2017届福建连城县朋口中学高三上期中数学(理)试卷(带解析)

适用年级:高三
试卷号:626303

试卷类型:期中
试卷考试时间:2017/7/26

1.单选题(共10题)

1.
已知集合,则中元素的个数是(  )
A.1 B.2 C.3 D.4
2.
设全集的子集,若,就称为好集,那么所有“好集”的个数为(  )
A.B.C.D.
3.
设集合,则“”是“”的(  )
A.充分不必要条件B.必要不充分条件
C.充分必要条件 D.既不充分也不必要条件
4.
已知函数为奇函数,函数为偶函数,且,则(  )
A.B.1C.D.2
5.
是定义在上的偶函数,它在上为增函数,且,则不等式的解集为(  )
A. 
B.
C.
D.
6.
若函数是偶函数,则常数等于(  )
A.B.1C.D.
7.
有反函数,又互为反函数,则的值为(  )
A.4006B.4008 C.2003D.2004
8.
定义运算,则的取值范围是(  )
A.B.C.D.
9.
若不等式对任意实数都成立,则实数的取值范围(  )
A.B.C.D.
10.
在100件产品中有6件次品,现从中任取3件产品,至少有1件次品的不同取法的种数是( )
A.B.C. D.

2.选择题(共1题)

11.

根据短文理解,选择正确答案。

    With all of the wonderful things life brings us, it also brings us stress. It is for this reason that I am an active supporter of mental health days.

    Although it's never good to ignore(忽视) responsibilities, sometimes it is good to unplug(拔除) from the world for a day. We eat healthy and stay active to keep us from getting sick, but sometimes we forget to care for our minds. Our minds and bodies are connected, and when only one is being cared for, the other may be suffering. It is important to try to combine self care with our lives and spend time on activities we enjoy. This helps relieve stress on a daily day.

    So, what do you do on a mental health day? The answer is anything you want. Growing up, my brother and I were allowed a few mental health days a year. We would stay home from school and relax. For him, it was playing games on the computer, while my days were spent reading or watching TV. My mental health days now include picking things up around my apartment, cooking a tasty meal, and then reading for a few hours. I completely shut myself off from work or school. To me, this is relaxing. Organize the clutter(凌乱的东西) that piles up during the week, cook the meals I don't have time to cook, and read the books that I've bought but don't have time to read.

    A mental health day is great, but only if it's supplemented(增补) with self care through the week. From my experience, if self care is not regularly provided in your week, taking a mental health day is just going to stress you out even more. But when it's needed, try hard to recognize that and take care of yourself. It will help keep you happy and healthy. A mental health day is not a day to avoid life, it is a day to recoup(恢复).

3.填空题(共4题)

12.
已知函数,则_________.
13.
已知,若关于的方程没有实根,则的取值范围是
14.
设函数,给出下列命题:①时,方程只有一个实数根;②时,是奇函数;③方程至多有两个实根.
上述三个命题中所有正确命题的序号是  
15.
函数的值域为   

4.解答题(共4题)

16.
已知函数满足:对任意,都有成立,且时,
(1)求的值,并证明:当时,
(2)判断的单调性并加以证明;
(3)若上单调递减,求实数的取值范围.
17.
已知,常数).
(1)讨论函数的奇偶性,并说明理由;
(2)若上为减函数,求的取值范围.
18.
是定义在上的奇函数,且对任意实数,恒有,当时,
(1)求证:是周期函数;
(2)当,求的解析式;
(3)计算:
19.
设不等式的解集为,如果,求实数的取值范围.
试卷分析
  • 【1】题量占比

    单选题:(10道)

    选择题:(1道)

    填空题:(4道)

    解答题:(4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:18