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dukun999:2015-2016年四川省德阳市中江县龙台中学高一上学期数学期中试卷和解析

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2015-2016 学年四川省德阳市中江县龙台中学高一(上)期中数 学试卷 一.选择题:本大题共 10 个小题,每小题 5 分,共 50 分.在每小题给出的四个 选项中,只有一项是符合题目要求的. 1. (5.00 分)已知全集 U={0,1,2,3,4,5,6,7,8,9},集合 A={0,1,3, 5,8},集合 B={2,4,5,6,8},则(?UA)∩(?UB)=( A.{5,8} B.{7,9} C.{0,1,3} D.{2,4,6} 2. (5.00 分)已知集合 A={﹣1,3,5},若 f:x→2x﹣1 是集合 A 到 B 的映射, 则集合 B 可以是( ) D.{﹣3,5,9} ) C.[﹣1,0)∪(0,+∞) ) A.{0,2,3} B.{1,2,3} C.{﹣3,5} 3. (5.00 分)函数 f(x)= A.[﹣1,+∞) D.R + 的定义域是( B. (﹣∞,0)∪(0,+∞) 4. (5.00 分)函数 f(x)=ax2+bx﹣2 是定义在[1+a,2]上的偶函数,则 f(x)在 区间[1,2]上是( ) D.先减后增函数 ) ,则 f(4)的值等于 A.增函数 B.减函数 C.先增后减函数 5. (5.00 分)如果幂函数 f(x)=xn 的图象经过点(2, ( ) C. D. A.16 B.2 6. (5.00 分)已知函数 f(x)= A.27 B. C.﹣27 D.﹣ =( ) ,那么 f[f( )]的值为( ) 7. (5.00 分)化简: A.4 B.2π﹣4 C.2π﹣4 或 4 D.4﹣2π ) 8. (5.00 分)在同一直角坐标系中,函数 y=ax 与 y=logax 的图象只能是( 第 1 页(共 15 页) A. B. C. D. 9. (5.00 分)如图所示的曲线是幂函数 y=xn 在第一象限内的图象.已知 n 分别 取﹣1,l, ,2 四个值,则与曲线 C1,C2,C3,C4 相应的 n 依次为( ) A.2,1, ,﹣1 B.2,﹣1,1, C. ,1,2,﹣1 D.﹣1,1,2, 10. (5.00 分)若指数函数 y=ax(0<a<1)在[﹣1,1]上的最大值与最小值的差 是 1,则底数 a 为( A. B. ) C. D. 二、填空题(本大题共 4 小题,每小题 5 分,共 15 分) 11. (5.00 分)计算: . 12. (5.00 分)若函数 f(x)在(﹣∞,0)∪(0,+∞)上为奇函数,且在(0, +∞)上是单调增函数,f(﹣2)=0,则不等式 xf(x)<0 的解集为 13. (5.00 分)方程 9x﹣6?3x﹣7=0 的解是 14. (5.00 分)关于下列命题: ①若函数 y=2x 的定义域是{x|x≤0},则它的值域是{y|y≤1}; ②若函数 y= 的定义域是{x|x>2},则它的值域是{y|y≤ }; ③若函数 y=x2 的值域是{y|0≤y≤4},则它的定义域一定是{x|﹣2≤x≤2}; ④若函数 y=log2x 的值域是{y|y≤3},则它的定义域是{x|0<x≤8}. 其中不正确的命题的序号是 上) . (注:把你认为不正确的命题的序号都填 . . 第 2 页(共 15 页) 三、解答题(本大题共 6 小题,共 70 分) 15. (10.00 分)已知函数 f(x)= (1)在给定的直角坐标系内画出 f(x)的图象 (2)写出 f(x)的单调递增区间与减区间. 16. (10.00 分)利用对数的换底公式化简下列各式: (1)logac?logca; (2)log23?log34?log45?log52; (3) (log43+log83) (log32+log92) . 17. (12.00 分)已知函数 f(x)= 小值. 18. (12.00 分)已知集合 A={x|2﹣a≤x≤2+a},B={x|x≤1 或 x≥4}. (1)当 a=3 时,求 A∩B; (2)若 A∩B=?,求实数 a 的取值范围. 19. (12.00 分)已知函数 f(x)=log2(1﹣x)﹣log2(1+x) . (1)求函数 f(x)的定义域; (2)判断 f(x)的奇偶性. 20. (14.00 分)若 f(x)是定义在(0,+∞)上的增函数,且对一切 x,y>0, 满足 f( )=f(x)﹣f(y) (1)求 f(1)的值, (2)若 f(6)=1,解不等式 f(x+3)﹣f( )<2. ,判断函数在区间[1,4]上的最大值与最 第 3 页(共 15 页) 2015-2016 学年四川省德阳市中江县龙台中学高一(上) 期中数学试卷 参考答案与试题解析 一.选择题:本大题共 10 个小题,每小题 5 分,共 50 分.在每小题给出的四个 选项中,只有一项是符合题目要求的. 1. (5.00 分)已知全集 U={0,1,2,3,4,5,6,7,8,9},集合 A={0,1,3, 5,8},集合 B={2,4,5,6,8},则(?UA)∩(?UB)=( A.{5,8} B.{7,9} C.{0,1,3} D.{2,4,6} 【解答】解:由题义知,全集 U={0,1,2,3,4,5,6,7,8,9},集合 A={0, 1,3,5,8},集合 B={2,4,5,6,8}, 所以 CUA={2,4,6,7,9},CUB={0,1,3,7,9}, 所以(CUA)∩(CUB)={7,9} 故选:B. ) 2. (5.00 分)已知集合 A={﹣1,3,5},若 f:x→2x﹣1 是集合 A 到 B 的映射, 则集合 B 可以是( ) D.{﹣3,5,9} A.{0,2,3} B.{1,2,3} C.{﹣3,5} 【解答】解:∵对应关系为 f:x→2x﹣1,x∈A={﹣1,3,5}, ∴2x﹣1=﹣3,5,9 共 3 个值, 则集合 B 可以是{﹣3,5,9}.

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