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

第2期所以-(-2)>-(+1).4)-+3=52版(2因为-号=0.5,-0.4=14.解：-2.5=2.5，-3=-3，1.2.3相反数2.A3.B0.4,且0.5>0.41.A-(-1)=1.4.05.-3所以-0.5<-0.4.在数轴上表示如图所示：63,37,-325,-14%所以-2<-044-31-120-(-101-251-5432012371号2)号(第14题图)310:(4-4号2所以4k-3<1分0<(-1<8.1或5所以<子1-2.5.1.2.4绝对值15.解：(1)-1.6.解：(1)①>.②=.③>.④=.第1课时(2)如果点B,E表示的数是(2)当a与b同号或a,b中至1.D2.A3.B互为相反数，那么点C所表示的数411.5:(2);(36:少有一个为0时，则|a地=a+b.是原点.此时点D表示的数是-5，当a与b异号时，则a+b<它的绝对值是5(4):(53:(60.a b.此时点A表示-2，点B表示5.解：(1)因为6=6，-6=综上，当a,b为有理数时，a+4,点c表示0，点D表示-5，点E|b|≥la+bl.6,所以正确；表示-4，所以点C表示的数的绝对3版(2)因为-6|=-6，-61=6，值最小是0.所以错误；一、选择题16.解：(1)因为-0.017<0.02，(3)因为-6=6，所以错误。1~6.BCBDBC-0.011<0.02,6.解：由题意知，x=3或-3，二、填空题所以2号和6号排球符合要求y=7或-7.7.0(2)因为+0.031>+0.023>(1)因为x-0.021>-0.017>所以x=3或-3，y=7.9长沙、南京、北京、哈尔滨1-0.0111,(2)因为y<0,所以6个排球按照质量最好所以=3，y=-7或=-3，y=7.10号到最差排名依次为6号，2号，4第2课时11.<号，5号，3号，1号1.A(3)因为检测结果的绝对值最12.152.B小，也就表示该球的质量越接近标三、解答题3.(1)k;(2)k;(3)k准质量，所以越符合要求13.解：(1)-(-3)=3；4.解：在数轴上表示略17.解：(1)①5；②-5；③-5；(2)+(-6.38)=-6.38;④5；⑤5；⑥-5.3>20-15>-5分(3)-[-(-2023)](2)当-5前面有2022个负号5.解：(1)因为-(+1)=-1，=-(+2023):时，化简后结果是-5；-(-2)=2,且2>-1，=-2023;当+5前面有2022个负号时，化简后结果是5.(3)结合(2)中的结论可知，当-5前面有偶数个负号时，化简结果是-5；当+5前面有偶数个负号时，化简结果是5.

第6期Se2×16x4=32(cm).五、解答题（三）2~3版22解：(1)可行理由如下：、选择题四、解答题（二）在△ABC和△DEC中，1-5.CDAAD 6~10.CBACB19.解：(1)证明：在△BPF和AC-DC,二、填空题△CEP中，∠ACB=∠DCE11.4BP=CE,CB=CE,12.50°∠B=∠C,.'△ABC≌△DEC(SAS)13.BF=EC或BC=EF或AB∥DEBF=CP,·AB=DE或∠A=∠D或∠B=∠E.△BPF≌△CEP(SAS).方案①可行14.3..PE=PF.(2)可行理由如下：15.2(2)在△ABC中，.∠A-44,∠B=∠C,.BF⊥AB,DE⊥BF三、解答题（一）∠B=∠C18044-68.∠B=∠CDE=9016.证明：AD∥BC在△ABC和△EDC中，∴.∠DAC∠BCA.'△BPF≌△CEP,∠B=∠CDE,DF∥BE,.∴.∠BFP=∠CPECB=CD,.∠DFA=∠BEC·.·∠FPC=B+∠BFP=∠FPE+∠BCA=∠DCE,在△AFD和△CEB中CPE,·,△ABC≌△EDC(ASA)I∠DAF=∠BCE,∴.∠FPE=∠B=68·.AB=DEAF=CE,20.解：（1)证明：，·射线AD分.方案②可行∠DFA=∠BEC,∠BAC,(3)AB∥DE.△AFD≌△CEB(ASA)∴.∠CAE=∠FAE23.解：(1)1

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】

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许济洛2023一2024学年高三第一次质量检测数学注意事项：1,答卷前，考生务必将自己的姓名、准考证号等填写在答题卡和试卷指定位置上。2.回答选择题时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。如需改动，用橡皮擦干净后，再选涂其他答案标号。回答非选择题时，将答案写在答题卡上。A写在本试卷上无效。3,考试结束后，将本试卷和答题卡一并交回。选择题：本题共8小题，每小题5分，共40分。在每小题给出的四个选项中，只有一个选项是符合题目要求的。2)大2桌<1房D2设全集0=R,集合A={yy=2,B={xx2-3x大2<0，则An(CB)=A.[2,+)B.(0,+x)C.(0,1]D.(0,1]U[2,+0)C2复数：满足0(2+)2-，则2A.-1+2i.B.1+2C.-1-2iD.1-2i已知椭圆C:。+若=1（口>b>0)的离心率为}4,4分别为G的左右顶点，B的C的上顶点若B不·叭=-2，则椭圆C的方程为B+6C.4+3=13-=1年4过圆=4内点P(1,1)有若干条弦，它们的长度构成公差为d的等差数列{a,},且A,仁O)、e(。,}),年中a,a分别为过点P的圆的最短弦长和最长弦长，则n的取值集合为A(a,0)6,369b)A.{4,5,6}B.{5,6,7)C.{5,6,7,8}D.{6,7,8,9}函(如图，正方形4BCD中，D正=2EC,P是线段BE上的动点，n且矿=店+y(:>0y>0)则+的最小值为屏萌A.22B.25C.4+233D.4定义在R上的偶函数fx)满足f(2-x)+f(x)=0,且)在[-2.，0]上单调递增若a=fam爱)，b=3),c=1og,3),则A.a

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

选择条件国：∈R，f)≥受(I)由题意得：f(x)=2cosx·cos(x+p)=2cosx(cosx.coso-sinx.sin)=2cos2x.coso-sin 2x.sino=cos2x·cosp-sin2x·sin⑩+cospcos(2x+)+cos因为x∈R,2受，所以了的最小值为/受，即c0誓+p=-1.所以p=2k+m号=2ae,因为水行所以。=号(Ⅱ)同选择条件①的（Ⅱ）.(18)(共12分)解：(1)由题意令4-x2=0得x=2.所以A(-2,0),B(2,0)因为点Pt,O)在线段AB上（不与端点重合），所以-2<1<2因为△APQ为等腰直角三角形，所以IPO AP1由题意可知点Q在x轴上方，所以Q,1+2).因为点Q在曲线C上，所以t+2=4-2所以1=-2（舍），13=1，即01,3)所以△iPe的面积为APPe方33号高三年级（数学）参考答案第3页（共7页）

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

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

亚.1.approaches2.pub3.crowded4.customs5.greet6.eagerly高能句式1.locked2.respectfulⅡ.1.To be honest,the movie is not as touching as I expected.2.What I didn't expect was that she could play the piano as well as professional pianists do.亚1.It is true that2.It is important that语法进阶√1.invited2.called3.puzzled4.repaired5.fallen●作定语：1,5作宾语补足语：2,3,401.moments2.however3.confident4.hiding5.accepted6.into7.is8.to ensure9.which10.comfortably第5期T3版Keys:(One possible version)高频词汇I.1.reaction2.equipment3.treatment4.satisfaction女1.paid off2.try out3.got through4.from then onⅢ.1.classical2.enables3.impact4.absorbed5.energy6.Moreover高能句式1.1.he will have the opportunity to meet thosefamous musicians2.you will have the opportunity to make a positive impact on those in needIL.1.It is an honour for me to have been invited to speak

W:That's pretty cool!So,what exactly do you do every day?M:Well,we act as a one-stop shop for anyone who wants to come in.So,it could be that they want a day-tripfrom London,which is a very popular request.And we can offer suggestions of where to go and how to getthere.If people want a two-week tour of Britain,we can plan out exactly where to visit,what roads to take.W:So,do you have any suggestions for people coming to Britain?M:A good suggestion is to see as much as you can,but try to come back again and again.(Text10)M:Good morning,boys and girls.I'm so glad to be here to give a speech!Many people asked me about my careerplan after graduation.Now,I'll share it with you in detail.I made up my mind to be a journalist when I visitedthe top news agency in our country last year.I chose it as my career based on the following two reasons.First,it is a job that can get me exposed to new things every day and thus keep me energetic all the time,since Ireally hate to follow the same routine every day.Second,working as a journalist can help me realize mychildhood dream of being a hero by spreading justice.To achieve this goal,I plan to apply for acommunication university,whose major,journalism,has been ranked the first for many years across the wholecountry.After getting my bachelor's degree in journalism,I will continue my study in this field to better fit myfuture post.That is all about my career plan.What do you think of it?阅读理解A【语篇解读】本文是一篇应用文。本文主要介绍了四个著名的国家公园。21·【B】细节理解题。根据文章第二段中Etosha means‘great white area',which refers to the park's huge saltarca.(Etosha的意思是“巨大的白色区域”，指的是这个公园的巨大盐区。)，及后文的Expect to seelions,,elephants,leopards and.”可知，Etosha National Park的吸引人之处在于它有一片巨大的盐区和令人印象深刻的野生动物。故选B项。22.【C】细节理解题。根据文章第三段中的You will find Yellowstone National Park atop a volcano hot spotin Wyoming(你会在怀俄明州的火山顶上发现黄石国家公园)”，及后文的Yellowstone is one of the bestnational parks in the world to study the geological activity of the Earth”（黄石公园是世界上研究地球地质活动最好的国家公园之一)可知，一个期待去学地球的地理知识的人会对黄石国家公园感兴趣。故选C项。23.【c】细节理解题。根据文章第四段Hike the high hills.”及第五段的Hill climbers will be kept busy withthe55 munros'可知，Goreme National Park及Caingorms National Park的共同点是它们都会吸引喜欢攀登高山的游客。故选C项。B【语篇解读】这是一篇记叙文。作者讲述了一位名叫Peterson的男子为流浪汉画肖像，并通过卖画所得改善流浪汉生活的故事。24.【A】细节理解题。根据第四段Peterson所说的话I saw beauty on the face of a man who hadn't shaved inprobably a year.But his story,,the life inside of him,inspired me..”,可以看出他之所以为Faris画像是因为被Faris的人生故事打动了。故选A。25.【C】推理判断题。第六段主要讲述了流浪汉们在Peterson的帮助下，如何展开新的生活。所以该段的写作目的(purpose)是为了体现其所创的公益组织Faces of Santa Ana的作用。故选C。26.【B】推理判断题。根据全文可知，Peterson受到一本书的启发，开始主动去了解流浪汉的生活，并在接触流浪汉之后，通过给他们画肖像来帮助他们，改善他们生活，由此可见，他是一个caig(关爱他人的)的人，A.Romantic浪漫的B.Caring关爱他人的C.Courageous有勇气的D.Persistent坚持不懈的。故选B。27.【D】推理判断题。根据最后一段Peterson所说的话“People often tell me,.'I was the one that would crossthe street..But I see homeless people differently now”,可以看出人们因为Peterson的画，对流浪汉改观了。因此是Peterson的努力产生了影响，故选D。【语篇解读】本文为说明文，一位视觉设计师通过A虹制作虚拟形象“复活”已逝的奶奶并与之对话，他把视频上传到网络后引起极大争论。28.【A】词义猜测题。划线词controversy意为“争论、争议”，debate意为“（各自发表不同意见的)争论、

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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

第二节（共10小趣：每小题1.5分，满分15分)阅读下面短文、在空白处填入！个话当的单词或括号内单词的正确形式Bigger.better gamesThe 19th Asian Games.56(host)in Hangzhou,capital of Zhejiang province.attracted worldwide attention.Despite57(delay)for a year due to the COVID-19pandemic.orgamizers said the sporting extravaganza retumed in stylc,with the openungceremony58(attract)a total of 503 million views.Although based originally on the format for the Olympic Games,the Asian Games boast59(region)sports with distinct Asian charactenstics,including dragon boat racing.kabaddi(a team contact sport),scpak takraw (kick volleyball)and kurash (a folk wrestlingdiscipline).Singh,the acting OCA president.said60 is important for the Games to atuactyoung people with the addition of new,action-packed events 61 appeal to thisaudience.such as brcaking (brcak dancing)and c-sports,which62(include)in theHangzhou Games."For young people,the Asian Games showcase the Olympic values oftcamwork devouon respect and friendship.They let people unite to feel the valuc and thrill of_63_(compete)and cooperation."Zhou Jingiang,a vice-nfinister of the General Administration of Sport of China,said:"Thesports at the Asian Games have strong Olympic clements,and are64_great opportunityfor Asian countrics and regions to display their cultures and traditons.The variety of sports atthe Games is the best testimony to the inclusivencss65 diversity of Asian sportsculture."第四部分写作（共两节，满分40分）第一节（满分15分）假定你是李华，外教Ryan给你的作业打了B,但你觉得应得A。请你给外教写一封B件.内容包括：】.说明你应得A的理由（至少两点）：2，提出希望：注意：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置作答。Dear Ryan.I'm Li Hua from Class 3.Yous、LiHua高三英语9/10

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·

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.”

evening? W:I'd love to,Mark.But I have to meet my friend Jack at the airport then.He's coming to see me. (Text 2) M:Are these your children in this photo? W:Yes.The oldest one is Tom.He is beside my father.This is Lily,the second oldest.This is Mike,the youngest.My hus- band Rick is behind him. (Text 3) W:Let's skip rope on the playground after lunch.We can get the teams together and two people can jump at a time. M:I'd rather play Find the Flag.I think we have enough people. That's my favourite game.

【答案与解析】 21.C细节题。根据第1段第2句可知，如果升级行程，就可以得 到伦敦眼的观光票，鸟瞰整个伦敦市。由此可知伦敦眼是需要 额外付费的旅游项目。 22.D细节题。根据Tower of London介绍中的第3句可知，在 伦敦塔内还珍藏了御宝。 23.B细节题。根据Buckingham Palace介绍中的最后一句可知， 在白金汉宫门前，游客可以看到延续几个世纪的禁卫军交接 仪式。

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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