江西省新余市第一中学2020届高三补习班上学期第三次模拟考试数学文试题Word版含答案

〈中国百强中学〉江西省新余一中补习年级第三次模拟考试数学（文）试题（含答案）命题人：数学备课组审题人：数学备课组1、.已知集合41Mxxx或，1,N，则MN····················()A.,B.1,14,C.D.1,14,2、.命题:pxR，31x，则p为·······················································()A.xR，31xB.xR，31xC.xR，31xD.xR，31x3、1,2,,4abk，若//ab，则下列结论中正确的是（B）A.6kB.2kC.6kD.2k4、.已知5log2a，0.5log0.2b，0.20.5c，则a，b，c的大小关系为········()A.acbB.abcC.bcaD.cab5、.为了得到函数32sinxy的图像，只需把xy2sin的图像上所有的点···()A.向左平行移动3个单位长度B.向右平行移动3个单位长度C.向右平行移动6个单位长度D.向左平行移动6个单位长度6、.函数()()lnxxfxeex的图像大致是··················································()7、.在ABC△中，“2AB”是“2cosabB”的············································()A.充要条件B.充分条件C.必要条件D.非充分非必要条件8、已知奇函数()fx满足()(4)fxfx，当(0,1)x时，()2xfx，则2log12f·············································································································()A.43B.2332C.34D.389、.已知直线ykxb的图像恒在曲线ln2yx的图像上方，则bk的取值范围是()A.[1,)B.(2,)C.(0,)D.(1,)10、.定义在R上的函数fx（）满足4(1)(2)()xefxfx，且对任意的1x都有()2()0fxfx(其中()fx为fx（）的导数)，则下列一定判断正确的是（）A.4e(2)(0)ffB.2e(3)(2)ffC.6e(3)(1)ffD.10e(3)(2)ff11、.已知ABC的内角A、B、C的对边分别为a、b、c，O为ABC内一点，若分别满足下列四个条件：①0aOAbOBcOC；②tantantan0AOABOBCOC；③sin2sin2sin20AOABOBCOC；④0OAOBOC；则点O分别为ABC的··············································································()A.外心、内心、垂心、重心B.内心、外心、垂心、重心C.垂心、内心、重心、外心D.内心、垂心、外心、重心12、.函数2222236()cos33xxxxeefxmeex有唯一零点，则m·················()A.3B.2C.32D.12二、填空题(每题分，计分)13、.已知3,3ak，6,7bk，若ab，则实数k的值为______.14、.化简：2cos4sin22___________.15、.已知函数()sinfxxx是R上的单调增函数，则关于x的方程211sin2cos488xxxx的实根为________16、已知函数24,041020,4xxfxxxxx，若有且仅有不相等的三个正数123,,xxx，使得123fxfxfx，则123xxx的值为_________，若存在12340xxxx，使得1234fxfxfxfx，则1234xxxx的取值范围是_________.三、解答题17．已知函数2lg2xxfx（1）试判断并证明函数fx的奇偶性:（2）解不等式lg3fxx.18、．将函数4sincos6gxxx的图象向左平移02个单位长度后得到fx的图象.(1)若fx为偶函数，求；(2)若fx在7,6上是单调函数，求的取值范围.19.在ABC中，若274sincos222BCA.(1)求角A的大小；(2)若3,3abc，分别求bc，的值.20、.在ABC中，角,,ABC的对边分别为,,abc.已知向量sin,16aA，向量1,cosbA，且12ab.(1)求角A的大小；(2)若4b，5c，求sin2B的值.21、.已知函数()ln(1)fxx与函数2()gxxaxb在0x处有公共的切线.(1)求实数a，b的值；(2)记()()()Fxfxgx，求()Fx的极值.22、．已知函数21()(21)2ln()2fxaxaxxaR.（1）求()fx的单调区间；（2）设21()1xgxxxe，若对任意1(0,2]x，均存在2(0,2]x使得121fxgx，求a的取值范围.新余一中补习年级第三次模拟考试数学（文）试题答案命题人：数学备课组审题人：数学备课组1、.已知集合41Mxxx或，1,N，则MN·····················(D)A.,B.1,14,C.D.1,14,2、.命题:pxR，31x，则p为························································(C)A.xR，31xB.xR，31xC.xR，31xD.xR，31x3、1,2,,4abk，若//ab，则下列结论中正确的是（B）A.6kB.2kC.6kD.2k4、.已知5log2a，0.5log0.2b，0.20.5c，则a，b，c的大小关系为··········(A)A.acbB.abcC.bcaD.cab5、.为了得到函数32sinxy的图像，只需把xy2sin的图像上所有的点···(C)A.向左平行移动3个单位长度B.向右平行移动3个单位长度C.向右平行移动6个单位长度D.向左平行移动6个单位长度6、.函数()()lnxxfxeex的图像大致是··················································(A)7、.在ABC△中，“2AB”是“2cosabB”的·············································(B)A.充要条件B.充分条件C.必要条件D.非充分非必要条件8、已知奇函数()fx满足()(4)fxfx，当(0,1)x时，()2xfx，则2log12f··············································································································(A)A.43B.2332C.34D.389、.已知直线ykxb的图像恒在曲线ln2yx的图像上方，则bk的取值范围是(D)A.[1,)B.(2,)C.(0,)D.(1,)10、.定义在R上的函数fx（）满足4(1)(2)()xefxfx，且对任意的1x都有()2()0fxfx(其中()fx为fx（）的导数)，则下列一定判断正确的是（D）A.4e(2)(0)ffB.2e(3)(2)ffC.6e(3)(1)ffD.10e(3)(2)ff11、.已知ABC的内角A、B、C的对边分别为a、b、c，O为ABC内一点，若分别满足下列四个条件：①0aOAbOBcOC；②tantantan0AOABOBCOC；③sin2sin2sin20AOABOBCOC；④0OAOBOC；则点O分别为ABC的···············································································(D)A.外心、内心、垂心、重心B.内心、外心、垂心、重心C.垂心、内心、重心、外心D.内心、垂心、外心、重心12、.函数2222236()cos33xxxxeefxmeex有唯一零点，则m·················(C)A.3B.2C.32D.12二、填空题(每题分，计分)13、.已知3,3ak，6,7bk，若ab，则实数k的值为______.7514、.化简：2cos4sin22___________.3cos215、.已知函数()sinfxxx是R上的单调增函数，则关于x的方程211sin2cos488xxxx的实根为________016、已知函数24,041020,4xxfxxxxx，若有且仅有不相等的三个正数123,,xxx，使得123fxfxfx，则123xxx的值为_________，若存在12340xxxx，使得1234fxfxfxfx，则1234xxxx的取值范围是_________.③④⑤三、解答题17．已知函数2lg2xxfx（1）试判断并证明函数fx的奇偶性:（2）解不等式lg3fxx.解（1）奇函数;（2）2(0,]1,23.（1）函数()fx为奇函数，理由如下：由题意知，2()lg2xfxx，则202xx，即(2)(2)0xx，解得22x则函数()fx的定义域为(2,2)，该定义域关于原点对称。当(2,2)x时，22()()lglg22xxfxfxxx(2)(2)lglg10(2)(2)xxxx，故函数()fx为奇函数。（2）当()lg(3)fxx时，即2lglg(3)2xxx时，由对数函数的性质可得2230232xxxxx，解得203x或12x。故不等式()lg(3)fxx的解集为2(0,]1,2318、．将函数4sincos6gxxx的图象向左平移02个单位长度后得到fx的图象.(1)若fx为偶函数，求；(2)若fx在7,6上是单调函数，求的取值范围.【答案】(1)6π；(2),62解：(1)314sincossin3sin21cos222gxxxxxx2sin216x，2sin2216fxx.又fx为偶函数，则262kkZ，02，6π；(2)7,6x，2222,22662x.02