2016届福建省福州市第八中学高三上学期第二次质量检查理科数学试题及答案

'1．设全集为，集合，则A.B.C.D.2．以下说法错误的是A.命题“若2-3+2=0,则=1”的逆否命题为“若≠1,则2-3+2≠0”B.“=1”是“2-3+2=0”的充分不必要条件C.若∧为假命题,则,均为假命题 D.若命题:∃0∈R,使得+0+1<0,则﹁:∀∈R,则2++1≥03．函数的零点所在的大致区间是A．(0,1)　　B．(1,2)C．(2，e)D．(3,4)4.若∈R，且，则“≠”是“||≠”的A．充分而不必要条件B．必要而不充分条件C．充要条件D．既不充分又不必要条件5．实数，，的大小关系正确的是A．B．C．D．6．已知函数若，则=A.B.C.D.7.若函数的一个值为A．B．0C．D．8．已知函数满足，且∈[－1,1]时，，则函数的零点个数是A．3B．4C．5D．6 9．已知函数是偶函数，且函数在[0,2]上是单调减函数，则A．B．C．D．10．已知函数，若互不相等，且满足，则的取值范围是A．B．C．D．第Ⅱ卷（非选择题共100分）二、填空题:本大题共5小题，每小题4分，共20分．把答案填在答题卡相应位置．11．已知幂函数为偶函数，则.12．函数的定义域是.13．定义在R上的奇函数，当时，，则当时，___14．函数的图象不过第Ⅱ象限，则的取值范围是___.15．某同学在研究函数时，分别给出下面几个结论：①等式对恒成立； ②函数的值域为；③函数为上的单调函数；④若，则一定有；⑤函数在上有三个零点。其中正确结论的序号有______________.（请将你认为正确的结论的序号都填上）三、解答题：本大题共6小题，共80分．解答应写出文字说明，证明过程或演算步骤.16．（本小题满分13分）已知函数，其中为常数，且是函数的一个零点。（Ⅰ）求函数的最小正周期和所有对称轴方程；（Ⅱ）当时，求函数的值域。17.（本小题满分13分）已知命题：函数为上单调减函数,实数满足不等式.命题：当，函数。若命题是命题的充分不必要条件，求实数的取值范围。18．（本小题满分13分） 某单位有员工1000名，平均每人每年创造利润10万元。为了增加企业竞争力，决定优化产业结构，调整出名员工从事第三产业，调整后他们平均每人每年创造利润为万元，剩下的员工平均每人每年创造的利润可以提高.（Ⅰ）若要保证剩余员工创造的年总利润不低于原来1000名员工创造的年总利润，则最多调整出多少名员工从事第三产业？（Ⅱ）在（Ⅰ）的条件下，若调整出的员工创造的年总利润始终不高于剩余员工创造的年总利润，则的取值范围是多少？19．（本小题满分13分）已知函数。（Ⅰ）当时，求曲线在处切线的斜率；（Ⅱ）求的单调区间；（Ⅲ）当时，求在区间上的最小值。 21．本题有（1）、（2）、（3）三个选答题，每题7分，请考生任选2题作答，满分14分．如果多做，则按所做的前两题记分．作答时，先用2B铅笔在答题卡上把所选题目对应的题号涂黑，并将所选题号填入括号中．（1）（本小题满分7分）选修4－2：矩阵与变换二阶矩阵M对应的变换将点(1，－1)与(－2，1)分别变换成点(－1，－1)与(0，－2).（Ⅰ）求矩阵M；（Ⅱ）设直线在变换M作用下得到了直线m：2x－y=4，求的方程．（2）（本小题满分7分)选修4—4：极坐标与参数方程在极坐标系中，已知直线l的极坐标方程为，圆C的圆心是，半径为。（Ⅰ）求圆C的极坐标方程；（Ⅱ）求直线l被圆C所截得的弦长。（3）（本小题满分7分)选修4—5：不等式选讲设函数。 （Ⅰ）解不等式；（Ⅱ）已知关于x的不等式恒成立，求实数a的取值范围。稿纸 福州八中2014—2015学年高三毕业班第二次质量检查数学(理)试卷参考答案及评分标准一、选择题：本大题考查基础知识和基本运算．每小题5分，满分50分．BCBBCAABDC二、填空题：本大题考查基础知识和基本运算．每小题4分，满分20分．11．112．13．14．（-∞，-10]15．①③④三、解答题：本大题共6小题，共80分．解答应写出文字说明，证明过程或演算步骤.16．（本小题满分13分）解：（Ⅰ）是方程的解，……………2分……………4分……………………5分对称轴方程为：……………………7分（Ⅱ）……………………9分……………………11分……………………13分17.（本小题满分13分） 17.………4分…………8分…………13分18．（本小题满分13分）解：（Ⅰ）由题意得10(1000－)(1＋0.2%)≥10×1000，……………………3分即2－500≤0，又>0，所以0<≤500.即最多调整出500名员工从事第三产业．……………………5分（Ⅱ）从事第三产业的员工创造的年总利润为万元，从事原来产业的员工创造的年总利润为10(1000－)(1＋0.2%)万元，则≤10(1000－)(1＋0.2%)，……………………8分所以，所以，即恒成立，……………………10分因为，当且仅当，即时等号成立．……………………12分所以，又，所以，即的取值范围为．…………13分19．（本小题满分13分）解：（Ⅰ）当时， ，……………………2分故曲线在处切线的斜率为。……………………3分（Ⅱ）。……………………4分①当时，由于，故。所以，的单调递减区间为。…………5分②当时，由，得。在区间上，，在区间上，。所以，函数的单调递减区间为，单调递增区间为。………7分综上，当时，的单调递减区间为；当时，函数的单调递减区间为，单调递增区间为。……………………8分（Ⅲ）根据（Ⅱ）得到的结论，当，即时，在区间上的最小值为，。……………………10分当，即时，在区间上的最小值为，。……………………12分综上，当时，在区间上的最小值为，当，在区间上的最小值为。……………………13分20.(本小题满分14分)解：（Ⅰ）因为，所以.因为的值域为，所以……………………………………………………3分所以.解得，.所以.所以………………………………………4分 （Ⅱ）因为=所以当时单调递减或时单调递增.…………………………8分即的范围是或时，是单调函数．……………9分（Ⅲ）因为为偶函数，所以.所以10分因为，依条件设，则.又，所以.所以.…………………………………………………12分此时.………14分21．（1）（本小题满分7分）选修4－2：矩阵与变换解：(Ⅰ)设,则有=,=,所以,……………2分解得所以M=………………4分高三数学（理）第二次月考试卷答案第3页共4页高三数学（理）第二次月考试卷答案第4页共4页(Ⅱ)因为且m：2，…………5分所以2(x+2y)－(3x+4y)=4,即x+4=0,这就是直线l的方程………7分（2）（本小题满分7分)选修4—4：极坐标与参数方程解：（Ⅰ）圆的极坐标方程为：·········3分（Ⅱ）圆心到直线距离为，圆半径为，所以弦长为···········7分（3）（本小题满分7分)选修4—5：不等式选讲解：（Ⅰ）的解集为： 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