形式。

10.某人在11次本卷考查：1随机变量及其分布：2.满分150分考试时间120分钟若P(X=kA.7合分人复分人第Ⅱ卷总分赛的学生中随机选择一名，他的竞赛成绩为A等的概率为()11.在某独立重事件A发生题号第I卷(附：若X~N(4,o2),则P(4-G≤X≤4+o)=0.6827,p∈(0,1).者得分第I卷选择题（共60分）P(u-20≤X≤u+2o)=0.9545每小题5分，共60分.在每小题给P(μ-30≤X≤u+3o)=0.9973)发生的次数是()本大题共12小题，A.0.0455B.0.0214C.0.0428一、出的四个选项中，只有一项是符合题目要求的。选择题：D.0.02275已知随机变量X的分布列为PX=)=。(1=1,2,3,4,则6.先后抛掷一颗质地均匀的骰子两次，观察向上的点数.在第一次A.pE(XB.(1-pa向上的点数为奇数的条件下，两次点数和不大于7的概率为1.（)C.E(ZP2≤X<4)=(.、7D.9A13718B.12.3D.「D(B.51001012.甲、乙、A.22.在四次独立重复试验中，事件A在每次试验中发生的概率相同，7.某次国际象棋比赛规定，胜一局得3分，一局得1分，负一局次传球时得0分，某参赛队员比赛一局胜的概率为a,局的概率为b,负人，则若事件4至少发生一次的概率为65则事件A发生次数5的期81的概率为c(a,b,c∈[0,1))，已知他比赛一局得分的数学期望为A.1-1,则ab的最大值为(望是(B.c.8D.832D.1463.一台机器生产某种产品，如果生产出一件甲等品可获利50元，生8.某群体中的每位成员使用移动支付的概率都为P,各成员的支付产出一件乙等品可获利30元，生产一件次品，要赔20元，已知方式相互独立，设X为该群体的10位成员中使用移动支付的人阳这台机器生产出甲等、乙等和次品的概率分别为0.6、0.3和0.1，数，D(X)=2.4,且P(X=4)

形结合思想，函数与方程思想等；考查直观想象，逻辑推理，数学运算等核心素养；体现基础性和综合性.满分12分.解法一：(1)如图1，取AB中点O,连接PO,CO因为PA=PB=V2,AB=2,所以PO⊥AB,PO=1,BO=1.又因为ABCD是菱形，∠ABC=60°，所以CO⊥AB,CO=V3因为PC=2,所以PC2=P02+C0,所以P0⊥C0.又因为ABC面ABCD,COC面ABCD,AB∩CO=O,所以P0L面ABCD..2分因为AD∥BC,BCC面PBC,AD文面PBC,所以AD∥面PBC,所以VD-Pac=VAPc=V,-ABC=x1x5x4=5433分因为VM-PBc==VD-P8’.4分62所以点M到面PBC的距离是点D到面PBC的距离的2，所以PM=MD.5分(图1)(图2)(2)由(1)知，B0⊥C0,PO⊥B0,P0⊥C0,如图2，以0为坐标原点，OC,OB,OP的方向分别为x轴，y轴，z轴正方向建立空间直角坐标系，6分则A(0,-1,0),B(0,10),C(V3,0.0,D(3,-2,0,P(0,01),所以M则c-,c-版-m-点-a.西-9-引因为Q∈AP,设AQ=AP=(0,,),则C0=A0-AC=-V3,2-1,),数学参考答案及评分细则第8页（共20页）

15.直线I:y=2x和2：y=kx+1与x轴围成的三角形是等腰三角形，写出满足条件的k的两个可能取值：和.(写对一个得3分，写对两个得5分)16.在同-面直角坐标系中，P,Q分别是函数f(x)=axe'-n(ax)和g(x）=2n(x-1图象上的动点，若对任意a>0,有1PQ1≥m恒成立，则实数m的最大值为四、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)》记数列{an}的前n项和为Sn,对任意neN',有Sn=n(an+n-1).(1)证明：{an}是等差数列；(2)若当且仅当n=7时，S,取得最大值，求a1的取值范围.18.(12分)设△ABC的内角A,B,C所对的边分别为a,b,c,且有2sin(B+)=6+C6a(1)求角A;(2)若BC边上的高h=4a,求cosBeosC.19.（12分)》如图，在边长为4的正三角形ABC中，E,F分别为边AB,AC的中点.将△AEF沿EF翻折至△AEF,得到四棱锥A,-EFCB,P为A,C的中点，(1)证明：FP∥面A,BE:(2)若面A,EF⊥面EFCB,求直线A,F与面BFP所成的角的正弦值数学试卷第4页（共5页）

C.|x-2|<|2-y二、填空题：本题共4小题，每小题5分，共20分。D.|x-3<|3-yA尖直面早特(3.已知图数n=T2若2三6.23.2=2，g2=1.则1(2)店D14.请写出一个与y轴利直线)一：都相切的圆的方遥B15.如图，正方体ARCD AB,CD的校长为4，则三棱锥CDB1一A1BC和三棱锥A,-AB,D,公共部分的体积为16.在一个正三角形的三边上，分别取个距顶点最近的十等分点，连接形成的三角形也为正角形如图1所示图中共有2个正三角形)，然后在拉小的正三角形中，以同样的方式形成一个更小的正三角形，如此重复多次，可得到如图2所示的优美图形（图中共有1个正三角形），这个过程称为迭代在边长为243的正三角形的三边上，分别取一个三等分点，连接成一个较小的正三角形，然后迭代得到如图3所示的图形（图中共有10个正三角形），其中最小的正三角形的面积为外立加林图1图2图3三、解答题：共70分.解答应写出文字说明、证明过程或演算步骤.第17~21题为必考题，每个试题考生都必须作答.第22、23题为选考题，考生根据要求作答(一)必考题：共60分17.(12分)已知△ABC的内角A,B,C的对边分别为a,bc,且cos2B-cos2C-sinA·(sinAsin B).(1)求角C的大小；(2)若CDLAB于点D,CD=3,求△ABC的面积的最小值.18.(12分)如图，矩形ABCD所在的面垂直于半圆所在的面，AB=2AD=2a,点E是半圆O上异于A,B的点(1)证明：EA⊥EC.全国100所名校最新高考冲刺卷第3页（共5页）【23·高考样卷·数学文科（二）一GQN·A】

∠FBD=∠ABD+∠ABF:∠BFD=∠DCB+∠CBF∠ABF=∠CBF,.∠FBD=∠BFD.BD=FD…10分六、（本题满分12分）2L.解：(1)总人数为9÷18%=50（人）50-9-14-6=21（人）.B级人数为21人，统计图略…4分(2)100.8°78.5…8分(3)650x(18%+42%)=390(人)》“.九年级达到良好及良好以上的学生人数约为390人…12分七、（本题满分12分）】22.解：(1y=x2+24-3=(x+1P-4顶点为(-1，-4)y=x24-3=-(x+22+1顶点为(-2,1)设根活数为y则广法村相你。,∴.根函数为y=-5x-9…4分(2①y=x24mx+4m34m+1-(x-2mP4m+1顶点为(2m,-4m+1)-4m+1=-2x2m+1∴.x=2m时，y=-2x+1:,满足二次函数C的所有二次函数的根函数为=-2x+1…8分②x=-3时，Jy=(-324mx(-3)+4m2-4m+1-4m248m+10,点P坐标为(-3,4m2+8m+10)设-4m+8m+10-4(m+1)+6.当m=-1时，点P纵坐标最小值为6即点P到x轴的最小距离为6，此时m=-1.…12分八、（本题满分14分）23.(1)证明：四边形ABCD是正方形，∠DBE=45△EBG是等腰直角三角形,能-妥：CD∥RCP/DE人四边形DEC为行西边形.EF-DC2:△BCD是等膜直角三角形÷品--孚∴配品BDBD2又：∠GEF=LEBD=45.∴.△BDE△EFG…4分(2)解：由(1)知△BDE∽△EFG∴，∠EFG=∠BDEg四边形DEFC为行四边形.∠EFC=∠EDC÷∠CFG=∠BDC=45°8分(3懈GE-V2EF-CDCD-②BE2BD 2…品∠FEG=∠DBE=135.△GEFM△EBD器品:H为BC中点∴，△DCH≌△EBH.BE=CD-4:..GE-2V2 DE=VADTAE=V4+8=4V5器-部2vV2 GrGF-2V1044V5DG-DB+BG-4V7+2V2-6V2 PC-2V10V5…14分DG 6V2 3-2-

“业考试冲刺试卷咒分钟哈磨光黑四、解答题（大题共2小题，每小题8分，满分16分）六名数学火透动阳而兴田西宽心o0子村●●●●●●●●●甜403422t●8265nt第1个题第2个第3个2第4个1门1小货配这种规律，第5个10字样的棋子个数是之第n个“100字样的棋s子数是nt2C2n十上)222)若有2023个这样的棋子，按这种摆法是否正好摆成一人100，若能。或摆出是X第几个“100？若不能，说明理由49p要的增0该条约是434大18某校数学兴趣小组借助无人机测量一条河流的宽度CD.如赤，一架水飞行的无望厦条约》、s2/7人机在A处测得正前方河流的左岸C处的俯角为α，无人船冰线AF方向继绮。(A、)D行40米至B处，测得正前方河流右岸D处的俯角为30°.线段AM的长为无人狗润典七山近朵化探索面的铅直高度，点M,C,D在同一年青新(1)无人机的飞行高度AM;30°(2)河流的宽度CD(结限留根号).25戈们说孙中山先生五、解答题（本大题共2小题，每小题10分，满分20分）以后要非常注意I9如图，在△4BC中，点D,E,F分别在边AB,AC,BC上，连接DE,EF,已知四日)边形BFED是行四边形，FC-=3FB(1)若AB=12,求线段AD的长会议共6页(2）若口BFED的面积为4，求△的面1N八2B20.如，点c在o0上，1B为直径，BD与过点c的年天D,BD与δ0交于点E.(1)求证：BC分∠DBA;(2)如果∠ABD=60°，圆的半径为2，求BD的长301冲刺试卷（一）数学第3页共10页

参考答案1.B解析：易知C={1,2},其子集个数为22=4，故选B.2.A解析：根据题意知，表示向量A的复数为1十5i,所以在复面上所对应的点为(1,5)，位于第一象限.故选A.3.D解析：根据雷达图，甲同学按照科目综合指标值从高到低顺序为物理、历史（化学）、地理、生物、政治，乙同学按照科目综合指标值从高到低顺序为历史、物理（政治）、地理、生物、化学.根据新高考选科模式规则，选考科目最合理的是：甲应选物理、化学、地理；乙应选历史、政治、地理.故选D.4.B解析：角a的始边与x轴非负半轴重合，终边过点A(a,2a)(其中a≠0)，tan a-2,cos 2a+cos'a-2cos'asin'a=2-tan'a2sina+cos2 x tana+15·故选B.A解析0a=3一2.u:2了5=-3-2,4=二2y5-2√3+1-3-2√3+1所以{am}是周期为3的数列，因为2023=3×674+1，所以a2o23=a1=1.故选A.6.C解析：由A和B是圆C:(x一1)2十y2=1上的两点，且AB=√2，则∠ACB=2不妨设A(1十cos6,sin6,则B(1+cos(0+5),sin(6+5),即B(1-sin0,cos6),PA=(cos 0-3,sin 0-1),PB=(-3-sin 0,cos 0-1),3 PA-PB=(sin 0++3cos 0-6,3sin 0-cos 0-2),|3PA-Pi12=(sin0+3cos0-6)2+(3sin0-cos0-2)2=50-8(3sin0+4cos0)=50-40sin(0+o),又sin(0+o)∈[-1,1]，即当sin(0+o)=-1时，3PA-PB12的最大值为90，则|3P才-PB的最大值为3√10，故选C.7.C解析：可以直接求导证明如下结构的不等式：e>1十x(x≠0)，x>sinx(x>0),xeo.1>sin(eo.1),从而a>c,对于b,c:l>eo.1>l-0.1=0.9,sin(e-o.1)>sin0.9,从而c>b,所以a>c>b,故选C.22023届高三“一起考”大联考（压轴卷）·数学参考答案

北京市朝阳区2022~2023学年度第一学期期末质量检测高三英语2023.1(考试时间90分钟满分100分)》本试卷共10页。考生务必在答题卡指定区域作答，在试卷上作答无效。第一部分知识运用（共两节，30分）第一节（共10小题；每小题1.5分，共15分）阅读下面短文，掌握其大意，从每题所给的A、B、C、D四个选项中，选出最佳选项，并在答题卡上将该项涂黑。Early in my teaching career,I heard countless make-believe stories for unfinished homework.Then I grew less trusting and quitted 1 any excuse.When the students at my new schooldidn't finish homework,I never asked why.Instead,I just sighed loudly and recorded a zero inthe grade book.I soon gained the 2 I thought I wanted.One day,Anthony approached me..“Could I talk to you?”he asked_3_·“I know yousaid no excuse,but I don't want you to think I'm 4 because I often come without myhomework."He then looked up at me for the first time."It's just that...my dad moved out,andmy mom works at night,so I have to look after my little brothers.Often,they cry a lot,and it'shard for me to_5_”I was about to ask why he didn't tell me earlier when I suddenly realized why.So I changedthe 6."Would it help if you stayed after school and worked on it before you go home?"He nodded hard.Anthony became the first student in my after-school study session.Several days later,Terrelljoined him,followed by Sandy and Randy.Before long,I had a room full of students.Theirstories were not amusing,but all very 7:The power company 8 our lights because we couldn't pay the bill.My dad says schoolwork is just a waste of time.·We don't have any paper i讥the house.I thus discovered not all kids come from families that are 9.Not all kids have a quietbedroom with a desk and study light.Some don't even have home.Most importantly,I learnedthat“I'll listen'”10 better than“No excuse!'”1.A.inventingB.findingC.acceptingD.offering2.A.reputationB.benefitC.experienceD.praise3.A.loudlyB.shylyC.curiouslyD.eagerly4.A.p00rB.meanC.lazyD.weak5.A.behaveB.concentrateC.struggleD.compete高三英语试卷第1页（共10页）

【第40期】第3章3.1~3.3同步测试题-、1.D2.C3.B4.D5.A6.C7.B8.B9.C10.B二、11.(5,2)12.-1013.(-3,4)14.315.(1.0)16.217.（3.3)或(-3.3)18.(-3，-2三、19.因为点P在过.点A(2,-3)且与x轴行的直线上，所以点P的纵坐标与点A的纵坐标均为-3，即m-1=-3.解得m=-2.故点P的坐标为(0，-3).20.(1)点M(2.3),N(-3,2),L(0,-2),0(0,0),P(2,-2).(2)点A,B,C,D的位置如图所示A-10ED第20题图21.(1)因为点A在y轴上，所以横坐标为0，即3a-5=0.解得a=号将a=号代入.可得点A的坐标为(0，》(2)依题意，有3a-5=a+1,即3a-5=a+1或3a-5=-(a+1).①当3a-5=a+1时，得a=3,此时点4的坐标为(4,4)；②当3a-5=-(a+1)时，得a=1.此时点4的坐标为(-2,2).因为点A在y轴的左侧，所以点A的横坐标为负数.所以a=1,点A的坐标为(-2,2).22.(1)△A'B'C如图所示.点B(-4,1),点C(-1,-1).(2)点p'的坐标为(a-5,b-2).y米AB2B4-3102第22题图23.台风的起始位置为(4，-8)，B市的位置为(4.0)当B市受影响时，台风的位置是点C(4,-3).所以100×(8-3)÷10=50（时）.所以经过50小时后，B市将受到台风的影响，画图略.

高三数学考试参考答案1.A【解析】本题考查集合的运算，考查数学运算的核心素养，因为A={x00,所以t∈(3,4).6.D【解析】本题考查解三角形的知识，考查数学运算的核心素养，因为bcos A=a(W3-cosB),所以sin Bcos A=√3sinA-sin Acos B,移项得sin Bcos A十sin Acos B=√3sinA,即sinC=√3sinA,所以c=√3a=2√3，7.C【解析】本题考查抽象函数的求值，考查数学抽象的核心素养！因为f(x+y)=f(x)+f(y),所以f(0+0)=f(0)+f(0)=2f(0),即f(0)=0.所以fln2023)+fln2023)=f1n2023-ln2023)=f0)=0.8.B【解析】本题考查数学文化与等比数列的求和，考查数学抽象与数学运算的核心素养由题意，若正整数m≤6，且与6“不互质，则这个数为偶数或3的倍数，共有号×6个，所以(6”)=号×6”=2X6"1,即数列{(6”)}是首项为2，公比为6的等比数列，所以S2=32g-号0t-10.9.AC【解析】本题考查直线与圆的位置关系，考查数学运算的核心素养对于A,因为圆心C(1,2)在直线y=kx十1上，所以2=k+1,解得k=1,A正确；【高三数学·参考答案第1页（共8页）】531C

13:10|4.9K/s2⊙o56Ho49ll☑0〈数学试卷.pdf●●●23.(本题13分)如图，已知二次函数y=-x+bx+c的图象交x轴寸点A(-1,0),B(5,0),交y轴于点C(1)求这个二次函数的表达式：(2)如图1，点M从点B出发，以每秒V2个单位长度的速度沿线段BC向点C运动，点N从点O出发，以每秒1个单位长度的速度沿线段OB向点B运动，点M,N同时出发.设运动时间为t秒(0<1<5).当t为何值时，△BMN的面积最大？最大面积是多少？(3)已知P是抛物线上一点，在直线BC上是否存在点Q,使以A,C,P,Q为顶点的四边形是行四边形？若存在，直接写出点Q坐标：若不存在，请说明理由.备用图718泪OD目录模式播放三▣

22.长方体的一个顶点上的三条棱长分别是3,4,5且它的8个顶点都在同一个球面上，则这个球的表面积为5>.三、解答题：本大题共3小题，共30分.解答应写出文字说明、证明过程或演算步骤24.(23.(本小题满分10分)某网校推出试听的收费标准为每课时100元，现推出学员优惠活动，具体收费标准如下（每次听课1课时)：第n次课第1次课第2次课第3次课第4次课或之后收费比例0.90.80.70.6现随机抽取100位学员并统计他们的听课次数，得到数据如下：听课课时数1课时2课时3课时不少于4课时频数50201020假设该网校的成本为每课时50元。(1)估计1位学员听课三次及以上的概率：(2)求一位学员听课4课时，该网校所获得的均利润的家中如0对，n日，前，盖阴动数激1。顺为第京+心1入是，数学·模拟卷四第4页（共5页）

丽水市2022学年第二学期普通高中教学质量监控高二数学答案(（2023.06)一、单项选择题DACDBBCC二、多项选择题9.BC10.ABD 11.ACD12.ABD三、填空题13.3-215.642114.242212516.四、解答题17.（I)图中所有矩形面积之和为1，得(0.04+2×0.08+0.12+0.16+2a+04+0.52)×0.5=1,得a=0.3;3(Ⅱ)月人均用水量低于2立方米的居民占比为(0.08+0.16+0.3+0.4)×0.5=47%,月人均用水量低于2.5立方米的居民占比为47%+0.5×0.52×100%=73%,所以M∈(2,2.5)，所以0.47+(M-2)×0.52=0.6,得M=2.25:6分(Ⅲ)由分层抽样知，[3,3.5)中抽3户，记作a,a2,a,[3.5,4)中抽2户，记作b,b2,[4,4.5)中抽1户，记作c,则从这6户中抽取2户有(a,a2),(a,a),(a,b),（a,b2),(a,c),（a2,a)；(a2,b),(a2,b2),(a2,c),(a3,b),(a3,b2),(a,c),(b,b2),(b,c),(b2,c)共15个基本事件；满足发言的2户来自不同组的有(a,b),（a,b2),(a,c),(a2,b),(4,b2),(a,c),(a,b),(a,b),(a,c),(6,c),(b2,c)共11个基本事件，所以发言的2户来自不同组的概率P=1川.10分18.（1)由恩f()=sin2x-cos2x+1=2sin2x-牙+1，周期T=π，高二数学试题卷第1页共4页

20.（12分)已知函数f(x)=x(x-c)2.(1)若函数f(x)在x=2处有极大值，求实数c的值：(2)若不等式f(x)≤8对任意x∈[0,2]恒成立，求实数c的取值范围.21.(12分)某校拟对全校学生进行体能检测，并规定：学生体能检测成绩不低于60分为合格，否则为不合格：若全年级不合格人数不超过总人数的5%，则该年级体能检测达标，否则该年级体能检测不达标，需加强锻炼(1)为准备体能检测，甲、乙两位同学计划每天开展一轮羽毛球比赛以提高体能，并约定每轮比赛均采用七局四胜制（一方获胜四局则本轮比赛结束）.假设甲同学每局比赛获胜的概率均为，求甲在一轮比赛中至少打了五局并获胜的条件下，前3局比赛均获胜的概率；(2)经过一段时间的体能训练后，该校进行了体能检测，并从高二年级1000名学生中随机抽取了40名学生的成绩作分析.将这40名学生体能检测的均成绩记为μ，标准差记为。，高二年级学生体能检测成绩近似服从正态分布N(4,σ2).已知4=74,0=7，请估计该校高二年级学生体能检测是否合格？附：若随机变量5~N(4,σ2)，则P(u-o<5≤4+o)≈0.6827，P(4-2o<5≤4+2o)≈0.9545，P(4-3σ<5≤4+3o)≈0.9973.高二数学试卷第5页共6页5

基础题与中考新考法·八年级·上·数学第3课时用“ASA”或“AAS”判定三角形全等(共424考：单独87考，在几何综合题、函数综合题等中涉及337考)】教材知识知识点①三角形全等的基本事实：角边角69考·重点点拔1.基本事实：两角和它们的夹边分别相等的两个三角形全等，注意：(1)“ASA”与“AAS”简记为ASA(或角边角)的区别：“ASA”中边是两角2.几何语言：如图，在△ABC和△DEF中，的夹边，“AAS”中边是其中∠B=∠E,一角的对边；(2)“ASA”与“AAS”的联BC=EF,系：由三角形内角和定理可∠C=∠F,知，“AAS”可由“ASA”推导..△ABC≌△DEF(ASA).得出.知识点(2三角形全等的基本事实：角角边5考1.基本事实：两角和其中一个角的对边分别相等的两个三角形全等.简记为AAS(或角角边).》注意2.几何语言：如图，在△ABC和△DEF中，∠B=∠E,∠C=∠F,AC=DF,..△ABC≌△DEF(AAS).重难题解法》答案见本册P68●“截长补短法”构造全等三角形8考·现学活用·练-1如图，在四边形AB例一题多？解法如图，在△ABC中，∠A=100°，∠ABC=40°，CD中，∠ABC=∠ADC=BD分∠ABC,延长BD至点E,连接CE,且∠DCE=∠DCB,90°，AD=DC,若BD=8cm,求证：BC=AB+CE.则四边形ABCD的面积为规范解题证法一：截长法练-1题图例题图18

则a=a=1a=号=子a=3a,=a,号8a-3035=23,所以b1=0,b2=1,b3=1,b4=2,b5=3,b6=3,b,=4,…,b33=21,b34=22,b35=23,所以数列{[am]}前35项的和为T35=(0+2十4+…+22)+2(1十3十5+…+21)+23=397.故答案为：397.17.解：(1)因为Sm=2am-a1,①所以S.-1=2a-1-a1(n≥2)，②1分①-②得an=Sn-S。-1=2an-2an-1,即an=2an-1,…3分则{a}为等比数列，且公比q=2,…4分因为Q1=2,所以n=Q1·g=2”.…5分(2)由(1)可得，Tm=1X2十+2X22+3X23十…十(n-1)·2m-1十n·2”,③…6分2Tn=1X22十2X23十3X24+…十(n-1)·2”+n·2+1,④…7分③-④得-Tm=2十22十23十24十…十2”-n·2m+1=(1-)·2+1-2,…9分故Tn=(n-1)。20+1十2.…10分18解：1)b+c)2-a2+(2+压)bc可化为+c2-a=5c.………2分2√/15由余弦定理得cosA=+c2一a22bc-=152bc4分26c4:A∈0，A=-sA=√1-（年）5分(2)设∠ACD=0,由∠BCD=2∠ACD可得∠BCD=20,2c在△ADC中，由正弦定理得3 CDsn2smA有350gS2可得7D6sm9,…7分43 CD在△BCD中由孩定理得n2nB可得0可得3sin29-6sin0,有6sin6cos0=6sin0,sin Bsin B又sin0>0,有sinB=c0s0,…………9分又由B为锐角，有sinB=sin(受-9），有B=受-0，可得B+0=罗，又由A+B+C=,可得∠BCD=20=受-A,有co∠BCD=simA=4,11分又出os20=2os0-1,有2cos0-1=,可得os0=不.即simB=……12分419.解：1以工龄长工人得高世约奖”的频车估计救率，每个工龄长工人得“高竹约奖”的赞率为需了………1分5人中，恰有3人得商节约奖“概率为心·（号）.（号）-架：40…………………………………………2分恰有4人得离节约奖“概率为《·（信）广·号-品：…………3分5人都得高节约奖“餐率为（分）°=0，.e...........。。.........……………4分【高三数学参考答案第3页（共6页）】24010C

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10:47|12.1K/s2⊙HD 5G HD 4G1615b2f35bff0ac5a4711a28d16222f06..文件预览1/6最新中考模拟训练试题·英语参考答案山西省2023年最新中考模拟训练试题·英语参考答案（四~六）》(四)一、情景反应本题共5个小题，每小题你将听到一组对话。请你从每小题所给的A、B、C三幅图片中，选出与你所听到的信息相关联的一项，并在答题卡上将该项涂黑。1.W:Do you like playing football?M:Yes,I do.2.W:Who's the woman with a pair of glasses?M:Oh,she is my English teacher.3.W:What will you do on the weekend?M:I will play the drums with my brother.4.W:Don't throw your bottle here.M:Sorry.5.W:You look tired,Tom.M:We ran for half an hour on the playground just now.二、对话理解本题共5个小题，每小题你将听到一组对话和一个问题。请你从每小题所给的A、B、C三个选项中，选出一个最佳选项，并在答题卡上将该项涂黑。6.M:Can you play the piano,Alice?W:No,but my sister can.Q:Who can play the piano?7.W:It has rained for three days,but it will be sunny tomorrow.M:I'm so glad to hear that because I'd like to have a picnic tomorrow.Q:What will the weather probably be like tomorrow?8.W:I am happy that we will go to Hainan together next week.M:So am I.Oh,we should buy something in the mall today.Q:Where will they go today?9.W:What's the matter,David?M:I have a stomachache.Q:What's the matter with David?10.W:I heard that Victor failed the driver's test last week.Is it true?M:Yes,it is.And it's really a pity.He had practiced it for a long time.But he feltnervous when he was having the test.Q:Why did Victor fail the driver's test?三、语篇理解本题你将听到一篇短文。请你根据短文内容和所提出的5个问题，从每小题所给的A、B、C三个选项中，选出一个最佳选项，并在答题卡上将该项涂黑。It is reported that a girl made a short video which swept the screen.In the video,youcould see a young Chinese girl playing guzheng on the street of Paris,the capital city ofFrance.She wore beautiful traditional Chinese clothes,performing Chinese traditional songs.Not only the local people but also the visitors from all over the world couldn't help stoping andlistening to her beautiful guzheng performance.She has become a special scenery in Paris.The girl's name is Peng Jingxuan.In 2010,she went to college in Wuhan for professionaltraining.In 2017,she went to Paris for further education.One day,as Peng watched a bandperforming in Paris,she had mixed feelings.She came up with the idea of spreading tradition-al Chinese music to the world.In 2018,she managed to take her guzheng to Paris and startedto play guzheng on the street.She also patiently taught foreigners to pronounce Chinese char-(7)【SHX】最新中考模拟训练试题·英语参考答案acters.The people were moved,just as an American visitor said in the video,"Although Ican't speak Chinese,I am moved by the wonderful Chinese music."The Chinese girl won the praise of the world for her spreading our national culture.四、听力填空本题你将听到一篇短文。请你根据所听内容，完成下面的句子，并将获取的信息填到答题卡相应的位置上。每空一词Do you know the "green"car?In 1891,William Morrison built the first working electriccar in the US.The "green"cars have become popular in recent years.They are called electriccars.In fact,they have a history of nearly more than 100 years.To begin with,although some electric cars could just run 40 miles at a time,people coulddrive them instead of walking.In 1908,the gas-powered car appeared.People stopped buyingelectric cars because gas cars could travel longer.But after over 60 years,the world was shortof the gas.So another electric car came out again.Although it was a pity that it had safetyproblems,it really helped people solve the problem of being short of gas.Nowadays,people all over the world are developing electric cars and want to use themmore in our life.China also makes great efforts.In many cities,the taxis were all changedinto electric cars,just because it can prevent the air pollution and it is helpful for三

LHtilPF=IPC=7--11分2即当PF=2时，二面角F-AB-C的余弦值为25网-12分1720.解：(1)fw=2e2-2a+10e+2a=2(e-le-a)11分①a=1时，由f'(x)20,f(x)在(-0，oo)上单调递增.-2分②a>1时，由f'(x)>0得x<0或x>na,f'(x)<0得00得x0,f'(x)<0得lna1时，由(1)得f(9在(0，l血a上单调递减，在（血a,+∞）上单调递增所以对任意x>0,f(x)zf(Ina)=e2a-2(a+l)eh@+2aln a=a2-2a(a+1)+2alna=2alna-a2-2a------8分Ag(a)=2alna-a2-2a (a>1),则g'(a)=21+lna）)-2a-2=2(na-a)<0.10分所以g(a)在(1，+oo)上单调递减，g(a)1,关于x的方程f(x)=k恒有正数解，所以k≥-3.-12分21解：(D因为0=1+m=克所以m=分1分)9stn2ax-1-co2o+,所以0)=sin(2wx+月.3分2又因为函数f(x)的最小正周期为π，所以w=1,所以：f)=sin(2x+君.5分当2x+君=2纸-受，keZ,即x=a-号，kez时，0)am=-1所以函数f(x)的最小值为-1，.-6分2》令m2x+合=0，则2x+名-，keZ,所以x=经-合keZ.-8分66试卷集68共8页

C.A kind heart.D.A charitable deed.6.What can be inferred from the "cupcake"experiment?A.Participants involved preferred sweeter cupcakes.B.Random kindness has much greater effects than expected.C.Extra ingredients make the tasty treat more special and unique.D.Kindness performers didn't realize it could make people feel good.7.What is the main idea of the text?A.Small kindness matters.B.Small kindness is a choice.C.Small acts are life-changing.D.Small decisions have a big impact.Just 130 years ago scientists weren't sure if any planets existed outside our solar system.Now they've detected more than 5,000 of them.But as astronomers have calculated theseexoplanets'sizes,a strange gap has emerged.There are plenty of "super-Earths"out there-rocky globes about 1.4 times wider than Earth.And there are lots of"mini-Neptunes"roughly2.4 times Earth's width.But very few planets fall in between;it's almost like most worldswere sized using one of two cookie cutters.A new model published in The Astrophysical Jour-nal Letters offers a fresh answer to why this is so:it's all about collisions ()Previous theories about the planetary“radius(半径)gap”suggested that extreme heatminify certain planets,says Rice University physicist Andre Iidoro,lead author of the new1study Planets tend to move coetotheir host stars over time,he says.This makes relativelylight planets sim down faster as rising heat takes away their outer gases,the thinking goes,whereas heavier planets have enough gravitytohold these gases and maintain theirseidrork challengesthis heat-basedxtion,suggesting the gap resmpnery collisions instead.AHis team ran computer simulations (based theories of how planetary systm全国100所名校最新高考冲刺卷第4页（共12页）【23·（新高考）高考样卷·英语（一）一SD】全国100所白X四

D(1)若BD=4,求线段AC的长度；(2)求证：C是⊙O的切线；(3)当∠D=30°时，求图中阴影部分面积.【答案】(1)255(2)证明见解析(3)V5-3【解析】【分析】(1)连接BC,由BD是⊙O的切线，得到？ABD90?,求得AD=2W5,结合BC⊥AD,即可求解；(2)连接OC,OE,因为AB为⊙O的直径，证得△OCE兰△OBE,得到∠OCE=∠OBE,由BD是⊙O的切线，得到∠OCE=∠BD=90°，进而证得C是⊙O的切线；(3)根据题意，求得四边形0BEC的面积为2S.og=V5,结合S四边形oBc-S形c,即可求解.【小问1详解】解：如图所示，连接BC,因为BD是⊙O的切线，可得？ABD90?,又因为AB=2,BD=4,所以AD=NAB2+BD2=2N5,因为AB为O0的直径，所以BC1AD,所以BC=B.BD_2×4_45AD2W55’所以AC-=VAB2-BC_25【小问2详解】证明：连接OC,OE,因为AB为⊙O的直径，所以∠ACB=90°，在Rt△BDC中，因为BE=ED,所以DE=EC=BE,又因为OC=OB,OE=OE,所以△OCE=△OBE,所以∠OCE=∠OBE,因为BD是⊙O的切线，所以？ABD90?,所以∠OCE=∠ABD=90°，第16硕/共26须

20.已知圆C经过点A(1,3),B(2,2),并且直线m:3x-2y=0分圆C、(1)求圆C的方程；(2)若直线l:y=c+2与圆C交于M,N两点，是否存在直线1，使得OM.ON=6（O为坐标原点)，若存在，求出k的值；若不存在，请说明理由，【详解】D线最8湖中点（侵引如=-1，故线段的中垂线方程为y-x号，即x-y+41=0因为圆C经过A,B两点，故圆心在线段AB的中垂线上又因为直线m:3x-2y=0分圆C,所以直线m经过圆心x-y+1=03x-2y=0解得=2=3即圆心的坐标为C2,3).而圆的半径r=BC=2-2}2+(2-32=1,所以圆C的方程为：（x-2)2+(y-3)=1.(2)设M(x,),N(,2),将y=c+2代入方程(x-2)2+(y-3)°=1，得(x-2)2+(ac-2=1,即(1+2)x2-(2k+4)x+4=0(,由△=(2t+4-16+H)>0,得-122+16>0，解得0

∴.点C到面ADE距离为d=AB=1;(也可利用等体积法求距离)…(4分)(2)依题意，建立以A为原点，分别以A言，A方，A立的方向为x轴，y轴，2轴正方向的空间直角坐标系（如图），可得A(0,0,0),B(1,0,0),C(1,2,0),D(0,1,0),E(0,0,2).设CF=h(h>0),则F(1,2,h).依题意，BD=(-1,1,0),BE=(-1,0,2)设n=(x,y,之)为面BDE的法向量，·BD=0-x十y=0则,即令之=1，可得n=(2,2,1),0.B2=0'-x+2x=0设m=(x,y,2)为面BDF的法向量，m.BD=0m-x十y=0味=0即2y+h=0令y=1,可得应=(1,1，-)，则,即由m·7=0得=号，所以，线段C的长为2…（12分)20.解：(1)根据给定数据，因为1=号1+2+3+4+5)=3所以(t:-)2=(1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2=10,(t:-t)(w:-w）i=1所以rV2,-√(,-o10X76.9769≈277≈0.98…(6分)27.227.227.2(t:-t)(-w)1(2)由(1)知b=uD27.2=2.72,10关于X的回阳方程y2,72x,又w和二0.8255所以当t=7时，则x=7-3=4,®=y十0=2.72×4十12.16=23.04，所以预测2024年移动物联网连接数23.04亿户.…(12分)21.解：(1)=1，a-2ta=t则b=t(t>0,已知”京=1过(2,1)∴t2=3椭圆C:无十名…（4分)(2)当斜率k不存在时：A(xoyo).B(x,一y0)由PA⊥PB知：(2-x0,1-yo)(2-xo,1十y0)=0有：(2-xo)2+1-y2=1代人2=31-6)知3x,2-8x+4=0.可得x=2或x-号2但w=2时与P重合合去此时，=号当斜率k存在时，设直线AB方程：y=kx十m,联立方程得：(1十2k2)x2+4kmx十2m2一6=0-4km2m2-6设A(x1,B(x),则x十x:1十2xx,=1十26，由直线PA,PB相互垂直得：数学试卷参考答案与评分细则第5页（共7页）

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人空白处的最佳选项。选项中有两项为多余选项。As a mind-body coach in professional sports,I work with medical staff and expert consultants everyyear during baseball spring training to help players prepare their bodies for the season.36 That's whyI provide some good tips to keep a healthy body.11Drink enough waterHow much water you drink affects all the functions of your body,including your mental performance.A body water loss of just 1%to 2%can damage cognitive()function.37.However,the amountcan vary depending on a person's activity level.Exercise regularly1,1The key to exercise's effectiveness is consistency.With as little as 11 minutes of.exercise per day,youcan enjoy numerous health benefits,including increasing your life span.38.Because of the alternatingand reciprocal(nature of your way of walking,it offers the opportunity to tune into your body andself-assess by noticing if there are any imbalances.n,,Breathe better to move better39.In addition to reducing your heart rate,blood pressure and stress response,learning how tobreathe better will improve the diaphragm()function and your movement and reduce back pain.Practicetaking breathing breaks a few minutes throughout your day.T6.1.40Sleep is essential for overall health.Adults need at least seven hours of sleep nightly,according to theUS Centers for Disease Control and Prevention.If you're not getting that minimum amount of shut-eye,it'stime to clean up your sleep routine and start prioritizing rest.ol guidool a10·./A.Get enough sleepf585B.Fall asleep as early as possible every night597%h4ii,.6.C.It means you have to follow their exercise routinelogol 3D.Breathing plays a vital role in how you feel and movea行iia国E.Walking outside is a great way to get in those.11 minutes1:F.To promote good health,I suggest drinking at least 1.5 liters of water dailyG.You may not be a professional athlete,but your body affects the quality of your life,立填圆第三部分语言知识运用（共两节，满分45分）·i,g15.fyi2::i-:031,5第一节。（共20小题；每小题1.5分，满分30分）阅读下面短文，从短文后各题所给的A、B、C和D四个选项中，选出可以填人空白处的最佳选项。Just weeks after being named the Hero of the Year,Nelly Cheboi traveled more than 7,000 miles tobring her award home.Far from the lights,cameras,and celebrities who 41 her at the gala()eventin New York City,Cheboi was 42 by her own heroes:the students she serves in rural Mogotio,Kenya."I felt a lot of43 just bringing the award to the kids,"Cheboi:said."For me,and for thecommunity here,it really means a lot to be celebrated.Like many of her students,Cheboi 44 in poverty (from childhood,without 45 toeducation.Cheboi watched her mother work 46 so Cheboi and her sisters could 47 school.She saweducation as an effective 48to end her own poverty.In 2012.Cheboi 49 a full scholarship toAugustana College in Illinois and began her 50 in computer science."The only tool I had at the time was51,"Cheboi said.【高三第一次联考（月考）试卷·英语第6页（共8页）】扫描全能王创建

5.已知偶数f(x)在(0，+∞)是增函数，则下列结论正确的是小，小1升国2023~2024学年第一学期高三年级期中学业诊断代0的A.f(x)=cosx数学试卷C.f(a)=tD.f(x)=-1(考试时间：上午8：00一10：00)说明：本试卷为闭卷笔答，答题时间120分钟，满分150分。6.几何定理：以任意三角形的三条边为边，向处构造三个等边三角形，则这三个等边三角形四总分的外接圆圆心恰为另一个等边三角形（称为拿破仑三角形）的顶点.在△ABC中，已知题号三171819202122A:w,AC=》3,C名V5,现以边A,BC,C4向外作三个等边三角形，其外接圆得分圆心依次记为D,E,F,则DE的长为B.2V7一、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，只有一项是符A.合题目要求的)D.2v5么：1m-1131.已知集合A={xx2-2x<0,B={xlx>1},则A∩B=7.已知f(x)=a(a>0,且a≠1)，m,∈(0，+则下列结论正确的是许232'313=2+23:2+8A.(0,+∞)B.(0,2)mn)-f(m)f(n)B.f(m+n)=f(m)+f(n)C.(0,1)D1,2)c"")2fm)22∠2.已知复数x满足(1+i)z=2,则z=22+iB.1-i8.在解决问题"已知1am80=m,请用m表示an20的值”时，甲的结果为m-Y3,乙的结果C.-1+iD.-1-im1+V3m为，则下别结论正确的是2X23.“x2>1”是“x>1”的A.充要条件B.充分不必要条件m2月2mA.甲、乙的结果都正确m2-11+5m￠.必要不充分条件D.既不充分也不必要条件B.甲的结果正确、乙的结果错误-)1片万m加还4.已知a=(1,0),b=(1,1),若(Aa-b)⊥b,则实数入=+5)B.2C.甲的结果错误、乙的结果正确(1+5)A.-2C.-1D.1D、乙的结果都错误4Em-mt百1乃A-+5高三数学第1页（共10页）高三数学第2页（共10页）数

2023~2024学年上学期期中质量检测八年级数学注意事项：1.本试卷分试题卷和答题卡两部分，试题卷共4页，三个大题，满分120分，考试时间100分钟.2.试题卷上不要答题，请用0.5毫米黑色签字水笔直接把答案写在答题卡上，答在试题卷上的答案无效。:3.答题前，考生务必将本人姓名、准考证号填写在答题卡第一面的指定位置，一、选择题（每小题3分，共30分）下列各小题均有四个答案，其中只有一个是正确的.1.下列四组数中，属于勾股数的是A.0.3,0.4,0.5B.8,15,17C.2,8,10D.1,2,32在v30,√公，V厄中最简二次根式的个数是A.3个B.2个C.1个D.0个3.如图是小唯关于诗歌《望洞庭》的书法展示，若“湖”的位置345678910望洞庭用有序数对(2,3)表示，那么“螺”的位置可以表示为湖光秋月两相和A.(5,9)潭面无风镜未磨4遥望洞庭山水翠舒B.(9,5)白银盘里仁情螺C.(5,8):D.(8,5)4.一次函数y=-3x+1的图象过点(1y),(x1+1,y2),(1+2,y3）,则A.y1

8.如今中国被誉为基建狂魔，可谓是逢山开路，遇水架桥公路里程、高铁里程双双都是世界第一.建设过程中研制出用于基建的大型龙门吊、衡盾构机等国之重器更是世界领先.如图是某重器上一零件结构模型，中间最大球为正四面体ABCD的内切球，中等球与最大球和正四面体三个面均相切，最小球与中等球和正四面体三个面均相切，已知正四面体ABCD棱长为2√6，则模型中九个球的表面积和为()31πA.6πB.9πD.21元4【答案】B【解析】作出辅助线，先求出正四面体的内切球半径，再利用三个球的半径之间的关系得到另外两个球的半径，得到答案如图，取BC的中点E,连接DE,AE,则CE=BE=V6,AE=DE=√24-6=3√2，过点A作AF⊥底面BCD,垂足在DE上，且DF=2EF,所以DF=2√2，EF=√2，故AF=√AD2-DF2=√24-8=4，点O为最大球的球心，连接DO并延长，交AE于点M,则DM⊥AE,设最大球的半径为R,则OF=OM=R,因为Rt△AOM∽R△AEF,所以4O_OMAE EF4-R R即322,解得R=1,MO即OM=OF=1,则AO=4-1=3,故Bsin∠EAF=OM 1A03设最小球的球心为J,中间球的球心为K,则两球均与直线AE相切，设切点分别为H,G,连接HJ,KG,则HJ,KG分别为最小球和中间球的半径，长度分别设为a,b,则AJ=3HJ=3a,AK=3GK=3b,则JK=AK-AJ=3b-3a,高二数学学科参考答案第5页（共20页）

.承8 GIOBAL TB8压in a row,put in,be patient with.芳美酒报社work out,no matterEARNING ENGLISH3.With my classmate David's help,I worked out九年级陕西第16期the math problem quickly yesterday.课时讲练4.The children were sitting in a rowat theback of the room to play a game.(Unit 14)5.Miss Li is a great nurse and she is patient witheach of her patients.⑧Ⅱ.根据汉语意思完成句子，每空一词：Section A(1a-2d)1.由于台风苏拉，中国的很多学校推迟了开学。要点归纳Because of Typhoon Saola,a lot of●remember doing sth..意为“记得做过某schools across China put off starting classes.事”，表示事情已经做完；remember to2.我哥哥空闲时，经常指导我做四川菜。do sth.意为“记得去做某事”，表示事In my brother's free time,he often guides情还没有做。me to cook Sichuan dishes.●in a row表示“排成一排”，还可表示“连3.我们要把窗户打开吗？房间里太热了。续地”。Shall we open the windows?It's too hotin the room.同步练用括号中所给单词的适当形式或根据汉语提示完成短文。In a P.E.class,all the students were4.即使他很忙，他每天都会花时间陪女儿。standing(1)in a row(排成一排).TheEven though he's busy,he takes theteacher said,"I remember (2)asking_(ask)time to stay with his daughter every dayeach of you to take a baseball bat for this5.在游戏开始前，我会先给你们解释游戏规则。class,right?"Tom forgot to take one.He toldBefore the game starts,I will explain the rules ofthe truth and said sorry..“There's an extra(多余的)one and you can use it..But rememberthe game to you first.(3)to be (be)careful next time,"said theteacher.◇基础训练1.根据句意及汉语提示填写单词。Section A(3a-4c)L.According to the survey_(调查)，over200 millionpeople went on a trip during the May Day holiday要点归纳in2023.2.There must be something wrong with mykeep one's cool意为“沉住气；保持冷静”，keyboard(键盘).Whatever I typed(打字)，it didn't其中cool用作名词。work.3.Failing to reach the required standard(标准)，sheg0by意为（时间）“逝去；过去”，为不can't take part in the competition.4.His teaching method (is different from others',及物动词短语，其后不能跟宾语。but it is popular with students.5.The manager gave clearinstructions()on how tofinish the next week's work.®Ⅱ.从方框中选择恰当的短语并用其适当形式完成同步练句子。根据汉语提示完成短文。in a row,put in,be patient withDavid used to get mad easily and he didn'twork out,no matterlisten to anyone.But as time (1)goes by1.No matter how far they go,they return home逝)，he has changed a lot..Now he is good atto spend the Spring Festival with family everyaccepting others'advice.And he can alsovear.(2)keep his cool(保持冷静)whenever2.As long as you put in effort,you will makesomething bad happens to him.progress in your study.

the holiday in the UK. Yours, Li Hua