2019-2020学年天津市滨海新区塘沽一中高一(上)期中数学试卷 (含答案解析)

2019-2020学年天津市滨海新区塘沽一中高一(上)期中数学试卷 (含答案解析)
2019-2020学年天津市滨海新区塘沽一中高一(上)期中数学试卷 (含答案解析)

2019-2020学年天津市滨海新区塘沽一中高一(上)期中数学试卷

一、选择题(本大题共9小题,共45.0分)

1. 已知集合M ={x|x 2?7x +6<0,x ∈Z},N =(1,5),则M ∩N =( )

A. (1,5)

B. {2,3,4}

C. (1,6)

D. {5}

2. 命题“?x ∈R ,tanx ≠1”的否定是( )

A. ?x ?R ,tanx ≠1

B. ?x ∈R ,tanx =1

C. ?x ?R ,tanx ≠1

D. ?x ∈R ,tanx =1

3. 对于实数a,b,c ,有下列命题:

①若a >b ,则ac >bc ;

②若ac 2

③若a ab >b 2;

④若c >a >b >0,则a c?a >b

c?b .

其中真命题的个数是( )

A. 1

B. 2

C. 3

D. 4

4. 已知a =243,b =425,c =251

3,则( )

A. b

B. a

C. b

D. c

5. “lgx >lgy ”是“10x >10y ”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

6. 已知函数f(x)=x 3+2x +sinx ,若f(a)+f(1?2a)>0,则实数a 的取值范围是(

) A. (1,+∞) B. (?∞,1) C. D.

7. 设a >b >0,且ab =2,则a 2+1

a (a?

b )的最小值是( )

A. 1

B. 2

C. 3

D. 4

8. 已知函数f(x)=(12)x?1

+b 的图像不经过第一象限,则实数b 的取值范围是( )

A. b

B. b ≤?1

C. b ≤?2

D. b

9. 设f(x)是奇函数,且在(0,+∞)内是增函数,又f(?3)=0,则x ?f(x)<0的解集是(

) A. {x|?33} B. {x|x

C. {x|x 3}

D. {x|?3

二、填空题(本大题共6小题,共30.0分)

10. 函数y =ln (3?x )+√2x ?4的定义域是__________.

11. 设函数f(x)={1+log 2

(2?x),x <1,

2x?1,x ≥1,则f(?2)+f(2)=______.

12.函数f(x)={x,x≥0,

x2,x<0的单调递增区间是

________,单调递减区间是________.

13.若x+2y=1,则2x+4y的最小值是____________;

14.设函数f(x)满足:对任意的x1,x2∈R都有(x1?x2)[f(x1)?f(x2)]>0,则f(?3)与f(?π)的大小关系

是__________.

15.设函数f(x)(x∈R)的周期为3,当x∈[?2,1)时,f(x)={x+a?,??2?x<0

(1

2

)

x

?,?0≤x<1

,则f(13

2

)=;

若f(x)有最小值,无最大值,则实数a的取值范围为____________________.

三、解答题(本大题共4小题,共45.0分)

16.已知集合A={x|0<2x+a≤3},B={x|?1

2

(1)当a=1时,求(?R B)∪A;

(2)若A∩B=A,求实数a的取值范围.

17.关于二次函数f(x)=x2+(m?1)x+1(1)若?x∈R,f(x)>0恒成立,求实数m的取值范围;

(2)若方程f(x)=0在区间[0,2]上有解,求实数m的取值范围.

18.已知函数f(x)=x2+bx+c(b、c∈R).

(1)当c=b时,解关于x的不等式f(x)>1;

(2)若f(x)的值域为[1,+∞),关于x的不等式f(x)

19.设函数f(x)=x2+ax+b的两个零点分别是2和?4;

(1)求函数f(x)的解析式;

(2)当函数f(x)的定义域是[?2,2]时,求函数f(x)的值域.

-------- 答案与解析 --------

1.答案:B

解析:

【分析】

本题考查描述法、区间法表示集合,以及一元二次不等式的解法,交集的运算,属于基础题.可以求出集合M,然后进行交集的运算即可.

【解答】

解:M={x|1

∴M∩N={2,3,4}.

故选:B.

2.答案:D

解析:解:命题为全称命题,则命题的否定为?x∈R,tanx=1,

故选:D

根据全称命题的否定是特称命题即可得到结论.

本题主要考查含有量词的命题的否定,比较基础.

3.答案:C

解析:

【分析】

本题主要考查不等关系与不等式、不等式的性质等基础知识,属于基础题.

根据不等式的性质逐项进行判定即可.

【解答】

解:①若a>b,当c=0时,ac=bc=0,

所以①错误.

②∵ac2

∴c≠0,

∴c2>0,

∴一定有a

③因为a

所以a2>ab>0,ab>b2>0,

所以a2>ab>b2;

所以③正确;

④若c>a>b>0,则c?a>0,c?b>0,且c?b>c?a>0,

所以1

c?a >1

c?b

>0,

因为a>b>0,

所以a

c?a >b

c?b

,所以④正确.

故选C.

4.答案:A

解析:

【分析】

本题考查利用指数函数和幂函数的单调性比较数的大小,难度一般.【解答】

解:a=243,b=425=245,

因为函数f(x)=2x单调递增,4

3>4

5

所以243>245,即a>b;

a=243=423,c=2513=523,

因为函数g(x)=x23在[0,+∞)上单调递增,4<5,

所以423<523,即a

综上所述得b

故选A.

5.答案:A

解析:解:∵lgx>lgy,

∴x>y>0,

∵10x>10y,

∴x>y,

∴x>y>0?x>y,反之则不能,

∴lgx>lgy是“10x>10y”的充分不必要条件,

故选A.

根据已知条件lgx>lgy,求出x,y的范围,再根据指数的性质根据10x>10y,求出x,y的范围,再根据充分条件和必要条件的定义进行求解;

此题主要考查指数函数和对数函数的性质及其单调性,还考查了必要条件和充分条件的定义,是一道基础题.

6.答案:B

解析:

【分析】

本题主要考查不等式的求解,根据条件判断函数的奇偶性和单调性是解决本题的关键.

根据条件判断函数的奇偶性和单调性,利用奇偶性和单调性的性质将不等式进行转化求解即可.【解答】

解:∵f(x)=x3+2x+sinx,

∴f(?x)=?x3?2x?sinx=?(x3+2x+sinx)=?f(x),则f(x)是奇函数,

函数的导数f′(x)=3x2+2+cosx>0,

则函数f(x)是增函数,

则由f(a)+f(1?2a)>0,,得f(a)>?f(1?2a)=f(2a?1),

得a>2a?1,

得a<1,

即实数a的取值范围是(?∞,1),

故选B.

7.答案:D

解析:

【分析】

本题考查了变形利用基本不等式的性质,属于基础题.

由a>b>0,a(a?b)>0,可得a2+1

a(a?b)=a2?ab+1

a(a?b)

+2,再利用基本不等式的性质即可

得出.

【解答】

解:∵a>b>0,∴a(a?b)>0,ab=2,

∴a2+1

a(a?b)=a2?ab+1

a(a?b)

+2≥2√(a2?ab)?1

a2?ab

+2=4,

当且仅当a(a?b)=1,ab=2即a=√3,b=2√3

3

时等号成立.故选:D.

8.答案:C

解析:

【分析】

本题考查了指数函数及其性质,属于基础题.

根据指数函数性质即可得到答案.

【解答】

解:∵函数f(x)=(12)x?1+b 为减函数,且图象不经过第一象限,

∴可知f (0)=2+b ≤0,得到b ≤?2,

故选C . 9.答案:D

解析:由x ?f(x)<0,得{x <0f(x)>0或{x >0f(x)<0而f(?3)=0,f(3)=0,即{x <0f(x)>f(?3)

或{x >0f(x)

解得{x|?3

解析:

【分析】

本题考查函数的定义域及其求法,是基础的计算题.

【解答】

解:由{?3?x >0?2x ?4≥0

,解得2≤x <3. ∴函数y =ln (3?x )+√2x ?4的定义域是[2,3).

故答案为[2,3).

11.答案:5

解析:

【分析】

本题考查分段函数求值,直接代入函数解析式求解即可.

【解答】

解:∵f(x)={1+log 2(2?x),x <12x?1,x ≥1

, ∴f(?2)=1+log 24=3,f(2)=22?1=2,

∴f(?2)+f(2)=5.

故答案为5.

12.答案:(0,+∞) (?∞,0)

解析:

【分析】

本题主要考查分段函数的单调区间,涉及到一次函数和二次函数的单调性.

【解答】

解:由题意可知:当x ≥0时,函数f(x)=x 为单调增函数;

当x <0时,函数f(x)=x 2在(?∞,0)上单调递减,

所以函数f(x)={x,x ≥0,x 2,x <0

的单调递增区间是(0,+∞), 单调递减区间是(?∞,0),

故答案为(0,+∞),(?∞,0).

13.答案:2√2

解析:解:由题意知2x +4y ≥2√2x ?22y

=2√2x+2y =2√2.

∴2x +4y 的最小值是2√2.

14.答案:f(?3)>f(?π)

解析:由(x 1?x2)[f(x1)?f(x2)]>0得f(x)是R 上的单调递增函数,又?3>?π,∴f(?3)>f(?π).

15.答案:√22;(1,52]

解析:

【分析】

本题主要考查了分段函数模型和函数的最值,属于中档题.

【解答】

解:f (132)=f(12)=√22

, 若f(x)有最小值,无最大值,则{?2+a ≤12a >1

, 解得1

故答案为√22;(1,52]. 16.答案:解:(1)当a =1时,集合A ={x|0<2x +1≤3}={x|?12

∵B ={x|?12

∴?R B ={x|x ≤?12或x ≥2},

∴(?R B)∪A ={x|x ≤1或x ≥2};

(2)若A ∩B =A ,则A ?B ,

∵A ={x|0<2x +a ≤3}={x|?a 2

2},易知A ≠?,

∴{?a 2≥?123?a 2

<2, 解得?1

∴实数a 的取值范围是(?1,1].

解析:本题考查了集合的混合运算,考查集合关系中的参数取值问题,属于基础题.

(1)求出当a =1时集合A ,根据并集和补集的定义写出(?R B)∪A ;

(2)根据A ∩B =A 可得A ?B ,由此列出不等式组求出a 的取值范围.

17.答案:解:(1)∵?x ∈R ,f(x)>0恒成立,

∴△=(m ?1)2?4<0

∴m 2?2m ?3<0

解得?1

(2)∵f(x)=0在区间[0,2]上有解,又f(0)=1≠0

∴f(x)=0在区间(0,2]上有解

由x 2+(m ?1)x +1=0得m =1?(x +1

x )…(8分)

当0

因此实数m 的取值范围是:(?∞,?1]…(12分)

解析:(1)由题意可得△=(m ?1)2?4<0,解不等式可求

(2)由f(0)=1≠0可知f(x)=0在区间(0,2]上有解,由x 2+(m ?1)x +1=0得m =1?(x +1

x ),结合基本不等式可求m 的范围

本题主要考查了二次函数的恒成立与基本不等式在函数的最值求解中的应用,解题的关键是熟练掌握基本知识 18.答案:解:(1)当c =b 时,由 f(x)>1得

所以当时,原不等式的解集为;

当b =2时,原不等式的解集为(?∞,?1)?(?1,+∞);

当b >2时,原不等式的解集为(?∞,1?b)?(?1,+∞).

(2)由f(x)的值域为[1,+∞),得4c?b 24=1,

又关于x 的不等式f(x)

所以m ,m +4是方程f(x)=a 的两个根,

即x 2+bx +c ?a =0的两根之差为4.所以4=√b 2?4(c ?a),

则{b 2?4(c ?a)=16,4c ?b 2=4,

解得a =5.

解析:本题主要考查了二次函数的性质,二次函数与不等式的关系,韦达定理;

(1)根据b =c 解出不等式的两根,然后根据b 的范围写出原不等式的解集;

(2)利用不等式的值域为[1,+∞),得

4c?b 24=1,找到b ,c 的关系,再解不等式f(x)

定理解得a 的值. 19.答案:解:(1)∵函数f(x)=x 2+ax +b 的两个零点分别是2和?4;

∴f(x)=x 2+ax +b =(x ?2)(x +4)=x 2+2x ?8,

(2)由(1)得:f(x)=(x +1)2?9,

对称轴x =?1,

∴f(x)在[?2,?1)单调递减,在(?1,2]单调递增,

f(?1)=?9,f(?2)=?8,f(2)=0,

∴f(x)min =?9,f(x)max =0,

∴函数f(x)的值域是:[?9,0].

解析:(1)根据函数的零点,即f(x)=0的根,从而求出函数的解析式;

(2)根据函数的解析式求出函数的单调区间,从而得到函数的最值,进而求出函数的值域; 本题考查了二次函数的解析式问题,考查了函数的值域问题,是一道基础题.

天津一中2015-2016上学期期中初一英语

天津一中2015-2016-1 七年级期中考试英语学科试卷 班级姓名成绩 I 卷:客观试题(70%) 注:请将 I 卷答案填写在机读卡上 I.单项选择(本题共25 小题,每小题1 分,共25 分) 1.There is a of something burning in this room. Please open the window. A.taste B. sound C. smell D. look 2.Your MP4 is quite cheap. Where did you buy ?I want to buy , too. A.one; one B. it; it C. one; it D. it; one 3.--Tomorrow I'm flying to New York.-- . A.Thank you B. Have a good trip C. Best wishes D. Yes 4.-- How old is she? -- She is . A.13-year-old B. 13-years-old C. 13 years old D. 13 year old 5.You look so tired. Why not stop ? A.to have a rest B. having a rest C. to having a rest D. have a rest 6.You cook than John. A.quickly and well B. quick and good C. more quickly and better D. much quickly and better 7.Don’t read in the sun. It’s your eyes. A.good at B. bad at C. good for D. bad for 8.There a football game tomorrow afternoon. A.will have B. is going to be C. has D. is going to have 9.Her way of teaching makes all her students . A.interesting B. interested C. interests D. interest 10.This is my friend John and this is Mary. They from England. 17.The students often forget their homework, so the teachers are angry. A.do B. to do C. doing D. did 18.When I got the news that the ship would sink(沉没), I was sc ared my legs couldn’t move forward. A.too, that B. very, that C. so, that D. too, to 19.He often rides a bike to school, but I to my school. A.by bus B. on a bus C. by a bus D. take a bus 20.I have two friends. One is a doctor, and is a teacher. A.another B. other C. the other D. others 21.“-- Would you please bring me some bananas, Amy?”“ -- .” A.That’s rig ht B. Yes, thanks. C. Not at all D. All right 22.-- do you visit your teacher? ---Once a month. A.What B. How often C. Who D. How many 23.Our school is 10 kilometers the train station. A.far B. from C. away D. to 24.My new bike is the same . A.as her B. with her C. with hers D. as hers 25.The farmers were busy _ ready for the next year in winter of 1999. A.getting, the B. getting, / C. to ge t, the D. to get, / II.完形填空(本题共10 小题,每小题1.5 分,共15 分) Do you live in a city? Do you know 26 cities began? Long long ago,there were only 27 people in the world.These people 28 from place to place.They moved over the land,hunting animals for 29 . No one knows how or when these people learned about growing food.But when they 30 that,their lives changed.They didn't have to look 31 food any more.They 32 stay in one place and grow it. People began to live near one another.And so the first villages grew.Many people came to work in the villages.These 33 became very big. A. all are B. are all C. both are D. are both 34 machines came along,life in the villages changed again. Factories were built.More and 11.These can speak Chinese well. A.woman teachers B. woman teacher C. women teachers D. women teacher 12.It’s time bed. You’d better watch TV now. A.to go to, not B. going, not to C. to go, don’t D. to go to, don’t 13.The students of Class Two are taller than of Class One. A.it B. they C. those D. that 14.Mother asked him forget to turn down the TV because his brother was sleeping. A.not to B. to not C. don’t D. mustn’t 15.There are a lot of people for the bus to come. A.to wait B. waiting C. waited D. is waiting 16.I think Amy smart. A.don’t, is B. /, isn’t C. /, / D. don’t,isn’t more people lived near the factories.And then the cities began and grew very 35 . 26. A. why B. how C. what D. where 27. A. thousand B. thousands C. thousands of D. thousand of 28. A. moved B. lived C. drove D. ran 29. A. games B. clothes C. food D. play 30. A. know B. had C. were D. learned 31. A. at B. for C. after D. into 32. A. able to B. can C. able D. could 33. A. houses B. families C. villages D. cities 34. A. Before B. When C. For D. Till 35. A. big B. small C. bigger D. smaller

【解析】天津市天津一中2019-2020学年高一下学期第一次月考英语试题

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天津一中2019-2020-1 高一年级英语学科期末 质量调查试卷 I. 听力(共20 小题;每小题0.5 分,满分10 分) 第一节听下面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。听完得处对话后,你都有10 秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。 1. What does the woman want to drink? A. Coffee. B. Juice. C. Green tea. 2. What are the speakers mainly talking about? A. Their vacation plans. B. Their summer trips. C. Their part-time jobs. 3. When can the woman go to classes? . A. In the morning. B. In the evening. C. In the afternoon. 4. Where does the conversation probably take place? A. At a park. B. At a library. C. At a restaurant. 5. How does the woman feel now? A. Nervous. B. Excited. C. Confident. 第二节听下面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。 6What does the man plan to give his mother? A. A dress. B. A handbag. C. A necklace. 7. What's the most probable relationship between the speakers? A. Brother and sister. B. Husband and wife. C. Father and daughter. 听第7 段材料,回答第8 至10 题。 8. How did the woman go to New York? A. By plane. B. By car. C. By train. 9. Whom did the woman travel to New York with?

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