BDM=GH,∴.AP∥GH.18.解：(1)因为SA⊥面ABC,BCC面ABC,所以SA⊥BC,因为AB⊥BC,AB∩SA=A,AB,SAC面SAB,所以BC⊥面SAB,又BCC面SBC,所以面SBC⊥面SAB.(2)由(1)知BC⊥面SAB,所以BC⊥AG,又AG⊥SB,且CB∩SB=B,所以AG⊥面SBC,又SCC面SBC,所以AGLSC.19.解：(1)取PD的中点E,连接EN,AE,.M,N,E分别为AB,PC,PD的中点，∴.EN∥AM且EN=2AB=AM,四边形AMNE为行四边形，故MN∥AE,:PA⊥面ABCD,CDC面ABCD,∴.PA⊥CD,又.'CD⊥AD,AD∩PA=A,AD,PAC面PAD,所以CD⊥面PAD,CDC面PCD,.面PCD⊥面PAD,.PA=AD,E为PD的中点，.AE⊥PD,又面PCD∩面PAD=PD,AEC面PAD,∴.AE⊥面PCD,'.MN⊥面PCD.(2)由(1)可知MN∥AE,∴.∠PAE即为异面直线PA与MN所成的角，在直角三角形PAD中，PA=AD,∴△PAD为等腰直角三角形，又E为PD中点∴∠PAE=∠PAD=45°，故直线PA与MN所成的角为45°.20.解：(1)连接CP,并延长与DA的延长线交于M点，因为四边形ABCD为正方形，所以BC∥AD.散△PC△PDM,所以需部=号，又因为品-部-号所以品-品=号，所以PQ∥MD.又MD,C面A,D,DA,PQt面A,D,DA,故PQ∥面A,DDA(2)当的值为时，面PQR/面AD,D1证明如下，因为号.即然号，所以然品所以PR/DA.又AC面AD,DA,PR学面A,DDA,所以PR分面A1D1DA,又PQ∩PR=P,PQ∥面A1D1DA,所以面PQR∥面A1DDA.DD、B1A、B1Q、0DUD。RB21.解：(1).ED∥AB,ED在面ABF,ABC面ABF,.ED∥面ABF,.ED面PED,面PED∩面ABF=FG,.ED∥FG,又ED∥AB,∴.AB∥FG:(2)设AB与CD交于点M,则MD的中点为C,由(I)知PG=3PD.易知点ME面ABF,点M∈面PCD,'.MG=面ABF∩面PCD,又H为PC与面ABF的交点，∴H=MGnPC,在△MPD中，如图，PG=3PD,C为MD的中点，由面几何知识易知H·43·【23新教材·DY·数学·参考答案一BSD一必修第二册一Y】

19.(8分)某同学在解方程2,1-寸4-2去分母时，方程右边的-2没有乘3，因而求得的方程20.(8分)某校分配学生住宿，如果每间住5人，就有30人没有宿舍住，如果每间住6人，就可空出3320个床位.该校有多少间宿舍？有多少住校学生？的解为x=2,试求a的值，并求出原方程的正确的解。第5页（共8页）第6页（共8页）

21.解析：(1)因为双曲线的右焦点为F(2,0),所以a2十b2=4,因为双曲线的渐近线方程为y-士x,所以。-5，即6-尽a,所以a2十b2=4a2=4,所以a=1,b=√3.(3分)所以双曲线C的方程为x2一号=1.3…(5分)(2)证明：设直线BP的斜率为k(k≠0)，则直线BP的方程为y=k(x一1)，又CQ∥PB,所以直线CQ的方程为y=k,Q点的坐标为（号，号）.y=k(x-1),联立直线BP与双曲线C的方程消去y得(k2-3)x2-2kx十b2+3=0,k2所以十23则M点的坐标为2二323.……(8分)又F2,0,易得，直线QF的斜率为一专直线OM的斜*为是，由于一台·月1，则直线OM与直线Qr垂直设直线OM与直线QF的交点为G(x,y),则GO·G=0,G0=(-x,-y),Gf=(2-x,-y),则G0.Gi=x2-2x+y2=0,即直线OM与直线QF的交点G在曲线(x一1)2十y2=1上.…(12分)22.解析：(1)f(x)=ex(sinx十c0sx),x∈[-π，π].…(1分)令f'(x)=0,得a=一至w=7当x∈[-，-开)或x∈(3开，π]时f'(x)<0;当x(-T,3)时，f'(x)>0.所以fx)的单调递减区间是[一，一]，[不]，单调递增区间是[一至，1。…(3分)又f-)=号e)-e放心的极小值为-号。i,极大值为号c。…(5分)2023届高三“一起考”大联考（模拟三）·数学参考答案9

WriterAnd more!For mosThe Admission Section receives and evaluates applications to the undergraduate(can help begprogram,in addition to answering applicants'questions by phone.Jenny,their schooPhone:613-562-5315books andTol-free:1-877-868-8292Regular Office Hours:Monday to Friday企小公新带两共微要资同猫二清she still p“DecCSeptember to May:9 am to 4:30 pmway of iJune to August:9amto3:30pm边个四)，A0的从，文设T宽help lea21.Who is the Work-Study Program intended for?into oneA.Technicians.B.Professors.DiC.Marketing managers.D.University students.in BritFUXI F22.How can you apply for a position of the program?thingsA.By letter.B.By phone.C.In person.D.Via the Internet.accep23.What should you do to get more information about the program?24.WA.Phone 613-562-5315 on weekdays.B.Phone 1-877-868-8292 on weekends.bloit nseod isr nt noiicoC.Go to the Admission Section in person.D.Ask other undergraduates for details.81Bhrons moo nso bas smi-lnd iow o25After deciding to move into a new house,Jessica,a full-time mother in London,broughtin a woman home organizer-Sharon."As a result,Sharon threw away 50 per cent of myclothes,decorations,shoes and books.The process of tidying up my house brought peace to2me and made me feel organized at heart,"Jessica told The Times.S0a000Like Jessica,more British people have started to seek for help from home organizers topursue minimalism(极简主义)lifestyles.This period has made many people appreciate everyday order and comfort.Having a comfortable living environment became more pressing forpeople who were forced to work at home and for families spending long hours together underone roof."People are fearful of the future,especially with this pandemic,"Sharon said."Willit get worse?Will it return...I think it is a good idea to clear your home as a way of clearingyour mind.This is an ideal time to tidy up and give some thought to what we have and tobethankful for it.”16【23新教材老高考·D·英】

由题意，即满足h(t)mx一h(t)min≤a2十l.…6分因为a>0,所以h(t)为开口朝上的二次函数，对称轴为t=1一4Aa当≥2-1时4=102∈(-0.①当=1a2∈(-0，-1DU(1,+∞)时，此时0

答案专期2022一2023学年广东专版九年级第13~16期品数学闭报MATHEMATICS WEEKLY即A,B两舰队的距离为8海甲(2)过点P作PF⊥AQ于点F易得1F=PE=20海里，PF=AE=28海里】所以QF=AQ-AF=2N29海里.在t△PQ中，由勾股定理，得PQ=PF+QF=28+(229=30(海里)所以30÷40=（小时）.答：救援船到点P处所需的最短时问为小时。

0-…品后19.【详解】(1)设4C与BD相交于点O,连接FO因为四边形ADCD为菱形，所以AC L BD,且O为AC中点，因为FA=FC,所以AC⊥FO,又FOO BD=O,FO,BDC面BDEF,所以AC⊥面BDEF,(2)连接DF,因为四边形BDEF为菱形，且∠DBF二60，所以△DBF为等边三角形，)【}因为O为BD中点，所以FO⊥BD,又AC⊥FO,BDOAC=O,AC,BDC面ABCD,所以FO⊥面ABCD所以OA,OB,OF两两垂直，如图所示，建立空间直角坐标系O-z,B因为四边形ABCD为菱形，∠DAB=60,AB=2,所以BD=2,AC=2√3、因为△DBF为等边三角形，所以OF=√5，所以A5.,00,B0.L0),D(0-1,0),F0,0V5，所以D=(5,-,0,=(5,0),B=(51,0),设面ABF的法向量为n=(名，y,2),则丽万=一5x+5=0,取，得=5列AB元=-5x+y=0以意(线0与r所为，则0w动小8品-雪

全国100所名校高三AB测试示范卷札记全国@迥所名校高三AB测试示范卷·数学第四套函数的概念及性质(A卷)(40分钟100分)眼微信扫码考情分析，口新高考对接点函数的概念及性质是高考必考点，主要考查客观题学疑难点函数性质的应用典型情境题10观看微课视频课外题解析下载复课件题序12356答案DABDDBC一、选择题：本题共6小题，每小题6分，共36分1.函数f(x)=x十1的定义域为A.[-1,+o∞)B.(-1,0)U(0,+)C.(0,+∞)D.[-1,0)U(0,+∞)|x+1≥0【解题分析】由得x≥一1且x≠0，所以函数f(x)的定义域为[一1,0)U(0,十o∞)x≠0【答案】D2.设函数f(x)=十1，则下列函数为奇函数的是A.f(x)-1B.f(.x-1)C.f(.x-1)-1D.f(.x)+1【解题分析】因为f)=1-1十，所以)-1=1十上-1=上，故函数()1为奇函数.y【答案】A3.设a∈R,则“a>0”是“函数f(x)=-x2十2a.x在（一∞，1]上单调递增”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【解题分析】函数f(x)=-x2十2a.x的图象的对称轴为x=a,又f(.x)在(-o∞，1上单调递增，所以a≥1，所以“a>0”是“函数f(x)=一x2十2a.x在(-oo,1]上单调递增”的必要不充分条件.【答案B4.若函数y=f(x)的大致图象如图所示，则f(.x)的解析式可能是A.f(x)-x2-1B.f)=1+x21-x2C.f(x)=1-元xx2D.f(x)=]-2【解题分析】当一1

7.2022年4月16日，神舟十三号载人飞船返回舱在东风着陆场成功着陆，返回舱呈钟形，将其近似地看作一个半球（上）和一个圆台（下）的组合体，其中半球的半径为1米，圆台的上底面与半球的底面重合，下底面半径为1.2米，若圆台的体积是半球的体积的2倍，则圆台的高约为8思A.1.0米B.1.1米C.1.2米D.1.3米8.将一枚质地均匀的骰子随机抛掷两次，甲表示事件“第一次点数为奇数”，乙表示事件“第二次点数为偶数”，丙表示“两次点数相同”，丁表示“两次点数之和为偶数”，则下列选项中的两个事件不相互独立的是A.甲与丙B.乙与丙C.乙与丁D.丙与丁二、多项选择题：本题共4小题，每小题5分，共20分.在每小题给出的四个选项中，有多项符合题目要求，全部选对的得5分，部分选对的得2分，有选错的得0分9.已知复数z满足z(1+)=-1-√5+(1-√5)i,则下列说法错误的是A.z的虚部为iB.z的共轭复数z=√5+iC.lal =2D.z2=4-25i10.某高中一年级共有甲、乙、丙3个班级，其中甲班40人，乙班50人，丙班40人，在某次数学月考中，甲班的及格率为50%，乙班的及格率为60%，丙班的及格率为70%，则A.若用简单随机抽样法从一年级所有学生中抽取13人，则甲班应抽取4人B.若按照各班人数比例用分层随机抽样法从一年级所有学生中抽取26人，则丙班应抽取8人C.这次一年级数学月考的均及格率为60%D.若从这次一年级数学月考及格的学生中随机抽1人，则该学生来自丙班的概率最大11.小张于2017年底贷款购置了2018年各项支出2022年各项支出一套房子，根据家庭收入情水、电、娱乐2%气、通讯其交车贷况，小张选择了10年期的等9%其他109%10%额本息的还贷方式（每月还饮食房贷娱乐10%房贷款数额相等)，2021年底贷款30%24%60%购置了一辆小汽车，且截至飘饮食2022年底，他没有再购买第23%10%二套房子.如图是2018年和2022年小张的家庭的各项支出占家庭收入的比例分配图.根据以上信息，判断下列结论中正确的是A.小张一家2022年的家庭收入比2018年增加了1倍B.小张一家2022年用于娱乐的支出费用为2018年的5倍C.小张一家2022年用于饮食的支出费用小于2018年D.小张一家2022年用于车贷的支出费用小于2018年用于饮食的支出费用数学试题第2页（共4页）扫描全能王创建

endorsement of those demands,a practice that continues to be important today.In 2020,Democratic presidential candidate Joseph Biden made a promise to select a woman as his vice-presidential nominee()and ultimately shared electoral victory with running mate KamalaHarris,the first woman and first person of color to be elected vice president.Men's voices are important.When men speak up against gender discrimination,they not onlybecome obvious as allies who can be counted on to support industry or company rules to advanceequality,but they also improve awareness and acceptance of gender inequality as a shared problem,not a special interest.28.What does paragraph 3 mainly talk about?A.The reason why gender equality is hard to achieve.B.The reason why men are powerful at work.C.The result that gender inequality brings to men.D.The result that women's advancement causes to companies.29.Which of the following best explains "endorsement"underlined in paragraph 4?A.Responsibility.B.Support.C.Ignorance.D.Misunderstanding.30.Which can be the best title for the text?A.Support of Men Is on the Sidelines.B.Gender Equality Is Women's Business.C.Gender Inequality Is a Common ProblemD.The Secret to Achieving Gender Equality at Work:Men31.In which section of a newspaper may you find this text?A.Education.B.Society.C.Health.D.Entertainment.DDuring a ransomware(勒索软件)attack,attackers enter a target's computer system andencrypt()its data.They then demand a payment before they will free the system.Ransomware is a collective problem,and solving it will require joint action from companies,theU.S.government and international partners.In 2020 the Federal Bureau of Investigation received more than 2,400 reports of ransomwareattacks,which cost victims at least $29 million.The numbers underestimate the total impact ofransomware because not all organizations are willing to report it when they fall victim to this kind ofcrime.Even these limited statistics,however,show the increasing fearlessness of ransomwareattackers:the number of attacks in 2020 increased by 20 percent compared with that of the previousyear,and the amount of money paid out more than tripled.As long as victims keep paying,attackers will keep profiting from this type of attack.Butcybersecurity experts are divided on whether the government should prohibit the paying of ransoms.Such a ban would discourage attackers,but it would also place some organizations in a moraldilemma.For,say,a hospital,unlocking the computer systems as quickly as possible could be amatter of life and death for patients,and the fastest option may be to pay up.Other solutions are more straightforward and involve pushing organizations to protectthemselves better.Cybersecurity defenses make it harder for attackers to access systems.Segmenting()one's network means that breaking through to one part of the system does notmake all data immediately available.And regular backups allow a company to function even if itsoriginal data are encrypted.All these measures,however,require resources that not all organizations have access to.Meanwhile,ransomware people are adopting increasingly advanced techniques.Some work forweeks to gain entry to a company's network and then enter their system,finding the most vital datato hold hostage().Some groups deliberately compromise an organization's data backups.英语试题第5页（共8页）

所以1=C2_1CP=3120.（本题满分12分)1981年，在大连召开的第一届全国数学普及工作会议上，确定将数学竞赛作为中国数学会及各省、市、自治区数学会的一项经常性工作，每年10月中旬的第一个星期日举行“全国高中数学联合竞赛”，竞赛分为一试（满分120分）和二试（满分180分），在这项竞赛中取得优异成绩的学生有资格参加由中国数学会奥林匹克委员会主办的“中国数学奥林匹克(CM0)暨全国中学生数学冬令营”（每年11月）.已知某地区有50人参加全国高中数学联赛，其取得的一试成绩绘制成如图所示的频率分布直方图.频率(1)根据频率分布直方图估计学生成绩个组距0.032的均数α和中位数b(同一组数据用该组区0.024间的中点值代替)；(2)若成绩在100分及以上的试卷需要0.0120.008主委会抽样进行二次审阅，评审员甲根据上表0.004>成绩在此地区100分以上的试卷中根据分层抽样的60708090100110120原则抽取3份进行审阅.已知A同学的成绩是第20题图105分，E同学的成绩是111分，求这两位同学的试卷同时被抽到的概率.解：（1)由上表可知，0.12+0.24+0.32+10m+0.08+0.04=1,解得m=0.02,均数a=65×0.12+75×0.24+85×0.32+95×0.2+105×0.08+115×0.04=85中位数b∈(80,90)，由题意可知，0.12+0.24+(b-80)×0.032=0.5,解得b=84.375,即均数a=85,中位数b=84.375.(2)由图可知，成绩在[100,110有50×0.08=4人，成绩在I110,120有50×0.04=2人，根据分层抽样的原则，成绩在100,110)抽2份，成绩在[110,120抽1份，设A,B,C,D四位同学的成绩在100110)，E,F两位同学的成绩在110,120，高一期末检测数学参考答案第5页（共8页）

第二十四章圆24.2.2直线和圆的位置关系第1课时直线和圆的位置关系(共24考：单独3考，在函数题、几何题中涉及21考)教材知识知识点直线和圆的位置关系24考注意·重点点拔。注意：圆心到直线的距离是直线与圆的相交相切相离指过圆心向直线所作的垂线位置关系段的长度，这个距离是点到直线的距离图示00判断直线与圆的位置关系的e方法：①根据直线与圆的公公共点个数0共点的个数；②根据圆心到直线的距离与圆的半径的大圆心到直线小关系的距离d与dr半径r的关系公共点交点切点的名称直线1与⊙0直线1与⊙0直线1与⊙0总结相交台dr第2课时切线的判定和性质(共342考：单独300考，在函数题中涉及42考)教材知识知识点1切线的判定定理66考·重点点拨1.定义：经过圆的半径的外端且垂直于这条半径的直线是圆的口诀：切线要想证明圆切线，垂直半径过外端；2.切线的判定方法》口诀直线与圆有共点，(1)定义法：与圆有唯一公共点的直线是圆的切线：半径连来证垂直；(2)数量关系法：到圆心的距离等于半径的直线是圆的切线；直线与圆未给，点，(3)位置关系（判定定理）法：经过圆的半径的外端且垂直于须作垂线证半径这条半径的直线是圆的切线，知识点②切线的性质定理28考定理：圆的切线垂直于经过切点的半径45

令函数h(x)=x一sinx,h'(x)=1一cosx≥0，所以h(x)是增函数当x>0时，h(x)>h(0)=0,即当x>0时，x-sinx>0,f(x)>0,所以f(x)在(0，十∞)上单调递增，不符合题意。…10分若g'(0)<0,即a>2,则存在x4∈(0，十∞)，使得当x∈(-x4,x4)时，g'(x)<0.所以f(x)在（一x4,x4)上单调递减：又因为f(0)=0,所以当x∈（一x4,0)时，f(x)>0,当x∈(0，x4)时，f(x)<0,即f(x)在（一x4,0)上单调递增，在(0，x4)上单调递减，符合题意综上，a的取值范围为(2，十∞).…12分【高二数学·参考答案第5页（共5页）】·23-559B·

9,已知正项数列a的前m项和为S,且=4-2a,-aeN.数列满足6。，乙为数列{bn}的前n项和.(1)求数列{an}的通项公式：(2)求数列{bn}的前n项和Tn:(3)若对任意的neN,不等式T,

become moreco humans take over more areas that used to be wild.couch can worl juat fine for thisas long you don't findofewminutes.32.What can we infer about the cockatoos from the text?A.They don't like living with people.一rn on的yo d vourl thinkingohbsilence is better for you.B.They are newly found in AustraliaC.They are very clever birds.A.Know concentration is the key.D.They like copying humans'behavior.B.Have something to drink or eat.33.What did the scentists want to kow in paragraph4ButyoushuddyngnbghtA.How humans responded to the birds'trick.B.Some people can study with lots of activities going onB Why the birds in more areas did the trick.E.Now this is for the perodm backgroudoundC.How the cockatoos learned the trick.Many peopl faldthisdonderwhy theyD.Why humans taught the birds to do the trick.C.The key ontke you feeorbe whileyoureyn34.What did the researchers find about cockatoos in their research?第三部分语言知识运用（共两节，满分45分）A.They wanted their habitat back.第-一节（共20小题；每小题1.5分，满分30分）B.They intended to make humans angry.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C.They could adopt new ways to open bins.D.They disliked looking for food themselves.Tiki Joyner Edwardslives far away from her mother and father.But,she doe35.What is the best title for the text?about them because there is somoe whom she can 42 tolook after themveday.HisA.A big problem of“homeless'”cockatoosname is Romemylion Mitchell,and he is a teenage boy who lives near the 43 of Tiki'sparB.A human-wildlife conflict all over Australiaents.The young man has no 44 relation with the Tiki's family,but he sure is 45C.A problem caused by cockatoos to humanswith them.D.A battle over trash bins between cockatoos and humansRomemylion has made it his 46 to watch over Tiki's parents,Trent and Cianne Jo第二节（共5小题；每小题2分，满分10分）ner.He 47 them every single day,asking them whether they need anything.He is领根据短文内容，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。48 ready to lend a hand and be their guide when something is 49 for them to doCreating a good study environment takes a little planning.It is well worth the time as thebecause of their age.Romemylion never 50 a day to visit the 51 couple,though heend result will be much more productive study time.36But after a couple of times ofhas tons of things to do in school.studying in the right way,most people will be surprised at how much they can actually enjoyNow,Romemylion may 52 a lot of things for Tiki's parents,but there is one thingstudying.Read on to learn how to create a good study environment.he 53 to do and that is to accept any 54 from them for whatever he is doing.Truly.Reduceevery psibdistraetion.T off the telvision and go inan areawheRomemylion is a 55 and kind boy.you will not be interrupted by people.If you can,turn off your cell phone.If you are studyingThe teen has been doing this for years,which made his 56 deeper as time went by.on your computer,don't get distracted by emails.He is now more of a family than just a simple 57.At one point,Tiki'smom was58Check out the level of lighting in your area,If it is too dim(黯淡的)，your eyes will bebecause of health issue and Romemylion paid a visit.He59herdveedfterinjured and you want to close your eyes.The sun is a light that naturally wakes you up andseeing the elderly woman.helps you think.Truly,kindness and genuine concecan relate people andtu 60 into family.Choose a comfortable seat.It should have a good back support and a good seat.NowaWhat's more,kindness can make the world we are living inbetter.【图高三英语第7页（共10页）图】【图高三英语第8页（共10页）图】

18.已知函数∫(x)=V5sin2ox+2cos2ox(o>0),若函数fw)图象相邻两条对称轴间的距离是2(1)求0及f(x)单调递减区间.元元(2)若方程f(x)=m在-44上有解，求实数m的取值范围.【管案】》a=1,单调运减区间为[红+云红+1ke乙：(2)m∈1-V5,3].【解析】【分析】(1)利用三角恒等变换得到f(x)=2sin(2ox+)+1,然后利用题意得到周期T=元，代入周期61的计算公式可得)，然后代入正弦函数即可求解：(2)结合(1)的结论，求出函数fx)在ππ4’4上的值域即可求解，【小问1详解】f(x)=3sin2@x+2cos'@x=sin2@x+cos2@x+1=2sin(2@x+")+1,6又了()图象相邻两条对称轴间的距离是了所以函数®的周期为T=元，所以2=元，则o=1,所以fx)=2sin(2x++1,206令2+32x+四2血土钙kGZ,解得+3≤血+kEZ663所以函数了(x)单调递减区间为[kx+,k:+21k∈Z).3【小问2详解】由(1)知：f(x)=2sin(2.x+)+1,61因为x∈-44所以2x+名e(-号.则2n2x+2e-6,2,6所以f(x)e(1-√3,3]，要使f(x)=m在-ππ-4’4上有解，则m∈1-5,3].19.设函数f(x)=a-(k-1)a(a>0且a≠1)是定义域为R的奇函数.(1)求实数k的值(2)若(1)>0，判断函数f(x)的单调性，并证明.第14页/共20页

综上所述，点M的坐标为(0,10)或(0,4)或(0，-10)【点睛】关键点点晴：本题考查了二次函数的解析式、一次函数的解析式、二次函数的性质、行四边形的性质，解题的关键是能够熟练应用待定系数法求得二次函数和一次函数的解析式26.在A4BC中，∠ACB=90°，AC=BC,将线段CB绕点C旋转a(0°

■口■口■口口■16.由题图可知A=2,因为f=1,所以2sin解得0+货，e么.又7>2，即2江22g且00，所以1,4k225500225500

0年0。。000010。年年00年0年年00”000”年00：年00年g年（广当且仅当1=一号即m=一号时取等号，此时三角形面积最小…（10分)35此时1的方程为-兮x-y+10=0,即5x+3y-30=0.…(12分)22.命题意图本题考查面面垂直的证明及空间向量的应用.解析(I)如图，连接BO:AB=BC=1,AC=√2,0为棱AC的中点014C,且0-号…(1分)》又PA=PB=PC=2P0⊥AC,且P0=2则PB2=P02+B02,则P0⊥0B.……(3分):OB∩AC=O,OB,ACC面ABC,∴.P0⊥面ABC,而P0C面PAC,顶PAC1面BC..（4分）(Ⅱ)建立以O为坐标原点，直线OB,OC,OP分别为x轴、y轴z轴的空间直角坐标系，如图所示，6则Ao,-ro.0)co号(0.0故网(0-风=o号-9瓜(-号号0)成(-是号}…(6分)设威=成-(-号0小0≤A1,则-+竖号小=（竖-竖+竖o小设面PAM的法向量为n=(x,y,),n…pi=--=0,(停-小+（停+》=，令=1，可得y=-5x=B,即n=(51+少，-5，……(8分》1-入1-入设直线PC与面PMM所成角为a,则in0=1s(P心.m1=心nl=51PC·lnl4x(--5x1,解得A=号或入=3（舍去），则面PAM的法向量为n=(25,-5,1).…(10分）易知面PAC的一个法向量为m=(1,0,0),设二面角M-PA-C为p,m·n3则cosp=lcos(m,n）l=1ml·1m=2,.二面角M-PA-C的大小为30°.……(12分)》天一文化TIANYI CULTURE

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uu3V33V105c0s0=mn2V5×V735故面4CD与面4BC,夹角余弦值为3N1053520.已知等差数列{a,}满足a1+a=-4,a6=1,数列{bn}的前n项和为Sn,且Sn=3bn-3,n∈N.(1)求数列{a},{b}的通项公式：(2)设{Cnm}满足cn=anbn，记{Cn}的前n项和为Tn，若Tn≤cn+21对任意n∈N恒成立，求实数元的取值范围【答案】）a,=n5:6.)e【解析】【分析】(1)根据等差数列的定义以及基本量计算和Sn与4n的关系即可：(2)先求出Cn的通项，再用错位相减法求得T,的值，再由T,≤2C,+21化简及分类讨论、分析函数的最值求得九的取值范围.【小问1详解】因为{an}是等差数列，4+a=-4,由等差数列中项性质可得2a3=-4,a3=-2,又因为a6=1,所以a。=a3+3d=-2+3d=1,解得d=1,所以43=41+2d=41+2=-2,可得a1=-4,所以an=-4+(n-1)×1=n-5;由Sn=3bn-3①，可得：当n=1时、么=边-3，得：4=当n≥2时，Sn1=3bn1-3②，bn 3①②得：2b=3动1’bn12第17页/共22页

15.10-45【解析】4：mx-y-4m+2=0变形得到：m(x-4)+(-y+2)=0,令「x-4=0,解得x=4-y+2=0y=2x-2=0x=2从而M(4,2),12:x+my-6m-2=0变形得到l2:m(y-6)+(x-2)=0,令(少-6=0，解得y=6’从而N(2,6),由PM⊥PN,由勾股定理得PM2+PNP=MN P=(4-2)2+(2-6)2=20,点P的轨迹为以MN为直径的圆，其中线段MW的中点坐标为Q3,④，半径为MW-V5,P,点轨迹方程为2(x-3)2+(y-42=5,圆x2+y2=9的圆心为00,0)，半径为3，设CD的中点为H,由垂径定理得CDOH=9√5，故H点的轨迹方程为x2+y2=5,国为P点轨迹方程为(x-32+(0y-42=5,则PH的最小值为圆心距减去两半径，即V32+42-V5-√5=5-2W5,其中|PC+PD=21P豆|，所以1PC+PD1的最小值为10-4516.号【解析】设椭圆长半轴为4，双曲线实半轴为4，5(-c,0,5(c,0)，P为两曲线在第一象限的交,点，Q为两曲线在第三象限的交点，如图所示，由椭圆和双曲线定义与对称性知PF+PF=2a,|PF-|PF=2a,|2F2=PF,lPF=a+a,PF=a-a,F2⊥F3P,则PE1F,P,:EF=|PF+lPF,即4c2=(a+a2+(a-)2=2a+2a,于是e+++s等}+层答当且当6e=3时取等号故答案为：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)【答案】见解析.【解析】(1)由正弦定理得(b-c)c=b2-a2,………1分整理得b2+c2-a2=bc,.cosA=b2+c2-a2bc由A∈(0，)，…3分2bc2bc 2∴.A=3…4分数学参考答案第4页（共7页)

14.、在面直角坐标系中，把直线y=3x沿y轴向下移后得到直线B,如果点N(m,n)是直线B上的一点，且3m-n=2,那么直线AB的函数表达式为32x15,已知面内有两条直线：y=x+2,山：y=-2x+4交于点A,与x轴分别交于B,C两点，P(m,2m-1)落在△BC内部（不含边界），则m的取值范围是三、解答题(8小题，共90分)16.(本小题8分)如图，在面直角坐标系xOy中，△ABC三个顶点的坐标分别为60A(-2,-2),B(3,1),C(0,2),将△ABC先向左移2个单位，再向上移3个单位得到△A'B'C(1)在图中画出移后的△A'B'C';(2)求△ABC的面积户第16题图)34v0秒)2N017.(本小题10分)如图，△ABC中，AE,CD是△ABC的两条高，AB=6,CD=3.(1)请用直尺和三角板画出AE,CD;。(2)若AE=4,求BC的长.4灯/B1b第17题图八年级数学试卷第3页（共6页）

至国U)所名役高三单元测试示范卷·数学B.1第二十三单元综合测试四D.9(120分钟150分)【解题考情分析所以鼠微信扫码集合与简易逻辑是常考点，复数、概率统计、函数导数、面向量、数列、立体几何、解同理高考对接点析几何、不等式、三角函数是必考点由余单元疑难点导数及其应用、圆锥曲线综合、立体几何综合即3h典型情境题4、19观看微课视频课外题解析【答索下载复课件题序12345678910115.函数12答案CBABDADDACDACBCD ACD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，只有一项是符合题目要求的1.设集合A={-1,0,1,2},B={xy=lg(-x2+2x+3)},则A∩B=A.[-1,2]B.{-1,0,1,2}C.{0,1,2}D.(-1,2]【解是【解题分析】集合B={xy=1g(-x2+2x+3)}={x-x2+2x+3>0}={x-1

4.sisters5.those6.isII.1.These are;jackets2.Who is3.Yes;they are4.Is that5.No;they aren't6.That is;pencilIII.1-4 BCCASection B(1a-2c)I.1.son 2.photos 3.dog 4.HereⅡ1.She's;daughter 2.In the next photo3.girls are;sisters 4.They are;parents 5.your uncle 6.Here is aIII.1.of2.are3.Who4.parents5.His6.color7.haveSection B(3a-Self Check)I.1-5 EBCDAII.1.She is Sally's aunt.2.It's yellow.3.They are in the USA.4.Four5.Sally and her grandparents.3/3

绝密★启用前滨城高中联盟2023-2024学年度上学期高三期中I考试英语命题人：大连市第一中学刘燕飞校对人：大连市第一中学郭晓伟第一部分听力（共两节，满分30分）第一节（共5小题；每小题1.5分，满分7.5分）听下面5段对话，每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。1.What will the woman probably do next?A.Take a nap.B.Prepare dinner.C.Go to the bathroom2.What is the woman dissatisfied with about Linda?A.Her learning attitude.B.Her exam results.C.Her communication skills.3.Who is Scott?A.A waiter.B.A salesman.C.A student.4.Wheredoestheconversationprobablytakeplace?A.At a furniture store.B.At the woman's home.C.In a restaurant.5.What are the speakers mainly talking about?A.A trip.B.A TV show.C.A university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，每小题将给出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、7题。6.What bothers the woman?A.She types too slowlyB.She forgot to save her report.C.Her computer is broken again7.When is the woman's report due?A.This Thursday.B.Next MondayC.Next Tuesday听第7段材料，回答第8、9题。8.What is the man reading at first?A.A poem.B.A novel.C.A magazine9.How does the woman feel about Mary Vanderbilt's story?A.Angry.B.Curious.C.Indifferent.听第8段材料，回答第10至12题。10.How will Helen get to Chicago?A.By rail.B.By plane.C.By car.11.Where did Helen and Lisa first meet?A.At a swimming pool.B.At Lisa's house.C.At a camp.12.What do Helen and Lisa both like doing?A.Going skiingB.Collecting stamps.C.Listening to music.听第9段材料，回答第13至16题。13.Why can the woman speak English fluently?A.She has a gift for languages.B.She has learned it for long.C.She signed up for an English course.14.What does the man want to do next year?A.Study abroad.B.Join a club.C.Tour Britain.15.Which of the woman's suggestions does the man take?A.The first one.B.The second one.C.The third one.16.What are the speakers going to do together this evening?A.Do their homework.B.Clean the house.C.See a film听第10段材料，回答第17至20题。17.How much does it cost to buy an adult ticket and a child ticket?A.About $36.B.About$38.C.About $40.18.What does the speaker think of whale-themed spaces?A.They're confusing.B.They're special.C.They're interesting19.What is the attraction on the 120th floor?A.A small cafe.B.An outdoor balcony.C.A glass floor.20.What does the speaker say about the restaurant?高三英语试卷第1页共6页

第l5期Bl版Keys:(One possible version客观题除外)课本链接1-3ABC主题漫步1.thick2.the sun3.heavier4.clear seasons第l5期B2版Keys:(One possible version)Part 1短语收藏夹1.travel around the earth2.send...into space3.make great progress4.一大群人5.踏上练一练1.sent;into space2.set foot on3.a large crowd句式梳理1.prove;to2.prove thatPart2短语收藏夹1.electronic controls2.对...了解甚少3.master computer technology4.下定决心练一练1.master computer technology2.made up his mind3.know little about句式梳理1.advised:to2.against making3.advises him againstPart3短语收藏夹1.be dangerous to2.come into being3.do business4.例如5.像往常一样句式梳理There is no doubt thatPart 4短语收藏夹1.肯定地2.cause problems3.on one's own4.不再语法运用1.who /that2.that3.which /that4.who/whom /that5.that

C.She wants her skin to feel younger. 听下面一段独白，回答第12至第15小题。 12.When was Shakespeare and Company first opened? A.In1919. B.In1941. C.In1951. 13.What service did Ms Beach's bookstore offer? A.Food to readers. B.Beds to writers. C.Writing lessons. 14.Why did Ms Beach close her bookstore? A.She was forced to close it. B.She faced strong competition. C.She didn't have enough money.

C.Consuming less protein. D.Harvesting other seafood less. 31.From which section of a magazine does the text come? A.Health. B.Science. C.Ecology. D.Entertainment.

第二节（共5小题；每小题5分，满分25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 People who seem to have all the luck are not usually blessed by a great amount of good fortune.15 Those who are closed- minded and negative simply don't allow as many good things into their lives,or if good things appear,they don't even recognize them.Here are four top tips for creating your own luck. Be flexible.Closed-minded people don't often come up with solutions,because they see only one way of achieving something. 16 If you open your mind to alternative possibilities,you'll find that things start working out where you thought they wouldn't.