∠F=∠CBO,BD=AF23.解：问题背景由(1)知DEG-=∠CBD如图心，取BC的中点O,连接AO,,·.∠D上=∠D0,E0..·BD∥AF.可知△ABD可以由△CAE绕点O四、解答题（逆时针旋转90°得到19解：答不唯∴.旋转中心为BC的中点O,旋转方23.2.1中元对称向是逆时针，旋转角度为90°.1.解：如图，对称中心0及△A'B'C(1)即为所求.BA(2)第7期2-3版,选择题15Bc6~10.BCBCA20解：(1).∠BCE=15°，∠D,CE=60(第23题图)(第2题图).∠0CB=∠B=45°.·.∠C0B=90°.尝试应用23.2.2中心对称图形填空题在四边形0CE,F中，∠0FE1=360°可以，旋转中心O是△ABC的三条1.D2.①⑥11.15°125(∠COB+/D.CE+LE,)=120角分线的交点理由如下：23.2.3关于原点对称的点的坐标13.(7,4)14.③(2)由(1)知，OC⊥AB.如图②，取△ABC的三条角分线15.V21的交点O,连接AO,B0,C0,D0,E02电图只知A22B-30、解答题（一）.0A=0C=0B=3.∴.0D=D,C-0C=7-3=4:△ABC为等边三角形，点O是C(-1,1),各点关于原点对称的16.解：如图,△MNC为所作在Rt△AOD1中，AD=VOA2+OD2=△ABC的三条角分线的交点，标分别是A(2,-2),B(3,0),C(1,1).图略23.3课题学图案设计V32+4·.∠ABO-∠BAOOAC-∠OCA-30=5(cm)解：如图所示1.(1)证明：.线段AD绕，点A逆时OA-OB-OC,∠AOB=∠AOC∠BOC-120.针旋转60得到AE】.点A绕点O逆时针旋转120与,∴.AD=AE,∠DAE=60点B重合，点C绕点O逆时针旋转120,∠BAC=60°，.∴，∠BAC=∠DAE与点A重合∴∠BAD=∠CAE,∠ADB=∠AEC-60在△ABD和△ACE中∴.∠ABD+∠BAD=120(AB=AC,·.∠BAC-60,:.∠BADr∠CAE-120」∠BAD=∠CAE,.∠ABD=∠CAEAD=AE.AB=AC,.△ABD≌△CAE(AAS..·AD=CE,BD=AE.(第16题图)∴.△ABD≌△ACE(SAS).BD=CE17.解：(1)如图，△A'BC即为所求(2)解：结论正确理由如下：∠ABD=∠CAE,∠ABO=∠CAO=30如图，“过点A作BD,CF的垂线，垂∴.∠DBO=∠EAO.足分别为点M,N.·△DBO≌△EAO(SAS)由(1)知，△ABD≌△ACE:.DO=EO,∠BOD=∠EOAQ∠ABD=∠ACE∴.∠DOE∠AOB=120°∠AGB=∠CGF,.点E绕点0逆时针旋转120与.∠BFC∠BA60°..∠BFE=120°点D重合.BD=CE,SAABD=SAACE,·,△ABD可以由△CAE绕点O逆时:BD·AMF2针旋转120°得到.·CE·AN4版(第17题图)·AM=AN23.1图形的旋转(2).·△ABC绕点B按逆时针方向又AMLBF,AN⊥CF第1课时旋转60得到△A'B:.BA=BA',∠ABA'=60°.∠AF=∠AFN.1.D2.至少旋转60可以完全重合.∴△ABA'是等边三角形.AA'=AB·.∠BFC∠AFB=∠AFE=609在Rt△ABC中，根据勾股定理，得B第2课时-.N1.AB=VAC+BC2=V/4+32=5.解：(1)如图，△ABC1即为所求AA'=AB=5181)证明：四边形ABCD是矩形，ABC=90°，AD/BC.∠CBDtB MLABE-0°，∠CBD=∠ADB.A由旋转的性质，可得∠AEF=∠ABC(第21题图)(第22题图)】90°，AE=AB.五、解答题（三）.∠DEGt∠AEB-90,∠ABE=∠AEB.∠DEG+∠ABE=90°22.解：探究发现：PB;PB.∴∠DEG∠CBD=∠ADB.DG=EG类比延伸：2PA2+PB2=PC∴.△DEG为等腰三角形.证明：如图，将△APC绕点A逆时针旋转90°，得到△APB,连接Pp',则(2)解：BD=AF且BD∥AF.理由：四边形ABCD是矩形PA=PA,∠P'AP=90°，P'B=PC..0B=AC=BD∴.∠BCO∠CBO..∠APP'=45°，PPP=PA2+PA2=2PA2(2)如图，△AB,C2即为所求由旋转的性质，可得∠F=∠BCA∠APB=135°，.∠BPP=90°.第3课时AC-AFPP+BP-PB22PA2+PB2=PC2解：答案不唯一，如图所示。

第八章面解析几何3.(2022浙江宁波镇海中学高三模拟)已知点M(1,角度2弦长问题2)是圆C:x2+y2=r2内一点，直线1是以M为例2(1)(2022山东枣庄期末)过点A(2,2),作中点的弦所在的直线，直线m的方程为2x-y=2,那么倾斜角为的直线1，则直线1被圆0：+y2=A.l⊥m且m与圆C相切16-85截得的弦长为B.l∥m且m与圆C相切A1③2B.2-√3c.l⊥m且m与圆C相离D.l∥m且m与圆C相离C.3-√3D.6-234.(2020全国Ⅱ，5,5分)若过点(2,1)的圆与两(2)(2022河南郑州高三模拟)若直线1：3x+4y+坐标轴都相切，则圆心到直线2x-y-3=0的a=0(a∈R)与圆0：x2+y2=9交于不同的两点距离为()A、B,且10+0i1=51应1，则a=（)D.42A.±55B.±3√5C.±25D.±55.若圆x2+y2=r2(r>0)上恒有4个点到直线l:x-方法感悟y-2=0的距离为1，则实数r的取值范围是1.求过某点的圆的切线问题时，首先应确定点与圆的位置关系，再求切线方程若点在圆上（即为切点），则过方法感悟该点的切线只有一条；若，点在圆外，则过该点的切线判断直线与圆的位置关系的常见方法有两条，此时注意斜率不存在时的切线。(1)几何法：利用d与r的关系判断。2.求圆的弦长问题的两种方法(2)代数法：联立方程之后利用△判断.(1)几何法：直线被圆藏得的半弦长}、弦心距d和2(3)点与圆的位置关系法：若直线恒过定点且定点在圆内，可判定直线与圆相交考点二圆的切线、弦长问题多元分析(2)代数法：利用弦长1AB1=√1+1x,-x21=√1+角度1圆的切线问题.1·√-4或1AB1=1+·yl例1已知点P(√2+1,2-√2)，点M(3,1),圆C:(x-1)2+(y-2)2=4.·√(y+y2)2-4yy2(k≠0)求解(1)求过点P的圆C的切线方程；(2)求过点M的圆C的切线方程，并求出切迁移应用线长1.(2022河南安阳高三模拟)已知圆C:(x-2)2+(y-6)2=4,点M为直线l:x-y+8=0上一个动点，过点M作圆C的两条切线，切点分别为A,B,则四边形CAMB周长的最小值为()A.8B.62C.5√2D.2+4√22.(2020天津，12,5分)已知直线x-√3y+8=0和圆x2+y2=r2(r>0)相交于A,B两点.若1AB1=6,则r的值为3.(2021山东东营模拟)若圆C:x2+y2+6x-2y+n=0截直线l:(2+m)x+(2m-1)y-5m=0所得的最短弦长为4√2，则实数n=。181·

第十三章轴对称第2课时用坐标表示轴对称建议用时：30分钟(共271考：单独22考，在网格作图题、函数综合题等中涉及249考)教材改编题知识点2坐标与图形变化92考》基础《3.`(教材P71第2题改编)如图，△AB0与△DEF关于y轴对称，若点A的坐标为(1，-2)，则对知识点1关于坐标轴对称的点的坐标9考称点D的坐标为()1.(教材P70第1题改编46考)一题多变A.(-1,2)B.(2,-1)1.1改变点坐标求关于x轴对称的坐标C.(-1,-2)D.(-2,-1)在面直角坐标系中，点A(-1,3)关于x轴2D的对称点坐标为A.(1,3)B.(3,-1)O(F)戈C.(-1,-3)D.（1,-3)A(1,-2)1.2改为关于y轴对称求字母的值第3题图第4题图在面直角坐标系中，点A(-4,a)与点B4.（教材P71第3题改编)已知长方形ABCD在(b,-2)关于y轴对称，则a,b的值为()坐标面上的位置如图所示，x轴，y轴分别是A.2,-4B.-2,4长方形的两条对称轴.若点A的坐标为(-3，C.-2,-4D.2,4-2),则点B的坐标为,点C的坐标1.3改为根据两点坐标判断两点关系为,点D的坐标为已知点Q(-2,-3)是由点P(-2,3)经过坐5.(教材P72第4题改编)如图，在面直角坐标的变化得到的，请直接写出它进行了怎样标系中，△ABC的顶点坐标分别为A(1,1),的运动：B(4,-1),C(2,3).2.（BS教材八上P72改编)在面直角坐标系(1)作出△ABC关于x轴对称的图形△A'B'C',中，已知点A(3,a+1)和点B(2b-1,2)并写出△A'B'C各顶点的坐标：(1)若点A到x轴和到y轴距离相等，求a(2)若将△ABC向下移4个单位，作出移的值；后的△A"B"C”,并写出△A"B"C"各顶点的坐标(2)若点A和点B关于y轴对称，求a+b的值..3-2-10第5题图49

第一章有理数>综合(1)这一天巡逻结束时，高速交警巡逻车位于A地哪个方向？离A地多少千米？6.2,-1,-2这三个数中，任意两个数之和的最(2)该巡逻车一共行驶了多少千米？大值为(A.-1B.0C.1D.27.（教材P12图改编)如图，做题时小刘不小心将墨水滴在了数轴上，根据图中的数值，判断被墨迹盖住的整数和是第7题图A.-6B.-3C.0D.8中考新考法8.(BS教材七上P74改编)x是最大的负整12.(数学文化应用·算筹)材料阅读：如图数，y是-3的绝对值，z的相反数是它本身，①，魏晋时期的数学家刘徽在其著作《九则x+y+z的值是章算术注》中用不同颜色的算筹（小棍形9.已知|a|=2,Ib1=7,且a>(2)用“>”“<”或“=”填空：+42_31图①lal1b1;a+b0;-c+b0;=一l·一(3)若每个单位长度为2，求a+c+b的值图②c b第12题图第10题图(1)图②的运算结果为：(2)请尝试猜想(+31)+(-54)可以通过如何摆放算筹来计算结果，画出你猜想的摆放方式及结果，并写出式子[陕西、山西、河南等地中考已考查]视频讲解途织可】11.春节期间，某地因天气原因，高速路况较中考新考法题差，高速交警为了维持道路畅通，特派遣巡逻车在东西方向的某地段巡逻，如果规定向东为正方向，一天巡逻车从A地出发，行驶记录如下（单位：千米）：+40,-25,+19,-32,+28,-12.13

一、单词辨音。请找出画线部分发音不同的单词。(C)1.A.bankB.man选C.skateD.panda(A)2.A.hotelB.frontC.moneyD.monkey题(C)3.A.spendB.leftC.behindD.restaurant(B)4.A.killB.climbC.listenD.animal(A)5.A.snowB.howgC.townD.brown二、完成句子。根据汉语意思完成英语句子。1.金先生在邮局上班。选Mr.King works in thepostoffice.2.这条街上没有付费电话。题There are no payphones on thisstreet.3.在下一个路口向左转。Turnleftat the next crossing.⑧4.这里离警察局有多远？选How far is it from here to the police做题station5.不要在电脑前坐太久。Don't sitinfrontofthe computer for too long.⑧10

(3)原命题等价于f(b)-b0),则等价于h(x)在(0，十∞)上单调递减，()=上-2-1≤0在(0，+0)恒成立，故m≥-2+x=-(x-2)2+子(x>0)恒成立，故m≥故m的取值范围是[号、+∞).(15分)12.(1)当a=2时，f(x)=e2-x2,则f(x)=e2-2x,令f1(x)=f(x)=e2-2x,则f1(x)=e2-2,令f1(x)=0,得x=ln2,故f(x)在x=ln2时取得最小值，f(ln2)=2-2ln2>0,.f(x)在(0，十∞)上为增函数，.f(x)>f(0)=1.(8分)(2)f(x)=e2-ax,由f(x)≥x2lnx,得e-ax≥x21nx对一切x>0恒成立，当x=l时，可得a≤e,∴.若存在，则正整数a的值只能取1,2.下面证明当a=2时，不等式恒成立，设g=兰-是lnx,则g(x)-,2+是-3(x-2)(e2-x)x3由(1)e>x2+1≥2x>x,.e-x>0(x>0),当02时，g(x)>0,即g(x)在(0,2)上是减函数，在(2，十∞)上是增函数，g(x)≥g2)=(e-4-4l2)>子(2.-4-4n2)>号(3-1n16)>0,当a=2时，不等式恒成立，.a的最大值是2.(16分)

49.A。根据If I give it up,what's left for me及to see himself as a vital part of the community可知，Freed觉得如果不能给病人看病，那他的生活中就什么都没有了，故推断，此处是说要让他继续把自已看成社区重要的一部分。50.D。51.C。根据he should write about his medical experiences if he was..to do it和a goodidea可知，“我”建议Freed如果可以的话，把他的医学经历写下来。52.B。根据pass on what've learned to the可知，Freed要把自己的所学传递给社区的人。本空与上文中的community构成原词复现：53.A。Freed医生80岁高龄还在努力，故可知，此处在说努力永远不嫌老。本空与下文中的older构成原词复现。54.B。根据上文Freed准备写书及during each phase of life可知，在生命的每个阶段都要做些调整55.A。根据my role now is to pass on what i''ve learned及a source of satisfaction可知，年老的时候，分享才智和经验往往让人感到满足。give of意为“贡献”，符合语境。第二节主题语境：人与自我一一做事本文是记叙文。Mazeda Begum通过种植有机蔬菜不仅改善了家里的经济状况，也激励着其他人投身农业56.settlement。.考查名词。设空处作hit的宾语，其前有Mazeda Begum's限定，应用名词。informal settlement意为“临时棚屋区”。57.barely。考查副词。设空处修饰enough,意为“勉强才能”，应用副词。本句中let alone意为“更不用说”。58.to close。考查动词不定式。force sb to do sth意为“迫使某人做某事”。59.who。考查关系代词。设空处引导非限制性定语从句说明Mazeda的具体情况，且在从句中作主语，故填who60.has created。考查现在完成时。since在句中是副词，意为“自从…以来”，与完成时连用，故填has created:61.affordable。考查形容词。设空处修饰produce(农产品)，意为“买得起的”，应用形容词。62.t。考查it的用法。设空处在句中作形式主语，真正的主语是动词不定式to be a farmer。63.adding。考查动词-ing形式。分析句子结构可知，设空处应填非谓语动词；add的逻辑主语是she,与add之间是逻辑上的主谓关系，应用动词-ing形式64.earns。考查一般现在时。根据and之前分句的时态和之后的时间状语per month可知，该句介绍了Mazeda每个月的收入情况，此处应用一般现在时。65.the。考查冠词。in the near future意为“在不久的将来”。【词汇链接】1.make ends meet(para.1):勉强维持生计2.stand(para.1:货摊3.spring up(para.2:迅速出现；突然兴起4.follow suit(para.2小：仿效5.BDT(para.3):孟加拉国的货币单位符号

21.（12分)在△1BC中，B-26,∠B-云4D是∠BAC的分线(1)若AD=2W2,求AC:(2)若AC=2√2，求AD2√62√2【解析】(I)在△ABD中，由正弦定理，得sin∠ADB sin’6所以sin∠ADB=2因为∠ADB∈O,),所以∠ADB=或，…2分3若2408-育则280=x-8骨员因为AD是∠BAC的分线，所以∠BAC=元，舍去.…3分若08兰则∠B0x君名所以∠B1C-号∠8CA-号AC=ABsin ZBAC=26x1=6.…5分22W62√2(2)在△ABC中，由正弦定理，得sin ZACBsin，6所以sin∠ACB=32因为∠1CB∈(0，)，所以∠ACB-或2T…7分3若∠ACB=5,则∠BAC=5,因为AD是∠BAC的分线，所以怨=装=5，所以D=1B+54C,V3+1V3+1所以而-(j证+c州

2版华师大中考版（河南）参考答案第4期数学周刊第11期参考答案26.3.2二次函数与一元二次方程情境导入：5米，课堂探究：例1>名且m0例2C26.3.1实际问题与二次函数即学即练：1.B2.A3.C4.B5.D课堂探究：例18解析：当喷头高2.5m时，可设抛物线6.87.x1=-2,x2=6的表达式为y=ax2+bx+2.5.将(2.5,0)代入，得6.25a+2.5b+2.5=8.解：(1)令y=0,得-x2+4x-3=0,解得x=1,x=3,则A(1,0.①0),B(3,0).因为y=-x2+4x-3=-(x-2)2+1,所以抛物线顶点P的当喷头高4m时，可设y=ax2+bx+4.将(3,0)代入，得9a+坐标为(2,1).(2)作出图象略，当103b+4=0.②9.解：(1)318，不符合题意，所以x的值为10.(3)因为y=-2x2+36x=-2(x-9)2+162,-2<0,所以当x=9时，800.所以当玩具的销售单价定为30元时，日销售利润最大，最y有最大值162.此时利用的墙长为36-2×9=18(m).所以矩形大利润是800元.ABCD空地的面积最大时，利用的墙长是18m,最大面积为即学即练：1.A2.D3.C4.C5.B6.87.10162m2.8.解：1冷y0.得-与+号0.解得-0含去).=817.(14分)解：(1)设y与x的函数表达式为y=kx+b(k≠0).答：球飞行的最大水距离为8m.由题意，得50k+h=I0,解得k=2。所以y与的函（2因为)=+受45所以当4时球飞60k+b=80,b=200.数表达式是y=-2x+200.行的最大高度为16m.(2)由题意，得W=(x-40)(-2x+200)=-2x2+280x-8000,即W与x的函数表达式是W=-2x2+280x-8000.根据题意，再一次击球，球飞行路线的顶点坐标为(3)因为W=-2x2+280x-8000=-2(x-70)2+1800,-2<0,且55,设抛物线的表达式为)=a(-5)+16.1640≤≤80，所以当40≤x<70时，W随x的增大而增大；当70

How's your new school life?Write and tell me.Yours,Li Hua第二节One possible version:Then,I noticed a man standing in front of a store.He looked at the dogs,looked at me,and thentook off after the dogs.He ran to them and stopped them just as they were about to cross a busyroad.I slowed down to catch my breath as I saw he had the dogs under control.Then a thoughtsprang to mind:How was I going to get the table back to the restaurant while controlling twolarge dogs?By the time I walked up to the man and the dogs,he had untied them and had the table up onone of his shoulders.I thanked him while he passed Zoe and Tyler's leashes to me and walked offto the restaurant.By the time Tyler,Zoe,and I got back to the coffee shop,the man had just puteverything in the outside dining area in place.It looked as if nothing had ever happened.Iwanted to show him my thanks with more than just words.So,I bought a cup of tea for him.Theman thanked me for the tea,saying it was the best he had ever had.写作选做题1.She helps in a local school as a volunteer every Wednesday.2.There was a big change in our lifestyle after we moved to the city.3.She spends two hours on the phone chatting to her friends every Sunday.4.We should play the game according to rules.5.I can't go to a movie tonight.I have to revise for my English exam tomorrow.部分解析阅读第一节A篇主题语境：人与社会一一社会服务本文是应用文。文章介绍了一个图书展览会。2l.D。理解具体信息。根据第三段中的But it's not only books that people are searching for;the Book Fair is also a great place to find records,,CDs,and DVDs可知，该图书展览会不仅展销图书，还有唱片、光盘和数码光碟。22.C。理解具体信息。根据第四段中的The Book Fair opens at4p.m.on Thursday,May4.Onthat day only,,aSl5 admission is required可知，该图书展览会于星期四下午四点开始，只有这天的门票是15美元。23.D。推断。根据第四段中的all remaining books are half--price from10a.m.to6p.m.onSunday可知，星期天，该图书展览会从上午十点开始到下午六点结束，所有图书半价销售。B篇主题语境：人与自我一一生活与学本文是记叙文。作者讲述了自己抉择大学专业的过程和感受。24.D。理解具体信息。根据第二段中的I came into college thinking that I would major inCommunications.It had been my dream to be a sportswriter That was my dream until I got theacceptance letter that stated I was not qualified for that major可知，作者的梦想是成为一名体育记者，所以，上大学时她以为自己会学传播学专业。然而，录取通知书上说她不符合传播学专业所要求的条件，所以她只好放弃当一名体育记者的梦想。25.C。推断。根据第三段的内容及第四段“What are you going to do with a degree in History?

2版湘教七年级参考答案第4期数学周刊第12期参考答案第4课时角与角的大小比较因为BP分∠ABD.所以LABP--ARD-122-61自主学：1.C11.解：(1)因为∠B0C=40°，所以∠A0C=180°-40°=140°2.(1)>(2)>(3)<因为0E是∠A0C的分线，所以∠A0E=70°课堂探究：B(2)图中与LEOC互余的角有∠COD,∠BOD.即学即练：1.C2.B3.A4.C5.A(3)∠COE的补角是∠BOE.6.③④理由：因为∠AOE=∠E0C,∠A0E+∠B0E=180°，所以7.解：由图可知，图中的角为：∠DOC,∠COB,∠BOA,∠COE+∠BOE=180°.所以∠BOE是∠COE的补角.∠DOB,∠COA,∠DOA.第4章图形的认识(4.3)同步诊断8.解：∠AOC=∠BOD.理由如下：一、选择题（每小题4分，共32分）因为∠AOB=∠COD,所以∠AOB-∠BOC=∠COD-∠BOC,即1.C2.D3.B4.C5.C6.A7.C8.A∠AOC=∠BOD二、填空题（每小题4分，共24分）第5课时角的度量与计算9.>10.60°11.20°或80°12.130自主学：C13.59.27514.45°或120课堂探究：因为∠ABC=90°，∠CBD=30°，BP分∠ABD,所三、解答题（共44分）以∠PRD-2ZARD--X(90+30)-60.所以∠CP=∠PBD-15.(每小题4分，共12分)解：(1)原式=80°74=81°14'(2)原式=89°5960"-79°18'6"=10°41'54".∠CBD=60°-30°=30°.(3)原式=115°70'-10625'=9°45'即学即练：1.A2.B3.C4.C5.A1116.(10分)解：因为OM分∠B0C,所以∠C0M=2∠B0C.6.15012247.>8.67.5°9.6512<40C.因为ON分2A0C,所以∠C0N=10.(1)32°36'33”；所以∠M0N=∠C0M-∠C0N=2(∠B0C-∠A0C)=2×(2)53°1635".1L.解：设∠AOB=x°，则∠B0C=2x°，所以∠AOC=∠AOB+∠10B=2×91°36'=4548.∠B0C=3x°.17.(10分)解：(1)LA0B∠C0D因为0m分LA0C,所以∠A0nA0C多(2)∠AOD与∠B0C互补.理由如下：因为∠AOC和∠BOD都是直角，所以∠AOB+∠B0C=3。所以LB0D=∠A0D-∠A0B=°-x=7°=25，所以x=50,∠C0OD+∠BOC=90°.因为∠AOD=∠AOB+∠B0C+∠COD,所以∠AOD+∠BOC=所以∠A0C=3x°=150°」∠AOB+∠BOC+∠COD+∠B0C=180°.第6课时余角和补角所以∠AOD与∠BOC互补，自主学：7016018.(12分)解：(1)因为∠A0B=∠A0C+∠B0C=120°，∠A0C:课堂探究：例1C例2B∠B0C=1:2.所以20G=3A0B=40,∠B0C=号2A0B=80.即学即练：1.B2.A3.A4.C5.C6.D因为∠BOC=∠BON+∠CON=80°，∠BON=3∠CON,所以7.125°55∠C0N=44B0C=208.52°20'9.38°10.解：因为∠ABP与∠CBP互余，所以∠ABP+∠CBP=90°因为0M分∠A0c.所以1c01=)A0C=20.所以即∠ABC=90°.∠M0N=∠C0M+∠C0N=40°.所以LABD=∠ABC+LCBD=90°+32°=122°.(2)32°或176

第4版详情请参考答案解析阅读理解1-4 CBDD完形填空1-5 DBACC6-10 ABDCB 11-15ADBAD阅读填空1-5 DFEAG2。

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项和为S,则S2023C.)2023.2025法国数学家傅里叶用三角函数诠释美妙音乐，代表任何周期性声音和动的函数表达式都是A.1012B.2020形如y=Asinox的简单正弦型函数之和，这些正弦型函数各项的频率是最低频率的正整数倍（频率是指单位时间内完成周期性变化的次数，是描述周期运动频繁程度的量).其中频率最低的一8项所代表的声音称为第一泛音，第二泛音的频率是第一泛音的2倍，第三泛音的频率是第一泛音的3倍…、例如，某小提琴演奏时发出声音对应的震动模型可以用如下函数表达：y=0.06sin10001+0.02sin2000t+0.01sin3000/(其中自变量1表示时间)，每一项从左至右依次称为第一泛音、第二泛音、第三泛音.若一个复合音的数学模型是函数∫()=inx+)inox(xeR)(从左至右依次为第-一泛音、第二泛音)，给出下列结论：①(x)的一个周期为3元：②f(x)的图象关于直线=2n对称：③()的极小值为-39，国()在区间[0,2网上有2个零点，其中正确结论的个数有D.4个A1个B.2个C.3个多项选择题：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.二、已知a>0,b>0,且a+b=2,则2°+202491og2a+log2b≤0a2+b2≥42a+=a-2ani(n∈N+),则下列结论正确的是10.i知数列{a,}满足4=2201侵斗为等比数列an0B,{a,}为递增数列的前n项和T.=2*2-2n-4{a,}的通项公式为a,=2-211.己知正方体ABCD-4C,D的棱长为1，若点P在线段AD,上运动（不含端点），则下列结论正确的是A.直线B,PI面BDCV1A0,△BPD周长的最小值为2+√2c.三棱维B-PD与三棱锥C-PCD的体积之和为后√当2AP=PD,时，DP与面BC,D,所成角的正切值为312.已知f(x)=2,则下列有aln(x+1),x≥0A.对于任意a∈R,函数f(x)有且只有两个零点V太1以当a<0时，函数f(x)有三个极值点C.当x∈(-0,0)时，函数∫()的图象的切线的斜率最小值为-】B.toC(12,o)黄数L上-上的0小值为则[）P0,14sho若款6 nePlus江西省，岸乡市202方692：)P:色P(-,y741X

2l.C。理解具体信息。根据What's Included部分An English-speaking driver guide可知，柏林周边四天旅行有导游陪同。22.D。理解具体信息。根据Day2:Berlin-Meissen部分.touring the oldest PorcelainManufactory in Europe,as well as the museum and production room inside.可知，Meissen的g独特之处在于其瓷器制作历史悠久。23.A。推断。根据Day4:Dresden-Weimar-Berlin部分the commemorative imagesGermany's most famous poets..可推知，诗歌爱好者可能最喜欢参观Weimar。B导语：本文是一篇记叙文，属于“人与自我”主题语境。文章讲述了作者·一夜间失明，经历了震惊、消沉，最终走出困境、重拾生活信心的故事。24.D。推断。根据第一段I was always looking for a real adventure,something new and excitingI enjoyed a joyful life.可推知，作者在33岁生日之前过着充满冒险的幸福生活。25.A。理解态度。根据第三段I couldn't process what I'd heard at first;:it just didn’t seem tomake sense.可推知，作者非常震惊，无法接受自己失明的事实。26.C。理解具体信息，根据第五段The turning point came...it made such a difference to be ableto talk to people who understood my situation.可知，与其他视力受损的人交谈之后，作者改变了之前对生活自暴自弃的态度，转而接受并适应失明后的生活。27.B。理解主旨要义。本文主要讲了作者一夜间失明，经历了震惊、消沉，最终走出困境、重拾生活信心的故事，故选用此标题。导语：本文是一篇说明文，属于“人与自然”主题语境。精准农业专家Strahl介绍了公司研发的新技术，该技术能够更精准地观测农业产量，以帮助农民调整种植策略。28.B。理解具体信息。根据第一段.there are so many new products...take time to test on thefarm to see if they can bring value可知，精密农业的新产品需要时间试验是否有效，这可能是一些农民不愿意应用新产品的原因。29.C。理解词汇。根据第二段he enjoys...testing the technologies.to see what is worth...usingthe data.study seeding methods.可推知，Strahl喜欢待在农田里，测试各种技术和产品是否“可行”。30.D。理解具体信息。根据第四段Optimus…provide growers with tools.It also allowsfarmers to see an in-depth study of variable--rate products..可知，Optimus为农民提供田间精准的数据和工具。3l.D。推断。根据末段Applying the variable rate will take a full growing season to get the resultsback,but it can help you make better management decisions for years to come.可推知，新产品虽然需要整个生长季节才得到结果，但能帮助农民在未来制定更好的种植策略，所以其长期的潜在益处很大。D导语：本文是一篇说明文，属于“人与自然”主题语境。利用椰子壳纤维制作的材料可以防止海水侵蚀海岸。32.C。理解具体信息。根据第二段The coconut material is easy to get and costs a lot less thanbarriers made of other materials可知，椰子壳纤维材料因其易得性和价格低廉而在建造海岸线屏障上得到广泛使用。33.C。理解具体信息。根据第四段.pre-seeded with shoreline plants and grasses.in the coirmaterial可知，提前种植海岸植物可以应对椰子壳纤维材料的老化问题。34.A。推断。根据末段It's not for every site;it has to be site-specific.it doesn't work in all

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阅读：21~23 DACA篇：本文是应用文。文章介绍了四种对人的记忆力有益的食物。21.D【解析】细节理解题。根据第二段第二句可知，作者建议我们每天至少要吃两份蔬菜。22.A【解析】细节理解题。根据四种食物的介绍可知，它们都对人的记忆力有益。23.C【解析】推理判断题。文章介绍了四种对人的记忆力有益的食物，所以本文最有可能选自一本健康杂志。2427DBBAB篇：本文是记叙文。在明尼苏达州，一只黑熊在涵洞中被困三天后获救。24.D【解析】细节理解题。根据第二段第二句可知，这只黑熊被困在涵洞中。25.B【解析】细节理解题。根据第三段最后一句可知，这只黑熊还处于冬眠状态。26.B【解析】主旨大意题。根据第五段的内容可知，本段主要描述了人们为救这只黑熊所做的事。27.A【解析】推理判断题。根据最后一段中Andrew说的话可知，就如何帮助受困的熊，他给出了自己的建议。28~31 ADABC篇：本文是说明文。考古学家发现了隐藏在尤卡坦半岛丛林深处的玛雅遗址。28.A【解析】细节理解题。根据第二段最后一句可知，这个遗址的核心区域遍布着用石头建造的建筑物。29.D【解析】推理判断题。根据第四段可知，Sprajc认为这个遗址是宝贵且有重要意义的。30.A【解析】推理判断题。根据第五段的内容可推知，这个遗址曾是一座繁荣的城市。31.B【解析】主旨大意题。通读全文可知，考古学家发现了隐藏在尤卡坦半岛丛林深处的玛雅遗址。32~35 CCBDD篇：本文是说明文。文章介绍了个体心理学。32.C【解析】推理判断题。通读全文可知，作者在第一段提及The Courage to be Disliked是为了引出文章的主题。33.C【解析】细节理解题。根据第二段最后两句可知，关于恐惧和悲伤，Adler认为它们是可以被个人选择克服的。34.B【解析】词义推测题。根据画线词所在句和上文可知，Adlr认为，一个人不愿意走出家门，因为这个人每次走出去都充满焦虑和恐惧。所以Adler断言，这个人制造了恐惧和焦虑，以便他待在家里。assert意为“断言”，与claim同义。35.D【解析】推理判断题。通读全文可知，通过介绍个体心理学，作者希望人们能够摆脱曾经的创伤，着眼现在和未来。36~40 CGBFD七选五：本文是说明文。文章介绍了关于黑匣子的一些知识。【高三英语·参考答案第5页（共10页）】·24-124C·

The Female Brain through the LifespanInstructor;Louann BrizendineDATE:September 30 (1 Saturday)Join bestselling author Dr.Louann Brizendine for aTIME:10:30AM-1:30PMdeep dive into the female bruin.Discover the inner-working,LOCATION:Corte Madera Storepossibilities,and opportunities that women are offered overtheir lifetimes.Race and the Constitution(宪法)Instructor:Joel Richard PaulDATES:October 1-22 (4 Sundays)Join Joel Paul,a law professor and author,for a livelyTIME:IPM-3PMwide-ranging discussion of the legal struggle for racial justiceLOCATION:Corte Madera Storein our count灯y.Impressionism:The International MovementInstructor:Kerrin MeisWe are familiar with Impressionism in France and howartists took up painting to record the fleeting moment.In thisDATES:November 3 17 (2 Fridays)class,Kerrin Meis will show us how artists in otherTIME:1PM-3:15PMLOCATION:Corte Madera Storecountries outside of France -shared the same idea withwonderful results,reflecting the particular light,landscapeand traditions of their country.21.Who might be most interested in Nina Schulyer's class?A.Those who are fond of technology.B.Those who major in preschool education.C.Those who are crazy about travelling.D.Those who serve as medical workers.22.Which class can offer a feast for eyes?A.AI for Amateurs.B.Race and the Constitution.C.The Female Brain through the Lifespan.D.Impressionism:The International Moyement.23.What do these classes have in common?A.They all last for two hours.B.They are about arts and culture.C.They are given in the same place.D.They take place on weekends.BNo matter how beautiful the weather may be,the ocean can turn deadly in the blink of an eye.South African local Tongai Matandirotya has worked as a bartender at the Brass Bell Kalk Bayrestaurant for the past 8 years.Coworkers describe him as a "wonderful,loveable,fun human being."After watching him jump into action to save lives after an unexpectd accident on the shore,they'readding another description to his character:Heroic.Tongai was tending the bar one aftemnoon on a beautiful day with crystal-clear blue skies andcalm seas.Tourists who had finished their lunch at the restaurant were walking along the water's edge,taking in the stunning ocean and mountain views,when suddenly a "wall of water"rose up andcarried dozens of people out to sea."I saw this wave come over the harbour and it covered the people,dragging them into theocean,"Tongai recalled."It was frightening but I immediately ran outside,undressed myself,anddived into the water because I saw a child go in as well.I have a very soft spot for kids,and myinstinct (just kicked in to see if I could help."There was a powerful riptide at play,making it difficult for the shocked victims to get back tohore.Clair Gardiner and her 8-year-old daughter,Arya van Hilten,were knocked into the water.英语试题第3页（共8页）

第l7期A2版Keys及重点解析：(One possible version,客观题除外)Passage 1 1-4 BCADPassage 2 1-5 CBGDEPassage 3 1.that/who2.decision3.beneficial4.to grow八resulting 6.has applied 7.in8.villagers 9.greatly10.an导语：本文是一篇新闻报道，属于“人与社会”主题语境。主要讲述了贵州姑娘王静在短视频台上传授蘑菇种植技术和帮助农户销售农产品的故事。4.to grow。考查非谓语动词。teach sb to do sth是固定搭配，意为“教某人做某事”。5.resulting。考查非谓语动词。分析句子结构可知，设空词在此处作结果状语，故填动词-ing形式resulting。6.has applied。考查动词的时态。根据时间状语Over the past decade可知，此处需用现在完成时，故填has applied。第l7期A3版Keys及重点解析：(One possible version,客观题除外)Passage 4 1-5 BADBC 6-10 ADBCA 11-15 CDBCA导语：本文是一篇记叙文，属于“人与社会”主题语境。天生患有唇裂的Jaya在慈善机构的赞助下进行了手术，最终痊愈了。1.B。根据全文语境可知，Jaya出生时患有唇裂，接受了手术，故知，此处指她婴儿时期经历”的这些事情。3.D。根据下文.Jaya was born with a cleft lip.可知，Jaya父母的心情由开心变为“担心”。4.B。根据上文Living on less than3aday.可知，Jaya家的生活并不富裕，所以他们“发愁”如何让Jaya进行手术。ll.C。根据上文.once she reached the right weight..可知，此处指Jaya足够“健康”，可以做手术。l4.C。根据下文jumping out of bed and rushing to school each morning to meet her friends.可知，Jaya现在很“活跃”。Passage 5 1.getting along with2.apply for3.information4.believed his fortune5.comforted第17期A4版Key:(One possible version)写作一招鲜Dear Eric.I'm very delighted to hear that you're considering learning Chinese calligraphy.It's truly abeautiful art form that reflects China's rich cultural heritage.I understand your concern about how this might affect your other courses.While it's importantto balance your time and commitments,I believe that pursuing your passion for Chinesecalligraphy can actuallyimprove your overall learning experience.You can set aside some specific time each week topractice calligraphy.This will ensure that you can focus on your other subjects without feelingstressed.I hope my suggestions can be helpful.Best regards!Yours.LiHua

【答案】3640 DBFEC

Still,Janet was growing more nervous y with each step closer to the old man's house.When they got close enough,Dawson looked up with his usual frown(皱眉)，but when he saw it was Amy,a broad smile changed his entire face as he said,"Hello, Miss Amy.I see you've got a little friend with you today. Amy smiled back and told him Janet was staying overnight and they were going to listen to music and play games.Mr Daw- son said that sounded fun,and offered them each a fresh picked apple off his tree.They gladly accepted.Mr Dawson had the best apples in the whole town. When they left,Janet asked Amy,"Everyone says he's the meanest man in town.How come he was so nice to us?" Amy explained that when she first started walking past his

答案专页10月第13-16期体中，试想D运动至A时，面B,EF不可能与面A,BD垂直，故B项错误；对于C项，在面ABBA,上，易知AA,与B,E必相交，故面BEF与面A,AC不行，故C项错误；对于D项，易知面AB,C∥面A,C,D,而面AB,C与面B,EF有公共点B,故面B,EF与面A,C,D不可能行，故D项错误故选A项.2.D解析：如图所示，在长方体ABCD-A,B,C,D,中，AB=BC=2,AA=3,点H,I,J,K为所在棱上靠近点B,C1,D,A的三等分点，O,L,M,N为所在棱的中点，则三视图所对应的几何体为长方体ABCD-A,B,C,D,去掉长方体ONWC,-LMIB,之后所得的几何体，该几何体的表面积和原来的长方体的表面积相比少2个边长为1的正方形，其表面积为：2×(2x2)+4×(2×3)-2×(1×1)=30.故选D项3.B解析：在△AOB中，∠AOB=120°，而OA=0B=V3,取AB的中点C,连接OC,P℃，有OC⊥AB,PC⊥AB,如图，∠ABO30°，0c-2,AB=2BC=3,由△PAB的面积为9Y3E、寻2一3xPC=,解得P=35,于是Pm=V-OC9V3V(于V6,所以圆维的体=0×PO=Tx(V3)×V6=V6π故选B项，年0②名校统考1.B解析：由三视图可得，该几何体是由一个正方体切去两个小三棱锥后余下的几何体，如图所示，该几何体的体积V=1-2x*-号故选2.B解析：充分性：直线1Cα，l∥B,可能是α∥B,也可能是anB=L,l∥1，即直线1与a和B的交线行，故“1∥B”是“a∥B”的不充分条件；必要性：当直线1Cα，且a∥时，l∥B,故“l∥B"是“α∥B的必要条件，故“1∥B”是“α∥B”的必要不充分条件，故选B项3.B解析：对于①，在题图b中记AC与BD的交点（中点）为O,取BE的中点为M,连接MO,MF(图略)，易证得四边形AOME为行四边形，即AC∥FM,.AC∥面BEF,故①正确：对于②，如果B、C、E、F四点共面，则由BC∥面ADEF→BC∥EF,BC∥AD→AD∥EF,与已知矛盾，故②正确：对于③，在梯形ADE中，易得EF⊥FD,又EF⊥CF,.EF⊥面CDF,∴.CD⊥EF,∴.CD⊥面ADEF,.面ADEF⊥面ABCD,故③正确；对于④，延长AF至G,使得AF=G,连接BG、EG.由题意得，面BCE⊥面ABF,过F作FN⊥BG于N,则FN⊥面BCE.若面BCE⊥面BEF,则过F作直线与面BCE垂直，其垂足在BE上，矛盾，故④错误故选B项4.2V3解析：由题意得，△AEB为等边三角形，所以底边BE上的高h=1xsin60=V,所以该几何体的正视图的面2积为S=4xV32=2V3

25.Which can best describe Fahey's ride experience in Africa? A.Incredible.B.Lonely. C.Free. D.Cosy. 26.Why did Fahey launch Apidura? A.To help cyclists carry traveling stuff. B.To make her investment profitable. C.To call for bicycle traveling. D.To guide people across Africa. 27.【典型情境题】What is the text mainly about? A.A tough path to fame. B.An adventure across Africa. C.The benefits of green traveling. D.The story behind Apidura.

D Lacking a nose,insects such as butterflies and bees use their antennae (to detect scents.Those scents help them find food and more.What happens,though,when air pollution over- whelms (the scents on which these living creatures de- pend?Those insects become less likely to visit a flower or to pol- linate (it.That's the finding of a new study. James Ryalls is a biologist at the University of Reading in England.Working in a field of black mustard plants,his group crafted a system made up of rings eight meters (26 feet)in diam- eter.Each area was open,so nearby insects could fly into it.The researchers pumped pollutant gases into these rings.Two rings received diesel smoke.Two more got ozone.Another two got

W:I was so busy.First I was late to meet my sister at the air- port,and then we went to the hotel and it was full! M:I hope everything's OK! (Text 6) W:Good evening,sir.I'm the Assistant Manager.We've had a complaint from your neighbor about the noise.He is trying to sleep as he has an early start tomorrow for an important meeting.I'm sure you understand. M:Oh,I see. W:Do you think it might be possible to ask your friends to be a little quieter? M:Oh.I'm sorry.I suppose we were talking rather loudly.It's just that we've reached an important agreement.We were

22.What do we know about Dickens from the text? A.He used to work as a painter. B.He lived a happy life in his childhood. C.His manuscripts are well preserved. D.He reflected social problems in his books. 23.What can visitors get if they book a trip online? A.Free credit cards. B.An afternoon entry. C.Lower prices. D.Stay in any hotel.

1、衡水金卷先享题2024答案数学分科综合卷 新教材乙卷A

四、解答题：本题共6题，共70分。解答应与山之、人记△ABC的内角A,B,C的对边分别为a,b,c,已知a=2,bsinA+23cosB=3c.17.(10分)(1)求A;(2)设C=泛D为边BC上一