1H如图所不的是卡塔尔世界杯足球比赛中某一时刻的鹰眼系统预测断面（图1）和截面示查图(图2)，足球的飞行轨迹可看成抛物线，足球离地面的高度（四）与足球被弱出后经过的时间（©）之间的关系的部分数据如下表012h/m15喇该运动员踢出的足球在第落地15.在菱形ACD中，∠ABC60,AC-6,对角线AC,BD交于点O,E.F分别是AB,AD边上的点，且∠ECF-60,BE-2,CF与BD交于点G.删爱的值为三，解答题（本大题共8个小题，共75分，解答应写出必要的文字说明，证明过程或演算步骤）16,(本题共2个小题，每小题5分，共10分))计算：-1+(-3-(2)+4×1-.(2)在数学课上，老师出了一道题，让甲，乙、丙、丁四位同学进行”接力游戏”规则如下，每位同学可以完成化简分式的一步变形，即前一个同学完成一步后，后一个同学接着前一个同学的步骤进行下一步化简变形，直至将该分式化简完毕请根据下面的接力游戏解答向题，接力游观老柳化m聘牛己司甲时取式岂带吉1-0乙同片。两同一已丁同学：=1任务一：①在“接力游戏”中，乙同学是依据进行变形的。A等式的基本性质B.不等式的基本性质C,分式的基本性质D乘法分配律②在“接力游戏”中，出现错误的是同学，错误的原因是任务二：在“接力游戏”中，该分式化简的正确结果是任务三：除纠正上述错误外，请你根据时的学经验，针对化简分式时还需要注意的事项给同学们提一条建议17,(木题7分)如图，在正方形ABCD中，E为边CD的中点，BF⊥AE交AD于点F,试猜想AF与CE之间的数量关系，并证明你的猜想，【数学第3页（共6页）】·23-CZ129c·

(新教材)高三大一轮总复多维特训卷数学所以曲线y=f(x)在点(a,f(a)处的切线方程为y-令f(x)≤f(-4),得x3+9x2+24x+16≤0，4即(x+4)(x2+5x+4)=(x+4)2(x+1)≤0，得x≤-1；=2(e-）,即3x-2y-1=0.令f(-2)≤f(x),得x3+9x2+24x十20≥0，即(x+2)(x2+7x+10)=(x+2)2(x十5)≥0，得x≥-5.选@f)=1+g,由f①=1+a=2a.所以不等式f(-2)≤f(x)≤f(-4)的解集为[-5，-1].答案：[-5，-1]解得a=1,所以f'(1)=2,f(1)=0,第11节导数与函数的极值、最值所以曲线y=f(x)在点(a,f(a)处的切线方程为y=2(x基础训练-1),即2x-y-2=0.1.C2.B3.B4.A5.B6.D7.AB(28(z)-f(z)-(a'+Dlnz-z-a-(a3+1)lnx,(x>0),8.ABD因为函数的极值是与它附近的函数值比较，是一个局x则g(x)=1+a_a3+1_x2-(a3+1)x+a3部概念，所以函数在闭区间上的极大值不一定比极小值大，所以A错误；因为函数在闭区间上的最大值在极大值或端点处x=（x-a3)(x-1)取得，所以函数在闭区间上的最大值不一定是极大值，所以B错误；由f(x)=x3+x2+2x+1,得f'(x)=3x2+2x+令g'(x)=0,则x=a3或x=1,2,当<√6时，△=42一24<0，所以f'(x)>0,所以f(x)当a3≤0，即a≤0时，x-a3>0,在R上递增，所以f(x)无极值，所以C正确；若函数在区间则当01时，g'(x)>0,(a,b)上是增函数或减函数，由于端点处函数无意义，所以函所以函数g(x)在(0,1)上单调递减，在(1，十∞)上单调数在区间(a,b)上没有最大值和最小值，所以D错误.故选ABD递增；9.210.111.212.60当a3=1,即a=1时，g'(x)≥0，13.解：(1).'f(x)=(x-2)e+a,.f'(x)=(x-1)e2,所以函数g(x)在(0，十∞)上单调递增；令f'(x)=0,解得x=1,所以x∈（一∞，1），f'(x)<0,当01时，g'(x)>0,>0,当a31,即a>1时，当0a3时，g'(x)>0,(2)由题可知f(x)mm≥0，由(1)可知，当11时，函数g(x)在(0,1)和(a3,+o∞)上单调递增，在b=4,(1,a3)上单调递减.1所以f(x)=3x-4x+4,经检验符合题意.高考预测18,解折：由题可得了)-二，@由0阅f)=号-4红+4，则了u)=-4令f'(x)=0,解得x=2或x=-2.因为在区间(1,2)上存在x1,x2(x1≠x2),所以当-40,使得f(x1)=f(x2)成立，所以西数了x)名-ar在区间1,2不是单调两数当-20,即a2>3b.则不等式f'(x)≤0的解集为[-4，-2]，设f'(x)=0有两个不等实根x0和x2,x,是极大值点，所以-4，-2是f'(x)=0的两根，则x0,xox2时，f'(x)>0,x2是极小值点B正确；由于x→十∞时，f(x)→十∞，因此A正确；故a=9,b=24,所以f(x)=x3+9x2+24x+c,f(-2)若a=0,则f'(x)=3.x2+b,b<0,f'(x)=0的两解互为相c-20,f(-4)=c-16.反数，即x2=一xo,C正确；154

基础题与中考新考法·八年级·上·数学14.2.2完全方公式第1课时完全方公式(共135考：单独33考，在整式的化简求值或函数中涉及102考)教材知识知识点完全方公式35考·重点点拨·1.完全方公式22考拓展：完全方公式的探究：》拓展图①中大正方形的面积的两公式(a+b)2=a2+2ab+b2;(a-b)2=a2-2ab+b2种表示方法：S=(a+b)2,S=文字两个数的和（或差）的方，等于它们的方和a2+b2+2ab,故(a+b)2=a2+叙述加上（或减去）它们的积的2倍b2+2ab;图②中阴影部分的(m+2n)2-4)1面积的两种表示方法：S=(aa ba b-b)2,S=a2-2ab+b2,故(a-示例=m2+2·m·2n+(2n)2=y2-2y4+42Tb)2=a2-2ab+b22abb2a'2ab b2b=m'+4mn+4n2=y2-8y+162.完全方公式的常见变形B考》注意ba(1)a2+b2=(a+b)2-2ab=(a-b)2+2ab;图①图②(2)(a+b)2=(a-b)2+4ab;注意：能用完全方公式计(3)(a-b)2=(a+b)2-4ab;算的式子特点：(1)两个公(4)(a+b)2+(a-b)2=2(a2+b2):式的等号左边都是一个二项(5)(a+b)2-(a-b)2=4ab;式的方；(2)等号右边都是二次三项式，其中有两项(6b-a6)-(a-6y1-“-2:是公式等号左边二项式中每(7)(a+b+c)2=a2+b2+c2+2ab+2bc+2ac;一项的方，中间一项是等号左边二项式中两项乘积的(8)a+b+c2+ah+bc+ac=2[(a+b)+(6+c)+(a+c)2].2倍.重难题解法》答案见本册P75●利用完全方公式的变形求值8考现学活用·练1（台州中考改编）若例1（教材P112第7题改编)已知a2+b2=74,a+b=12,求(a-(2a-b)2=9,(2a+b)2=b)2的值.169,求8ab的值.引导思路a+b=12(a+b)2=a2+b2+2ab2ab=(a+b)2-(a2+b3)a2+b2=74(a-b)2=a2+b2-2ab46

答案与详解0.06=0.5,解得x≈86.67.所以估计这部分人的s甲2>s乙2.D正确.故选B.测试成绩的均数和中位数分别是86.75,86.67.6.AB由题意，+十…+2=五，故选B.n4.A设7个数为x1,x2,x3,x4,x5,x6,x7,则[,-z列+，-a++u.-门，x1十x2十x十x,十x十6十x1=4,对于A,ax1,ax2,…,axm的均数为7(x1-402+(x2-4)2+(x3-4)2+z4-40)2+(x-4)2+x6-4)2+x,-4ax1十ax2十…十axn=a(x1十x2十十xn）nax,A正确；对于B,ax1十b,ax2+b,…,axm+b=2,所以x1十x2+x3十x4十x5+x6十x7=28,所以(x1-4)2+(x2-4)2+(x-4)2+(x4-4)2+的均数为+6+az+6十+a,+b=an(x-4)2+(x6一4)2+(x7-4)2=14,则这8个数的均数为云-名红，十：十云，+：十红，十：计+6,其方差为([a+b)-ar+b]+[(a.x2十b)-(ax+b)]+…+[(axn+b)-(a元十b)]x,+4)=日×(28+4)=4，方差为2=日×11[(ax,-ax)2+(ax2-ax)2+…+n[(x1-4)2+(x2-4)2+(x3-4)2+(x4-4)2+(ax,-az)2](x,-4)2+(x6-4)2+(x,-4)2+(4-4)2]==a27[(x1-a)2+(x,-z)2+.+日×14+0)=子<2故选A(xn-x)2]5.B对于A,甲的步数：16000,7965,12700，=a2·s2,B正确；对于C,举反例，如1,2,3这32435,16800,9500,11600.从小到大排列为：个数的均数为2，但1,2,3这3个数的均数2435,7965,9500,11600,12700,16000,16800.中位数是11600.A正确；对于B,乙的星为+-兰≠2，C不正确：对于D3期三步数7030，星期四步数12970因为号[红-+(x-+…+（匹，-1.84<2,所以没有增加1倍上.B不正确；对于C,u-2++,2xz+)+x甲=2(16000+7965+12700+2435+16800+(x.2-2.xnx+x2)]+9500+11600)-11000,x2=714200+-[c+++)-2z++12300+7030+12970+5340+11600+10060)x,)+nx]=10500.所以x甲>xz.C正确；对于D,5甲2=（z牛+…+x,)-2·版计壶7[16000-11000)y+(7965-100)2+12-,D不正确，故选AB,ni-)(12700-11000)2+(2435-11000)2+(168007.8因为30%×10=3,50%×6=3，且甲组数据的-11000)2+(9500-111000)2+第30百分位数和乙组数据的第50百分位数相等，160-1100)y2]≈20958636sz'-7[14200-则36十m=n士44，解得m-n=8.故答案为：8.2210500)2+(12300-10500)2+(7030-10500)2+8.ABD因为总体的中位数为90，所以x十y=180,(12970-10500)2+(5340-10500)2+(1160010500)2+(10060-10500)2]≈9014429所以所以该组数据的均值为(81十84+84+87十z十87

零假设为H。:小区居民对垃圾分类的了解程则A(0,0,0),P(0,0,2),B(0,2,0),C(3,1,度与性别无关，……2分根据列联表中的数据，经计算得到0,D5,-1,0,E(9-1小…5分X-10or85x8030X15'≈9.091<10.828，设点M(0,a,b),则AC=(√3,1,0)，A它=50×50×55×45…4分(停-合1小=0a60其中6∈02，依据小概率值a=0.001的独立性检验，没有,点M在线段PB上，充分的证据推断H。不成立，因此可以认为H。.BM=入BP(其中λ∈R),成立，即小区居民对垃圾分类的了解与性别无.(0,a-2,b)=λ(0，-2,2)，关.…6分/a-2=-2x,(2)不低于80分的居民的样本中，男性有91b=2λ，人，女性有6人，放轴取男性早5×5=3人，抽.a=2-b,.M(0,2-b,b)…6分设m=(,y1,之)为面AEC的法向量，取女性6×5=2人，…7分(m·AC=0,3x十y=0,则即的可能取值为1,2,3，则m·Ai=0,12-2y+名1=0，P=1D=SC=品P=2》=C=号C51令x1=1,则m=(1,一√5，一√5).…8分pg=3)-8-:设n=(x2,y2,)为面MAC的法向量，分布列为：则n·AC=0,nW3x2十%=0，即〈1n·AM=0,(2-b)2+b2=0,123令y2=3b,则n=(-b3b√5(b-2),…3……9分510lomm1=牙1l=牙710分G的数学期望为：Bc)=1×是+2×号+3×|-b-3b-3(b-2)√7√(-6b)2+36+3(6-2)77-号12分即78-12b=0,即6=号或6=0（舍）…1分19.解：(1)PA⊥面ABCD,则PA⊥BD,…故存在点M(o,号，号)使得二面角EACM的…】分连接AC,BD,则AC⊥BD,…2分余弦值为阿…12分则BD⊥面PAC,…3分又BDC面PBD,则面PBD⊥面PAC.20.解：(1)当n=1时，S,=台(2ai+a1-1)=a1=…4分1,=1,…1分(2)取DC的中点H,连接AH,则AH⊥AB,s=(2a:+a-10.依题意易知AP,AB,AH三条线两两互相垂直，以A为原点建立空间坐标系如图S1=22a1ta1-10∴S1-S=a1=合(2ata1-1）-z(2d+a,-10..(an+1十an)(2a+1-2an-1)=0,…3分“a>02a1-2a-1=0,即a1-a,=分，数学试题参考答案第4页共6页

二全国©0所名校高考模拟金典卷@⊙所名校高考模拟金典卷·数学（四）4.已知抛物线C:y2=2px(p>0)的焦点为F,抛物线C的准线与坐标轴相交于点P点M(3,2),且△MFP的面积为2，若Q是抛物线C上一点，则△FMQ的周长的最(120分钟150分)小值为考生须知：A.4+√2B.4+22C.4+10D.4+2√101.本卷侧重：高考评价体系之综合性5.将一个数字表示成a与10的n次幂相乘的形式，其中1≤a<10,n∈Z,这种记数2.本卷怎么考：①考查同一层面、横向的交互融合的综合能力（题15）：②考查不同层面之间、纵向方法叫科学计数法.已知当x>0时，lgx=n十1ga,若一个正整数m的25次方是的融会贯通的综合能力（题8）.18位数，则m=(参考数据：lg2≈0.30,1g3≈0.48)》3.本卷典型情境题：题3、11、22.本卷拔高题：题8、12、16.A.5B.6C.7D.84.本卷测试内容：高考全部范围6.已知AB是⊙O的直径，MA垂直于⊙O所在的面，C是圆周上不同于A,B两点的任意一点，若AB=2,MA=BC,则四面体MABC的体积的最大值为、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，只有项是符合题目要求的：A③3B339C439D83271.已知复数之(2+i)=1一3i,则之的共轭复数乏=7.在一个单位方格的四边形中，若有两条边染了颜色α，另两条边分别染了A异于a色的另两种不同的颜色，则称该单位方格是“a色主导”的.如图，现C.要对这10条线段染色，每条线段染为红、黄、蓝三色之一，使得上红色主D-号+导，右黄色主导，下蓝色主导，这样的染色方式种数为封2已知集合A=y=V3t,B=x∈Z引吕∈Z,且EANB,.则e的所有取值A.72B.137C.171D.1938.【拔高题】已知函数f(.x)=x2·e-1一2lnx-(a+3)x,且对于Vx∈(0，十∞)，的和为f(x)≥0，则实数a的最大值为A.-20B.-17C.-13D.5A.-3B.-2C.-1D.03.小李最近一个星期的总开支如图1所示，他这个星期的食品开支如图2所示，则二、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，有多项符合其他5%120开支/元题目要求.全部选对的得5分，部分选对的得2分，有选错的得0分1009.已知向量a=(7,3),b=(m十1，一2m),m∈R,则下列说法正确的是食品开支8030%线A.若a⊥b,则m=一3B若alb,则a+1=2V2940日常开支20%20通讯开支5%C若a/b.则m=是D.若a∥b,则a+b1=383娱乐开支10%鸡蛋牛奶肉类蔬菜其他食品种类10.已知公差为d的等差数列{am}的前n项和为S,n,若a39十Ss=0,则下列说法正确图1图2A.小李这个星期的食品开支为270元的是B.小李这个星期的牛奶开支占总开支的5%A.当d=3时，an=3n-27B.当S14=42时，d=一3C.小李在食品开支中除了鸡蛋、牛奶、肉类、蔬菜的其他开支占他这个星期的总开C.当Sn有最小值时，S6S2支的5%11.定义新运算“☒”，使其具有下列性质：①对Hm,n∈R,m⑧m=n⑧m;②对Hm∈R,D.小李这个星期的娱乐开支占总开支的比例最小m&0=;③对Hm,n,k∈R,(m☒)☒k=k&(mm)+(m☒k)+(n&k)-2k.若函数学（四）第1页（共8页）【24新高考·JD·数学-N】数学（四）第2页（共8页）【24新高考·JD·数学-N】

语法填空【答案详解】56.returned考查动词的时态，根据时间状语on the afternoon of April27,2023确定用一般过去式。57.concluding考查非谓语动词做状语。孟菲斯动物园将大熊猫丫丫送还中国，结束了20年的合作研究工作。58.who考查定语从句。修饰前面的experts,指代人，在定语从句中做主语。59.with考查介词搭配。get familiar with,与变得熟悉60.to ensure考查不定式做目的状语。原句They also worked along with staff on the US sidefor Ya Ya's breeding,nursing,and health assessment and made further preparations for her return toensure a safe and sound trip.他们还与美方工作人员一道，为丫丫的育种、护理和健康评估做了进一步的准备工作来确保丫丫安全完美的返程。6l.gestures考查名词单复数。gesture可数名词，前面由some修饰，用复数。62.set考查非谓语动词短语做后置定语。一名被送去孟菲斯的北京动物园的管理员。63.is needed考查动词的时态和语态。最后一段描述的是丫丫回国后现在的护理状况，care和need是动宾关系，所以用一般现在时的被动语态。64.carefully考查副词的词性转换。修饰后面的动词短语look at her mouth,back,and hands。65.adaptable adaptive考查动词的词性转换。形容词做表语。adaptable或adaptive与smart并列，做表语，表示适应性强的。第6页共7页

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工智能技术驱动的自然语言处理工具，它能够通过理解和学人类的语言来进行对话，还能根据聊天的上下文进行互动，真正像人类一样来聊天交流，甚至能完成撰写邮件、视频脚本、文案、翻译、代码、论文等任务。D篇主题语境：人与社会一一艺术本文是说明文。一项新的研究发现，对音乐的掌控感是用音乐缓解疼痛的关键。32.D。理解具体信息。根据第一段中的However,,how music can do this is unclear,,especiallyfor acute pain work in the past has largely focused on lab-based findings that did not exploreacute pain in the real world可知，之前的研究没有过多关注现实生活中的急性疼痛。33.C。理解主台要义。根据第二段中的Dr.Claire Howlin.and his team asked286 adults、.Thetrack was specially produced in two different versions of different complexity Studyparticipants were asked to listen to either the low-or high-complexity version可知，文章第二段主要讲述了该研究的实验过程。track意为“一首乐曲，一首歌曲”。34.D。理解具体信息。根据第三段中的The researchers found that participants who felt theyhad control over the music experienced greater relief Participants ..experienced evengreater pain relief by having a sense of control over the track used in this study可知，该研究表明让人们产生对音乐的掌控感是用音乐缓解疼痛的关键。35.A。理解观点、态度。根据最后一段中的It's encouraging to know和Our research makes itpossible可知，Howlin对该研究持肯定态度。第二节主题语境：人与社会一一科学与技术本文是说明文。文章介绍了有关风力发电的知识。36.A。根据上文中的It stopped being used for much of the20 th century和下文中的Increasingly,.it is being used to produce electricity可知，风在过去被用来驱动船只和转动风车(windmills),但在20世纪的大部分时间里被停止开发，如今风又再次回归大众视野，人们开始用它发电(electricity),因此A项符合此处内容。A项中的comeback意为“复出；重返；再度受欢迎”，与下文中的Increasingly相照应。37.B。根据上文中的Today,wind energy is produced with wind turbines和When the windturns the blades,the blades turn a generator可知，作者在此处介绍风力发电的原理，因此B项符合此处内容。B项中的The generator指代上文中的a generator,同时B项通过then与上文内容构成顺承关系。38.D.根据上文中的To produce more electricity,,wind turbines are often set up in large groups.These groups are called wind farms可知，作者在此处介绍风力发电场(wind farms)。为了提高发电效率，风力涡轮机经常成组安装，形成风力发电场，因此D项符合此处内容。D项中的They指代上文中的wind farms;made up of hundreds of turbines与上文中的set up in largegroups相照应。39.C。根据上文中的Wind is not steady可知，设空处应填入一个可以解释风为何是一种不稳定的能量来源的句子，因此C项符合此处内容。C项中的its指代上文中的Wind;changeoften与上文中的not steady相照应。40.E。根据本段的主旨句Wind energy also has its own problems可知，作者在本段主要介绍风力发电的不足。根据上文中的Wind energy is cheap to produce once a wind farm has beenbut可知，风力发电的成本较低，但是风力发电场本身的建设成本相当高，因此E项符合此处内容。E项通过However与上文在内容上形成转折关系，点明风力发电的成本问题。语言运用

直点为x0,若选择题答题卡18.(★★)（本小题满分1题号123456789101112得分已知函数f(x)=ae3(1)讨论f(x)的单调答案三、填空题：本大题共4小题，每小题5分，共20分，把答率填在中线(2)若f(x)≥0恒成5线上13.(★)已知函数f(x)=x2十a,x≤0，若f[f(-1)]=4,且a,则小题给出的2x,x>0,的得2分，a=A114(女)关于x的不等式(a十1Dz十a<0的解集中恰有1个整数，则实数a的取值范围是LD))15.(★★)已知a>0,b∈R,若>0时，关于x的不等式(ax-1)+bx4)≥0恒成立，则6+4的最小值为义16.(★★)函数f(x)=a2十a+1(a>0,且a≠1)在[-1,1]上的最大值为13，则实数a的值为四、解答题：本大题共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）已知函数f(x)=2x-lnx+3(1)求曲线y=f(x)在点(1，f(1)处的切线方程；(2)求函数f(x)的极值.,且当x∈R,有],且43

报高考歌学新漯标贩少16.C解析：易知x)的定义域为Rf-x)=e+12e+1子则-)-0，所以是奇函数函数)1显e+12然在R上是减函数，7.A解析：因为f(x)没有零点，所以关于x的方程fx)=0,即a=已无实数解.令g(x)=二，h(x)=a,则函数y=g(x),y=h(x)的图象无公共点g(上，令se0,则l当时，ge<0,函数g(x)单调递减，且g(x)<0;当00;当x>1时，g'(x)>0,函数g(x)单调递增。所以函数g(x)有极小值g(1)=e,作出g(x)的图象，如图所示，结合图象可知0≤a0,f(x)单调递增，所以f(x)的极小值-1)=2-，又x)2,因此x)-2无解.此时x)=-要有两解，则2-。<2，又x)是奇函数，所以o0时x)-2仍然无解，八x)=-要有两解，则-2<-1<-2.综上，ae(-2,2)U(2-1,2).故选C项9.BC解析：要使g,3<1g,3成立，只要g3:g31石lglg6,或ga<0,lgb>0.求得>6>0，或b>1>0,故1选BC项10.BCD解析：令f(x)=t,则函数F(x)可化为y=f(t)-2t3则函数x)的零点间题可转化为方程)-240的问题令)-2-0，则-2+子分男别作曲0和-2的图象，如图1所示，由图象可得有两个交点，横坐标分别设2为，42，且，<42，则，=0,1<，<2：作函数式x)和y=的图象，如图2所示，结合图象，当fx)=0时，有一解，即x=2;当fx)=t,时，结合图象，有3个解所以=x)]-2x)-；共有4个零点.3y=ft)v=f(t)122t图1图2n9解析：因为g21,所以=g2。=l0g23,所以-x=31-1og3alog3'=lg3,所以2-2=3,2"2=,所以2+2=1103+-3312.1解析：由f代x)的解析式作出fx)的图象，如图所示，f爪x)=m恰有4个不相等实数根等价于f代x)与y=m的图象恰有4个不同交点，且x

sl7%☐100：24人辽宁实验高三上(…试题+答案.pdf第1页/共5页A.-1BC.1D.27.已知函数f()=二，若对任意的正数a、6,满足f@+f(2b-2)=0,则2+的最小值为e'+1a b()A.2B.4C.6D.88在锐角三角形ABC中，A、B、C的对边分别为a、b、c,且满足6=a(a+c,则+S的取值范围为()A.(1,5)B.(2+1,5)c.(山，5+2D.(W2+l,5+2二、多选题.本大题共4小题，每小题5分，甚20分，在每小题的选项中，有多项符合题目要求，全部选对的得5分，有选错的得0分，部分选对的得2分9.m、n是两条不同的直线，a、B是两个不重合的面，下列说法正确的是()A.m、n是异面直线，若m11a,m/IB,nlMa,nlWB,则alBB.若allB,m11a,则m/1BC.若m⊥n,mca,ncB,则a⊥BD.若m⊥a,mlm,nllB,则a⊥B10关手子函数f)=2m3红-，下列说法正角的是《）A.由f(:)=f(:)=0,可得x-x必是π的整数倍Bf)=-2a3x-cf儿)图像可由y=2sn3x向右移个单位得到Df在[上为增函数11.《九章算术》是我国古代数学中的经典，书中将底面为长方形且有一条侧棱与底面垂直的四棱锥称之为阳马，将四个面都为直角三角形的四面体称之为整臑.在阳马P-ABCD中，侧棱PD⊥底面ABCD,且PD=CD=a,点E是PC的中点，连接DE,BD,BE.以下结论正确的有()第2页/共5页A.DE//面PAB兰心④也宣目录打开方式转存下载云打印I

第The results of a digital detox can be rewarding."Although I get 33 for working hard,workinghard was the easy part,"he says.第二部分Staton was 34 for all the support he receivedG.A few days after starting your digital detox,check in with yourself on how it's going.分and he wanted to pay it forward.And now he wants toMore control of your time.lead a professional sports team-he still hasn'tDo you always feel an overwhelming desire to check35 his childhood dream.your smart phone or social media?Al8 On average,语阅people check their smart phone 96 times a day and spendmore than two hours on social media.For many people,读checking their phone or social media whenever there are a言运33.A.respectB.helpC.gratitudecreditfew free minutes is a reflex action(下意识动作)that isn't34.A.eager●thankfulbased on any real need.Taking a break from digital用C.famousD.responsibledevices helps you fight against this reflex action.35.A.announcedB.discoveredgforgottenD.chosen第第二节第阅读下面短文，在空白处填入1个适当的单词或括E.For some pecan cotoo much inform二号内单词的正确形式。。g yoself on how it's goingRegularly finding time to take a nap(小睡)Less stress and anxiety.分36.helps (help)keep our brain bigger for longer,分E19 Constant exposure to notifications,emailssay University College London researchers.and social media can create a sense of being constantly"on".The result of that may increase stress and anxiety.语However,the researchers recommend 37.limitingA digital detox can provide a break from these constant(limit)naps to less than half an hour.distractions and allow for relaxation.读运The brain 38.naturally (natural)shrinks20B)with age,but whether naps could help preventAvoiding digital distractions creates moreopportunities to pay attention to people around you.For用diseases like Alzheimer's will still need extraexample,without devices around at dinner,you interactresearch.and connect more with your family or friends.第第一节完形填空第Staton grew up with his brother and they wereBrain health is important for protecting againstraised by their father,who did multiple jobs to support二部Alzheimer's and 39.what causes it is poor sleep.their family.They had a 21 supply of food andThe researchers suggest poor sleep is damagingelectricity back then."There were22 in the ceilings.There were a lot of areas in the house that didn't have分the brain over time by affecting the connectionsfloors,"Staton says,describing their former livingbetween brain cells."Thus,40.reasonablesituation.At a young age,he 23 of becoming a语(reason)naps could protect against言professional boxer,in the hope of getting his family outneurodegeneration(神经变性)by making up forof 24 through sports money.运poor sleep,"researcher Valentina Paz said.用21.A.large.limitedC.safeD.readyThe researchers used a clever method22.A.lightsB.drawingsholesD.decorations41.to prove (prove)that napping is beneficia23.A.spokeB.heardC.knew鰱.dreamed24.A.illnesspovertyC.heatD.dangerg第Sadly,he 25from a shoulder injury which madehim give up his dream too early.So after high school,第They used 42.a natural experiment based on二部he 26 to look for a job.the DNA.Previous studies have identified 97 partsWhat was worse,both Staton and his 27 hadof our DNA which either make us more likely to beto stop their education when their father had a stroke(中风.Staton eventually28 a job as a sanitary(环分nappers 43.or to power through the day.So境卫生的)worker in Maryland,which helped histhe team took data from 35,000 people,aged 40 tofamily make ends meet.Some of his co-workers told69,and simply compared those genetic "nappers"语言him not to be like them and encouraged him to语continue his education.and "non-nappers".The results,44.published(publish)in the journal Sleep Health,showed a 15-25.A.learned B.benefitedsuffered D.escaped运cubic--centimeter(立方厘米)45.difference用26.0 determinedagreed D.pretended..brother D.sister用(different)-equal to 2.6 to 6.5 years of aging.27.A.motherB.father28.foundB.offeredC.lostD.describedg第With everyone's help,Staton entered the University ofMaryland.His hard work 29.In 2018 he finished第第一节his undergraduate study successfully.In less than ayear,he 30 the Law School Admission Test and假定你是李华，是某国际学校的学生会分applied to Harvard Law School.部主席。本周六，你校将举办主题为How toStaton knew how 31 it was to get accepted but分prepare to study abroad的英语讲座。请你根he still tried his best.To his32 he got accepted and据以下要点提示，写一则通知，发布在校英received much praise文网站上，内容包括：29.A.ended upB.turned up写言运用C.worked outpaid off作1.时间地点；30.A.graded.passedC.facedD.failed2.讲座内容；31.0 toughB.inspiringC.funnyD.vital3.注意事项。32.A.regretB.disappointment●注意：写作词数应为80左右。C.annoyancesurprise

2π2【答案】①②.V10+V63【解析】【分析】以P为球心，以PB为半径的球与底面ABCD的交线为以A为圆心，AB为半径的圆弧，求出圆心角即可求出弧长，将面PDC翻折到与面PBC共面，连接BD交PC于点Q,此时QB+QD取得最小值为BD,再在面四边形BCDP中求出BD的长度，即可得解【详解】因为PA⊥面ABCD,底面ABCD为矩形，则以P为球心，以PB为半径的球与底面ABCD的交线为以A为圆心，AB为半径的圆弧，在CD上取一点E，使得AE=AB=2,连接AE，则BE的长度即为以P为球心，以PB为半径的球，被底面ABCD截得的弧长，由AD=5,AB=2,所以cos∠DMAE=4D-5,则∠DME=天，所以∠BAE=AE 263则BE的长度为×2=2红，33即以P为球心，以PB为半径的球，被底面ABCD截得的弧长为2π3DB将面PDC翻折到与面PBC共面，连接BD交PC于点Q,此时QB+QD取得最小值为BD(面图形如下所示)，因为AD=V5,AB=2,PA=1,所以PD=VAD2+PA2=2,CD=AB=2,PB=VAB+Ap=5,PC=1P+22+3=2反，BC=AD=V5,所以cos∠BCP=BC+PC2-Bp-5,又cos∠DCP=DC2+PC2-Dp-52BC.PC42DC·PC2

所以g(x)<0,所以g(x)在(1，+∞)上单调递减，所以g(x)1时.nx--水0，即2n

河南省商丘市第一高级中学2023-2024学年第一学期期中考试高三数学试卷一、单选题：（本题共8小题，每题5分，共40分）1.若i是虚数单位，则复数z=i2019.(2-3i)的虚部等于()A.2B.-2C.2iD.-2i2.设集合A={xy=ln(x-3)},B={xx≤-1}，则{x-1

【高三英语参考答案，第，3页（共4页）】24092CM:Well,I'm expecting an important phone call,and I don't want to miss it.W:Is it anything I should know about?M:Not really.It has something to do with work and isn't really related to us here at home.W:Well,why don't you go ahead and do what you want to do outside.I'll call you if the phone rings for you.M:Thanks.I think I will.I need to go outside for some fresh air.(Text 8)W:Honey,what are you doing?Come and have your breakfast.You don't want to be late for work a secondtime this week,do you？M:Of course I don't.But I can't find my glasses.Have you seen them?W:Oh,dear.You're always forgetting where you put them.What did you do just now?M:I took a shower just a few minutes ago.W:Maybe you left them in the bathroom.M:No.I checked there but I didn't find them.W:What else did you do?M:After the shower,I went to the living room.Oh,I remember I read a magazine there.You know I can'tread without my glasses.W:Then you must have left them there.Go there quickly.I'm sure you'll find them.(Text 9)W:Laurance,how did the car acciderit happen?M:It was dark and it was Christmas Day.And I was on my bicycle and my telephone rang.And I took it out ofmy pocket while riding my bike.And then,I rode straight into the back of a parked black car.W:Oh,no.M:I hit the back of it and I broke a few bones.W:I'd say it's terrible.Then you went to the hospital.M:No.I was a bit stubborn.I don't know why.I had the worst night sleep I've ever had but yet,I didn't go tothe hospital until the next day.W:Oh,a nightmare.M:Yeah,actually,three months later in March,I was lucky enough to win a place in the Tokyo marathon.There are so many people who apply to get a position.So I was trying to rush it,really and I shouldn'thave.But I did.I got the third prize.W:Did you?M:Yeah.W:Oh,my goodness.(Text 10)W:A primary school at Sanmenli Village in Gongzhuling City has been paid attention to-two teachersteach just one 12-year-old student,Wang Hao.Chen Hongyan works as the class teacher while Liu Haitao asthe PE teacher.The situation has started several years ago,Xinhua reported.Although there is only onestudent at the school,Wang never misses a single class on Chinese,mathematics,English or early-morningindividual study.Wang has seven classes a day.Chen has set 14 alarm clocks as Wang's school bells."I treatmy only student seriously as well,otherwise my heart cannot justify what I do,"said Chen who has been in herpost at the school for 18 years."I certainly can not give up on any student."Chen also encourages Wang to playwith other kids in the village for fear that he may feel lonely.Wang's father often checks in on his son when hepasses the school on his way to herd sheep and he appreciates the persistence of the two teachers.Villagesecretary Wang Lixin said the school once had dozens of teachers and more than 200 students.But teachersretired and students moved to schools in towns nearby after 2010.【高三英语参考答案，第，4页（共4页）】24092C

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annual ological regulation of fish populations in Erhai Lake began n August 21.darkness fall eac night,fishing bots traveshnigh5Days ater,Ipaseboard,which listed itemsforsae variousjobs@(dual)theith fishing netermadeihand at the bottom,as ffering ianossosOtime-ape（延时拍摄的)hotogaphy,kyppar tof,My voice trembled when I called the number the next day.When the tutor named58 (create)a fantastical and dreamlike shape of incredible beauty.mThe 2023ctio of fis poputio iEhaiamomMeloded thatwashe studet he hesitated.She had ever taught a busy adut5(hbiodiversityrotking ftehetureoleaer,but she was willing totry if I was determined to leaMWhen my first lesson ended as arranged,Melody opened the door to her next student,asix-year old boy full of enthusiasm.Melody introduced us and told me his name was Jeff."IOppulations and effectively gurdingaisand ongdangerousspecesBased on various fis61ype),this yearegution frare divided into theesgesacross the lake's waters,the ore protected areas of the Cangshan Erhai Nationalgoing tolearn to play the piano,he told me.No doubtsor insecurities got in the boy's way.HisNature Reserve not 62(include).includythusiasm stuck me,and my way home,I whispered,m going toa toplay the piane."However,I wasn't astar pupil Ididn't have instant recall on how to read music.GettingOThe first stage63(schedule)toast from August 21toSeptember 20,with a focusNon the sharpbelly and other species of smal-sized fish6umber of families appyingboth hands toeratewas difficult and then I was introduced to the pedal ()Maybe Iand recciving ooca regulation permits reached as many0 with65 they oudhad bee just too psychologically stressed out.Cosequty,Melody blamed me forno如enter the lake to conduct fishing activities during the permitted periods.practicing enough.Therefore,I had to look at my tight schedule to see where I could maketime to improve myself.第四部分写作（共两节，满分40分）第一节（满分15分）The following week,Melody told me I would need to participate in the December假定你是李华，你的外国好友Steven沉迷于网络，导致成绩下降，请你用英语给他写一封performance and that I had to play by memory.I would have one month to memorize two邮件，帮助他戒除网瘾，内容包括：pieces and I hadn't even seen them yet!I was in despair and wanted to give up."It's the1.表示安慰；conventional(依照惯例的)way,”Melody said to me in a firm voice,“and even Jeff ismemorizing the pieces he is playing.Think why you came here!"2.说明网瘾的危害；注意：3.介绍戒除网瘾的方法。1.续写词数应为150左右：注意：2.请按如下格式在答题卡的相应位置作答。1.写作词数应为80左右；2.请按如下格式在答题卡的相应位撒作答。Her words suddenly had reminded me of my secret dream.Dear Steven,岗On the day of the performance,I stepped slowly onto the stage.Yours,第二节（满分25分）Li Hua阅读下面材料，根据其内容和所给段落开头语续写两段，使之构成一篇完整的短文.Myhusbaand Ihad purchascd the piud daughterouklBuedream that did not shre wthedthe piano and so that I could sit on a piano bench and perform one day.【高三英语第9页（共10页）】·2A-146C【高三莫语第10页（共10页）】·24-146C

The white crane is one of the largest and heaviestcranes.It's also one of the longest-living birds,with a四Back home,when I put my packaged presents语言life of30-40 years in62 the wild.In captivity(圈养)，under the tree,I noticed other packages which hadsome can even live to 75 years old.However,with abeen placed by Steve,my sister and my parents.small population left,the white crane is under China'sfirst-class 63 national (nation)protection.作After dinner,Dad told us that he would go tocollege and that our family would have a tight (识Since the white crane plays a big part in Chinesebudget.And he felt sorry for that.Suddenly,I knewculture,we hope more and more people will takewhat I would use my 12 dollars for.I ran to myefforts to love 64 and care for this bird.I believeroom,and wrote on a card,"Dear Dad,this is for用as long as we all are responsible for 65 protectingyour education,.”(protect)the bird,its number will increase quickly注意：四第一节四1.续写词数应为150左右；2.请按如下格式作答。假定你是李华，周六下午你们社区有一场地写And I put the paper and the money into a方戏曲讲座。请你给爱好中国戏曲的留学生Lucyshoebox.作发一封邮件邀请她参加，内容包括：1.写邮件目的：2.讲座时间、地点和主题；When I thought about that blue bike,Mom3.希望她接受邀请。suddenly said,"Terry,could you go to the kitchen注意：写作词数应为80左右。to see if the coffee is ready?"gOne possible version:One possible version:四Dear Lucy,I'm writing to invite you to attend a lecture.Here is the四And I put the paper and the money into a shoeboxdetailed information.I put it under the tree.On Christmas morning,myAs scheduled,it will take place at our community centerthis Saturday afternoon,with the theme of Chinese local operasfamily began opening gifts.Steve and my sister作作found the presents they wanted.My mom put on thewhich you've always been interested in.In that case,you willblue earrings and smiled at me.Then,Dad held thedefinitely find it worthwhile.The lecture will cover three aspectsof the local operas:the history,the cultural significance,famousshoebox,confused.Carefully he opened it,takingfigures as well as their masterpieces.out the note.When he finished reading,his eyesI wish you said yes to my invitation!Then let's meet at theseemed to fill with tears.He laughed and said to me,gate of the center at 2 o'clock,ten minutes before the activity"It looks like I'm all ready for college.This is thebegins.most wonderful Christmas I've ever had.I hope it isfor you too..”第二节阅读下面材料，根据其内容和所给段落开头语四续写两段，使之构成一篇完整的短文。四When I thought about that blue bike,Mom suddenlyWhen I was 11,I quite wanted a bicycle-not any bicycle.said,"Terry,could you go to the kitchen to see if the写but a blue bicycle from Johnston's bike store on the Hill,a smallshopping area that was six blocks away from our house.coffee is ready?"I hurried to the kitchen.I couldn'tbelieve my eyes.There,parked next to the table wasThe Monday before Christmas,my 9-year-old brother Steve作the blue bike from Johnston's bike store.And thereand I ran to the Hill to do our Christmas shopping.Past the ice-cream shop and the pet store,we entered the five--and-dime store.was a card,reading,"Merry Christmas,Terry."IMy brother had his savings (65 cents)held in his hand,and I hadcouldn't help rushing to hug my parents,excited andfour dollars,some of which I had got by cleaning the neighbor'sgrateful.Then,taking a deep breath,I ran over andyard.At the store,I picked out writing paper for our sister,a pairgently touched the bike.Now,the bike is long gone,of earrings for our mom,and a notebook for our 45-year-old dadbut I still remember that Christmas when my parentssince he would be going back to college to get a Ph.D.degreeenough money left to buy baseball cards for Steve.and I brought each other surprise and joy.We went home by way of the bike store,so I could23-24上新课程外研高一四look at my bike.It wasn't my bike actually,but I was第16期其余版面参考答案saving money to buy it.I wanted it more than anythingelse in the world.It was a blue Italian model;I had neverA1版seen another one like it.I planned to ride it to school.Paragraph 1:The history of Chinese Bonsai作参考However,to my shock,the blue bike had been sold.ItParagraph 2:Designing Bonsai is a way for peopleseemed like my heart stopped and time stood still.Forto meditatethree months,ever since the first day I saw it,I had been案Paragraph 3:Different schools and different typessaving money to buy it.I ran from the store,fighting backof Chinese Bonsaifears.On the way home,I thought I no longer needed thParagraph 4:Famous places of Chinese Bonsai12 dollars I had saved.I started to think what I shoulParagraph 5:How to make sure a Bonsai tree canbuy with it.live long8

2023年赣州市十八县（市、区）二十三校期中联考高三英语试卷参考答案听力部分录音材料听力部分。该部分分为第一、第二两节。注意：做题时，先将答案标在试卷上。录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。停顿00'10”现在是听力试音时间。M:Hello.International Friends Club.Can I help you?W:Oh,hello.I read about your club in the paper today and I thought I'd phone to find out abit more.M:Yes,certainly.Well,we are a sort of social club for people from different countries.It'squite a new club-we have about 50 members at the moment,but we are growing all thetime.W:That sounds interesting.I'm British actually,and I came to Washington about threemonths ago.I'm looking for ways to meet people.Er,what kinds of events do youorganize?M:Well,we have social get-togethers,and sports events,and we also have language evenings.W:Could you tell me something about the language evenings?M:Yes.Every day except Thursday we have a language evening.People can come andpractice their languages-you know,over a drink or something.We have differentlanguages on different evenings.Monday-Spanish;Tuesday-Italian;Wednesday-German;and Friday-French.On Thursday we usually have a meal in a restaurant foranyone who wants to come.W:Well,that sounds great.I really need to practice my French.M:OK.Well,if you can just give me your name and address,I'll send you the form and somemore information.If you join now,you can have the first month free.试音到此结束。听力考试正式开始。停顿00'10”请看听力部分第一节。第一节听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。【高三英语·参考答案第1页（共10页）】·24-124C·

7.What does the woman think of the man's question? A.Interesting. B.Creative. C.Foolish. 听第7段材料，回答第8、9题。 8.What are the speakers getting ready for? A.Timmy's birthday. B.Christmas Day. C.New Year's Day. 9.What will the woman do later? A.Pack the presents. B.Send holiday cards. C.Go to the mall.

A.The future of green farming. B.Consumers'worry about food. C.People's respect for farmer's work. D.People's access to the information of food. 31.What does the text mainly talk about? A.A company. B.A person. C.A farming machine. D.A kind of food.

ry out tasks or activities that the human brain usually handles. Ackerman isn't the only one using Al for songwriting.Some programs generate music for many instruments.Al also is find- ing its way into other arts.Painters,dancers and photographers have found new ways to cooperate with AI algorithms.Ahmed Elgammal runs a computer-science lab that focuses on using Al to influence art."Al is a creative tool that will be accepted as an art form,"he says."It will affect the way art is made,and what art will be.”

【答案与解析】 21.B考查形容词。Wanda Smith一直想成为一名教师，但现实 生活的艰难意味着梦想被推迟。 22.A考查动词。 23.A 考查动词。她是三个孩子的妈妈，还要照顾自己的妈妈。 24.C考查名词。她直接承担起了家庭责任，在得克萨斯州的布伦 汉姆独立学区做校车监督员和看管人。 25.D 考查名词。她这段时间很辛苦，但她没有让梦想破灭。 26.D 考查动词。 27.B 考查名词。她在日程安排中增加了读夜校。 28.C若查动词。九年后，她顺利毕业了。 29.C 考查形容词。她终于成为一名有资格证书的教师了。 30.D 考查名词。她回到了曾经工作过的地方。

【答案】 One possible version: Dear Mr Geller, You can't imagine how overjoyed I am hearing about your plan!I'd like to offer my advice for your reference. As a big fan of Chinese calligraphy myself,I'll recommend it without hesitation because it's a natural combination of beauty, strength,history and technique.In order to learn it well,first, she needs to devote herself to long hours of practice.Second, signing up for a calligraphy course would be a wise choice,which would help her study in a systematic way.Besides,it'd also be beneficial to study and imitate the works of famous calligraphers. I hope you'll find my advice helpful.Best wishes for her

第二节（满分25分） 阅读下面材料，根据其内容和所给段落开头语续写两段，使之 构成一篇完整的短文。续写的词数应为150左右。 "Get out of my house,you rude,unwanted,ugly and stupid child!"Aunt Foully shouted at Justin before closing the front door.Justin looked out at the grass that surrounded his aunt's garden.He sighed as he remembered the list of housework that his evil aunt had planned for him after he got home from school. It was just not fair.If his parents had not died,he would not have to spend his entire life with Aunt Foully.Aunt Foully was a woman y with crazy,curly,orange hair.She had small,black eyes,a big nose and a mouth so wide that you could have fitted a dining plate in it.Worst still,she had a heart so cold that you

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