山东省莱西市第二中学2020-2021学年高二下学期期中模拟数学试题 Word版含答案

本试卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。共150分，考试时间120

分钟。注意事项： 1、第Ⅰ卷每小题选出答案后，将答案写在答题卡上对应的位置。

2、第Ⅱ卷必须用0.5毫米黑色签字笔（中性笔）作答，答案必须写在答题

卡各题目指定区域内相应的位置，不能写在试题卷上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用涂改液、胶带纸、修正带。

第Ⅰ卷 (选择题，共60分)

一、单项选择题：本大题共8小题，每小题5分，共40分.在每小题给出的四个选项中，只有一项是符合题要求的.

1．

已知离散型随机变量X 的分布列服从两点分布，且()()0341P X P X a ==-==，则a =（） A ．

B ．

C ．

D ．

2．设函数()y f x =在R 上可导，则0

(1)(1)

lim

3x f x f x

?→+?-?等于（）

A ．(1)f '

B ．3(1)f '

C ．

(1)3

f ' D ．以上都不对

3．

设随机变量ξ服从正态分布(2,9)N ，若(21)(1)P m P m ξξ<+=>-，则实数m 的值是（） A ．

B ．

C ．

D ．2

4．已知随机变量()~12,B p ξ，且()235E ξ-=，则()3D ξ=（） A ．

B ．8

C ．12

D ．24

5．上饶市婺源县被誉为“茶乡”，婺源茶业千年不衰，新时代更是方兴未艾，其中由农业部监制的婺源大山顶特供茶“擂鼓峰茶尤为出名，为了解每壶“擂鼓峰”茶中所放茶叶量x 克与食客的满意率y 的关系，抽样得一组数据如下表：

根据表中的全部数据，用最小二乘法得出y 与x 的线性回归方程为? 6.517.5y

x =+，则莱西市第二中学2019级高二 (下)期中数学模拟试题(一)

A ．39.5

B ．40

C ．43.5

D ．45

6．设函数()()x

f x F x e

是定义在R 上的函数，其中()f x 的导函数()'

f x 满足()()f x f x '<对于x ∈R 恒成立，则（）

A ．22021(2)(0),(2021)(0)f e f f e f >>

B ．22021(2)(0),(2021)(0)f e f f e f <>

C ．22021(2)(0),(2021)(0)f e f f e f <<

D ．22021(2)(0),(2021)(0)f e f f e f ><

7．下面的散点图与相关系数r 一定不符合的是（）

A ．①②③

B ．①②④

C ．①③④

D ．②③④

8．关于x 的方程ln 1x

x k

e x

=在()0,∞+上只有一个实根，则实数k =（） A ．1e - B ．1

C ．0

D ．e

二、多项选择题：本大题共4小题,每小题5分,共20分.在每小题给出的四个选项中，有多项符合题要求.全部选对的得5分,选对但不全的得3分,有选错的得0分.

9．已知随机变量X 的分布列如下表(其中a 为常数)： X

1 2 3

P 0.1 0.2

0.4

0.2 a

则下列计算结果正确的有（）

A ．a ＝0.1

B ．P (X ≥2)＝0.7

C ．P (X ≥3)＝0.4

D ．P (X ≤1)＝0.3

10．对两个变量y 和x 进行回归分析，得到一组样本数据：(x 1，y 1)，(x 2，y 2)，…，(x n ，y n )，则下列说法中正确的是（）

A ．由样本数据得到的回归方程y bx a =+必过样本中心()

,x y B ．残差平方和越小的模型，拟合的效果越好

C ．用相关指数R 2来刻画回归效果，R 2越小，说明模型的拟合效果越好

D ．若变量y 和x 之间的相关系数为r =﹣0.9362，则变量y 和x 之间具有线性相关关系

11．某课外兴趣小组通过随机调查，利用22?残联表和2K 统计量研究数学成绩优秀是否与性别有关.计算得2 6.748K =，经查阅临界值表知(

)

6.6350.010P K ≥=，则下列判断正确的是（）

A ．每100个数学成绩优秀的人当中就会有1名是女生

B ．若某人数学成绩优秀，那么他为男生的概率是0.010

C ．有99%的把握认为“数学成绩优秀与性别有关”

D ．在犯错误的概率不超过1%的前提下认为“数学成绩优秀与性别有关” 12．关于函数()2

ln f x x x

+，下列判断正确的是（） A ．2x =是()f x 的极大值点 B ．函数y

f x

x 有且只有1个零点

C ．存在正实数k ，使得()f x kx >恒成立

D ．对任意两个正实数1x ，2x ，且21x x >，若()()12f x f x =，则124x x +>

第II 卷（非选择题共90分）

三、填空题：本大题共4小题，每小题5分，共20分.把答案填在题中的横线上. 13．袋中有a 个白球和b 个黑球，不放回地摸球两次，则第二次摸到白球的概率为_________.

14．已知函数3

()31f x x x =-+，求曲线()y f x =过点()1,2-处的切线方程________.

16．回归方程?? 2.50.2x y

=+在样本(4,1.2)处的残差为________. 四、解答题：（本大题共6个小题，满分70分，解答应写出必要的文字说明、证明过程和演算步骤。）

17．

（本小题满分10分）为了解决消费者在网购退货过程中和商家由于运费问题产生的纠纷，某保险公司推出退货“运费险”.消费者在购买商品时可选择是否购买运费险.当购买运费险的消费者退货时，保险公司将按约定对消费者的退货运费进行赔付.该保险公司随机调查了100名消费者，统计数据如下：

（1）请将上面列联表补充完整，并求若在农村消费者和城镇消费者中按分层抽样抽取一个容量为15的样本时，农村消费者和城镇消费者各应抽取的人数；（2）是否有95%的把握认为消费者购买运费险与城镇农村有关？

附：()()()()()2

2n ad bc K a b c d a c b d -=++++，其中n a b c d =+++.

18.（本小题满分12分）

某公司在市场调查中，发现某产品的单位定价x (单位：万元/吨)对月销售量y (单位：吨)有影响.对不同定价i x 和月销售量()1,2,...8i y i =数据作了初步处理，

=∑

i z

=∑

i i

i x y =∑

i i

i z y =∑

0.24 43 9 0.164 820 68 3956

表中z x =

.经过分析发现可以用y a x

=+来拟合y 与x 的关系. （1）求^

y 关于x 的回归方程；

（2）若生产1吨产品的成本为1.6万元，那么预计价格定位多少时，该产品的月利润取最大值，求此时的月利润.

附：对于一组数据11(),v ω，22(,)ων，…，(,)n n V ω，其回归直线线???v α

βω=+的的斜率和截距的最小二乘估计分别为：^

()()()

n n

i i i i n

i i v n v v v

n ωωωωβωωω

====---?=

--?∑∑∑∑，

v αβω=-.

19.（本小题满分12分）玻璃杯成箱出售，每箱20只，假设各箱含0,1,2只残次品的概率分别为0.8,0.1,0.1，一顾客欲购一箱玻璃杯，售货员随意取一箱，顾客开箱随意地察看四只，若无残次品，则买下该箱，否则退回．试求：（1）顾客买下该箱的概率α；

（2）在顾客买下的一箱中，求无残次品的概率β.

20.（本小题满分12分）函数()cos f x ax x x =+ （1）若2a =-，求函数()f x 在2

x π

=-处的切线；（2）若()f x 在区间0,2π??

????

上单调递减，求实数a 的取值范围.

21.（本小题满分12分）

已知函数()()()ln 1f x a a x x a =++∈R ．（1）求讨论函数()f x 的单调性；

（2）若函数()f x 的图像恒在21y x =+的图像的下方，求实数a 的取值范围．

22.（本小题满分12分）某医院为筛查某种疾病，需要检验血液是否为阳性，现有

*()n n N ∈份血液样本，有以下两种检验方式：①逐份检验，需要检验n 次；②混合检

验，将其(k k N *∈且2k ≥)份血液样木分别取样混合在一起检验．若检验结果为阴性，这k 份的血液全为阴性，因而这k 份血液样本只要检验一次就够了，如果检验结果为阳性，为了明确这k 份血液究竟哪几份为阳性，就要对这k 份再逐份检验，此时这k 份血液的检验次数总共为1k +次．假设在接受检验的血液样本中，每份样本的检验结果是阳性还是阴性都是独立的，且每份样本是阳性结果的概率为()01p p <<.

（1）假设有5份血液样本，其中只有2份样本为阳性，若采用逐份检验的方式，求恰好经过3次检验就能把阳性样本全部检验出来的概率．

（2）现取其中(k k N *∈且2k ≥)份血液样本，记采用逐份检验方式，样本需要检验的总次数为1ξ，采用混合检验方式，样本需要检验的总次数为2ξ．

①记E (ξ)为随机变量ξ的数学期望．若12()=(),E E ξξ运用概率统计的知识，求出p 关于k 的函数关系式()p f k =，并写出定义域；

②若1

41p e -=-，

且采用混合检验方式可以使得样本需要检验的总次数的期望值比逐份检验的总次数期望值更少，求k 的最大值．参考数据：ln2≈0.6931，ln3≈1.0986，ln5≈1.6094．

一、单项选择题：CCBD BCCB

二、多项选择题：9．ABD 10．ABD 11．C D 12.BD 三、填空题： 13．

a a b

+； 14．31y x =-+或1523

44y x =- ； 15．3； 16．-9；四、解答题：（本大题共6个小题，满分70分，解答应写出必要的文字说明、证明过程和演算步骤。） 17．

（本小题满分10分) 解：解：（1）列联表如下：

农村消费者应抽取156100

?=人；城镇消费者应抽取60

159100

=人. （2）()2

2100757333 4.167 3.84110904060

K ??-?=≈>???， .………………………………………………10分 18.（本小题满分12分）解：（1）令1

z x

，则y a b z =+?，则8

1239568943

58208988i i

i i i z y z y

b z z

==-??=

=-?--∑∑，

2a y b z =-?=-，

∴^

52y x

=-+

, （2）月利润()()^

1.62 1.68.22y x x x x x T ???

??-=--=-+ ? ???

=??

2019级高二 (上)期中数学模拟试题(一)

参考答案及评分标准

8.20.2≤-= (当且仅当8

2x x

即2x =时取等号) 答：（1）y 关于x 的回归方程为^

2y x

=-+；

（2）预计价格定位2万元/吨时，该产品的月利润取最大值，最大值为0.2万元. …………………………………………………12分 19．（本小题满分12分）解：设A ＝‘顾客买下该箱’， B ＝‘箱中恰有i 件残次品’，i ＝0,1,2，

(1)α＝P (A )＝P (B 0)P (A |B 0)＋P (B 1)P (A |B 1)＋P (B 2)P (A |B 2)＝0.8＋0.1×419420C C ＋0.1×4

420

C C ≈0.94.

(2)β＝P (B 0|A )＝

()()

00.8

0.94

P AB P A =

≈0.85. …………………………………………………12分 20．（本小题满分12分)

解：（1

）()sin f x a x x '=-，当2a =-

时，()2sin f x x x '=--，函数()f x 在2x π=-

处的切线的斜率12f π??

'-=- ???

，

切点坐标,2ππ?-

+ ?，斜率1k =-，

则切线方程为(12y x ππ?

-+=-?+ ??

，

即02

x y π

（2）()f x 在0,

2π??

????

上单调递减，()sin 0f x a x x '=-≤对0,2x π??∈????

恒成立可得：a

≤sin 2sin 3x x x π?

?+=+ ??

当02

x π

≤≤

时

6x π

π≤+

≤

，1sin ,132x π?

???+∈ ????

???，

所以[]2sin 1,23x π??

∈ ??

?，所以2sin 3x π?

?+ ??

?最小值为1，所以实数a 的取值范围：1a ≤.

.……………………………………………………………………12分 21.（本小题满分12分）

（1）函数()()()ln 1f x a a x x a =++∈R 的定义域是()0,∞+，

()()1a a x a f x a x x +??'=+= ???

．

当0a =时，()1f x =是常数函数，不具有单调性；

当0a >时，()0f x '>对任意()0,x ∈+∞恒成立，故函数()f x 在()0,∞+上单调递增；当0a <时，令()0f x '<，得x a >-，令()0f x '>，得0x a <<-，故函数()f x 在()0,a -上单调递增，在(),a -+∞上单调递减．综上：当0a >时，函数()f x 在()0,∞+上单调递增；当0a =时，()f x 不具有单调性；

当0a <时，函数()f x 在()0,a -上单调递增，在(),a -+∞上单调递减．

（2）函数()f x 的图像恒在21y x =+的图像的下方等价于()2

1f x x <+恒成立，

即()2

ln 11a a x x x ++<+，得()2

ln a a x x x +<，即22ln 0a x ax x +-<．

令()2

ln g x a x ax x =+-，则()0g x <恒成立，所以()max 0g x <．

可知()()()222222x a x a a x ax a g x x a x x x

+-+-++'=-+==

． ①当0a >时，令()0g x '=，得x a =，所以当0x a <<时，()0g x '>，当x a >时，()0g x '<，因此()g x 在()0,a 上单调递增，在(),a +∞上单调递减．

所以()()2

max ln ln 0g x g a a a a a a a ==-+=<，所以01a <<．

②当0a =时，()2

0g x x =-<在()0,∞+上恒成立．

③当0a <时，令()0g x '=，得2a x =-，所以当02a

x <<-时，()0g x '>，当2

a x >-时，()0g x '<，

因此()g x 在0,2a ??- ?

??上单调递增，在,2a ??

-+∞ ???

上单调递减．所以()2

22max

3ln ln 0224224

a a a a a g x g a a a ??????=-=---=--< ? ? ???????，即3ln 24a ??-< ???，则

<34e ，解得3420e a -<<．综上所述，实数a 的取值范围为3

42,1e ??

- ???

．

22.（本小题满分12分）

解：解：（1）记恰好经过3次检验就能把阳性样本全部检验出来为A 事件，

则()3121

32233

P A A C A C A +==. （2）①根据题意，可知()1E k ξ=，2ξ的可能值为1，1k +，则()()211k

P p ξ==-，()()2111k

P k p ξ=+=--，

所以()()()()

(

)()2111111k

E p k p k k p ξ=-++--=+--，

由()()12E E ξξ=，得()11k

k k k p =+--，

所以111k

p k ??=- ?

（*k N ∈且2k ≥）. ②由于1

41p e -

=-，则

()4

21k E k ke ξ-

=+-，

所以

1k k ke

+-<，即ln 04

k -

>，设()ln 4x

f x x =-

，()11444x f x x x

-'=-=，0x >，当()0,4x ∈时，()0f x '>，()f x 在()0,4上单调递增，当()4,x ∈+∞时，()0f x '<，()f x 在()4,+∞上单调递减，

()ln823n 2208l f =-=->，()99

ln 92ln 30494

f =-=-<，

所以k 的最大值为8.

.………………………………………………………………12分

2020年最新高二下册期中考试英语试题有答案

第二学期期中考试高二英语试题本试卷分第I卷（选择题）和第II卷（非选择题）两部分。满分150分。考试时间120分钟。第Ⅰ卷第一部分听力（共两节，满分20分）第一节（共5小题；每小题1分，满分5分）听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。听完每段对话后，你都有10秒钟的时间回答有关小题和阅读下一小题。每段对话仅读一遍。 1. What kind of poems does the man dislike? A. Realistic poems. B. Romantic poems. C. Humorous poems. 2. What is the woman doing? A. Enjoying her music. B. Preparing for a contest. C. Looking for her earphones. 3. Where are the speakers? A. In a post office. B. In a hotel. C. In a taxi. 4. What time is it now? A. 1010. B.1030. C. 1100. 5. What does the woman mean? A. She wants to practice French with the man. B. She will move to the quiet section. C. She won’t do what the man asks. 第二节（共15小题；每小题1分，满分15分）听下面5段对话或独白。每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置，听每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各小题给出5秒钟的作答时间，每段对话或独白读两遍。听第6段材料，回答第6-7题。 6. Which place is the woman looking for? A.A hotel. B. A street. C. A park. 7. Where will the woman turn right? A. On the next block. B. At the second street. C. At the very end of the street. 听第 7 段材料，回答第8-9题。 8. How did the man intend to change his appointment? A. By cancelling it. B. By changing it to another day. C. By making it earlier that day. 9. When did the man decide to see Dr. Benjamin in the end? A. At 300 p.m. on Wednesday. B. At 430 p.m. on Wednesday. C. At 1000 a.m. on Thursday. 听第 8 段材料，回答第10-12题。 10. Where is the woman going for her vacation? A. To New ealand. B. To Australia. C. To Spain. 11. How long did the woman’s mother travel with the man in Spain? A. For two months. B. For two weeks. C. For six months. 12. Who might Terri be? A. The woman’s mother. B. The man’s aunt. C. The man’s wife. 听第 9 段材料，回答第 13-16 题。

江苏省—高二第一学期英语期中模拟试题一

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本试卷分Ⅰ卷（选择题）和Ⅱ卷（非选择题）两部分。满分165分。考试时间：120分。第Ⅰ卷（选择题，共119分）第一节：单项选择( 共15小题，满分22分) 1．— Irene won the first place in the physics competition. —______ ? I don’t like science, anyway. A．Why not B．So what C. What if D．How come ★2．experiment took as five months and turned out great success. A．The; 不填B．不填; a C．The ;a D．The; the 3．I can ___the house being untidy, but I hate it if it's not clean. A. come up with B. put up with C. turn to D. stick to 4．—Have you heard of this new brand of computer, Mike? —Yes, of course and I’ve decided to buy. A．it B．one C．this D．that 5．In order to ______ consumers, it’s extremely important to consider what information should be included in the advertisement. A．adapt to B．apply to C．contribute to D．appeal to ★6．The people, ______ had been damaged by the earthquake, were given help by the Red Cross. A．all whose homes B．all their homes C．all of their home D．all of whose homes 7. The next thing he saw was smoke from behind the house. A. rose B. rising C. to rise D. risen ★★8. It was not until the beginning of the meeting _____ he realized _____ I told him was the only possible way to deal with the problem. A. that; what B. what; that C. when; what D. when; that 9. Peter _____ the book he was reading and reached for his cigarettes and matches. A. set out B. set off C. set in D. set aside 10. When ___ in court, the man didn’t admit having taken the old lady’s necklace. A. questioning B. having questioned C. being questioned D. to be questioned ★11. I like getting up early in summer. The morning air is so good . A. to be breathed B. to breathe C. breathing D. being breathe 12. Being a student, I am often ______ not to spend too much time playing computer games and chatting online.