2023年高考数学强基计划模拟题（一）（含答案）.doc

绝密启用前2023年高考数学强基计划模拟题一一单选题当0119891211990911989111990921198911199091198911199092设119891119909在01上有定义要使函数119891119909119886119891119909119886有定义则119886的取值范围为121212121212已知119875为119860119861119862内部任一点不包括边界且满足11987511986111987511986011987511986111987511986021198751198620则119860119861119862一定为直角三角形等边三角形等腰直角三角形等腰三角形已知1198911199091199092119886211988721119909119886221198861198871198872是偶函数则函数图像与119910轴交点的纵坐标的最大值是22224已知函数119891119909119909241199093集合1198721199091199101198911199091198911199100集合1198731199091199101198911199091198911199100则在平面直角坐标系内集合119872119873所表示的区域的面积是120587412058721205872120587函数1198911199091199093123119909的值域为121313212设119891119909有反函数1198911119909将11991011989121199093的图像向左平移2个单位再关于119909轴对称后所得函数的反函数是119910119891111990912119910111989111199092119910111989111199092119910119891111990912化简三角有理式cos4119909sin4119909sin2119909cos2119909sin6119909cos61199092sin2119909cos2119909的值为1sin119909cos119909sin119909cos1199091sin119909cos119909设119886119887为两个相互垂直的单位向量已知119874119875119886119874119876119887119874119877119903119886119896119887若119875119876119877为等边三角形则119896119903的取值为119896119903132119896132119903132119896119903132119896132119903132设119886119899119887119899分别为等差数列与等比数列且119886111988714119886411988741则以下结论正确的是1198862119887211988631198865119887511988661198876已知抛物线11986211991028119909的焦点为119865准线为119897119875是119897上一点119876是直线119875119865与119862的一个交点若1198651198753119865119876则119876119865835232设有复数120596112321198941205962cos25120587119894sin25120587令12059612059611205962则复数120596120596212059631205962011120596120596212059631205964119860119861119862为等边三角形边长为3119875为平面外一点119875满足119875119860311987511986141198751198625则119881119875119860119861119862为11105232一个盒子里装有红白蓝绿四种颜色的玻璃球每种颜色的玻璃球至少有一个从中随机拿出4个玻璃球这4个球都是红色的概率为1199011恰好有3个红色和1个白色的概率为1199012恰好有2个红色1个白色和1个蓝色的概率为1199013四种颜色各1个的概率为1199014若恰好有1199011119901211990131199014则这个盒子里玻璃球的个数的最小值等于171921以上选项都不正确已知多项式1199094211990931198982119909241198982119909411989810恒成立则119898的取值范围为0012112如图所示已知正方体1198601198611198621198631198601119861111986211198631的棱长为4点119867在棱1198601198601上且11986711986011在侧面11986111986211986211198611内作边长为1的正方形1198641198651198661198621119875是侧面11986111986211986211198611内一动点且点119875到平面11986211986311986311198621的距离等于线段119875119865的长当点119875运动时1198671198752的最小值是21222325已知抛物线11991024119909的焦点为119865过点11987520的直线交抛物线于119860119861两点直线119860119865119861119865分别与抛物线交于点119862119863设直线119860119861119862119863的斜率分别为11989611198962则11989611198962等于131212已知119875119909119910为区域1199102119909200119909119886内的任意一点当该区域的面积为4时1199112119909119910的最大值是60222答案和解析答案119862解析解当0119891119909119909lg11990911989111990921199092lg11990921198912119909119909lg11990920因为119909lg1199091199092lg1199092211990911990922lg11990921199091199092lg119909答案119861解析解函数119891119909119886119891119909119886的定义域为11988611198861198861119886当1198860时应有1198861119886即11988612当1198860时应有1198861119886即11988612答案119863解析解因为1198751198611198751198601198601198611198751198611198751198602119875119862119862119861119862119860所以已知条件可改写为1198601198611198621198611198621198600容易得到此三角形为等腰三角形答案119860解析解由已知条件可知1198862119887210函数图像与119910轴交点的纵坐标为119886221198861198871198872令119886cos120579119887sin120579则119886221198861198871198872cos21205792sin120579cos120579sin2120579cos2120579sin21205792答案119862解析解由已知可得119872119909119910119891119909119891119910011990911991011990922119910222119873119909119910119891119909119891119910011990911991011990911991011990911991040则1198721198731199092211991022211990911991011990911991040作出其交集部分可知其面积为圆面积的一半即为1212058722120587答案119863解析解119891119909的定义域为31199094故011990931令1199093sin212057901205791205872则119891119909119909334119909sin12057931sin2120579sin1205793cos1205792sin1205791205873因1205873120579120587351205876故12sin1205791205873112sin12057912058732答案119860解析解设11991011989121199093上有一点11990901199100左移2个单位即119909021199100再关于119909轴对称后为119909021199100取反函数119910011990902所以119910011990911990902119910119909011991021199100119909代入11991011989121199093可得11990911989121199101211991011198911119909119910119891111990912答案119860解析解分母sin2119909cos2119909sin4119909cos4119909sin2119909cos21199092sin2119909cos2119909sin4119909cos4119909sin2119909cos2119909也可以用特殊值法答案119862解析解119875119876119876119877119875119877即1199032119896121199031211989622解得119896119903132答案119860解析解设等差数列的公差为119889等比数列的公比为119902由119886111988714119886411988741得1198891119902232故11988623119887222311988632119887343119886501198875232119886611198876434答案119860解析由题意及抛物线的定义即可得答案119860解析根据题意有120596cos2312058725120587119894sin2312058725120587cos1615120587119894sin1615120587因此120596151于是1205961205962120596201112059611205962011112059612059611205961341511120596120596答案119860解析119875119861119862为直角三角形外心为119875119862的中点取119875119862的中点为119872由于1198601198611198601198621198601198753因此119860点在平面119875119861119862的射影就是点119872则119860119872就是高112所以体积为11答案119862解析不妨设红白蓝绿四种颜色的玻璃球个数分别为1198991119899211989931198994由题意可以得到1198624119899111986211989913119899211986211989912119899211989931198991119899211989931198994所以119899121198994111989913119899321198991411989923故11989911198992119899311989942511989912312注意到1198991119899211989931198994均为整数所以1198991的最小值为111198991119899211989931198994251198991231221答案119860解析配方得到11990921199091211989811990922119909120取1199091代入得到1198980为必要条件反之若1198980则原式0答案119861解析在1198611198611上取点119870使得11986111198701则119867119870面11986111986211986211198611连接119875119870则119867119875211986711987021198751198702161198751198702在平面11986111986211986211198611上以1198621198621所在直线为119909轴以119866119865所在直线为119910轴由题意可知119875点轨迹为抛物线其方程为119909221199101119870点坐标为04设119875119909119910则119909221199101其中119909311199101272故11987511987021199092119910422119910111991028119910161199102611991015当11991031272时119875119870min26故119867119875min216622本题考查正方体和抛物线的综合应用答案119861解析设直线119860119861的方程为11991011989611199092联立1199101198961119909211991024119909得119896111991024119910811989610设1198601199091119910111986111990921199102直线119860119862的方程为1199101199101119909111199091联立119910119910111990911119909111991024119909得119910141199091111991021199101199101119909110则11991011199101198624故11991011986241199101同理11991011986341199102故1198962119910119863119910119862119909119863119909119862411991011986311991011986244119910111991021199101119910221198961可得1198961119896212本题考查直线与抛物线相交问题答案119860解析由1199102119909200119909119886作出可行域如图所示由图可得119860119886119886119875119886119886由1198781221198861198864解得1198862即11986022目标函数1199112119909119910变形为1199102119909119911当1199102119909119911过119860点时119911最大119911max2226本题考查线性规划