湖北省荆门市龙泉中学2019-2020学年高一上学期期中数学试题

适用年级:高一
试卷号:529425

试卷类型:期中
试卷考试时间:2019/11/26

1.单选题(共12题)

1.
将集合 表示成列举法,正确的是(  )
A.{2,3}B.{(2,3)}
C.{x=2,y=3}D.(2,3)
2.
已知集合,则(   )
A.B.C.D.
3.
是全集的子集,,则满足的个数是(   )
A.5B.4C.3D.2
4.
已知函数满足对任意都有成立,则实数的取值范围是(   )
A.B.C.D.
5.
某同学家门前有一笔直公路直通长城,星期天,他骑自行车匀速前往旅游,他先前进了,觉得有点累,就休息了一段时间,想想路途遥远,有些泄气,就沿原路返回骑了, 当他记起诗句“不到长城非好汉”,便调转车头继续前进. 则该同学离起点的距离与时间的函数关系的图象大致为( )
A.B.
C.D.
6.
已知,且,则的值为(   )
A.4B.0C.D.
7.
若变量xy满足|x|﹣ln0,则y关于x的函数图象大致是(  )
A.B.
C.D.
8.
设函数 ,则使得成立的的取值范围是(   )
A.B.C.D.
9.
若函数的定义域是[0,4],则函数的定义域是(   )
A.B.C.D.
10.
下列各式中错误的是(   )
A.B.C.D.
11.
设函数,(),表示不超过实数的最大正数,则函数的值域是(   )
A.B.C.D.
12.
·=(   )
A.B.C.1D.2

2.选择题(共1题)

13.

   At school many things happen to us. We may feel excited when we have success in a school play. We may feel sorry if we lose an important game. We want to remember all the important things in our lives.
   How to keep the memory? Our English teacher, Miss Wang, taught us a good way of remembering things to make our own yearbook. What is a yearbook? A yearbook is a kind of book which is used to keep the memory of exciting moments. It's usually made at the end of the year.
   Last December, we began to make our yearbook. First we chose the persons who did something special, then some students interviewed (采访) them, some wrote down their stories, others took photos of them. Everyone in our class had something to do. Finally our teacher helped us to put the things together. We had our first yearbook.
   All of us put a lot of love into making the yearbook. It is so wonderful that not only the students but also our parents and teachers will remember the special time for ever.

3.填空题(共4题)

14.
已知,则_________
15.
(e为自然对数的底数),且,其中是奇函数,为偶函数,则_________.
16.
已知函数如表,则______
x
1
2
3
f(x)
3
2
1
 
17.
一个驾驶员喝了少量酒后,血液中的酒精含量迅速上升到mg/mL,在停止喝酒后,血液中的酒精含量以每小时25%的速度减少.为了保障交通安全,规定驾驶员血液中的酒精含量不得超过mg/mL,那么这个驾驶员至少要经过________小时才能开车.(精确到1小时,参考数据).

4.解答题(共6题)

18.
已知函数

(1)当=0时,画出函数的简图,并指出的单调区间;
(2)若方程有4个不等的实根,求的取值范围.
19.
已知函数,且
(I)求实数的值及函数的定义域;
(II)判断函数在上的单调性,并用定义加以证明.
20.
已知函数是定义在上的奇函数
(1)求并求的值域;
(2)若函数满足,若对任意,不等式恒成立,求实数m的最大值.
21.
已知函数
(1)求的定义域,并证明的奇偶性;
(2)求关于x的不等式的解集.
22.
(1)
(2)
23.
已知函数, 关于的不等式的解集为,且.
(1)求的值.
(2)是否存在实数,使函数的最小值为?若存在,求出的值;若不存在,说明理由.
试卷分析
  • 【1】题量占比

    单选题:(12道)

    选择题:(1道)

    填空题:(4道)

    解答题:(6道)

  • 【2】:难度分析

    1星难题:0

    2星难题:0

    3星难题:0

    4星难题:0

    5星难题:0

    6星难题:0

    7星难题:0

    8星难题:0

    9星难题:22