去.保得所以69.AD对于B项，有可能a⊥(b一c);对于C项，向量的数量积不满足结合律.易知A项和D项正确。10.BCA选项，A>90°，ab,△ABC有两解，故d61正确；1②D选项，由正弦定理得sinB=bsin A、22,b

答案解析第3版本文的语篇类型是说明文，主题语境是人与自然之人与动植物。为了使城市对野生动物更加友好，建筑师Rene Hougaard和设计师AlexanderQual打造了一系列为这些生物提供躲藏和觅食空间的户外装置。1.D。细节理解题。根据第一段最后两句可知，一些建筑师用非本土的植被创造了整洁的草地空间，但这些自然元素实际上并没有增加生物多样性。2.B。推理判断题。根据第二段第二句可知，专家指出，野生动物的世界看起来是混乱的，但在混乱之中仍然存在着一定的秩序。随后，作者以蜜蜂的生活性对其物种发展的影响为例来说明野生动物世界中的秩序。3.A。词义猜测题。根据画线词上文可知，Decay Edge可以为动物们提供躲藏和觅食的空间，也可以让它们与土壤中的蚯蚓和其他生物互动。因此，这种设施能构建一个更为活跃的生态系统。4.D。段落大意题。最后一段中，作者讨论了现代人类对野生动物的态度，说明了文中的设施对人与动物关系的好处以及人类对待野生动物的正确态度。因此，本段主要关注人类与野生动物的关系。第4版本文的语篇类型是说明文，主题语境是人与自然之人与环境。面对无处不在的海洋塑料污染，尤其是大家每天都在使用的塑料吸管和塑料杯，艺术家Von Wong用塑料垃圾建造雕塑来唤起人们对塑料垃圾的关注。1.C。推理判断题。根据第一段最后一句可知，Von Wong用塑料垃圾建造了巨大的雕塑，使观看者重新审视他们与一次性塑料产品的关系。由此可推知，他的艺术作品台在引起公众对塑料垃圾的关注。2.A。细节理解题。根据第三段最后一句可知，塑料吸管不能被回收利用，需要几个世纪的时间才能降解掉，由此说明塑料吸管回收困难。3.B。推理判断题。根据第四段的内容可知，在2018年的一件作品中，VonWong想说明这一明确的统计数据：每60秒就有一卡车的塑料进入海洋。由此可知，他创作的“Truckload of Plastic”看起来就像从一辆卡车中被全部倒出，这样的场景会引起观看者的不安与恐慌。4.D。文章标题题。通读全文内容可知，文章主要讲述了艺术家Von Wong用

4妇+h的最大值是号B.2+2的最小值是4V万C.a+sinb<2D.b+Ina>111.(多选题)声音是由物体振动产生的声波，其中包含着正弦函数.纯音的数学模型是函数y=As@t,我们听到的声音是由纯音合成的，称之为复合音.若一个复合音的数学模型是函数f(x)=sinx+二sin2x,则下列结论正确的是()A.f(x)的图象关于直线x=π对称B.f(在44上是增函数C.f()的最大值为3n若f)()=名-l。=行2712.设函数∫(x)=1中X中x>0,若了)之饵成立，则满足条件的正整数k可能是()一A.2B.3C.4D.5三、填空题：本题共4小题，每小题5分，共20分.13.已知函数f(x)=x(a2+2)是偶函数，则实数a=一14.写出一个定义域为R值域为[0，]的函数15.已知a>0,b>0,直线y=x+a与曲线y=c1-2b+1相切，则2+的最小值为16.己知函数f(x)=21山x,直线1的方程为y=x+2,过函数f(x)上任意一点P作与1夹角为30的直线，交I于点A,则P4A的最小值为一·四、解答题：本题共6小题，第17题10分，第1B=22题各12分，共70分，解答应写出文字说明、证明过程或演算步骤。17.设函数f(x)=x2-(a+3)x+3a,aeR.(1)解关于x的不等式f(x)<0:(2)当xe[4,+时，不等式f(x)≥-9恒成立，求a的取值范围.

再从这6人中先后抽取2人的成绩作分析，心/频率分布直方图中的x=0.030下列结论正确的是(B.估计100名学生成绩的中位数是85C.估计100名学生成绩的80%分位数是95D.从6人中先后抽取2人作分析时，若先抽取的学生成绩位于[70,80)，则后抽取的学生成绩在[80,90)的概率是4510设数了)=lg时在a切上的最小值为m,函敬8闭=n受在0a上的最大值为M。,若M。-m。=2,则满足条件的实数a可以是(BD》A.2B.C.10√10D√1o31.已知抛物线C:x2=2y(p>0)的焦点F与圆M:x2+0+2)2=1上点的距离的最小值为2，过点F的动直线1与抛物线C交于A,B两点，以A,B为切点的抛物线的两条切线的交点为P,则下列结论正确的是（小BA.p=2年B.当与M相切时，1的斜率是士4C点P在定直线上+○，D.以AB为直径的圆与直线y=-1相切12.在中国共产党第二十次全国代表大会召开期间，某学校组织了“喜庆二十大，永远跟党走，奋进新征程”书画作品比赛如图①，本次比赛的冠军奖杯由一个铜球和一个托盘组成，若球的体积为4；如图②，托盘由边长为4的正三角形铜片沿各边中点的连线垂直向上折叠而成，则下列结论正确的是(OD)图①图②本)81A.直线AD与面BEF所成的角为6B.经过三个顶点A,B,C的球的截面圆的面积为工5C异面直线AD与CF所成的角的余弦值为8D球离球托底面DEF的最小距离为5+y6三、填空题：本题共4小题，每小题5分，共20分。国道理始高三二模数学试卷第3页（共6页）

no parking at all.At last,I'd like to recommendyou some street food.The first is...and参考答案1-5 ACBCB6-10 CBACC11-15ABABAset16-20 BAABC21-25 CDBBC26-30ABDAA36-40 CFBAD41-45 BDCACwe31-35 CACDBthe46-50 DABDC51-55ABDCA56-60 CBABD61.themselves62.at63.but64.who65.constantly66.battling67.is68.third69.disagreement70.healthyke短文改错Spring had come.Our teacher informs us thatinformedes,adwe were going to have a class outing.The newswas so much cheering that we jumped excitedly.We set off at 8 o'clock on a brighter Saturday.Webrightacewalked in lines with a student hold a flag in frontholdingof us.They were many colourful flowers and greenTherefftrees along the road.We admired the beauty ofspring,as well A breathing the fresh air in aasthecountryside.After an hour,we reachedourdestination,that had fantastic scenery,and decidedwhichto eaten our picnic lunch by the river.The foodeatwas surprisingly delicious after such a long walkTiring as we were,the trip was worth it.Tired书面表达One possible version:Dear Mr O'Leary,I have read your job advertisement in amagazine and I believe I am qualified for the job.First,1 will have a two-month summer holidayafter sitting the college entrance examinations,which means your working time is suitable for me.Secondly,I am experienced in dealing withchildren.I have an 11-year-old brother and we getalong very well.Thirdly,I like outdoor activitiesand often go hiking at the weekend.Finally,I hostan on-air English learning program in our school,so I canEnglish.communicate fluently with others inteam.I look forward to the opportunity to join your

二·透择题杰颗共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分苏州码子发源于苏州，作为种民同的药韩符号流行一时披广泛应用于条种商场会“苏州码子的写法依次为心、、义家、1二，三、发某铁路的里程碑所刻数代表距离始发车站的里程，如某处里程碑上刻者的○”代表距离始发车站的里程为0公里，刻号涂着的“○代表距离始发车站的里程为60公里，已知每隔3公里摆放一个里程碑，A点处里程碑上刻着“”，B点处里程碑上刻着“我”，则写在A.从始发车站到A点的所有里程碑个数为14B.从A点到B点的所有里程碑个数为16C.从A点到B点的所有里程碑上所刻数之和为987第六D.从A点到B点的所有里程碑上所刻数之知为984由数字0,1,2,3组成一个没有重复数字的四位数，下列结论正确的是A.可以组成18个不同的数B.可以组成8个奇数于2有3十21预是符合C.可以组成8个偶数3X3X2=18D.若数字1和2相邻，则可以组成8个不同的数226A在如图所际的数表中：第工行是从1开始的正整数，从第2行开始每个效是它肩上两个数之和，则方法有21820。208.36A.第5行第1个数为48284869>2022ly=f)B.第2023行第1个数为253×2012包第2023行的数从左到右构成公差为的等差数列D.第2023行第2023个数为1517×222312.已知定义在R上的函数f(x),g(x),其导函数分别为f(x),g(x),若f(x)=f(-x),g(-2)=0,f(x)+g'(x-2)=cosx,f(x-2)+g(x)=x-2,则A.g'(x)的图象关于直线x=-2对称B.g(x)的图象关于点(-2,0)对称成十十个装个人甚(1、南、C.g(x)是周期函数D.f(4)=0为三、填空题：本题共4小题，每小题5分，共20分把答案填在答题卡的相应位置，13.函数f(x)=4lnx3x的图象在x=1处的切线方程为▲3X114设等差数列a.松两斋项养分别为s1名产-青▲3b10可供4名女生，15.一个装有水的圆柱形水杯水放在桌面上，在杯内放入一个圆柱形铁块后，有一名水面刚好和铁块的上底面齐，如图所示.已知该水杯的底面圆半径为lcm/s6cm,铁块底面圆半径为3cm,放入铁块后的水面高度为6m,若从一0：时刻开始，将铁块以1©即的速度竖直向上匀速提起，在铁块没有完全离开水面的过程中，水面将非原(填“匀速”或“非匀速”)下降；在=3s时刻，水面下降的速度为cm/s.(本题第一空2分，第二空3分)【高二数学第2页共4页】·23-376B·376B.

trousers"over skinny trousers any day.Parents have noticed this"retro and reimagined"phenomenon,too.Four infiveparents say they often see their kids wearing a set of clothes similar to one theywould have worn when they were in school.This back-to-school season,retro styles.DIY self-expression,andpersonalization are becoming key trends,and 99%of parents say it's at leastsomewhat important to consider their kids'opinions on purchasing decisions when itcomes to back to school shopping.More than half (51)also think their child'sgeneration actually has a better fashion sense than their own.Yet,the survey,conducted by OnePoll on behalf of Zulily,found that it's notjust retro styles that are trending this back-to-school season.A second phenomenonshowed by the survey shows that kids see style as a way to express their confidence.Ninety percent think being able to express their personal style helps them feel moreproductive at school,and nearly half of kids (48%)think a cool or fashionable suitis vital to their success at school.28.What can we learn from Paragraph 2?A.Kids can make their own closets.B.Wearing“mom trousers'”is a retro fashion.C.Kids show no interest in styles in the past.D.Kids can draw inspiration from school uniforms.29.What does the underlined word "retro"refer to?A.Old.B.Simple.C.Unique.D.Popular.30.What's most parents'opinion on their kids'daily clothes?A.It is important for kids to DIY their daily clothes.B.Kids tend to wear their parents'old clothes to school.英语试题（七）第8页（共16页）

标just a child,meaning he controls63 bat with his mouth and sets up serves with his foot.He needs to strengthen his legs 64 (constant)because he relies on his legs morethan any other player.The same goes for his neck and teeth.The paddle should not moveat all between his 65(tooth)because if it does,he loses everything.It was tough for him 66 (play)table tennis after the accident.He tried to tuckthe bat under 67 his arm used to be,but in vain.Then adopting the mouth technique,he had to practice hard on a daily basis.At the beginning,people were amazed andsurprised seeing him playing.Later,it was his willing,perseverance and(determine)that won people's encouragement and support.68=He 69(win)silver medals at the 2011 and 2013 African Championships.】一The star made his Paralympics debut in Rio at the age of 43 and,now 48,he continuesto compete with the best athletes of 70 (he)class.第四部分写作（共两节，满分35分）第一节短文改错（共10小题；每小题1分，满分10分)假定英语课上老师要求同桌之间交换修改作文，请你修改你同桌写的以下作文。文中共有10处语言错误，每句中最多有两处。每处错误仅涉及一个单词的增加、删除或修改。增加：在缺词处加一个漏字符号（∧），并在其下面写出该加的词。删除：把多余的词用斜线(\)划掉。修改：在错的词下划一横线，并在该词下面写出修改后的词。注意：1.每处错误及其修改均仅限一词；2.只允许修改10处，多者（从第11处起）不计分。Thursday,June 21stI came to Russia on vacation this summer with my family.Having stayed in Moscowfor three days,we arrive in St.Petersburg this morning by train.Summer in St.Petersburg is a wonderful time of daylight,with about 23 hours theday.Today is the White Nights Festival where people stay up late to enjoy the summerwith different kinds of activity,such as concerts,art festivals and many other games.Wejoined in them this year and had an enjoyable time.And I also enjoyed take a walk alongthe river.What was the more impressive is that I visited some museums where I saw manyI feel luckily because I can also watch soccer games here.There will have a soccerbeautiful paintings.game in St.Petersburg tomorrow.Eager and excited,I will go to watch with my parents..mI can't wait to watch the game!由于疫情原因，开学后只能在国内上网课。明天是开学的假如你是用厅交提待肉茶宽技原因、开学后只能在同内主侧界明第二节书面表达（满分25分）面不码第一天，请你准备一篇演讲稿。060116w1L90h初自我介绍；dois o.1.2.表达期待,22oJ2.2nM时/图注意：1.词数80左右；3279了1n,1s与1/0122.可适当增加情节。NT精准考点检测卷·英语（三）第8页共8页

又1P2=V2+1Vx-x)2=Vk2+1V(x+x)2-4xx2,4k242-31=8+,8分所以PQP=e+)-G+x广-4=+2+-42+」(2k2+1)2(RNF--2K+1-ww=0+.9分2k2IPRP+IORP-IPQP-21RNP-IPQP-242水+2k2+20%+k》-42+132k2+1'(2k2+1)22器岛4k2+102=2x2+22-4221=0+4+22-42k2+12k2+12k2+1=2x,2+2,2-4,+1+4k+4,-5,…10分2k2+15所以4=0,解符-子此时1R+1QF-PO=2.R0=名…1分4x0-5=0,y0=0,②当e的斜*不在时，P阳的方程为：=，时方Q1分：PRP+IORP-IPOP=2RP.RO-_8综上，可知存在定点R,0),即O=OF.…12分解法五：（1)同解法三.…4分(2)因为点F是以AB为直径的圆上AB的中点，所以点F在x轴上，不妨设点FL,O).…5分假设存在满足条件的点R(x,y)·①当PQ的斜率存在时，设PQ的方程为y=k(x-1),P(x,y),Q(x2,y2),y=k(x-1),由x22+y2=1,消去y,得x2+2k2(x-1)2=2,高三数学试题参考答案第15页（共15页)

17.(本题8分)如图，在菱形ABCD中，对角线AC和BD相交于点O.(1)实践与操作：过点D作DE∥AC交BC的延长线于点E.(要求：尺规作图，保留作图痕迹，不写作法，标明字母)(2)猜想与证明：试猜想线段DC与BE之间的数量关系，并证明你的猜想，A18.(本题7分)在今年植树节期间，运城市某学校计划在校园每天种植相同数量的树木，该活动开始后，实际每天比原计划多植树25棵，实际植树200棵所需要的时间与原计划150棵所需的时间相同，求实际每天植树多少棵.19.(本题8分)为落实“双减提质”，进一步深化“数学提升工程”，提升学生数学核心素养，某学校拟开展“双减”背景下的初中数学活动型作业成果展示现场会，为了解学生最喜爱的项目，现随机抽取若干名学生进行调查，并将调查结果绘制成如下两幅不完整的统计图：（注：记A为测量，B为七巧板，C为调查活动，D为无字证明，E为数学园地设计)↑人数5045B20%30…20201030%0A B C D E项目根据以上信息，解答下列问题：(1)参与此次抽样调查的学生人数是,在扇形统计图中，扇形B的圆心角度数为(2)把条形统计图补充完整（要求写出计算过程，并在条形统计图上方注明人数）(3)若参加成果展示活动的学生共有1600人，请估计其中最喜爱“℃.调查活动”项目的学生人数【数学第4页（共6页）】

way possible,with thousands of volunteers from all walks of life fighting the fires withprofessionals.Under a hot sun,some residents cut down trees to make fire barriers ()Others rodemotorcycles on newly-formed paths to take firefighters and supplies up a mountain,while somevolunteers carried food and drinks on their backs on foot.Women and children helped organizesupplies and clear the ground,and performed other important tasks.On Thursday night,as wildfiresmoved towards a man-made barrier on Jinyun Mountain in Beibei District,a total of more than 1,000 firefighters and volunteers stood alongside the barrier with fire extinguishers ()Seenfrom overhead,their lights formed a silver wall against the increasing fire line.The residents'stories have touched many people."Chongqing people are really amazing,"said Du Hailang,head of the Beijing Emergency Rescue Association.Du and 10 other members ofthe association joined the fire rescue team in Chongqing."The man-made wall was unbelievable,but shocking.It really showed Chinese people's determination to defend their homeland,Dusaid.Zou Yu,from the Chongqing Emergency Management Bureau,said at a news conference thatby Friday morning,the wildfires in the city had been put out and efforts were being made toprevent new ones from breaking out.He said Chongqing had experienced several forest wildfires insummer due to heat wave and drought since 1961.The city has experienced record-high localtemperatures,with those in Beibei District reaching 45C.21.What does paragraph 2 mainly focus on?A.The ways to fight the wildfire.B.The quick spread of the wildfireC.The determination of the firefighters.D.The fighting efforts of Chongqing people.22.What caused the fire?A.Someone's smokingB.The hot and dry weather.C.No fire prevention workD.The shortage of fire barriers.23.What type of writing is the text?A.A research paper.B.A book reviewC.A news report.D.A travel diary.小When Thomas Panek lost his eyesight more than 25 years ago,he doubted whether he wouldever follow his lifelong dream again."I was too scared to run,he told CBS this morning.Indeed,although Panek had been running since high school,the idea of running blind seemed tooscared.But he did manage to keep his dream alivewith help from human guides who assisted himon each run.Even so,the real joy of the run-the excitement of independence that comes frompassing a course on your own terms-doesn't exist."When you're tied to another person,it's nolonger your own race,the 48-year-old told CBS."The independence isn't quite there."But Panek found a friend-indeed,man's best friend-who would help him regain that senseof purpose.He started running with a guide dog named Gus.Not only did Panek rediscover his lovefor running,but also found his best dog friend.Gus remained a great helper at Panek's side formany races.And,last Sunday,the old dog ran across the finish line with Panek at the New YorkCity Half Marathon.At that moment.they were both recorded in the history books.Panek,who第3页

分数学闭报2022-2023学年四川专版（人教版）九年级第27~30期MATHEMATICS WEEKLY答案专期囚为CD∥AB,所以∠DCA=∠BAC因为∠DHC=∠B=90°，所以△DCH∽△CAB.所以光=治，即羊名，整理，得y=因为AB0,故①正确；因为二次函数的对称轴是直线x=1,所以x=会=1，即2a+6=0,故②错误：从图象可知当x=-2时，y<0,即y=4a-2b+c<0.故③错误；因为二次函数的图象和x轴的一个交点坐标是(-1,0),对称轴是直线x=1,所以另一个交点的坐标是(3.0).则抛物线的解析式是y=a2+br+c=a(x-3)(x+1)=ax2-2x-3a,即b=-2a,c=-34,所以a:b:c=a:(-2a):(-3a)=-1:2:3.即④止确做下确的个数是27.延长BA交y轴于点D,连接OB.由反比例函数的比例系数k的儿何意义，得w=号×7=SAm=号×3=号.所以Sam=Samm-San=子-号=2所以5m=2Sm=4.故选C8.H题意，得y的函数图象如图所示.观察函数图象，知点A为函数y的图象的最高点，所以的最大值为4.故选A【第29期】“函数”综合验收题-、1.D2.C3.D4.D5.A6.B7.C8.A9.D10.D提示：1.由移的规律，知新抛物线的解析式为y=(x+第8题图2)2+2-4=x2+4x+2.9.过点B作BDLOA于点D,过点C作CE⊥OA于点E2.H于·次函数y=-x+2中的k=-1<0.囚为∠B0A=45°，所以B)=OD.所以y随x的增大而减小，即选项A正确：直线y=-x+2中的k=-1,直线y=x-1中的改8a,a).则a=2k=1,所以这两直线不行，即选项B正确；解得a=3或-3（舍去）.一次函数y=-x+2图象经过第一、二、四象限，所以BD=0D=3,即B(3,3)即选项C错误；因为BC:=2AC,所以AB=3MCH线y=-x向上移2个单位长度得到y=-x+因为BD⊥OA,CE⊥OA,所以BD∥GE.2,即选项D止确所以△MD一△MCE,甲0=长-3故选C3.H次承数的象，知a<0.b>0,且1x=1时，所以己=3，解得Ck=1y=a+B<0.所以y=a+也的图象位于第二因为图象经过点C,所以1=9四象限；解得x=9,即C(9,1).闪为a<0.x=云>0，所以二次函数的图象设直线BC的解析式为y=x+b开口向下，对称轴在y轴的右侧，故选D.将点B,C的坐标代入后，解得k=-,6=44.由题意，知D咀垂直分AC,所以CD=D=y,所以y=-了x+4CH=AC=2.当.x=2022时，y=-670

三、填空题：本题共4小题，每小题5分，共20分20.(12分)13.已知角a满足3osa=8sina,则sn(受-2a)三已知正方形ABCD的边长为4，E、F分别为ADBC的中点，以EF为棱将正方形AB.14.(1+之)(2x-)°的展开式中含2项的系数为CD折成如图所示的60的二面角，点M在线段AB上.D15.已知抛物线C:y2=2px(p>0)经过x轴上方一点M(1,b),F为C的焦点且IMF1=2,直线1：y=k(x-2)与C交于A,B两点（其中点A在x轴上方），若1AF1=)1FB引，则△ABM的面积为延意16若西数)-以-。”+2在：与和与两处取到极值，日2≥2，则实数。的取M值范围是(1)若M为AB的中点，且直线MF与由A,D,E三点所确定面的交点为O,试确定四、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。点O的位置，并证明直线OD∥面EMC;17.（10分)(2)是否存在点M,使直线DE与面EMC所成的角为60°？若存在，求此时二面角已知等差数列{an}的前n项和为Sn,且,n∈N°.数列1bn}中，b1=2,bm+n=M-EC-F的正弦值；若不存在，说明理由.bmb.0共，伦2浸小海，补？共醋本球式，从①a.+1>a.,a4·a5=63,S8=64,②S6=4S3,a2n=2a.+1,③S10=100,a,=13,这21.(12分)三个条件中任选一个补充在上面的问题中，并解答下列问题(1)求数列{a.},{bn}的通项公式；已知频圆c话+卡1(a>b>0),四点6(a,9,6(0,2,5(1,5.5,4.rbn,n为奇数，9)中怡有三点在精圆C上(2)设cn=,n为偶数，求数列c的前2n+1项的和21LanQn+2(1)求椭圆C的方程；(2)若A,B分别为C的左、右顶点，P为C上任一点（不与A、B重合），直线1过点B18.(12分)且垂直于x轴，延长AP交I于点N,以BN为直径的圆交BP于点M,设O为坐标原点，求在△ABC中，设角A,B,C的对边分别为a,b,c,且b=2 acosAcosC+2ccos2A.证：0、M、N三点共线.(1)求角A;22.(12分)o)者△aC的百职号求：9时的最小酒已知函数f(x)=ax-sinx,x∈[0，+o),(aeR):每体量的面9△(1)若f(x)≥0，求a的取值范围；19.(12分)甲、乙两人进行对抗赛，每场比赛均能分出胜负.已知本次比赛的主办方提供8000元(2)证明：当x≥0时，2xe+sin2x+cos2x字4sinx+1.天而克克学量乙奖金，并规定：①若其中一人赢的场数先达到4场，则比赛终止，同时这个人获得全部奖的质科里负的出用年大的上更竿是厚起，反零具了爱有的节园金；②若比赛意外终止时无人先赢4场，则按照比赛继续进行各自赢得全部奖金的概率之性最上京的是小的)卧发个县，费地讯雪工北可漫收部比给甲、乙分配奖金.已知每场比赛甲赢的概率为p(0

根据题意，得AE=EF,∠A=∠BFE-90°，∠D-90°.ED∴.∠DF∠EFM-90°.在Rt△EFM和Rt△EDM中，,'FM=DM,EM=EM,∴.Rt△EFM≌Rt△EDM.(第22题答图3)∴EF=ED,…11分AE=ED.点E是AD的中点AD=6,AE-3.综上所述，4E的长是2或3，…12分>23.(本题13分)解：(1)抛物线y=r2+bx+4过点4A(-2,0)和B(4,0),「4a-2b+4=0,…】分16a+4b+4=0数学（二）参考答案第5页（共6页）1解，得a=--2…3分b=1∴抛物线的函数表达式是y=-+x+4.…4分22)当0时，y=+x+44.C(0,4…5分A-2,0),B(4,0),∴.OB=OC=4,AB=5.…6分∠B0C-90，·∠ABC-}580°-∠B0C=45°.……7.△BCD≌△BCA,∴.∠DBC=∠ABC=45°，BD=BA=5.∴.∠ABD=∠DBC+∠ABC=90°.…8分∴BDLx轴于点B.点D的坐标是(4,5)·……9分(3)点E的坐标是(1+5，-3)，(1-5，-3)，(1+√3,3)和(1-√5,3).…13分评分说明：解答题的其它解法参照上述标准评分.

23.(本题满分11分)解①当0=2时，=+2x-4110...2分(Ⅱ)已知a>1,则1,。1,1f)=l+aa1-2+112+12+1+10f(1)=loga1+a.1+-+i=a+20,由零点存在定理知，存在∈（京），使得()-0…………4分设0<为1,0<4<,可得1og.点<0，a）<06+1X+1)0”x2(x+1)(x2+1)于是f(x)-f(,2)<0,由单调性定义可知f(x)在(0，+∞)上单调递增因此函数(x)的零点个数为1个.6分(I)由()知∈(，)，从而∈()，又f田)在0，+o)上单调递增于是哈-合后1111。+12,8分a又由f(xo)=0,得loga x0++0,即得loga0=-0(6+0)16+1所-+a+a+√x+12(+D由=-+分分得6加，111111由6<1，得<，从而6+12%+0%+12+D2+D2所以)0+分因此G)……...11分第2页共5页

8:16ll令61数学511A答案(1).pdfES=E0-S0'=号EG-1=?EG-号L=反x-2,所以IS=EP-ES-√FK2-ES=√一4x+8,又-4x十8>0，所以12则后+2k<2x十吾<+2x∈刀，得x

Ⅷ。阅读理解（共20小题；每小题2分，满分40分）阅读下列短文，从每小题所给的A、B、C、D四个选项中选出C.Where Peter is studyingD.Why Peteris late for schoo.A.Dick's trousers are一个最佳选项。B.One of Dick's T-shAAnnie has got some messages on her mobile phone.Mike is at his grandparents'home.It's in a small village and far fromthe cityC.Dick often plays soD.Dick buys the sweaJennyAe I'm going to have a birthday party at homecould we eat in the restaurant today?"Mike asks.Tto eat fish."Grandpa says no.He takes Mike to the north of the villageDear Zhao Min.next Saturday.Can you come?Thank you for yourBuy some sandwiches and milk on your way home.Andand gets a fish in the river.Then he brings it to Grandma."We can haveJackisha homeGrandpa sayNow let me tell you somesome fruit.Nothing for dinner today!"Grandpa,I want to play computer games,"Mike says.Grandpa saysI go to school frommoming and two in theSteveH,Annie!I have fixed your bicye You an comeadno.He takes Mike to the village park.Some boys are plaving baskethall"oandayith themGrandpain the moming.We learit now.AliceWhereare you,Annie?ne of y students is looking forGrandpa,canonhar condio(开空调2I'maiand P.E.My favorite sucold,"Mike asks.Grandpa says no.He takes Mike to the vegetableclassmates.There are alplay baseball,basketbayou in your school office.I teld him to come back later.We can also learn to plA56.Who will have a birthday party soon?deehind th houseWork with me hereand yo will feel hotGrandpa says.Now I am in the art clulA.Jenny..Jack"Howis your weekend,Mike?"Mom calls and asks.I like my new scheC.Steve.A57.D.Alice.A63."I have a great time here,"says Mike.What do we know about Steve?Grandpa gets a fishA.He can fix bikes.A.in the riverB.in the kitchen70.What is Cindy's fC.He loves sandwichesB.He is good at cooking.D.He is looking for Alice64.C.in the restaurantD.in the supermarketA.EnglishWhat does Annie do?Grandpa takes Mike to the park so that he canC.Music.A,A student.A.play computer games71What kind of speC.A doctor.B.Ateacher.B.play with some boysA.BaseballD.A reporter.C.VolleyballBC.give a call to his momD.have a talk with the boys7Little Peter is a boy ofnine.He is in Grade Three now.He lives nearWhy is Cindy in65.Grandpa asks Mike to work in the vegetable garden becaA.Because shethe school but he's often late for class.He likes watching TV in theA.Mike feels coldB.Because sheevening and goes to bed late,so he can't get up on time in the morning.C.Because sheThis term Mrs.Black,Peter's aunt,works in Peter's school.SheB.he needs Mike's helpD.Because sheteaches math in Peter's grade.She's strict,and she often tells the boy toC.Mike has to exercise to keep healthyfollow the school rules and come to school on time.Yesterday morning,D.he doesn't want Mike to stay at home阅读下面短文Peter got up late.When he hurried to school,it was a quarter past eight.D66.Which is the best title of the text?A.Mike's grandpaB.Mike's weekendam a 14-yHis aunt was waiting for him at the school gate.C.Let's have funD.Life in the villageProvince.Like ma"You're fifteen minutes late for the first class,Peter."Mrs.Blacklive with my grandsaid angrily,"why are you often late for class?"Hello!My name is Dick.This is my wardrobe.Thereare manyThey tell me to lis"Every time,when I get to the street corner,I always see a guidepostclothes in it.I like sports very much.So I have many clothes for sports.month to ask abou(路标).It says,.SCHOOL一GO SLOW!”C59.How old is Peter?Look!These are black shorts.I wear them when I play basketball.TheseJune 17th isA.Eleventrousers are nice.They are only fourteen yuan.I have many T-shirts,too.But my parents caB.Ten.They are in different colors.One is yellow.Two of them are blue and theold and they don'C.Nine.D.Eight.others are white.Whose green sweater is this?It's too big for me!I can'tfor me.There are4.Mrs.Black is a(n)wear it.It's a surprise for my father!Oh!Today is Father's Day I buy itI reafly missA.English teacherB.math teacherC.history teacherfor my father.73How old isA61 PeterD.music teacher7.What does the underlined word"wardrobe"mean in Chinese?minutes late for school.A.抽屉B.衣柜74What doesA.15B.20C.桌子D.书房CakeC.30D.40What do th62.What does the story mainly tell us?68.How many colors of T-shirts does Dick have?A.What Peter's favorite subject is.A.Only oneB.Two.me eagC.Three.D.Four.B.What subject Mrs.Black teachesWhich of the following is TRUE?2023年安徽中考第一轮复试卷·英语试题（一）第3页共4页

大一轮复学案数学能力强化练17.已知函数f(x)=xm-x|(x∈R),且f(4)=0.(1)求实数m的值；13.(2023辽宁葫芦岛模拟)函数f(x)=(2)作出函数f(x)的图象；的大致图象为(3)若方程f(x)=a只有一个实数根，求a的取值范围。14.多选题(2022山东青岛一模)已知函数f(x)是定义在R上的奇函数，当x<0时，f(x)=e(x+1),则下列命题正确的是A.当x>0时，f(x)=-e(x-1)B.方程f代x)=0有3个解Cf(x)<0的解集为(-0，-1)U(0,1)》D.Hx1,x2∈R,都有f(x1)-f(x2)1<2(In x,x>0,15.已知函数f(x)=若3x0∈（-0,0)，使g(x),x<0,得f代x)+f(-x)=0成立，请写出一个符合条件的函数g(x)的表达式：16.（2023福建三明模拟)已知函数f（x)=(sin,0≤x≤1若实数a,b,c互不相等，且f(a)(log2 022x,x>1,=f(b)=f(c),求a+b+c的取值范围，素养综合练18.若面直角坐标系内的A,B两点满足：①点A,B都在f(x)的图象上；②点A,B关于原点对称，则称点(A,B)与点(B,A)是函数f(x)的一个“和谐点对”.x2+2x(x<0),已知函数f(x)=(x≥0)，2则f(x)的“和谐点对”有()A.1个B.2个C.3个D.4个·286·

()A.若PO=|PF,则双曲线的离心率e≥2B.若△POE是面积为√5的正三角形，则b2=2√5C.若4为双曲线的右顶点，PF⊥x轴，则FA=FPD.若射线FP与双曲线的一条渐近线交于点Q,则2F-2F>2a第II卷（非选择题）三、填空题（本大题共4小题，每题5分，共20分）13.己知展开式(2x-1)°=a。+ax+a,x2+…+a,x(n∈N)中，所有项的二项式系数之和为64，则a1+a2+…+a。=·(用数字作答)14.已知a,万为单位向量，且云在6方向上的投影为-分，则+2讽-15.已知抛物线y=4x的焦点为F,点P,0在抛物线上，且满足∠PFQ-行，设弦PQ的中点M到y轴的距离为d,则P巴的最小值为d+116.若函数g(x)=2x2-x-(x-)在区间[0,2]上是严格减函数，则实数1的取值范围是四、解答题（本题共6个小题，共70分）17.己知数列{an}的前n项和为Sn,满足nan1+Sn1=0,a,=1.(I)求数列{an}的通项公式：(2)设bn=S。·Sn1,数列{bn}的前n项和为Tn,证明：Tn<1.18.如图，已知面四边形ABCD存在外接圆，且AB=5,BC=2,cos∠ADC=54(I)求△ABC的面积：(2)求△ADC的周长的最大值.I9.在四棱锥P-ABCD中，侧面PCD⊥底面ABCD,PD⊥CD,底面ABCD是直角梯形，AB/DC,∠ADC=90°，AB=AD=PD=1,CD=2.(1)求证：BC∠面PBD:试卷第3页，共5页

2023一2024学年宁德一中高三年级第一次考试数学试题参考答案及评分标准一、选择题：本大题共8小题，每小题5分，共40分.1.C2.C3.B4.C5.C6.A7.B8.A二、多项选择题：本大题共4小题，每小题5分，共20分.9.BD10.BCD11.BD12.ABD三、填空题：本大题共4小题，每小题5分，共20分.13.1014.[-1,2]516.8四、解答题7.Da2时，A=x1二3<0=x20，d+2>a21447as2A={x|20.又当xe2时，2+时()2>0恒成立，所(（2+22+,x[2时恒成立，………82-1令1=2-1，则-m<+3北+2）-+51+6=1+5+5,13]时恒成立，t而1++522,5+5=26+5，当且仅当1=6，即1=6时，等号成立，….….10所以m>-2√6-5，即m的取值范围是(-2V6-5,+∞)）.……12

全国教辅类一级报纸GLSH岁并LEARNINGR新课程高二课标(选择性必修3)第36期总19705期CE19832023年3月7日星期管单位山西省教育厅主办单位山西教育教辅传媒集团编辑出版学英语报社社长吕夺明总编李若编审Nancy E.Riley国内统一刊号CN14-0702(F)网址http/www.xyybs..com(温馨提示：登录学英语报社官网http:lwww.xyybs.com下载本期配套教学PPT)TEST YOURSELF本期资源码：td5deUnits4-5,(选择性必修)Book3众号。复上ClassNanMarks试题命制：英培》报社试题测评组第一部分听力（共两节，满分30分）节（共5小题；每小题1.5分，满分7.5分）Who is the woman?例：How much is the shirt??A.A tour guide听第9段材料，回答第14至17题。A.￡19.15.B.A student.B.￡9.18C.￡9.15C.A teacher.14.What does the woman think of her current life?案是C。听第7段材料，回答第8至10题。A.It is relaxing.B.It is boring.8.What happened to the woman?C.It is busy.5.Which place does the man think highly of?What does the woman want to see?A.She had no driving license.B She went th.Key WestB.Lake Wales.

20.(12分)已知Sn为数列{a,}的前n项和，a=l,Sn1+Sn=(n+)2.(1)证明：an1+an=2n+1.(2)求{a}的通项公式.(3)若之票，求数列6)的前n项和21.（12分)已知抛物线C:y2=2px经过点(2，-2W6),直线l:y=a+m(km≠0)与C交于A,B两点（异于坐标原点O).(1)若OA0死=0，证明：直线过定点.(2)已知k=2,直线2在直线的右侧，4∥2,4与4之间的距离d=5,交C于M,N两点，试问是否存在m,使得MN-A=10?若存在，求m的值：若不存在，说明理由.

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报·高中数学·新果标版龙务性必修线的斜率为-1.若方程组mx+4,=2有唯一解，则两直线的斜率x+y=1不等，即-≠-1m≠4.1-a12325.5解析：由题意，得,'a>0,∴.a=5./24第4期《2.1直线的倾斜角与斜率，2.2直线的方程，23直线的交点坐标与距离公式》能力检测基础巩固1.D解析：设直线的斜率为k,则直线方程为y-2=(x-1),所以直线在轴上的藏距为1-2，令-3123，解得k<1或612.A解析：设直线ar+y-3=0的倾斜角为0，则tan0=-a,因为直线ar+-3-0的顿斜角大于牙，所以-心1或-<0，解得a<-1或a>0,所以a的取值范围是(-9，-1)U(0,+∞)解析：由-=1，得=”-由-=1，得ymxm3.Bm nmn mm,即两直线的斜率同号且互为倒数，排除A,C,D项，故选B项，4.A解析：根据题意画出图形，如图所示，直线，：x-2y+1=0与直线L2:mx+y+3=0的交点为A,且M为PQ的中点，若|AM=之|PO,则PA1QA,即，1，所以·(-m)=-1,解得m=2,mx+y+3=0x-2y+1=0x-5+3x-15.AC解析：设P(x,5-3x),则d=V2,化简V1+(-1)月得l4x-61=2,解得=1或x=2,故P1,2)或(2，-1).故选AC项6.BC解析：设经过直线L,与L,交点的直线的方程为2x+3y-8+A(x-2y+3)=0(A∈R),即(2+λ)x+(3-2λ)y+3A-8=0.由题意，得112-8λ+3λ-81=2,化简得5λ-8入-36=0，解得入=-2V(2+A)+(3-2A)月8,故直线的方程为-2或4x-3y+2=0,故选BC项7.2x-y+5=0或x+2y=0解析：直线经过点P(-2,1),当直线的斜率不存在时，直线的方程为x=-2,点A(-1,-2)到的距离d=1,不成立；当直线的斜率k存在时，直线的方程为y-1=k(x+2),即kx-y+2k+1=0,:点A(-1,-2)到l的距离等于5，1-k+2+2k+11k+3引=V5,解得k=2或k=-2…直线Vk+1的方程为y-122减-1=2).即2y45城+3-08-石解折：州的几何意义是过w,).-,-1)两点的直线的斜率.由于点M(x,y)在函数y=-2x+8的图象上，当xe[2,5]时，设该线段为AB,且A(2,4),B(5,-2),k4=56x+39.解：(1)设过点A且与直线1，垂直的直线方程为4x+3y+m=0.把点A(-2,2)代入，得-8+6+m=0,解得m=2.故所求的直线方程为4x+3y+2=0.(2)设过点A且和直线，行的直线，的方程为3x-4y+n=0.把点A(-2,2)代入，得-6-8+n=0,解得n=14.故直线，的方程为3x-4y+14=0.114-212所以行直线L,l,的距离d=V3+(-4)310.解：(1)由题意得，k,:乏，故1B边所在直线的方程为y43（x-3,即3x-2-1-0,2(2)联立3x-2y-1=0,解得所以A(1,1),则AC的中点x-4y+3=0y=1,为(3，弓)，则1G边的中线所在直线的方程为x=3,能力挑战1.C解析：直线(m-1)x-y+2m+1=0可化简为m(x+2)+(-xy+1)=0,令+2=0，解得x=-2,故无论m为何实数，直线-x-y+1=0y=3(m-1)x-y+2m+1=0恒过定点(-2,3).答案专页第4页

19.(12分)24已知△ABC的三个内角A,B,C所对的边分别为a,b,c,且2 bcsin A=3(a2--c2).(1)求角A的大小；(2)若b=2,D'为BC边上一点，DA⊥BA,且BD=4DC,求cosC酥)bcsm小=31b2)502多)、)bLt以—02c2ab啊cm2bl-(4记2-23bctan-5EL兄封2)内即和A毛Z CAD6朴6（府D中报店正旋4化险中由乎说存经5n合574Aa3又3D24P根据纺移(九△9%中a命2udS(3a松，72乃=4*6-x4)811142x2527227【24·G3DY(新高考)·数学（十）一XB一必考-Qd·77·A-29

Let's play sports together from now on!That's all.Thank you.第4期B3版Keys:(One possible version)词语狙击1.famous2.heroes3.during4.nothing5.chance6.exercise7.musicians 8.through9.finish10.excited11.angry12.dream13.follow14.another15.throw16.whether17.healthy18.successful19.held20.players21.scientist22.beginning句型演练1.play against2.take part in3.grows up4.at least5.shout at6.such as7.somewhere else 8.try my best9.say sorry to10.high jump11.Mary will go to cheer her best friend on tomorrow.12.I saw Mom put the keys into the bag just now.13.Staying up late isn't good for your health.14.What do these colors stand for?15.Would you mind my opening the window?16.My grandmother spends an hour watching TV every evening2/3

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21.What is paragraph 1 mainly about? A.The countries producing wine. B.The different wineries in America. C.The history of Lodi Wine Country. D.The information about Lodi Wine Country. 22.How long has Lodi been growing winegrapes? A.Over 170 years. B.About 250 years. C.Nearly 300 years. D.Almost 1,800 years. 23.What helps Lodi make various types of wine? A.Different wine makers. B.Different soils in the area.

and belonging. The mood boost (of talking to strangers may seem brief,but the research on well-being,Epley says,suggests that a happy life is made up of a high frequency of positive events,and even small positive experiences make a difference."Happiness seems a little bit like a leaky tire on a car,"Epley explains."We just sort of have to keep pumping it up a bit to remain it. 28.What conclusion can we draw from the test in paragraph 1? A.Short conversations with strangers could lift moods. B.The customers at Starbucks have a sense of belonging. C.The cashier has a good skill to get along with the custom ers. D.The first half of the participants spent more money than