(2)某教育部门为了调查学生语数外三科成绩与选科之间的关系，现从当地不同层次的学校中抽取高一学生4000名参加语数外的网络测试，满分450分，并给前640名颁发荣誉证书，假设该次网络测试成绩服从正态分布，①考生甲得知他的成绩为260分，考试后不久了解到如下情况：“此次测试均成绩为210分，290分以上共有91人”，问甲能否获得荣誉证书，请说明理由：②考生丙得知他的实际成绩为425分，而考生乙告诉考生丙：“这次测试均成绩为240分，360分以上共有91人”，请结合统计学知识帮助丙同学辨别乙同学信息的真伪.附：P(4-o≤X≤4+o)≈0.6827，P(4-2o≤X≤4+2o)≈0.9545，P(4-3o≤X≤4+3o)≈0.9973.21.(本小题满分12分)己知圆E:（x+2)}+y2=24,动圆N过点F(2,0)且与圆E相切，记动圆圆心N的轨迹为曲线C(1)求曲线C的方程：(2)过点F(2,0)的直线m交椭圆C于点M,N,且满足tan∠MBN=8√6,(E为圆E的3EM.EN圆心)，求直线m的方程22.（本小题满分12分)设函数f(x)=e-(ax-1)ln(ax-1)+(a+1)x.(e为自然常数)(1)当a=1时，求F(x)=e-f(x)的单调区间：2)若（在区间[已]单调递增，求实数a的取值范围，高三年级调研测试·数学·第6页共6页

203年普通高等学校招生全国统一考则T数学注意事项：1,答卷前，考生务必将自己的姓名、考生号和座号填写在答题卡和试卷指定位置上。2.回答选择题时，选出每小题答案后，用铅笔把答题卡对应题目的答案标号涂黑。如需改动，用橡皮擦干净后，再选涂其他答案标号。回答非选择题时，将答案写在答题卡上。写在本试卷上无效。3.考试结束后，将本试卷和答题卡一并交回。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.〈力<1.已知集合A={x1(x-2)(x+1)<0},B={yly=log2(x2+2)},则A∩B=A.(-1,2)B.[1,2)C.(-1,+∞)D.(1,2)2.已知x,y是任意实数，则p:x+y≥3是g:x≥1且y≥2的C充要条件充分不必要条件C.必要不充分条件D.既不充分也不必要条件3.已知正方形ABCD的外接圆半径为1，点P在边AD上，则A·P元的最大A.1c号D.0B”:门画卫口画删卫华唑画黜阳今年素☒米雏+。=1(a>6>0)的左，右焦点分别为F,F2,且P为“正椭圆”C的下顶点，且△F,PF,的面积为4√3，则椭圆的方程为心B.2C.81D22832+24=15.已知函数f(x)=Asin(ux+p)+BA>0,w>0,1psTc.562的部分图象如图所示，则.A.A=2B.B=1C:w=1D.e=号数学测评（一）第1页（共4页）

联合测评(N)6.巴知函数g)二+号是在1心)上存在概值，则实数口的取值范围为A.(,)B6,号)C.(0,1)D.(0,e)姓名二、选择题：本题共4小题，每小题5分，共20分.每题给出的选项中有多项符合要求，全都选对得5分，部分选对得2分，错选得0分.9.已知函数∫(x)的图象关于直线x=1对称，关于(2,0)对称，则下列说法正确的是A.f(2-x)=f(x)B.f(4-x)=f(x)日的答案标号涂黑，C.f(4-x)=-f(x)D.f(4+x)=f(x)案写在答题卡上10.已知抛物线x2=2y(p>0)的焦点为F,过点F且斜率为3的直线L与该抛物线相交于M(x1y),N(x2,y2)两点（其中工1>0），则下面说法正确的是A.若=2，则x1x2=-4B.若y1y2=1,则p=2项符合题意，请C若力=2，则5aw-学D.若=2，则MF1=8+4311.已知各项均为正数的数列{an》满足a1=2,an=3a-1+2(n≥2)，b.=na,数列{b.}的前是n项和为Tn,则下面说法正确的是A.a3=26f人w器1B.an=3”一2BC.T.-(2m=1)X3+1=2n2-2m+3a十1a2十11.星a,+11Daia2 aza3 ana+412.已知矩形ABCD中，AD=3AB=25,△ABD沿着BD折起使得形成二面角A'-BD的夹角为锐设二面角A'一BD一C的面角为日，则下面说法正确的是，排A.在翻折的过程中，A'、B、C、D四点始终在一个球面上，且该外接球的表面积为12πB.存在0，使得A'B⊥CD的（米之语温交斜猫B放入到同C.当tan0=2√2时，|A'C|=2√2D,当cos0=3时，直线A'C与直线BD的夹角为45三、填空题：本题共4小题，每小题5分，共20分.公漫：l3.已知正项等差数列{an}满足a号十2a2a6十a-4=0,则a4元兰油m.胎范围为14.已知病毒A在某溶液中的存活个数传)的概率满足P(X=)3e(0,2知只要该溶液中存在一个A病毒，就可以导致生物C死亡，则该溶液能够导致生ABC所亡的概率为x。2x+2,00)的解为x1、x2x3、x4,则x1十x2十x十x4的取值范围为(本题第一个空2分，第二个空3分)细丽数fu)=5nx十22-ar≥0在xE[0,十w)上恒成立，则实数a的高三数学第2页（共4页）

当n=1,T=c1=1<1+29分10分所以1.=6+ca+s+…+,<1+1+专(1-2)+1+号（合3）++1+号(n)=时合(1-+-3+)=+号(1-)=-+所以对于任意的n∈N,T,6.63501，25×75×70×306310分依据小概率值α=0.01的X独立性检验，我们推断H。不成立，可以认为亚健康与锻炼时间有关联，该推断犯错误的概率不超过0.01.……00……·1220.解：(1)取PA的中点G,连接DG,EG,如图所示：则GE∥AB,且AB,∥CD,GE-号AB=DC.所以四边形CDGE为行四边形.2分G在R△DPG中，DG=√1+(g)-5,CE=DG-5,D所以CE的长为汽…4分(2)在面ABCD内过点A作BC的行线，交CD的延长线于点M,如图所示，以点M为坐标原点，分别以MA,MC为x轴和y轴，以与面MABC垂直之的直线为之轴，建立空间直角坐标系M-xyz,取AD的中点为N,连接PN,MN,在面PMN中过点P作PF⊥MN,垂足为F,则∠PNM=O,则A(1,0,0),D(0,1,0),C(0,2,0),设P(x0,y%,0).…5分C因为PN=号所以PF-号nAFN-号s0.Mr-号C1-cs0.D2所以，=-号1-s0>×号-古1-s0》-号m0【高三年级下学期第九次模拟考试·数学试卷参考答案第4页（共6页）】233647D

).A3EtyC.To make his executive team more productive.nable clothes.25.D.To see if Lee's productivity method would workWhat do we know about the sixth task on the to-do list?A.It was the least important of all.ntsB.It was as important as the other tasks.C.It was more important than the other tasks.orporation,whichD.It was more important than the seventh task.26rranged a mectingWhat can be inferred about Warren Buffett's 5/25 Rule?to increase theA.It encourages you to do as much as possible.B.It encourages you to focus on what matters most.saidC.It encourages you to complete your work in time.D.It encourages you to keep on doing something creativeachieving peak27What is the purpose of talking about world-class experts in the last paragraph?A.To raise doubts about multitasking.ant things youB.To explain how Lee's method works.C.To support the concept of prioritizing.D.To prove success can be achieved in any field.Work untilFor years,life went something like this:We'd grow up in one place,head offof the day,to college,then find a city to live in for a few years to pursue a job or highereducation.The end goal was to find somewhere to settle down,buy a house,start afamily,and begin the whole cycle all over again.But a new model for living islehem Steelemerging:Some people are increasingly opting to move from city to city throughoutis companytheir entire lives,sometimes as frequently as every month.Just ask Alex Chatzielefteriou,who has had a front-row seat watching thiswhy is itevolution unfold.Six years ago,he launched a startup called Blueground that rentsout beautifully designed,fully furnished apartments for a month at a time,at rentsngle bestthat are cheaper than hotels.Today,the company has 3,000 properties in six U.S.hat isn'tcities,along with Dubai,Istanbul,London,Paris,and Chatzielefteriou's nativeRule.Athens,and a staff of 400.hing.The company just landed $50 million in Series B funding,bringing its totalt beinginvestment to $78 million,to continue its rapid expansion.It hopes to have 50,000es leadsproperties in 50 cities over the next three years,and the goal is to make each onertists,feel unique and cozy,rather than standardized,like what you might find in aroughtraditional hotel.yourChatzielefteriou first came up with the idea for Blueground while he wasworking as a management consultant for McKinsey."The accommodation of choicefor consultants is the hotel,"he says."I had to spend five years in a hotel room,living in 12 different cities.I loved seeing the world,but I didn't love feeling likeIdidn't have a home."

分数学用报2022一2023学年聊城专版九年级第9~12期MATHEMATICS WEEKLY答案专期即b=-4a.①因为抛物线经过点A(0,a),点B(1,2),所以a+6+c=2,lc=a.所以b=2-2a.②H①②，得-4a=2-2a.得a=-1.所以c=-122.(1)当=40时.1=1.所以1=40解得k=40.所以函数表达式为：=40【第12期】第5章综合测试题当v=m时，t=0.5,所以0.5=40-、1.C2.B3.D4.B5.B6.B解得m=80.7.C8.D9.B10.B11.B12.D（2)把=60代入1=40，得：=子提示：因为40>0，t随x的增大而诚小.y=x,1.将=与y=号联立.即，=1所以最大值为60km/h时，t有最小值为名h所以汽车通过该路段最少需要名h,解得任：长23.(1)根据题意，得点A的坐标为(-12,0).点B中点A在第象限.可其坐标为(1.1)。的坐标为(12.0).设直线AB的表达式为y=-x+a.设抛物线的表达式为y=a(x-12)(x+12)将点A(1.1)代人，得1=-1+因为抛物线的顶点C的坐标为(0,8)，解得b=2.将c(0,8)代人抛物线的表达式，得a=-8所以直线AB的函数表达式为y=-x+2当y=0时，-x+2=0.解得x=2.所以抛物线的表达式为)=皮+8。故点5的坐标为(2,0.(2)能.二、13.-号14.x=1,(1,-9),(0.-8)理l:当x=122,即x=62时.215.y=-316.117.2y=3×62)+8=4.提示：因为3.5<4，所以这条河鱼餐船能到桥卜17.山计算，得n=3n=2=-分=-…24.(1)设直线AB的表达式为y=+所以y的值每三个一循环闪为直线AB过点A(2,0),B(1,1).因为2021÷3=673…2所以”解得传=2·所以ya=2=2.所以直线AB的表达式为y=-x+2三、18.设这个二次函数的表达式为y=ax2+bx+c.因为抛物线y=ax过点B(1.1).[a-b+c=2,所以a=1.根据题意，得c=-3,a+b+c=-3所以抛物线的表达式为y=x.a=5(2)因为直线y=-x+2与抛物线y=x2父于点B,C,解得6=-3所以另一个交点C的坐标为(-2,4)c=-3.所以S左mc=SaWE-S益R=3.所以二次函数的表达式为y=3-3x-3。因为SA=S6c,且OA=2,所以点D的纵坐标为3.19.（)设函数表达式为y=是因为点D在抛物线y=xX上，当x=-2时y=3.所以3=专所以x2=3,即x=±3.解得k=-6所以点D的坐标为(-3,3)或(3,3)所以y关于x的函数表达式为y=-名25.(1)x=100+x,y.=7x（2)1y=4时，则4=-(2)根据题意，得y=00+100-月解得x=-号-2x-50+11250.20.(1)山题意，得k-1>0.因为a=-号<0，所以当x=50时，y的值最大.解得>1因为每次提价为20元，(2)将双曲线向右移2个单位长度后经过所以每问包房晚餐应提高40元或60元，获得点(4,1)包房总收人相同，所以双曲线y=-1必经过点(2,1).但从“投资少而利润大”的角度来看，应该尽所以1=，1.解得k=3量减少租出包房所以每天晚餐每间包房应提高60元，方可21.因为抛物线的对称轴是直线x=2.获得最大包房总收入，此时最大总收入为所以-会=2.11200元.

第二节书面表达One Possible Version:Boys and girls,To enrich the after-class activities of senior three students,the school English Club is goingto hold an English inspirational speech activity themed "My Growth Experience"in the schoollecture hall from 3 to 5 this Friday afternoon.The activity is arranged as follows.We have invited Li Hua,a schoolmate who graduated from Peking University,to deliver aspeech,in which he'll introduce his own experience of how he changed from a student who didnot love learning to a super learner.After the speech,there's a question-and-answer session.He'll answer the questions raised by the audience.All senior three students are welcome to attend on time,and we believe you'll certainly getsomething from the activity.(118 words)The English Club(一)评分原则1.本题总分为25分，按5个档次给分。2.评分时，先根据文章的内容和语言初步确定其所属档次，然后以该档次的要求来衡量，确定或调整档次，最后给分。3.词数少于80和多于130的，酌情扣分。4.评分时应注意的主要内容为：内容要点、应用词汇和语法结构的丰富性和准确性及上下文的连贯性。5.拼写与标点符号是语言准确性的一个方面。评分时应视其对交际的影响程度予以考虑。英、美拼写及词汇用法均可接受。(二)内容要点1.时间地点(7分)；2.活动安排(8分)；3.表达希望(6分)。4.适当发挥(4分)。(三)评分标准第五档(21一25分)：完全完成了试题规定的任务，完全达到了预期的写作目的一覆盖所有内容要点。应用了较多的语法结构和词汇。语法结构或词汇方面有些许错误，但为尽力使用较复杂结构或较高级词汇所致；具备较强的语言运用能力。英语试题答案第2页（共3页）

所以P(M)=P(Do)P(E3)+P(D1)P(E2)十P(D2)P(E1)+P(D3)P(E)·10分=×+×告+×号+×分员故“少年队”在三轮比赛中恰好射中3次的概率为247…12分22.(1)证明：连接BD交AC于O,连接ON.因为AD/BC,BC=2AD,所以根据相似的性质可得器%=2.…1分因为直线MB∥面ACN,MBC面MBD,面ACN∩Be0面MBD=ON,…2分所以MB∥ON,…3分【高一数学·参考答案第4页（共5页）】·23-523A·则-0-2所以MN=2ND.…4分(2)解：取AD的中点E,AC的中点F,连接ME,EF,MF因为△MAD为等边三角形，所以不妨设MA=AD=MD=6,则ME=33,MELAD.…5分因为面MAD⊥面ABCD,面MAD∩面ABCD=AD,所以ME面ABCD,所以ME⊥EF,MEAC.…6分又因为E,F分别为AD,AC的中点，所以EF∥CD,而AC⊥CD,所以AC⊥EF,又ME∩EF=E,则AC⊥面MEF,得AC⊥MF,所以∠MFE是二面角M一AC-D的面角，即∠MFE=a.…7分设Ef=m则1m6深-∈[3.3].得e11.…8分过N作NH⊥AD交AD于H,连接CH,易得NH⊥面ABCD,则∠NCH为直线CN与面ABCD所成的角，即∠NCH=Q.…9分NH-ME-/3.DH-ED-1.CD-2m.因为6as∠AC-器-g所以CH-V4m+1-2x2m×/8m2+3=√3…10分则am广是3…11分/8m2+3√8m2+33因为m∈[1，√3]，所以tan0=3√8m2+3故an0的取值范围为5,3亚，…12分311【高一数学·参考答案第5页（共5页）】·23-523A·

20.【答案】W当1时，C=C6即点D,E分别为BC,BG的中点，在直三棱柱ABC-AB,C,中，B,C∥BC,所以B,EIBD,所以四边形BBED为行四边形，所以BB,∥DE,又AA,∥BB,所以AA∥DE,所以四边形AAED为行四边形，则ADAE.又因为AD文面AEB,AEC面AEB,所以ADW面AEB、…5分C(2)AA⊥面ABC,又∠BAC=90°，以{AB,AC,AA}为正交基底建立如图所示的空间直角坐标系A-yz,则点A(0,0,0),C(0,3,3),A(0,0,3),B(3,0,0)，C(0,3,0)由BD-C5=0<1<)得E6x3-33),BC CB所以AC=(0,3,-3)，AB=(3,0,-3),AE=(0,3,-3)设面ABE的一个法向量m=(a,b,c),则mA=0即{00取a=1,得m-1,m·AE=0,3t0+(3-3t)b=0,t√6令直线AC与面ABE所成角为0，则sin8=cos33w52+台所以得12r-16+5=0,所以1号或名，叉因为：>行所以：=名…9分h6而AC=(0,3,3),AB=(3,0,0),BC=(-3,3,0),BD=tBC=(-3t,3t,0),所以=a+而--0-20设面ACD的一个法向量为%=K.,),则AC=0即{，3y+3=0,2·AD=0,3(1-t)x+3y=0,取--1-0=官6岩又面ADC的一个法向量为n,=(0,0,1),积0网风，见察得丙角G-AD-C为能角所以二面角C-AD-C的余弦值为…12分9第2页（共4页)

18.(本题满分12分)如图，在三棱锥P-ABC中，已知PA⊥面ABC,面PAC⊥面PBC.(1)求证：BC⊥面PAC;(2)若C-VC,M是PB的中点，AM与面PBC所成的正弦值为子，求面PBC与面ABC夹角的余弦值，第18题图解：(1)过点A作AD⊥PC于点D,因为面PAC⊥面PBC,面PAC∩面PBC=PC,ADc面PAC,所以AD⊥面PBC.......4分则AD⊥BC,又因为PA⊥面ABC,所以PA⊥BC,PA∩AD=A,故BC⊥面PAC..….6分(2)几何法：因为BC⊥面PAC,所以BC⊥AC,又因为AD⊥面PBC,所以∠AMD为AM与面PBC的所成角，….8分令C=6,ACM0用0M粉+222a则sina@+G+子，解得a=V2..10分因为PC⊥BC,AC⊥BC,且面ABC∩面PBC=BC,所以∠PCA为P-BC-A的面角，cos∠PCA=4C=1-3.12分坐标法：因为BC⊥面PAC,所以BC⊥AC,则以CA为x轴，CB为y轴建立空间直角坐标系，z轴∥AP,取BC=V3,AC=1,PA=a,则AL,0,0),B(0,V5,0),P1,0,a),590=,=a50,西=9M(高二期末检测数学参考答案第4页（共9页）

the mos undand lifechanging discoveries in scentifi history and RoyalSoetystomake outstanding contributions to science in many research ideas.eonyto boyande一etha,more of us will pass our exams."What we doOur motto is"take nobody's word for it"and academic strietness is at the heartofverthngwedo.Weare away ekingdiverseand cuio minds who can jonusoTherivbehind N DIYwer intitive Indeedtheissin()and help us in shaping tomorrows socety.Work with us and you will playchaReorhniygedDerneah1okeptenheworkagaNkosi already gives hands-on lessons in the basics of engineering to village children.andcntralroleinpromotingscicnceanditsbenefits,rccognizing,execlcnceimscieatificthinlking.p0cwao中h】coaaooiadvice developinntton and globaperation andntpotohelpme ufmyp fback toshol tofrher mywdgd assnwhat I've learned to others.general public.What we offerWhy does the author mentionA.To compare Edison and Nkosi.In return,we offer flexible working arrangements,development and a comprehensive package of benefits including:extensive space for careerB.Toinroduce the top of the te30 daysholiday (plus three given days)CTotrethe importance of inventioOGenerous pension provision (defined contribution scheme)D.TowtheofmodeOInterest-free season ticket loan25.What can we know about the country Malawi?Subsidized medical and dental insuranceisedofbadly●Onsite restaurantB.Many people are addicted ogmes.OEmployee Assistance Programf tspopulation hastoeducation.We would like you to be aware of the Society's position that animals are forbidden to beD.Manysdncan as themduethirekilled wastefully in research before applying for a role at the Royal Society.A 26.Why did Nkosi invent the turbine?Find usA.To make a profit.Find out where we are by visiting the contact us page.If you would like to discuss one ofB.To show off his knowledge.our opportunities,please contact humanresources@royalsociety.orgC.To bring eleciricity to his villae.D21.What does the motto of the Royal Society mean?D.To win the award from the Queen of England.A.Starving to learn.B.Believing nobody.27.Which of the follownbest deNC.Being a serious style.A.Brave and proud.22.What should you do you are in the Royal Society?D.Accepting excellent science.C.Confident and calm.B.Strong and patientD.Creative and generous.A.Respect the animals.B.Have a 30-day holiday.C.Borrow an interest-free loan.D.Purchase health insurance.23.What is the probable purpose of the teIt's no secret that walking is good for you.Many of us are trying to get in thoserecommended 10,000 stepsaday that our wearable fitness technology urgesutoachieve.ButA.To entertain.B.To advertise.C.To instruct.D.To persuade.how can we get the most out of those steps?BYou burn more calories in a shorter amount of time with higher-intensity()exercise“To invent,,”Thomas Edison said,“you need a good imagination and a pile of junk.”that pushes you into a higher heart rate.Walking,however,is a moderate-intensity form ofColrerd Nkosi had all the junk he needed and the will to bring electricity to his small village inexercise.To get the most calorie-burning benefits,then,it would seem that walking at aMalawi.He not only accomplished his goal,but won an award from the Queen of England.consistently quick pace that keeps your heart pumping would make the most sense.Using a repurposed corn-shelling (machine motor and a fast-moving river,NkosiThe Amcrican Collcge of Sports Medicine (ACSM)puts your target heart rate forcreated an electric turbine()that's now lighting up homes for him and his neighbors formoderate-intensity physical activity at 64%to 76%of your maximum heart rate.According tofree in the town of Mzimba.the Centers for Disease Control and Prevention,to estimate your maximum age-related heartJust like Edison.he did a lot of experiments.In the beginning.he put a bicycle in therate,subtract()your age from 220.For example,if you're 28 years old.your estimatedriver and brainstormed about how the water moved the pedals(),and how it might bemaximum heart rate is calculated as 220-28-192 beats per minute.turned into power.Then,he used another kind of old part from the refrigerator to transformKeeping with our example of a 28-year-old person,a moderate-intensity heart rate wouldpower for 6 homes.But that's not enough,so he continued to upgrade.be between 123 and 146 beats per minute.During this type of exercise,you will feel yourAccording to the self-taught inventor,his latest turbine has the potential to produceenough power to provide electricity to 1,000 homes and he says another turbine can be fixedbreathing rate increase bu sostill be able to speak in compeedownstream to produce more electricity.In 2018.Mr.Nkosi won an award from the Queen ofThere is also research showing that changing your pace to vary your intensity,and,England.consequently,your heart rae,throughout your walk inrease your metabolic(新陈f代谢In a country where only 11%of the population has access to electricity,having a reliablerate bymre than reminingsedypace throughou the durationand renewable source of energy has been a game-changer-especially in the schools."In thealkBased on thisyo houd break up your pace todlight intensity.【高三英语第3页（共8页）】23368C【高三英语第4页（共8页）】23368C

(2)由(1)知AMBC,OD⊥面ABC,过M作之轴行于OD,则之轴垂直于面ABC,如图建立空间直角坐标系，在△ABC中，由(I)与等腰三角形三线合一可知M是BC的中点，又AC=AB=4,BC=2,则AM=VAB-BM=V5,SAc=号AM,BC=万，设AO=r,则BO=r,又OMP十BMP=OB,所以(V压-+1P=P,解得，8，故0M=M-A07沿15因为三棱锥A-BCD的体积为1，所以号Sa·0D=子×V丽·OD-1,则OD=,5则c01,0,B0,-1,0,0(1,0.0）A5,0.0,D(70,）,故0i-(8o）a访-(-8o,)0-(-71.0).因为E为AD上套近A的四等分点，所以成-0i+}-(2压0，），n0i-2匹+=05设n=(x,y,z)为面ECO的一个法向量，则.d=7ey-0取x=需则)日=西故m(需日)7，……10分易得m=(0,0,1)是面COB的一个法向量，设二面角E-CO-B的面角为0，则0为钝角，√/15所以cos0=-|cos(m,m)l=一mmm·n7w151xV需+4,所以二面角E-C0-B的余弦值为一西412分22.【解析】(1)根据题意，乙获连负两场，所以1、4均负，所以乙拔连负两场的滋率为P-导X号-是。…4分(2)甲获得冠军，则甲参加的比赛结果有三种情况：1胜3胜6胜；1负4胜5胜6胜；1胜3负5胜6胜，所以甲我得慰不的瓶率为P=()广+2X()广×子-离…8分(3)若乙的决赛对手是甲，则两人参加的比赛结果有两种情况：甲1胜3胜，乙1负4胜5胜；甲1负4胜5胜，乙1胜3胜，所以甲与乙在决案相遇的概为：P-是×子×日×日+子×月××号品，若乙的决赛对手是丙，则两人只可能在第3场和第6场相遇，两人参加的比赛的结果有两种：乙1胜3胜，丙2胜3负5胜；乙1胜3负5胜，丙2胜3胜，同时考虑甲在第4场和第5场的结果，乙与丙在第3场和第6场相遇的概率为：P×号×号×（是×+×号）+×号××（×+×号）离5若乙的决赛对手是丁，则其概率与乙的决赛对手是丙相同，1537赛，且乙与其决赛对手是第二次相遇的概率为8十1282828……数学参考答案（长郡版）一5

参考答案听力：1-5：CBBCA6-10 BCCAB11-15 ACACB16-20 ABBAC阅读理解：21-23BCD24-27:BAAD28-31:DACC32-35:CDBA36-40:GBAEF完形填空41-45：BCACB46-50 DCBAD51-55 CDABB56-60 AADDC语法填空：61.have flooded62.which63.a64.meaning65.how66.compared67.be considered 68.importantly 69.to70.healthier短文改错：One day I was wandering in the canteen alone while I met Li Hua.She kind offered to dinewhenkindlywith me.We ordered our food and choose the seats near the window with warm sunshinechosepoured in.When we were eating,I shared my doubts or worries about my new campus lifepouringandwith her.Hearing my concerns,Li Hua said she also had same feeling when she at first came个hehere.She encouraged me,"As long as I embrace the new high school life with enthusiasm,youyou will see surprises in your new life."Her word gave me that I would need to welcome awordswhatbrand-new life.书面表达：One possible versionMy teachers and fellow students,It is accepted by all that a dream is a beacon that leads one to success,or at least to thepursuit of success.As for me,my dream is to go on adventures around the world.To be moreexact.I would like to walk under the hot desert sun,climb in a damp rainforest.which will allbecome valuable experiences I'd like to recall in later years.However,to realize my fantastic dream is by no means an easy task.Most importantly,I haveto maintain excellent physical strength and strong willpower because travelling is always tiringand visiting what have not yet been fully developed is extremely so.Only with a strong body andsoul will I manage to conquer all the difficulties.In addition,I shall learn living skills in the wildeither by personal experience or from those who have the similar dream.Furthermore,it is alsoessential to equip myself with geographic and historical knowledge in order to enjoy thelandscapes better.As you can see,my dream is not far beyond reach as long as i set about pursuing it.命题：罗增礼游华杨静张青谭丽华王琪李小倩李清

B F G因为A4,=AC,则行四边形1CC4是菱形，则4AG1AC,作B0L4G,因为面ACC41面ABC,所以B,01面1CC4,则B0LAC,过C作B0的行线，与4B交于点G,则CGLAC,又CGn4C=C,则4C上面ACG,在AB上取一点H,作HE1AC,HF1/AG,分别交线段4C,A,B,上于点E,F,易得HE1/面ACG,HF1/面ACG,又HEN HF=-H,所以面HEF1/面ACG,则ACL面HEF,所以AC LEF,因为点H有无数个，所以有无数条直线EF,使得EFLA,C,故A错误.如图所示：一一一一一一一4(F)若A4=AC,则△ACA是正三角形，设E是AC中点，F与4重合，则EF1AC,且四边形ACC4的面积为2W33E2.面ACC41面ABC,EFL面ABC,EF1面AB,C.:4BC面AB,C,当E不是25EF2AC中点，或F不与4重合时，线段EF的长度将增加，四边形MCC4的面积不再等于·故B正确.如图所示：答案第10页，共24页

6.为落实党的二十大提出的“加快建设农业强国，扎实推动乡村振兴”的目标，银行拟在乡村开展小额贷款业务.根据调查的数据，建立了实际还款比例P关十还款人的年收人x(单位：万的g加原爽P团。已知暗货意人的年致人为y万元时，其头际还放比衡50%.若银行希望实际还款比例为40%，则贷款人的年收入约为()（参考数据：31.1,ln2≈0.7)A.4万元B.8万元C.6万元D.5万元,7.已知抛物线C的焦点F在x轴的正半轴上，且焦点到准线的距离为2，过点F且倾斜角为60°的直线交抛物线C于A,B两点，则FA·FB1=（)A华B.5cD.28.已知函数/)=mor+孕，对于xeR,f)s/(),且因在区间018上单调递增，则0的最大值是()A.-Bc号D.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.已知向量ā=(1，m),方=(2,4)，则下列说法正确的是（）A.若a+=√10，则m=5B.若a∥6，则m=-2C.若a⊥6，则m=-1D.若m=1,则向量ā，b的夹角为饨角10.随机抽取某班20名学生在一次数学测验中的得分如下：50,58,65,66,70,72,75,77，78,78,80,81,81,83,84,85,88,90,95,98,下面说法正确的是()A.这组数据的极差为48B.为便于计算均数，将这组数据都减去70后得到的均数与原数据的均数相差70C.为便于计算方差，将这组数据都减去70后得到的方差与原数据的方差相差0D.这组数据的第75百分位数是84.511.已知直线(m+2)x+y-m-3=0,P(x,y)是圆Cx2+y2+2x-3=0上的一点，则()A.直线1过定点(1,1)B.圆C的半径是V2C.点P可能在圆x+y2=1上D.点P到直线1的最大距离是5+212.已知正方体ABCD-A,B,C,D,的棱长为2，P为底面ABCD内（包括边界）的动点，则下列结论正确的是()A.三棱锥B-CD,P的体积为定值B.存在点P,使得D,P⊥面A,BCC.若D,P⊥B,D,则P点在正方形底面ABCD内的运动轨迹长为22D.若点P是AB的中点，点Q是C的中点，经过D,P,三点的正方体的藏面周长为25+32三、填空题：本题共4小题，每小题5分，共20分。13.在x+的展开式中，常数项等于(用数字作答)√x【24届的服二串新高考高三摸底调所洲浅数学第2页（共4页）】

21.解析：(1)由已知得渐近线方程为bx±ay=0,右焦点F(c,0),=5,又a2+b2=c2,解得b=√5.2分Na+b又因为离心率e=S,解得a=l,c=2.3分a双曲线的标准方程为x-上=13.4分(2)解法1：当直线1的斜率不存在时，其方程为x=1,此时，△FMN的面积S.FAOV=3;.5分当直线I的斜率存在时，设其方程为y=c+m,直线与双曲线联立得x-号=1→-+2x+m+3=0,…6分y=kx+m因为相切，所以△=4k2m2-4(k2-3(m2+3)=0,解得m2=k2-3>0..7分另设：M(x,y),N(x2,2)联立3x,y广=0(2-3x+2kx+m=0y=kx+m-2km -2kX+x3=k2-3m,xx2=1y+为=kx+5)+2m=-3m2=k2.xx2+km(x+x2)+m2=-3在△OMN中，OM=2x,ON=2x2万Sow=MWkin∠oN=2x号...10分所以S.w=S,om+.ow-S,ow=0Fby-V5,所以sm=0+为P-4g房-5是+12-6.11分9因为m=k-3>0,所以S.A-V+12-5>25-5=5

首项，公差为21的等差数列，其和为10X31+10×9X21当n=1时，a1=1,2=1255,选项D正确.故选ABD.当≥2时，可得号十器++号=7.由题意，数列{a,}满足a1=5,am+1=a-an十1，可得会-是--2=2-a+1-1=a2-a.=a,(a.-1),211a+1-1a,(a,-d当n=1时，a1=2-1=1也符合，故an=2-n.(6分)12-n,n为奇数1 a-m1一1，即1=1一（2)由(1)知b.={2-·,m为偶数(1S2n=[1+(-1)+(-3)+…+3-2n]+(2°+a3a1-1-)+(a2-12-2+…十22-2m)ta++(-1（a2020-1a221-）=1+3-2m)n+1-111.11211as-1 daou-7互-1aai=4-a可，144又由an+1=a片-an十l,可得an+1-an=a房-2am+1==n2-m+号(1-)a.-1≥0.a=号>1，a1-a>0,9a1>上-W+2a+号-3x15分)a,数列{a}单调递增，计算可知，a1=三，11.(1)由题意，令b。=2a-5’n16,a3256a4-103441=361=65536,a5≈1.91，a6≈2.74，a2021-1>设数列6，)的前n项和为S则S.=子-1八1.4-a与∈(3,4)，甲m的整数都分是当=1时，6=S=子3.8,根据题意，数列《S}是首项为号，公比为号的等比数当22时6=8-S=骨”写-日数列6}是常数列，即6=2a”=对1列，故5.=（号）”，故S+S+S,十…+S=故a,=35,n∈N.7分)守”-98+81-号(2由)知ad,8n+3m+D+可4=[3n+53m+D+],11岩脚台1-等台)≥是支形可得：9≥20×，又由mT.=1+1+…+1∈N*,则有n≥4.alaz aza3anan+19.由题意可知，a1=2,n≥2时，an一am-1=n+1,则am=(3×+书-3×2+5)+音(3x2+5=47111a1+(a2-a1)+(ag-a2)+…+(an-am-1)=2+3十…十n十1=n(2+n+1)_-nn+3》,n=1时，a1=2也3X3+5)+…+4[111223L3m+5厂3(n+1)+5]1成立，an=n(n十3)，1nn29(m+2)a,(n+2)×n时3=号[3x2+X255x+2+…1-a+2+-2十23.=2（日-青+23m+53(m+1)+5]-4「11子-+…+中2-2（号-）3L3×1+53(n+1)+5J=台哈-3m十+512n3n+9114解答题=6-9n+2410.(1)由2"-1a1+2m-2a2十…+a.=n的两边同时除以2m6m+16(15分)可得号+器+…十会=12.(1)由题设2Sn=an十a且am>038

15,在面直角坐标系0中，若圆Cx++(+2=户(>1)上任意一点关于原点的对称点都不在圆C2:(x-2)2+(y-1)2=1上，则r的取值范围为16在三棱柱ABC-ABG中，已知各棱长都为2，侧面AMCC1底面ABC,且∠AMC-胥，则三棱柱ABC-ABC的侧面积为」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.(本小题满分10分)D在长方体ABCD-AB,CD中，已知AA1=2AB=2BC=4,O为AB,CD0的中心(1)求异面直线OB,AC,所成角a的余弦值：(2)求证：OB//面ACD1.·D18.(本小题满分12分)在△ABC中，设角A,B,C的对边长分别为a,b,C.(1)若点D是BC边上一点，且CD=1,BD=2,2b2+c2=9,求AD的长：2)若C=2B=T,且AB+AC=AB.AC,求△ABC的面积319.(本小题满分12分)已知圆M关于x轴对称，且与直线：x-2y+m=0相交于P、Q两个不同的点，过P、Q分别作直线1的垂线与x轴交于S(-2,0),R(3,0),且梯形PQRS的中位线长与面积分别为35,152(1)求m的值：(2)求圆M的标准方程.

4版鲁教八年级参考答案第4期主编：卞彩虹责编：田雪丽排版：周家伊电子邮箱：renjiaoshuxue8@126.com数学周刊第16期参考答案情境导入：该机器人所走的总路程为24米。二、填空题（每小题4分，共24分）5.4第1课时多边形的内角和9.36010.16211.712.8813.(n-1)14.720知识清单：1.(1)12(2)23(3)342.720三、解答题（共44分）即学即练：1.B2.A3.B4.C5.九6.13215.(8分)解：因为正多边形的每个内角都等于150°，所以7.解：七边形的内角和为(7-2)×180°=900°正多边形每个外角的度数为180°-150°=30°.因为六个内角的和为780°，所以这个七边形的另一个内因为多边形的外角和等于360°，所以该正多边形的边数是360°÷30°=12.角的度数为900°-780°=120°.16.(10分)解：(1)设多边形的外角为x°，则有x+x+60=180,8.(1)这个多边形的内角和为1620°.解得x=60.(2)n的值为12.360°÷60°=6.9.解：(1)(n-3)(6-2)×180°=720°(2)根据题意，得n=2(n-3),解得n=6.所以这个多边形的内角和是720°(6-2)×180°=720°.(2)这个多边形所有对角线的条数为6×(6-3)9（条）。答：该n边形的内角和为720°210.解：(1)因为n边形的内角和是(n-2)·180°，所以多边17.（12分)解：设两个边数相等的多边形的边数为m,另形的内角和一定是180°的整数倍.因为2023÷180=11…43，一个多边形的边数为n.(m≥3，n≥3，m,n为正整数)(1)根据题意，得2m+n=20.所以多边形的内角和不可能为2023°，这三个多边形的内角和为2(m-2)×180°+(n-2)×180°=(2)设小敏求的是n边形的内角和，错加的外角为x°，则(2m+n-6)×180°=(20-6)×180°=2520°.0n,所以n<10.180m.因为0

八-】①②③不妨记第n(n=1,2,3,)个图中的图形的周长为0，则4=()256256512512A.9B.27C.27D.818.设函数f的定义域为[0,3)，满足特足f(x+)=2fx)+,且当x∈[0,1)时，f,=1-9.则不等式5f(x)≥8的解集是()[5,7u2,3c4'40「45U(2,3)D.33二、多选题：本大题共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.下列命题正确的是A.3a,b∈R,la-2+(b+1)2≤0B.a∈R,x∈R,使得ax>2az-bC.ab≠0是a2+b2≠0的充要条件.D.a≥b>-1,则1+a1+b10.已知等差数列a,的前n项和为S。,满足4+a,+a=21,S,=25,下列说法正确的是()A.an 2n+3B.S,=-n2+10n110c.5.}的最大值为，D.(a,am1J的前10项和为991,已知函数f()的定义域为R,且f(O)=0.若y=f(x+2)+1为奇函数，y=f(x+4)为偶函数，则()A.f(4)=0B.f(8)=0c.f(0)+f3)=2D.f)=f(7)12.对于三次函数(x)=ar+hr+cx+d(a≠0），给出定义：f'()是函数y=f(x)的导数，第3页/共6页

oneother.Now,they often communicate by WeChat.Yesterday,my father told th me with excitement,英语参考答案"Michael,with his family,will come to China to see usthis summer."How amazed it is!We're looking forward①本套试题考试范围：高一高二内容amazing大交②全卷品、中、难比例：6：3·1，金卷难度系数预to see him!seeing估：0.68左右。，。au为是第二节书面表达,级理两点西为中鸡合有One possible version:第一部分听力Dear Peter,1-5 CABAB 6-10 ACACB 11--15 CBCABIn the last email,you asked me to talk about the16-20 ACABCA动款层，言，家physical exercise in the long break time in our school.第二部分阅读理解Here's something about it.第一节In order to ensure that students have one hour of21-23ABD24-27 CCAB 28-31 BCDAphysical exercise time every day,our school conducts32-35 CBDDsports activities during the break time after the second第二节0深2class,which lasts for 30 minutes.During this period,the36-40 AEGDF成遮首图喻students participate in various sports activities,such as第三部分语言知识运用running on the playground,doing eye exercises,and our第一节完形填空self-developed basketball exercises and so on.41-45 ABCAD 46-50 DBDCA 51-55 CBBADThese activities have attracted students to step into56-60 CDABCthe sunshine from the classroom.Obviously,they're人第二节语法填空beneficial for enhancing the physical fitness of our61.groups 62.to 63.than 64.their 65.astudents.Now,we've truly understood the concept of66.exactly 67.causes68.social 69.to become"exercising one hour a day,working healthily for fifty70.settingyears,and living happily for a lifetime."第四部分，写作Do you also have such sports activities in your第一节短文改错school?(117 words)Having friends are a blessing.An old saying statesBest wishes!is政Yours,that a true friendship never dies.But can it lasted forLiHualastmore than 30 years without A single meeting?That's(一)评分原则a1.本题总分为25分，按5个档次给分。that has happened between my father and his English2.评分时，先根据文章的内容和语言初步确定其所whatpen friend Michael.We started writing to each other in属档次，然后以该档次的要求来衡量，确定或调整档次，They最后给分。their teens.My father was thirteen,six months old than3.词数少于80和多于130的，的情扣分。olderMichael,as he sent Michael the first letter.Over the4,评分时应注意的主要内容为：内容要点、应用词year,they've written more than 200 letters to each汇和语法结构的丰富性和准确性及上下文的连贯性。years5.拼写与标点符号是语言准确性的一个方面。评英语参考答案第1页（共8页）

高二数学参考答案1.C因为A={p,e,a,c,h},B={a,p,l,e},所以A∩B={p,e,a}.2(因为已品当-1i所以叶=-23.A直线a2x+y-1=0的斜率为-a2>-4,解得-2

国©©所名校高三单元测试示范卷nE=0，n·C市=0，故y+z=0-(-22n,取n=(2,1,-1).设直线BQ与面PEC所成的角为a,则sna=|cosB成，n=1·nL=BQ·n61a+25为0√212×√22-41+312即Q为线段AP的中点，此时AQ=2(12分)如图，在多面体ABCDEP中，底面ABCD是菱形，AP⊥面ABCD,AP∥Cn重BEQF-,CaDE,PA=AB=3,AC=23,DE=1,点F在棱PA上.(1)求证：BF∥面CDE.(2)求面PBC与面CDE夹角的余弦值.(3)若AF=2,求点F到面PBC的距离.(0,4-0【解题分析】(I)由题意知AB∥CD,因为AB吐面CDE,CDC面CDE,所以AB∥面CDE,又AP∥DE,因为PA丈面CDE,DEC面CDE,所以PA∥面CDE.又因为PAC面PAB,ABC面PAB,PA∩AB=A,=0,解得1-号所以面PAB∥面CDE,BFC面PAB,则BF∥面CDE.…4分(2)在菱形ABCD中，AB=3,AC=√AB+BC-2AB·BC·cOs∠ABC=23,21解得cOs∠ABC=号，AB·c0s∠ABC=1,则取BC上靠近B点的三等分点G,连接,易知AGLBC,且AG=2√2.由AD,AG,AP两两垂直，可建立空间直角坐标系A-z,如图所示，则B(2√2，-1,0)，C(22,2,0),P(0,0,3),E(0,3,1),D(0,3,0),CV2CD=2,E为ACD=(-22,1,0),D=(0,0,1),CB=(0,-3,0),C=(-2√2，-2,3).G,且PB=C1n·Ci=0设面CDE的法向量为n=(x,y,2),则|-2W2x+y=0取n=(1,2√2,0).Q与面P所成m·C2=0设面PBC的法向量为m=(a,b,c),则.|-22a-2b+3c=0m南-0仁60在，请说明厘血取m=(3,0,2√2)则cos(m,n)=m·n3m1n3X√/17，故面PBC与面CDE夫角的余整值为哥17…9分(3)由(2)知F(0,0,2),BF=(-22,1,2),点F到面PBC的距离d=萨.m-22-2图m√171712分2.(12分)如图，在三楼台ABC-A,B,C中，面BCCB⊥面ABC,∠BAC-受，BC=2AB=4A1B1=4,BB1=CC=5.(1)求三棱台ABC-A,B,C的体积；(2)求直线AC和BB,所成角的余弦值；(⊙)在侧楼B,上是否存在点D,使得面ACD与面ACB夹角的余弦值为5？若存在，说明点D的位置；若不存在，请说明理由。【解题分析】1)由题意知四边形BCC,B,是等腰梯形，BC=2AB=AB,=4,则B,C=2,【24·G3DY(新高考)数学-必考-N】131

第13期B1版Keys:(One possible version客观题除外)课本链接1.Cold2.eat it3.on their bowls 4.Soup5.proud of主题漫步1-5 TTFFF第13期B2版Keys:(One possible version)知识“串联”For Section A1.握手2.一…就…3.令某人惊讶的是4.应该做某事5.伸出手6.drop by7.after all8.get mad9.make an effort10.clean...off11.take off12.worth the troubleIL.1.To our surprise,a simple act like shaking hands can make a big difference.2.In China,when we meet someone for the first time,we're supposed to shake hands with himor her.3.有些人在没有得到他们所希望的回应时就会生气。4.在我们的个人生活中，我们也应该努力与人握手。For Section B1.空碗2.指向3.犯错4.特地；格外努力5.make...feel at home6.be comfortable doing sth7.cut up8.get used to9.be excited about10.not...anymoreIL.1.to point at2.got used to3.make me feel at home4.cut up5.not;anymore语法点击1.Those animals are not supposed to live in the wild.2.When is Jenny expected to finish the report?3.When was the plane supposed to land?4.Are you expected to give a speech in front of all the students and teachers?5.Parents should help their kids learn to control their feelings.写作一招鲜Dear Jason,

35.What's the last paragraph mainly about? A.Cheetahs'abilities to run faster. B.Lessons runners can learn from cheetahs. C.A running form different from other animals. D.Differences between two animals'running frequency

(Text 6) M:I'm going to work at the Riverside Hotel this summer. W:What exactly will you be doing? M:I'll be doing some small repairs inside and outside the hotel. I'll be cutting grass and taking care of the flowers. W:Sounds interesting.What's the pay? M:Well,uh...about fifteen dollars an hour,five hours a day, and Sunday free. W:That's good money.What are you going to do with it? M:I'll pay for the textbooks for next term. (Text 7) M:Linda!I was looking for you.I wanted to ask you what you are planning to do this weekend.

【答案与解析】 人们总是以忙为借口说没有时间写感谢信。本文通过一位总 裁给员工写感谢信的故事告诉我们写信表达感谢和善意的重要 性。 41.A一项研究表明，大多数参与调查的人不到五分钟就能写一 封感谢信。 42.A然而，在这个快节奏的世界，我们似乎从没有想过动笔写感 谢信。 43.D 44.C根据下文a quick text or an email可知，我们总是做对我们 来说方便的事情一发一条短信或一封电子邮件。 45.B 我们很容易以忙为借口。 46.C根据下文when Doug Conant became CEO of Campbell's

W:What's your name? M:James Thompson.J-A-M-E-S. W:OK.What flight will you be travelling on? M:It's Air Canada,flight number AC936,from London Heath- row, W:That's $45,please. M:My VISA card number is 3303 8450. W:OK.That's everything.Have a nice trip. M:Thanks. (Text 10) W:Mountain Elementary School is hosting an event to honor the artist Sheldon Williams.Please join us in the gym at 7:00 pm on Wednesday for a view of his artwork.Food and drinks will be served.Admission is free although we are asking for a donation of 5 at the door,which will go to the school's art department.

47.A.vaguely B.meaningfully C.individually D.cautiously 48.A.adventure B.research C.setting D.assignment 49.A.controversial B.constructive C.temporary D.permanent 50.A.shadow B.pressure C.donation D.duty 51.A.life B.homework C.credits D.degrees 52.A.arranged B,forced C.expected D.forbade 53.A.present B.imagine C.pause D.insert 54.A.shabby B.relaxing C.harmonious D.original 55.A.task B.meeting C.appointment D.travelling 56.A.content B.strict C.familiar D.associated 57.A.unhappy B.unhelpful C.unbearable D.unpopular

Japan is particularly easily affected by natural disasters be- cause of its climate and topography(地形)，and it has experi- enced many earthquakes,typhoons,and other types of disasters. A number of factors contribute to the high incidence of natu- ral disasters in Japan.First,the country faces extreme climatic changes,such as seasonal storms and typhoons,as well as heavy snowfall on the Sea of Japan.Second,Japan's topography is rug ged(崎岖不的).Third,Japan is located in the Pacific earth quake belt and is frequently struck by earthquakes.And fourth, Japan is located in the circum-Pacific zone,in which almost all the volcanoes of the world are concentrated,and has 83 active volcanoes-one-tenth of the world total.