甘肃省临夏中学2018-2019学年高二下学期期中考试数学(理)试题

适用年级:高二
试卷号:565555

试卷类型:期中
试卷考试时间:2019/7/1

1.单选题(共10题)

1.
“复数在复平面内对应的点在第三象限”是“”的
A.充分不必要条件B.必要不充分条件
C.充要条件D.既不充分也不必要条件
2.
用反证法证明命题:“若能被3整除,那么中至少有一个能被3整除”时,假设应为(  )
A.都能被3整除B.都不能被3整除
C.不都能被3整除D.都能被3整除
3.
分别是定义在上的奇函数和偶函数,当时,,则不等式的解是( )
A.B.C.D.
4.
若函数在点处的切线与垂直,则=(   )
A.2B.0C.D.
5.
已知函数,则( )
A.B.C.D.
6.
(  )
A.B.C.D.
7.
在不等边三角形中,为最大边,想要得到为钝角的结论,三边应满足的条件是(  )
A.B.C.D.
8.
若直线过点,则的最小值等于()
A.2B.3C.4D.5
9.
将3张不同的演唱会门票分给10名同学中的3人,每人1张,则不同分法的种数是(  )
A.2160B.720C.240D.120
10.
若等差数列的公差为,前项和为,则数列为等差数列,公差为,类似地,若各项均为正数的等比数列的公比为,前项积为,则等比数列的公比为(   )
A.B.C.D.

2.选择题(共3题)

11.阅读下面的文章,从文章后的选项中选出能填入空白处的最佳选项。选项中有两项为多余选项。

    Universities are doing everything they can to become a green campus. But there are also items students can do to make your campus more eco-friendly.

1)Recycle everything, especially paper!

    There is a large amount of paper a college student goes through every term.{#blank#}1{#/blank#} We know that these things can't be avoided, but the way you handle the use of all the paper can really help create a better green campus.

2)Buy green.

    {#blank#}2{#/blank#} Paper, cleaning products and water are products that can be bought as recycled goods. They're slightly more expensive than the normal products, but it's worth it to make a green campus.

3)Walk and bike to school.

    Most campuses, especially those that are trying to become a more eco-friendly campus, have pretty good public transit (公共交通系统).{#blank#}3{#/blank#} Walking or biking will help make your campus a green university.

4) {#blank#}4{#/blank#}

    A water bottle can be refilled at any water fountain and can easily be drunk in class or while riding a bike. This will save the environment by decreasing the amount of plastic waste on your campus.

5)Buy used clothing.

    It is usually thought of as something to do to save money. {#blank#}5{#/blank#} Recycling clothes minimizes the use of resources to make clothing and puts a dent in the problem of worldwide sweatshops.

A. Carry a water bottle.

B. It is also good for the environment!

C. Buy recycled goods as much as possible.

D. Paper made of this kind of wood is much stronger.

E. On top of that, almost all universities are pedestrian (步行者) friendly.

F. It includes class notes, term papers, student newspapers and so on.

G. Universities call on all the students to learn to recycle all the waste paper.

12.阅读下面的文章,从文章后的选项中选出能填入空白处的最佳选项。选项中有两项为多余选项。

    Universities are doing everything they can to become a green campus. But there are also items students can do to make your campus more eco-friendly.

1)Recycle everything, especially paper!

    There is a large amount of paper a college student goes through every term.{#blank#}1{#/blank#} We know that these things can't be avoided, but the way you handle the use of all the paper can really help create a better green campus.

2)Buy green.

    {#blank#}2{#/blank#} Paper, cleaning products and water are products that can be bought as recycled goods. They're slightly more expensive than the normal products, but it's worth it to make a green campus.

3)Walk and bike to school.

    Most campuses, especially those that are trying to become a more eco-friendly campus, have pretty good public transit (公共交通系统).{#blank#}3{#/blank#} Walking or biking will help make your campus a green university.

4) {#blank#}4{#/blank#}

    A water bottle can be refilled at any water fountain and can easily be drunk in class or while riding a bike. This will save the environment by decreasing the amount of plastic waste on your campus.

5)Buy used clothing.

    It is usually thought of as something to do to save money. {#blank#}5{#/blank#} Recycling clothes minimizes the use of resources to make clothing and puts a dent in the problem of worldwide sweatshops.

A. Carry a water bottle.

B. It is also good for the environment!

C. Buy recycled goods as much as possible.

D. Paper made of this kind of wood is much stronger.

E. On top of that, almost all universities are pedestrian (步行者) friendly.

F. It includes class notes, term papers, student newspapers and so on.

G. Universities call on all the students to learn to recycle all the waste paper.

13.

某校六年级有甲、乙两个班,甲班学生人数是乙班的 57 .如果从乙班调3人到甲班,甲班人数是乙班的 45 .甲、乙两班原来各有学生多少人?

3.填空题(共4题)

14.
曲线,则的导函数________
15.
如图为导函数的图象,则下列判断正确的是________.(填序号)①内是增函数;②的极小值点;③内是减函数,在内是增函数;④的极大值点.
16.
若函数在区间上为减函数,在区间上为增函数,试求实数的取值范围.
17.
用数学归纳法证明,第一步要证的不等式是_________

4.解答题(共4题)

18.
设函数,若处取得极值.
(1)求的值;
(2)若存在,使得不等式成立,求的取值范围.
19.
(1)设,求证:.
(2)已知函数,比较的大小.
20.
已知数列为该数列的前项和.
(1)写出数列的通项公式;
(2)计算,猜想的表达式,并用数学归纳法证明;
(3)求数列的前项和的取值范围.
21.
(1)若均为实数,且,求证:中至少有一个大于0.
(2)计算
试卷分析
  • 【1】题量占比

    单选题:(10道)

    选择题:(3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