数学(文)卷· 湖北省荆州中学高三第一次质量检查

'全品高考网gk.canpoint.cn荆州中学2012届高三第一次质量检查数学试卷（文科卷）一、选择题（本题共10个小题，每小题5分，共50分　在每小题给出的四个选项中，有且只有一个是正确的）1.已知集合，，则集合()A.{0，1}B.{0，2}C.{1，2}D.{0}2.若点（,9）在函数的图像上，则tan的值为（）A.0B.C.1D.3.若函数，则函数的定义域为（）A.B.C.D.4.设函数的最小正周期为，且，则（）A.在单调递减B.在单调递减 C.在单调递增D.在单调递增5.设的大小关系是（）A.B.C.D.6.根据统计，一名工人组装第件某产品所用的时间（单位：分钟）为（A，为常数）.已知工人组装第4件产品用时30分钟，组装第A件产品用时15www.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页 全品高考网gk.canpoint.cn分钟，那么和A的值分别是（）A.75,25B.75,16C.60,25D.60,167.设函数，若f（a）＞1，则实数a的取值范围是（）A.　B.∪C.（1，+∞）　D.∪（0，+∞）8.若函数在R上既是奇函数，又是减函数，则函数的图像是（）9.已知函数，若有，则b的取值范围为（）A.B.C.D.10.设双曲线的左准线与两条渐近线交于两点，左焦点在以为直径的圆内，则该双曲线的离心率的取值范围为（）A.B.C.D.，二、填空题：本大题共5小题，每小题5分，共25分．将答案填在答题卷相应位置上．11.已知为奇函数,．12.双曲线P到左准线的距离是.13.已知关于的方程－(2m－8)x+－16=0的两个实根满足＜＜，则实数m的取值范围_______________.www.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页 全品高考网gk.canpoint.cn14.设函数，将的图像向右平移个单位长度后，所得的图像与原图像重合，则的最小值等于15.若函数()满足且时，,函数,则函数在区间内零点的个数有___个三、解答题：本大题共6小题，共计74分.解答应写出文字说明，证明过程或演算步骤16.（1）先化简,再求值:(1),其中；（2）化简：17.已知函数.（1）求的最小正周期及的最小值；（2）若,且,求的值.18.某民营企业生产A，B两种产品，根据市场调查和预测，A产品的利润与投资成正比，其关系如图1，B产品的利润与投资的算术平方根成正比，其关系如图2（注：利润与投资单位是万元）（1）分别将A，B两种产品的利润表示为投资的函数，并写出它们的函数关系式。（2）该企业已筹集到10万元资金，并全部投入A，B两种产品的生产，问：怎样分配这10万元投资，才能使企业获得最大利润，其最大利润约为多少万元。（精确到1万元）。www.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页 全品高考网gk.canpoint.cn19.已知函数，其中是大于0的常数（1）求函数的定义域；（2）当时，求函数在[2，上的最小值；（3）若对任意恒有，试确定的取值范围20.已知过抛物线的焦点，斜率为的直线交抛物线于（）两点，且．（1）求该抛物线的方程；（2）为坐标原点，为抛物线上一点，若，求的值21.设关于的函数，其中为上的常数，若函数在处取得极大值．(1)求实数的值；(2)若函数的图像与直线有两个交点，求实数的取值范围；(3)设函数，若对任意的，恒成立，求实数的取值范围.www.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页 全品高考网gk.canpoint.cn数学（文）参考答案一、选择题1．B2.D　3.A4.A5.B6.D7.B8.A9.B10.B二、填空题11.612.1613..14.15.8三、解答题16.解：(1)原式=（2）解：原式17.解：（1）=.因此的最小正周期为,最小值为.(2)由得=2,即.而由得.故.解得.18．（1）投资为万元，A产品的利润为万元，B产品的利润为万元，由题设=，=，．由图知，又从而=，=，（2）设A产品投入万元，则B产品投入10-万元，设企业的利润为y万元Y=+=，（），www.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页 全品高考网gk.canpoint.cn令当，，此时=3．75当A产品投入3．75万元，B产品投入6．25万元时，企业获得最大利润约为4万元。19.解（1）由得，解得时，定义域为，时，定义域为且时，定义域为或}（2）设，当，时则恒成立，∴在上是增函数∴在上是增函数∴在上的最小值为（3）对任意恒有，即对恒成立∴，而在上是减函数∴，∴20.解：（1）直线AB的方程是与联立，从而有所以：，由抛物线定义得：，所以p=4，抛物线方程为：（2）由p=4，化简得，从而,从而A:(1,),B(4,)www.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页 全品高考网gk.canpoint.cn设=，又，即8（4），即，解得21.解：(1)因为函数在处取得极大值所以,解(2)由（Ⅰ）知，令得或（舍去）在上函数单调递增，在上函数单调递减当时，，所以,函数在区间上单调递增，在区间上单调递减，所以,当时，函数取得最大值，当时，即所以，当时，函数的图象与直线有两个交点，(3)设当时,，在递增，不成立，（舍）当时当，即时，在递增，，不成立当，即时，在递增，所以，解得，所以，此时当时，在递增，成立；当时，不成立，综上，www.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页 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全品高考网gk.canpoint.cnwww.canpoint.cn010-全品高考网邮箱：canpoint@188.com第9页共9页'