全国100所名校最新高考模纵示范喜全国100所名校最所高考模拟示括格11.已知函数f(x)=sin+V3 cos(u>0),点A,B,C是直线y=m(m>0)与函数三，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)的图象从左至右的某三个相邻交点，且1AB1-3BC一不，则下列说法正确2021年9月30日，电影（长津湖》在各大影院上映，并获得一致好评，该片是以长17.(10分)津潮战役为背景，讲述了一个中国志愿军连队在极度严酷的环境下坚守阵地，奋勇DA的是下EIAB+IBc=T小w=A.mJf(x)=2gin(2x)杀敌，为长津湖战役胜利作出重要贡献的感人的历史故事，某同学看完电影后以抗美援朝时期的历史为内容制作了一份知识向卷，并邀请了该校10名同学（男女名B,函数了四在单调递增-至2kTs2x+Fs2kT+交，K6Z人EtTX空水Tk(7半)参与了问卷的知识竞赛，将得分情况统计如下表：得分(30,40](40,50](50,60](60,70](70,80](80,90]C散X譬关于直线一价行X吞nmxi02添冷)-厅[20,30]性别8134105X十还5D,将函数f()的图象向右移个单位长度后得到的函数图象关于原点对称男生12105104女生12.如图，已知多面体ABCDEF的底面ABCD是边长为2，√2的正方形，四边形ACFE将比赛成绩超过60分的考生视为对抗美授朝的历史了解。为等腰梯形，面ABCD1面ACFE,且EF=号AC,AE=2AB,则该几何体外1)从这100名同学中随机抽选一人，求该位同学对抗美援朝的历史了解的频率，接球的表面积为C连接BDAC泸0，承EF的中0(2)能否有95%的把握认为对抗美援朝的历史了解与性别有关？A.12π连接MF.0Mh.OM=n+in(ad-bc)2附：K2=(a+b)(c十d)(a+c)(b+d①'B.16πR2=h4=(1h)十0.050.010R=下.0n2℃0)20P(K≥k)0.10C.20π2.7063.8416.635D.24π-S4TR2可6=ko(0)02=10stt65件：1题序120)=3456910111210020答案2)(寻二、填空题：本题共4小题，每小题5分，共20分.Cb=k1×(o<0b>=3不sit已知单位向量a,b满足a·b=2,则a,b)co8<0b>=)5e×1XT2x).10-b7=生2030504.曲线f(x)=x2e在x=1处的切线方程为3eX-2eUo3-3e.已知[x]表示不超过x的最大整数，若a,表示[x门x∈(m,n千1)所有可能取值生IS353elx的个数，其中n∈N,则数列(a,}的前20项和Sw=4D寸35bs1002ey=16.如图，在直角坐标系x0中，已知椭圆C,着+y=1的左、K100×(35×0-30×15)0×0X3×651.096<38+右焦点分别为F,F2,点M,N为椭圆上位于x轴上方的两点，且FM/FN,则/EN+/FM的取值范围为(.有9，的把握L为美泊的沥确然1打肤广9X←(n.门)人0n=(nt1)1-n+1八门

四、解答题：本题共6小避，共70分.解答应写出必要的文字说明、证明过程及演算步骤，20.(本小题满分12分)】17.（本小题满分10分)如图，在三棱柱ABC-A,BC中，面ABBA1⊥面ABC,四边形ABB,A,是边长为21已知数列{a,}中.a=3am1=2一a的菱形，△ABC为等边三角形，∠A:AB=60°，E为BC的中点，D为CC,的中点，P为线段AC上的动点，AB,∥面PDE.D记6，一。1，证明：数列6，}为等比数列(1)请确定点P在线段AC上的位置：(2)求数列{0n}的通项公式：(2)求面PDE和面AB,C:所成二面角的正弦值.(3)记cn=2aa+1,求数列{c.}的前n项和S.18.(本小题满分12分)在△ABC中.内角A,B,C所对的边分别为a,b,c,且满足a2+b2一2=a2cosC+accos A.21.(本小题满分12分)(1)求角C的大小：已知椭圆C号+芳=1(。>6>0)的短轴长为2v3.月点1，-受)在树园上(2)如图，若CD=2Di,E为BC的中点，△CDE的面积√3，△CDE的周长为6，求AB边(1)求椭圆C的标准方程：的长度(2)椭圆C的左、右顶点分别为A、B,点P.Q是椭圆C上异于A、B的不同两点，直线BP的斜率为k(k≠0)，直线AQ的斜*为2k,求证：直浅PQ过定点19.(本小题满分12分)通过改酸检测可以初步判定被检测者是否感染新冠病毒，检测方式分为单检和混检.单检是22.(本小题满分12分)将一个人的采集拭子放人一个采样管中单独检测；混检是将多个人的采集拭子放人一个采已知函数f(x)=(2x2-4r+4)e-a.r2-c(a∈R).样管中合为一个样本进行检测，若检测结果呈阳性，再对这多个人重新采集单管拭子，逐一(1)若曲线y=(x)在点(1.f(1))处的切线/过点(0.1一e).求实数a的值：进行检测.以确定当中的阳性样木.混检按一个采样管中放人的采集拭子个数可具休分为(2)当u>0时，若函数∫(.x)有且仅有3个零点，求实数u的取值范围.“3合1”混检，5合1”混检.“10台1”混检等.调查研究显示，在体总阳性率铰低（低于0.1%)时，混检能较大幅度地提高检测效力、降低检测成本.根据流行病学调查结果显示，某城市每位居民感染新冠病毒的概率为(0<<1).若对该城市全体居民进行一轮核酸检测，记每一组n位居民采用“n合1”(n∈N”)混检方式共需检测X次.(1)求随机变量X的分布列和数学期望；全科试题炙费下找公众号《（高中僧课堂）(2)已知当U

爹考管案分数学用报MATHEMATICS WEEKLY主编：张瑞资编：孟晓玲~美编：花玉人教版八年级2022-2023学年·第43~50期三、17.(1)原式=5+25-35-6=-5-1：乙车到达B地后，甲车继续行驶.由图象可知力>1>0的解集为-2

四、解答题：本题共6小题，共0分。解答应写出文字说明、证明过程或演算步骤。17.(10分)数列{a,}中，a,=1,S,是数列{a.}的前n项和，数列25)是公差为1的等差数列，a.(1)求数列{a,}的通项公式：+1L<22)证明：SS,S-十十18.(12分)如图，在圆台OO中，AB,AB分别为上、下底面圆的直径，且AB,AB，4B=3AB，CC为异于AM,BB的一条母线，点M在线段AC上，且MM=AC,(1)求证：CM∥面ABB,A:(2)若O0=4,AB=4,∠ABC=30°，求二面角A-CC-0的正弦值.19.(12分)记△A8C的三个内角AB,C的对边分别为a,6,e,已知A=行，a=4,D是BC上的一点(1)若CD=2DB,且AD分∠BAC,求c:(2)若imBD+si血∠CMD-5，求AD的长.220.(12分)强基计划主要选拔培养有志于服务国家重大战略需求且综合素质或基础学科拔尖的学生，聚焦高端芯片与软件、智能科技、新材料、先进制造和国家安全等关键领域，由有关高校结合自身办学特色，合理安排招生.强基计划的校考由试点高校自主命题，校考过程中通过笔试才能进入面试环节.(1)某研究机构为了更好地服务于高三学生，随机抽取了某校5名高三学生，对其记忆力测试指标x和分析判断力测试指标y进行统计分析，得到下表数据：19101113y34567请用线性相关系数判断该组数据中y与x之间的关系是否可用线性回归模型进行拟合：（精确到0.01)数学试题第3页共4页

22.(本题13分)综合与实践问题情境：在数学活动课上，老师出了这样一道题：在矩形ABCD中，AB=6,BC=l0,将矩形ABCD绕着点C顺时针旋转a到矩形CEFC的位置，点D恰好在边CG上」问题解决：(1)如图1，连接AC,CF,AF,AF与CC交于点H.①a的值为AF=②求GH的长.(2)如图2，若将四边形ABCP沿着直线CP折登，得到四边形A'PCB',使得点B的对应点B恰好在EF上，点A的对应点为A',点G在A'P上，求AP的长GHD贸BBEC牌图1图2將&23.(本题13分)综合与探究如图，抛物线y=一x2+bx十c与x轴交于点A(一3,0)，B(1,0),与y轴交于点C,连接AC.(1)求抛物线与直线AC的函数表达式(2)设Q是抛物线上的一个动点（不与A,B重合），过点Q作QH⊥x轴，垂足为H,交直线烟AC于点P,当QP=PH时，求点Q的坐标，(3)在(2)的条件下，抛物线的对称轴上是否存在点D,使得以点C,Q,D为顶点的三角形与哦△ABC相似，若存在，求点D的坐标；若不存在，请说明理由.医【数学第6页（共6页）】

得14分的有10×40%=4（次）.得15分的有10×30%=3（次）.所以这10次测试成绩的均数x=(13×3+14×4+15×3)÷10=14.方差=03(14-13)护+414-14+3(15-14)2=0.6.17.(1)=100+6(-1+0-2+0+0+3)=10,=100+号(-1+0+2-1+0+0)=100,-2[99-100+100-100°+(98-100+(100-10P+(10-100F+(103-100P=3,2=若[99-100P+(100-100P+102-100°+(99-100)2+(100-100)2+(100-100)2]=1.(2)由(1)可知，m=2,且s>s2,所以乙机床加工这种零件更符合要求18.(1)由题意，得m=(5+6+7+6+6)=6:乙的成绩中数据6出现的次数最多，所以乙的众数为6；吃=5[(3-6)2+(6-6)”+(6-6)2+(7-6)2+(8-6)2]=2.8.故从上至下，从左至右依次填6,6.2.8.(2)因为甲、乙成绩的均数与众数都相同，但甲的方差较小.所以甲的发挥更稳定19.(1)列表如下：环数68910甲命中的环数02乙命中的环数0023(2)①因为m=若8×2+9×2+10×2)=9.=66x1+9×2+10x3)=9.所以品=6[(8-9)×2+(9-9)×2+(10-9×2]=号，2=6[6-9)°+(9-9)2×2+(10-9)”×3]=2所以=z,弹<2：所以选甲参加获奖机会更大：②因为6次射击中，乙有3次射中10环，甲只有2次，所以选乙参加更有可能破纪录.

全国100所名校高三AB测试示范卷教学当C≠②时，一52m-号,即-2<≤1：m<-2或m>若p为假命题，9为真命题，则,即m<-2∴.实数m的取值范围为（一∞，1].11.(18分)已知f(x)=x+40(.x>0)的值域为M,不等式(x-a)(x-3a)<0的解集为N.(1)若x∈M是x∈N的必要不充分条件，求正整数a的最小值；(2)求证：“f(x)在(6，十∞)上单调递增”的充要条件是“a≤9”.【解题分析]1)a为正整数.且>0)=十址≥2√·g=4a,当且仅当x=红，即x=2va时，等号成立，∴M={yy≥4va(x-a)(x-3a)<0,∴.解得a

三、填空题：本大题共4个小题，每小题5分，共20分.○8中08谢五市，813.若(a+x)(1+x)‘的展开式中，x的奇数次幂的系数之和为32，则该展开式中的系20.(12分)随着时代的不断发展，社会对高素质人才的需求不断扩大，我国本科毕业生中考研人数为14已知4，B分别为号着-1左右支上的点，设u是行于：销的单位向是则数也不断攀升，2022年的考研人数是341万人，2021年考研人数是377万人.某省统计了该省其中四所大学2022年的毕业生人数及考研人数（单位：千人），得到如下表格：|AB·ul的最小值为A大学B大学C大学D大学15.设xe(0,+o),yeR,不等式xlnx-x(y+a)+e≥0恒成立，则a的取值范围为2022年毕业人数x(千人)4321事意16.正四面体是一种柏拉图多面体，正四面体与自身对偶，正四面体的重心，四条高的交2022年考研人数y(千人)0.50.40.30.2点，外接球、内切球球心共点.现将4个半径为1的小球装入一个正四面体内，则该正(1)已知y与x具有较强的线性相关关系，求y关于x的线性回归方程y=6x+a;需四面体高的最小值是(2)假设该省对选择考研的大学生每人发放0.3万元的补贴四、解答题：共70分，解答应写出文字说明、证明过程或演算步骤。(ⅰ)若该省2022年毕业生人数为2万人，估计该省要发放补贴的总金额；17.(10分)(ⅱ)若A大学的毕业生中李华、张明选择考研的概率分别为P、3p-1,该省对李华设Sn为数列{a,}前n项和，满足a1=3,Sn+1=a1+2an+n-4.张明两人的考研补贴总金额的期望不超过0.6万元，求p的取值范围.共大本暖(1)证明{a。-1}为等比数列；(2)设b.=(-1)°·n·lg2(a+1-1),求数列{b.}的前2n项和T参考公式：6=4-n(-刀∑xy:-n·y18.(12分)4-,a=y-6x.合量如图所示，AOCB是由三角形OAB和扇形OBC组成的21.(12分)面图形，∠A0C=90,L0AB=60,c0s∠A0B-2万，0A=3,7已知抛物线的顶点为坐标原点，焦点F在x轴的正半轴上，过焦点F斜率为√3的直线点D为扇形OBC的弧上的动点(1)求0B的长；交抛物线于P,Q两点（点Q在第一象限），交抛物线准线于G,且满足1PG1=8(2)求四边形A0CD面积的最大值，(1)求抛物线的标准方程；，。3(2)过点F作互相垂直的两条直线l1,l2,l与抛物线C交于A,B两点，l2与抛物线C19.(12分)交于C,D两点，M,N分别为弦AB,CD的中点，求IMFI·INFI的最小值.如图1，在直角梯形ABCD中，已知AD∥BC,AD=AB=2,∠BAD=90°，BC=4.将△ABD沿BD折起，使面ABD⊥面BCD,得到几何体A-BCD,如图2所示.22.(12分)(1)求证：面ABC⊥面ACD;(2)若M在线段BC上，直线已知函数)=r-,(eeR.DM与面ABC所成角的正弦值为否，求二面角的余弦值B-AD-M(1)在xe[1,+0),函数f(x)≥0恒成立，求实数a的取值范围；图1的余弦值2求证ha>写+写+方++aeN)数学模拟（一）第3页（共4页）数学模拟（一）第4页（共4页）

全国©0所名校高三月考卷教学(2)由题意知f0)=-1,得6=-1.了()=x+(2)+a+1,了0)=0，得a=-1,f(r)=-13》.当0或>3时，f()<0:当0<<3时，f(r)>0.函数f(x)在(-∞，0)，(3，+十∞)上单调递减，在(0,3)上单调递增，且当x>3时，f(x)>0,则a=-1,b=-1符合题意，函数f)的极大值为f代3)，且f3)=5.…12分e3·20.(12分)已知函数f(x)=lg(x+2+|x一a)是偶函数.(1)求a的值：(2)若f(2m-1)0,故x∈R由题意知f(x)=f(-x),函数y=lgx在(0，十∞)上单调递增，则|x十2十|x-a=|-x十2十|x十a对Hx∈R恒成立，函数)=x十2+|x-的图象关于直线x=“2对称，面数)=一十2十z十a的国象关于直线x-222对称，则2，之2，么解得=2，经枪验，符合题意，…6分(2)当0x2时，f(x)=lg4,当x>2时，f(x)=lg(2x),即函数f(x)在[0,2]上是常函数，在(2，十∞)上单调递增解得22，即1<3，|2m-1|2由题意得①{(m-1或m>1②2<2m-112.得m<-号或m>是.3由2m-10.当m>号时，m-2m+4>m-2m+4=(m-1)2+3>0,m(m-2m+4)>0:当m<0时设gm)=m-2m十4，则g0m)=3m-2,易知gm)在(-0-雪)上单调道增，在(-50)上单3调递减，又g(0)=4,g(-2)=0,则当m<-2时，m(m3-2n十4)>0.综上，m<-2或m>1.…12分21.(12分)已知函数f(x)=e'(x-2)十ax.(1)当x>0时，f(x)>一2恒成立，求a的取值范围；(2ta∈N,i证明：号+5+号++n+1以【解题分析】(1)令g(x)=f(x)十2，g(0)=0,由题意即证当x>0时，g(x)>g(0).g'(x)=e(x-1)十a,设h(x)=e(x-1)十a,则h'(x)=xe,易知h(x)在（一o∞，0）上单调递减，在(0，十o∞)上单调递增，h(.x)≥h(0)=a一1.①若a-1<0,则3xo>0,使得当x∈(0，m)时，g'(x)<0,函数g(.x)在(0，x0)上单调递减，则有g(x0)0时，g(x)>g(0).综上，≥1.…6分(2)由(1)知，当a=1,x>0时，e(x-2)十x十2>0，令=n公1.化简得受n>分家->1。nn2m+1，1累加得号十号大7十叶2号n(》…正12分【24G3YK(新高考).数学-必考-N】

2023年九年级质量调讲（二）剂国)点着议点的3以数学试题(点温馨提示：1.数学试卷6页，八大题，共23小题，满分150分，考试时间120分钟，请合理分配时间。2.请你仔细核对每页试卷下方页码和题数，核实无误后再答题。3.请将答案写在答题卷上，在试卷上答题无效，考试结束只收答题卷。4.请你仔细思考，认真答题，不要过于紧张，祝考试顺利！一、选择题（本大题共10小题，每小题4分，满分40分）每小题都给出A,B,C,D四个选项，其中只有一个是符合题目要求的，1.-6的绝对值是A、6B.-6C.±6D2.131直师中国人民解放军海军福建舰是中国的第三镀航空母舰，也是中国完全自主设计建造的首艘武管盒省的8弹射型航空母舰.采用直通长飞行甲板，配置电磁弹射和阻拦装置，满载排水童80000余吨，数据80000用科学记数法表示为蛋编完*于A.8×105B.8×104C.0.8×105D.0.8×1043.下列运算正确的是CA.a2.a=asB.(a-b)2=a2-b2C.a6÷a2=a2D.(-2a2b)2=4a4b24.如图所示的几何体是由一个长方体和一个圆柱组成的，则它的主视图是主视方向5.将一直角三角形和矩形如图放置，若∠1=42°，则∠2=A.5800克=03B.0540心年D0C.48°D.44°D第5题图第7题图6.若关于x的一元二次方程mx2+4x=x2+2有实数根，则m的值有可能是A.-3B,-2C,1D、-17.如图，菱形BCD中，点E,P,G分别为4，ACCD的点，BF2,FG=4,则菱形ABCD的面积为A.12B.16C,20D.322023年九年级质址调研（一）数学试题第1页共6页

基础点18等比数列[14考，主要考查通项公式及前n项和公式]答案见P30怎么解题(2019年全国Ⅲ卷)已知各项均为正数的等比数列{an}的前4项和为15，且a=3a3+4a1,则a3=A.16B.8C.4D.2【考查点】本题考查等比数列【腾远解题法】第一步：根据已知求解首项和公比设等比数列{an}的公比为q,因为等比数列{an}的各项均为正数，所以q[1](>或<)0，因为a,=3a3+4a1,可得a19=[2](通项公式)+4a,①，又S4=15,可得[3](求和公式)=15②，联立①②，解得q=[41,a1[5]第二步：利用等比数列的通项公式求解α故a3=[6]腾远原创好题教材改编题建议用时：20分钟1.(新人教A版选择性必修第二册P31T3改编)在正项等比数列{an}中，a1+a4=18,a2a6=256,则q=1A.2B.2C.3D.42.(新人教A版选择性必修第二册P37T3改编)已知正项等比数列{an}的前n项和为Sn,若a36a1=a2且a2=3,则S6=A.40B.84C.121D.364人教A版选择性必修第二册P41T11改编)已知数列1&，}的首项a,三，且满足03.an,则22-2a965A.165D.294.（新人教A版选择性必修第二册P34T2改编)（多选）已知等比数列{an}的前n项和为Sn,则下列说法正确的是A.数列/2为等比数列B.数列{an+an1}为等比数列aD.若S=16r-4-,则r=41C.数列{a。·an+1}为等比数列5.(新人教A版选择性必修第二册P37T4改编)记Sn为递增的等比数列{a,}的前n项和，S,=13,a1a2a3=27,则Sn=70

生活的方法。53.B。根据上文可知，“我”的儿子锁骨受伤后要借助支架恢复，因此学会了耐心等待身体的康复。54.C.my child may have learned more from this injury than anything else he's gonethrough this year可知，“我”最大的感悟是，儿子从这次受伤中学到的东西可能比他今年经历的任何事情都要多。55.A。根据it will serve him for life可知，但愿他从这次受伤中学到的东西会让他受用一生。第二节主题语境：人与自然一一自然生态本文是说明文。文章介绍了杭州西溪国家湿地公园的情况。56.in。考查固定搭配。in the first place意为“首先”。57.attractive。考查形容词。设空处修饰spot,意为“吸引人的”，应用形容词。58.situated。考查动词-ed形式。本句的主干是Xixi National Wetland Park is,设空处应填非谓语动词；设空处与其逻辑主语Xixi National Wetland Park之间是动宾关系，应用动词-ed形式。59.covers。考查一般现在时。设空处客观介绍该公园的情况，应用一般现在时。60.which。考查关系词。“70%of+设空处”引导非限制性定语从句，对area补充说明，且设空处作of的宾语，故填which。61.streams..考查名词复数。stream在逗号后的分句中作主语，是可数名词，其前有countless(无数的)修饰，其后的谓语动词cross也表明主语应用复数形式。62.wisdom。考查名词。设空处作Thanks to的宾语，其前有the修饰，应用名词。63.a。考查冠词。a bunch of意为“许多”。64.has been。考查现在完成时。根据时间状语for over40 years可知，应用现在完成时；主语为who,指代a craftswoman,故填has been。.5.to acquire。考查动词不定式。be eager to do sth意为“渴望做某事”。

解析(I)因为EF/AD,8F=之AD=2,M是AD的中点，所以EF∥DM,且EF=DM,所以四边形DEFM是行四边形，从而MF∥DE.…(2分)因为MFt面ECD,DEC面ECD,所以MF∥面ECD.…(4分同理NF∥面ECD,又MF∩NF=F,所以面NMF∥面ECD.…(6分)(Ⅱ)设AB的中点为H,连接FH,则FH⊥AB.因为面ABF⊥面ABCD,面ABFn面ABCD=AB,FHC面ABF,所以FH⊥面ABCD,·(7分)因为EF∥AD,EF丈面ABCD,所以EF∥面ABCD,…(8分)】所以E到面ABCD的距离为FH=25,…(10分)》所以m=号×4x4)x25-…(12分)》19.命题意图本题考查均数与方差的计算解析(1)由题意知(90+10+x+y+150)=10,则x+y=20.…(2分因为x

【部分题目详解参考】阅读A篇【答案】21.B22.D23.A【导语】本文是一篇应用文。文章主要介绍了来自不同国家的四个传统游戏。【21题详解】细节理解题。根据Fengzheng(China)一节中By the fifth century AD,paper kites were beingused for military purposes such as signaling and measuring distances.(到公元5世纪，纸风筝被用于军事目的，如发送信号和测量距离。)”可知Fengzheng曾被用于战争。故选B。【22题详解】细节理解题。根据Topfschlagen(Germany)一节中“Germany is the world's top exporter ofchocolate,so no wonder this game is based on the sweet reward.(德国是世界上最大的巧克力出口国，难怪这个游戏是基于甜蜜的奖励。)'可知Topfschlagen选手的奖励是巧克力。故选D。【23题详解】推理判断题。对比其他三个游戏，尤其根据EI Gatoy EI Raton(Costa Rica)一节中“It is afavorite group circle game for kids.(这是孩子们最喜欢的一种小组游戏。)”及其细节可推断，“猫捉老鼠游戏”必须要有四个及以上的人一起玩。故选A。B篇【答案】24.B25.C26.D27.C【导语】这是一篇新闻报道。文章主要介绍了被评为2022年最美教师”之一的天津职业学院教师李建国，介绍了他为培养学生职业技能和国家技术专家所做出的贡献和成就。【24题详解】推理判断题。根据第二段Li has stood out by taking the lead in the training of students invocational skills,gaining a number of honors including being named a national role model teacherHe has mentored seven national-level technique experts and a team of 14 technique"masters".One of his students,Guo Jinpeng,who graduated from the institute in 2007,became a collegeteacher at the Chengdu Auto Vocational and Technical School and was named a national rolemodel teacher in20l9.(李老师在培养学生职业技能方面走在了前列，获得了包括被评为全国模范教师在内的多项荣誉。培养了7名国家级技术专家和14名技术“大师”团队。他的一名学生郭金鹏2007年毕业于该学院，成为成都汽车职业技术学校的一名大学教师，并于2019年被评为全国模范教师)可推知，作者在第二段提到郭金鹏是为了展示李建国的成就。故选B。【25题详解】细节理解题。根据倒数第二段Vocational education has the mission of fostering a qualityworkforce and technical experts for the country.(职业教育的使命是为国家培养高素质的劳动力和技术专家)”可知，李认为职业教育培养合格、熟练的人才。故选C。

所以与A=0互斥，故B正确；5+4+3+2+15P(a1>a2)=6×612,故C正确：A=4当4=3,4=2时，a2，此时事件0，=1与A=0均未发生，所以事件4，=1与A=0不对立，故D错误.故选：BC12.BC【分析】首先证明过抛物线上一点的切线方程结论，利用结论即可得到切点弦所在直线方程，即可判断A,求出点M的坐标，从而得到'p=yM即可判断B,求出PM的中点，代入抛物线方程即可判断C,对D举反例即可.【详解】首先推导抛物线的切线方程，设过抛物线广=2px上一点M(X,y)的切线的斜率为k,则，由点斜式得切线方程为：y-=k(x-)y-y。=k(x-x)联合抛物线方程，有：y2=2px消去y,得x2-2(2x-,+p)x+(+k2x-2x）=0相切，A=0,即「-2(3x-,+P-4k2×(+kG-2）0整理得：2xk2-2,k+p=0k=2%±V42-8p2×2x:点Mx)是抛物线2=2x上的点，=2p…4%-8p匹，=0，…k=2x,名≠0，代入得：y-y=。0(x-X),整理，得2y=(x+x0)即：oy=p(x+),当k不存在时，此时M(0,0),切线方程为x=0,适合上式切线方程，所以，过抛物线广=2pr上一点M(x,:)的切线的方程为：Wy=p(x+)故对于本题来说，设P(-2,,4(,y),B(,2)对A,则过点A的切线方程为y=3(x+x),代入P坐标有=3(-2+)过点B的切线方程为y=3(x+),代入P坐标有，=3(-2+)故切点弦方程为4心=3(x-2),当y=0时，x=2,故过定点(2,0)，答案第12页，共24页

ailerons but wires and pulleys that twisted the wood-and-canvas wings,to 35.What will the drones made by the new wings be firstly used to do?46.A.skicontrol the plane,A.Carry passengers.B.Save people in danger得分评卷人第三部分：英语知识运用（共两节，满分45分）47.A.surScientists have long sought to develop aircrafts that can alter theirC.Test planes.D.Monitor the villages.第一节完形填空（共20小题；每小题1.5分，满分30分）48.A.suitwings during flight,just as birds can.However,most previous attempts have阅读下面短文，从短文后所给各题的四个选项(A、B、C和D)中，49.A.pefailed because they relied on heavy mechanical control structures within the第二节根据短文内容，从短文后的选项中，选出能填人空白处的最佳选出可以填入空白处的最佳选项。50.A.diswings.These structures were also complex and unreliable,said Neil Gersh-选项，选项中有两项为多余选项。enfeld,a physicist and director of the Center for Bits and Atoms at Massa-Madison Williams was studying in her bedroom in Dublin,Ohio,in51.A.obvchusetts Institute of Technology(MIT).Here are some easy steps to create better habits that will surelyAugust 2016 when the door burst open.It was her mother,Leigh Williams,52.A.notimprove your mental health.The new wing consists of a system of tiny,strong,lightweight modules.with a(an)41_story:“A little boy fell into a septic tank(化粪池)，53.A.atteThe shape of the wing can be changed uniformly along its length using twoGet enough sleep.Keeping a consistent sleep schedule will ensureand no one can 42 him."Then she made this 43 of her 13-year-54.A.left段that your body and mind will function properly.Experts recommend thatsmall motors,which apply a twisting pressure to each wingtip.These wingsold daughter:Can you help?55.A.picare covered in "skins"of overlapping strips of flexible material resemblingeach person should sleep for at least 6.5 to8 hours a night.36 WhenMadison and Leigh ran to a neighbor's yard,where they found the56.A.brefish sizes.These strips move across each other as the wings alter,providingyou restart,it refreshes everything and helps your machine function fasterboy's 44 mother and other adults surrounding a septic tank opening.57.A.plaand better.a smooth outer surface,the researchers explained.Its diameter was 45 wider than a basketball.The boy had 46 in58.A.heaWind-tunnel tests of these wings showed that they at least matched theDo some exercise.You should know that regular exercise is necessaryand was drowning in the sewage(污水).59.A.droaerodynamic properties of conventional wings,at about one-tenth thefor a healthy body and soul.Some workout motivation tips from experts arethat you should determine what exercises interest you and work your way upMadison quickly 47 the situation.She was the only one who could60.A.attweight.Initial tests using remotely piloted aircrafts made with these wings48 through the small hole.Without 49,she told the adults,"LowerC.mhave shown great promise,said Benjamin Jenett,a graduate student at thefrom there.Still no idea how to start?37Mind what you eat.38 You know your body and you also knowme in.Inside,the tank was dark,and the air 50.In the process of题号Center for Bits and Atoms at MIT.finding the boy,her left wrist was injured by a hidden pole so 51 that答案The new modular structures the scientists developed could be manu-potato chips have done nothing except make you feel sluggish and guilty.题号factured quickly in mass quantities and then installed by teams of smallDo your heart and waistline a favor by feeding your body healthy thing like.the hand was useless.But Madison went on skimming the surface of the答案题号robots.These modular structures also can be disassembled more easily,lean protein,whole grains and fiber.sewage,hoping to 52 the boy."Every once in a while,I'd see his little答案making repairs simpler.●_39_Use jouraling as a way to release(释放)tension you maytoes she says."Then I would try to grab them."After several failed 53题号"Still,the first aircraft built using this strategy will not be a passengerbe holding in.You can also use it as a way to organize your thoughts,transfershe finally managed to grasp his foot tightly with her 54 hand."Pull答案jet,"Gershenfeld said."Instead,the technology will likely first be tested on题号the chaos from head to paper.You don't necessarily have to write for anme up!"she shouted to the others above.Ten minutes after Madison had答案unmanned aircraft,leading to drones(无人机)that can fly for a longaudience.In fact,writing for yourself can be regarded as self-treatment andentered the tank,she and the boy were 55 out.time,to help deliver internet access or medicine to remote villages and dohelp you become more aware of yourself and your own thoughts.But the boy wasn't out of 56.He had been taken away from得分some rescue works."oxygen long enough that he wasn't breathing He was 57 on his side,32.Why did most previous aircrafts fail to fly like birds?Explore the world.You don't need your passport for this one.40A.The previous wings were complicated and weighed a lot.No matter how old you are,there are many things in this life that you haveand an adult gave him several hard beats on the 58,one right after the第二节other,until the boy coughed up liquids.It was only when Madison heardB.The previous aircraft relied on ailerons to control directions.yet to experience.Get out of your comfort zone and see what the world hasto offer you.You may actually be pleasantly surprised to try things you havehim cry that she knew he was all right.C.There were few scientists to do research on the lighter wings.词的正never done before and how enjoyable they are.It took Madison longer to 59 than the boy.She experiencedD.There was little fuel in the aircrafts to make them fly in the air.Fo33.What is the fourth paragraph mainly about?A.Start writingmonths of physical treatment for her wrist,which,says neighbor Mary,madeare6A.The shape of the new wings.B.Balance yourself.the girl's actions more 60danceB.The result of the tested wings.C.Put down the hamburger and accept whole grains!41.A.amazingB.puzzling62C.The function of the small motors.D.Hire a personal trainer to help you get off your sofa.C.embarrassingD.frighteningD.The working principle of the new wings.E.Think of your body as a computer that needs some rebooting().42.A.reachB.findC.seeD.holdalone34.Which of the following can replace the underlined word"disassembled'F.Go out to new restaurants or hiking trails to expand your experiences.43.A.decisionB.requestbackin Paragraph 6?G.Even if you have to work out slow at first,it's better to start than notC.recommendationD.orderroadA.put awayB.taken apartat all.44.A.cautiousB.curiousC.anxiousD.courageousbeerC.inventedD.analyzed45.A.tightlyB.closelyC.slightlyD.specially【群力压轴卷·2023届高三第三次·有听力英语试题·第3页（共4页）】

ENGLISH高一外研综合(0TJ)掌上周报微信小程序英语周报智能小助手关洽阁轴(2022-2023)第40期KEY CORNER听力材料必修三Umit3综合评估听力材料、参考答案及部分解析40.C。理解目的。根据文中的内容可知，文(Text 1)章介绍了四个海外游学项日。B篇W:How about going out for fish and chips?After you've seen the animals,why not14.D。考查现在完成时的被动语态。句意主题语境：人与社会文化M:Have we got time?The film starts at eight.eat in one of our cafes?Our latest oneThe由于计算机能力的增强，医学和环境科学本文是记叙文Marissa Dates和自己的Maybe we should just have soup.There'sSandwich Place-serves great snacks.Thesome in the fridge from yesterday.Green Restaurant is in the forest and serves a在过去几年取得了重大进展。advance与朋友学做传统莱看，共度优太新年W:I ate it this morning.Let's make somemake之间为被动关系。in the past few41.D。理解具体信息。根据第一段中的启choice of hot meals if you'd prefer that.years是现在完成时的时间标志。They all were spending Rosh HashanahsandwichesIf you're interested,we're running aaway from home for the first time,so they(名师在(Text 2)15.C。考查情态动词。句意：既然没有人给competition.You have to answer some里德尔任何帮助，他一定是自己做了这项wanted to celebrate the Jewish New Year是由山西畅大M:Is Nancycoming to your partythisquestions from the information boards you'll研究。together可知，Marissa Dates和朋友们决围主管、（英语afternoon?find around the park.I'll give you a sheetmust have done对过去的肯定推测。定一起在学校里欢度犹太新年(Rosh主办的教育类W:No,she can't come.She's got to go to thelater.Hand it in before you leave and we'll let完形填空Hashanah)。hospital and visit her uncle.一连线出版you know who the winner is on 23rd May.It's主题语境：人与自我一做人与做事42.A。理解词汇。根据划线词前的aloM:That's a pity.Nancy loves seeing her oldthe 19th now,so not long to wait!G4,国际棕本文是记叙文。89岁的Ella Washingtonour grandmothers have a brisket recipe,butfriends.参考答案获得副学士学位，再续上学梦想。they really aren'tall that different可知，作1SSN2097(Text 3)1-5ABABA6-10 CDCCDl6.D。She put her kids through school和she者和朋友们的祖母们制作牛胸肉的方法96页。本到W:Did you like the campsite where you11-15 DBBDC16-20 DABCDhad to put her own education on the back都大同小异，因此可推知resemble意为线牧师资汤stayed on holiday?21-25 CAABD26-30 BCDBAburner之间为转折关系。back burner意“像”研讨”的方M:Yes,it was nice.But the showers in the31-35ABDCC36-40 BCDCC为“次要地位”43.A。理解具体信息。根据第一段中的数师专业bathroom were old and broken.Luckily,41-45 DAADD46-50AABDCl7.A。根据上文中的put her own educationThey all were spending Rosh Hashanah51-55 ACCBA念，提高we were by the sea so I swam when Ion the back burner和下文中的Ellaaway from home for the first time,so theyneeded to wash.The campsite was really56.He worked as a cashier at a garden center息化和出Washington received her associate degreewanted to celebrate the Jewish New Yeaquiet too.57.Manage time well.at89 years old可知，Washington为了家庭together可知答案。本1(Text 4)58.He pushed the author closer towards很早就放弃了自己的学业，而如今情况发44.D。推断。根据倒数第二段中的they're总局认：W:Hello.What time is the bus to the zoocollege.生了改变一在89岁时她获得了副学士all like,'That's not my brisket.I don't知网(Carriving?59.All people should be respected.学位(associate degree)。know what you did.It looks wrong,.'以及盘版，M:I have no idea.It's supposed to be every60.After-school jobs offer a taste of real world18.B。19.C。根据上文中的raised12anger seven Jewish grandmothers in one15 minutes,but I've been here for 30responsibilities.They help students learnchildren和两空之间的took on several jobstext message可知，祖母们对作者和朋友会科minutes and there's no sign of it.to manage time and interact with people可知，当Washington有了自己的家庭后，们制作的牛胸肉并不满意。nssd.(Text 5)outside of their social circles她搬到了Washington D.C,辛苦劳作，养45.D。理解观点、态度。根据最后一段中的库、W:Mr.Grant,I think that's all we ask you.Do61.One possible version:育自己的孩子们。provide for sb.意为“养Food continues to connect her withyou have any questions you'd like to askYou Are Wanted!育：供养”。relatives who don't live nearby.She saidus?Do you want to improve your English?20.D。21.C。根据上文中的Washingtonmaking brisket helped her stay connectedM:Well,you asked me earlier if I had anyDo you want to make new friends?Thewas only able to complete grade6和下文to family in Chicago you have somethingproject management experience.Are youEnglish Club is the right choice for you.中的how to read,.write,and do the maththat reminds you so much of home llooking for people with this kind ofAimed at developing students'interest inbefore they even began school可知，虽然also reminds Dates of her connection withthe larger Jewish community可知，Dates认experience?learning English,the club holds many fantasticWashington的文化水很有限，但是她依旧教自已的孩子们读书、写字和算术。为制作牛胸肉是她怀念家人和犹太社区(Text 6)activities all year round from the.EnglishM:Hi.You're new at this school,aren't you?Speech Contest to the English Drama Festival22.A。23.A。根据上文中的内容和两空之的一种方式。and has become one of the most popular间的I learned how to be strong可知，女儿C篇W:That'sright.I started here a week ago.student organizations in our school.Mitchell认为自己的母亲Washington是-主题语境：人与自我一做人与做事M:Last Wednesday?W:Well,it wasn't exactly a week ago.It wasIf you're interested,come to the office of位伟大的女性，是母亲的精神让自己学会本文是记叙文。中学生Nora Sun成立公the Student Center(Room 301)from April 5th了坚强。益组织帮助更多女孩学STEM课程.Thursday or Friday...Oh,it was certainlyto April 7th.Join us.You're all welcome!24.B。根据上文中的内容可知，Washington46.A。理解文章结构。根据第一段中的内Friday.The English Club非常渴望学。容可知，Sun和她的祖父Zhaoshe用两个M:So who's your favourite teacher here?62-66 BCAAB67-71 CACAB25.D。根据上文中的working a full--time乐高小人，一个白帽子、个绿帽子，当床W:Well,it's a bit early to say but Ireally like72-76 CBCAB前故事中的人物，他们称其为“两个宇航Mr.Clarke,the art teacher.I never liked artjob、took on several jobs和下文中的omly部分解析retired six years ago可知，Washington大半员”，因此划线词指的应是Sun和她的祖before.单项填空生都在工作。父ZhaosheM:So is art your new favourite subject?1,A。考查交际用语。Go for it.加油，大胆试26.B。27.C。根据下文中的sud小y at Liberty47,A。推断。根据第二段中的her love forW:Ne.I still like Spanish best.一试。Enjoy yourself.玩得开心点。TakeUniversity可知，Washington认为自己可all things science stuck可知，祖父的床前M:Really?I'm rubbish at languages.I like theyour time.别着急。That's right.没错。以实现的目标还有很多，因此在83岁时放事激发了Sum对科学的浓厚兴趣。

千是Sr=lC=162k(1+k2)+9驮29+k21k+=162”k4…小09X+石+82162r162271=+之2，有58安+西分当且收当1=学2，代c.84小小…12。试卷第6页，共6页

第三部分写作（共两节，满分40分）你的留学生朋友Pal要参加“中国古诗词朗读大赛”，请你给他推荐一首古诗，用唐朝诗第一节（满分15分）人王之涣的《登鹳雀楼》或其他你喜欢的古诗进行推荐。要点如下：30g1.诗歌名称及作者；o4、月2.推荐理由：写作手法及内涵等。登鹳雀楼On the Stork Tower附：王之涣Wang Zhihuan白日依山尽，The sun beyond the mountain glows;Bsicde黄河入海流。The Yellow River seawards flows.owult.(欲穷千里目，You can enjoy a grander sight;醉：思/小01共角更上一层楼。By climbing to a greater height..(许渊冲译)文联面可货注意：1.词数应为80左右；2.请按如下格式在答题卡的相应位置作答。Dear Paul,Delighted to know you will participate in the contest,I'd like to recommendYours,Li Hua第二节（满分25分）阅读下面材料，根据其内容和所给段落开头语续写一段，使之构成一篇完整的短文。The atmobile industry is pending billions on self-drivingrsusecan sit in the backseat like some high-powered corporate executive.But what if we quite like driving?On holiday a few years ago,I spent hours being transported on trains,buses and planes.Then,finally,came the section of the holiday during which I hired a set of wheels.Ater decades of marriage,it was not often that you received real praise from your partner,butthe highways of Crete compliments came with every successful action.h well done!"said英语试题第9页（共10页）

0.012成绩在[60,70)有12×0004+008+0.0126人，12×则5可取0,1,2,3P-0叭-号P(5=1)=CC=28Ci255P6=2)e=2p5=)C5C=1所以分布列为02318115555555E(5)=0x1281255+1+2×+3×所555555119.在aABC中，内角A,B,C所对的边分别为a,b,c,己知c=2 asin C-2 ccos A,(1)求sin2A:(2)若a=2,求△ABC面积的最大值.3【答案】(1)42+V万(2)3【解析】【分析】(1)利用正弦定理把已知等式中的边转化为角的正弦，化简整理可求得1sin A-cos A=2,方进而求得sin2A:(2)利用余弦定理表示出b+℃2，根据三角形面积公式和基本不等式求得最值.【小问1详解】b因为c=2 asin C-2 ccosA,由正弦定理sinA sin B sinc,sin C=2sin Asin C-2sin CcosA,第16页/共23页

描述的事情发生在过去，应用一般过去时，且House Zero project与complete之间为被动关系，应用被动语态，故填was completed。59.that/which。考查关系代词。设空处引导限制性定语从句，指代Wolf Ranch community,且在从句中作主语，故填that或which。60.building。考查动词-ing形式。设空处作介词of的宾语，应用动词-ing形式，故填building。.61.and。考查连词。both…and.为固定搭配，表示“既…又…”，故填and。62.buyers。考查名词复数。buyer为可数名词，此处表示泛指，且其前无冠词修饰，应用其复数形式，故填buyers。.63.excellently。考查副词。设空处作状语，修饰performing,应用副词，故填excellently。64.togo。考查动词不定式。have a long way to go为固定用法，表示“有很长的路要走”，故填togo。65.exciting。考查形容词。设空处作定语，修饰turn,应用形容词，表示“令人激动的”，故填exciting。

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当n=1时，2S1=2a1=a1+a,可得a1=1;当n≥2时，2(Sn-Sn-1)=2an=an十a2-am-1=2,于是3V4-7a品-1=合-F≤1则an十an-1=a-a-1=(an十an-1)(an-am-1);.+=号（当退仅当=不7，即=时2由an十an-1>0,故an-an-1=1,∴.an是首项、公差均为1的等差数列，故an=n.取等号)，此时l=2,r=√2，h=√-r=√2，母线与(7分)底面所成角的正弦值为上=故选A2)号+≤m+m3m能使号十只≤m皮立的n的最大值为2m-1。方朱所得表画为由BDEF,品-器=λ，λ∈(0，∴.bnm=2m-1(m≥3)，1],AB=1,则Sm0=(1+A)VR-2以+3-∴.{bm}的前50项和为0+1+5+7+…+99=0合V瓜-1)+21+x,令h(A)=(x-1)++1+5+99)×48=2497.(16分)22(1+λ)2，h'()=42(a+1)>0,.h(λ)mx=h(1)=8,(SEFBD)max=SBDED=√2，当0∈(0，Y门时，显然面高三·数学·高频考点二十·参考答案a截正方体所得截面面积最大时，截面为面CBD,S50-9,当g=0时，*面D选择题1.C2.A3.C4.A5.BCD6.AB。截正方体所得截面为填空题ABCD,SABCD=1,.面a截99正方体所得截面面积最大时7.①④⑤8.73截面为面BDB1D1,同理面提示：B过A、D时，截正方体所得1.如图所示截面面积最大时截面为面ADBC.连接BD,AC,B1C,面a与面B所成锐二面角为B1一BD1一C.B1CL面AD1BC1,AC⊥面BDB,D,∴AC,BC的所成角大小为二面角B1一BD一C大小，：∠BCA=60°，.面a与面B所成锐二面角大小为60°.故选C,折叠后，AB=PC=AB=DC=1,BC=√2，∴.PC+4.由题意，PA,PB,PC,PD,PE在DPB2=2=BC,.PC⊥PB,又P(A)E⊥P(A)B,面ABCDE上的射影P'A,P(D)E⊥P(D)C,PE⊥面PBC,.EP,BP,CPPB,P'C,P'D,PE,如图所示，两两相互垂直，以EP,BP,CP为相邻三条棱的长方五个三角形都是等腰三角形体如图所示，根据长方体的对称性可知长方体的外接且∠AP'B=72°，P'A=729球就是三棱锥P一BCE的外接球，长方体的体对角线AB2sin36,又cos36°≈0.8，令AB√小+1+吗-罗其外接球*径为a4,则=BC=CD=DE=AE=a,.'.P'A=2√1-c0s236无我西软为xx()-受散选C5,又正二十面体的每一个面均为等边三角形，即2.设圆锥底面半径为r,高为h,母线长为l,则l=2,h=PA=AB=a,且PP'⊥面ABCDE,∴.PA与面-7=4子，V=号2h=分r4-7,s39

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noise...W:What do you mean,late?I come back around eleven!That's not late at all.M:Well,you spend hours after that going in and out,in and out,until my head feels ready to burst.W:Oh,I'm so sorry to hear that.I'll see what I can do with the door this weekend.M:Thank you so much,Miss Ames!You're the kindest lady in the world.Text 8W:We're finally in our last year of high school.How exciting!I can't wait to graduate.M:Neither can I,but I don't think this year is going to be that easy.W:What do you mean?M:Well,in order to get into a good college,we have to take challenging classes this year.W:Of course.But we'll still have some time for fun.M:I don't know...I'm taking advanced math,English,two different science classes...W:Oh,don't worry.You've taken difficult classes before.M:Yes,but I'm also volunteering at the hospital three times a week.I think it will help me getinto medical school.W:I'm volunteering,too.I expect to be busy this year,but I still plan to enjoy myself.M:Where are you volunteering?W:At the zoo.You should come visit.I'll be there every Saturday and Sunday.Text 9M:How was your doctor's appointment?W:It was fine.He says that I'm pretty healthy overall.But I told him that I have trouble sleepingsometimes,and he offered me sleeping pills.M:Did you take them?W:No.I'm afraid they're harmful to my healthM:So what are you going to do?W:I think I will schedule an appointment with a psychologist.Maybe I can't sleep because I havetoo much anxiety.Talking to someone may help.M:You know,I used to have trouble sleeping.And I found a few things that help.If I exerciseoutdoors in the morning,it relaxes me all day.Also,if I don't use my phone or computer after8:00 p.m.,then I can easily fall asleep at 10:00.W:Those are good suggestions.Maybe I should try those things before I pay to see apsychologist.M:Yeah,you might as well try.Text 10This is a statement from the National Weather Service.The biggest storm in twenty years hitLos Angeles this afternoon.Over the past three hours,the downtown area has gotten 2.5 inches ofrain.Several roads are closed because of flooding.People who live in low areas have even beenrescued by boat.Along the coast,the highway has been closed.Sections of the hills have fallenonto the road.Back in the city,high winds have already knocked down several trees.Hundreds ofpeople are without power.Thousands more homes and businesses are expected to lose powertonight.The Weather Service strongly suggests that people stay at home.If you must drivesomewhere,never drive through water that is covering the road.You won't know how deep it is,and your car might get stuck.

由题意可知N心1000，即CD>1000,解得≥45，nEN2即N出现在第44组之后.又第及组的和为}二瓷=公-1前k组的和为1十(1十2)十…十(1+2十…十2-1)=(21-1)十(22-1)十…十(2-1)=(21+22+…+2)-k=2+1-k-2,设满足条件的的N在第b+1(∈N*)组(k≥44)，且第N项为第+1组的第m(m∈N*)个数，第k十1组的前m项和为1十2十22十…十2m-1=2m一1，要使该数列的前N项和为2的整数幂，即2m一1与一k一2互为相反数，即2m-1=2+k,所以=2m一3，由k≥44，所以2m-3≥44，m≥6，取m=6,此时k=26-3=61,对应满足的最小条件为N=61(6】+1D+6=1897.2四、解答题（本大题共6小题，共70分.解答时应写出必要的文字说明、证明过程或演算步骤）17.【解析】(1)因为a1=2,a2+1一2an+1=a2十2am所以，a2+1一a2=（an+1一an)(an+1十an)=2(a+1十an),因为数列{an}各项均为正数，即an+1十an>0,所以，an+1一an=2,即数列{an}为等差数列，公差为d=2,首项为a=2.所以a=2(n1)X2=2n.…5分(2)由(1)知an=2m,其公差为d=2,所以，bn=(-1)"an=(-1)”·2n所以，b十b2十b3+…十b20=(-a十a2)七(-ag十a4)+…+(-a19十a20)=10d=20.…10分18.【解析】(1)方法一：因为BC⊥面PAB,PEC面PAB,所以BC⊥PE.因为PE⊥EC,EC∩BC=C,EC,BCC面BCD,所以PE⊥面BCD,又BDC面BCD,所以PE⊥BD.又因为tan∠ABD=an∠BCE=号，所以∠ABD=∠BCE,∠ABD+∠CEB=90°，即BD1CE.因为PE∩CE=E,PE,CEC面PEC,所以BD面PEC.…6分方法二：依题意得AD⊥面PAB,以A为坐标原点，AB方向为x轴正方向，建立如图所示的空间直角坐标系A-xy2.DB设∠PAB=0,0∈(0，π)，则B(2,0,0),C(2,2,0),D(0,1,0),E(1,0,0),P(2cos0,0,2sin0),PE=(1-2cos0,0,-2sin0),CE=(-1,-2,0).因为PELEC,所以P应.C应-2cos0-1-0,0s0-,所以0-于.所以P(1,0,3),P元=(1,2，-3)，Pi=(0,0,-3),Pi=(-1,1,-3).设面PEC的法向量为m=(x,y,之).由PC·m=0,PE·m=0,得x+2y-√3x=0,令y=1,则x=-2,即m=(-2,1,0).-√3x=0,由BD=(-2,l,0)=m,所以BDL面PEC.…6分(2)方法一：由(1)得PELAB,E为AB的中，点，所以PB=PA=AB=2.以E为坐标原点，EB,EP所在直线分别为x轴，之轴，过点E作BC的行线为y轴，建立空间直角坐标系E-xyz,z◆DH.B数学试题参考答案（长郡版）一4

17.Please pass the hat to me.玩转语法1.will;stay.2.will be3.won't visit4.will take5.will go6.When will;climb7.Are;going8.How is;going to9.won't go10.Can you show me your photos?11.Mom made me a kite yesterday.12.Please give Anna the letter.13.We plan to buy our mother some flowers tomorrow.14.My grandfather told me a story yesterday.。3/3

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moved into third gear.I was feeling pretty good as I came to a stop and looked to Daddy for approval. He glared at me and then barked,"You've been driving, haven't you?"He must have thought I'd been practicing in some- body else's car.I quickly explained that my training was all done on the Ford. That was about 60 years ago.I can still see the nod he gave me when he said,“Well,you did a good job.” 21.How did the author learn to drive at the beginning? A.He was taught by his mother. B.He learned it at Shawnee High School. C.He learned it with the help of his father. D.He taught himself with an instruction handbook

B.People should find and value positive things. C.Happiness is difficult to find. D.Happiness sometimes arises from bad moments.