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【测试】阶段性测试题1

【测试】阶段性测试题1
【测试】阶段性测试题1

【关键字】测试

阶段性测试题一(集合与常用逻辑用语) 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(选择题共50分)

一、选择题(本大题共10个小题,每小题5分,共50分,在每小题给出的四个选项中,只有一项是符合题目要求的)

1.(2015·长沙模拟)已知集合A={1,3,},B={1,m},A∪B=A,则m=( )

A.0或B.0或3

C.1或D.1或3

[答案] B

[解析] 由A∪B=A得B?A,∴m=3或m=.

当m=3时,经验证适合题意;

当m=时,m=0或m=1,经验证m=0适合题意,

m=1不适合题意.

∴m=0或m=3.

2.(文)设集合U={1,2,3,4,5,6},M={1,3,5},则?UM=( )

A.{2,4,6} B.{1,3,5}

C.{1,2,4} D.U

[答案] A

[解析] 本题考查补集的运算:∵M={1,3,5},U={1,2,3,4,5,6},∴?UM={2,4,6}.(理)设集合U={1,2,3,4},M={1,2,3},N={2,3,4},则?U(M∩N)=( )

A.{1,2} B.{2,3}

C.{2,4} D.{1,4}

[答案] D

[解析] 本题主要考查了集合的交集、补集运算.

∵M={1,2,3},N={2,3,4},

∴M∩N={2,3},又∵U={1,2,3,4},

∴?U(M∩N)={1,4}.

3.(文)集合A={x|-4≤x≤2},B={y|y=,0≤x≤4},则下列关系正确的是( )

A.?RA??RB B.A??RB

C.B??RA D.A∪B=R

[答案] A

[解析] B={y|y=,0≤x≤4}={y|0≤y≤2},B?A,?RA??RB.

(理)(2014·江西文,6)下列叙述中正确的是( )

A.若a,b,c∈R,则“ax2+bx+c≥的充分条件是“b2-≤

B.若a,b,c∈R,则“ab2>cb的充要条件是“a>c”

C.命题“对任意x∈R,有x2≥的否定是“存在x∈R,有x2≥

D.l是一条直线,α,β是两个不同的平面,若l⊥α,l⊥β,则α∥β

[答案] D

[解析] 本题主要考查逻辑与联结词,A选项中ax2+bx+c≥0不仅仅与b2-有关,还要取决于x2的系数a,因此这个是即不充分也不必要条件,B项中当b2=0时,a>c?\ ab2>cb2,C项的否定应是x2<0,D项正确,垂直于同一直线的两平面平行,本题较容易出错的选项是A、B,易忽略对a=0和b2=0的特殊情况考虑.

4. 设A,B是非空集合,定义A×B={x|x∈(A∪B)且x?(A∩B)},已知A={x|0≤x≤2},B={y|y≥0},则A×B等于( )

A.(2,+∞) B.[0,1]∪[2,+∞)

C.[0,1)∪(2,+∞) D.[0,1]∪(2,+∞)

[答案] A

[解析] 由题意知,A∪B=[0,+∞),A∩B=[0,2].

所以A×B=(2,+∞).

5.(2015·广州调研)命题:“若x2<1,则-1

A.若x2≥1,则x≥1或x≤-1

B.若-1

C.若x>1或x<-1,则x2>1

D.若x≥1或x≤-1,则x2≥1

[答案] D

[解析] “若p,则q”的逆否命题是“若非q,则非p”.故选D.

6.(2015·大连双基尝试)在△ABC中,“A>B”是“sinA>sinB”的( )

A.充分必要条件

B.充分不必要条件

C.必要不充分条件

D.既不充分也不必要条件

[答案] A

[解析]在△ABC中,A>B?2R sin A>2R sin B(其中2R是△ABC的外接圆直径),即sin A>sin B.因此在△ABC中,“A>B”是“sin A>sin B”的充分必要条件,选A.

7.(文)已知全集U={1,2,3,4,5,6},集合A={2,3,4},集合B={2,4,5},则图中的阴影部分表示()

A.{2,4} B.{1,3}

C.{5}D.{2,3,4,5}

[答案] C

[解析]已知全集U={1,2,3,4,5,6},集合A={2,3,4},集合B={2,4,5},?U A={1,5,6},阴影为(?U A)∩B={1,5,6}∩{2,4,5}={5},故选C.

(理)设全集U是实数集R,集合M={x|x2>2x},N={x|log2(x-1)≤0},则(?U M)∩N=()

A.{x|1

C.{x|1

[答案] C

[解析]因为M={x|x2>2x}={x|x>2或x<0},N={x|log2(x-1)≤0}={x|1

8.(2015·武汉调研)给定两个命题p,q.若非p是q的必要不充分条件,则p是非q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

[答案] A

[解析]依题意,“若非p,则q”是假命题,“若q,则非p”是真命题,所以“若非q,则p”是假命题,“若p,则非q”是真命题,故p是非q的充分不必要条件.9.若命题“存在x0∈R,使得x20+mx0+2m-3<0”为假命题,则实数m的取值范围是()

A.[2,6]B.[-6,2]

C.(2,6)D.(-6,-2)

[答案] A

[解析]因命题“存在x0∈R,使得x20+mx0+2m-3<0”为假命题,故其否命题“任意x∈R,x2+mx+2m-3≥0恒成立”为真命题,由二次函数开口向上,故Δ=m2+4(2m-3)≤0,∴m∈[2,6].

10.已知条件p:x2-3x-4≤0;条件q:x2-6x+9-m2≤0,若p是q的充分不必要条件,则m的取值范围是()

A.[-1,1]

B .[-4,4]

C .(-∞,-4]∪[4,+∞)

D .(-∞,-1]∪[1,+∞)

[答案] C

[解析] p :-1≤x ≤4,q :3-m ≤x ≤3+m (m >0)或3+m ≤x ≤3-m (m <0),

依题意,????? m >0,3-m ≤-1

3+m ≥4,或????? m <0,3+m ≤-1,3-m ≥4,

解得m ≤-4或m ≥4.选C.

第Ⅱ卷(非选择题 共100分)

二、填空题(本大题共5个小题,每小题5分,共25分,把正确答案填在题中横线上)

11.已知A ,B 均为集合U ={2,4,6,8,10}的子集,且A ∩B ={4},(?U B )∩A ={10},则A =________.

[答案] {4,10}

[解析] 设元素x 0∈A ,若x 0∈B ,则x 0∈A ∩B ,若x 0?B ,则x 0∈?U B ,∴x 0∈(?U B )∩A ; ∵A ∩B ={4},(?U B )∩A ={10},∴A ={4,10}.

12.命题“对任意x ∈R ,|x -2|+|x -4|>3”的否定是________.

[答案] 存在x ∈R ,|x -2|+|x -4|≤3

[解析] 本题考查全称命题的否定,注意量词改变后,把它变为特称命题.

13.设全集U =R ,A ={x |x -2x +1

<0},B ={x |sin x ≥32},则A ∩B =________. [答案] [π3

,2) [解析] ∵A ={x |-1

,2). 14.(2015·湘潭模拟)已知函数y =lg(4-x )的定义域为A ,集合B ={x |x

[答案] (4,+∞)

[解析] 由4-x >0,知A =(-∞,4).

又B ={x |x

∴A B ,∴a >4.

15.设有两个命题:①关于x 的不等式mx 2+1>0的解集是R ;②函数f (x )=log m x 是减函数,如果这两个命题中有且只有一个真命题,则实数m 的取值范围是________.

[答案] {m |m ≥1或m =0}

[解析] ①若不等式mx 2+1>0的解集是R ,则m ≥0;②若函数f (x )=log m x 是减函数,

则0

三、解答题(本大题共6个小题,共75分,解答应写出文字说明,证明过程或演算步骤)

16.(本小题满分12分)已知集合A ={x |2-a ≤x ≤2+a },B ={x |x 2-5x +4≥0},

(1)当a =3时,求A ∩B ,A ∪(?R B );

(2)若A ∩B =?,求实数a 的取值范围.

[解析] (1)当a =3时,A ={x |-1≤x ≤5},B ={x |x ≥4或x ≤1},

∴A ∩B ={x |-1≤x ≤1或4≤x ≤5},

又?R B ={x |1

∴A ∪(?R B )={x |-1≤x ≤5}.

(2)当A =?时,A ∩B =?,

此时2-a >2+a ,∴a <0,

当A ≠?时,要使A ∩B =?,

需满足????? a ≥02-a >1,

2+a <4.∴0≤a <1.

综上知a 的取值范围为{a |a <1}.

17.(本小题满分12分)设集合A ={x |x 2<4},B ={x |1<4x +3

}. (1)求集合A ∩B ;

(2)若不等式2x 2+ax +b <0的解集是B ,求a ,b 的值.

[解析] A ={x |x 2<4}={x |-2

B ={x |1<4x +3}={x |x -1x +3

<0}={x |-3

(2)∵2x 2+ax +b <0的解集为B ={x |-3

∴-3和1为方程2x 2+ax +b =0的两根,

∴??? -a 2=-3+1,b 2=-3×1,

∴a =4,b =-6.

18.(本小题满分12分)定义运算x *y =(x -2)(y +2),集合A ={a |(a -1)*(a +1)<0},B ={y |y =|x +2|,x ∈A }.求A ∩B 与A ∪B .

[解析] (a -1)*(a +1)=(a -3)(a +3)<0,

∴-3

又x ∈A ,∴-3

则-1

A ∩

B ={x |0≤x <3},则A ∪B ={x |-3

19.(本小题满分12分)设命题p :函数f (x )=lg(ax 2-4x +a )的定义域为R ;命题q :不等式2x 2+x >2+ax 对任意x ∈(-∞,-1)上恒成立,如果命题“p 或q ”为真命题,命题“p 且q ”为假命题,求实数a 的取值范围.

[解析] 由题意可知对命题p 需满足Δ<0且a >0,即?????

a >016-4a 2<0,解得a >2; 命题q 即:a >2x -2x +1,对?x ∈(-∞,-1)上恒成立,又增函数y =(2x -2x

+1)<1,故a ≥1.

“p 或q ”为真命题,命题“p 且q ”为假命题,等价于p ,q 一真一假.

因此当p 真q 假时有??? a >2a <1

,解集为?; 当p 假q 真时有?????

a ≤2a ≥1,即1≤a ≤2, 综上所述a 的取值范围为1≤a ≤2.

20.(本小题满分13分)已知命题p :A ={x |a -1

(1)若A ∩B =?,A ∪B =R ,求实数a ;

(2)若非q 是p 的必要条件,求实数a .

[解析] 由题意得B ={x |x ≥3或x ≤1},

(1)由A ∩B =?,A ∪B =R ,可知A =?R B =(1,3),

∴?????

a +1=3a -1=1,∴a =2. (2)∵B ={x |x ≥3或x ≤1},∴非q :{x |1

∴非q 是p 的必要条件,即p ?非q ,

∴A ??R B =(1,3),∴?????

a +1≤3,a -1≥1, ∴2≤a ≤2,∴a =2.

21.(本小题满分14分)(文)已知集合M ={x |x (x -a -1)<0(a ∈R )},N ={x |x 2-2x -3≤0},若M ∪N =N ,求实数a 的取值范围.

[解析] 由已知得N ={x |-1≤x ≤3},因为M ∪N =N ,∴N ?N .

又M ={x |x (x -a -1)<0(a ∈R )}.

①当a +1<0即a <-1时,集合M ={x |a +1

要使M ?N 成立,只需-1≤a +1<0,解得-2≤a <-1.

②当a +1=0即a =-1时,M =?,显然有M ?N ,所以a =-1符合.

③当a +1>0即a >-1时,集合M ={x |0

要使M ?N 成立,只需0

综上所述,a 的取值范围是[-2,2].

(理)设集合A 为函数y =ln(-x 2-2x +8)的定义域,集合B 为函数y =x +1x +1

的值域,集合C 为不等式(ax -1a

)(x +4)≤0的解集. (1)求A ∩B ;

(2)若C ??R A ,求a 的取值范围.

[解析] (1)由-x 2-2x +8>0,解得A =(-4,2),

又y =x +1x +1=(x +1)+1x +1

-1, 所以B =(-∞,-3]∪[1,+∞).

所以A ∩B =(-4,-3]∪[1,2).

(2)因为?R A =(-∞,-4]∪[2,+∞).

由(ax -1a

)(x +4)≤0,知a ≠0. ①当a >0时,由(x -1a 2)(x +4)≤0,得C =[-4,1a 2],不满足C ??R A; ②当a <0时,由(x -1a 2)(x +4)≥0,得C =(-∞,-4]∪[1a 2,+∞), 欲使C ??R A ,则1a 2≥2, 解得-22≤a <0或0

≤a <0. 综上所述,所求a 的取值范围是[-

22

,0).

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春季常见呼吸道传染病的预防知识教学内容

春季常见呼吸道传染病的预防知识

春季常见呼吸道传染病的预防知识 春季是呼吸道传染病的高发季节。常见传染性疾病包括:流脑、水痘、普通感冒、流行性感冒、麻疹、风疹、单纯疱疹、流行性腮腺炎、猩红热,传染性非典型肺炎(SARS)和人感染高致病性禽流感两类新病种。呼吸道传染病主要通过空气、短距离飞沫或接触呼吸道分泌物等途径传播。 流行性感冒 流行性感冒(简称流感),是由流感病毒引起的急性呼吸道传染病。常于冬、春季流行,通过空气飞沫传播。该病潜伏期短,一般1~3日,最短数小时,最长4日,传染性强,传播迅速。临床症状为急起高热,全身症状较重,呼吸道症状较轻。显著头痛、身痛、乏力、咽干及食欲减退等。部分病人有鼻阻、流涕、干咳等。查体可见急性热病容,面颊潮红,眼结膜及咽部充血。肺部可闻及干罗音。发热多于1~2日内达高峰,3~4日内退热,其他症状随之缓解,但上呼吸道症状常持续1~2周后才逐渐消失,体力恢复亦较慢。 预防措施 1、常洗手。病毒可以在患者手摸过的地方存活3个小时,所以你应经常洗手。 2、办公室、居室多通风换气。

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