17.解：1)连接EKCD,AB,因为E,F分别为棱AA1,AB的中点，所以EF∥A,B,由题易知，CD,/A B,所以EFCD,所以E,F,C,D四点共面」个5分2连接BB由知，EF/CD:且F=CD:所以ADEP的面积容ADrC面我产的2，所以三棱锥D-D,EF的体积等于四棱锥D一EFCD,的体积子版印别即因为AB=2AD=2AA1=2,所以△DD,E的面积等于2×1X1二影所似三棱锥F一DD,E的体积等于}×号X1-,所以三棱锥D一D,EF的体积等于号，故四棱锥D一EFCD,的体积为}×3-是10分18.解：(1)取AD的中点为H,连接PH,EH,FH,由题知，PH⊥AD,且PH=2,又因为AE1EB,棱柱ABE一DCF为直三棱柱，所以EF,EA,EB三条直线两两垂直，故AE⊥面EBCF,BE面AEFD.因为面PAD∥面EBCF,所以AE⊥面PAD,因为PHC面PAD,所设AELPH,又因为AEDAD=A,所以PH⊥面AEFD,所以PH∥BE,又因为PH=BE=2,所以四边形PHEB为行四边形，所以PB∥HE,因为HEG乎面6分EFD,PB面AEFD,所以PB面AEFD.…2)由题知，直三棱柱ABE-DCP的体积y二号XEB×EAXEF=4,四被锥P-ARCD的体积沙m2n2X专X5 XADXPHXAE-专所以有3半阳12分19.解：(1)由题意知，圆台O0上底面半径r=2,下底面半径R=4,高h=23,体积V-号x(2+4+2×4)×2556,53元.6分(2)将梯形OAA'O补成一直角三角形，设AA'与OO的延长线交于点B,易求得A'B=4,圆锥B0的侧面积为4X2Xπ=8元.…12分20.解：(1)该棱柱的侧面展开图的对角线长为√97……5分(2)根据题意，将正三棱柱ABC一A1B,C,展开，如图所示，则√61=(PC+CA)2M=√/(PC+3)+6,解得PC=2,由行线分BP C线段成比倒创海入NC=号21.解：(1，E,Q分别是矩形ABCD的对边AD,BC的中点，.ED一BQ,ED∥Q,:四边形卷六参考答案第3页（共4页）23·ZXQH·数学文科

上期参考答案第二十章综合测试题一、1.B2.B3.A4.C5.B6.B7.B8.A9.C.10.C二、11.512.均数13.2714.8.315.z)16.变大三、17.这组数据的均数为61，中位数为54，众数为53.18.小康将被录用：19.行)甲各项得分的众数为9，乙各项得分的中位数为8(2)乙将被录用.20.(1)该作品在民主测评中得到“不赞成”的票数为5040三10.2)升量(8+87+8894+91+90=90.(3)y40×3+10×(-1)=110,所以S=0.7x+0.3y=0.7×90+0.3×11096.所以该作品的“综合得分”S的值为9分21.1)=7,b=7,c=7.5(2)乙班选手进球数的方差为14型(3)乙班.理由略：22.)环年级(1)班5名学生的成绩按照由小到大的顺序排列，处于中间位置的一数是8，故中位数是8，即c=8.其中，8出现的次数最多，故b=8.八年级(2)班的均数a=59F7+10+9)=8.方差日[5-8)2+(9-8)2+(7-8)2+(10-8)2+(9-8)2]=3.2.

2x-4>02x-4<021.解：根据“两数相乘，同号得正，异号得负”可得01+x<0或②1+x>0解不等式组①可得不等式组无解，解不等式组②得-1

1l.冰壶(curling)作为2022年北京冬奥会上的体育项目，被大家誉为冰上的“国际象棋”，冰球比赛场地两端有两个直径为1.83米的圆形区域称作营垒，图案为由内到外的三个圆环（左图），圆环的外边缘可看作以O为圆心，半径比为1：2：3的三个同心圆，现在三个圆上分别取A,B,C三点（右图)，当△ABC面积最大时，则对于向量OA,OB,OC有A.3 0A+2OB+OC=0BOA+武？=？+CA?C.OA+OB+OC-0D.OA.OB=OB.OC12.已知直线y一Q与曲线y=二相交于A,B两点，与曲线y-相交于B,C两点，A,B,C的横坐标分别为x1,x2,x3,则A.x2-ae2B.x2=In xICr;=exD.x1+x3>2x2三、填空题：本题共4小题，每小题5分，共20分.13.某工厂的某种产品的误差~N(0.5,0),若误差在1g以上的产品占15.87%，从该厂任取100件该产品，则产品误差在-1g至1g之间的件数传为6小，水公6少（附：若随机变量X~N(u,o2),则P(u-o≤X≤u+o)≈0.6826，P(u-2g≤X≤+2g)≈0.9544，P(u-3a≤X≤u十3)≈0.9974)14.如图，在三棱锥A-BCD中，侧面ABD,ACD是全等的直角三角形，AD是公共的斜边，且BD=CD=1,另一个侧面ABC是正三角形，若三棱锥A-BCD外接球的表面积为3元，则∠BCD=15.已知双曲线C言-若-1。>0,6>0)的左，右焦点分别为F和F,0为坐标原点，P为双曲线渐近线上的一点，若∠FPF,=,且R户.O驴-0，则双曲线的离心率为16.在数列{an}中，已知a=1,a2=2,a+2=∫an十2，n=2k-1(3an,n=2k(k∈N*).(1)ao=16(2)设数列{a,)的前n项和为S,若存在正整数m,n满足S=mS-1,则m所有可能取值的和为四、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)已知数列{a,}的各项均为非零实数，其前n项和为S,a,-1,且对于任意的正整数n均有S+1+Sn=a2+1.(1)求所有满足条件数列(an}的前三项a1,a2,a3;（2)是否存在满足条件的无穷数列{a.,使得a=一2022？若存在，求出这样的无穷数列的一个通项公式；若不存在，说明理由数学试题第3页（共4页）

11.如图，圆锥的轴截面是边长为2的正三角形，圆锥的内接圆柱的底面半径为？，圆柱的体积为V(r),则02A.圆锥的表面积为3xB圆柱的体积最大值为4(1,0))【,0C.圆锥的外接球体积为32327D.V(0((v2·1)已③A别的C门阳人：函小图.12.若f')为函数f0x)的导函数，数列（红}满足x1=x.一f(x.),则称{x。}为“牛顿数列”.已知函数f(x)=x一1，数列{x》为“牛顿数列”，其中x1=3,则A.(n EN)2x.B.数列{x.}是单调递减数列,5C.x1xx.≤22-1)附/八城，8D.关于n的不等式x.-11<21的解有无限个三、填空题：本题共4小题，每小题5分，共20分.13.已知正数x,y满足4x+2y=xy,则x+2y的最小值为105，14.已知随机变量X,Y,其中XB(6,了)，Y~N4),E(X)=E2,P(IY1<2)=0,3,且则P(Y>6)=,,个两位冷用得人天，州川，创图文英，合行了能是15.山东省科技馆新馆目前成为济南科教新地标（如图1），其主体建筑采用与地形吻合的矩形设计，将数学符号“∞”完美嵌人其中，寓意无限未知、无限发展、无限可能和无限的科技创新.如图2，为了测量科技馆最高点A与其附近一建筑物楼顶B之间的距离，无人机在点C测得点A和点B的俯角分别为75°，30°，随后无人机沿水方向飞行600米到点D,此时测得点A和点B的俯角分别为45°和60°(A,B,C,D在同一铅垂面内)，则A,B两点之间的距离为米t人女(图1)(图2)16.已知函数f(x)=(xe+1)(lnx+x)-xe+1,g(x)=x+ke,当实数x。满足f(x。)≥0时，不等式g(x。+1nx。十2)≤0恒成立，则实数k的取值范围为四、解答题：本题共6小题，共70分解答应写出文字说明、证明过程或演算步骤，17.(10分)已知等差数列{a.}的前n项和为S,,且满足a1+a,十a,=15,S,=49.M11(1)求{a.)的通项公式；,的4(2)若数列{b.)满足b。=a.'·3”,求b.)的前n项和T,·日t1心高三数学试题第3页？（共4页）

力U的函数表达式为F=G计b(k≠0)，则k十h=0.7肝rb=0.5为F=0.2G+0,5,当G=7时，F=1.9,枚②错送：由图象知，拉力F是重力G的一次函数，故③错G=0时，F=0.5,故①正确.故选C.二、填空题（本大题共4小题，每小题5分，满分20分）1山.函数y=中x的取值范围是x-2【答案】x>2.【解析】√-2是二次根式，同时也是分母，x一2>0，x>212三个能够重合的正六边形的位置如图.已知点B的坐标是（一√3,3），则点A的坐标是第12题图【答案】(W3,-3).【解析】点A和点B关于原点对称，点B的坐标是（一√5,3），则.点A的坐标是(3，一3)，故答案为(W3,一3).13.一个装有进水管和出水管的容器，开始时，先打开进水管注水，3分钟时，再打开出水管排水，8分钟时，关！进水管，直至容器中的水全部排完.在整个过程中，容器中的水y(升)与时间x(分钟)之间的函数关系如图】示，则图中a的值为x/升30··201008 ax7分钟第13题图【省案唱【解析】设出水管每分钟排水x升.由题意进水管每分钟进水10升，则有80-5.x=20,∴x=12,8分钟后的水时间=侣号8叶号-碧0=9故客案为号14.如图，等边△ABO的边长为2，O为坐标原点，A在x轴上，B在第二象限.△ABO沿x轴正方向作无滑动翻滚，经第一次翻滚后得△A,B,O,探究完成下面问题：(1)翻滚3次后点B的对应点的坐标是(2)翻滚2023次后AB中点M的纵坐标为B,第14题图中考必刷卷·2023年安徽中考第一轮复卷数学第14页（共76页）扫描全能王创建

全国100所名枝最新高考模纵示花暮"When I have to have a rest before we can lo anything es in thetruck,please think aboutwhat you want to take with us"He walked into the house.acalled y m honey How the pcling going?Mom sd.nall going to fit,"I said,trying not to break into tears.“What's not going to fit?”"The kitchen table,the rocking chrndIfelten down my cheeks.knowtsuststand wf doemtteruthard!Is in that rocking chair andread stories to Azure and Seamus.I've sat at that kitchen table every night with my familysince we moved into this house...""Honey,the stuff isn't the memories.You don't need the roking chairs to remember的reading books to the children.You don't need your kitchen table to remember family dinners.You'll always have those memories,whether the stuff comes with you to your new house ornot.Okay?”My mom was right.We've been happy in our new home.We have half as much stuff aswe did before.We don't miss it,and we haven't lost the happy memories of our old home.Those came with us,and they were the only things we never had to box up or unpack.24.Why did the author decide to move home?A.To live together with her loved ones.B.To make her husband work conveniently.C.To take good care of her parents.盈D.To get her children better education.25.What can we learn about the author's husband?A.He wasn't willing to move home.B.He missed the author very much.C.He was going to call a bigger truck for the stuff.D.He thought it unnecessary to take the kitchen table.26.Why did the large four-bedroom house impress the author?A.It made her children proud.B.It represented a life of luxury.C.It offered chances to make friends.D.It held a lot of her fond memories.27.What does the underlined word "Those"in the last paragraph referto?A.Family members.B.Happy memories.C.Old items of furniture.D.Pleasures of moving.。英语卷（二）第5共12页)【3,N,英语·N

第33期参考答案第1一2版Unit 1Grammar情态动词should表建议1.should take 2.shouldn't go 3.shouldn't eat4.should stop反身代词I.1-4 DDCCII.1.herself 2.myself 3.itself4.yourselvesLanguage Points1.(1)hit a/the bridge (2)hit me on the head(3)gave him a hit2.(1)take risks (2)risked his lifeLexical ChunksA)1.have a cold 2.have a fever 3.have a cough4.have a sore back 5.have a sore throat6.have a stomachache 7.have a toothache8.have a headache 9.have a nosebleedB)1.有心脏问题2.呼吸困难3.发生事故；遭遇意外4.被球击中5.硒伤C)1.lie down 2.get an X-ray3.take one's temperature4.take breaks a break5.put some medicine on the cut6.rest for a few daysD)1.认真思考；权衡利弊2.下车3.冒险4.做决定5.放弃E)1.get into 2.run out (of)3.cut off4.get out of 5.be in control of6.to one's surprise 7.right awayUnit 2GrammarI.1-5 ACBBAII.1.to send 2.to make 3.change 4.(to)doLanguage Points1.(1)volunteers(2)volunteers (3)voluntary2.(1)preparing(2)notices (3)come (4)noticedLexical ChunksA)1.分发；散发2.分发3.参加…选拔；试用4.推迟5.照顾；非常喜欢6.赠送；捐赠7.(外貌或行为)像B)1.clean up 2.cheer up 3.call up 4.fix up

A.Parents often take their children to the hall.B.There are several standards a toy has to meet.Stonefish,who has helped create a dictionaryC.It looks quite different compared to other museumsof Munsee words,has his doubts about onlyD.So it was moved from its original home to New YorkE.Toys and their creators are an important part of history.counting on technology to save a language.He读F.And each member of the committee votes for his or hertop picksbelieves knowing cultural teachings is important,G.The others are beloved unbranded toys,such as the kite and thepaper airplane.especially for a language such as Munsee that isThere is a specific process for selecting the toy thatlargely based on oral(口头的)traditions.Yet空makes it into the National Toy Hall of Fame.Anyone canStonefish remains hopeful that the tools will worknominate (a toy through the US mail or the Internet.well with the help of cultural teachings.Some professionals review the nominations and determinewhich toys meet the requirements.A National SelectionCommittee then reviews the list of toys.3_F Finally,thetoys that get the most votes are included in the National ToyHall of Fame.A.Parents often take their children to the hall.BB.There are several standards a toy has to meet.1.What does the first paragraph mainly talk about?C.It looks quite different compared to other museums.A.Munsee is difficult to learn.D.So it was moved from its original home to New York.B.Munsee is at risk of disappearing阅E.Toys and their creators are an important part of history.C.The Delaware Nation has a long history.读F.And each member of the committee votes for his or her top picks.G.The others are beloved unbranded toys,such as the kite and theD.People of the Delaware Nation have a special填paper airplane.lifestyle.A 2.What can we learn about Bruce Stonefish?空A.He learnt Munsee from Dianne Snake.4 B First,the toy must be widely recognizedB.He is the only one who can speak Munsee.and remembered.And it must have enjoyedC.He is now teaching Munsee in a university.popularity for several generations.In addition,theD.He used to communicate with his parents intoy must have greatly changed the way people playMunsee.or the toy's design was new and creative.A 3.What is mentioned about the online tool developedA.Parents often take their children to the hall.B.There are several standards a toy has to meet.by Ndayiragije's team?C.It looks quite different compared to other museums.A.It is still being tested.B.It has proven to be very successfulD.So it was moved from its original home to New YorkE.Toys and their creators are an important part of history.C.It records the development of endangered读F.And each member of the committee votes for his or hertop pickslanguages.G.The others are beloved unbranded toys,such as the kite and theD.It allows users to learn several languages at thepaper airplane.same time.D 4.What is important to learn a language like MunseeCreated not only to recognize the importance ofaccording to Stonefish?those classic toys,the Hall of Fame also celebratesA.Finding a local to teach.the imagination of the toy makers.5 E They holdB.Having a good dictionary.the memories,symbolize the ideas,and reflect theC.Taking advantage of online resources.D.Understanding the culture behind the language.values of the generation who created them.A3版A.Parents often take their children to the hall.B.There are several standards a toy has to meet.C.It looks quite different compared to other museums.Babcock Ranch in southwest Florida is the阅D.So it was moved from its original home to New York.五E.Toys and their creators are an important part of history.first solar-powered town in the US.Its power读F.And each member of the committee votes for his or her top picks.comes from nearly700,000 solar panels(太阳能电G.The others are beloved unbranded toys,such as the kite and thepaper airplane.池板)that supply electricity1._to_more than2,000 homes.空The National Toy Hall of Fame is an American空The town is special in another way.It hadmuseum that was created to celebrate the nation'salmost no damage from hurricane Ian,which hitclassic toys and playthings.There are more than 80the area with winds over 160 kph.By comparison,toys already in the National Toy Hall of Fame.the storm 2.destroyed_(destroy)many parts ofAbout half are branded(有品牌的)toys,like LegoFort Myers,about 50 kilometers away.and the Rubik's Cube.1 GA.Parents often take their children to the hall.B.There are several standards a toy has to meet.C.It looks quite different compared to other museums.Babcock Ranch 3.was built (build)on a higher阅D.So it was moved from its original home to New YorkE.Toys and their creators are an important part of history.highland to be above the storm surge(风暴潮).The读F.And each member of the committee votes for his or her top picksbuildings could stand up to hurricane-force winds,G.The others are beloved unbranded toys,such as the kite and thepaper airplane.and the streets were designed 4.to control (control)huge amounts of water.空The museum was founded in 1998.By 2002,thisBecause of these measures,Shannon Treece andmuseum had grown a lot and needed more space.2 D There it became a part of the Strong Nationalher family are among the 4,600 residents 5.who/thatMuseum of Play,which houses over 70,000 toys,decided not to leave the town before the storm hit."Itdolls,and games.made me feel a little 6.scared_(scare),"she said ofbeing in a hurricane for the first time."I am glad ourhouse held up.”2

that city's main monument on my phone's wallpaper.After a year in 2022,I finally gave my best audition of that academy on the Internet and Igot in!I was happy but sometimes I wondered whether my parents were going to agree to it ornot.Fortunately,my parents agreed and I flew to that country to give the last phase of aninterview to join that academy.I passed and later was sent there for training.It was not surprising that I finally got the chance to live in the city of my dream and trainin the academy of my dream,as I believed everything was going to work out as long as I heldon to my dream.24.What can we infer about the 13-year-old Lucy?A.She had fun every day.B.Everyone supported her.C.She was unhappy with her life.D.A dream started in her heart.25.Who first led Lucy to the musical path?A.Her teacher.B.Her mother.C.Her friend.D.Her father.26.What played a key role in Lucy's success?A.Her effort and determination.B.Her family background.C.Her curiosity about new things.D.Her talent for performance.27.What did Lucy think of attending her ideal academy?A.It was a stage to make her famous.B.It was within her expectation after hard workC.It made her love her mother more.D.It was a new way to make friends.CIn the Chinese lunar calendar,san fu refers to the three 10-day periods that are said to bethe hottest days of the year,which are called toufu,zhong fu and mofu.Sanfu is usuallybetween mid-July and mid-August.When san fu is mentioned,people can't stop thinking of san futie,which is a bandage(made of traditional Chinese herbal medicine.Those who have experienced traditionalChinese medicine (TCM)believe that receiving sanfutie during the hottest summer days iseffective for coughs.The treatment is based on the TCM principle of yin and yang,whichbelieves the balance of both elements (in the body is important for good health.Sanfutie contains a paste of herbs that are "hot"in nature.Tou fu is the first stage of san fu.When the hot days come,people tend to lose theirappetites.As the weather in Changsha,the capital of Hunan province,is hot with heavyrainfall in summer,people there eat chicken especially a rooster during tou fu.They believethat the rooster is“yang”and can clear the damp(气).There is an old saying that goes“Arooster at the start of sanfu,a healthy body the whole year.Another favourite food duringthis stage is jiaozi,which is thought to refresh people's feelings toward food.In fact,jiaoziis an all-time classic with 2,000 years of history.The second stage of sanfu is called zhongfu,which traditionally is a time for eatingnoodles because it is believed to help people sweat and remove internal heat.When mofu or the third fu arrives,it is still very hot at noon and the sun is very strong.People feel uncomfortable,so they call this period "Autumn Tiger".During mofu,people,especially those living in North China,customarily eat Chinese egg pancakes.During sanfu time when yang energy is at its prime,it's also beneficial to have foodwhich is "cold"in nature,like watermelon and cucumber,according to Chinese dietarytherapy.【高一年级期末考试·英语第4页（共8页）】231388D

,0=001,(2分)设80%分位数为x,前3组的频率之和为0.65，前4组的频率之和为0.9，,X后[80,90），4444…(4分)且x=80+8906答×10=86，即这20名学生得分的80%分位数为86.…(6分】(Ⅱ)由已知可得：得分在[50,60)内的人数为0.01×10×20=2，得分在[60,70)内的人数为0.02×10×20=4.…(8分）记得分在[50,60)内的学生为a,b,得分在[60,70)内的学生为c,d,ef,则所有的样本点为：(a,b),(a,c),(a,d),(a,e),(a,f),(b,c),(b,d),(b,e）,(b,f),(c,d),(c,e),(c,f),(d,）,(d,f),(ef),共15个，…(9分)）其中恰有1人的得分在[60,70)内的样本点为：(a,c）,(a,d),(a,e),(a,f),(b,c）,(b,d),(b,e）,(bf),共8个，…(10分）故所求事件的概率P=8小小44…(12分）》20.命题意图本题考查事件的关系，相互独立事件的概率计算解析记K,K,,K,K四个开关闭合分别为事件A,B,C,D(I)四个开关均断开的概率为P=P()P(E)P(C)P(D)=(1-)×1-子)×(1-)×(1-）夜小小小4小小44…(4分)(Ⅱ)考虑“电路为通路”的对立事件“电路为断路”，分3种情况：①四个开关均断开.=43…(5分】②K闭合，其余开关均断开，P=子×(1-子)×(1-分)×(1-）=6：…(7分)③K闭合，其余开关均断开，八=号×(1-子)×(1-)×(1-）=方…(8分)》所以电路为通路的概率为P=1-(B+B+B)=1-(g+石+)了…(12分)】21,命题意图本题综合考查正、余弦定理，和基本不等式有关的三角形最值问题，解折(I)由正弦定理得snC=s如AcsB+ninA,①(2分):C=T-(A+B),.sinC=sin(A+B)=sin Acos B+cos Asin B,②…(4s分）由①2和Be(0,m),得5(5分)》1Λ三00明A,5444anA=5,又A∈(0，r),A=3,小…(6分)）(Ⅱ)在△ABC中，LBAC=号，a=5,由余弦定理a2=b2+c2-2bcco8∠BAC,得b2+c2=bc+3,(7分)》由基本不等式得2+c2=be+3≥2bc,.bc≤3（当且仅当b=c时取等号）.…(8分)在△ABC中，M=(i+A心)，…(9分)

(2)y=100(是+）≥100×2√g-100a(元.当子u=时，得u=2a,因为0<≤80，所以当0

nfr about biodicael production fom thehA.It needs enough water.B.It goes without any risks.C.It requires little attention.Wha is the text mainlyu?D.It needs to be improvedA.Some research on biodiesel.B.An experiment on biodiesel.C.The importance of biodiesel.第节共5小题：每小题25分，满分125分)D.One way to make biodiesel.阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。选项中有两项为多余进项Fanily mealsre imporant and omect family members.Thereorryougoing to school,work and more.sudishave shown family mealtime increases positivechoondethe frequeny of negative behavior37 Tndor ntreicdouged.Children who engage in family mealtimeare likely to havenrnhswho share frcquent family mealsremore likelytolargerffritbles and be less picky about food.38For example,we need to consider the budget,the time for mealprepb的of recommended foods or supplements((补充物品)at a typical grocery.32besmay have various cultural or dietary preferences.In view ofthis,we shoulaingplan offered nutritional vale for different caore andidofeaedifferent activity levelsand heath codoHealthy eating should be a family affair,and some recommended diets will helpyourhtby highlighting eating plans that are safe,flexibe and nutritious forveryonabeInhefoods in the diets cn be purchased fresh,caedA.They prefer junk food like hamburgers,fried chicken.B.A team of health experts think family meals are difficult.C.They can get people to relax and make their relationship closer.D.It also offers an opportunity to set healthy eating habits for kids.E.Thus,it is convenient and easy for families to have family meals.F.We also considered how adaptable this diet would be for a whole family.G.We should have a balanced diet and pay attention to what we have every day.第三部分语言运用（共两节，满分30分）第-节（共15小题；每小题1分，满分15分）阅读下面短文，从每题所给的A、B、C、D四个选项中选出可以填入空白处的最佳选项。One day I was approaching several massive creatures when I came to a sudden stop.Itwaebeyond me that these huge animals should be limited by only some ropes.It was 41that themimals could easily escape from these small ropes tied to their front legs.However,42 they didt I spotted a 43 close by and wondered why the elephants just44where they were anddo intention to break away."Well,"he replied,"as they're very 45 we tie them with the same46 rope and it'senough to 47themn for their age.As they grow up,they're 48to hold the belief that they英语试题第6页（共8页）

17.己知△ABC的内角A、B,C所对的边分别为a、b、c,且c0sB+C=1-cosA.2(I)求角A的值.(IⅡ)若△ABC的面积为3√3，且b+c=7(b>C),求a的值.18.己知函数f()=3sin(ox+p)w>0,lpK2的部分图象如图所示，其中A,352π3V323,-2B（1)求f(x)的解析式：(2)设函数g(x)=f(2x),X∈03求g(x)的值域19.如图，在四棱锥P-ABCD中，PC⊥面ABCD,AB/1CD,AB⊥AD,AB=2AD=2CD=2,PD=V5,E为PB的中点.EA-----------BC(1)证明：面EAC⊥面PBC:(2)求直线PD与面AEC所成角的正弦值.20.如图，四棱锥P-ABCD,面PAB⊥面ABCD,PA⊥AB,AB∥CD,∠DAB=90°，PA=AD,DC=2AB,E为PC中点.DE

念与性质10.解：(1)令t=x十1，则x=i一1，…1分2则f()=(t-1)2-4(t-1)-4=2-62+1,4分所以f(x)=x2-6x十1.…6分0),②由a蜘-1+日≥2-6=-4，10分当且仅当|x=1,即x=士1时，等号成立，11分象关于y轴对杯，则f(x)的图象关于直故的最小值为-4…13分所以f(x)在（一∞，一1]上单调递减.因11,解：(1)函数g(x)=a(x-1)2+1+b-a,>0,g()为开口向上的抛物线，且图象的对称轴为直线工=1，……2分义域为R,值域为{0,1)，故A,B错误∴g(x)在区间[2,3]上是增函数，f(x)=f(0)=1或f(f(x)=f1)85分解得a=1,b=0.为有理数，则f(x十T)=f(x)=1;（2)由0可得g田=2-2x+1,则f)与十22，6分=0.1R恒成立，即D正确.fg:)-2ox≥0在x∈2,8]正有解，等价于1o82x10gz一2>2 og在z[2,8]),放西数f(x)为奇函数，对于定义18分数(x)为诚函数据此判断，BCD项上有锅，即2Ka可十1在x[2,8上有解令z“z[2,8],c号2≤2-2+1在e[号，1]上有解.…10分+f(-x+2)=2,又f(x)+f(x÷=2对称，B正确.因为f(0)十f(2)记g0=-+1=-12,∴号，1，则0在[号，1]上为减函数g(0==(号)=意，2,得f(x十2)+f(x十4)=2，又2≤号则≤号，的取值范固为(-∞，名113分x)=f(x十4)，C正确.Ar2)=6,D错误12.解：(1)由题意得f(x)的定义域为（一1，+∞），…1分由f(x)>f2x-1),可得1og2(x+1)>1og2(2x),x+1>2x,f(x)关于点(1,1)对称，因为当0则x>-1,(2x>0,3分1,所以f号)=1，又f八0)=解得0

AB则△BCD是正三角形，∠BCD=60°，于是房形BCD面积S=60mx2_2红3603而△BCD的面积为BCCDsin血60°=5×2：=5，4所以阴影部分图形的面积2-5.3故答案为：y-3y+1、1317.若关于y的不等式组43L2的解集力V0,数a使关于的盼式方程化+32(y-a)<0的解为非负数，则符合条件的所有整数a的和为【答案】12【解析】【分析】先用a表示方程的解，根据解是非负数，且x-1≠0，结合不等式组的解集确定α的范围，求得整数解计算即可.【详解】：x+2+,0=3,x-11-x去分母，得x+2-a=3x-3,移项、合并同类项，得2x=5-a,系数化为1，得x=5-口，2数口使关于x的盼式方程+2+，。=3的解为非灸数，且x-1≠0，x-11-x:5=>0,58≠1，22∴.≤5，a≠3，y-3_y+12-1304-32-20,2y-a)<0②第9顷共27顶

(Text 9)W:Wake up,Eric.It's time to rise and stay awake.M:Oh,hi,Kate,I must have fallen asleep while I was reading.W:It looks more like a campground than a library.M:Well,the classroom is too noisy to study in and I guess this place is too quiet.What's thetime?W:A quarter to eleven.Have you had any luck finding a topic for your paper?M:No.Professor Grant told us to write about anything on Eastern culture.W:Well,why not write about Chinese culture?You've been there and you enjoyed your tripvery much.M:That's not a bad idea.I brought lots of books about Beijing back with me last summer.That would be great resource material.Now,if only I could remember where I put them.W:Well,remember we need some time to relax,too.By the way,do you know about the newrestaurants in town?M:Yes,I went to town for the first time last night and ate there with my mother.W:What do you think of it?I may go there this weekend.M:Well,the decoration was simple but the food was good.The bad part was that it took agesto wait for the food to arrive.However,I have to say that it certainly was worth waitingfor.听下面一段独白，回答第17至第20四个小题。现在，你有20秒钟的时间阅读这四个小题。(Text 10)W:Good morning,I'm Ann.Now let's go over to today's traffic and travel news.Nowthe sun is high in the sky,but the heavy rain in the morning caused problems on the M3 road.Four cars hit each other and there were long delays between London and Guildford.It doesnot look very good on the M4 road because a truck broke down near Swindon,causing a hugetraffic jam.Peter from Bristol said there is a long line now,so if you need to get to Swindon,you'd better go on the main road.Unusually,most trains are working in a normal way.Ifyou're going away,check before you go.If you're flying from Gatwick Airport,please phoneyour airline before you set off.The computer systems at the airport aren't working this morn-ing and many flights will be canceled today.Jackie and Bob phoned to say their flight to Indiawas delayed and they had to check into a hotel room near the airport for the night.But I'mpleased to see they boarded their plane and now are on their way.第二节到此结束。现在，你有两分钟的时间将试卷上的答案转涂到答题卡上。听力部分到此结束。【日高三英语·参考答案第4页（共9页）日】·有听·

2023-2024学年上学期高二课标（新教材)第2、4、6、7期参考答案及解析选择性必修一UNIT1参考答案及部分解析参考答案1-5 ACBAC6-10 CBBAC11-15 BBACB16-20 ACBCA21-25 DADAB26-30 BCDBC31-35 BCADA36-40 EADBC41-45 DCBBD46-50 ACBDA51-55 CABAC56.oldest57.which58.to study59.Eventually60.obtained61.mapping62.on upon63.was awarded64.important65.and写作第一节One possible version:Humans have achieved countless amazing things that make our life better.Some of themencourage me to stop doubting people's individual abilities to make a difference in the world.Forme,walking on the moon has been the most inspiring.Humans have always been fascinated by the stars,but it has taken determination,science andskillful engineering to finally allow people to actually leave the planet.One of the biggestmoments in space exploration history happened when Neil Armstrong walked on the moon.Itbecame the start of more advanced space programs.This reminds me never to be afraid to followour dreams第二节One possible version:I could have never prepared for what I found in the backyard:an underground treasure.However,it was locked.I figured the key should be somewhere in Dad's room,so I went back home andsoon found it.I opened the lock,and to my amazement,all our valuables were in there,amongsta couple of documents I couldn't quite understand.I then decided to call on my father's lawyer."Your father's case was sorted out a couple of months back.He was cleared of all charges putagainst him,"said the lawyer.The lawyer handed me a note.In the note,my father explained that he had thought moneywould help us and improve our lives,but it never provided a sense of purpose.So,he decided toleave the life of wealth in hopes of teaching us how to live without it.Looking back at what welearned in this difficult period,I am grateful for the lessons my sister and I learned.I am gratefulfor my father and what he taught us.部分解析阅读第一节A篇主题语境：人与自我一一生活本文是应用文。文章为适合青少年参加的四个活动。

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ENGLISH⊙》高二黄谈凉谷34WEEKLY四共语/团板wo:aot390Tme55 minutes度*FOCUSHow a chinese cale becamethe best place to eat in Canada语箱导读：温得华的一家中餐厅被评为2023年加拿大最佳用餐场所areof theirjoineymeats agoNad5omemust passs byin active woomix ofse Canadiansaurant is so pusy onburgersas wonk tovet the Cmorninga longline formsweekd forklifts(铲车).Many of the earlybethich sits above a DIYcanadian culture and hyin Canadian smallstore,has the honour off being the best place toimmigrant-run restaurantsCanada in 2023,according to theowns and large cities initially served familiardine inChinese dishesrestaurantreview site Yelp.Since Yelpdiner-style food.But over time,announced the diner's steaks and spring rollswere slowly added to menus by enterprisinghad drawn the highest customer reviews of anyowners to give something "special"to diners.Aeatery across Canada,some visitors have waitedreporter noted,"As time went on,these dishesWord bankInthinkable:turnp way paying cbutstomersor pcdhas become th心exact owiththeblessed,sexperimentingVe'reOther than&Have you noticed howlming.We like to think our mottooccasional new dish,Raymond says he has littleped these shelves are?'Our house is your house'-is what helpspeople feel so welcome,"said Richard Mah,whointerest in departing from the main dishes his扫描二维码可听family have perfected over the years."These arephrase that expresses the aims音频并下载课件recently gave up a corporate job to work here.His parents,Jimmy and Connie Mah,whofamily recipes.This is a menu my dad created.and beliefs of a person,aThe wontons are my mother's recipe.My rolegroup,an institution,etc.andinitially bought the 73-year-old restaurant in2008 as a way of relieving the boredom ofhere is just to better what they've achieved overis used as a rule of behaviour座右铭；格言；箴言the years.From:www.theguardian.come.g.The school's motto is:‘Duty,Honour,,Countryexotic adj.from or in anothercountry;seeming excitingand unusual because it isconnectedwith foreignountries来自异国的；奇异的；异国风味的g.She travels to all kinds ofotic locations all over theorldWannabee's unc er Stul登网彩CAFE画线句表明，随着时间的推移，这家温Sentences哥华餐厅里曾人4“女下司座嗣的“亦本根采输中心

A0.90.70.9B0.80.7A.0.19738B.0.00018C.0.01092D.0.09828【答案】A【解析】【分析】首先根据独立事件概率公式求能听到声音的概率，再利用对立事件概率公式，即可求解.【详解】设能听到声音为事件M,则P(M)=[1-P(AB)P(C)1-P(D)]=[1-P(AP(B)]P(C)[1-P(D)P(E)]=(1-0.1×0.2)×0.9×(1-0.3×0.3)=0.80262所以听不到声音的概率P(M）=1-0.80262=0.19738故选：A6.己知数列{a}满足an+1+a,=2n+3(n∈N),则a+a24=()A.2023B.2024C.2027D.4046【答案】C【解析】【分析】由a+1+an=2n+3可得an+2+an+1=2n+5,进而可得am+2-an=2,则有数列{an}的偶数项是以2为公差的等差数列，再根据等差数列的通项即可得解.【详解】由ant1+an=2n+3①，得a1+a2=5,am+2+an+1=2n+5②，由②-①得an+2-an=2,所以数列{an}的偶数项是以2为公差的等差数列，2024则a2024=42+2×a2+2022,2第3页/共22页

(2D回知椭圆C的方程为2十自w心…5分易得△FAB的面积是四边形ABMN面积的？，即SA=354由题意得l1,l2的斜率不为0，F1(-1,0),F2(1,0),设l2:x=my十1.…6分6my1十y2=3m2+4’由43=1,得(3m2+4)y2+6y-9=0,则…8分9(x=my+1,y1y2=3m2+4’所以S858=号FF:111-为=VO十为)P-4w为36m236=V(3m2+4)23m2+412Vm2+1=3W53m2+44…10分化简得45m-136m2-176=(45m2+44)(m2-4)=0,得m2=4,即m=士2.…11分故。的斜率为士2：……12分22.解：(1)由题意得QF的最小值为号，则多=1，得p=2.…2分所以D的方程为y2=4℃.……3分(2)因为A,C不重合，所以直线AB,BC,AC的斜率必然存在.…·4分设Aw),By).C.直线AB的斜率kB=。一出4yo-yi yo+y1=w=十2yo5分-344得y=612y+2%=-2%+12yo+2·……………………6分直线BC的斜率kx=一当4=kov=2十67分y3-y1y2+y1y2一344得=-126y2+12………………………………………………………………y%+68分由y=-y%+22十6，消去可得2=12，2y+12=_6y2+12…9分直线AC的斜率kc=。一些=4,…10分yo-ya yo+y24所以直线AC的方程为y=4(x-)+w=4+0必=十12=，4（红+3》.…yo+y24yo +y2yo+y2 yo+y2…11分故直线AC过定点（一3,0）.……12分【高二数学·参考答案第4页（共4页）】·24-145B·

则+x-+y+1+1-1+2+3222+3,a≤2W5+3.x-1t故实数a的取值范围是(-0,2√2+3]10分18。解：（1)由题意得A=2,了-，∴最小正周期T=π，则0=.222元-2T∴f(x)=2sin(2x+p).若选①，〔-君为商数则引=023sm+pj-0.即m(号+p小-0.0<<即写+<+=0.即33331若选@.当x=0时f)=52sn=5,即s如=50<<分=f=22r+写引若选③，x=云是函数)的一条对称轴，12x号+p-受+ka(xe2).即0-号+ka22x000-号fe=2n2x+6分a0=.2sm24+写}-5.即sm24+}-5A∈0，)24引后)24+号Ξ即4-君又C=3△M8C的面积Se=356csnA=35得b=4W5,在△4BC中，由余弦定理得a2=2+c2-2bcc0sA=48+9-2x4W5x3xY5=21,解得2a=2i.12分19.(1)证明：由题意，当n=1时，a2=2a1+1=2×0+1=1,

的了看，结果发现小女孩又笑了笑，作者自己也一起笑了，share that smile意为“一起笑”，符合语境。故选B项。39.B考查形容词词义辨析。句意：我们一起笑了起来，我知道我永远不会忘记她的勇气和内心的力量。根据句意可知，此处指永远不会忘记小女孩的勇气和内心的力量，inner符合语境。故选B项。【参考范文】Seven months into the school year,when the contestday finally arrived,the kids felt ready to take on theworld!They warmed up,listened to my talk,and madetheir way to the performance area.As my choir mountedthe risers,I looked at the three judges and rememberedhow improbable this scenario had seemed at the begin-ning of the school year."Smile!"I mouthed.Theylooked confident.I took a deep breath,and we began.They performed masterfully.We finished our songs,and I wanted to scream at the top of my lungs,"YOUDID IT!”After all the choirs had performed,we waited in ourassigned room for the results.While waiting for the jud-ges'scores,the kids gazed at the clock,went forsnacks,gazed at the clock,drew on the chalkboard,gazed at the clock....Two very long hours later the re-sults were posted.I stood frozen,staring at the list indisbelief.There was our name at the very top:a FirstPlace award with the highest marks of all.All aroundkids were squealing and embracing.Warm tears wet mycheeks.And I realized that I was surrounded by kidswho had a dream-kids who refused to give up-kidswho taught me to never doubt the possibility of success.

20.解：(1)在△ABD中，设∠BAD=0,则∠BCD=π-0，由余弦定理得BD2=AD十AB2-2AD·ABcos0,即BD=5-4c0s0,①…2分同理在△BCD中，BD2=BC+CD2-2BC·CDcos(π-O),即BD2=13+12c0S0,②……4分①②联立消去c0s0,得4BD=28,所以BD=√7.…5分BEBD_√7_2√212在△BDE中，由正弦定理，得sin/DBE$in/BDEn…7分√332所以DE=2②Isin∠DBE,BE=2Y2Isin∠BDE..8分33设∠BDE-e,则∠DBE-经-e,所以BE-DE=2[sm(g-。）1sma】10分因为0

【答案与解析】 英国的环保人士反对近几年来非常风靡的人工草皮，希望政 府能采取措施阻止人工草皮的发展。 32.B根据第2段第2、3句可知，过去，在英国人眼中，拥有护理 良好的草坪意味着富有。 33.A通读第3段可知，本段主要介绍人工草坪的使用急剧增加。 34.C根据画线词上文可知，研究发现，在人工草皮下活动的蚯蚓 的体重会减少14%，这对人工草皮的粉丝们来说可能不是问 题，因为虫洞在他们眼里是很烦人的。根据上下文的转折关系 可推知，这让绿色环保的人感到沮丧。 35.C根据最后一段第2句可知，英国政府称强行规定人们禁止 使用人工草皮是错误的。

听第9段材料，回答第14至16题。 14.What does the woman tell the man? A.She will order later. B.She first travels to China. C.She learns to cook Chinese food. 15.What special dish does the man suggest? A.Fried rice. B.Roast duck. C.Roast potatoes. 16.What service can the woman enjoy while waiting for her food? A.Free milk. B.The dancing performance. C.The piano performance.

pollution,although it does play a significant role.It is actually something many people have never heard about-government subsidies(补贴)，”says Cristina Mittermeier,co-founder of SeaLegacy.Mittermeier explains that in Spain,for example,one in three fish caught is paid by the government."Some govern ments seem more e concerned about keeping jobs alive in the fish ing industry in the short-term than the long-term health of our oceans,she says.The US has a range of fishing subsidies that critics say drive fishing to excessive(过度的)levels. These subsidies can lead to overfishing,which is when fish are removed from a body of water at a faster rate than they can reproduce,causing the fish population to continue decreasing. 'While pollution is a problem to be sure,the biggest issue 1S

试题答案 1~5 CABCA 6~10 AABCA 11~15 BCCCB 16~20 ACABA