以34723123111231231347+=-+≤-+≤+-=-mm ，且111≠-+m m ，即34734721+≤≤-k k ，且121≠k k，所以]347,1()1,347[21+-∈ k k .21.解：（1）由已知得1,0≠>x x ，a x x b x f --=2)(ln )1(ln )('，则22)(2222e ae be e f -=-=，且434)('2-=-=a b e f ，解之得1,1==b a . （2）当1=b 时，a x x x f --=2)(ln 1ln )('，又a x a x x a x x x f -+--=-+-=--=41)21ln 1(ln 1)ln 1()(ln 1ln )('222+故当21ln 1=x 即2e x =时，a x f -=41)('max . “存在],[,221e e x x ∈，使a x f x f +≤)(')(21成立”等价于“当],[2e e x ∈时，有a xf x f +≤max min )(')(”又当],[2e e x ∈时，a xf -=41)('max ，∴41)('max =+a x f ， 问题等价于“当],[2e e x ∈时，有41)(min ≤x f ”.①当41≥a 时，)(x f 在],[2e e 上为减函数，则412)()(22min ≤-==ax e ef x f ，故24121ea -≥； ②当41<a 时，a x x f -+--=41)21ln 1()('2在],[2e e 上的值域为]41,[a a --， （i ）当0≥-a ，即0≤a 时，0)('≥x f 在],[2e e 上恒成立，故)(xf 在],[2e e 上为增函数，于是41)()(min >≥-==e ae e e f x f ，不合题意； （ii ）当0<-a ，即410<<a 时，由)('x f 的单调性和值域知，存在唯一∈0x ),(2e e ，使0)('=xf ，且满足当∈0x ),(0x e 时，0)('<x f ，)(x f 为减函数；当∈0x ),(20e x 时，0)('>x f ，)(x f 为增函数.所以),(,41ln )()(200000min e e x ax x x x f x f ∈≤-==，所以412141ln 141ln 22000-<->-≥e e x x x a ，与410<<a 矛盾. 综上，得a 的最小值为24121e -. 22.解：（1）由0cos 4sin 2=-θθρ得0cos 4sin 22=-θρθρ，所以曲线C 的直角坐标方程为042=-x y ，即x y 42=，所以直线l 的参数方程为是⎪⎪⎩⎪⎪⎨⎧+-=+-=t y tx 224222（t 为参数）.（2）将直线l 的参数方程代入x y 42=中，得到0482122=+-t t ，设N M ,对应的参数分别为21,t t ，则21221=+t t ，04821>=t t ，故212||||||||2121=+=+=+t t t t PN PM .23.解：（1）若21-≤x ，原不等式可化为52312≤+---x x ，解得54-≥x ，即2154-≤≤-x ； 若3221<<-x ，原不等式可化为52312≤+-+x x ，解得2-≥x ，即3221<<-x ；若32≥x ，原不等式可化为52312≤-++x x ，解得56≤x ，即5632≤≤x ；综上所述，不等式5|23||12|≤-++x x 的解集为]56,54[-，所以2,1==b a .（2）由（1）知2,1==b a ，所以3|21||2||1|||||=---≥++-=++-x x x x b x a x ， 故3532≤+-m m ，0232≤+-m m ，所以21≤≤m ，即实数m 的最大值为2.。

河北省衡水中学2016-2017学年高三文综下学期期中试题(扫描版)
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