河北省辛集中学2018-2019学年高二上学期第二次月考数学试题

适用年级:高二
试卷号:631613

试卷类型:月考
试卷考试时间:2019/4/1

1.单选题(共13题)

1.
已知的定义域为的导函数,且满足,则不等式的解集是(   )
A.B.C.D.
2.
函数 在点处的切线斜率的最小值是()
A.B.C.D.
3.
如图所示的三角形数阵满足:其中第一行共有一项是 ,第二行共有二项是,第三行共有三项是 ,依此类推第行共有项,若该数阵的第15行中的第5个数是 ,则m=(  )
A.105B.109C.110D.215
4.
已知两点,点P是椭圆上任意一点,则点P到直线AB的距离最大值为(  )
A.B.C.6D.
5.
若直线和⊙O∶相离,则过点的直线与椭圆的交点个数为(    )
A.至多一个B.2个C.1个D.0个
6.
椭圆的短轴长为(  )
A.B.C.2D.4
7.
在区间内随机取一个数,则方程表示焦点在轴上的椭圆的概率是(   )
A.B.C.D.
8.
已知两变量x与y的统计数据如下表:
x
4
2
3
5
y
49
26
39
54
 
根据上表可得回归方程 中=9.4,则当x=6时,的值为(  )
A.63.6B.65.5C.67.7D.72.0
9.
某班50名学生在一次百米测试中,成绩全部介于13秒到19秒之间,下图是这次测试成绩的频率分布直方图.设成绩小于17秒的学生人数占全班总人数的百分比为x,成绩大于等于15秒且小于17秒的学生人数为y,则x和y分别为(  )
A.10%,45B.90%,45C.10%,35D.90%,35
10.
《朗读者》以精美的文字,最平实的情感读出文字背后的价值,感染了众多听众,中央电视台在2018年推出了《朗读者第二季》,电视台节目组要从2018名观众中抽取50名幸运观众.先用简单随机抽样从2018人中剔除18人,剩下的2000人再按系统抽样方法抽取50人,则在2018人中,每个人被抽取的可能性 ( )
A.都相等,且为B.都相等,且为C.均不相等D.不全相等
11.
某同学同时抛掷两颗骰子,得到的点数分别记为,则双曲线的离心率的概率是(  )
A.B.C.D.
12.
证明等式 时,某学生的证明过程如下
(1)当n=1时, ,等式成立;
(2)假设时,等式成立,即
则当时, ,所以当时,等式也成立,故原式成立.
那么上述证明(  )
A.过程全都正确B.当n=1时验证不正确
C.归纳假设不正确D.从的推理不正确
13.
阅读程序框图,如果输出i=5,那么在空白矩形框中应填入的语句为( )
A.S=2*i-2B.S=2*i-1C.S=2*iD.S=2*i+4

2.选择题(共4题)

14.

随着共享单车的投放,绿色环保的骑车出行又成为了许多人的首选.

15.

随着共享单车的投放,绿色环保的骑车出行又成为了许多人的首选.

16.用方框中所给单词的适当形式完成下面的短文

make, with, everything, like, other, it, photo, interesting

    Skin-diving (轻装潜水)is a new sport today. Many people show interest in this sport. Some go under water to see beautiful scenes(景色).{#blank#}1{#/blank#}go down into deep(深的) water to take pictures of swimming fish. It is not dark under water and there are a lot of big or little fish living there. Some of them use the sand to {#blank#}2{#/blank#}their homes. If you are under water, you will find you are just in a fish village.

    There is no wind under water.{#blank#}3{#/blank#} is blue and green. During the day, there is much light. Sometimes people do not have to use a flash(闪关灯)to take {#blank#}4{#/blank#}under water.

    This sport takes you into a wonderful new world. When you are under water,{#blank#}5{#/blank#} is easy for you to carry a big stone(石头). It is{#blank#}6{#/blank#}a trip to the moon!

    Catching fish is one of the most {#blank#}7{#/blank#} parts of this sport. When fish swim nearby, you can catch them{#blank#}8{#/blank#} your hands.

17.用方框中所给单词的适当形式完成下面的短文

make, with, everything, like, other, it, photo, interesting

    Skin-diving (轻装潜水)is a new sport today. Many people show interest in this sport. Some go under water to see beautiful scenes(景色).{#blank#}1{#/blank#}go down into deep(深的) water to take pictures of swimming fish. It is not dark under water and there are a lot of big or little fish living there. Some of them use the sand to {#blank#}2{#/blank#}their homes. If you are under water, you will find you are just in a fish village.

    There is no wind under water.{#blank#}3{#/blank#} is blue and green. During the day, there is much light. Sometimes people do not have to use a flash(闪关灯)to take {#blank#}4{#/blank#}under water.

    This sport takes you into a wonderful new world. When you are under water,{#blank#}5{#/blank#} is easy for you to carry a big stone(石头). It is{#blank#}6{#/blank#}a trip to the moon!

    Catching fish is one of the most {#blank#}7{#/blank#} parts of this sport. When fish swim nearby, you can catch them{#blank#}8{#/blank#} your hands.

3.填空题(共4题)

18.
命题“若,则”的逆命题是_______ 命题(填“真”或“假”).
19.
设函数,若的极大值点,则a取值范围为_______________.
20.
由曲线,直线轴围成的封闭图形的面积为__________。
21.
已知F为抛物线的焦点,过F作两条互相垂直的直线,直线与抛物线交于A、B两点,直线与抛物线交于C、D两点,则AB+DE的最小值为________

4.解答题(共4题)

22.
已知函数有两个零点.
(1)若为假命题,求实数的取值范围;
(2)若为真命题, 为假命题,求实数的取值范围.
23.
已知函数
(1)若曲线在点处的切线经过点,求a的值;
(2)若内存在极值,求a的取值范围;
(3)当时,恒成立,求a的取值范围.
24.
如图所示,四边形是矩形,四边形是梯形, ,平面平面, 点的中点.

(1)求证:∥平面
(2)求二面角的余弦值.
25.
某工厂生产两种元件,其质量按测试指标划分为:大于或等于为正品,小于为次品.现从一批产品中随机抽取这两种元件各件进行检测,检测结果记录如下:






B





 
由于表格被污损,数据看不清,统计员只记得,且两种元件的检测数据的平均值相等,方差也相等.
(1)求表格中的值;
(2)从被检测的种元件中任取件,求件都为正品的概率.
试卷分析
  • 【1】题量占比

    单选题:(13道)

    选择题:(4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:21