山西省长治二中、晋城一中、康杰中学、临汾一中、忻州一中五校2017届高三第四次联考英语试卷及答案

2016—2017年度第五次五校联考数学试卷（文科）第Ⅰ卷（选择题 共60分）一、选择题：本大题共12小题，每小题5分，共60分.在每个小题给出的四个选项中，有且只有一项符合题目要求.1.已知,a b R ∈，若3234bi i a i--=+，则a b +等于 A.9- B.5 C.13 D. 92.已知集合{}()(){}0,1,2,3,4,|50,A B x x x m m Z ==+-<∈，若A B 有三个元素，则实数m 的值是A. -2B. 2C.-3D.33.已知向量()()2,2sin ,3cos ,1,sin 23a mb θθθ==-=，若//a b ，则实数m 的值为A. -4B. -2C. 2D. 44.某仪器厂从新生产的一批零件中随机抽取40个检测.如图是根据抽样检测后零件的质量（单位：克）绘制的频率分布直方图，样本数据分8组，分别为[)[)[)[]80,82,82,84,84,86,,94,96，则样本的中位数在是单调函数的概率为A.第三组B. 第四组C. 第五组D. 第六组5.若在区间[]1,5-上任取一个数b ，则函数()()1xf x x b e =--在()3,+∞内 A. 12 B.13 C.23 D.256. 已知双曲线()222210,0x y a b a b-=>>的左焦点为F ，右顶为A,过F 且与x 轴垂直的直线交双曲线于B,C 两点，若ABC ∆为直角三角形，则双曲线的离心率为D. 27. 我国古代数学名著《九章算术》有这样的问题“今有垣厚五尺，两鼠对穿，大鼠日一尺，小鼠亦一尺.大鼠日自倍，小鼠日自半.问几何日相逢，各穿几何？”意思是“今有一堵墙厚5尺，两只老鼠相向打洞窗墙.大老鼠第一天打洞1 尺，小老鼠第一天也打洞1尺.以后大鼠每天穿墙尺数是前一天的2倍，小老鼠每天穿墙尺数是前一天的12，问大、小老鼠几天后相遇？”若将题中条件“墙厚5尺”和“大鼠每天穿墙尺数是前一天的2倍”分别改为“墙厚10尺”和“大鼠每天穿墙尺数是前一天的32”，问在第几天会出现“大鼠穿墙总尺数是小鼠穿墙总尺数的4倍”情况A. 3B. 4C. 5D. 68.执行如图所示的程序框图，则下列说法正确的是A. ()2,4a ∀∈，输出i 的值为5B. ()4,5a ∃∈，输出i 的值为5C. ()3,4a ∀∈，输出i 的值为5D. ()2,4a ∃∈，输出i 的值为59.某几何体的三视图如下图所示，则该几何体的外接球的表面积为A.13πB. 16πC.17πD.21π10. 将函数()2cos 26f x x π⎛⎫=- ⎪⎝⎭的图象向左平移4π个单位得到()g x 的图象，记函数()g x 在区间,4t t π⎡⎤+⎢⎥⎣⎦内的最大值为t M ,最小值为t m ，设函数()t t h t M m =-，若,42t ππ⎡⎤∈⎢⎥⎣⎦，则函数()h t 的最小值为1 B. 2-111. 已知抛物线()2:20C y px p =>的焦点为F ，点(00,2p M x x ⎛⎫> ⎪⎝⎭是抛物线C 上一点，圆M 与线段MF 相交于点A,且被直线2p x =MA ，若2MA AF =，则AF 等于A.1B. 2C. 3D.412.设{}min ,m n 表示,m n 二者中较小的一个，已知函数()2814,f x x x =++ ()()221min ,log 4,02x g x x x -⎧⎫⎪⎪⎛⎫=>⎨⎬ ⎪⎝⎭⎪⎪⎩⎭，若[]()()125,4,0,x a a x ∀∈-≥-∃∈+∞，使得()()12f x g x =成立，则a 的最大值为A. -4B. -3C. -2D.0第Ⅱ卷（非选择题 共90分）二、填空题：本大题共4小题，每小题5分，共20分.13.在等差数列{}n a 中，若352588,18a a a a a +=++=，则1a = .14. 若实数,x y 满足不等式组20240250x y x y x y -+≥⎧⎪+-≥⎨⎪+-≤⎩，且()()321x a y -++的最大值为5，则a = .15.已知函数()f x 为偶函数，当0x ≥时，()f x 是减函数，则不等式()()22log 23log 3f x f ->⎡⎤⎣⎦的解集为 .16.在长方体1111ABCD A B C D -中，底面ABCD的正方形，13,AA E =是1AA 的中点，过1C 作1C F ⊥平面BDE 与平面11ABB A 交于点F ，则1AF AA = .三、解答题：本大题共6小题，共70分.解答应写出必要的文字说明或推理、验算过程.17.（本题满分12分）在ABC ∆中，角,,A B C 的对边分别为,,a b c ，且2cos cos 3.ac B bc A b -=（1）求sin sin A B的值； （2）若C角为锐角，3c C ==，求ABC ∆的面积.18.（本题满分12分）某中学举行了一次“环保知识竞赛”，全校学生参加了这次竞赛.为了了解本次竞赛成绩情况，从中抽取了部分学生的成绩（得分为正整数，满分100分）作为样本进行统计，请根据下面尚未完成并有局部污损的频率分布直方表（如图所示），解决下面问题.（1）求,a b 出的值；（2）在选取的样本中，从竞赛成绩是80分以上（含80分）的同学中随机抽取2名同学到广场参加环保知识的志愿宣传活动.（ⅰ）求所抽取的2名同学中至少有1名同学来自第5组的概率；（ⅱ）求所抽取的2名同学来自同一组的概率.19.（本题满分12分）如图，在多面体ABCDPE 中，四边形ABCD 和CDPE 都是直角梯形，//,//,,AB DC PE DC AD DC PD ⊥⊥平面ABCD ，2,AB PD DA PE F ===是CE 的中点.（1）求证：//BF 平面ADP ；（2）已知O 是BD 的中点，求证：BD ⊥平面AOF .20.（本题满分12分）已知()()12,0,,0F c F c -分别是椭圆()2222:103x y G b a a b+=<<<的左、右焦点，点(是椭圆G 上一点，且12.PF PF a -=.（1）求椭圆G 的方程；（2设直线l 与椭圆G 相交于A,B 两点，若OA OB ⊥，其中O 是坐标原点，判断O 到直线l 的距离是否是定值？若是，求出该定值；若不是，请说明理由.21.（本题满分12分）已知函数()()()212221ln .2f x x a x a x =-+++ （1）若曲线()y f x =在点()()2,2f 处的切线的斜率小于0，求()f x 的单调区间；（2）对任意的35,22a ⎡⎤∈⎢⎥⎣⎦，函数()()g x f x x λ=-在区间[]1,2上是增函数， 求λ的取值范围.请考生在第22、23两题中任选一题作答，如果两题都做，则按照所做的第一题给分；作答时，请用2B 铅笔将答题卡上相应的题号涂黑。

2017届高三第一次五校联考历史试题命题：长治二中忻州一中临汾一中康杰中学晋城一中(考试时间90分钟满分100分)第I卷选择题(50分)一、单项选择题(本大题共25小题，每小题2分，共计50分。

在每小题列出的四个选项中，只有一项是符合题目要求的。

)1.王国维说：“中国政治与文化之变革，莫剧于殷、周之际。

”这里的“政治变革”指的是A．从“公天下”到“家天下” B．从民主禅让到王位世袭C．从方国联盟到封邦建国 D．从列国纷争到中央集权2. 《新唐书·礼三本》说：“夫君者，民众父母也”；《周易·家天下>说：“家人有严君焉，父母之谓也”；马克思说：“就像皇帝通常被尊为全国的君父一样，皇帝的各个官吏也都在他所管辖的地区内被看作是这种父权的代表”。

以上材料实质上揭示了A．宗法关系渗透到社会生活诸多方面 B．君父在国家政治生活中的特殊地位C．家长制作风体现了封建特权思想 D．古代社会家国同构的社会特征3.钱穆认为：“从前封建时代，政府和家庭，有分不开的关系。

现在则不然了,组织政府的是一个一个人，不再是一个一个家。

”这一变化A．促进了“民本”思想的产生 B．有利于防止地方势力的膨胀C．瓦解了宗法观念 D．形成了“家国一体”的观念4. 自秦朝建立以来，君权与相权的矛盾、中央与地方的矛盾一直是古代政治体制演进过程中的重要问题，其实质是A．权力分配和权力结构调整 B．不同集团和阶层的利益之争C．强化职能和提高行政效率 D．稳定统治秩序和巩固国家统一5. 西晋文学家傅咸曾经对中国古代的四大发明之一这样描述，说：“夫其何物，厥美可珍。

廉方有则，体洁性贞。

含章蕴藻，实好斯文。

取彼之弊，以为此新。

揽之则舒，舍之则卷；可伸可屈，能幽能显。

”对这一发明理解正确的是　A．大大提高印刷效率；有利于版本的统一,有利于文化的传播与留存B．引起了书写材料的一场革命，促进了文化的传播、交流和教育的普及C．是欧洲开辟新航路的重要条件之一，是中华文明对世界航海事业发展的重大贡献D．标志人类改造自然的能力大大增强，对军事武器的进步也有着重要意义，但同时也造成许多惨剧6.清代学者赵翼提到：“宋开国时，设官分职，尚有定数。

2014-2015学年第四次四校联考理科综合物理试题命题：忻州一中 临汾一中 康杰中学 长治二中（考试时间150分钟 满分300分）以下数据可供解题时参考：可能用到的相对原子质量有：H 1 C 12 O 16 Mn 55 Zn 65 As 75 Ga 70第Ⅰ卷 (选择题 126分)二、选择题：本题共8小题，每小题6分，共48分。

每小题给出的四个选项中，第14～18题只有一项符合题目要求，第19～21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，有选错的得0分.14．下列关于物理学中的思想和方法叙述不正确．．．的是 A ．一个物体受到几个力共同作用产生的效果与某一个力产生的效果相同，这个力叫做那几个力的合力，这里包含了“等效替代”的思想B ．根据速度定义式t x v ∆∆=，当t ∆极短时，tx ∆∆就可以表示物体在t 时刻的瞬时速度，这种方法叫“微元法”C ．在探究加速度与力、质量的关系时，先保持质量不变试题类型：B探究加速度与力的关系，再保持力不变探究加速度与质量的关系，这种方法叫“控制变量法”D．在“探究弹性势能的表达式”时，为计算弹簧弹力所做的功，把拉伸弹簧的过程分为许多小段，把每一小段的弹力认为是恒力，用每小段做功的代数和代表弹力在整个过程中所做的功，这种方法叫“微元法”15．返回式卫星在回收时一般要采用变轨的方法：在远地点和近地点分别点火变轨，使其从高轨道进入椭圆轨道，再回到近地轨道，最后进入大气层落回地面。

某次回收卫星的示意图如图所示，则下列说法正确的是A．不论在A点还是在B点，两次变轨前后,卫星的机械能都增加了B．卫星在轨道1上经过B点的加速度大于在轨道2上经过B点的加速度C．卫星在轨道2上运动时，经过A点时的动能大于经过B点时的动能D．卫星在轨道2上运动的周期小于在轨道3上运动的周期16．边长为L的正方形线框在恒力F的作用下沿x轴运动，穿越如图所示的有界匀强磁场。

2017届山西省长治二中、晋城一中、康杰中学、临汾一中、忻州一中五校高三第四次联考英语试卷学校:___________姓名：___________班级：___________考号：___________一、阅读理解Steep Rock Skills $100 per person. This course will focus on techniques about climbing steep routes. Edging, off hands, high-stepping are some techniques you will work on. This course is best for women that have experience of top roping or climbing occasionally in a gym but have not had much experience outdoors.Half-Day Rappelling (绳索下降）Skills $100 per person. There’s a law that says, “What goes up must come down.” Though it may be safer to walk off many climbs, there are climbs that require you ladies to come back down to the ground. Learn various rappel techniques and use various types of rappel devices through this course. On Saturday the practice is in the morning.Hard Women Rock leader Skills $100 per person. Designed for any women with a desire to lead, efficient rope management will be covered. Bring your own equipment if you have any. Any leading will be done on top-rope. A fun and safe way to take a look at the “sharp” end of thing.Half-Day Rock Rescue $50 per person. A course for experienced women climbers wishing to build fundamental rock rescue skills in order to deal with a possible emergency situation on the cliff. Participants should bring their own personal equipment if they have. On Saturday and Sunday the practice is in the morning.1．Which course is the least expensive?A．Hard Women Rock Leader Skills.B．Steep Rock Skills.C．Half-Day Rock Rescue.D．Half-Day Rappelling skills.2．If Mary wants to be a rock-climbing leader, which of the following should she choose?A．Steep Rock Skills.B．Half-Day Rappelling Skills.C．Half-Day Rock Rescue.D．Hard Women Rock Leader Skills.3．It can be inferred from the text that________A．the courses are specially for womenB．the courses are limited to 100 personsC．it may take half a day to attend the coursesD．men are allowed to participate in the practice4．The author’s purpose in writing the text is to introduce ________.A．how to be women rock climbersB．various courses on rock climbingC．what to do at weekendsD．how to keep fitIn 2014 my best friend’s mother died of cancer. It was a tragedy, but as usual, Alice, my mother, used her power of healing and got his family back on their feet. If you asked my friends about my mother, they would say, “That woman has a heart of gold.” I agreeone-hundred percent.I think the reason why she is such a wonderful person is that the Holy Spirit lives within her. She is very holy and has persuaded me to go to church with her every Sunday.About six years ago my mom decided to pursue her lifelong goal of becoming a teacher. She knew it would be hard work raising three kids, doing housework and studying at the same time. However, she believed it would pay off. What my mother didn’t realize was that not all things pay off in this unfair world. After four hard years of school, she graduated on a warm spring day. It was unbelievable. My aunt drove up from Virginia to celebrate this fantastic day. It was the first time I had ever cried from being happy.It’s strange how fast a life can change. Two months later, the unpredictable happened. My mother was diagnosed with multiple sclerosis (多发性硬化症). I could not believe this could happen after all the good she had done for people. I was very confused and cried every day. My faith in God just disappeared and so did my mom’s dream of becoming a teacher.Then, I decided I must move on with my life and accept the fact that she might never get better. Since my decision, I have become more mature, responsible and active in school and work. I have found a wonderful girlfriend with whom I plan to spend the rest of my life. Through the years I have always been able to change negative situations into positive ones. I’m happy with my life now.5．Which of the following can best describe Alice?A．Honest.B．Helpful.C．Greedy.D．Unconcerned. 6．What else did Alice have to do when studying?A．Drive a car and go to church.B．Teach students and raise kids.C．Do housework and teach at school.D．look after children and keep house.7．According to the text, the author's mother ________.A．recovered from illnessB．no longer had faith in GodC．didn’t realize her dream as a teacherD．changed negative situations into positive ones unwillingly8．What may be the best title for the text?A．Fighting against Kinds of DiseasesB．Mother Gave Me Life ExperienceC．Belief in God Brought Me Good LuckD．How to Become a Responsible and Active ManA new study has found that social media could be affecting the sleep of young adults.The study is a project of researchers at the University of Pittsburgh's School of Medicine. They found that young people who often use social media are more likely to suffer from sleep disorders than those who use social media less. The researchers say doctors should ask young adults about their use of social media when treating sleep issues.“This is one of the first pieces of evidence that social media use really can influence your sleep.” said Jessica C Levenson. She was the lead author of a report on the study.The researchers set out to examine the connection between social media use and sleep among young adults. Levenson noted that these young adults are possibly the first “generation to grow up with social media.”The researchers wanted to find out how often young people used social media sites like Facebook, Twitter, Credit and Tumbler. For the study, they gave questionnaires to nearly 1,800 adults, aged 19 to 32. On average, members of the study group used social media sites one hour a day. They also "visited various social media 30 times per week.”Thirty percent of the study's participants reported having serious problems with sleeping. Those people who used social media a lot were three times more likely to have a sleep disorder. And those who spent the most time on social media were two times as likely to suffer from sleep disturbances.Levenson said the number of times a person visits social media is a better predictor of sleep problems than overall time spent on social media. If this is true, she adds, then practices that stop such behaviors may be the most effective.9．What's the main idea of the text?A．The researchers focus on social media.B．The researchers manage to handle sleep problems.C．Doctors treat young patients.D．Social media affects sleep.10．When treating sleep problems, doctors are advised to ________.A．offer some advice about giving up social mediaB．ask the patients about young adults’ use of social mediaC．give young adults some medicineD．ask about the patients' living conditions11．How did the researchers mainly carry out the study?A．By doing online research.B．By giving an example.C．By collecting published data.D．By doing questionnaires.12．What can be inferred from the text?A．Men are more likely to suffer from a sleep disorder than women.B．People often using social media are less likely to have a sleep disorder.C．Using computers less helps avoid sleep problems completely.D．Sleep problems can be determined by the times of a person visiting social media.A quarter of today’s UK children are living in families which cause more than one risk to their educational development, a study says.Institute of Education researchers analyzed 10 risk factors affecting more than 18,000 families. Risks included financial stress, teenage parenthood, depression, low skills and alcohol abuse. Previous research suggests families with multiple risk factors are the most damaging. According to the research, just over four in ten people experienced no risk factors in their early childhood, while a third faced only one. It would mean 192.000 UK children born 10 years ago have been growing up in families with multiple risks to their development.The paper's authors found that those who had grown up with two or more risk factors had poorer behavioral development scores at ages three and five. They also did worse instandard vocabulary tests at these ages. The report, published by the Centre for Longitudinal Studies, said. “Children living in families with both multiple risks and low income faced the worst across most developmental outcomes.”“These children achieved the lowest change in vocabulary test scores between ages three and five.” Professor Dex added. “The most reassuring thing is that if you come into contact with just one of these risk factors, there is a fairly modest effect on children. She suggested that health visitors could be aware of families where there were two or more of these indicators, and offer help. ”The government has pledged to turn around the lives of England's 120.000 most troubled families by 2015. To qualify for help, the families need to meet five out of seven criteria including truanting (旷课的）children, parents with addiction and anti -social behavior. 13．According to the research, what families are the most damaging to children's educational development?A．Families with no risk factors.B．Families with two or more children.C．Families with two or more risk factors.D．Families with the only financial stress.14．What can we learn about the children growing up with multiple risk factors?A．They didn't care about developmental outcomes.B．They had poorer behavioral development in high school.C．They tended to behave better in dealing with different risks.D．They tended to perform worse in vocabulary tests in their early childhood. 15．The underlined word “pledged” in the last paragraph can be replaced by__________ .A．promised B．refusedC．hesitated D．failed二、七选五When we were children, we were taught the simplest lessons to be able to buildrelationship?Be willing to shareOnce you are in a good relationship, you are not just thinking about yourself. You learn to share what you have. 17 You should also share your thoughts, your ideas, your dreams and even your frustrations.Learn to carePeople in a good relationship are kind to each other. They make efforts to show how they value each others' space. They both take the time to know what matters to the other and also give time to try out each others' interests. 18 .Learn to play fair19 Each one is allowed to move freely as an individual However, each action is done with consideration of the other one's feelings. No one is above the other.20A healthy union is bound by cooperation. The people involved work as a team to achieve one goal. Each one helps and supports the other to succeed in their individual endeavors. They appreciate each other and they grow together and as individuals as well.A．Learn to cooperateB．learn to work hard towards your goalC．A good relationship is a two-way traffic.D．This does not just include material things.E．Everyone knows that the relationship they have won't slay strongF．Having good relationships will make you never have to live your life alone.G．Most of all, they care enough to listen to each other and do nice things for each other.三、完形填空Why would they move to Alaska, the 27 of polar bears and Eskimos? When I asked, they said, “We wanted to experience adventure.” My grandparents thought that they were28 and said, “It is a horrible thing to do to those kids.”29 my parents moved, with nothing but a few clothes and $500 dollars. Through hard work and perseverance, they have not only survived, but are 30 than ever. My father has gotten his 31 job as a wildlife technician for the Department of Fish and Game. My 32 is now the manager of the high school kitchen.These two people had the courage to 33 for their dreams—no matter what others thought. Through good and bad times, my parents never lost sight of their 34 . What they wanted most in the world was to raise their children to be 35 . I honor and thank them. Because of their 36 , I have become an independent young man.37 their hard work and strong will, they have become happy and successful. I have learned through their actions and mistakes that anything is 38 .So, when I ask myself why I am in Alaska, I 39 myself how I got here. No matter how 40 it gets, I can’t think of a better place to grow up. I sure do love Alaska!21．A．ways B．plans C．questions D．wishes 22．A．left B．moved C．searched D．forgot 23．A．farming B．building C．nursing D．training 24．A．look for B．put away C．take over D．find out 25．A．prove B．change C．begin D．save 26．A．ate B．lost C．used D．wanted 27．A．land B．sight C．visit D．protection 28．A．strong B．brave C．crazy D．young 29．A．So B．And C．But D．If 30．A．wiser B．happier C．earlier D．heavier 31．A．old B．dream C．lucky D．rich 32．A．mother B．brother C．friend D．grandpa 33．A．go B．ask C．care D．wait 34．A．problems B．feelings C．goals D．experiences 35．A．healthy B．safe C．kind D．successful 36．A．jobs B．teachings C．failures D．permissions37．A．Despite B．Without C．Through D．Beyond 38．A．easy B．useful C．painful D．possible 39．A．doubt B．remind C．believe D．persuade 40．A．cold B．long C．much D．far四、用单词的适当形式完成短文Here is a true story. A man came out of his home to admire his new truck. To his surprise,五、短文改错51．假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。

山西省长治二中、晋城一中、康杰中学、临汾一中、忻州一中五校2017届高三第四次联考英语试卷第I卷第一部分听力(共两节,满分30分)第一节(共5小题;每小题1．5分,满分7．5分)听下面5段对话.每段对话后有一个小题,从题中所给的A．B．C三个选项中选出最佳选项,并标在试卷的相应位置.听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题.每段对话仅读一遍.例:How much is the shirt?A．￡19．15 B．￡9．18 C．￡9．151．Where did this conversation most probably take place? __________A．In a restaurant B．In a shop C．In a vegetable market2．What did the man do last night? __________A．He went to visit a friendB．He went to say goodbye to his friend at the airportC．He went to another city with his friend3．What can we learn about the man from the conversation? __________A．He enjoys using e-mailsB．He often receives letters from friendsC．He never writes letters to his friends4．What time does the next plane to London leave? __________A．At 10:00 B．At 11:00 C．At 12:005．What is the man’s problem? __________A．He isn’t feeling wellB．He is caught in bad weatherC．He feels very cold第二节(共15小题;每小题1．5分,满分22．5分)听下面5段对话或独白.每段对话或独白后有几个小题,从题中所给的A．B．C三个选项中选出最佳选项,并标在试卷的相应位置.听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间.每段对话或独白读两遍.听第6段材料,回答第6至8题.6．What is the man going to do? __________A．Buy some stamps B．Have his car fixed C．Buy some drugs7．Where will the woman go? __________A．The department store B．The stamp market C．The drugstore8．When will the speakers meet? __________A．An hour later B．Ah hour and a half later C．Half an hour later 听第7段材料,回答第9至11题.9．What is the special offer? __________A．If you buy now, you get a free ticket for one yearB．If you buy one ticket, you get another one for freeC．If you buy two round-trip tickets, you get one free ticket10．How much does a ticket for an 11-year-old child cost? __________A．It is half of the regular priceB．It is one third of the regular priceC．It is free11．When will the family leave for Los Angeles? __________A．This Friday morning B．This weekend C．Next week听第8段材料,回答第12至14题.12．Where is the man making the telephone call now? __________A．At his home B．In the hospital C．In Dr Carter’s office 13．Why does the man want to see Dr Carter? __________A．He was hit by a ladder B．He broke his leg C．He hurt his foot 14．What does the woman tell the man to do in the end? __________A．Come to the office right awayB．Wait for Dr Carter at homeC．Take off the paint can himself听第9段材料,回答第15至17题.15．What are the people in the house doing? __________A．Dancing a ballet B．Having a party C．Singing songs 16．What do we know about Cariol? __________A．She is the woman’s sisterB．She is sitting on the chairC．She has short black hair17．How does the woman know Bob? __________A．He has just been introduced to herB．They have met at a party beforeC．She has taken lessons from him听第10段材料,回答第18至20题.18．What can we learn about the radio station? __________A．It broadcasts an advertisement for a coffee shopB．It is on Montana at Seventh Street in Santa MonicaC．It is open twenty-four hours a day19．What will the weather be like in the afternoon? __________A．Cloudy B．Rainy C．Fine20．What can we learn about Santa Monica Beach? __________A．It is a good place for surfingB．It is a good place for parking carsC．It is a good place for swimming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.ASteep Rock Skills $100 per person. This course will focus on techniques about climbing steep routes. Edging, off hands, high-stepping are some techniques you will work on. This course is best for women that have experience of top roping or climbing occasionally in a gym but have not had much experience outdoors.Half-Day Rappelling（绳索下降）Skills $ 100 per person. There’s a law that says, “What goes up must come down.” Though it may be safer to walk off many climbs, there are climbs that require you ladies to come back down to the ground. Learn various rappel techniques and use various types of rappel devices through this course. On Saturday the practice is in the morning.Hard Women Rock leader Skills $ 100 per person. Designed for any women with a desire to lead, efficient rope management will be covered. Bring your own equipment if you have any. Any leading will be done on top-rope. A fun and safe way to take a look at the “sharp” end of thing.Half-Day Rock Rescue $ 50 per person. A course for experienced women climbers wishing to build fundamental rock rescue skills in order to deal with a possible emergency situation on the cliff. Participants should bring their own personal equipment if they have. On Saturday and Sunday the practice is in the morning. 21．Which course is the least expensive? _______A．Hard Women Rock Leader Skills. B．Steep Rock Skills.C Half-Day Rock Rescue. D．Half-Day Rappelling skills.22．If Mary wants to be a rock-climbing leader, which of the following should she choose? _______A．Steep Rock Skills. B．Half-Day Rappelling Skills.C．Half-Day Rock Rescue. D．Hard Women Rock Leader Skills. 23．It can be inferred from the text that__________.A．the courses are specially for womenB．the courses are limited to 100 personsC．it may take half a day to attend the coursesD．men are allowed to participate in the practice24．The author's purpose in writing the text is to introduce______________.A．how to be women rock climbersB．various courses on rock climbingC．what to do at weekendsD．how to keep fitBIn 2014 my best friend’s mother died of cancer. It was a tragedy, but as usual, Alice, my mother, used her power of healing and got his family back on their feet. If you asked my friends about my mother, they would say, “That woman has a heart of gold.” I agree one-hundred percent.I think the reason why she is such a wonderful person is that the Holy Spirit lives within her. She is very holy and has persuaded me to go to church with her every Sunday.About six years ago my mom decided to pursue her lifelong goal of becoming a teacher. She knew it would be hard work raising three kids, doing housework and studying at the same time. However, she believed it would pay off. What my mother didn’t realize was that not all things pay off in this unfair world. After four hard years of school, she graduated on a warm spring day. It was unbelievable. My aunt drove up from Virginia to celebrate this fantastic day. It was the first time I had ever cried from being happy.It’s strange how fast a life can change. Two months later, the unpredictable happened. My mother was diagnosed with multiple sclerosis（多发性硬化症）. I could not believe this could happen after all the good she had done for people. I was very confused and cried every day. My faith in God just disappeared and so did my mom’s dream of becoming a teacher.Then, I decided I must move on with my life and accept the fact that she might never get better. Since my decision, I have become more mature, responsible and active in school and work. I have found a wonderful girlfriend with whom 1 plan to spend the rest of my life. Through the years I have always been able to change negative situations into positive ones. I'm happy with my life now.25．Which of the following can best describe Alice? _______A．Honest. B．Helpful.C．Greedy. D．Unconcerned.26．What else did Alice have to do when studying? _______A．Drive a car and go to church.B．Teach students and raise kids.C．Do housework and teach at school.D．look after children and keep house.27．According to the text, the author's mother___________.A．recovered from illnessB．no longer had faith in GodC．didn’t realize her dream as a teacherD．changed negative situations into positive ones unwillingly28．What may be the best title for the text? _______A．Fighting against Kinds of DiseasesB．Mother Gave Me Life ExperienceC．Belief in God Brought Me Good LuckD．How to Become a Responsible and Active ManCA new study has found that social media could be affecting the sleep of young adults.The study is a project of researchers at the University of Pittsburgh's School of Medicine. They found that young people who often use social media are more likely to suffer from sleep disorders than those who use social media less. The researchers say doctors should ask young adults about their use of social media when treating sleep issues.“This is one of the first pieces of evidence that social media use really can influence your sleep.” said Jessica C Levenson. She was the lead author of a report on the study.The researchers set out to examine the connection between social media use and sleep among young adults. Levenson noted that these young adults are possibly the f irst “generation to grow up with social media.”The researchers wanted to find out how often young people used social media sites like Face book, Twitter, Credit and Tumbler. For the study, they gave questionnaires to nearly 1, 800 adults, aged 19 to 32．On average, members of the study group used social media sites one hour a day. They also "visited various social media 30 times per week.”Thirty percent of the study's participants reported having serious problems with sleeping. Those people who used social media a lot were three times more likely to have a sleep disorder. And those who spent the most time on social media were two times as likely to suffer from sleep disturbances.Levenson said the number of times a person visits social media is a better predictor of sleep problems than overall time spent on social media. If this is true, she adds, then practices that stop such behaviors may be the most effective.29．What's the main idea of the text? _______A．The researchers focus on social media.B．The researchers manage to handle sleep problemsC．Doctors treat young patients.D．Social media affects sleep.30．When treating sleep problems, doctors are advised to___________.A．offer some advice about giving up social mediaB．ask the patients about young adults’ use of social mediaC．give young adults some medicineD．ask about the patients' living conditions31．How did the researchers mainly carry out the study? _______A．By doing online research. B．By giving an example.C．By collecting published data. D．By doing questionnaires.32．What can be inferred from the text? _______A．Men are more likely to suffer from a sleep disorder than women.B．People often using social media are less likely to have a sleep disorder.C．Using computers less helps avoid sleep problems completely.D．Sleep problems can be determined by the times of a person visiting social media.DA quarter of today’s UK children are living in families which cause more than one risk to their educational development, a study says.Institute of Education researchers analyzed 10 risk factors affecting more than 18, 000 families. Risks included financial stress, teenage parenthood, depression, low skills and alcohol abuse. Previous research suggests families with multiple risk factors are the most damaging. According to the research, just over four in ten people experienced no risk factors in their early childhood, while a third faced only one. It would mean 192．000 UK children born 10 years ago have been growing up in families with multiple risks to their development.The paper's authors found that those who had grown up with two or more risk factors had poorer behavioral development scores at ages three and five. They also did worse in standard vocabulary tests at these ages. The report, publis hed by the Centre for Longitudinal Studies, said. “Children living in families with both multiple risks and low income faced the worst across most developmental outcomes.”“These children achieved the lowest change in vocabulary test scores between ages three and five.” Professor Dex added. “The most reassuring thing is that if you come into contact with just one of these risk factors, there is a fairly modest effect on children. She suggested that health visitors could be aware of families where there were two or more of these indicators, and offer help.”The government has pledged to turn around the lives of England’s 120. 000 most troubled families by 2015. To qualify for help, the families need to meet five out of seven criteria including truanting（旷课的）children, parents with addiction and anti -social behavior.33．According to the research, what families are the most damaging to children’s educational development? _______A．Families with no risk factors.B．Families with two or more children.C．Families with two or more risk factors.D．Families with the only financial stress.34．What can we learn about the children growing up with multiple risk factors? _______A．They didn't care about developmental outcomes.B．They had poorer behavioral development in high school.C．They tended to behave better in dealing with different risks.D．They tended to perform worse in vocabulary tests in their early childhood.35．The underlined word “pledged” in the last paragraph can be replaced by__________.A．promised B．refusedC．hesitated D．failed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.When we were children, we were taught the simplest lessons to be able to build good relationships with others.36 However, the question is: what makes a good relationship?Be willing to shareOnce you are in a good relationship, you are not just thinking about yourself. You learn to share what you have. 37 You should also share your thoughts, your ideas, your dreams and even your frustrations.Learn to carePeople in a good relationship are kind to each other. They make efforts to show how they value each others’ space. They both take the time to know what matters to the other and also give lime to try out each others’ interests 38Learn to play fair39 Each one is allowed to move freely as an individual However, each action is done with consideration of the other one's feelings. No one is above the other.40A healthy union is bound by cooperation. The people involved work as a team to achieve one goal. Each one helps and supports the other to succeed in their individual endeavors. They appreciate each other and they grow together and as individuals as well.A．Learn to cooperateB．learn to work hard towards your goalC A good relationship is a two-way traffic.D．This does not just include material things.Everyone knows that the relationship they have won't slay strongF．Having good relationships will make you never have to live your life alone.G．Most of all, they care enough to listen to each other and do nice things for each other.第三部分:语言知识运用(共两节,满分45分)第一节完形填空(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四个选项(A．B．C和D)中,选出可以填入空白处的最佳选项.As I walked through the door, I felt sharp coldness. While my fingers began to numb, many 41 ran through my head. Why am I here? What were my parents thinking when they 42 here?My parents were born and raised a 43 family in southwestern lows. From a very young age, they wereexpected to 44 the family farm.Five years after my birth, my parents made a decision that would 45 our lives forever. They decided they 46 more in life. They told their families that they were moving to Alaska!Why would they move to Alaska, the 47 of polar bears and Eskimos? When I asked, they said, “We wanted to experience adventure.”My grandparents thought that they were 48 and said, “It is a horrible thing to do to those kids.”49 my parents moved, with nothing but a few clothes and $500 dollars. Through hard work and perseverance, they have not only survived, but are 50 than ever. My father has gotten his 51 job as a wildlife technician for the Department of Fish and Game. My 52 is now the manager of the high school kitchen.These two people had the courage to 53 for their dreams—no matter what others thought. Through good and bad times, my parents never lost sight of their 54 .What they wanted most in the world was to raise their children to be 55 .I honor and thank them. Because of their 56 , I have become an independent young man. 57 their hard work and strong will, they have become happy and successful. I have learned through their actions and mistakes that anything is 58 .So, when I ask myself why I am in Alaska, I 59 myself how I got here. No matter how 60 it gets, I can’t think of a better place to grow up. I sure do love Alaska!41．A．ways B．plans C．questions D．wishes42．A．left B．moved C．searched D．forgot43．A．farming B．building C．nursing D．training44．A．look for B．put away C．take over D．find out45．A．prove B．change C．begin D．save46．A．ate B．lost C．used D．wanted47．A．land B．sight C．visit D．protection48．A．strong B．brave C．crazy D．young49．A．So B．And C．But D．If50. A．wiser B．happier C．earlier D．heavier51．A．old B．dream C．lucky D．rich52．A．mother B．brother C．friend D．grandpa53．A．go B．ask C．care D．wait54．A．problems B．feelings C．goals D．experiences55．A．healthy B．safe C．kind D．successful56．A．jobs B．teachings C．failures D．permissions57．A．Despite B．Without C．Through D．Beyond58．A．easy B．useful C．painful D．possible59．A．doubt B．remind C．believe D．persuade60．A．cold B．long C．much D．far第II卷第三部分英语知识运用(共两节,满分45分)第二节(共10小题;每小题1．5分,满分15分)阅读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式.Here is a true story. A man came out of his home to admire his new truck. To his surprise, his three-year-old son was happily scraping（刮）the shiny paint of the truck 61 （use）a sharp knife. The man ran to his son and drove him away. 62 （scare）, the boy ran away quickly. Unfortunately, the boy fell down and hurt his right hand 63 （serious）with the knife sticking into his fingers. The father rushed his son to the hospital immediately.Although the doctor tried desperately 64 （save）the injured fingers, he finally had to cut them off. When the boy woke up from the 65 （operate）, he innocently said, “Daddy, I’m sorry about your truck.”Then he asked, “But 66 are me fingers going to grow back?” The father began crying sadly 67 his head down.Think about this story the next time someone 68 (step)on your feet or you wish to take revenge（报仇）. Think first before you lose your patience with someone you love. Trucks can 69 （repair）, but broken bones and hurt feelings often can’t. Too often we fail to recognize 70 difference between the person and the performance. We forget that for giveness is greater than revenge.第四部分写作(共两节, 满分35分)第一节短文改错(共10小题;每小题1分,满分10分)假定英语课上老师要求同桌之间交换修改作文,请你修改你同桌写的以下作文.文中共有10处语言错误,每句中最多有两处.每处错误仅涉及一个单词的增加、删除或修改.增加:在缺词处加一个漏字符号(∧),并在其下面写出该加的词.删除:把多余的词用斜线(＼)划掉.修改:在错的词下划一横线,并在该词下面写出修改后的词.注意:1．每处错误及其修改均仅限一词;2．只允许修改10处,多者(从第11处起)不计分.Mr. Green is a London taxi driver who love going to the theater. Last week his mother gave him two tickets for play. The tickets were for Sunday evening. Then Mr. Green read some reviews of the play, that said it was a terribly one! He wouldn’t go to see the play that no one liked. So two hours after the beginning of the play, he left the tickets on the back sea of his taxi. He thought perhaps someone who wants to see the play would take it. However, when Mr. Green went back to home, the tickets were still there. On fact, there were four tickets on the seat. Someone had placed another pair of ticket on top of them!第二节书面表达(满分25分)假定你是李华,你的美国朋友Jack因爸爸过度饮酒而感到非常苦恼,就此请你用英语给他写一封邮件.主要内容包括:1．表示安慰:2．给出建议;3．寄予希望.注意:1．词数100左右;2．可以适当增加细节,以使行文流畅;3．开头和结尾已给出,不计入总词数.Dear Jack,I’m sorry to hear that your father is addicted to drinking. ____________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________ Best wishes. I’m looking forward to your reply.Yours,Li Hua山西省长治二中、晋城一中、康杰中学、临汾一中、忻州一中五校2017届高三第四次联考英语试卷答案1~5．ABCBA 6~10．BABCA 11~15．CACAB 16~20．ACACA21~24．DCABD 26~30．DCBDB 31~35．DDCDA 36~40．FDGCA41~45．CBACB 46~50．DACCB 51~55．BAACD 56~60．BCDBA61．using62．Scared63．seriously64．to save65．operation66．when67．with68．steps69．be repaired70．the71~80．Mr. Green is a London taxi driver who love going to the theater. Last week his mother gave him two tickets forloves∧play. The tickets were for Sunday evening. Then Mr. Green read some reviews of the play, that said it was aa whichterribly one! He wouldn’t go to see the play that no one liked. So two hours after the beginning of the play, he left terrible beforetickets on the back sea of his taxi. He thought perhaps someone who wants to see the play would take it. However,wanted themwhen Mr. Green went back to home, the tickets were still there. On fact, there were four tickets on the seat. Someone﹨Inhad placed another pair of ticket on top of them!tickets81．One possible version:Dear Jack,I’m sorry to hear that your father is addicted to drinking. I can understand how you feel. It must be a big problem for your family, and it may disturb your daily life. As his son, it’s normal for you to give him your concern.However, you shouldn’t become upset about it. Certainly, you should try your best in your spare time to help him get rid of drinking little by little. Meanwhile, you can ask some doctors and experts for more professional help. Making some rules for him to follow is another way you can try.We know quitting drinking is very different, so you should give him time and care. I wish your father could give up drinking with your help and become healthier and happier.Best wishes, I’m looking forward to your reply.Yours,Li Hua。

山西省长治二中、晋城一中、康杰中学、临汾一中、忻州一中五校2017届高三第四次联考文综地理试卷第Ⅰ卷（选择题共140分）本卷共35个小题，每小题4分，共140，在每小题给出的四个选项中，只有一项是符合题目要求的。

2016年7月12日，国务院同意《南京市城市总体规划（201102020年）方案》，提出做好南京市江北新区规划建设的要求。

天际线是西方城市规划学者定型的理念，它是城市里面高楼大厦构成的整体结构，又称城市的全景。

下图为南京市2000~2012年城市天际线变化示意图。

1．南京市江北新区开发的最大优势是()A．科技力量雄厚B．交通便利C．土地成本低D．资源丰富2．为增强南京市中心区对城北的辐射带动作用，南京市亟需加强的是()A．交通建设B．市场开拓C．环境保护D．产业调整3．据图判断2000~2012年南京城区建设发展最快的方向是()A．东南B．西南C．西北D．东北下图为内蒙古自治区人口年龄结构金字塔变化示意图。

读图，完成4~5题。

4．1990年和2010年内蒙古人口结构比较，差异最大的是()A．人口性别比B．老年人口比重C．青壮年人口比重D．少儿人口比重5．1990年内蒙古劳动年龄（15~60岁）人口结构特点的主要成因是()A．人口出生率和自然增长率高B．资源开发、经济发展吸引大批劳动力迁入C．大量人口迁往东部沿海地区D．计划生育政策大力推行读我国某区域（图中阴影区域）分布图，完成6~8题。

6．该区域（）A．地处我国地势的二、三级阶梯过渡地带B．年平均气温接近0℃C．年降水量接近800mm D．是长江流域与海河流域的分水岭7．该区域物种丰富、植被类型复杂，其主要原因是（）①地势低平，湿地广布②地处北亚热带与暖温带的生物交错带③地势起伏大，气候垂直差异显著④全球气候变暖A.①②B．②③C．③④D．①④8．该区域南北两侧的共同地理特征是（）A．气候类型B．作物熟制C．植被类型D．河流补给来源右图为局部日照图，MN为晨线的一部分，MN与20°N、20°S分别相交于A、B两点。

山西省长治二中、晋城一中、康杰中学、临汾一中、忻州一中五校2017届高三第四次联考文数试题第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. 已知集合错误！未找到引用源。

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若从一个只有3枚的一元硬币和2枚五角硬币的储钱罐内随机取出2枚硬币（假设每枚被抽到都是等可能的），则总共取到2元钱的概率为错误！未找到引用源。

.那么，下列命题为真命题的是（）A. 错误！未找到引用源。

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2017届高三第一次五校联考文科数学试题命题：长治二中晋城一中康杰中学临汾一中忻州一中(考试时间120分钟满分150分)一、选择题(本大题共12小题，每小题5分，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．已知全集为R ，集合{|2A x x =<-或}3x >，{}2,0,2,4B =-，则R ()C A B =A ．{}2,0,2-B ．{}4,2,2-C ．{}3,0,2-D ．{}4,2,0 2．已知复数34i z =-+（i 是虚数单位），则复数1iz+的虚部为 A ．21-B ．1i 2C ．21D ．1i 2-3．从1，2，3，4，5中任取两个数，则这两个数的乘积为偶数的概率为 A ．110B ．310C ．35D ．7104．一个空间几何体的三视图如图所示，其中正视图为等腰直角三角形， 侧视图与俯视图为正方形，则该几何体的体积为 A ．64B ．32 C ．364D ．332 5．执行如图所示的程序框图，则输出的结果是 A ．x sin B ．x sin - C ．x cos D ．x cos -6．设等差数列{}n a 的前n 项和为n S ，若1008100710080,0a a a >+<，则满足01<+n n S S 的正整数n 为A ．2013B ．2014C ．2015D ．2016 7．下列说法中错误的个数是①命题“,,212,1x x M x x ≠∈∃有0))](()([1221>--x x x f x f ”的否定是“,,212,1x x M x x ≠∉∀有0))](()([1221≤--x x x f x f ”；第5题图开始 f 0(x)=cosx i ＝0 i ＝i ＋1 i =2016？结束是否输出f i (x) f i (x)=f 'i-1(x)第4题图②若一个命题的逆命题为真命题，则它的否命题也一定为真命题； ③已知032:2>-+x x p ，131:>-xq ，若命题p q ∧⌝)(为真命题，则x 的取值范围是(,3)(1,2)[3,)-∞-+∞；④“3≠x ”是“3≠x ”成立的充分条件． A ．1B ．2C ．3D ．48．已知函数()sin cos f x x a x =+(a ∈R )图象的一条对称轴是4x π=，则函数()sin ()g x x f x =+的最大值为 A ．5B ．3CD9．已知定义在R 上的函数)(x f 满足：(2)()f x f x +=，在区间)1,1[-上，224,10()log ,01x a x f x x x x ⎧+-≤≤=⎨-<<⎩，若0)29()25(=--f f ，则=)4(a f A ．1B ．1-C ．21D ．21- 10．已知直线ax y =与圆0222:22=+--+y ax y x C 交于两点B A ,，且CAB ∆为等边三角形，则圆C 的面积为A ．49πB ．36πC ．π7D ．π611．已知抛物线x y C 4:2=的焦点为F ，定点)2,0(-A ，若射线FA 与抛物线C 交于点M ，与抛物线C 的准线交于点N ，则FN MN :的值是 A ．5:)25(-B ．5:2 C ．52:1D(1+ 12．已知函数⎩⎨⎧>+-≤-=0,0,2)(2x x x x x x f ，若函数a x f x g -=)()(恰有三个互不相同的零点321,,x x x ，则321x x x 的取值范围是 A ．)0,321(-B ．)0,161(-C ．)321,0(D ．)161,0(二、填空题（本大题共4小题，每小题5分，共20分，将答案填写在答题卷指定位置） 13．已知点)1,2(),3,1(),2,1(C B A -，则=+⋅)2(BC AC AB ．14．若实数y x ,满足⎪⎩⎪⎨⎧≥-+≤-≥-03002y x y x y x ，则y x z +=3的最小值为．15．已知ABC ∆的面积为S ，三内角C B A ,,的对边分别为c b a ,,．若2224c b a S +=+，则)4πcos(sin +-B C 取最大值时C =．16．已知双曲线)0,0(12222>>=-b a by a x 的左、右焦点分别为21,F F ，等边三角形21F PF 与双曲线交于N M ,两点，若N M ,分别为线段21,PF PF 的中点，则该双曲线的离心率为． 三、解答题（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12分）设数列{}n a 的前n 项和为n S ，且22(n n a S n =+∈N *)． （1）求数列{}n a 的通项公式； （2）设2log n n b a =，求数列21n n b b +⎧⎫⎨⎬⎩⎭的前n 项和n T ．18．（本小题满分12分）如图所示，在四棱锥P ABCD -中，底面ABCD 为菱形，E 为AC 与BD 的交点，PA ⊥平面ABCD ，M 为PA 中点，N 为BC 中点．（1）证明：直线//MN 平面PCD ；（2）若点Q 为PC 中点，120,3,1BAD PA AB ∠===，求三棱锥A QCD -的体积．19．（本小题满分12分）学业水平考试（满分为100分）中，成绩在[]80,100为A 等，在[)60,80为B 等，在[)40,60为C 等，不到40分为D 等．某校高二年级共有1200名学生，其中男生720名，女生480名，该校组织了一次物理学业水平模拟考试．为研究这次物理考试成绩为A 等是否与性别有关，现按性别采用分层抽样抽取100名学生的成绩，按从低到高分成[)[)[)[)[)[)[]30,40,40,50,50,60,60,70,70,80,80,90,90,100七组，并绘制成如图所示的频率分布直方图．22(),()()()()n ad bc K a b c d a c b d -=++++（1）估计该校高二年级学生在物理学业水平考试中，成绩为D 等的人数；（2）请你根据已知条件将下列22⨯列联表补充完整，并判断是否有90%的把握认为“该校高二年级学生在本次考试中物理成绩为A 等与性别有关”？附：20．（本小题满分12分）椭圆2222:1(0)x y C a b a b+=>>的离心率为2，且过点P ．（1）求椭圆C 的方程；（2）若12,A A 分别是椭圆的左、右顶点，动点M 满足212MA A A ⊥，且1MA 交椭圆C 于不同于1A 的点R ，求证：OR OM ⋅为定值．21．（本小题满分12分）已知函数∈+=a a x x f x(e )(R ）． （1）讨论函数)(x f 的单调性；（2）当1,0≤<a x 时，证明：)()1(2x f x x a x '>++．请考生在第22、23、24题中任选一题做答，如果多做，则按所做的第一题计分22．（本小题满分10分）如图，已知AB 为圆O 的直径，D C ,是圆O 上的两个点，C 是劣弧BD 的中点,AB CE ⊥于E ,BD 交AC 于G ，交CE 于F . （1）求证：FG CF =（2）求证：CE AG AC DG ⋅=⋅.23．（本小题满分10分）在直角坐标系xOy 中，直线l 的参数方程为为参数）t t y t x (222221⎪⎪⎩⎪⎪⎨⎧+=+=，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2C 的极坐标方程为θρsin 4=.（1）写出直线l 的普通方程和曲线2C 的直角坐标方程； （2）直线l 与曲线2C 交于B A 、两点，求AB .24．（本小题满分10分）已知函数12)(-++=x x x f （1）求不等式5)(>x f 的解集；（2）若对于任意的实数x 恒有1)(-≥a x f 成立，XX 数a 的取值范围.2017届高三第一次五校联考文科数学参考答案一、选择题：题号 1 2 3 4 5 6 7 8 9 10 11 12 答案AADBCBCCADDA二、填空题：13．-14 14．5 15．4π16．3+1 三、解答题:17．解：(1)由22n n a S =+得，-1-122n n a S =+（2n ≥），两式相减得12n n a a -=（2n ≥）．当n =1时，1a =2，所以数列{a n }是首项为2、公比为2的等比数列，则2nn a =．⋯⋯6分(2)由(1)知，b n =n ，所以1b n b n +2=12(1n －1n +2)．则数列{1b n b n +2}的前n 项和T n =12[(1－13)+(12－14)+(13－15)+…+(1n －1n +2)]=12(32－1n +1－1n +2)．…12分18．解：（1）取PD 中点R ，连结,MR RC ，1//,//,2MR AD NC AD MR NC AD ==， //,MR NC MR NC ∴=，∴四边形MNCR 为平行四边形，//MN RC ∴，又RC ⊂平面PCD ，MN ⊄平面PCD ,//MN ∴平面PCD ．⋯⋯⋯6分（2）由已知条件得1,AC AD CD ===所以34ACD S ∆=． 所以111328A QCD Q ACD ACD V V S PA --∆==⨯⨯=．……….....................................12分 19．解：（1）设抽取的100名学生中，本次考试成绩为D 等的有x 人，根据题意得：100[110(0.0080.0120.0120.0160.024+0.026]=2x =⨯-⨯++++），据此估计该校高二年级学生在物理学业水平考试中，成绩为D 等的人数为21200=24100⨯（人）．................................4分 （2）根据已知条件得列联表如下：物理成绩为A 等 物理成绩不为A 等 合计男生 14a = 46b = 60 女生 6c =34d =40合计2080100n =因为22100(1434646)251.0422.7062080604024K ⨯⨯-⨯==≈<⨯⨯⨯．.....................10分 所以，没有90%的把握认为“该校高二年级学生在本次考试中物理成绩为A 等与性别有关”．......12分20．解：（1）由题得:2221+=1a b,因为2222c a b e a a -===，解得224,2a b ==．R所以椭圆C 的方程为22142x y +=．....................................5分 （2）由（1）知12(2,0),(2,0)A A -，由题意设011(2,),(,)M y R x y ，易知直线1MA 的方程为：0042y y y x =+，代入椭圆22142x y +=，得2222000(1)40822y y y x x +++-=．所以201204(8)(2)8y x y --⨯=+，解得201202(8)8y x y --=+，从而012088y y y =+， 所以22200000222200002(8)84(8)8(,)(2,)48888y y y y OR OM y y y y y ----⋅=⋅=+=++++，即OR OM ⋅为定值．....................................12分 21.（1）解：由()xf x x ae=+可得()1xf x ae '=+．当0a ≥时，()0f x '>，则函数()f x 在(,)-∞+∞上为增函数．当0a <时，由()0f x '>可得1ln()x a <-，由()0f x '<可得1ln()x a>-； 则函数()f x 在1-ln())a ∞-（，上为增函数，在1(ln(),)a-+∞上为减函数．..............6分 （2）证明：令2()(1)()F x x a x xf x '=++-．则xax ax x x f x x a x x F e )()1()(22-+='-++=)e (xa a x x -+= 令=)(x H xa a x e -+，则=')(x H xa e 1-．1e 0,0<<∴<x x ，又1≤a ，0e 1e 1>-≥-∴x x a ．)(x H ∴在)0,(-∞上为增函数，则0)0()(=<H x H ，即0e <-+x a a x ．由0<x 可得0)e ()(>-+=xa a x x x F ，所以)()1(2x f x x a x '>++．................................12分22.解：（1）C 是劣弧BD 的中点CAB DAC ∠=∠∴在AEC RT ADG RT ∆∆与中，90=∠=∠AEC ADBACE DGA ∠=∠∴,又CGF DGA ∠=∠,所以CGF ACE ∠=∠.从而，在CGF ∆中，FG CF=.................................5分（2）在AEC RT ADG RT ∆∆与中，,CAB DAC ∠=∠ 因此，ADG RT ∆∽AEC RT ∆，由此可得ACCEAG DG =,即CE AG AC DG ⋅=⋅...........10分 23.解：（1）直线l 的普通方程为01=+-y x ,曲线2C 的直角坐标方程为4)2(22=-+y x ;..........5分 （2）解法一、曲线2C ：4)2(22=-+y x 是以点（0,2）为圆心，2为半径的圆，圆心（0,2）到直线01=+-y x 的距离22=d ，则142142=-=AB ..........10分解法二、由⎩⎨⎧=-+=+-040122y y x y x 可解得A,B 两点的坐标为⎪⎪⎭⎫ ⎝⎛--⎪⎪⎭⎫ ⎝⎛++273,271,273,271，由两点间距离公式可得14=AB ..........10分 解法三、设B A 、两点所对应的参数分别为B A t t ,将为参数）t t y tx (222221⎪⎪⎩⎪⎪⎨⎧+=+=代入0422=-+y y x 并化简整理可得 0322=-+t t ，从而⎩⎨⎧-=-=+32B A B A t t t t 因此，144)(2=-+=B A B A t t t t AB ..........10分24.解：（1）不等式5)(>x f 即为512>-++x x ，等价于⎩⎨⎧>+----<5122x x x 或⎩⎨⎧>+-+≤≤-51212x x x 或⎩⎨⎧>-++>5121x x x ，解得23>-<x x 或. 因此，原不等式的解集为{}23>-<x x x 或...........5分（2）3)1()2(12)(=--+≥-++=x x x x x f要使()1f x a ≥-对任意实数R x ∈成立，须使，13a -≤解得：24a -≤≤。

2017届高三第一次五校联考政治试题命题：长治二中忻州一中临汾一中康杰中学晋城一中(考试时间90分钟满分100分)第Ⅰ卷（选择题）（共48分）本卷共24小题，每小题2分，共48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. 假定去年某国待售商品价格总额为4 000亿元，货币流通次数为8次。

今年该国待售商品价格总额增加了20%，实际纸币发行量为900亿元。

在其他条件不变的情况下,去年售价60元的商品今年的售价应为A.108元B.96元C.90元D.80元2. 从2016年6月份以来,羊肉的价格不断上涨,究其原因是由于养殖成本提高和产量减少。

图像中横轴为供求量Q,纵轴为价格P,D为需求线,S为供给线,E为均衡价格,变动的方向为D→D1,S→S1,E→E1。

下面能够正确反映这种变化的图像是3. 2015年12月1日，国际货币基金组织主席宣布将人民币纳入特别提款权(SDR)货币篮子并于2016年10月1日正式生效。

人民币入篮之后，小明计划在美国购买一套100万美元的房产，下列说法正确的是①可以直接用人民币购买②手持人民币币值更加稳定，无须担心本币贬值③降低汇兑成本并且避免货币风险④人民币将不断升值A.①②B.①③C.②④D.①④2016年上半年国内智能手机销量统计,华为以4377万部销量的成绩远胜屈居第二名的OPPO，国产一哥地位坚不可摧。

据此回答4、5题。

4．华为手机以其清新的屏幕，超强的PC级处理器，精细的做工，强大的拍照技术等优点吸引来大批消费者。

消费者对华为手机的青睐，也推动着它的不断升级。

这说明①消费是实现社会再生产顺利进行的桥梁和纽带②生产决定消费的方式③新的消费需求对产品的升级换代起着导向作用④生产决定消费的质量和水平并为消费创造动力A.①②B.②④C.①③D.③④5．周某花999元买了一部华为手机，电信公司除分期返还500元话费外，两年内每月还赠送150兆的流量。

在这里①999元是手机价值的货币表现②电信公司优惠的目的在于提高用户体验③150兆流量的价值是通过服务体现的④返还的500元话费执行流通手段的职能A.①③B.①②C.②④D.③④6. 对同一商品或服务，不同消费者的支付意愿(即买者愿意为某种物品支付的最高量)是不同的。

山西省长治二中、晋城一中、康杰中学、临汾一中、忻州一中五校2017届高三第四次联考试题(文)一、选择题(共12小题，每小题4分，共48分)1．已知a ∈R ，则“a ＞2”是“a 2＞2a ”成立的( )A ．充分不必要条件B ．必要不充分条件C ．充要条件D ．既不充分也不必要条件2．若a ，b ∈R ，且ab ＞0，则下列不等式中，恒成立的是( )A ．a 2＋b 2＞2abB ．a ＋b ≥2ab C.1a ＋1b ＞2ab D.b a ＋a b≥2 3．设0＜a ＜1，m ＝log a (a 2＋1)，n ＝log a (a ＋1)，p ＝log a (2a )，则m ，n ，p 的大小关系是( )A ．n ＞m ＞pB ．m ＞p ＞nC ．m ＞n ＞pD ．p ＞m ＞n4．已知等差数列{a n }与等比数列{b n }，满足a 3＝b 3,2b 3－b 2b 4＝0，则{a n }前5项的和S 5为( )A ．5B ．20C ．10D ．405．等差数列{a n }的前n 项和为S n ，已知a m －1＋a m ＋1－a 2m ＝0，S 2m －1＝38，则m 等于( )A ．2B ．9C ．10D ．196．各项均为正数的等比数列{a n }的前n 项和为S n ，若S n ＝3，S 3n ＝39，则S 4n 等于( )A ．80B ．90C ．120D ．130 7．当x ，y 满足⎩⎪⎨⎪⎧ |x －1|≤1，y ≥0，y ≤x ＋1时，则t ＝x ＋y 的最大值是( ) A ．1B ．2C ．3D ．58．在△ABC 中，已知a 2－b 2－c 2＝2bc ，则B ＋C 等于( )A.π4B.3π4C.5π4D.π4或3π49．若{a n }是等差数列，首项a 1＞0，a 2016＋a 2017＞0，a 2016·a 2017＜0，则使前n 项和S n ＞0成立的最大自然数n 是( )A ．4031B ．4033C ．4034D ．403210．已知二次函数f (x )＝cx 2－4x ＋a ＋1的值域是[1，＋∞)，则1a ＋9c的最小值是( ) A ．1B ．2C ．3D ．411．已知a ，b ，m ，n ，x ，y 都是正实数，且a ＜b ，又知a ，m ，b ，x 成等差数列，a ，n ，b ，y 成等比数列，则有( )A ．m ＞n ，x ＞yB ．m ＞n ，x ＜yC ．m ＜n ，x ＞yD ．m ＜n ，x ＜y12．两个等差数列{a n }和{b n }的前n 项和分别为S n 和T n ，已知S n T n ＝5n －9n ＋3，则使a n ＝tb n 成立的正整数t 的个数是( )A ．3B ．6C ．4D ．5二、填空题(包括4小题，每小题4分，共16分)13．不等式－x 2＋|x |＋2＜0的解集是____________．14．已知由正数组成等差数列{a n }的前20项和为100，那么a 7·a 14的最大值为________．15．设等差数列{a n }的前n 项和为S n ，若2a 6＝6＋a 7，则S 9的值是______．16．若a ＞1，设函数f (x )＝a x ＋x －4的零点为m ，函数g (x )＝log a x ＋x －4的零点为n ，则1m＋1n的最小值为______．三、解答题(包括6个题，17、18题各8分，19、20、21,22题10分，共56分，请写必要的解答过程)17．(8分)已知函数f (x )＝log 2(|x ＋1|＋|x －2|－m )．(1)当m ＝7时，求函数f (x )的定义域；(2)若关于x 的不等式f (x )≥2的解集是R ，求m 的取值范围．18．(8分)在△ABC 中，a ，b ，c 分别为内角A ，B ，C 所对的边长，a ＝3，b ＝2，1＋2cos(B ＋C )＝0，求：(1)∠A 的大小；(2)边BC 上的高．19．(10分)在△ABC 中，角A ，B ，C 所对的边分别为a ，b ，c ，已知cos C ＋(cos A －3sin A )cos B ＝0.(1)求∠B 的大小；(2)若a ＋c ＝1，求b 的取值范围．20．(10分)已知在正整数数列{a n }中，前n 项和S n 满足S n ＝18(a n ＋2)2. (1)求数列{a n }的通项公式；(2)若b n ＝12a n －30，求数列{b n }的前n 项和的最小值．21．(10分)已知在等差数列{a n }中，公差d ＞0，其前n 项和为S n ，且满足：a 2·a 3＝45，a 1＋a 4＝14.(1)求数列{a n }的通项公式；(2)令b n ＝2S n 2n －1，f (n )＝b n n ＋25 ·b n ＋1(n ∈N *)，求f (n )的最大值．22．(10分)数列{a n }的前n 项和为S n ，若a 1＝3，S n 和S n ＋1满足等式S n ＋1＝n ＋1n S n＋n ＋1， (1)求S 2的值；(2)求证：数列{S n n}是等差数列； (3)若数列{b n }满足b n ＝a n ·2a n ，求数列{b n }的前n 项和T n ；(4)设C n ＝T n 22n ＋3，求证：C 1＋C 2＋…＋C n ＞2027.参考答案1．A [由a 2＞2a ，得a ＞2或a ＜0，则“a ＞2”是“a 2＞2a ”成立充分不必要条件．]2．D [对于A ，a 2＋b 2≥2ab 所以A 错；对于B ，C ，ab ＞0，只能说明a ，b 同号，若a ，b 都小于0，则B ，C 不成立； ∵ab ＞0，∴b a ＋a b≥2.] 3．D [取a ＝0.5，则a 2＋1，a ＋1,2a 的大小分别为1.25,1.5,1，又因为0＜a ＜1时，y ＝log a x 为减函数，所以p ＞m ＞n .]4．C [2b 3－b 2b 4＝2b 3－b 23＝0，求得b 3＝2，∴a 3＝b 3＝2，∴S 5＝ a 1＋a 5 ·52＝a 3·5＝10.] 5．C [由等差数列的性质可得a m －1＋a m ＋1＝2a m ，又∵a m －1＋a m ＋1－a 2m ＝0，∴2a m －a 2m ＝0，解得a m ＝0或a m ＝2，又S 2m －1＝ 2m －1 a 1＋a 2m －1 2＝ 2m －1 ×2a m 2＝(2m －1)a m ＝38， ∴a m ＝0应舍去，∴a m ＝2，∴2(2m －1)＝38，解得m ＝10.]6．C [由已知可得，公比q ≠1，q ＞0.∵S n ＝3，S 3n ＝39，∴a 1 1－q n 1－q ＝3，a 1 1－q 3n 1－q＝39，化为q 2n ＋q n －12＝0，解得q n ＝3.∴a 11－q＝－32. 则S 4n ＝a 1 1－q 4n 1－q＝－32×(1－34)＝120.] 7．C[满足约束条件⎩⎪⎨⎪⎧ |x －1|≤1，y ≥0，y ≤x ＋1的平面区域如图示：由图得，当t ＝x ＋y 过点B (1,2)时，x ＋y 有最大值3.]8．A [在△ABC 中，由a 2－b 2－c 2＝2bc ，利用余弦定理可得cos A ＝b 2＋c 2－a 22bc ＝－22， ∴A ＝3π4，∴B ＋C ＝π－A ＝π4.] 9．D [∵{a n }是等差数列，首项a 1＞0，a 2016＋a 2017＞0，a 2016·a 2017＜0，∴a 2016＞0，a 2017＜0，公差d ＜0，∴S 4032＝4032 a 1＋a 4032 2＝2016(a 2016＋a 2017)＞0， S 4033＝4033 a 1＋a 4033 2＝4033a 2017＜0. 使前n 项和S n ＞0成立的最大自然数n 是4032.]10．C [∵二次函数f (x )＝cx 2－4x ＋a ＋1的值域是[1，＋∞)，∴c ＞0，且4c a ＋1 －164c＝1，即ac ＝4， ∴a ＞0， ∴1a ＋9c ≥21a ·9c ＝3，当且仅当1a ＝9c时取等号， 又∵ac ＝4，c ＝6，a ＝23， ∴1a ＋9c的最小值为3.] 11．B [因为a ，m ，b ，x 成等差数列，a ，n ，b ，y 成等比数列，所以m ＝a ＋b 2，n ＝ab ， 由基本不等式得m ≥n ，又a ＜b ，所以a ，b ，m ，n ，x ，y 互不相等，所以m ＞n ，b ＝m ＋x 2由均值不等式得mx ＜m ＋x 2， 即 b ＞mx ，b ＝ny ＞mx ，因为m ＞n ，所以x ＜y ，综上，得m ＞n ，x ＜y .]12．C [当5n －9n ＋3＝1，即n ＝3时，S 3T 3＝a 1＋a 2＋a 3b 1＋b 2＋b 3＝3a 23b 2＝a 2b 2，则a 2＝b 2，此时t ＝1；当5n －9n ＋3＝2，即n ＝5时，S 5T 5＝a 1＋a 2＋…＋a 5b 1＋b 2＋…＋b 5＝5a 35b 3＝a 3b 3＝2，则a 3＝2b 3，此时t ＝2； 当5n －9n ＋3＝3，即n ＝9时，S 9T 9＝a 1＋a 2＋…＋a 9b 1＋b 2＋…＋b 9＝9a 59b 5＝a 5b 5＝3，则a 5＝3b 5，此时t ＝3； 当5n －9n ＋3＝4，即n ＝21时，S 21T 21＝a 1＋a 2＋…＋a 21b 1＋b 2＋…＋b 21 ＝21a 1121b 11＝4，则a 11＝4b 11，此时t ＝4， 当5n －9n ＋3≥5时，解得的n 不为正整数， 所以满足题意的正整数t 的个数是4.]13．{x |x ＜－2或x ＞2}解析 x ≥0时，－x 2＋x ＋2＜0，解得x ＞2或x ＜－1(舍)；x ＜0时，－x 2－x ＋2＜0，解得x ＞1(舍)或x ＜－2，故答案为{x |x ＜－2或x ＞2}．14．25解析 ∵由正数组成等差数列{a n }的前20项和为100，∴a 1＋a 20＝10010＝10， ∴a 7＋a 14＝10，∴a 7·a 14≤⎝⎛⎭⎫a 7·a 1422＝25.∴a 7·a 14≤25. 15．54解析 ∵等差数列{a n }的前n 项和为S n,2a 6＝6＋a 7，∴2(a 1＋5d )＝6＋a 1＋6d ，∴a 1＋4d ＝a 5＝6，∴S 9＝92×(a 1＋a 9)＝9a 5＝9×6＝54. 16．1解析 由题意，构建函数F (x )＝a x ，G (x )＝log a x ，h (x )＝4－x ，则h (x )与F (x )，G (x )的交点A ，B 的横坐标分别为m ，n .注意到F (x )＝a x ，G (x )＝log a x ，关于直线y ＝x 对称，可以知道A ，B 关于y ＝x 对称， 由于y ＝x 与y ＝4－x 交点的横坐标为2，∴m ＋n ＝4.则1m ＋1n ＝14(1m ＋1n )(m ＋n )＝14(2＋n m ＋m n )≥14(2＋2n m ·m n)＝1， 当且仅当m ＝n 时等号成立，故1m ＋1n的最小值为1.17．解 (1)由题设知当m ＝7时，|x ＋1|＋|x －2|＞7，不等式的解集是以下不等式组解集的并集⎩⎪⎨⎪⎧ x ≥2，x ＋1＋x －2＞7或⎩⎪⎨⎪⎧ －1≤x ＜2，x ＋1＋2－x ＞7或⎩⎪⎨⎪⎧x ＜1，－x －1－x ＋2＞7， 解得函数f (x )的定义域为(－∞，－3)∪(4，＋∞)．(2)不等式f (x )≥2，即|x ＋1|＋|x －2|≥m ＋4，∵x ∈R 时，恒有|x ＋1|＋|x －2|≥|(x ＋1)－(x －2)|＝3，∵不等式|x ＋1|＋|x －2|≥m ＋4的解集是R ，∴m ＋4≤3，故m 的取值范围是(－∞，－1]．18．解 (1)因为1＋2cos(B ＋C )＝0，A ＋B ＋C ＝π，所以cos A ＝12，sin A ＝32，A ＝π3. (2)由正弦定理得sin B ＝b sin A a ＝22， 由b ＜a 知B ＜A ，所以B 不是最大角，B ＜π2.从而cos B ＝1－sin 2B ＝22， 由上述结果知B ＝π4，C ＝5π12， sin C ＝sin(A ＋B )＝sin(π4＋π3)， 设边BC 上的高为h 则有h ＝b sin C ＝2sin(π4＋π3)＝2(22×12＋22×32)＝3＋12. 19．解 (1)由已知得－cos(A ＋B )＋cos A cos B －3sin A cos B ＝0，即sin A sin B －3sin A cos B ＝0，∵sin A ≠0，∴sin B －3cos B ＝0，即tan B ＝3，又∵B 为三角形的内角，则B ＝π3. (2)∵a ＋c ＝1，即c ＝1－a ，cos B ＝12， ∴由余弦定理得b 2＝a 2＋c 2－2ac ·cos B ，即b 2＝a 2＋c 2－ac ＝(a ＋c )2－3ac ＝1－3a (1－a )＝3(a －12)2＋14， ∵0＜a ＜1，∴14≤b 2＜1，则12≤b ＜1. 20．解 (1)∵S n ＝18(a n ＋2)2，∴当n ＝1时，a 1＝18(a 1＋2)2，化为(a 1－2)2＝0，解得a 1＝2. 当n ≥2时，a n ＝S n －S n －1＝18(a n ＋2)2－18(a n －1＋2)2，化为(a n －a n －1－4)(a n ＋a n －1)＝0， ∵∀n ∈N *，a n ＞0，∴a n －a n －1－4＝0，∴a n －a n －1＝4.∴数列{a n }是等差数列，其首项为2，公差为4，∴a n ＝2＋4(n －1)＝4n －2.(2)b n ＝12a n －30＝12(4n －2)－30＝2n －31. 由b n ≤0，解得n ≤312，因此前15项的和最小． 又数列{b n }是等差数列，∴数列{b n }的前15项和T 15＝15× －29＋2×15－31 2＝－225. ∴数列{b n }的前n 项和的最小值为－225.21．解 (1)∵数列{a n }是等差数列，∴a 1＋a 4＝a 2＋a 3＝14.又a 2·a 3＝45，∴⎩⎪⎨⎪⎧a 2＝5，a 3＝9或⎩⎪⎨⎪⎧ a 2＝9，a 3＝5. ∵公差d ＞0，∴⎩⎪⎨⎪⎧ a 2＝5，a 3＝9，解得d ＝4，a 1＝1. ∴a n ＝1＋4(n －1)＝4n －3.(2)∵S n ＝na 1＋n n －1 d 2＝2n 2－n ， ∴b n ＝2S n 2n －1＝2n ， ∴f (n )＝b n n ＋25 ·b n ＋1＝2n n ＋25 ·2 n ＋1＝n n 2＋26n ＋25＝1n ＋25n ＋26≤126＋2 25n ·n＝126＋10＝136，当且仅当n ＝25n ，即n ＝5时，f (n )取得最大值136. 22．(1)解 ∵S n ＋1＝n ＋1n S n＋n ＋1， 当n ＝1时，S 2＝2S 1＋2＝2a 1＋2＝8，故S 2＝8.(2)证明 ∵S n ＋1＝n ＋1n S n＋n ＋1， ∴S n ＋1n ＋1＝S n n ＋1，即S n ＋1n ＋1－S n n＝1. 又∵S 11＝a 1＝3， 故{S n n}是以3为首项，以1为公差的等差数列． (3)解 由(2)可知，S n n＝n ＋2， ∴S n ＝n 2＋2n (n ∈N *)，∴当n ＝1时，a 1＝3，当n ≥2时，a n ＝S n －S n －1＝2n ＋1，经检验，当n ＝1时也成立，∴a n ＝2n ＋1(n ∈N *)，又∵b n ＝a n ·2a n ，∴b n ＝(2n ＋1)·22n ＋1， T n ＝b 1＋b 2＋…＋b n －1＋b n ，∴T n ＝3·23＋5·25＋…＋(2n －1)·22n －1＋(2n ＋1)·22n ＋1 ∴4T n ＝3·25＋…＋(2n －3)·22n －1＋(2n －1)·22n ＋1＋(2n ＋1)·22n ＋3 解得T n ＝⎝⎛⎭⎫23n ＋19·22n ＋3－89. (4)解 ∵C n ＝T n 22n ＋3＝2n 3＋19－19·(14)n ， ∴C 1＋C 2＋…＋C n ＝23·n n ＋1 2＋19·n －19·14[1－ 14 n ]1－14＝3n 2＋4n 9－127＋127·(14)n ＞3n 2＋4n 9－127≥79－127＝2027.。