2018高考数学模拟7.doc

2011年高考模拟试题（7）(文理合卷) 一.选择题（本大题共12题，每小题5分，共60分）1.(理)复数的值是A. B. C. D.（文）的值是A. w.w.w.k.s.5 u.c.o.m B. C. D.2.已知集合，则集合=A. w.w.w.k.s.5 u.c.o.mB.C.D.3.若,下列命题中正确的是A.若, 则 B.若, 则C.若, 则 w.w.w.k.s.5 u.c.o.m D.若 , 则4.已知函数的反函数是，则是A.奇函数且在上单调递减 B.偶函数且在上单调递增C.奇函数且在上单调递减 D.偶函数且在上单调递增5.已知实数、满足约束条件,则的最大值 A.24 w.w.w.k.s.5 u.c.o.m B.20 C.16 D.126.设向量，向量，则与的夹角是A. B. C. D. 7.若半径是的球与正三棱柱的各个面都相切，则球与正三棱柱的体积比是A. B. C. D. O8.若函数()的部分图象如图所示，则有A. B. C. D. 9.定义在上的偶函数对于任意的都有，且，则的值为A. B. C. D.10. 在边长为1的等边中，设( ) A B0 C D311. 在等差数列an中，其前n项和为Sn ，若a2,a10是方程x2+12x-8=0的两个根，那么S11的值为( ) A.44 B.-44 C.66 D.-6612. 设，二次函数的图像为下列之一，则的值为（ ）A1B1CD二.填空题（本大题共4小题，每小题4分，共16分）13.在的展开式中，的系数是15，则实数_.14.（理）已知，则_.（文）函数的单调递减区间是_.15.编号为1、2、3、4、5的五个人分别去坐编号为1、2、3、4、5的五个座位，其中有且只有两个人的编号与座位号一致的坐法有_种.16. 已知抛物线的准线与双曲线的左准线重合，则抛物线的焦点坐标为 .三.解答题（本大题共6小题，共76分）17.（本小题满分12分） 已知（为常数）.（1）求的单调递增区间；（2）若在上的最大值与最小值之和为3，求的值.18.（本小题满分12分） 在举办的奥运知识有奖问答比赛中，甲、乙、丙同时回答一道有关奥运知识的问题，已知甲回答对这道题目的概率是，甲、丙两人都回答错的概率是，乙、丙两人都回答对的概率是.（1）求乙、丙两人各自回答对这道题目的概率.（2）（理）求回答对这道题目的人数的随机变量的分布列和期望.（文）求甲、乙、丙三人中至少有两人回答对这道题目的概率.19.（本小题满分12分）在三棱柱中， ，是的中点，F是上一点，且.(1) 求证：；(2) 求平面与平面所成角的正弦值.ABCDFA1B1C120（本小题满分12分）=, =,（1）求证：为等差数列； (2) 若,问是否存在, 对于任意（），不等式成立.21. （本小题满分12分）如图，已知点，直线：， 为平面上的动点，过作直线的垂线，垂足为点,且。（）求动点的轨迹的方程；（）过点的直线交轨迹于，22(本题满分14分)（理）（本小题满分12分）已知. (1) 如果函数的单调递减区间为，求函数的解析式； （2）若的导函数为，对任意，不等式恒成恒成立，求实数的取值范围.（文（本小题满分12分）已知. (1) 如果函数的单调递减区间为，求函数的解析式； （2）若的导函数为，对任意，不等式恒成立，求实数的取值范围.2011年高考模拟试题（6）(文理合卷) 参考解答一.选择题1.(理) B（文）A2. C3. B4. D 5. B 6. C7. B8.C9. A10.A11.D12. B二.填空题14.（理）1（文）15.2016. 三.解答题（本大题共6小题，共76分）17.解：（1），即 ， 的单调递增区间是 6分（2），则 ， . 12分18.（本小题满分12分） 解：（1）设乙、丙各自回答对的概率分别是，根据题意，得 解得 ，； 6分（2）（理）可能取值0，1，2，3，； ； .分布列如下：0123期望为 . 12分（文） 12分19.（本小题满分12分）ABCDFA1B1C1解：（1）因为,是的中点，所以.又，所以 又，所以 在中 ，在中 所以 ， 即，所以。 6分（2）延长交于，则为所求二面角的棱.由得：。过作，且与交于，又 ，为所求二面角的平面角. 由和相似得：。又，所以 。即所求二面角的正弦值是. 12分20（本小题满分12分）解：（1） 为等差数列 6分（2） 12分21. （本小题满分12分）解：（）设点，则，由得：，化简得 （）设直线的方程为:.设,又,联立方程组,消去得：，故由，得：，整理得：，。22(本题满分14分)（1）.2分由题意 的解集是，即 的两根分别是.4分将代入方程得. .6分（2） 由题意知 恒成立，即恒成立.8分设，则.令，得.当时，；当时，10分当时，取得最大值，.因此的取值范围是.12分（文）（1）.2分由题意 的解集是，即 的两根分别是.4分将代入方程得. .6分（2） 由题意知 时恒成立，即，所以.由于，于是，得 9分而，所以为所求. 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