2016-2017学年辽宁省六校协作体高二下学期期初数学(理)试卷(带解析)

适用年级:高二
试卷号:632684

试卷类型:开学考试
试卷考试时间:2017/4/20

1.单选题(共10题)

1.
已知全集,集合等于(   )
A.B.C.D.
2.
已知函数,且)在上单调递减,且关于x的方程恰有两个不相等的实数解,则的取值范围是
A.B.[]C.[]{}D.[{}
3.
下列函数中,既是偶函数又在区间上单调递增的是
A.B.C.D.
4.
已知平面向量满足,且,则向量夹角的正弦值为()
A.B.C.D.
5.
《九章算术》是我国古代数学名著,在其中有道“竹九问题”“今有竹九节,下三节容量四升,上四节容量三升.问中间二节欲均容各多少?”意思为 :今有竹九节,下三节容量和为4升,上四节容量之和为3升,且每一节容量变化均匀(即每节容量成等差数列).问每节容量各为多少?在这个问题中,中间一节的容量为(   )
A.B.C.D.
6.
若正数x,y满足x+3y=5xy,则3x+4y的最小值是
A.B.C.5D.6
7.
一个三棱锥的三视图是三个直角三角形,如图所示,则该三棱锥的外接球表面积为(  )
A.B.C.D.
8.
是两条不同的直线,是两个不重合的平面,给出下列四个命题:
①若,则
②若,则
③若,则
④若,则
其中真命题的个数是(  )
A.1B.2C.3D.4
9.
如图,已知平面平面是平面与平面的交线上的两个定点,,且,在平面上有一个动点,使,则四棱锥体积的最大值是(  )
A.B.16C.144D.48
10.
某校高三年级有1000名学生,随机编号为0001,0002,...,1000,现按系统抽样方法,从中抽出200人,若0122号被抽到了,则下列编号也被抽到的是(  )
A.0927B.0834C.0726D.0116

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.
函数的最大值为,最小值为,则等于________.
13.
上定义运算,若存在,则实数的取值范围为_______.
14.
设变量满足约束条件,且目标函数的最小值为,则实数等于_____.
15.
如图,输入时,则输出的________.

4.解答题(共5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.
中,边的对角分别为;且,面积
(1)求的值;
(2)设,将图象上所有点的横坐标变为原来的(纵坐标不变)得到的图象,求的单调增区间.
18.
已知圆的圆心在坐标原点,且与直线相切.
(1)求直线被圆所截得的弦的长;
(2)过点作两条与圆相切的直线,切点分别为求直线的方程;
(3)若与直线垂直的直线与圆交于不同的两点,若为钝角,求直线 在轴上的截距的取值范围.
19.
已知数列中,.
(1)求证:是等比数列,并求的通项公式
(2)数列满足,数列的前项和为,若不等式对一切恒成立,求的取值范围.
20.
某校从参加某次知识竞赛的同学中,选取名同学将其成绩(百分制,均为整数)分成六组后,得到部分频率分布直方图(如图),观察图形中的信息,回答下列问题:

(1)求分数在内的频率,并补全这个频率分布直方图;
(2)从频率分布直方图中,估计本次考试成绩的中位数;
(3)若从第1组和第6组两组学生中,随机抽取2人,求所抽取2人成绩之差的绝对值大于10的概率.
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:(5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:19