(2)为调查消费者对该汽车的评价情况，随机抽查了200名消费者，得到如下列联表，请了。填写下面的22列联表，依据。001的独立性检验，能否认为消费者是否喜欢该汽17车与性别有关联喜欢不喜欢总计男100女60总计110(x-y-列参考公式：相关系数”2-到2-列参考数据：√10≈3.162.线性回归方程：-aa天中6含-∑xy-阿n(ad-be)2(-到之-,a=y-6版，t=(a+bc+d(a+cb+d临界值表：0.0100.0050.001Xa6.6357.87910.82821.(12分)已知A(-1,0),B(1,0),直线1与2分别过A、B点，且直线1与直线2交于点P且1与2的斜率之积为3，若动点P的轨迹为曲线C(1)求曲线C的标准方程，(2)设Q为y轴右侧曲线C上的一个动点，F(2,0),在x轴的负半轴上是否存在定点M.使得∠QFM=2∠QMF？若存在，求出点M的坐标；若不存在，请说明理由22.(12分)已知函数f(x)=xlnx-a2-x,aeR.4-01)若关于x不等式xlnx-ax2-x>0有解，求a的取值范围：(2)设fx)有两个极值点x,x(:
教学爱好者七年级同步训练下册（华师大版）。SHUXUE AIHAO ZHE3.从n边形的内角和公式(n-2)·1807.一个正多边形的一个内角的度数比相邻外可知n边形的内角和一定是180°的整数倍，角的6倍还多12°，求这个正多边形的内且每增加一条边，内角和就增加180°.多边形角和.的外角和恒等于360°，与边数多少无关四随堂演练A组基础巩固1.五边形的内角和是A.180B.360°C.540°D.7202.已知一个多边形的内角和为1080°，则这个多边形是A.九边形B.八边形C.七边形D.六边形3.一个多边形的每个内角均为108°，则这个多边形是(A.七边形B.六边形C.五边形D.四边形4.内角和与外角和相等的多边形是5.一个多边形的内角和为720°，从这个多边8.若∠A与∠B的两边分别垂直，请判断这形同一个顶点画对角线，可以将这个多边两个角的等量关系。形分成个三角形6.图1是我国古代建筑中的一种窗格，其中冰裂纹图案象征着坚冰出现裂纹并开始消融，形状无一定规则，代表一种自然和谐美.图2是从图1冰裂纹窗格图案中提取图1图2的由五条线段组成的图形，则∠1+∠2+(1)如图1，∠A与∠B的关系是∠3+∠4+∠5=如图2，∠A与∠B的关系是对于上面两种情况，请用文字语言叙述图1图2。106·
2,解：1)因为S与(n一1)a,的等差中项是号，所以Sm十(n十1)am=3,可得S1+2a1=3,即a1十2a1=3,獬得a1=1.(2)由(1)知Sm+(n+1)am=3,当n≥2时，Sm-1+nan-1=3,两式相减得(n+2)am=nam-1,所以十2≥2.(3)结合1.(2)知a=1a21n”22,所以an=a1Xa2XaXa4X…Xam1Xamal az a3an-2 an-1=1×星×g××…×Xn6n+i×n+2-(n+1)(n+2)6当n=1时，+1)1十2=1,4=1也符合上式，所以数列{an}的通项公式为a.=(n十1)(n+2)意·5·【23新教材·YK·数学·参考答案一RA一选择性必修第二册一G DONG】
es主题语境：入一本文是议论文。善良具有ostol.但真正的善良并不是一味满足他人的要求，也要54.学会拒绝。根据第一段中的在作32.A。理解具体信息。According to the Mayo Clinic,whenwe虑或perform acts of kindness,the pleasure center in55Aobrainisactivated,releasingthemoveourstress-reducing hormone可知，梅奥诊所发现，my le当我们做善事时，我们大脑中的快感中枢被把自激活，释放出减压激素。即做善事可帮助减(clos轻压力，有益心理健康。57.B。33.C。推断。第三段和第四段假设了一段情景：假设你是团队新人，你很友好，告诉团队说自可知己随时准备帮忙。可是当你己经在这个团队有iff工作了一年，你的同事还是不断请求你的帮59.B。2V助，他们与你唯一的互动就是他们需要帮助和it,根的时候，并且他们很少给予你回报。再结合静地ber第三段中的interpret your kindness as a本空可weakness.This can lead to you being taken60.advantage of by others可知，有的人将你的善实的良理解为软弱，他们在利用你。由此可推知，【背此时你可能会感觉受挫和失望。PT到34.D。推断。根据you need to be willing to saydisorde“no.”和Recognize when可推知，划线部分表应，症ith明何时应该拒绝别人。结合后面的Whn创伤事ompeople ask you for a favor,assess if you have地震the time,energy,and attention to give to themors(当别人请求帮助时，你要看看你是否有时题请泳间、精力和注意力来帮他们)可推知，划线部分是指当你没有时间、精力和注意力的时候，ble要勇于拒绝别人。61.thIf35.B。理解主旨要义。本文阐释了虽然善良有ny益身心，但是真正的善良并不是一味满足他62athe人要求，因为有人会将善良理解为软弱。因此要勇于拒绝别人，否则我们会被善良所累，636B项作标题最为恰当。kill sb with kindness意为“过分好心反而害了某人”64.【词汇链接】that said(para.2)意为“话虽如此”第二节主题语境：人与社会一文化65的本文是记叙文。作者是爱尔兰学生，参加了and孔子学院举办的到中国交流的活动，被中国人的a及友好和中国文化打动6636.C。根据设空处后面的It involved oneornhundred.visit Shanghai for two weeks可知，cled设空处应点明指代什么。结合设空处前面67ack读产的I was lucky enough to visit China和后面的68系列visit Shanghai可知，lt指代中国之旅，C项“我比可参加了一次孔子学院举办的旅行”符合语境。末段37.F。根据设空处后面的She even invited me to69have lunch with her可知，设空处应点明She指hion代谁。结合设空处前面的I was alone,.ying70sevicto order an ice cream in a shop H My Chinese接着wasn't good enough to convey what I wanted可知，“我”想买冰淇淋，但汉语不好，故可知F
按秘密级事项管理★启用前2023年替通高等学校招生全国统一考试数学冲刺卷（三）15x,圆柱的侧面积为18π，则该毡帐的体积为A.39π6.已知抛物线C,r=2pp>0)的焦点为.点E2,0,线段年与驰物线C相交于B.18rC.38xD.45x交回本以感共2题印分，寺议时间10分的，考试特求后将本改意和客海卡一并程为注意事项：点M,若抛物线C在点M处的切线与直线2x+y十2=0戴，则驰物线C的方A.x2=3y意清题前，考生先精自已的姓名、考生号、考场号和座位号填写清地，将条形码准骑B.x2=12yC.2=9y粘贴在条形码区域内，D.2-6y2造拼题必须睫用B铅笔填涂，非选择必须使用Q,5毫米果色字迹的签字笔书7.已知函数(x)是定义在R上的奇函数，f0-2x)为偶函数，且f(-1)=1,则写，字体工整，笔迹清楚1f(-10)1+1f-9)1+…+1f0)1+1f1)1++1f9)1+f101=A.10B.20清技期是号顺序在答题卡含题目的答短区域内作答，超出答题区域书写的答案无C.15效：在草稿纸、试卷上答题无效。8已知实数西满足心=会，nx=号D.5A.1,则1=上作图可先使用铝笔百出，确定后必须用黑色字迹的签字笔描黑B.2保持卡面清言，不要折叠，不要弄破、弄皱不准使用涂改液、修正带、刮纸刀.一选择题：本题共8小题，每小通5分，共40分.在每小题给出的四个选项中，只有一二、选择题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合C.4D.8题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分。项是符合题目要求的，9.某公司经营五种产业，为应对市场变化，在五年前进行了产业结构调整，优化后的产1.设全集U=rEZ-3Kx<2,A={-1,1,B={0,则(A)UB业结构使公司总利润不断增长，今年总利润比五年前增加了一倍，调整前后的各产A.{-3,-2,0}B.{-2,0}业利润与总利润的占比如图所示，则下列传媒2.复数x满足x+i十2=0，则|z=C.{0}结论错误的是、图书D.{-2,0,1}10%图书25%传蝶)12%32%A.1A.调整后传媒的利润增量小于杂志B.345%5%C.2D.2B.调整后房地产的利润有所下降房地15%25%&已知圆C号+号1的左，右焦点分别为R,R,过点乃的直线！与椭圆C的C.调整后试卷的利润增加不到一倍23%试卷房地产X试卷D.调整后图书的利润增长了一倍以上调整前调整后个交点为A,若AF,=4,则△AFF2的面积为A23B.√13C.44.设函数fx)在R上可导，且f(nx)=x十lnx,则f(0)=D.√1510.如图所示，四边形ABCD为等腰梯形，CD∥AB,CD=AB,EF分别为DC,AEA.0的中点，若AD=入A店+：B(a∈R),则B.1C.25,在马致远邮汉宫秋)楔子中写道：“毡帐秋风迷宿草，穹庐夜月听D.3AA=号B.μ=2悲笳”毡帐是古代北方游牧民族以为居室，毡制帷幔，如图所示，某毯帐可视作-个圆锥与圆柱的组合体，圆锥的高为4，侧面积为D.a=111,已知正方体ABCD-A1B,CD,的棱长为2，O,为四边形ABGD的中心，P为全细m彩级最新高考种南卷第1页C失8页列【23·（断离考）00·数学（三）一门线段AO,上的一个动点，Q为线段CD,1上一点，若三棱能Q-PBD的体积为定值，则全细10所名校最新高考冲刺卷第2页（共8页）【25·（惭高考）0四数学（三）一门
第15期第1-4版参考答案第1版FOCUS 1-3 ACDAROUND THE WORLD1.Because they are most likely to have negative type blood.2.In 2015.At the age of three.第2版KEY POINTSSection A1.putting 2.to take 3.in a row4.Shall weSection B1.believe in 2.for 3.Ahead of4.isMY COLLECTION【重点单词】1.survey 2.standard 3.keyboard4.instruction 5.double6.overcome7.text 8.level 9.degree10.manager11.congratulate 12.thirsty13.task 14.ahead 15.separate16.wing 17.caring 18.thankful【必背短语】1.do a survey 2.in a row 3.be patient with sb.4.work out5.look back at 6.prepare for..7.make a mess 8.keep one's cool9.look forward to10.go by 11.believe in 12.first of all
3100分以上的试卷中抽取的份数为)14已知点A是焦点为P的抛物线Py二：工的动点，且不与坐标原0重合，线段OA的垂直分线交x轴于点B.若AF=2C京，则AB一AC=15者项数为n的数列但，满足：a,=-,23,我们称其为n项的对称数列例如：数列12,2,1为4项的对称数列：数列1,23,2,1为5项的“对称数列”设数列(c)为2-1(>2)项的“对称数列”，其中c,2c,…,0是公差为2的等差数列，数列{(c,)的最大项等于8.记数列(c)的前2k一1项和为S2-1,若S24-1=32,则k=16,如图，点P是半径为2的圆0上一点，现将如图放置的边长为2的正方形ABCD(顶点A与P重合)沿圆周逆时针滚动，若从点A离开圆周的这一刻开始，正方形滚动至使点A再次回到圆周上为止，称为正方形滚动了一轮，则当点A第一次回到点P的位置时，正方(A形滚动了轮，此时点A走过的路径的长度为四、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、证明过程及演算步骤，(第一空2分，第二空3分)17.(10分)如图，在直三棱柱ABC-A1B,C中，AC⊥BC,AA=BC=2,且二面角为A1-BC-A为45°.(1)求棱AC的长；(2)若D为棱A1B的中点，求面CCD与面A,BC夹角的正切值18.(12分)》已知函数f(x),g(x)满足关系g(x)=f(x)·f(x+a),其中a是常数.(1)设f(x)=cosx+sinx,a=受，求g(x)的解析式；(2)当f(x)=|sinx十cosx,a=5时，存在x,∈R,对任意x∈R,g(x)≤g(x)≤g(2)恒成立，求|x1一x2|的最小值.2水19.(12分)若等差数列(a)的前n项和为S,数列6，是等比数列，并且6>0a=3,6=1,6十S,19,a4-2b2=a2.(1)求数列{an}和{bn}的通项公式；(2)求数列b的前n项和Tn个共，代盟小君，服小共国大本每空射【2023届高三⑦联·数学第3页（共4页）N,AH,SX,HJJL)
【/8题详解】上文“I'm happy as the day goes along,,”a senior fitness expert says.(一位资深健身专家说，我一天都过得很开心)”说明了锻炼给他带来的好处，与t项“I exercise in the morning to get my body functioning..(我在早上锻炼身体，这让我的身体机能开始正常运转)”构成因果关系，同时与小标题“Make Time for Exercise(腾出时间来锻炼)”相照应。故选￡。【19题详解】上文“As you grow older,.you may lose interest in staying active..(随着年龄的增长，你可能会渐渐变得不再积极)”说明了人们往往会随着年龄的增长变得懒散，疏于锻炼，与A项“But life lies in constant motion.(但生命在于不断地锻炼)”构成转折关系，告诫大家不要停下来，继续锻炼，同时引出下文。故选A。【20题详解】上文“The aim of exercise is to relax..(锻炼的目的是放松)”说明在锻炼过程中遇到疼痛，要学会去缓解，最终达到放松的目的，而不是无限制地逼迫自己，与G项“Remember not to push yourself too far or past your limits.(记得不要把自己逼得太凶，超过自己的极限)”表述一致，构成递进关系。故选白。第三部分语言知识运用（共两节，满分45分)第一节（共20小题；每小题1.5分，满分0分)阅读下面短文，从短文后各题所给的A、B、C和D四个选项中，选出可以填入空白处的最佳选项。A series of severe thunder storms struck our area recently.Heavy rains,strong winds,and lots of lightening had__21flash flooding and even swept down trees.I had spent the afternoon22branches out of my yard.Then just before I was getting23to take my dogs for their last walk of the day the24come on mytelevision and over my phone that another storm was __25_I quickly took my dogs outside.Huge and_26_clouds were rolling in while thunder27over thehills.Despite this,I knew that the stars were shining and the moon was smiling up_28_but I just couldn't seethem.The blink of light,up high,at the far end of the meadow (might hide behind my__29.I smiled.Itamazed me how far their light30 in the darkness of the night and how they didn't seem31at all by the approaching storm.I felt that the32_no longer seemed so scary and thatmy fear had been33_with relief and joy.Life does have its34of storms,some caused by35and some caused by us.We can'tgo through life being scared of them,36.We are here to shine our light.We are here to share our love.Weare bound to ride through the __37_,clean up after them,and make this world a38_place.Lightmay seem tiny but you will be39at how far it can be seen and how easily it can40the dark
按秘密级事项管理★启用前2023年普通高等学校招生全国统一考试数学样卷（二）交本试春共2题，共150分，考试时同120分钟，考孩结来后，将本线%和名1注意事项：密1.答题前，考生先将自己的姓名、考生号、考场号和座位号填写清楚，名务形粘贴在条形码区域内.2.选择题必须使用2B铅笔填涂：非选择题必须使用0,5毫米黑色字透的签写，字体工整，笔迹清楚，3.请按照题号顺序在答题卡各题目的答题区域内作答，超出答题区域书写的答效；在草稿纸、试卷上答题无效，4,作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑，5.保持卡面清洁，不要折叠，不要弄破、弄皱.不准使用涂改液、修正带、刮纸)封一、选择题：本题共8小题，每小题5分，共40分.在每小题给出的四个选项中，项是符合题目要求的1.已知集合A={x∈Zx2+x-2<0),B={-1,2),那么AUB=A.{-1,0,1,2}B.{-1,0,2)C.{-1,2}D.{-1}C2.设3z-z=2+4i,则z=n A1-2iB.1+2iC.1+i汉1-i已知命题p:Hx>0,e≥1或sinx<1,则p为A.]x<0,e2<1且sinx>1B.]x>0,e'<1且sinx≥1C.]x≥0，e<1或sinx≥1D.3x<0,e≥1或sinx≤1修色知单位向量a,b满足a·(b一a)=一则a与b夹角的大小XRc肾D.A全国100所名校最新高考冲刺卷第1页（共8页）【23·（新高考）高考样卷·数学（二）一N
图1图2第21题图:1)如图1，直线OP即为所求；…(6分)(2)如图2.△MNP即为所求.…(12分)七、（本题满分12分）忽综合与实践：宽与长的比是5，约为0,618)的矩形叫黄金矩形.黄金矩形给我们以协调、匀称的美感，世界各国许多著名的建筑，为取得最佳的视觉效果，都采用的黄金矩形的设计，如希腊的巴特农神庙等，下面我们折叠出一个黄金矩形（如图所示）：第一步：在一张矩形纸片的一端，利用图1的方法折出一个正方形，然后把纸展.MM72图1图2第22题图第二步：如图2，把这个正方形折成两个相等的矩形，再把纸片展，第三步：折出内侧矩形的对角线AB,并把AB折到图3中所示的AD处.M图3图4第22题图第四步：展纸片，按照所得的点D折出DE,矩形BCDE(图4)就是黄金矩形.(1)证明：图1中的四边形MNCB是正方形；2)若MN=4,请通过计算瓷米说明矩形BCDE是黄金矩形.:1)证明：由矩形的性质可知∠BMN=∠N=90°，由折叠可知∠MBC=∠N=90°，MN=MB,∠BMN=∠N=∠MBC=90°，.四边形MNCB是矩形，又，MN=MB,∴.矩形MNCB是正方形：…(6分）/2):MN=4,∴.AC=2,在△ABC中，AB=√AC2+BC=√2+4=2√5，由折叠可知AD=AB=2√5，∴.BE=CD=AD-AC=2V5-2,又DE=BC=MN=4,=25-2-5-1BC2中考必制卷·2023年安徽中考第一轮复卷数学第67面1什？6面)扫描全能王创建
n off the airwhile continuing to build your chosen career.the guy looked so surWe want toMany times,students grouped in traditional classrooms are unwilling tosaid no one 58 harais the hands to either ask oraweruWith distanee learninghim to have a great dHe was in 60heir fields inprograms,studentsare able to join conversations in the bulletin board discussionand think through a question and then post the answer online.tasted really good.Internet ofareas,on a larger39Without the need to spend a semester or a year in a distant city,youC41.A.clothescan save ransportation,housing and food coss.It goes without saying that youA2.A.line可④3.A.forgethnologies tocan keep your full or part time job at the same time you matriculate()to ail to look atdistance learning institution.B44.A.crowdedimaging-With that being said,working at home can have its own set of distractions(B45.A.get by)The sound of television,or the noise coming from kids or pets can be majorC46.A.friends047.A.arealy plants,”distractions.40,such as chatting via instant messaging or surfing the web.Things like browsing()can take a lot of time in your day that could have been48.A.decidedith plants,used towards your distance learning program.A49.A.embarrassech they dident.”A.Working online can also make you more creativeC50.A.optionB.Financial benefits of distance learning exist as well51.A.dutyC 52.A.annoyedeC.Everyone in an online classroom gets a chance to contribute53.A.happycientists.D.Working online can also lead to an attempt to do something more fungive aways?E.In a room full of fellow students,pressure to avoid embarrassment is highb54.A.F.You can learn more in distance learning programs than in traditional classrooms85.A.followedG.Additionally,you may take distance learning courses from anywhere in the56.A.windowworld.A.upset第三部分语言知识运用（共两节，满分45分）》△58.A.willingly第一节（共20小题；每小题1.5分，满分30分）》liances?D59.A.instructe阅读下面短文，从短文后各题所给的A、B、C和D四个选项中，选出可以填入空C60.A.ordr白处的最佳选项。第二节(共10I stopped at a local drive-through(免下车餐馆)a while back,and remembered阅读下面短a story my high school English teacher told me.Mr.Tackett told me and a coupleLaws aredozen kids how he bought 41 for the two cars behind him in 42 at a drive-problem.A laythrough.Our young minds could not 43 why he would do such a thing.Thisthrowing awayschool was not in a very 44 neighborhood and some families were definitelyare required tostruggling to 45.The thought of a reason to be giving money away to 46(provide)milliwas beyond usfor63(th两项Now I am in a more abundant(富足的)4？_in my life and I can give back.SoSupermarlwhen at the local drive-through on a busy weekday morning I 48 in the rear-attempt to stoview mirror the man in the work truck behind me looked 49 and impatient.Ifood.A grovningsaw an 50.When it was my 51 to pay for my meal I asked the cashier if Isearching they atcould pay for the man behind me as well.They seemed 52,asked me if I wasbleach(漂白齐micsureand I said no problem,just 53 to help.I received my food and wentwho want tovithdown the parking lot to 54 what was mine and what belonged to my kiddos.FrenchThe truck came racing my way,55 next to me.I rolled down my56 andwill also incr英语试题第8页（共10页）
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1/5高一期末考试质量监测数学参考答案1.A(1-2i)(1-i)=1-i-2i+2i=-1-3i.562.C抽取的玉米中糯玉米的个数为40×42+7十56+35=16.3.B空间四边形的四个点不共面，A错误.若直线m上有无数个点不在面a内，则m∥a或m与a相交，D错误.若m∥a,则面a内存在直线与直线m不行，C错误.B正确.4.D设这5名登山爱好者为a,b,c,d,e,其中a,b为成功登顶珠穆朗玛峰的2人.从中任选2人，基本事件为(a,b),(a,c),(a,d),(a,e),(b,c),(b,d),(b,e),(c,d),(c,e),(d,e),共10个，则“恰有1人成功登顶珠穆朗玛峰”包含的基本事件有6个，故被选中的2人中恰有1人成功登顶珠穆朗玛峰的概率是品一子。5.B因为在直观图中，OA=AB=√10，所以OB=√10+10=25，所以原图形是一个底边长为√10，高为2×25=45的直角三角形，故原图形的面积为7×√10×4V5=102.6.D因为向量b在向量a上的投影向量为7a,所以。冷-号，所以ab=17.B因为A+C=2B,所以B=号，则3a2+3c2-2 acsin5=5a2+5c2-5ac=95,得a2十c2-ac=9.根据余弦定理可得b2=a2十c2-2 accos B=a2十c2-ac=9,故b=3.8.B延长FE交AA1的延长线于M,取ME的中点V,连接AN,QN,QA1.因为E,F分别为所在棱的中点，所以AE=AM,则AN⊥ME.易得FQ∥CD,则FQ⊥面ADDA1,所以FQ⊥AN.又ME∩FQ=F,所以AN⊥面EFQ.因为H为AA:的中点，所以CH∥AQ,则直线HC与面EFQ所成的角即直线A1Q与面EFQ所成的角∠AQN.设AB=4,则AQ=√32+4=6A,N=E.所以m∠AQN-会8-号.放直线HC与半面EF0所成角的正弦值为号9.ABD由图可知，2有8个顶点，13条棱，7个面，面BCD∩面ABBA=BD.10.ABD2-21i-202D_4-2i+2i-11-15+20i-3+4i1z=V9+16=2+i(2+i)(2-i)555,A正确.之=3一4i,B正确.之在复面内对应的点为(3,4)，在第一象限，C错误.之一4i=3十4i一4i=3∈R,D正确.11.AC根据正弦定理a"sin A-sin B,可得1=bsin元sinB,解得sinB=.因为b>a,所以B【高一数学·参考答案第1页（共5页）】·23-523A·吾或，则C-受或君12.BCD因为事件A={2,4,6,8},事件B={1,3,5,8},事件C={1,6,7,8},所以A∩B∩C=(8,AnB=8,AnC=(6,8,BnC=1,8),所以P(A)=P(B)=P(C)=,P(AB)=,PAC)=,PBC)=子，P(ABC)=日，所以PAB)≠P(AP(B,事件A,B不相互1独立，A错误；P(AC)=P(A)P(C),事件A,C相互独立，B正确；P(BC)=P(B)P(C),事件B,C相互独立，C正确；P(ABC)=P(A)P(B)P(C),D正确.13.9将该组数据从小到大排列为2,4,5,6,7,8,9,10，因为8×80%=6.4，所以该组数据的80%分位数为9.14.2,号由1a+b1-25,得1a+b1=12,即。2+2ab+=12.因为a-6,b-2.所
after three yearsher tacher sid."oberved hedcindand she lovedtoShe added thatringtheesbig eyesreal)watch me and how I demonstrate."She says Brigitte's concentration level is highcontinues to improve.Nicole Sun says her daughter may have more skills and interestnmusien other children."We are really lucky to have met Felicia and have her asBrigitte's first piano teacher,she said.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）限定英资课5者聚有麻之间交换修改作文，请你修改你同泉写的以下作文。文中共有,处语言错误，每何中量多有防处每处带仅涉及一个单词的增加制除或修政。增加：在缺词处加用有漏字符号（人，并在其下面写出该加的词制除：把多余的词用斜线)划掉。修：在错的词双横线：并在该词下面写出修改后的问。注意1.每处特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。是保，京十出少头Th DMV is not usully apace that peopitbdon'th!went thereknthoutapoiatment,twithplentyofrcadingmaterialstokcepmebis,wibouiknowiagC队I wuld end bethere.ThereforeIuek mthething asSoon itwasat the couerIremarked to thegentedeht was the beat run DMVer been in.Aod Icouldpride!also todhm that how much appreed that theywereefrommany different walks of life and background were all there,waiting in lineo peneden第二节书面表达（满分25分）》我们身边有许许多多值得我们学的榜样。请你以“The Power of an Example”为题写篇短文，投稿于你校英文报，内容包括：1.你的学榜样；excelient2该榜样对你的影响。注意：1.100词左右；2.题目已为你写好。The Power of an Example160he和.语第8风mw
参考答案a.-2=15(n-1),所以an=15n-13,当n=135时，a135=15×135-13=2012<2022,(2)6=2(x,-x)(y:-)14=0.1,当n=136时，a136=15×136-13=2027>2022,2(x:-元)2=1所以n=1,2,3,…,135,数列{an}共有135项，则a=y-ix=7-6×0.7=2.8,因此中位数为第68项，a6=15×68一13=1007.∴y关于x的经验回归方程为y=0.7x十2.8，答案：100714.解析：因为样本的数据互不相同，所以不妨设x1
13.已知2展开式中的常数项为80，则实数a=14.已知随机变量X~B(3,p),Y~N(4,o2),若E(X)=1P(2≤Y<4)=p,则P(Y>6)=15.已知椭圆C:父+上-1过点M(0,1)的直线1与椭圆C交于A,B两点（点A位于X轴43上方)，若AM=MB,则直线I的斜率k的值为2x16.已知X+m≤em”对任意的x∈(-m+o)恒成立，则mn的最小值为四、解答题：本题共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.(10分)已知Sn是公差不为0的等差数列{an}的前n项和，a2是a与a4的等比中项，S,=45(1)求数列{an}的通项公式；(2)已知b,=an131,求数列{h,}的前n项和Tn.18.(12分)记△ABC的内角A,B,C的对边分别为a,b,C,已知abcosA-√3c+a2cosB=0(1)求a的值：(2)如图，点D在边BC上，∠BAC=150,∠BAD=30,CD=2W33,求△ABC的面积ABD
W:Nice to meet you,Henry.I'm Betty,your student assistant.I'm here to help answer any questions you may have.Youarrived on Monday,right?M:Yes.I remember there will be an important greeting meeting on Wednesday.Do I need to prepare something?W:No,just relax.Let's get you registered so that you can get your student card.M:Do I need to bring my passport or ID card to finish the registration?I accidentally left them in my dorm.W:Never mind.I'll help to sign you in.Okay,here's your student card.Be sure to keep it with you at all times.You'llneed it for access to the library,the cafeteria,and other places.M:I will.Thanks a lot.W:My pleasure.Next,let's go to the library to get all the books you need.And don't forget to attend the greeting meetingtomorrow morning at 9 o'clock!M:Sure.Text 9W:Bob,this is Julie.Do you have a second?M:Sure.What's up?W:I'm running out of my money again.I really need to balance my budget.M:You did spend too much money and some of the expense was unnecessary.W:I earned the money through my efforts to make a better life.And I deserve to enjoy myself.M:Quite true.But the point is that you don't have to spend every penny you make.You know that money managementmeans we can handle the money we make,not simply use up all we have.W:I should have made arrangements on my spending.M:What things did you buy?W:I have no idea.I didn't pay attention.Maybe too much on entertainment,I think.M:You should reconsider your spending habits and start to save in case of an emergency.We should get ready for arainy day.W:Thanks,I'll try.But while the grass grows,the horse starves.Could you lend me 200?M:Sorry,you promised last month when you made the same request.Text 10M:Good morning,children and parents.Welcome to the Neighbourhood Children's Club.To celebrate the end of theschool year,we've bought many kinds of gifts for the children,such as chocolate,bookmarks,and pencils.Just forfun,we've hidden them around this building!First,all children will be divided into age groups.Their names should bewritten on the paper on the wall.If you haven't done that yet,please do it now.Preschool children will be going out of thefront door with their parents.Outside this door,you will see flags that will mark your area.The parents of this groupare welcome to go with the children.If you are in the first to third grade,you're going right outside the back door tosearch in the yard.There will be some helpers to direct you.Finally,the fourth grade children,please follow me downthe hall through the double doors and to the other side of the building.You'll be going to look for your gifts there.There are over 200 gifts hidden around this building,which should be plenty for everyone.答案：1-5 CABBA6-10 CBACB11-15 CACBA16-20 CBCBA【语篇解读】这是一篇应用文。本文介绍了香港四个受欢迎的市场。2l.A细节理解题。由文章第二段In the establishments,you can find good food.While the dining experience may belimited to plastic tables and chairs,some of the restaurants here are worthy of a repeat visit..可知，在庙街夜市，游客可以享用到美食，尽管条件略简陋，但美食的体验让这里值得再次光顾。故选A。22.D细节理解题。由文章第三段Unlike other markets,which are active at night,.the Reclamation Street Market is aday market and lively in the early morning.可知，新填地街市场与其他市场不同之处在于它有早市。故选D。23.D细节理解题。由文中If you are looking to pick up a souvenir,wander through Cat Street Market.一句可知，如果游英语第18页
数学参考答案及解析作直线m垂直于面DEBC,如图所示，以O为坐P(X=1)=1-P(X2=0)-P(X2=2)=1-274标原点，OA,O正，Om分别为x,y,z轴的正方向建立716空间直角坐标系，27=271(3分)21122或P(X:=1)=3×3×3+3X×3+3X3273=27P(X=2)=×+号×号×号-品×3-27(4分)所以X2的分布列为易知D(0,-√2,0)，E(0W2,0),B(-√2,2√2,0)，X202C(-2√2√2,0)，设二面角P-DE一C为0，则P(-√2cos0,0N2sin0),则Di=(0,22,0)6722DP-(-2cos 0.2./2sin 0).CB=(22.0),(5分)CP=(-/2cos 0+22,-2Zsin0).(7分)(2)Xm的所有可能取值为0,1,2，设面PDE的法向量为m=(x1,y,之)，〔m·DE=2√2y=0且PX.=2)=号×号×P(X1=1D+号PX-1=则2)+0XP(Xm-1=0)(m·Dp=-√2cos0x1+√2y+v2sin0x1=0令x1=sin0,解得1=cos0,y=0,=号P(X.-1=10+gP(X.-1=2.(6分)即m=(sin0,0,cos0),(9分)设面PBC的法向量n=(x2,y2,2),又PX,=D=号P(X=0+(号×号+号×则3）P(X-1=1D+号PX-=2)(n·CB=√2x2+√22=0n…Cp=(-2cos0叶22)xm-2y+V2sin,=0=号1-PX-=1)-PX-1=2]+号P(X.-1=1D令x2=sin0,解得2=一sin0,x2=cos0-3,+号P(X-1=2)n=(sin 0,-sin 0,cos 0-3),(11分)=-PX-D+号(7分)因为面PDE⊥面PBC,所以m·n=sin0+cos0-3os0=0,解得cos0=子，则二面角P-DE-C又E(Xn)=0×P(Xn=0)+1×P(Xn=1)+2XP(Xn=2)=P(Xn=1)+2P(Xn=2),(8分)的余弦值为号(12分)且P(X.=1)+2P(X.=2)=-号P(X.-1=1)+号21.解：(1)由题意可知X2的所有可能取值为0,1,2，(1分)+2×[号P(X-1=1D+号PX.-1=2)]且P(X=0)=号×号×号=高：(2分)：=专P(X.-=1D+号P(X.-=2)+号，(9分)·4。
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programme,Jonny.You地：freely自由地；luckily幸运地。4.B。经足以鼓舞人心，但是Washington并不想女孩学STEM课程work part-time as a DJ on local radio考查过去分词作状语。句意：由于不能在这部新电影中扮演角色，玛丽亚感到止步于此。49.D。理解具体信息。根据倒数第二段When did you first want to become a DJ?很沮丧。31.A。根据上文中的内容可知，WashingtonDuguay对Sun的评价可知，Duguay认为Sun为其他女核树立了光辉的榜样M:My uncle once worked as a DJ.He used to5.A。考查语。句意：我们现在离发明“时用自己的故事证明了教育可以改变人生wcll-rounded意为“全才的：全面i发展的”tell me stories about his job and all theconcerts he'd been to see.But I didn't间机器”还有很长的路要走。但谁知道呢？32.B。33.D。根据上文中的she aimsatNever say never.别轻易说不。Loose lipsmajoring in history和两空之间的a degree50.C。理解具体信息。根据最后一段中的in history可知，Washington决定继续深Sun made 2022 the most meaningful yeardecide to do that until I saw a film about aof her life.She spoke at the 77th Unitedfamous DJ on the Internet.sink ships..祸从口出。Great minds thinkalike.英雄所见略同。It ticks all the righ造，并将获得历史学学位定为自己的目标。Nations General Assembly可知，2022年，W:How did you feel during your first show?boxes.一切顺利34.C。根据上文Washington在89岁高龄获Sun在第77届联合国大会(the77hM:It was a mid-afternoon programme,so I6.C。考查冠词的使用。United Nations General Assembly)上发表句意：我记不清会得副学士学位的故事可知，无论年纪多didn't worry about having议的具体日期了，但是我知道是一个星期了演讲a huge大，我们都可以追逐梦想。D篇audience.And I prepared everything before五。第一个空特指“会议的日期”，用定冠35.C。根据上文中的Tome,history is a主题语境：人与自然词；第二个空指某一个星期五，用不定冠~环境保护the show,so I was really calm.great subject可知，Washington认为历史是本文是说明文。研究团队利用3D打印W:You do interviews on your show too.Who词门非常重要的学科，每个人都应该了解技术建造可回收房屋。are the mostinteresting7.D。考查形容词辨析。句意：该项目着眼自己的历史。people to51A。理解具体信息。根据第二，段中的interview?于我们如何能够更加有效地鼓励学生参与阅读理解from natural materials f But theM:I get the most positive comments from教师培训。passive被动的：impressive印象A篇listeners when I speak to footballers or深刻的：major重要的；effective有效的。主题语境：人与自我一生活与学BioHome?3 D is fully recyclable以及最后basketball players.However,I have more8.C。考查非限定性定语从句。句意：几个段中的The materials used are100%本文是应用文。文章介绍了四个海外游fun when I'm talking to musicians,月后，瑞安筹集了2000美元，他用这笔钱学项目recyclable,so our great-grandchildren can在乌干达的小学附近修建了一口井。先行fully recycle BioHome3D可可知although actors come a close second.36.B。理解具体信息。根据AIFS StudyBioHome3D可以被完全回收利用。W:What are your plans for the future?词$2,000在定语从句中作宾语，因而用Abroad部分中的I picked AIFS because it52.C。理解具体信息。根据第四段中的aM:I'd love to get into full-time radio work.with which。was the cheapest option of all of theBut there are so few opportunities.I can't9.C。考查名词性从句。句意：随着时间的programs that I looked at可知，Greta选择one -bedroom,one-bathroom house,thesee it happening.I think I'll have more流逝，曾经在我们生命中似乎至关重要的AIFS Study Abroad项目是因为该项目价roof curves down to meet the walls.格最便宜。creating a large and clean living spacechance of introducing shows on television,东西现在已经不再那么重要了。分析句子so that's what I'm aiming for.I wondered结构可知，名词性从句在句中作主语，同时37.C。推断。根据IES Abroad部分中的知，BioHome.3D内部的居住环境非常舒适about being a singer,but I don't think I'm从句中缺少主语，因此用what。learn all about music,Take courses in53.C。理解具体信息。根据第四段中的内10.D。good enough考查名词辨析。句意：他由于为世界Music History,Music Theory,and(Text 8)和做出贡献而获奖。declaration声明，Performance Studies,in the musical capital容The building was printed in four parts可知答案Good afternoon,my name's Angel宣告；confirmation证实，证明；procedureof Europe以及conduct your own way54.B。推断。根据第五段中的TheBright.Thanks for coming to visit Appleton程序，步骤：contribution贡献。toward musical mastery可知，IES AbroadUniversity of Maine team hopes to bringAnimal Park!At the park you can see farm11.D。考查非谓语动词。句意：联合国儿童项目会吸引爱好音乐的学生。printing time down to two days可知，研究animals like sheep.Then there are the tigers基金会的成立是为了向第二次世界大战38.D。理解具体信息。根据Siena Summer团队希望能够提高打印速度，缩短打印BioHome3D的时间.and the monkeys,which the visitors like best.中受害国家的儿童提供食物和保健。动部分中的Study abroad in Siena for an词过去分词作后置定语。experience that will fill your mind with55,A。理解观点、态度。根据第三段内容和And some exciting news-a baby giraffe was12.B。考查连词。句意：不要犹豫，做出决Italian culture可知答案倒数第二段中的the printed home couldborn just this morning!So don't miss the定，否则你会让这样一个好机会从你的手39.C。理解具体信息。根据AIFS Studybe a game changer for accommodationchance to see him.He's at the top of the park,指上溜走，Abroad部分中的My summer timeshortages,Janet Mills said It can help usnext to the dolphin pool.Many visitors want to13,B。考查动词辨析。句意：虽然很穷，但College Year in Athens部分中的anwiththehomelesspopulation.thefeed the animals,You are not allowed to do白方礼总共捐赠了大约35万元，以支持amazing summer,IES Abroad部分中的homeless problem可知，Janet Mills认为this at the moment.If you're into riding.那些因为家庭太穷而无法上学的孩子Take a summer和Siena Summer部分中BioHome:3D可以有效为无家可归人群解however.you can now do this at the horse们。attach绑，贴：donate捐赠，捐献：aid的a summer experience可知，这四个项目决住房问题，因此她对BioHome3D的发帮助，援助：conduct传导会在夏季举办游学活动展充满希望阅报纸，10份（含）以下，每学期每次加收邮费5.00元，10份以上免收邮费，可随时补订、增订。订阅热线：0351-7333565编辑部投稿电话：0351-7773977、7773979（初中）7773955、7773908（高中
=sin(一x)=0,所以f(x)的图象关于直线x=买对称，f(x)的图象关于点(-亚.0)对称.f(x)+f(-x)=sin(x+)+sin(-x+)=2cosx.10.ACD【解析】本题考查统计中的极差、中位数、均数、方差、百分位数，考查数据处理能力与推理论证能力，对于A选项，如果删去的不是最大值或最小值，那么极差不变，所以A正确，对于B选项，删除前有6个数据，中位数是按从小到大的顺序排列后中间两个数的均数，因为任何两个数据都不相等，所以中位数不会等于6个数据中的任何一个，而删除后有5个数据，中位数是6个数据中的某一个，所以B错误，对于C选项，均数不变意味着删去的数据刚好等于均数，在方差公式中，分子不变，分母变小，所以方差变大，所以C正确对于D选项，均数不变意味着删去的数据刚好等于均数，在按从小到大的顺序排列的6个数据中，因为6×20%=1.2,5×20%=1，所以原数据的20%分位数是第2个数，新数据的20%分位数是前2个数的均数，且该数值小于第2个数，所以D正确，11.BC【解析】本题考查抽象函数与具体函数的奇偶性，考查逻辑推理与数学抽象的核心素养令x=v=0,得f(0)=0,令y=0,得f(x)=xf(0)=0,则f(-x)=f(x)=-f(x)=0,所以f(.x)既是奇函数又是偶函数.由g(x+1)=(x十1)(x2+2x)=(x十1)[(x十1)2-1]，得g(x)=x3一x,因为g(一x)=一g(x),所以g(x)是奇函数，12.ACD【解析】本题考查立体几何初步中的体积、距离、二面角，考查空间想象能力与运算求解能力如图，取AB的中点G,连接CG,因为面ABC⊥面ABD,且面ABC∩面ABD=AB,所以CG⊥面ABD.取AD的中点E,连接BE,因为AB=BD,所以BE⊥AD,则BE=√JAB2一AE=2√2.因为CG-3x3_3/221所以Vm=方×2×号×2×2反=后，A正确取AE的中点R连接PG.CF,则G∥BE,所以FG⊥AD.因为CG⊥面ABD,所以CG⊥AD,又CG∩FG=G,所以AD⊥面CPC,则AD1CF,则CF=VCG+FG=,∠CPG为二面角B-AD-C的面角，且an∠CFG-器-3.B错误，C正确设△ABD,△ABC的外心分别为K,M,则GKAB,又面ABD⊥面ABC,所以GK⊥面ABC.设三棱锥D一ABC外接球的球心为O,则OK⊥面ABD,OML面ABC,所以四边形OMGK为矩形，则OK=MG=号CG=【高三数学·参考答案第2页（共7页）】
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l免费增值服务介绍1。学科网6组卷网www.zxxK.com学科网(https:/www.zxxk.com/)致力于提供K12教育资源方服务。组卷网(https:/zujuan.xkw.com)是学科网旗下智能题库，拥有小初高全√网校通合作校还提供学科网高端社群学科超千万精品试题，提供智能组卷、出品的《老师请开讲》私享直播课等拍照选题、作业、考试测评等服务。增值服务。▣说动▣▣▣扫码关注学科网每日领取免费资源扫码关注组卷网回复“ppt”免费领I80套PPT模板解锁更多功能回复“天天领券”来抢免费下载券
个©分名交高三单元一贝小式=忘送2活直线AP与B0的斜率之和为一之，求直线1的方程.恤交(心aaA0议心。Q油n的新命教学厘为x=my十6，x6小札记由y得m十40+12+32=0测y+212m4了2=32m248所以P=一m又因为大十=一号所以-1，)为版师我风时方程为联立将045以直线的方程为y6（t6),即)店x+1c12分56，9.(12分)已知抛物线C:)=2px(D>0)的焦点为F点E在圆Q:(x十2)P十(y-3)=1上，且EP1的最小值为4.(1)求p的值：②)P(o),A,B是抛物线C上不同的三点，M1,0),若。>0，≥0，且点P到直线AB的距离为2，PA+PB=4Pi,求点P的坐标，【保题分折D由题知，F(号，0，因为EF的最个值为41底的0-1卖政)所以)PQ-1=4,所以FQ=5,所以（号+2r+0-3)-25,8=,表n0由>0，解得p=4.8所以=4分2由(1D知抛物线C:y=8,F(2,0),根据题意可知直线AB的斜率不为0，直38-)9京心设直线AB的方程为x=y十m,A(m1,h),B(2,2).果果y6-0。x,点家长○处直：国(1所以4=64k2十32m>0,即22+m>0,且1十3%-8说，6=8况，△9长点家○5类直(1)所以x1十x2=b(y十y2)十2m=8k2十2m.家y1填，绿食爱碳0△售，F奇x由1【R温i市-4应4小+国-=0级酸十一2=44，所以4|xo=一4k2一m十2处78人s8k-2%=-4y6即P(-42-m十2，-4)，又点P在C上，所以16k2=8(-42一m+2),即62+m=2,所以2k2+m=2k+2心条得-号<人号又点P在第-桌限，所以-秋>0，所以-0又AP到直线AB的更青日-m上-2m士2=2，所以m-1=开图为号<0，年释m=青=尽所以√1+k2V√1+22）.…12分20.(12分)已知点E3,3)在双曲线C号一芳-1。>0,6>0)的渐近线上，双直线C的右熊点为Fc,0【24G3DY(新高考)数学-必考-Y】129
河北名校强基联盟高一期中联考数学参考答案1.【答案】D【解析】因为梯形的四条边可以都不相等，所以选D.2.【答案】A【解析】根据同一集合的概念可知，两个集合中的元素应一样，A:根据集合元素具有无序性，则M=N,故A正确；B:(3,4)和(4,3)是不同元素，故B错误；C:因为M中的元素是有序实数对，而N中的元素是实数，所以C错误：D:因为M中有两个元素，即4,3，而N中有一个元素，即(4,3)，所以D错误.故选A.3.【答案】B【解析】要使函数y=22+4有意义，则2x+4≥0，解得x≥一2且x≠0，x≠0，所以函数=√2+的定义域是[-2,0)U(0,十∞).故选B4.【答案】B5.【答案】C【解析】当a≥0时，令2a十1=a,a=一1，与a≥0矛盾，不合题意；当a<0时，令-a,a=士3，取a=-3,符合题意.放选C6.【答案】B●【解析】当a>0,b>0时，a+b≥2√ab,则当a十b≤2时，有2√ab≤a十b≤2，解得ab≤1，必要性成立；当a=令，b=4时，满足a≤1，但此时a十b>2,充分性不成立.综上所述，“ab1”是“a十b≤2”的必要不充分条件7.【答案】A【解析】由题意可知，函数fx)=2的定义域为R,又因为f(一x)=∫()，x2+1所以函数2为R上的偶西数，故排除选项C和D.又因为当>0时，函数)=纤>0,故排除选项B,故选A.8.【答案】C【解析】因为一3≤1
评估第2期B版测试题听力原文23-24Text 1W:Dad.can you help me with my English双语paper?I'm kind of stuck on it.M:Coming right up.Penny.Let me finishthe gardening first.(上接B2版)Text 2M:Linda,I have two tickets to Avar 2First,you should make pain Madrid,andtonight.Would you like to watch it withme?with 0%interest,any moneconfident thatW:Thanks,but I've already seen Avaar1.to the principal(本金).SecIt's not my thing.Why not ask Karen?She probably hasn't watched it yet.where your money is goinText 3he road to theW:What is your trouble,Mr.Brown?Walls:food,utilities,shewhat stressesM:I hurt my foot in a football match lastweek.I took some medicine,but it didn'tthat you can cut altogetherwork.W:Don't worry.Let me give you an exam-takes some sacrifice(牺牲ination first.Lie down,please.M:I hope it's not serious.I have a matchstudent loans faster-it'sthis weekend.Text 432.What do the data mentW:Look at Danny.Why is he wearing suchA.Applying for studea long face?M:Haven't you heard of it?He went out ofB.Paying back studenbusiness this week.W:Oh my!Poor Danny.Hope he could getC.Interest rates of stuthrough it soon.Text 5D.The US was sufferW:Guess what!I've decided to go back toschool!M:Good for you,Mary!You're one stepduardo in thecloser to your dream.Have you chosenyour favorite college?W:Not yet.I'm considering some colleges第二节（共5小题；每小in New York and I'll send applicationscited.before March.阅读下面短文，从M:I hope everything goes well.项。选项中有两项为多Text 6M:Susan,guess what I found this afternoon!W:I have no idea.What is it?With the busy lifestyle ofM:I found a puppy on the way back fromschool.It seems lost.our time,napping(小睡)done.W:What a poor little thing!How will youand children of society.Ho
220.(本小题满分12分)已0藏明a有连推关系了eNa一，8记a-山，(te工)，者7an-8数列{b,的递推式形如b1T,9,rR且P,r≠0)，也即分子中不再含有常数项pb+q(I)求实数k的值：(2)令，士求数列的通明公式0e7x921.(本小题满分12分)在三棱柱ABC-A,B,C,中，∠ABC=2T,AB=BC=2,且A,BA3B⊥AC.(1)证明：A,A=A,C;A(2)若A4=2,二面角A,-AC-B的大小为？求面4水∞CB,与面BCC,B,夹角的余弦值62十(-2u52848x8十4I【高三第三次联考·数学·共6页·第5页】
会高三·英语·高频考点七·参考答案1.committee2.traditions3,further4.historical5.comparison6.funds7.worthwhile8.issue9.protest10.balanced11.turned to满科是12.take down13.piece by piece14.lead to15.give way to16.made a proposal17.As is known to all 18.took part in19.In my opinion20.improve the quality of life,【解题导语】这是一篇说明文。文章主要讲的是印刷术的发展历史。2l.D推理判断题。根据文章第一段“Human historyhas a few common themes,one of which is thewritten word.Humans have been printing aswell as writing since 3,000 BC-the Ancient9
在△ABD中，∠BAD-S0,sin∠ADB-品.所以AB=4厅s∠ADB…9分故提-影AD10分27sin∠ADB18.解：(1)当E为PD的中点时，AE∥面PBC.理由如下：…1分设F为PC的中点，连接EF,FB,AE.…2分在△PCD中，EF/∥CD,EF=CD因为CD=2AB,AB∥CD,所以EF∥AB,EF=AB,所以四边形EFBA为行四边形，所以AE∥BF.……4分因为BFC面PBC,所以AE∥面PBC.…5分(2)以D为坐标原点，DA,DC,DP所在直线分别为x,y,:轴，建立如图所示的空间直角坐标系。……6分设PD=CD=AD=2AB=2,则P(0,0,2),C(0,2,0),B(2,1,0),P3=(2.1,-2),P℃=(0,2.-2).D设面PBC的法向量为m=(x,y,),(m·PB=0,{2x+y→2x=0,则m·p心-0,2y-2:=0即令y=2,则m=(1,2,2).……8分设G为AP的中点，连接DG(图略)，易证得DG⊥面PAB.所以D心是面PAB的一个法向量。又D(0,0,0).G(1,0,1),所以D心=(1.0,1).…10分设面PBC与面PAB的夹角为0，cos0=cos(m.D哈1=m.交1=2mDGI2所以0-共，即面PBC与面PAB的夹角的大小为……12分19.(1)证明：令n=1,可得a2=2。…1分因为2a+1-a,=n+2①，所以2a.-a。-1=n+1(n>≥2)②.①-②得2a+1-a。-(2a.-am-1)=1,即2(a+1-an一1)=a.-a。-1-1.…3分因为a:一a1一1=0，所以数列{a+1一an一1》为常数列。…5分(2)解：由(1)可得a+1一a.一1=0，所以{an}是公差为1的等差数列，所以公=儿，…7分因为么=所以工=+是+是+十③，…8分红.-++是++08【高三数学·参考答案第4页（共7页）】·HEN·
