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czl518888:长郡梅溪湖中学高一月考复习数学试卷(答案版)

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长郡梅溪湖中学高一月考复习数学试卷 班级:_______ 姓名:_______ 一. 选择题: (本题共 15 个小题,每题 3 分,共 45 分) 1.设集合 A ? {x | x ? ?1, x ? Q} ,则 A. ? ? A B. 2 ? A C. { 2}? A D. ( ) ? 2? A 2.若函数 y ? f ( x) 的定义域是 [0, 2] ,则函数 g ( x ) ? A. [0,1] B. [0,1) 4 2 3. 已知集合 A ? ?1, 2,3, k ? , B ? 4, 7, a , a ? 3a ,且 a ? N * , x ? A, y ? B 使 B 中元素 ? f (2 x) 的定义域是() x ?1 C. [0,1) (1,4] D. (0,1) ? y ? 3x ? 1 和 A 中的元素 x 对应,则 a, k 的值分别为( ) A. 2, 3 B. 3, 4 C. 3, 5 D. 2, 5 4.已知函数 f ( x) 是定义在 ? 1 ? a,5?上的偶函数,则 a 的值是 A.6 B.1 C.0 D.-6 5.定义在 R 上的奇函数 f ( x) ,当 x ? 0 时, f ( x ) ? A. 2 3 6. 函数 y ? B. - 2 3 C.2 ) ( ) 1 1 ,则 f ( ) 等于( 2 x ?1 D. -2 ) x x ? x 的图象是( 7. 设全集 U={x∈Z|-1≤x≤5}, A={1,2,5}, B={x∈N|-1<x<4}, 则 B∩(?UA)=( A.{3} B.{0,3} C.{0,4} D.{0,3,4} ) ) 8. 已知集合 A={0,1,2},则集合 B={x-y|x∈A,y∈A}中元素的个数是( A.1 B.3 C.5 D.9 9. 定义在 R 上的奇函数 f(x)满足:对任意的 x1,x2∈[0,+∞)(x1≠x2),有(x2-x1)(f(x2) -f(x1))>0,则( ) B.f(1)<f(-2)<f(3) D.f(3)<f(1)<f(-2) A.f(3)<f(-2)<f(1) C.f(-2)<f(1)<f(3) 10. 若 f(x)是偶函数且在(0, +∞)上减函数, 又 f(-3)=1, 则不等式 f(x)<1 的解集为( ) A.{x|x<-3 或 x>3} C.{x|x>3 或-3<x<0} B.{x|x<-3 或 0<x<3} D.{x|-3<x<0 或 0<x<3} 11.某学生离家去学校,由于怕迟到,所以一开始就跑步,等跑累了再走余下的路程. 在下图中 纵轴表示离学校的距离, 横轴表示出发后的时间, 则下图中的四个图形中较符合该学生走法的是 ( ) d d0 O A. t0 t d d0 O B. t0 t d d0 O C. t0 t d d0 O D. t0 t 1 12. 设函数 f(x)(x∈R)为奇函数,f(1)= ,f(x+2)=f(x)+f(2),则 f(5)=( ) 2 5 A.0 B.1 C. D.5 2 13. 一辆中型客车的营运总利润 y(单位: 万元)与营运年数 x(x∈N)的变化关系如下表所示, 要使总利润达到最大值,则该客车的营运年数是( ) 6 11 8 7 … … x(年) y=ax2+bx+c A.6 B.9 4 7 D.10 25 2 14. 若函数 f(x)=x -3x-4 的定义域为[0, m], 值域为[- , -4], 则 m 的取值范围( ) 4 3 3 3 A.(0,4] B.[ ,4] C.[ ,3] D.[ ,+∞) 2 2 2 15. 设 A 是整数集的一个非空子集,对于 k ? A ,如果 k ? 1 ? A 且 k ? 1 ? A ,那么 k 是 A 的一个“孤立元” ,给定 S ? {1, 2,3, 4,5,6,7,8,} ,由 S 的 3 个元素构成的所有集合中,不含 “孤立元”的集合的个数共( )个 A. 5 B.6 C.7 D.7 序号 答案 1 B 2 B 3 D 4 A 5 D 6 D 7 B 8 C 9 C 10 A 11 B 12 C 13 A 14 C 15 B C.15 二. 填空题: (本题共 5 个小题,每题 3 分) 16. 2 已 知 集 合 A ? 3, a ? ? , 1 , 集 合 B ? ?0 , b ? ? a, 且 A ? B ? ?1? , 则 . 17. 设 f(x)为定义在 R 上的奇函数,当 x≥0 时,f(x)=x2+2x+b+1(b 为常数),则 f(-1)=_-3_______. 18.当 A,B 是非空集合,定义运算 A-B={x|x∈A,且 x?B},若 M={x|y= 1-x},N={y|y =x2,-1≤x≤1},则 M-N=_{x|x<0}_____. 19.已知函数 f ( x) ? x 2 ? 2 x ? a 在区间 ?? 3,2?上的最大值是 4,则 a = -4 。 A ? B ? {0,1,2,3} 20.下列命题中所有正确的序号是_①_③_④____. ①A=B=N,对应 f:x→y=(x+1) -1 是映射; ②函数 f(x)= x -1+ 1-x 和 y= x-1+ 1-x都是既奇又偶函数; 1 ?1? ③已知对任意的非零实数 x 都有 f(x)+2f? ?=2x+1,则 f(2)=- ; 3 ?x? ④函数 f(x-1)的定义域是(1,3),则函数 f(x)的定义域为(0,2); ⑤函数 f(x)在(a,b]和(b,c)上都是增函数,则函数 f(x)在(a,c)上一定是增函数. 三.解答题: (本题共 5 个题,共 40 分) 21. (6 分)全集 S ? 1,3, x 3 ? 3x 2 ? 2 x , A ? 1, 2 x ? 1 ,如果 CS A ? ?0?,则这样的实数 2 2 2 ?

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