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高一质量检测数学评分细则考查时间:120分钟考查内容:第一、二、三章一.选择题(本题共12小题,1-10题为单选,在每小题给出的四个选项中只有一个选项符合题目要求.11-12为多选,至少有两个选项符合题目要求
.每小题5分,共计60分)123456789101112ACDDBDAABBCDBD二.填空题(本题共4小题,每小题5分,共20分.)13.8314.815.816.2,13二.填空题(本题共6大题,共70分.)17.(本题10分)解:(1)当
1m时,22xxB.......................................................................2分∴32xxBA............
.....................................................................................5分(2)∵BA,∴B,则有:31121
2mmmm,........................................................................................................
...............8分解之得:m≤2∴实数m的取值范围是2mm;............................................................
.....................10分18.(本题12分)解:(1)设()fxkxb,..........................................................
..................................2分则(1)(1)fxkxbkxkb,又因为(1)64fxx,所以64kkb,6k,2b,......................
.............4分所以()62fxx...........................................................................................
..................6分(2)设1xu,1xu则.....................................................................................2分22()(1)(1)32fuuuuu
,.....................................................................4分所以2()32fxxx...................................................
...............................................6分19.(本题12分)【解析】(1)因为1x,10x,.........................................................
.....................1分111112113111xxxxxx,..................................................3分当且仅当111xx
时,即当2x时等号成立,...............................................................5分11xx的最小值为3;.........................................
................................................................6分(2)由100xx知010x......................................
.....................................................1分当0x或10时,100xx;当010x时,100x,由基本不等式可得101052xxxx....................3分
当且仅当10xx,即当5x时等号成立................................................................................5分综上,10xx的最大值为5..........................
..........................................................................6分20.(本题12分)解:(1)由20,()2xfxxx时
,当0,0xx时2()2fxxx.......................................2分又函数()fx为偶函数,2()2fxxx故函数的解析式为222(0)(){2(0)xxxfxxxx......................
....................................................................................................4分...............6分(2)由函数的图像可
知,函数()fx的单调递增区间为...............................................8分单调递减区间为,...........................
....................................................................................10分函数()fx的值域为1
,.........................................................................................................
.................12分21.(本题12分)【解析】(1)4444134mmf,解得1m;...............................................................
..........2分(2)因为4fxxx,定义域为0xx,关于原点对称,.........................................................3
分又44fxxxfxxx,因此,函数yfx为奇函数;................................5分(3)设120xx,则12121212214444fxfxxxxxxxxx
1212121212441xxxxxxxxxx,因为120xx,所以120xx,所以12fxfx,...................................
..............................10分因此,函数yfx在0,上为单调增函数........................................................................
............12分22.(本题12分)试题解析:(1)为奇函数,且有定义,则,..............................................2分则,,得,......
.......................................4分所以解析式.............................................................................
...............6分(2)在恒成立,即在恒成立,...............8分其中,........................................................................
..................10分分母在取得最小值,..............................................................................
...........11分得到,即....................................................................................................12分