安徽省滁州市2022-2023学年高考数学模拟试卷（含解析）.doc

键入文字高考数学模拟试卷一单选题本大题共8小题共40分在每小题列出的选项中选出符合题目的一项1已知函数119891119909119909119890119909过点119886119887作曲线119891119909的切线当0取值为41198861198902或11988611989011988641198861198902或11988611989021198861198902或11988611989011988621198861198902或1198861198902已知全集119868119909119909201198721199091199092211990931199092311990921199092311990921199093空气质量指数是评估空气质量状况的一组数字空气质量指数划分为05050100100150150200200300和300500六档分别对应优良轻度污染中度污染重度污染和严重污染六个等级如图是某市2月1日至14日连续14天的空气质量指数趋势图则下面说法中正确的是这14天中有5天空气质量为中度污染从2日到5日空气质量越来越好这14天中空气质量指数的中位数是214连续三天中空气质量指数方差最小是5日到7日4已知函数119891119909211990911199090119909221199091199090若实数11989801则函数119892119909119891119909119898的零点个数为32105如图119875119860垂直于以119860119861为直径的圆119874所在的平面119862为圆上异于119860119861的任一点现有下列命题119875119860119861119862119861119862平面119875119860119862119860119862119875119861119875119862119861119862其中真命题的个数是键入文字12346阿基米德螺线是一个点匀速离开一个固定点的同时又以固定的角速度绕该固定点转动而产生的轨迹如图在平面直角坐标系119909119874119910中螺线与坐标轴依次交于点119860110119860202119860330119860404119860550119860606119860770119860808并按这样的规律继续下去若四边形119860119899119860119899111986011989921198601198993的面积为760则119899的值为181921227已知双曲线11986211199092119886211991021198872111988601198870的左右焦点分别为11986511198652点1198652与抛物线1198622119910221199011199091199010的焦点重合点119875为1198621与1198622的一个交点若11987511986511198652的内切圆圆心的横坐标为41198622的准线与1198621交于119860119861两点且11986011986192则1198621的离心率为945495748已知1198971198992069设1198862711989011989711989981198873532351198883613则119886119888119887119887119888119886119886119887119888119887119886119888二多选题本大题共4小题共20分在每小题有多项符合题目要求9下列命题正确的是若11988311987311205902且1198751198833076则1198751对于随机事件119860和119861若119875119860119861119875119860则事件119860与事件119861独立回归分析中若相关指数1198772越接近于1说明模型的拟合效果越好反之则模型的拟合键入文字效果越差用等高条形图粗略估计两类变量119883和119884的相关关系时等高条形图差异明显说明119883与119884无关10已知119886119887是两个单位向量且119886119887119886119887则下列说法正确的是119886119887对于平面内的任意向量119888有且只有一对实数119898119899使119888119898119886211988711989911988712119886已知1198740011986011设119860119861119886119860119862119887119860119861119860119862119860119863则119874119861119874119862119874119860119874119863若向量119888满足1198881198861198872则2211已知函数119891119909的定义域119863关于原点对称119898119863且1198911198981当1199090119898时1198911199090且对任意119909119863119910119863119909119910119863都有1198911199091199101198911199091198911199101119891119910119891119909则119891119909是奇函数11989131198980119891119909是周期函数119891119909在21198983119898上单调递减12设119909119877当119899121199091198861198871198861198871198861198871198771198992119899119899119899119873设函数119910119904119894119899119909119888119900119904119909的值域为119872则119872的子集个数为321199091211990912111989911990912211989911990912119899111989911989911990912119899119873三填空题本大题共4小题共20分13已知复数119911满足11991111198942119905119894119905119877若11991122则119905的值为14斐波那契螺旋线被誉为自然界最完美的黄金螺旋线它的画法是以斐波那契数11235813为边长的正方形拼成长方形然后在每个正方形中画一个圆心角为90的圆弧这些圆弧所连起来的弧线就是斐波那契螺旋线如图为该螺旋线在边长为112358的正方形的中的部分建立平面直角坐标系规定小方格的边长为1则接下来的一段圆弧所在圆的方程为键入文字15若11990901199100则11990931199101199092311991024的最大值为16柏拉图多面体并不是由柏拉图所发明但却是由柏拉图及其追随者对它们所作的研究而得名由于它们具有高度的对称性及次序感因而通常被称为正多面体柏拉图视四古典元素中的火元素为正四面体空气为正八面体水为正二十面体土为正六面体如图在一个棱长为4119889119898的正八面体正八面体是每个面都是正三角形的八面体内有一个内切圆柱圆柱的底面与构成正八面体的两个正四棱锥的底面平行则这个圆柱的体积的最大值为1198891198983四解答题本大题共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10分已知等差数列119886119899的前119899项和为11987811989911987845119886311988622119886311求119886119899与1198781198992在下列两个条件中选一个求数列119887119899的前30项和119887119899111988611989951198861198996119887119899119886119899注如选择多个条件分别解答按第一个解答计分18本小题12分已知119860119861119862中点119863在边119860119861上满足1198621198631205821198621198601198621198601198621198611198621198611205820且cos119861263119862119860119863的面积与119862119861119863面积的比为2631求119904119894119899119860的值2若1198601198615求边119860119861上的高119862119864的值19本小题12分如图直角梯形119860119861119862119863中11986011986111986311986211986011986111986111986211986011986111986111986221198621198632直角梯形119860119861119862119863绕119861119862旋转一周形成一个圆台键入文字1求圆台的表面积和体积2若直角梯形119860119861119862119863绕119861119862逆时针旋转角1205791205790到11986011198611198621198631且直线1198601119863与平面119860119861119862119863所成角的正弦值为217求角120579的最小值20本小题12分某校举行强基计划数学核心素养测评要求以班级为单位参赛最终高三一班45人和高三二班30人进入决赛决赛规则如下现有甲乙两个纸箱甲箱中有4个选择题和2个填空题乙箱中有3个选择题和3个填空题决赛由两个环节组成环节一要求两班级每位同学在甲或乙两个纸箱中随机抽取两题作答作答后放回原箱并分别统计两班级学生测评成绩的相关数据环节二由一班班长王刚和二班班长李明进行比赛并分别统计两人的测评成绩的相关数据两个环节按照相关比赛规则分别累计得分以累计得分的高低决定班级的名次1环节一结束后按照分层抽样的方法从两个班级抽取20名同学并统计每位同学答对题目的数量统计数据为一班抽取同学答对题目的平均数为1方差为1二班抽取同学答对题目的平均数为15方差为025求这20人答对题目的均值与方差2环节二王刚先从甲箱中依次抽取了两道题目答题结束后将题目一起放入乙箱中然后李明再抽取题目已知李明从乙箱中抽取的第一题是选择题求王刚从甲箱中取出的是两道选择题的概率21本小题12分已知动点119875与两定点119860120119860220直线1198751198601与1198751198602的斜率之积为34记动点119875的轨迹为曲线1198621求曲线119862的方程2设11986311988601119867119864119866119864119867119863依次为等比数列119887119899的第119898119899119901119902项且119898119899119901119902求实数119886的值键入文字22本小题12分已知函数119910119891119909的表达式为11989111990912119886119909211988611199091198971198991199091198861198771若1是119891119909对的极值点求119886的值2求119891119909的单调区间3若119891119909121198861199092119909有两个实数解119909111990921199091119894直接写出119886的取值范围119894119894120582为正实数若对于符合题意的任意11990911199092当11990412058211990911199092时都有119891119904值范围键入文字答案和解析答案119860解析解由119891119909119909119890119909可得1198911199091119909119890119909设切点坐标为11990901199100所以119910011990901198901199090则切线的斜率为119896111990901198901199090切线方程为119910119909011989011990901119909011989011990901199091199090当01119909011989011990901199091199090得119887119909011989011990901119909011989011990901198861199090则11988711990902111990901198861198901199090设11990511990911990921119909119886119890119909则1199051199092119886119909119909221198861198901199091199091198862119909119890119909因为00119905119909单调递增所以当119909119886时119905119909所以当1199092时119905119909119909119886时119905119909有极小值为1199051198861198862111988611988611989011988611988611989011988601199092时119905119909有极大值为11990524121198861198902411988611989020可画出函数119905119909的大致图象结合图象若作两条切线则119887的取值为41198861198902或119886119890119886故选119860设切点坐标为11990901199100利用导数求出切线方程为119910119909011989011990901119909011989011990901199091199090由题可得11988711990902111990901198861198901199090设11990511990911990921119909119886119890119909利用导数研究函数的性质利用数形结合即得本题主要考查了导数的几何意义还考查了导数与单调性关系的应用属于中档题答案119861键入文字解析解全集119868119909119909201199091199092119872119909119909221199093则11198721199092故选119861求出全集119868和集合119872利用补集定义能求出1119872本题考查集合的运算考查补集交集定义不等式性质等基础知识考查运算求解能力是基础题答案119861解析解根据题意依次分析选项对于119860这14天中有4天空气质量指数在150200之间则有4天为中度污染错误对于119861从2日到5日空气质量逐渐下降即空气质量越来越好正确对于119862将14组数据从小到大排列8083138155157165179214214221243260263275其中位数为121792141965错误对于1198635日到7日的三天数据相差比较大则连续三天中空气质量指数方差最小不是5日到7日错误故选119861根据题意由折线图分析数据由此分析选项是否正确即可得答案本题考查由折线图分析数据涉及中位数方差的意义属于基础题答案119860解析解令1198921199091198911199091198980得119891119909119898根据分段函数119891119909的解析式做出函数119891119909的图象如下图所示因为11989801由图象可得出函数119892119909119891119909119898的零点个数为3个键入文字故选119860根据分段函数做出函数的图象运用数形结合的思想可求出函数的零点的个数得出选项本题考查函数零点与方程根的关系的应用属于中档题答案119862解析解因119860119861为圆119874的直径119862为圆上异于119860119861的任一点则119860119862119861119862又119875119860平面119860119861119862有119875119862119860为锐角119861119862平面119860119861119862于是得119875119860119861119862又119875119860119860119862119860119875119860119860119862平面119875119860119862从而得119861119862平面119875119860119862119875119862平面119875119860119862有119875119862119861119862正确假定119860119862119875119861又119860119862119861119862119875119861119861119862119861必有119860119862平面119875119861119862119860119862119875119862与119875119862119860为锐角矛盾不正确所以真命题的个数是3故选119862根据给定条件利用线面垂直的判定性质推理判断作答本题主要考查了直线与平面垂直的判定定理属于基础题答案119860解析解根据题意四边形119860119899119860119899111986011989921198601198993中1198601198991119860119899421198994119860119899到11986011989911198601198993的距离为1198991198601198992到11986011989911198601198993的距离为1198992若四边形119860119899119860119899111986011989921198601198993的面积为760则有121198992119899411989922211989942119899261198994760解可得11989918或21舍故11989918故选119860根据题意分析可得1198601198991119860119899421198994且119860119899到11986011989911198601198993的距离为1198991198601198992到11986011989911198601198993的距离为1198992进而可得121198992119899411989922211989942119899261198994760解可得答案本题考查合情推理的应用注意分析119860119899的规律属于中档题答案119861键入文字解析解由题设1198651119888011986521198880又点1198652与抛物线的焦点重合即11988811990120由11988821198862119910211988721119886211988721198882则1199101198872119886故1198601198612119887211988692即411988729119886如下图示内切圆与11987511986511198652各边的切点为119863119864119870所以1198751198631198751198641198631198651119870119865111986411986521198701198652又119875119865111987511986522119886则1198751198631198631198651119875119864119864119865211986311986511198641198652119870119865111987011986522119886所以119870为双曲线右顶点又11987511986511198652的内切圆圆心的横坐标为4即1198864故11988729则1198885所以离心率为11989011988811988654故选119861令1198651119888011986521198880由题设知11988811990120且11986011986121198872119886求得411988729119886再由内切圆中切线长性质及双曲线定义性质确定与11986511198652的切点119862的位置进而求离心率本题考查双曲线的几何性质直线与双曲线的位置关系数形结合思想属中档题答案119863解析解1198862783323令11989111990911990932119909则11989111990911990923119909119897119899221199091199090则119891119909在31198971198992上单调递增又31198971198992435119891351198913即119887119886因为11988611988827836136381304119886119888则119887119886119888键入文字故选119863构造函数11989111990911990932119909利用单调性比较大小即可本题考查利用单调性比较大小属于基础题答案119861119862解析解对于119860由1198751198833111987511988330241198751错误对于119861由条件概率公式可得119875119860119861119875119860119861119875119861119875119860即119875119860119875119861119875119860119861事件119860119861相互独立故正确对于119862根据相关指数的意义可知相关指数1198772越接近于1说明模型的拟合效果越好反之则模型的拟合效果越差故正确对于119863由等高条形图于列联表关系可知差异明显表明119883与119884相关可能很大故错误故选119861119862根据正态分布曲线的对称性可判断119860根据条件概率公式可判断119861根据相关指数的意义可判断119862根据等高条形图的性质可判断119863本题主要考查了正态分布曲线的对称性考查了条件概率公式以及相关指数的意义属于基础题答案119860119862解析解已知119886119887是两个单位向量且119886119887119886119887则119886221198861198871198872119886221198861198871198872则1198861198870对于选项1198861198870119886119887即选项正确对于选项11988621198872119887121198861198862119887与11988712119886共线1198862119887与11988712119886不能作为平面向量的一组基底即选项错误对于选项11987411986111987411986211987411986011986011986111987411986011986011986211987411986021198741198601198601198611198601198621198741198602119874119860119860119863119874119860119874119860119860119863119874119860119874119863即选项正确对于选项设119888与119886119887的夹角为120579向量119888满足1198881198861198872键入文字则1198882211988611988711988811988811990011990412057911988611988724又1198861198872则11988822221198881198881199001199041205792211988822119888则1198882221198882011988822211988820即2211988822即选项错误故选119860119862由平面向量的线性运算结合平面向量数量积的运算及平面向量基本定理逐一判断即可得解本题考查了平面向量的线性运算重点考查了平面向量数量积的运算属中档题答案119860119862119863解析解对于119860令119905119909119910则11989111990511989111990911991011989111990911989111991011198911199101198911199091198911199091198911199101119891119909119891119910119891119910119909119891119905所以函数119891119909是奇函数故正确对于119861由1198911198981得119891119898119891211989811989811989121198981198911198981119891119898119891211989811989121198981111989121198981所以11989121198980则1198912119898119891311989811989811989131198981198911198981119891119898119891311989811989131198981111989131198980所以11989131198981故错误对于119862由1198911199091199101198911199091198911199101119891119910119891119909可得119891119909119898119891119909119891119898111989111989811989111990911989111990911119891119909则119891119909211989811989111990911989811989811989111990911989811989111989811198911198981198911199091198981198911199091111989111990911119891119909111198911199091119891119909由11989111990941198981198911199092119898211989811198911199092119898119891119909所以函数119891119909是以4119898为周期的周期函数故正确对于119863令2119898则1198911199092119898119891119909119898119891119898111989111989811989111990911989811198911199090所以1198911199091198911199102119898119891119910119898119891119898111989111989811989111991011989811198911199100所以119891119910所以119891119909119891119910011989111990911991011989111990911989111991011198911199101198911199090因为1198911199091198911199100所以11989111990911989111991010键入文字所以1198911199101198911199090即119891119910119891119909所以119891119909在21198983119898上单调递减故正确故选119860119862119863对于119860令119905119909119910根据1198911199091199101198911199091198911199101119891119910119891119909证明119891119905119891119905即可判断对于119861根据1198911198981结合1198911199091199101198911199091198911199101119891119910119891119909即可求得11989121198981198913119898即可判断对于119862先求出119891119909119898再根据1198911199092119898119891119909119898119898求出1198911199092119898即可判断对于119863令2119898119891119910即可判断本题考查了抽象函数的奇偶性周期性及单调性119862选项的关键在于根据1198911199092119898119891119909119898119898判断1198911199092119898与119891119909的关系119863选项的关键在于令2119898号属于中档题答案119861119862119863解析解对于119860例如1则1112可得所以错误对于119861由1198992119899所以1198992119899所以119899所以119899所以正确对于119862因为1119904119894119899119909111198881199001199041199091可得119904119894119899119909101119888119900119904119909101当11990951205874120587312058741205874时可得11991021012即函数119910的值域为11987221012所以集合119872的子集个数为2532所以正确对于中设119891119909119899119873因为119899119873所以119899键入文字所以11则1198911199091119899119891119909110所以119891119909的周期为1119899又当0119909012121119899119909121119899012121198991119899119909121198991119899012119899119909120所以11989111990900119909所以正确故选119861119862119863举反例可判定错误结合119899正确结合正弦余弦函数的值域得到119910的值域为11987221012可判定正确设119891119909119899119873得到119891119909的周期为1119899证得119891119909恒为0可判定正确本题属于新概念题考查了函数的周期性值域也考查了逻辑推理能力和计算能力属于中档题答案2解析解1199111119894211990511989411990511987711991121199051198941119894211990511989411198941119894111989411990511990511989411991122119905211990528解得1199052故答案为2先对119911化简再结合复数模公式即可求解键入文字本题主要考查复数的运算法则以及复数模公式属于基础题答案1199094211991022169解析解根据题意接下来的一段圆弧所在圆的半径1199035813其圆心为42根据题中图象规律发现则其标准方程为1199094211991022169故答案为1199094211991022169根据题意分析要求的圆的圆心和半径从而可得圆的标准方程本题主要考查圆的标准方程考查运算求解能力属于基础题答案12解析解119909311991011990923119910241199093119910119909213119910231199093119910211990921231199102311990931199102119909611991012当且仅当11990921且311991023即1199091199101时取等号所以11990931199101199092311991024的最大值为12故答案为12由11990931199101199092311991024119909311991011990921311991023再利用基本不等式即可得解本题主要考查基本不等式及其应用属于中档题答案64212058727解析解如图设该圆柱的底面半径为119903119861119864高2119861119862由题可知119862119863211986011986323则11986011986222又119860119861119860119862119861119864119862119863222221199032222119903圆柱的体积119881120587119903222120587211990321199033119881221205874119903311990322212058711990343119903可知当119903043时1198810当119903432时119881所以当119903043时11988122120587211990321199033单调递增当119903432时11988122120587211990321199033单调递减键入文字当11990343时11988111989811988611990964212058727故答案为64212058727根据题意得到119862119863211986011986323然后利用勾股定理得到11986011986222在119860119861119862中根据相似列方程222221199032整理得222119903然后根据圆柱的体积公式求体积最后求导根据单调性求最值即可本题主要考查圆柱的体积公式考查利用导数研究函数的最值考查运算求解能力属于中档题答案解1由119878451198863得411988616119889511988611011988911988614119889由1198862211988631得11988611198892119886141198891119886131198891联立解得119886141198891119886119899119899511987811989941198995119899211989922911989922选11988711989911198861198995119886119899611198991198991111989911198991数列119887119899的前30项和为11987911989911121213130131111313031选1198871198991198861198995119899119899411989951198995数列119887119899的前30项和为11987911989943210125252335解析1由条件得出1198861与119889的方程组求解即可由公式法得出结果2由裂项相消法求和由分组求和法求和本题考查等差数列的通项公式与求和公式的应用裂项求和法的应用属中档题答案解1点119863在边119860119861上满足1198621198631205821198621198601198621198601198621198611198621198611205820119862119863为119860119862119861的平分线键入文字又119862119860119863的面积与119862119861119863面积的比为263由角平分线定理可知119862119860119862119861119860119863119861119863263由正弦定理得119904119894119899119861119904119894119899119860119862119860119862119861263且119861119860又cos119861263119888119900119904119861211988811990011990421198612113119904119894119899119861223且119861为说角119904119894119899119860332由1知119860为锐角且1198881199001199041198601sin211986063119860119861119862120587119888119900119904119862cos11986011986111988811990011990411986011988811990011990411986111990411989411989911986011990411989411989911986169又11986011986226311986111986211988811990011990411986269在119860119861119862中1198611198622263119861119862221198611198622631198611198626952解得1198611198623故119862119864119861119862119904119894119899119861322322解析1由已知条件可得119862119863为119860119862119861的平分线再结合角平分线定理以及正弦定理二倍角公式即可求解2先求出119888119900119904119860再结合余弦的两角和公式求出119888119900119904119862并运用余弦定理即可求解本题主要考查解三角形考查转化能力属于中档题答案解1由题意直角梯形119860119861119862119863旋转形成下底面半径为2上底面半径为1高为2的圆台可得该圆台的母线长为5所以该圆台的表面积1198781205871251205874120587355120587该圆台的体积11988113212058712058741205874120587143120587故所求圆台的表面积和体积分别为355120587143120587键入文字2作119861119872119861119860以点119861为坐标原点119861119860119861119872119861119862所在的直线为119909119910119911轴建立空间直角坐标系则1198631021198601211988811990011990412057921199041198941198991205790即11986011198631211988811990011990412057921199041198941198991205792又平面119860119861119862119863的一个法向量119899010设1198601119863与平面119860119861119862119863所成的角为120572则119904119894119899120572cos11986011198631198992119904119894119899120579121198881199001199041205792211990411989411989912057924211990411989411989912057994119888119900119904120579217两边平方并结合sin2120579cos21205791解得11988811990011990412057912或119888119900119904120579114故11988811990011990412057912时所求120579的最小值为1205873解析1利用圆台的表面积体积公式求圆台的表面积和体积2构建空间直角坐标系确定1198601119863面119860119861119862119863的法向量应用空间向量夹角的坐标表示列方程求119888119900119904120579进而可求120579的最小值本题考查了圆台的体积和表面积的计算考查了直线与平面所成的角的计算问题属于中档题答案解1一班抽取45752012人二班抽取3075208人一班样本平均数为1样本方差为1二班样本的平均数为15样本方差为025总样本的平均数为12181512812记总样本的样本方差为121112280251512220076所以这20人答对题目的样本均值为12样本方差为0762设事件119860为李明同学从乙箱中抽出的第1个题是选择题事件1198611为王刚同学从甲箱中取出2个题都是选择题事件1198612为王刚同学从甲箱中取出1个选择题1个填空题事件1198613为王刚同学从甲箱中取出2个题都是填空题则119861111986121198613彼此互斥且11986111198612119861312057011987511986111198624211986262251198751198612119862411198622111986262815119875119861311986222119862621151198751198601198611581198751198601198612815119875119860119861338键入文字119875119860119875119861111987511986011986111198751198612119875119860119861211987511986131198751198601198613255851812115381324所求概率即是119860发生的条件下1198611发生的概率119875119861111986011987511986111198601198751198601198751198611119875119860119861111987511986025581324613解析1首先求分层抽取的两个班的人数再根据两个班抽取人数的平均数和方差结合总体平均数和方差公式代入求值2根据全概率公式和条件概率公式即可求解本题考查均值与方差的计算考查全概率公式是中档题答案解1设动点119875的坐标为119909119910由题意得1199101199092119910119909234化简得119909241199102311199092故所求119862的方程为1199092411991023111990922设11986421198861199051199050设直线119863119864的方程为119910119905119886119909119886设1198661199091119910111986711990921199102联立方程11991011990511988611990911988611990924119910231消去119910得31198862411990521199092811988611990521199094119886211990521211988620所以11990911199092811988611990523119886241199052119909111990924119886211990521211988623119886241199052由题意得119887119898119887119899119887119901119887119902所以119866119863119867119864119866119864119867119863即1198661198631198671198641198661198641198671198630即1119905211988621198861199091211988611990921119905211988622119886119909111990921198860从而1198861199091211988611990922119886119909111990921198860所以211990911199092311988611990911199092411988620即241198862119905212119886231198862411990523119886811988611990523119886241199052411988620所以11988622又1解析1设点119875坐标依据题意列出等式化简可求出轨迹方程2依据等比数列的性质可得119866119863119867119864119866119864119867119863代入弦长公式化简结合韦达定理可求出119886的值键入文字本题主要考查轨迹方程的求法直线与椭圆的综合考查运算求解能力属于中档题答案解11198911199091211988611990921198861119909119897119899119909119886119877119909011989111990911988611990911988611119909119886119909111990911199091是119891119909对的极值点1198911119886119886110解得119886111989111990911990911199091119909可得1199091是函数119891119909的极大值点满足题意11988612119891119909119886119909111990911199091198860时1198911199090函数119891119909在0上单调递增11988611990901119886时11989111990901199091119886时119891119909函数119891119909的单调递增区间为01119886单调递减区间为1119886综上可得1198860时函数119891119909单调递增区间为01198863119891119909121198861199092119909化为1198861199091198971198991199090119886119897119899119909119909119894令11989211990911989711989911990911990911990901198921199091119897119899119909119909211989211989001199090119890时1198921199090函数119892119909单调递增119909119890时119892119909119909119890时函数119892119909取得极大值1198921198901119890119891119909121198861199092119909有两个实数解1199091119909211990910119886的取值范围是11198900键入文字119894119894由2可得若1198911199041119886120582为正实数若对于符合题意的任意11990911199092当11990412058211990911199092时都有1198911199041205821199091119909211198861198861199091119909211988611990911198971198991199091011988611990921198971198991199092011988611990911199092ln11990911199092化为ln119909111990921120582另一方面由119886119909111989711989911990910119886119909211989711989911990920可得11988611990911199092ln11990911199092ln11990911199092ln11990911199092119909111990921119909111990921不妨设119909111990921119909111990921199051ln1199091119909211990511199051119897119899119905119905111990511198971198991199051120582化为119897119899119905119905112058211990510令119892119905119897119899119905119905112058211990511199051119892101198921199051119905119905111990511205821199051212058211990512211990512058211990511990512令119906119905120582119905122119905120582119905221205821119905120582120582119905112058212058222120582112058212058212时11990611990501198921199050函数119892119905在1上单调递增11989211990511989210满足题意01119906119905在11120582120582上单调递减119906119905119892119905综上可得120582的取值范围是12键入文字解析111989111990912119886119909211988611199091198971198991199091198861198771199090可得11989111990911988611990911199091119909根据1是119891119909对的极值点可得11989110解得119886经过验证即可得出119886211989111990911988611990911199091119909对119886分类讨论即可得出函数119891119909的单调区间3119891119909121198861199092119909化为1198861199091198971198991199090119886119897119899119909119909119894令1198921199091198971198991199091199091199090利用导数研究其单调性与极值及其最值画出图象即可得出119886的取值范围119894119894由2可得若1198911199041119886由题意可得120582119909111990921119886即11988611990911199092合119886119909111989711989911990910119886119909211989711989911990920化为ln119909111990921120582进而化为ln11990911199092ln11990911199092119909111990921119909111990921不妨设119909111990921119909111990921199051可得ln1199091119909211990511199051119897119899119905于是119905111990511198971198991199051120582化为119897119899119905119905112058211990510令11989211990511989711989911990511990511205821199051119905111989210利用导数研究函数的单调性即可得出结论本题考查了利用导数研究函数的单调性与极值一元二次方程的实数根与判别式的关系换元法不等式的解法等价转化方法数形结合方法考查了推理能力与计算能力属于难题