数学爱好者七年级同步训练下册（华师大版）。SHUXUE AIHAO ZHEx=9,x=9,所以，原方程组的解为C组拓展探索y=14.y=14.请你参考小明同学的做法解方程组：13.已知关于x、y的方程组(mx+y=m,2x+y=2,分x十y+t义=3，610别按下列要求答题：(1)x+y-_x-y=-1;(1)当m≠2时，解这个方程组；610(2)若m=2,方程组解的情况怎样？5+2=11,mx+y=m,(3)若m=2,方程组的解的(2)32x+y=13_2=13.x y情况怎样？。44

5扬州市2023届高三第二次调研测试数学本试卷共6页，22小题，满分150分。考试用时120分钟。注意事项：1.答餐前，考生务必将自已的姓名者车号，专场号和座位号填写在答题卡上。将条形码横贴在答题卡“条形码粘贴处”。2.作答选择题时，选出每小题答案后，用B铅笔在答题卡上对应题目选项的答案信息点涂照：如需改动，用橡皮擦干净后，再远涂其他答案。答案不能答在试卷上。3.非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上：如需改动，先划掉原来的答案，然后再写上新答案；不准使用铅笔和涂改液。不按以上要求作答无效。4.考生必须保持答题卡的整洁。考试结束后，将试卷和答题卡一并交回。一、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，只有一项是符合题目要求的。1.若M,N是U的非空子集，MnN=M,则、光0<(<，李1A.M∈NB.NEMC.CoM-N D.CuN=M2.若iz=(1-2i)2,则z=A.4+31B.4-3iC.-4+3iD.-4-3iB3.已知(：+是)”的展开式中各项系数和为243，则服开式中常数项为A.60B.80C.100D.120了4。古代数学家刘徽编撰的《重差)是中国最早的一部测量学著作，也为地图学提供了数学基础.现根据刘徽的《重差》测量一个球体建筑物的高度，已知点A是球体建筑物与水地面的接触点（切点），地面上B,C两点与点A在同一条直线上，且在点A的同侧.若在B,C处分别测得球体建筑物的最大仰角为60°和20°，且BC=100m,则该球体建筑物的高度约为(cos10°≈0.985)J3rtpo7++SincoA.49.25mB.50.76mC.56.74mD.58.60m10206Sx00rt1oo数学试卷第1页（共6页)-o9张9不

12.设定义在R上的函数f()与g()的导函数分别为f"(x)和g(),若f(x+2)-g0-x)=2,f'(x)=g'(x+1),g(x+1)+g0一)=0，则下列说法中一定正确的是19.(12g(1)=09⊙t02)-0.C.B.g(x)=g'(4-x))(2g0+g(2)++g202)=0D.f0g0)+f2g2+…f220g22D=0三、填空题：本题共4个小题，每小题5分，共20分2013.已知2X-的展开式共有9项，则该展开式中常数项为」门14.过直线1：4x+3y=0上一动点P作圆C:(x99B,则四边形PACB面积的最小值为ZA4)子+(y-3)}=1的两条切线，切点分别为A、15.已知椭圆B:鴛大a>0.b>0的左右焦点分别为RCc0.rC0,项有0线1过点R和点B,直线1与圆O:x2+y2=r2(

22.(12分)21.(12分)已知函数f(.x)=e一a.x2,a∈R,f'(x)为函数f(.x)的导函数(1)讨论函数f(x)的单调性；已知猫线C看-苦-1a>0,6>0)的右焦点，右顶点分别为P,AB0b,(2)若方程f(x)十f(.x)=2-a.x2在(0,1)上有实根，求a的取值范围.IAF,点M在线段AB上，且满足BM1=3MA1,直线OM的斜率为1，O为坐标原点，(1)求双曲线C的方程(2)过点F的直线！与双曲线C的右支相交于P,Q两点，在x轴上是否存在与F不同的定点E,使得EP1·IFQ1=EQI·|FP|恒成立？若存在，求出点E的坐标；若不存在，请说明理由.密封线全细10所名校最新高考冲喇卷第7页（共8页列）【23，（新高考）CC,数学（三）一门全国10所名校最新高考冲刺卷第8页（共8页）【23·（新高考）C0·数学（三）一】

上期参考答案19.1.1变量与函数(1)1.变量，常量2.B3.（1)水池的容积抽水机的台数、每台抽水机每小时抽水的体积；抽水时间、水池中水的体积(2)280-3×15×2=190(立方米)，即抽水2小时后，池中还有190立方米水故填190.4.D5.(1)S,h:5.(2)10.19.1.1变量与函数(2)1.自变量，函数，函数值2.函数关系式，实际意义3.D4.B5.D6.x≤5且x≠37.（1)因为矩形的周长为40，所以2(x+y）=40,所以20F(2)当xF13时y=20-13=7.故填7，(3)当y8时，20-x8所以x=12.所以矩形的面积=12×8=96.19.1.2函数的图象(1)1:横、纵坐标2.D3.在4.8℃5.(1)由图象，知体育场离小明家2.5千米.

8.2消元一解二元一次方程组(1)1.多，少2.含另一个未知数，另一个，代人法3.B4作.(2)/r5.y=1.5.c6.2800,31008.2消元一解二元一次方程组(2)1.相反，相等，相加，相减，加减法2.B3.m长=4a5g4子5.甲种笔记本的单价为3元/本，乙种笔记本的单价为5元/本.8.2消元”一解二元-次方程组(3)1.代人消元法，相等2.C3.145.-436.2第八章8.1~8.2同步测试题-、1.D2.A.3.A4.B5.C6.D7.C8.A二、9.①④10.11.-112售66-4(下转第2、3版中缝)人教版七年级

in singing,dancing,and acting while also allowing them to feel as though they were 49 ofThe researchers found evidence 68 the snake,a young Egyptian cobra,had been deniedsomething.This camp 50 impacted the way I view both the world and the profound impact peoplewater while alive.It was likely killed by a severe break of its backbonecan have.The children came from all backgrounds,and we had some homeless children,undocumentedThe researchers found the snake's mouth open.These 69 (find)suggest the snake had beenchildren,and many children who had experienced gang-related 51 throughout their lives.I cannotpart of an“opening of the mouth”ceremony.fully 52 the happiness it brings me to be able to 53 a creative outlet for them.I 54 believeGraves-Brown noted that the finding supports 70 early)evidence that the act was carriedin the importance of art and expression and I feel incredibly grateful to have been able to share thatout with animals.The scientist added,"We know it was carried out on humans.'with them.This experience has reminded me how 56 it is to give back to others.I have alsofound a greater 57for everything I have been 58 enough to experience.第四部分写作（共两节，满分35分）Volunteering59 me a better person because it gets me outside of myself.It puts my 60第一节短文改错（共10小题；每小题1分，满分10分on others.I am grateful to those I have met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41.A.reviewingB.approvingC.volunteeringD.attempting10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42.A.raisingB.distributingC.varyingD.counting增加：在缺词处加一个漏字符号（∧），并在其下面写出该加的词43.A.noticedB.rememberedC.motivatedD.intended删除：把多余的词用斜线(\)划掉44.A.experienceB.projectC.dreamD.schedule修改：在错的词下画一横线，并在该词下面写出修改后的词：45.A.zoneB.workC.lineD.secret注意：1.每处错误及其修改均仅限一词46.A.choseB.receivedC.movedD.served2.只允许修改10处，多者（从第11处起）不计分47.A.howeverB.otherwiseC.insteadD.certainlyI found it difficulty to study in senior high school because I couldn't keep up class and nearly48.A.delayB.regretC.joyD.educationdropped out.The problem was what I was not confident.Then coming Miss Li,my English teacher.49.A.partB.centerC.reminderD.burdenShe told me to try much hard.Whenever I lost heart,he would encourage me:You can make it.I50.A.slowlyB.carelesslyC.basicallyD.carefullyspent a plenty of time memorizing words.We meet in her office each morning and she would urge me51.A.connectionB.touchC.violenceD.witnessto read English for at least 20 minutes.Eventually,something amazed happened and I got high marks52.A.copyB.expressC.indicateD.presentin English.I really owe my great progresses to my teacher53.A.constructB.organizeC.relateD.share第二节书面表达（满分25分）》54.A.trulyB.formerlyC.temporarilyD.casually55.A.tradeB.trickC.skillD.gift56.A.regular盟中学生英语杂志《Today Teens》昨天组织了全国中学生防疫知识大赛。请以“PandemicPrevention Knowledge Contest Held Yesterday”为题，写一篇新闻报道，内容包括B.importantC.anxiousD.attractive1.大赛的基本情况；57.A.appreciationB.informationC.restrictionD.experiment2.大赛的意义。58.A.slightB.gradualC.openD.lucky参考词汇：pandemic传染病59.A.comparesB.exchangesC.makesD.selects注意：1.词数100左右60.A.significanceB.focusC.recognitionD.response2.可以适当增加细节，以使行文连贯第二节（共10小题；每小题1.5分，满分15分）阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。Pandemic Prevention Knowledge Contest Held YesterdayScientists recently used 3D imaging technology to look inside the mummies (of a cat,abird,and a snake.The research is helping experts learn more about how ancient Egyptians 61(treat)animals.Researchers said that they used a special technique,X-ray micro CTscanning,to look inside themummies.The scanning process permits the scientists 62 (study)the mummies while keepingthem whole.The CT scans were much more 63 (detail)than medical CT scans.Carolyn Graves-Brown,a writer of the study,64 (lead)the Egypt Centre at SwanseaUniversity in Britain,noted that 65 three mummies were likely made as gifts to the gods thatEgyptians believed in.The dead animals were thought to serve 66 a link between Egyptian godsand living people.The mummies had long been in Swansea's collection.Experts are not sure of 67 (they)exact age.上轮复联考（四）全国卷英语试卷第7页（共8页）一轮复联考（四）全国卷英语试卷第8页（共8页

commen sectncom websitermd Tell them"like your product.but Im worried about this package.Is itreeyeble?"Ak them.Wait for an answer.Don't be too hard on yourself.Personally,you are not going to solve the plastie waste problem,but you're notalone in wanting to do so.A lot of people are also making decisions based on theirconcerns.If you join them in adopting some of the small changes we've discussedhere,it could add up to something meaningful.40A.tell companies how you feel.B.So just do the best that you can.C.Look for sustainable“swaps'”.D.Replace old items with new ones.E.Many people come up with a lot of solutions.F.Once you have your list,do a little more homeworkG.The following is something we can do to be part of the solution.第三部分语言知识运用（共两节，满分45分）第一节（共20小题：每小题1.5分，满分30分）阅读下面短文，从短文后各题所给的A、B,C和D四个选项中，选出可以填入空白处的最佳选项。As I work in the garden,I take my time and the garden is teaching me aboutworking with the earth.I 41 that there will be both successes and 42 andthere are many things that affect them both.The quality of the seeds planted is 43 to how the plants will grow.The英语试题（七）第12页（共16页）

501四21：351℃的令36%心：以学14小：以T心小，八小小小)生温，学1少小：以十心小心)八小4小量严重超标，则P(A)=C1-p)p2=3(1-p)p2,P(B)=Cp3=p3,即f(p)=P(4)+P(B)=31-p)p2+p3=3p2-2p0

7.已知三棱锥P-ABC中，PA⊥面ABC,AB⊥AC,PA=AB=2,AC=4,M是BC上一点，则PM的最小值为3√5B66C.23D.43558.如图所示的四边形ABCD中，△ACD是等边三角形，B是AC边的中线延长线上一点，AB=2,AC=23,点E在四边形ABCD的边上运动，则E第·ED的取值范围为A.[-3,1]B.[-1,1]C.[-1,0]D.[-3,0]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.股有商意c方玉下列金家透C18A若ac=bc,则a=bB.若a∥b,则a·b=abC若a+b=a-b1,则ab的obD.若a·c=b·c=0,则a∥b/月行知为两条不可直线，a为两个不同面，则下列命题中给灵的是A.若a∥B,mCa,n二B,则m∥nB.若m⊥n,m⊥a,mLB,则a∥RC.若m∥n,m⊥a,n⊥β，则a∥B/D.若m⊥n,m⊥a,则n∥a11.如图，四棱锥P-ABCD的底面ABCD是边长为2的正方形，PD⊥底面ABCD,PD=1,点CE是PC的中点，过A,D,E三点的面。与面PBC的交线为1，则下列说法延确的是A.L⊥ADB.⊥面PCDC,三楼锥P-ADE的体积为号2X2D直线PB与1所成角的余弦值为号12.△ABC中，内角A,B,C的对边分别为a,b,c,Q=2,BC边上的中线AD=2,则下列说法正确的有A.AB·AC=3B.6+c2=9C.c0s A<1D.∠BAD的最大值为30°三、填空题：本题共4小题，每小题5分，共20分13.已知空间中两个角a9,且角。与角8的两边分别行，若a=70°，则8=7.l014.在△ABC中，E为AC上一点，AC=3A忘，P为BE上任一点，若A市=mA店+nAC(m>0,n>0),则m十3n=.【高一5月份调研测试·数学第2页（共4页）】

方差是×(6-8)2+(8-8)2×3+(10方面的能力，21.(1)甲运动员这10次跳水成绩组成数据的8)2=1.6.因为广宇的方差小丁于承义的方差所以)广宇的训练成绩比承义的训练成绩更加均数m=0×(82×2+83×2+84+85+稳定，故选项A、B、C错误，选项D止确.86+87+88+90)=85,方差=0×[(2×10.由统图，可得a=20+5=25,故①错误；八(82-85)2+2×(83-85)2+(84-85)2+年级八有7+33+25+12+3=80（人），故②(85-85)2+(86-85)2+(87-85)2+(88正确：一班植树3棵的人数最多为20人，故③85)2+(90-85)2)]=6.6.止价；内为一班的人数7+21+5+7+2=乙运动员这10次跳水成绩组成数据的均42,且班每人种2棵树的人数有21人，所以中位数是2.做④正价.数=10×(80+81+82+83+84×2+85×二、11.912.30.613.23.414.42+86+90)=84,方差号=0×1(80-84)P+15.10016.-2(81-84)2+(82-84)2+(83-84)2+2×提示：11,由于9出现的次数为14次，频数最多，所以众(84-84)2+2×(85-84)2+(86-84)2+数为9.(90-84)2)」=7.2.12.=5×4+10×16+20×15+50×9+100×6=(2)选甲运动员参加比赛更合适，因为甲运50动员的均成绩比乙运动员高，且甲运动员30.6(元)的方差比乙运动员的小，成绩更稳定13.将折线统计图"的5个数据按大小顺序排列22.(1)因为甲数据的众数是58.所以m=58.为21.9,22.4,23.4,24.9,25.4，所以位数是因为甲、乙两人的均心跳次数相同，23.4.所以可解得n=5714.设被污损的数为x,则4×2+x+2+5×2+3×故填58,57，2=4×8.解得x=6.所以这组数据按从小(2)根据表中的数据分别求甲、乙两组数据到人的顺序排列为2,3,3,4,4,5.5,6.排在的均数、众数、中位数和方差，所得数据整最中间的两个数是4，故中位数为4.理如下表所示：15.中位数a=94,因为均数x=×(92+94+队员均数众数巾位数方弟98+91+95)=94,所以方差6=×[(92-94)2+58589(94-94)+(98-94)2+(91-94)2+(95585757.594)2]=6.所以a+b=94+6=100.16.若m=3,由均数为2，得4+3+2+3+n=从两人心脏跳动情况的均数和方差和结合5×2.解得n=-2,符合m>n.所以n=-2看，他J两人均每分钟心脏跳动都是58次，若n=3,则4+3+2+m+3=5×2.解得但乙飞行员的波动小，所以乙飞行员的心律m=-2,不符合m>,舍去.所以n=-2.史规则，心脏史好些」三、17.x=(3+4+4+6+8)÷5=25÷5=5,在止常池围内，心跳次数越少说明心脏能越52=5×[(3-5)2+(4-5)2+(4-5)2+(6-好，故从众数、中位数的角度看，乙飞行员每分钟的心跳次数较少，所以乙的心脏更好些5P+(8-5)=1=32.综合以上分析，乙飞行员的心脏更好些所以这组数据的均数为5，方差为3.223.(1)本次随机调查的学生人数为4÷10%=18.(1)学生代表评分中9.2出现次数最多，40.故填40.所以为学生代表给张馨评分的众数为9.2.(2)由统计图表，可得m=40×17.5%=7,n=将学生代表评分的6个数据按从小到大的顺40-7-11-4=18,a=40×100%=27.5%,63序排列为9.0,9.2,9.2.9.2,9.3,9.3，排在最中间的两个数据都是9.2，所以学生代表给张馨48×100%=45%评分的中位数为9.2故填7,18,27.5%，45%(2)由题意，得9,5×20%+6×(9.2×3+9.0×(3)因为共有40个数据，所以其中位数是第20和第21个数据的均数，而这两个数据均1+9.3×2)×50%+9.0×30%=9.2(分).落在第3组，所以中位数落在第3组.故填3.所以张蓉的最后得分是9.2分.(4)该校学生中唾眠时间符合要求的人数为190)本饮描取的学牛共有20+0=20人)800×18+4=440.40所以背浦4首的人数为120×器°=45（人》所以估计该校学牛中睡眠时间符合要求的人因为15+45=60，所以这组数据最中问的两数为440.个数是4和5.24.（1)该作品在民主测评得到“不赞成”的票所以中位数为45=45.数为50-40=10.因为背诵4首的人数最多，为45人，所以这组(2)x=(88+87+94+91+90)=90.数据的众数是4(3)y=40×3+10×(-1)=110,所以S=放填4,4.5.0.7x+0.3y=0.7×90+0.3×110=96.(2)因为1200×40+25+20=850（人），所以该作品的“综合得分”S的值为96分12025.(1)由题意，得八年级的Ψ均成锁为(6×7+所以仙川人赛结束后一个月该校学生一周诗7×15+8×10+9×7+10×11)÷50=8(分)：词背诵6首（含6首）以上的人数为850人.儿年级的均成绩为(6×8+7×9+8×14+20.(1)甲队的Ψ均分为，=85+70+64=73（分），9×13+10×6)÷50=8(分).乙队的均分为=72+66+84=74（分）.】所以用均数无法判定哪个年级的成绩比较好因为理<元，所以乙队将被推荐(2)①8,1.56.(2)由题意，得，=85×5+70×3+64×2=5+3+2②如果从众数的角度看，八年级竞赛成绩76.3(分)，的众数为7分，儿年级竞赛成绩的众数为8分8,=72×5+66×3+84×2=72.6(分).所以应该给儿年级颁奖；如果从方差的角度5+3+2看，八年级竞赛成绩的方差为1.88，九年级竞因为x>x,,赛成绩的方差为1.56，H两个年级的均分所以甲队将被推荐，乙队应加强创意与设计相同，九年级竞赛成绩的波动小，所以应该给

全国100所名校高三AB测试示范卷教学记全国@@所名校高三AB测试示范卷·数学第四套函数的概念及性质(A卷)》(40分钟100分)鼠微信扫码】考情分析，▣2▣高考对接点函数的概念及性质是高考必考点，主要考查客观题学疑难点函数性质的应用同茶典型情境题3观看微课视频课外题解析下载复课件题序123456答案ABDBBA一、选择题：本题共6小题，每小题6分，共36分.在每小题给出的四个选项中，只有一项是符合题目要求的1.已知函数f(.x)=2x2十3|x十4，若f(a-1)>f(2a),则实数a的取值范围为A-1.B(-1,-)D.(1D【解题分析】由题意知，函数f(x)为R上的偶函数，且在区间[0，十)上单调递增，因为f(a一1)>f(2a),所以a-1>2a,解得-13所以函数f(x)-x,0x3在区间（一∞，3）上单调递减，在区间(3，十∞)上单调递增，所以f(x)≥f(3)=一3，即函数f(x)的最小值为一3.【答案D1-x,x14.若f(.x)则满足等式f(f(m)=1的实数m的个数为x2-5.x+7,x>1A.6B.5C.4D.3【24G3AB(新教材老高考)·数学-必考-N】15

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10.(17分)已知函数fx)=2x2+ax-a(a∈R),11.(18分)(1)解关于x的不等式f(x)≥x,(2)若命题“3∈[1,4]，使得f(x)≤2a一a一8”为假命题，求实数a的取值范围已知函数w-reR.增人三盒容有国(1)求不等式f八x)-fx-1)>1的解集M(2)若函数y=八)在(0，+)上的最小值为一。-1，求实数a的值：(3)若对任意的正实数a,存在工∈之门，使得：)m,求实数m的最大值S型错误（技能型错误）区型错误色只型错良S试卷分析错误类型涉及题序失分错误内容沙及题序失分【24·G3AB(新高号)·数学（三）一0考-N

则∠BDE+∠GDE=90°怎么作：∠ABC=∠ADC=90°，故△ABCDE⊥AD,.∠GDE+∠ADG=90°和AADC为直角三角形，由于E,F为∴.∠ADG=∠BDE.AC,BD的中点，故考虑构造直角三角形∠BAC=90°，∠ABC=30°，∴.∠C=60°斜边上的中线，连接BE,DE,.BE∥AC,.∠EBD=180°-∠C=120°.得到什么：BE=2AC,DE=2AC∠ABC=30°，DG⊥BC,.∠BGD=60°..∠AGD=120°=∠EBD解：如解图，连接BE,DE△GDA∽△BDE.DEBDDA GD在Rt△BDG中，BDan30°=y3DGAD√3DE3,即DE=3AD第1题解图思路分析.·∠ABC=∠ADC=90°，E为AC的中点，为什么作：要证明AD=AE+2AB,AE与AB共线，但与AD不在同一条直线上，且B-Ac.DE4cB肱=DE=4C=5不存在线段数量关系，缺少与2AB相等.△BED为等腰三角形的线段，需要构造将这三条线段进行数又F为BD的中点，量转化或放在同一直线上怎么作：∠B=90°，故延长AB至点F,使EFLBD,BF=DF=2BD=4在R△DEF得BF=AB,连接CF.中，EF=√DE2-DF2=√52-4=3.得到什么：△CAF为等腰三角形思路分析证明：如解图，延长AB至点F,使得BF=AB,为什么作：要证DE=√3AD,根据DE=连接CF,延长DC,AF交于点G.3AD可得0=3DE 3=tan30°，题干中∠ABC=30°，但此角与AD,DE不在同个三角形中，需构造相似三角形怎么作：∠ABC=30°，故过点D作DG⊥第3题解图BC交AB于点G.得到什么：△BDG是直角三角形CB⊥AF,AB=BF,.CA=CF.AC分∠BAD,∴.∠CFA=∠CAF=∠CAD.证明：如解图，过点D作DG⊥BC交AB于点G,∠ACD=90°，∴.△ADG是等腰三角形，点C是DG的中点，∠G=∠ADC.DE⊥AB,∴.CG=CE..∠G=∠AEC.∴.∠ADC=∠AECD(或.∠ACD=90°，DE⊥AB,∴.A,C,D,E四第2题解图点共圆.∴.∠ADC=∠AEC.)万唯数理化QQ交流群：66843586019

ENGLISH￥全国教辅类一级报纸®新课程高二课标(选择性必修3)第33期总19702期2023年2月14日星期二主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杜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:/ww,xyybs.com(温馨提示：登录学英语报社官网htp:lwww.xyybs..com下载本期配套教学PPT)TEST YOURSELF学英语)服务号《学英语》订阅号Jnit4,(选择性必修)Book3本期资源码：td6c1c关注报社微信公号，回复ClassName入资源码获取对应资源Marks■试题命制：《学英语》报社试题测评组第一部分听力（共两节，满分30分）》第一节（共5小题；每小题1.5分，满分7.5分）7.What happened to the woman's computer?例：How much is the shirt?A.Its software didn't work.听第9段材料，回答第14至17题。What does the woman do?A.￡19.15.B.￡9.18.C.￡9.15B.Its screen turned blackA writer.答案是C。C.Its screon turned blue.B.A reporter.听第7段材料，回答第8至10甄A hostess

6.已知角“的顶点在原点，始边与x轴的非负半轴重合，终边经过点P(2,-1),求的值(9AB.-1010c5D7.直线x+y2c0s0=0被圆x2+y2+2√3x+2=0截得的弦长最大值为()C.25108.已知定义在R上的函数f(x)满足f(-x)+f(x-2)=4,且当x>-1时，f'(x)≥x+1,则不等式/)-2e-)小0的解集为（)A.(0,+0)B.(-1,0)C.（-0,-1)D.（-0,-1)U(0,+∞)）二、多项选择题：本题共4小题，每小题5分，共20分.在每小题给出的选项中，有多项符合题目要求.全部选对的得5分，部分选对的得3分，有选错的得0分，9.某学校随机抽取200名学生数学周测成绩的频率分布直方图如图所示，据此估计该校本次数学周测的总体情况（同一组中的数据用该组区间的中点值为代表），下列说法正确的是(1额率组距A.众数为60或700.04B.25%分位数为650.03…C.均数为730.02D.中位数为750.00510.下列不等式正确的是()05060708090100成绩1分b+0≥2a-b≠0)A.a bB.b>a>0,则a+2>9b+2 b一2

18.（12分)已知点A(0,4)与点B(一6，一2)关于直线1对称，(1)求直线1的方程；(2)若直线1到直线，的距离是直线1到直线2：x十y十4=0的距离的，求直线1的方程，封线·44【24新教材·DY·数学（六）一RA一选择性必修第一册一Y】

又点=h-h→f(k)=f(nx,又飞>l,nx>1ne=l,又当x>1时，f(x)单调递减，所以x2=lnx,之品品女，专品合千见有产兰=发，所以选项D正疏，X X2故选：ABD【点睛】关键点睛：利用数形结合思想，结合等式a=be“是解题的关键.16.解：作出函数6闭=Hogp,0,-sinπx,-1≤x≤0的图象如下：令f(a)=f(b)=f(c)=f(d)=k,则00时，可得B=(a,3a).因为命题p是命题9的充分不必要条件，则AB,可得日，等号不能同时成立，解得s,所以实数a的取值范围为...10分18.解：(1)油2-1≠0，得x≠0，f(x)定义域为{x|x∈R,x≠0}.1分由f(x)为奇函数，得f(-x)+f(x)=0,*a-0.”+02a培-011“2-12-11∴.2a=1,得a26分（用特殊值没检验的，扣2分）@调知x>0,不等式-门x<0可化为2支nx0,@消0<1时，hx<0,不等式批为写士>行01时，nx>0,不等式可化为2一不2'11x>1,2>2,2"-1>0,.2-1>2,即2>3，解得x>l0g23综上，x的范围为{x0log23}12分19.解：(1)由题意f”(x)=x2-(k+1)x·f(x)在区间(2，+0)上为增函数，∴.f'(x)=x2-(k+1)x≥0在区间(2，+∞)上恒成立…2分即k+1≤x恒成立，又x>2,∴.k+1≤2，故k≤1∴.k的取值范围为k≤14分（没有等号扣2分)（2》设=因-g网=苦-：+吉2'(x)=x2-(k+1)x+k=(x-)(x-1)6分令h'(x)=0得x=k或x=1由(1)知k≤1，①当k=1时，h'(x)=(x-1)2≥0，h(x)在R上递增，显然不合题意.7分②当k<1时，h(x),h'(x)随x的变化情况如下表：x(-0,k)k(k,1)1(1,+0∞)h'(x)+00+h(x)极大值RK1极小值k-16232

第一册答案专页第1-4期5.14解析：由题意，得A它-AA+A,d+D在-A+M市+A店。-a-++-43om6040+子46.1解析：由题意，得(a+3b)(7a-5b)=7a+16ab-151b1=0①，(a-4b)(7a-5b)=7a-33a-b+201b=0②，①-2得46-356i,肌以ab8f3x①162得a-高.所u号b1735.2b所以eos(a,b)=ab-4935b1=1.lallbl lallbl 49 lal7.解：(1)证明：设=a,V=b,V元=c,正四面体的棱长为1，则i（+店4元)abe)ad-4+市名b+c-a).Bd-m4-m+}亦名（ac-b).d=+d=立+】i(a+h-5c),所以ad:Bd-2(b+e-5a)-(a+c-366)-6（2a64h6ae-6-dd-石26x1m60-4x1×1xc0s60°×2-5-5+1)=0，所以Ad⊥Bò，即A01B0.同理得，A0⊥C0,B0LC0.所以A0,B0,C0两两垂直2油1得.i-D,i}（abe4c（-2a-2bc.26m-V云(-2a-2e号又m名eo-Y竖md名(-2a-2ber石bc-a)号DM-A04所以cos(Di,Ad=DMA 1 V2 222又oe0,,所以o成.4-年8解：由题意，得元-子亦号0励-a)子（o+心01=号(o+0心-子成.0-o耐+Mt衣-0+号(oar0心-子0-gabe又Gi=0i-0元，且oi号d号x宁o.ote.3..C-(be)-(atbse)--ja.回顾经典1B解析：如图，取AB的中点为D,连接DN,DC,D亦=22(+=+=(0+d)+2(O4C+d-a+be)故选B项2.B解析：四棱锥P-ABCD的底面ABCD是行四边形，.Ai=B元：.Pi=P+A市=P+BC-P+(P心-Pi)=P-Pi+P心=ab+c.故选B项.

名念·会a(由（马）.(）1=+1…9分(3）由(2)b621=n(m十1）..11分an∴坛++…太-2+2ks+叶十D-1-号+号言+叶是-=1-<1…12分2.【解析11)由条件c=1,设A(w),则C+差-1，又B(0,0,(0,-0,,·,=少电.+也_后==-生=-3，6a24a2=号8=号a2-Da=8,6=5.即箱图C的标准方程为号+苦-1…5分(2)由对称性可知，四边形PQNM为行四边形，设MN:x=y十1，与椭圆方程联立得：(3m2十4)y十6y-9=0.…7分-6m设Man),N(),则n十为=3m4Mh=3m+4-9…8分wN=I十成以=V什√+w=36-12(1+m2)3m2+4…9分2设点F2(1,0)到直线☑1的距离为d,则d=,所以四边形PQWM面积为：/1+m2S=MNId=24 1m………………………10分3m2+41V图2在泽弱透诚24t所以S的取值范围为(0,6]。……12分数学试题参考答案（长郡版）一6

令x=1,得n=(1,-6,3).…9分因为FE=(3,1,0),…10分所以点F到面CDE的距离d=ln·F它=3=346n46…12分/4622.(1)证明：圆C的方程可化为λ(.x2十y2一5)一2x一4y+6=0.…1分x=-1,=4令1-2x-4y十6=0，得v=25、得或…3分2y=5故圆C恒过两个定点，且这两个定点的坐标为（一1,2）和（号，号）…4分(2)解：当λ=1时，圆C的方程可化为x2+y2一2x一4y十1=0.由题知直线1的斜率k存在且不为0，设直线l的方程为y=k(x十1).…5分x2+y2-2x-4y+1=0,联立消去x得(1十2)y2-4k(1+b)y十4k2=0,…7分y=k(x+1),y1十2=4k(1+k)1+21新以8分4k2y12=1+△=16k2(1+k)2-16k(1+2)>0,解得k>0.9分因为1+1=M十业=1+k………………………………………………………10分所以=，解得152…11分又>0，所以=1+⑤2…12分【高二数学·参考答案第5页（共5页）】·24-99B·

取k=0..6分因此，函数y=f(x)在区间.7分(2)又因为x∈R,f(x)+f(2t-x)=0,所以函数f(x)图象的对称中心为(t,0),.8分则f)=5sn2+-0,所以2+君=kre7列，..10分6解得1=kπ-石(k∈Z),.11分212】当k=1时，1取到了最小正值为5π..12分1219.解：(1)设等差数列{an}的公差为d,则等差数列{an}通项公式为an=a1+(n-1)d=a1-d+dn,所以(n+1)(a-d+dn)=dn2+a,n+(a,-d)=4n2+n+k,d=4d=4所以a=1，所以a=1，所以an=1+4(n-1)=4n-3,.3分a-d=kk=-3又因为2Tn=3bn-3,所以当n≥2时，2Tn1=3bn-1-3,两式相减可得2bn=3bn-3bn-1,即bn=3bn-1,令n=1,则2b=36-3,解得b=3,所以数列{b}是以3为首项，3为公比的等比数列，所以bn=3”...6分定a+%=城+a可告，a8,g-94所以4+a,-5++39+k_49+3张=2a,-36+2,解得k=-3,(其他同上)2443法三、(n+)a,=4+n+可得a,=4n+n+k_4n+12-7n+1)+3+kn+1n+1解得k=-3,(其他同上)(2)由(1)可知，41=1，a2=5,43=9,…,a21=81,…,a50=197,a51=201,a32=205,b=3,b2=9,b3=27,b4=81,b=243,第4页共8页

第1期A1版Keys:(One possible version)封面故事1.They used yeast cells.2.Because many of the mechanisms that cause cells to age are similar in living things.九年级Unit1基础能力训练听力原文及参考答案听力原文第一节：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，并标在试卷的相应位置。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。1.W:Michael,I know you can speak English very well.What about other foreign languages?M:I can also speak French.2.W:The summer holiday is coming soon.How are you going to spend it?M:I will go to Beijing with my cousin Jim.We are going to take part in an English summer campin a college.3.W:English is my favorite subject.How about yours,John?M:I like Chinese best,but I always get good grades in physics.W:Wow,I'm glad to hear that.I do badly in physics.Can you help me with it?M:Sure.Maybe we could study together on weekends.4.M:You speak English so well.Are you from America,Linda?W:No,I'm from Australia.I started to learn English from an early age.5.M:Our singing club is amazing.Would you like to join it?W:I'd love to,but I have already joined the dancing club and the reading club.第二节：听下面3段对话或独白。每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。听每段对话或独白前你有时间阅读各小题，每小题5秒钟。听完后，各小题将给出5秒钟的作答时间。每段对话或独白读两遍。听下面一段对话，回答第6至第8三个小题。W:You look sad,Kevin.What's the matter?M:I didn't pass the English final exam last Friday.W:I am sorry to hear that.What problems do you have?M:I have trouble understanding English grammar.W:Maybe you should buy a good grammar book.It can be helpful.M:OK,I will buy one.Then how should I improve my reading skills?W:I think you should read some English magazines.M:Good idea.But the new words also trouble me.W:Don't worry about that.When you meet new words,you can guess their meanings or lookthem up in a dictionary.M:Thank you.I hope I can do better next time.听下面一段对话，回答第9至第11三个小题。W:Jim.You came back really late today.Did you stay at school to do homework again?M:No.But I played chess with my classmates.W:I called you,but you didn't answer the phone.

Thank you for your email!Everything is going well for me at my new school.I have a newfriend named Zhang Wei.We are friends because we both like playing soccer and swimmingWe also share some common interests,like reading books and watching movies.However,there are some differences between us too.Zhang Wei is really good at math andscience,but I like English and social studies more.He also likes spicy food,but I don't.All in all,I'm really glad that I met Zhang Wei and that we became friends.It's nice to havesomeone to talk to and play with.I hope we can stay friends for a long time!Yours,LiHua【书面表达写作指导】本次写作要求回复一封邮件。在写作时，需要将自己的新朋友是谁、你们成为好朋友的原因以及和这位朋友的相似之处和不同之处写清楚。可适当发挥。人称以第一人称和第三人称为主，时态主要用一般现在时。注意行文逻辑、语言简练，无单词拼写、语法错误。。5/5

第二部分1 阅读（共两节，满分50分) 第一节（共15小题；每小题2.5分，满分37.5分） 阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳 选项。 A Do you know there are apps that make it easy to help others, our planet,and ourselves,so we lead more meaningful lives? Check out four of the best ones and spring into action! My Windows This app connects visually impaired people in need of some help with sighted people with a few minutes of spare time to offer through video calls.The help needed may be something like find- ing a missing object in the home.This app is available in over 150

第二节（共5小题；每小题5分，满分25分） 阅读下面短文，从短文后的选项中选出可以填入空白处的最 佳选项。选项中有两项为多余选项。 Here's a new reason to be an optimist. 15 Pessimists, of course,might have suspected this all along-but now there's actual research behind it. Scientists found the most optimistic people live an average of 11 to 15 percent longer than their more pessimistic peers.In pre vious studies,researchers have found that more optimistic people tend to have a lower risk of diseases and early death,said Lewina Lee,the lead researcher and a psychiatry professor at Boston U- niversity School of Medicine."16 Optimists generally expect good things to happen in the fu-

fortable in Beijing then. M:That sounds like a good idea! W:So what's your plan for the summer? M:I planned to go to London with some friends.But they're not available.So I'll just stay in Los Angeles and do some part- time work. (Text 10) W:Hello,everyone.Welcome to our program.I'm Jenny Jackson.The weather here in Juarez has become unbearable. With no rains for over a year,the city is suffering from unusually hot weather.Some light showers have been forecast since last month,but all of them have been effective in surrounding areas. Summer has not even started yet,but temperatures have reached

3.How does the man feel about Dr Smith's speech? A.Interesting. B.Moving. C.Disappointing. 4.What is the woman's monthly salary? A.$250. B.$500. C.$750. 5.What does the woman most probably do? A.She is an editor. B.She is an athlete. C.She is a housewife. 第二节（共15小题；每小题1分，满分15分） 听下面5段对话或独白。每段对话或独白后有几个小题，从题 中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位

48.D每一份作业都经过了她全面的研究和分析，这样她就可以 给我们高质量的意见和建设性的建议。 49.B 50.D 在她看来，她的职责并不会在学年结束时停止。 51.A 直到她的学生的生命的终点，她的职责才会停止。 52.C AIrs Roos不会轻易给学生A,但是她期望自己的学生能够 去争取。 53.A 此外，当学生需要她的帮助时，她更愿意提出B计划。 54.D 当我们无法完成每周一次的任务时，她愿意在原有的课堂 之外花时间帮助我们。 55.A 56.B 因为她对学生极其严格，我原以为这让她不受欢迎。 57.D