2019-2020学年上海市七宝中学高一上期中考试试卷

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上海市七宝中学2023-2024学年高一上学期期中语文试题(含解析)

上海市七宝中学2023-2024学年高一上学期期中语文试题(含解析)

上海七宝中学高一年级期中考试语文试卷(含解析)(2023.11)(说明:本试卷满分150分,时间150分钟,所有答案均写在答题纸的相应位置上)一、积累与运用(10分)(一)(5分)1.按要求填空。

(1)______________,渚清沙白鸟飞回。

(杜甫《登高》)(2)_________,食野之苹。

(曹操《短歌行》)(3)鹰击长空,___________,万类霜天竞自由。

(毛泽东《沁园春·长沙》)(4)李白《梦游天姥吟留别》中的“__________,_________”两句,正面描写出天姥山直插云霄、耸立天外的雄伟气势。

【答案】①.风急天高猿啸哀②.呦呦鹿鸣③.鱼翔浅底④.天姥连天向天横⑤.势拔五岳掩赤城【解析】【详解】本题考查学生默写常见的名句名篇的能力。

易错字词:啸、呦、翔、拔。

(二)(5分)按要求选择。

2.假设你为学校“读书节”设计一张宣传海报,下列最适合选用的一项是()A.纸上得来终觉浅,绝知此事要躬行。

(实践)B.世事洞明皆学问,人情练达即文章。

规律C.察己则可以知人,察今则可以知古。

反省、知新D.问渠那得清如许,为有源头活水来。

3.下面是某高三学生参加高校自主招生的自荐信,画线部分可能存在不得体的表达。

尊敬的学校领导:您好!①感谢您在百忙之中阅读我的自荐信。

我是XX,来自XX市XX中学,学习成绩优秀,曾担任校学生会文艺部部长,爱好写作。

我获得过第十九届“语文报杯”全国中学生作文竞赛高中组一等奖;也曾代表学校参加市中学生辩论大赛,②以敏捷的反应和出众的口才令对手自惭形秽,③获得“最佳辩手”称号。

贵校历史悠久,底蕴深厚,④能进入贵校中文系学习是我的理想。

⑤贵校的自主招生条件也非常符合我的标准。

⑥请您一定不要拒绝我,⑦圆我的大学中文系之梦。

此致敬礼!自荐人:XXXXX年X月X日有几处画线部分存在不得体...的表达?()A.1处B.2处C.3处D.4处【答案】2.D 3.C【解析】【2题详解】本题考查学生语言表达得体的能力。

【20套试卷合集】上海市七宝中学2019-2020学年物理高一上期中模拟试卷含答案

【20套试卷合集】上海市七宝中学2019-2020学年物理高一上期中模拟试卷含答案

2019-2020学年高一上物理期中模拟试卷含答案满分[ 100]分,时间[90]分钟2013年11月一.单项选择题。

(本题共10小题,每小题4分,共40分)1.下列关于质点的描述,正确的是()A.研究郭晶晶跳水的动作,可以将郭晶晶看成质点.B.凡是体积大的物体,都不能把它看作质点.C.只有静止的物体,才可以看作质点.D.在研究地球公转时,地球可以看作质点.2.下列关于加速度的说法中,正确的是:()A.加速度越大,速度变化越大B.加速度越大,速度变化越快C.加速度-3m/s2比1m/s2小D.物体的加速度为1 m/s2,则物体做加速运动3.下列关于重力的说法,正确的是()A.物体上只有重心处才受到重力作用B.物体的重心一定在物体上C.在广州的物体与在北京的物体,受到的重力方向相同D.不管物体是否运动,受到的重力大小都相同4.关于摩擦力,下列说法正确的是:()A 摩擦力总与物体运动方向相反B 相互压紧而且接触面粗糙的两物体之间总存在静摩擦力的作用C 物体受到的静摩擦力大小与接触材料的粗糙程度无关D 自行车在前进过程中,前后轮受到摩擦力均向前5.某质点作直线运动,位移随时间变化的关系式为x =(4t +2t2)m,则对这个质点运动描述,正确的是().A.初速度为4 m/sB.加速度为2 m/s2C. 加速度为1 m/sD.10 s时的速度为36 m/s26.如图,物体在轴上做直线运动,0时刻从O点向右运动,此后各时刻的位置如表所示。

则在0到8秒内( )A.该物体一定做匀变速直线运动B.该物体可能做匀变速直线运动C.第2内与第4秒到第6秒内的位移相同D.以上说法都错误7.如图所示,一木块放在水平桌面上,在水平方向共受三个力即F1、F2和摩擦力作用,木块处于静止状态,其中F1=10N、F2=2N。

若撤去力F1,则木块受到的摩擦力力为:( )A.8N,方向向左B.8N,方向向右C.2N,方向向右D.2N,方向向左8.一个物体从某一高度做自由落体运动, 已知它第一秒内的位移恰为它最后一秒内位移的一半, g取10 m/s2, 则它开始下落时距地面的高度为:( )A. 5 m;B.11.25 m;C. 20 m;D. 31.25 m。

【精品高一化学试卷】2019-2020学年上海市普通高一(上)期中化学试卷+答案

【精品高一化学试卷】2019-2020学年上海市普通高一(上)期中化学试卷+答案

2019-2020学年上海市普通高一(上)期中化学试卷一、选择题(每小题只有一个正确选项,每小题2分,共80分)1.(2分)道尔顿的原子学说包含以下三个论点:①原子是不能再分的微粒。

②同种元素原子的各种性质和质量都相同。

③原子是微小的实心球体。

从现代的观点来看,你认为这三个论点中不正确的是()A.只有②B.有①③C.有②③D.有①②③2.(2分)在含有多个电子的原子中,能量最高的电子是()A.最靠近原子核的电子B.离原子核最远的的电子C.L层上的电子D.最不易失去的电子3.(2分)13C﹣NMR(核磁共振)、15N﹣NMR可用于测定蛋白质、核酸等生物大分子的空间结构,Kurt Wu thrich等人为此获得2002年诺贝尔化学奖。

下面有关13C、15N叙述正确的是()A.13C与15N有相同的中子数B.13C与C60互为同素异形体C.15N与14N互为同位素D.15N的核外电子数与中子数相同4.(2分)第三层为最外层时,该电子层最多容纳的电子数数目是()A.2个B.8个C.18个D.32个5.(2分)氢的两种同位素1H、2H,与16O,若形成水分子,则水分子的相对分子质量有几种()A.3B.5C.7D.96.(2分)科学家发现C60后,近年又合成了许多球形分子(富勒烯),如C50、C70、C120、C540等它们互称为()A.同系物B.同分异构体C.同素异形体D.同位素7.(2分)下列不符合当今化学研究方向的是()A.发现新物质B.合成新材料C.研究化学反应的微观过程D.研究化学反应中原子守恒关系8.(2分)氯有两种同位素1735Cl和1737Cl,下列说法错误的是()A.这两种原子的化学性质几乎完全相同B.这两种原子的物理性质不同C.这两种同位素的中子数不同D.这两种原子的相对质量相同9.(2分)根据下列四种粒子的结构示意图,所获取的信息正确的是()A.它们表示四种元素B.①④表示的是阳离子C.④表示的元素是非金属元素D.②表示的元素在化合物中通常显+2价10.(2分)化学科学需要借助化学专用语言描述,下列有关化学用语正确的是()A.镁离子的电子式•Mg•B.Cl﹣的结构示意图C.氯离子的电子式Cl﹣D.质量数为37的氯原子1737Cl11.(2分)关于Cl2和Cl﹣的说法正确的是()A.都有毒B.加到硝酸银溶液中都生成白色沉淀C.都能与金属反应D.都呈黄绿色12.(2分)X原子的核电荷数为a,它的阴离子X m﹣与Y原子的阳离子Y n+的电子层结构相同,则Y原子的核电荷数为()A.a+m+n B.a﹣m﹣n C.m+n﹣a D.m﹣n﹣a 13.(2分)下面是纯净物的是()A.液氯B.纯净的盐酸C.漂粉精D.氯水14.(2分)818O2气体称为“重氧”,科学研究中有重要应用。

2019-2020学年上海中学高一(上)期中数学试卷 (含答案解析)

2019-2020学年上海中学高一(上)期中数学试卷 (含答案解析)

2019-2020学年上海中学高一(上)期中数学试卷一、选择题(本大题共4小题,共12.0分) 1. 已知集合A ={0,1},则下列式子错误的是( )A. 0∈AB. {1}∈AC. ⌀⊆AD. {0,1}⊆A2. 已知x <0,函数y =4x +x 的最大值是( )A. 5B. −4C. −8D. 63. 已知不等式m −1<x <m +1成立的充分条件是13<x <12,则实数m 的取值范围是( )A. (−∞,−12)∪(43,+∞) B. (−∞,−12)∪[43,+∞) C. (−12,43) D. [−12,43] 4. 若关于x 的不等式x 2+2ax +1≥0在[0,+∞)上恒成立,则实数a 的取值范围为( )A. (0,+∞)B. [−1,+∞)C. [−1,1]D. [0,+∞)二、填空题(本大题共10小题,共30.0分)5. 已知集合U ={0,1,2,3},A ={1,2,3},则C U A =________.6. 解关于x 的不等式:2|x −3|+|x −4|<2.7. 命题“如果√x −2+(y +1)2=0,那么x =2且y =−1”的逆否命题为________.8. 已知全集U ={0,1,2,3,4,5,6,7,8,9},集合A ={0,1,3,5,8},集合B ={2,4,5,6,8},则(∁U A)∩(∁U B)= ______ .9. 已知a ∈R ,b ∈R ,若{a,ba ,1}={a 2,a +b,0},则a = ______ ,b = ______ . 10. 已知x ,y 为正实数,则x2x+y +yx+2y 的最大值为________. 11. 已知集合A ={0,2,4,6},B ={x|3<x <7},则A ∩B =_____. 12. 已知函数f (x )={−x,x ≤0,x 2−2x,x >0,则满足f(x)<1的x 的取值范围是________13. 函数f(x)=1x−1在[a,b]上的最大值为1,最小值为13,则a +b = ______ . 14. 已知集合A ={−1,0,a },B ={0,√a}.若B ⊆A ,则实数a 的值为________. 三、解答题(本大题共5小题,共60.0分) 15. (1)比较a 2+b 2与2(2a −b)−5的大小;(2)已知a,b,c ∈R +,且a +b +c =1,求证:(1a −1)(1b −1)(1c −1)⩾816. 解下列不等式:(Ⅰ)|2x +1|−2|x −1|>0; (Ⅱ)||x −2|−1|≤1.17. 为了保护环境,发展低碳经济,某企业在国家科研部门的支持下,进行技术攻关,新上了一项把二氧化碳处理转化为一种可利用的化工产品的项目,经测算,该项目月处理成本y(元)与月处理量x(吨)之间的函数关系可近似的表示为:y ={13x 3−80x 2+5040x,x ∈[120,144)12x 2−200x +80000,x ∈[144,500),且每处理一吨二氧化碳得到可利用的化工产品价值为200元,若该项目不获利,亏损数额国家将给予补偿.(I)当x ∈[200,300]时,判断该项目能否获利?如果亏损,则国家每月补偿数额的范围是多少? (Ⅱ)该项目每月处理量为多少吨时,才能使每吨的平均处理成本最低?18. 已知命题是真命题.(1)求实数m 的取值集合M ;(2)设不等式(x−a)[x−(2−a)]<0的解集为N,若N⊆M,求实数a的取值范围.19.已知二次函数y=x2−2tx+t2−1(t∈R).(1)若该二次函数有两个互为相反数的零点,解不等式x2−2tx+t2−1≥0;(2)若关于x的方程x2−2tx+t2−1=0的两个实根均大于−2且小于4,求实数t的取值范围.-------- 答案与解析 --------1.答案:B解析: 【分析】本题考查元素与集合、集合与集合的关系,属于基础题型,直接求解即可. 【解答】解:∵集合A ={0,1}, ∴易得A ,C ,D 正确,B 选项,集合与集合的关系不能用∈, 故选B .2.答案:B解析:解:∵x <0,∴函数y =4x +x =−(−x +4−x )≤−2√−x ⋅4−x =−4,当且仅当x =−2时取等号.∴x <0,函数y =4x +x 的最大值是−4. 故选B .变形利用基本不等式即可得出.变形利用基本不等式和掌握使用基本不等式时注意“一正,二定,三相等”是解题的关键.3.答案:D解析:由题意可知m −1≤13且12≤m +1,解得m ∈[−12,43].4.答案:B解析: 【分析】本题考查恒成立问题,考查二次函数知识的综合运用,属于基础题.分两种情况讨论,当a ≥0时,二次函数在[0,+∞)单调递增且f(0)>0,当a <0时,要求Δ≤0,从而得到结果. 【解答】解:∵x 2+2ax +1≥0在[0,+∞)上恒成立,1)当a ≥0时,函数f(x)=x 2+2ax +1在(−a,+∞)上为单调增函数,则函数f(x)=x 2+2ax +1在[0,+∞)上为单调增函数, 所以f(x)≥f(0),∵f(0)=1>0,∴符合题意,2)当a <0时,因为f(0)=1>0,所以要使x 2+2ax +1≥0在[0,+∞)上恒成立, 则4a 2−4≤0,即−1≤a ≤1, 此时有−1≤a <0, 综上a ≥−1. 故选B .5.答案:{0}解析: 【分析】本题主要考查了集合的补集,属于基础题. 【解答】解:集合U ={0,1,2,3},A ={1,2,3}, 则C U A ={0}. 故答案为{0}.6.答案:解:当x ≥4时,原不等式即为2(x −3)+(x −4)<2,即3x −10<2,解得x <4,则有x ∈⌀; 当3<x <4时,原不等式即为2(x −3)+(4−x)<2,即x −2<2,解得,x <4,则有3<x <4; 当x ≤3时,原不等式即为2(3−x)+(4−x)<2,即10−3x <2,解得,x >83,则有83<x ≤3. 则原不等式的解集为{x|83<x ≤3或3<x <4}={x|83<x <4}.解析:运用零点分区间方法,讨论当x ≥4时,当3<x <4时,当x ≤3时,去绝对值,解不等式,最后求并集即可.本题考查绝对值不等式的解法,考查分类讨论的思想方法,考查运算能力,属于基础题.7.答案:如果x ≠2或y ≠−1,则√x −2+(y +1)2≠0解析: 【分析】本题考查考查四种命题的定义和关系,根据四种命题之间的关系和定义即可得到命题的逆否命题. 【解答】解: 根据逆否命题的定义可知,命题的逆否命题为:如果x≠2或y≠−1,则√x−2+(y+1)2≠0,故答案为如果x≠2或y≠−1,则√x−2+(y+1)2≠0.8.答案:{7,9}解析:解:∵集合A={0,1,3,5,8},集合B={2,4,5,6,8},∴∁U A={2,4,6,7,9},∁U B={0,1,3,7,9},则(∁U A)∩(∁U B)={7.9},故答案为:{7,9}根据集合的基本运算进行求解即可.本题主要考查集合的基本运算,根据补集和交集的定义是解决本题的关键.9.答案:−1;0解析:解:由题意知,1}={a2,a+b,0},∵{a,ba∴根据集合相等的定义可知:有以下几种情况①当a=0时,不符合题意,故a≠0=0时,b=0②当ba即这时集合化简为{a,0,1}={a2,a,0}∴当a=1时不满足集合元素的互异性,故a≠1∴当a2=1时,a=1或a=−1经验证a=−1成立.即此时集合为{−1,0,1}∴可知:a=−1,b=0故答案为:−1,0.根据集合相等的定义,分类讨论,结合集合元素的互异性,即可得出结论.本题考查集合元素的互异性,考查集合相等的定义,比较基础.10.答案:23解析:【分析】本题主要考查基本不等式的运用,求最值,考查运算能力,属于中档题.对原式子进行换元变形,以及基本不等式应用时应该满足的条件:一正二定三等.解:令2x +y =m ,x +2y =n , 则x =2m−n 3,y =−m+2n3,且m >0,n >0,因此:x 2x +y +y x +2y =2m −n 3m +−m +2n3n =2m −n 3m +−m +2n 3n =43−(n 3m +m3n) ≤43−2√19=23,当且仅当m =n 时取等号, 则x2x+y +yx+2y 的最大值为23, 故答案为23.11.答案:{4,6}解析: 【分析】本题主要考查集合的交集运算,考查学生分析问题解决问题的能力,属于基础题. 利用交集运算定义直接计算即可. 【解答】解:因为集合A ={0,2,4,6},B ={x|3<x <7}, 所以A ∩B ={4,6}. 故答案为{4,6}.12.答案:解析: 【分析】本题考查了一元二次不等式的解法,考查了分类讨论的数学思想方法,属中档题. 【解答】解:因为函数f (x )={−x,x ≤0,x 2−2x,x >0,则f(x)<1等价于{x ≤0−x <1①或{x >0x 2−2x <1②. 解得①得−1<x ≤0,解②得0<x <1+√2√2. 所以f(x)<1的x 的取值范围是(−1,1+√2). 故答案为.解析:解:由题意,a >1,则1a−1=1,1b−1=13,∴a =2,b =4,∴a +b =6; a <1则1a−1=13,不成立. 故答案为:6.分类讨论,利用函数的单调性,结合函数f(x)=1x−1在[a,b]上的最大值为1,最小值为13,求出a ,b ,即可求出a +b .本题考查函数的最值及其几何意义,考查学生的计算能力,比较基础.14.答案:1解析: 【分析】本题主要考查子集的概念,集合的表示,考查学生对基本概念的理解和应用能力,考查核心素养是计算能力,属于基础题.利用子集关系得√a =a ,求解即可,注意集合元素的互异性. 【解答】解:因为B ⊆A ,所以√a ∈A ,因为A ={−1,0,a},所以√a ≠0,√a ≠−1, 所以√a =a ,解得a =1; 故答案为1.15.答案:(1)解:因为a 2+b 2−2(2a −b)+5=a 2−4a +4+b 2+2b +1=(a −2)2+(b −1)2⩾0,所以a 2+b 2⩾ 2(2a −b)−5;(2)证明:∵a +b +c =1,a ,b ,c ∈R +, ∴(1a −1)(1b −1)(1c −1)=b+c a×a+c b×a+b c⩾2√bca×2√ac b×2√ab c=8,当且仅当a =b =c 时,取等号.解析: 【分析】(1)本题考查作差法比较大小,两式作差与零比较,即可比较出两式大小;(2)本题考查不等式的证明,将a +b +c =1分别代入分子并化简,进而利用基本不等式即可证明原不等式.16.答案:解:(Ⅰ)原不等式化为|2x +1|>2|x −1|,两边平方得(2x +1)2>4(x −1)2,展开得4x 2+4x +1>4x 2−8x +4,即得原不等式的解集为(14,+∞). (Ⅱ)由||x −2|−1|≤1得−1≤|x −2|−1≤1,即0≤|x −2|≤2,此不等式可转化为{|x −2|≥0|x −2|≤2,求得{x ∈R0≤x ≤4,所以原不等式的解集为{x|0≤x ≤4}.解析:(Ⅰ)原不等式化为|2x +1|>2|x −1|,两边平方得(2x +1)2>4(x −1)2,展开化简求得原不等式的解集.(Ⅱ)把此不等式可转化为{|x −2|≥0|x −2|≤2,求得{x ∈R0≤x ≤4,由此可得原不等式的解集.本题主要考查绝对值不等式的解法,体现了转化的数学思想,属于基础题.17.答案:解:(I)设x ∈[200,300]时,获利为S ,则S =200x −(12x 2−200x +80000)=−12(x −400)2, 所以在x ∈[200,300]时,S 为单调递增函数, S max =−5000,S min =−20000, 所以补偿范围是[5000,20000].(Ⅱ)二氧化碳的平均每吨的处理成本为y x ={13x 2−80x +5040,x ∈[120,144),12x −200+80000x,x ∈[144,500], 当x ∈[120,144)时,当x =120时,yx 取得最小值240, 当x ∈[144,500)时,yx=12x +80000x−200⩾2√12x ⋅80000x−200=200,当且仅当12x =80000x,即x =400时,yx 取得最小值200,∵200<240,所以每月的处理量为400吨时,才能使每吨的处理成本最低.解析:本题考查分段函数模型的应用以及基本不等式实际应用,是中档题. (I)根据x ∈[200,300],求出函数y 的值域即可判断求解.(Ⅱ)写出每吨的平均处理成本的函数表达式,利用基本不等式求解.18.答案:解:(1)命题“∃x ∈[−1,0],x 2+2x +m <0”是真命题,则m <(−x 2−2x)max ,∵x ∈[−1,0],∴(−x 2−2x)max =1,则m <1,即M =(−∞,1); (2)当a <2−a ,即a <1时,N =(a,2−a), ∵N ⊆M ,∴2−a ≤1,即a ≥1,此时a 无解;当a=2−a,即a=1时,N为空集,满足题意;当a>2−a,即a>1时,N=(2−a,a),∵N⊆M,∴a≤1,此时a无解.综上:a=1.解析:(1)把原命题转化为m<(−x2−2x)max,再由二次函数求最值得答案;(2)对a分类求解不等式(x−a)[x−(2−a)]<0,再由两集合端点值间的关系列式求解.19.答案:解:(1)设二次函数y=x2−2tx+t2−1(t∈R)的两个零点分别为x1,x2,由已知得x1+x2=0,而x1+x2=2t,所以2t=0,故t=0.不等式x2−2tx+t2−1≥0即x2−1≥0,解得x≥1或x≤−1,故不等式的解集为{x|x≥1或x≤−1}.(2)因为方程x2−2tx+t2−1=0的两个实根均大于−2且小于4,所以即.解得−1<t<3.解析:本题考查了函数与方程以及一元二次不等式的解法,是一般题.(1)根据韦达定理求出t,然后根据一元二次不等式的解法得出答案.(2)根据一元二次方程根的分布建立关于t的不等式组,解不等式组即可.。

2019-2020学年上海市七宝中学高一上期中考试试卷

2019-2020学年上海市七宝中学高一上期中考试试卷

2019-2020学年上海市七宝中学高一上期中考试试卷七宝高一英语期中考试(2019年11月)满分:150分I. Listening Comprehension (25%)Section ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. 5:00. B. 4:30. C. 5:30. D. 6:00.2. A. In a factory. B. In a hotel room. C. At a reception desk.D. In the hell.3. A. She doesn’t like eating the cake. B. She is trying to buy some cake.C. She is leaving to take a flight.D. She is going on a diet now.4. A. She’s a housewife. B. She’s a nurse.C. She’s a babysitter.D. She’s a teacher.5. A. Painting the room. B. Pleasure in helping others.C. Preparing for a surprise party.D. Asking Mike for help.6. A. She is working in the hospital as a doctor.B. She is a patient in the hospital.C. She is not allowed to be visited by her friends.D. She is seeing patients of injuries on the fourth floor.7. A. Nervous. B. Relaxed. C. Confident. D. Fine.8. A. He is not afraid of driving in the terrible rush hour.B. Driving is much faster than taking the bus to work.C. He has to leave the seat when the bus gets to his stop.D. He doesn’t like standing all the way on his way to work.9. A. Because s he doesn’t want a good rest.B. Because she doesn’t take a bad cold seriously.C. Because she will lose her job if she does.D. Because she wants to keep on working.10. A. Her English class is interesting. B. Mr. Jackson is stricter than Mr. White.C. She wants to shout in English class.D. She doesn’t like being sleepy in class.Section BDirections: In Section B, you will hear two short passages, and you will be asked to questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. How to say a nd spell “horse”. B. A few simple spelling tricks.C. A comfortable pattern of numbers.D. Rules in math without a problem.12. A. He learned the spelling “rules” in high school.B. He spent hours online playing word games.C. He entered himself in competitions of all levels.D. He learned Spanish to play in another language.13. A. He was good with words in elementary school.B. He didn’t realize his talent in words until high school.C. He competed in order to win Word Game Player of the Year.D. Becoming a word game addict did harm to his life.Questions 14 through 16 are based on the following news.14. A. To take up some time. B. To plan a training.C. To learn from adventure.D. To develop leadership skills.15. A. Lectures on public relations. B. Tests on management.C. Climbing mountains.D. Long-distance running.16. A. The company decides the employees’ income according to the report.B. The employees in the company cannot handle difficult conditions.C. The employees have to ask for leave for 20 days in July for the program.D. The company provides the program as welfare for its employees.Section CDirections: I n Section C, you will hear a longer conversation. The conversation will be read twice. After you hear the conversation, you are required to answer the following questions.17. A. Their opinions about making friends online.B. Their time of going to bed at night.C. The popularity of social networks.D. Spending time in a more meaningful way.18. A. Crazy. B. Necessary. C. Interesting. D. Unreal.19. A. Making friends online is very interesting.B. He can share secrets safely with others.C. He won’t meet someone he knows online.D. He can practice his English when chatting.20. A. Come to her house.B. Get up early in the morning.C. Sleep more in the evening.D. Do some more important things.II. Grammar and vocabulary (50%)Section A (30%)Directions: fill in the blank with the proper form of the given verb.21.If you don’t come this afternoon, you ________(miss) a lot of nice things.22.A family may have a member who ________(think) of as a black sheep, a person who brings trouble.23. The glasses I thought I ________(lose) are here, right under my nose.24. Last month, an Alabama school leader suggested a dress code that ______ (ban) Capri pants (七分裤) andscarves and include restrictions on eye makeup and nail polish.25. Zootopia ___________(praise) for its sharp humor and strong message since its release.26. Amilia Earthart was the first woman ________(fly) the Atlantic Ocean alone.27. Do you have trouble ________(express) yourself in written English?28. People’s awareness of personal information protection remains ________(raise).29. The way to avoid ________(fine) is to obey the traffic rules when you drive.30. I seem ________(leave) my homework at home, so I have to do it again during the break.Directions: Read the following passage. Fill in the blanks to make the passage coherent. Fill in each blank with the proper form of the given verb. Make sure that your answers are grammatically correct.Discover new ways to travelWe’ve probably all met someone who likes to boast about how many places he or she has been to. It’s annoying but it’s true that to some people, traveling is all about the number of destinations one _____31.____(set) foot on. But fortunately, the old “been there, seen that” mode is changing.Last year’s travel trend was “experiential travel”. This is where tourists look for ways to get to know local culture and interact with local people, so they feel less like an outsider but more like a resident. So what about this year? Can thoughtful tourists get even more out of their traveling experience?Transformative travelTransformative travel is much like “experiential travel”, but takes it a step further.It usually ____32.____(go) through three phases – you go to a place that has a very different background than where you come from, you learn wisdom from the new culture and the people you meet, and finally you return home and use the knowledge in your own life and the lives of those around you. This last phase is how the “transformation” ____33.____(complete) and what ____34.____(separate) transformative travel from experiential travel.“This allows our travelers ____35.____(start) to see the world less in black and white, and to begin to appreciate hownuanced(微妙的) many issues are when ____36.____(see) from very different perspectives,” Jennine Cohen, director of US travel company GeoEx, told V ogue magazine.Go greenAccording to Rebecca Warren, managing editor at Lonely Planet, eco-friendly and sustainable travel will be one of this year’s top trends.One way to plan a low-impact trip is to travel a shorter distance, which can reduce your carbon footprint. “One trans-Atlantic flight equals a year’s worth of driving, so con sider ____37.____(plan) an adventure closer to home,” suggested Warren, according to US News.Another way to involve sustainability in your travel plans is to choose a destination that ____38.____(benefit) the most from your trip. For example, places like Nepal will enjoy a boost of its local economy from the money it will make through tourism.Disappearing destinationsDestinations at risk of disappearing are also welcoming an increasing number of tourists.Everett Potter, a USA Today writer, says that the Arctic and Antarctic have become popular destinations since they ____39.____(threaten) by climate changes.Another top destination is the Great Barrier Reef in Australia. Due to pollution and global warming, it’s predicted that the reef ____40.____(damage) in just a few decades. Travelers are longing to see the coral “before it’s gone or completely changed”, Potter told US News.Section B (20%)Directions: Complete the following passages by using the words in the box. Each word can only be used once. Note thatthere is one word more than you need.At the end of a long day, it’s all too easy to take a hot shower, throw on some pajamas, brush your teeth, and then jump into bed. But have you ever stopped to think about the _____41.___ of sleeping with wet hair? As it turns out, going to bed with wet hair isn’t as ____42.____ as you probably thought.The first negative result of sleeping with wet hair is purely cosmetic: you can’t predict how your wet hair is go ing to look in the morning. “If you try to ____43.____ your hair in the morning after sleeping on it wet, you’re probably going to have funny waves, flat sides, and crinkles,” says hairstylist Olga Gilbert of J. Russell Salon in Southern California.“When you wake up to unruly bedhead, you’re probably going to have to re-wet it again to properly dry it and regain control. This ____44.____ adds time to your morning routine,” she says.Gilbert says that sleeping with wet hair does not immediately damage your hair follicles or shaft, but it can certainly lead to hair breakage, because wet hair is weakest when wet, making it easier to break. “If you pull your wet hair up into a tight ponytail or bun, you have a much greater chance of breaking it during the night,” Gilbert says. To help with that, here’s how to repair ____45.____ hair with items you already have at home.If you absolutely must sleep with wet hair because you have to wake up early for work, there are a few easy ways to minimize the damage. First, you can change your cotton pillowcases for silk or satin ones like these. Silk has a much smoother surface, soyou won’t experience as much unfortunate breakage. Not using the silk pillowcase is one of the nighttime habits that could ____46.____ your hair.Next, you can make sure to sleep with your hair down or in a(n) ____47.____ braid(辫子), instead of up in a tight bun or ponytail. In addition, you should replace your tight, elastic bands with a soft scrunchy(束发带) that isn’t going to roughly pull at night. If you’re willing, it’s also very helpful (but less comfortable) to wrap your hair in a silk scarf.Finally, if you’re going to bed with wet hair, the most important rule is never to forget to ____48.____ product! Protective serums(精华液), dry oils, and texturizing mousses are some of the best ways to ____49.____ you don’t wake up looking like an alpaca(羊驼) while protecting your precious hair from damage. Now that you know how bad sleeping with wet hair is, make sure you’re not making these hairstyle mistakes that ____50.____ your face.Heritage list on Saturday as an early _____51._____ to globalization.The decision was made at the ongoing 41st session of World Heritage Committee in Krakow, Poland, which designated Kulangsu a Historic International Settlement.____52._____ a mere 1.88 square kilometers, the island hosted settlements from 13 countries from the end of the First Opium War (1840-42) to the early 20th century.The committee found that Kulangsu was China’s major gateway in early-stage globalization and ____53.____ mixed architectural characteristics from the local, Southeast Asian andWestern styles. It _____54.____ reflected cross-border communication.Today, 931 historical buildings and gardens in various styles remain, most of them former tycoo ns’residences, overseas companies and public institutions like hospitals. Many pioneers of Chinese modernization were born and left their former residences on Kulangsu. "The island has deep traditional Chinese culture roots and inclusiveness to embrace different values and cultures," said Song Xinchao, deputy director of the State Administration of Cultural Heritage. "It also shows a(n) ____55._____ of ancient thought and modern living concepts."Since 2014, preparations have been made for World Heritage status, Liang said. For example, a digital monitoring network was set up at the sites and a special office was opened within his committee for the ____56._____ of cultural relics."Kulangsu is not only a scenic spot, but also a community," Liang said. "We’ve tried to encourage local residents to participate in the protection."New museums have opened on the island to better present its cultural resources. An abandoned hospital, for example, was renovated to be used as a satellite gallery of Beijing’s Palace Museum to display its _____57._____ of foreign artifacts."The central government will continue to encourage improving the quality of island residents` lives and improving visitors’experiences there," Song said. "An even more beautiful Kulangsu will be ____58.____ to the public."As a popular tourism destination, Kulangsu has had problems with crowding. Song said the daily number of visitors will be capped to meet crowd-control ____59._____ from World Heritage Committee. More measures will follow to better studyand preserve historical heritage on the island.About 1,600 delegates from 107 countries and 167 international organizations attended the conference, which will continue through July 12. Delegates are judging 35 candidate World Heritage Sites from around the world and also discussing the status and protection of ____60._____ World Heritage Sites in Syria.III. Reading Comprehension (55%)Section A (15%)Directions: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Why did the ancient Maya abandon their citiesThe ancient Maya built many large cities in the Classic Period, which lasted from about 250 until about 900. Each city had its own king and _____61_____ class. The cities traded with one another but often ____62_____ with one another as well. In about 900, the Maya ___63_____ many of their cities. Archaeologists and other scientists have long puzzled over why the Maya left. They have formed theories by examining those cities carefully and studying the settlements that surround them. Researchers think that the _____64____ in some places may have been so large that people left because there was not enough ____65____ for everyone.Archaeologists studied ___66____ from one city and its surroundings to learn what had happened there. In Copan they found many tools dating from 500 to about 1000 and a few tools dating from about 1000 to 1200. They found that no new monuments had been built after 822. From studying plant remains, scientists concluded that the area around Copan hadbeen ___67_____. Other evidence suggested that the land was overfarmed. In view of the evidence, the scientists concluded that a large population lived in Copan until about 1000. As more people farmed the land, the soil ____68____ its richness and produced few crops, which caused the Maya who lived there to ____69_____ malnutrition, as analysis of skulls show. As a result, people began to leave Copan in about 1000, but they did not completely abandon the city until about 1200.____70____ also may have caused the Maya to abandon some of their cities. For example, it is thought that a rival city, Caracol, may have once conquered Tikal. Then, after more than 100 years had passed, Tikal returned to power, and the ruling family built temples to ____71____ its victory. ____72____, by the end of the 800s, Tikal was no longer powerful. Its inhabitants left the city. Some archaeologists and historians think that war may have broken out again and caused the citizens to leave.Although we do not know for certain why many ancient Maya abandoned their cities, we may find some clues by observing today’s Maya. Modern Maya still live in the lands, including Mexico and Guatemala, that their ancestors ___73_____. Many present-day Maya ___74_____ a variety of ancient beliefs and customs, such as farming practices. Studying their beliefs and practices may ____75____ scientist to discover more about ancient Mayan culture.61.A. ruling B. living C. educating D. farming62.A. communicated B. fought C. quarreled D. bargain63.A. destroyed B. restored C. decorated D. abandoned64.A. population B. area C. family D. profit65.A. land B. water C. food D. space66.A. routes B. clues C. soil D. monuments67.A. wasteland B. ruins C. battlefield D. farmland68.A. developed B. created C. lost D. kept69.A. get rid of B. result from C. suffer from D. show sympathy for70.A. Malnutrition B. War C. Flood D. Earthquake71.A. honor B. record C. secure D. taste72.A. Otherwise B. Besides C. Therefore D. However73.A. cleared B. approached C. isolated D. occupied74.A. practice B. declare C. respect D. challenge75.A. remind B. help C. force D. forbidSection B (32%)Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.AOne Friday morning, before Michael was leaving for work he told his wife that he had finally determined to ask his boss for a salary raise. All day Michael felt nervous and anxious as he thought about the upcoming showdown. What if Mr. Duncan refused to grant his request? Michael had worked so hard in the last 18 months and brought some great benefits to Braer and Hopkins Advertising Agency. Of course, he deserved a wage increase.The thought of walking into Mr Duncan’s office left Michael weak in the knees. Late in the afternoon he was finally courageous enough to approach his superior. To his delight and surprise, the ever-frugal (一惯节省的) Rowland Duncan agreed to give Michael a raise!Michael arrived home that evenin g—despite breaking all city and state limits—to a beautiful table set with their best china, and candles lit. His wife, Cassie, had prepared a delicate meal including his favourite dishes. Immediately he thought someone from the office had tipped her off!Next to his plate Michael found a beautiful lettered note. It was from his wife. It read: “Congratulations, my love! I knew you’d get the raise! I prepared this dinner to show just how much I love you. I am so proud of your accomplishments!” He read it and stopped to think about how sensitive and caring Cassie was.After dinner, Michael was on his way to the kitchen to get dessert when he observed that a second card had slipped out of Cassie’s pocket onto the floor. He bent forward to pick it up. It read: “Don’t worry about not getting the raise! You do deserve one! You are a wonderful provider and I prepared this dinner to show you just how much I love you even though you did not get the increase.”Suddenly tears swelled in Michael’s eyes. Total acceptance! Cassie’s support for him was not conditional upon his succe ss at work.The fear of rejection is often softened and we can undergo almost any setback or rejection when we know someone loves us regardless of our success or failure.76. What was Michael’s plan that Friday?A. To find a job with the Braer and Hopkins Advertising Agency.B. To ask for a wage increase from his boss.C. To celebrate his success.D. To ask his boss to come for dinner.77. On his way back home, Michael __________.A. felt weak in the kneesB. was punished by the traffic policemanC. was too anxious to share the news with his wifeD. couldn’t wait to enjoy a meal78. Which of the following statements about the story is FALSE?A. Michael was afraid that his request would lead to a disaster.B. Michael had worked very hard and done his part for the company.C. Michael’s boss agreed to his request.D. One of Michael’s colleagues had told his wife the good news.79.According to the passage, which of the following can best describe Michael’s wife, Cassie?A. Passionate, thoughtful and talented.B. Considerate, generous and reliable.C. Decisive, optimistic and energetic.D. Caring, tolerant and supportive.BSuppose you’re in a rush, felling tired, not paying attention to your screen, and you send an email that could get you in trouble.Realisation will probably set in seconds after you’ve clicked “send”. You freeze in horror and burn with shame.What to do? Here are four common email accidents, and how to recover.Clicking “send” too soonDon’t waste your time trying to find out if the receivers has read it yet. Write another email as swiftly as you can and send itwith a brief explaining that this is the correct version and the previous version should be ignored.Writing the wrong nameThe sooner you notice, the better. Respond quickly and briefly, apologizing for your mistake. Keep the tone measured: don’t handle it too lightly, as people can be offended, especially if your error suggests a misunderstanding of their culture(i.e. incorrect ordering of Chinese names).Clicking “reply all” unintentiona llyYou accidentally reveal(透露)to the entire company what menu choices you would prefer at the staff Christmas dinner, or what holiday you’d like to take. In this instance, the best solution is to send a quick, light-hearted apology to explain your awkwardness. But it can quickly rise to something worse, when everyone starts hitting “reply all” to join in a long and unpleasant conversation. In this instance, step away from your keyboard to allow everyone to calm down.Sending an offensive message to its subjectThe most awkward email mistake is usually committed in anger. You write an unkind message about someone, intending to send it to a friend, but accidentally send it to the person you’re discussing. In that case, ask to speak in person as soon as possible and say sorry. Explain your frustrations calmly and sensibly—see it as an opportunity to clear up any difficulties you may have with this person.80. After realising an email accident, you are likely to feel _______.A. curiousB. tiredC. awfulD. funny81. If you have written the wrong name in an email, it is best to ________.A. apologise in a serious mannerB. tell the receiver to ignore the errorC. learn to write the name correctlyD. send a short notice to everyone82. What should you do when an unpleasant conversation is started by your “reply all” email?A. Try offering other choices.B. Avoid further involvement.C. Meet other staff members.D. Make a light-hearted apology.83. How should you deal with the problem caused by an offensive email?A. By promising not to offend the receiver again.B. By seeking support from the receiver’s friends.C. By asking the receiver to control his anger.D. By talking to the receiver face to face.COne windy spring day, I observed young people having fun using the wind to fly their kites. Multicolored creations of varying shapes and sizes filled the skies like beautiful birds racing and dancing. As the strong winds blew against the kites, a string kept them in check.Instead of blowing away with the wind, they arose against it to achieve great heights. They shook and pulled, but the string and the tail kept them attached, facing upward and against the wind. The kites struggled and kept being dragged behind, facing upward and against the wind. As the kites struggled andtrembled against the string, they seemed to say, “Let me go! Let me go! I want to be free!” They soared beautifully even as they fought the restriction of the string. Finally, one of the kites succeeded in breaking loose. “Free at last,” it seemed to say. “Free to fly with the wind.”Yet freedom from restriction simply put it at the mercy of a cruel breeze. It flew ungracefully to the ground and landed in a messed mass of weeds and string against a dead bush. “Free at last”, free to lie powerless i n the dirt, to be blown helplessly along the ground, and to stop lifeless against the first obstruction.How much like kites we sometimes are. The heaven gives us misfortune and limitations, and rules to follow from which we can grow and gain strength. Restriction is a necessary companion to the winds of opposition. Some of us resist the rules so hard that we never soar to reach the heights we might have obtained. We keep part of the order and never rise high enough to get our tails off the ground.Let us each rise to the great heights, recognizing that some of the restrictions that we may be annoyed at are actually the steadying force that helps us improve and achieve.84. According to paragraph 2, “Let me go!” is said by _______.A. the kiteB. the windC. the birdD. the flyer85. Which of the following words has the meaning closest to the underlined word “obstruction” in paragraph 3?A. destructionB. miracleC. observationD. obstacle86. According to the writer, in what way is man similar to kites?A. Man will never reach the desirable height unless he breaks some rules.B. Man can be empowered by difficulties to go further and higher.C. Man desires freedom but only a few will succeed.D. Man is limited by his surroundings.87. By telling the story of kite flying, the writer wants to share the lesson that _______.A. rules are made to be brokenB. flying a kite involves skills and patienceC. sometimes difficulties can be potential blessingsD. it’s no use complaining about the difficulties we encounterDMassive rubbish dumps and sprawling landfills constitute one of the more uncomfortable impacts that humans have on wildlife. They have led some birds to give up on migration. Instead of flying thousands of miles in search of food, they make the waste sites their winter feeding grounds.Researchers in Germany used miniature GPS tags to track the migrations of 70 white storks (鹳) from different sites across Europe and Asia during the first five months of their lives. While many birds travelled along well-known routes to warmer climates, others stopped short and spent the winter on landfills, feeding on food waste, and the multitudes of insects that thrive on the dumps.In the short-term, the birds seem to benefit fromoverwintering(过冬) on rubbish dumps. Andrea Flack of the Max Planck Institute found that birds following traditional migration routes were more likely to die than German storks that flew only as far as northern Morocco, and spent the winter there on rubbish dumps. “For the birds it’s a very conv eni ent way to get food. There are a lot of organic waste they can feed on,” said Flack. The meals are not particularly delicious, or even safe. Much of the waste is discarded(丢弃的) rotten meat, mixed in with other human debris such as plastic bags and old toys.“It’s very risky. The birds can easily eat pieces of plastic or rubber bands and they can die,” said Flack. “And we don’t know about the long-term consequences. They might eat something poisonous and damage their health. We cannot estimate that yet.”The scientists tracked white storks from different colonies in Europe and Africa. The Russian, Greek and Polish storks flew as far as South Africa, while those from Spain, Tunisia and Germany flew only as far as the Sahel.Landfill sites on the Iberian peninsula have long attracted local white storks, but all of the Spanish birds tagged in the study flew across the Sahara desert to the western Sahel. Writing in the journal, the scientists describe how the storks from Germany were clearly affected by the presence of waste sites, with four out of six birds that survived for at least five months overwintering on rubbish dumps in northern Morocco, instead of migrating to the Sahel.Flack said it was too early to know whether the benefits of plentiful food outweighed the risks of feeding on landfills. But that’s not the only uncertainty. Migrating birds affect ecosystems both at home and at their winter destinations, and。

2019-2020学年上海市七宝中学高一上学期期中考试数学试卷

2019-2020学年上海市七宝中学高一上学期期中考试数学试卷

2019-2020学年上海市七宝中学高一上学期期中考试数学试卷一、单选题1.“ ”是“”成立的 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.若实数a 、b 满足条件 ,则下列不等式一定成立的是 A .B .C .D .3.设集合 , 对任意 恒成立,则P 与Q 的关系是 A .B .C .D .4.已知集合 2,3, ,集合 是集合A 的子集,若 且 2, , ,满足集合B 的个数记为 ,则 A .9 B .10 C .11 D .12二、填空题6.集合{},a b 的真子集的个数为_________5.设集合{}21,A x x x R =-<?,集合B Z =,则A B ?__________ 7.“2x <”是“24x <”的__________8.命题“已知,x y R Î,如果2x y +?,那么0x ¹或2y ¹.”是__________命题.(填“真”或“假”)9.函数()f x =__________. 10.已知()214f x x +=-,则()f x 的解析式为__________.11.集合(){}(){}2,|1,,23A x y y ax B x y y x ==+==+,A B Ç的元素只有1个,则a 的取值范围是__________.12.若函数()()2225f x x a x =+-+在区间()4,+?上是增函数,则实数a Î__________.13.已知函数()f x 是定义在R 上的奇函数,且当0x £时,()2f x x x =--,则()2f =__________.14.已知函数()2x g x =,且()()2g a g b ?,则ab 的最大值是__________.15.已知关于x 的一元二次不等式20ax bx c ++>的解集为()2,3-.则关于x 的不等式0cx a +<的解集为__________.16.设3,0a b b +=>,则当a =__________时,13aa b+取得最小值三、解答题17.已知x ,y 是实数,求证: .18.已知全集 ,集合, ,求 , .19.已知命题p :关于x 的一元二次方程 有两个不相等的实数根;命题q :关于x 的一元二次方程 对于任意实数a 都没有实数根.若命题p 为真命题,求实数m 的取值范围;若命题p 和命题q 中有且只有一个为真命题,求实数m 的取值范围. 20.已知集合 ,集合当 时,求集合 和集合B ;若集合 为单元素集,求实数m 的取值集合;若集合 的元素个数为 个,求实数m 的取值集合 21.已知集合P 的元素个数为 个且元素为正整数,将集合P 分成元素个数相同且两两没有公共元素的三个集合A 、B 、C ,即 , , , ,其中 , , 若集合A 、B 、C 中的元素满足 , , ,2, ,则称集合P 为“完美集合”.若集合2,,2,3,4,5,,判断集合P和集合Q是否为“完美集合”?并说明理由;已知集合x,3,4,5,为“完美集合”,求正整数x的值;2019-2020学年上海市七宝中学高一上学期期中考试数学试卷一、单选题1.“”是“”成立的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】试题分析:由题意得“”,解得或,所以“”是“”的充分不必要条件,故选A.【考点】充分不必要条件的判定.2.若实数a、b满足条件,则下列不等式一定成立的是A.B.C.D.【答案】D【解析】根据题意,由不等式的性质依次分析选项,综合即可得答案.【详解】根据题意,依次分析选项:对于A、,时,有成立,故A错误;对于B、,时,有成立,故B错误;对于C、,时,有成立,故C错误;对于D、由不等式的性质分析可得若,必有成立,则D正确;故选:D.【点睛】本题考查不等式的性质,对于错误的结论举出反例即可.3.设集合,对任意恒成立,则P与Q的关系是A.B.C.D.【答案】C【解析】先分别求出集合P,Q,由此能求出P与Q的关系.【详解】集合,对任意恒成立,当m=0时,-1<0,满足题意,当时,结合二次函数的性质得到.与Q的关系是.故选:C.【点睛】本题考查集合的关系的判断,考查不等式性质等基础知识,考查运算求解能力,是基础题.4.已知集合2,3,,集合是集合A的子集,若且2,,,满足集合B的个数记为,则A.9 B.10 C.11 D.12【答案】B【解析】根据和,可得,,,集合2,3,4,5,6,;集合,满足集合B的个数列罗列出来,可得答案.【详解】由题意可得,,,那么集合2,3,4,5,6,;集合,,满足集合B的个数列罗列出来,可得:3,,3,,3,,4,,4,;5,,4,,4,,5,,5,,故选:B.【点睛】本题考查子集与真子集,并且即时定义新的集合,主要考查学生的阅读理解能力.二、填空题5.集合{},a b 的真子集的个数为_________ 【答案】3 【解析】 【分析】由真子集的定义,将集合{},a b 的真子集列举出来即可. 【详解】集合{},A a b =的真子集有{}{},,a b f , 共3个,故答案为3.【点睛】集合的真子集是指属于该集合的部分(不是所有)元素组成的集合,包括空集.6.设集合{}21,A x x x R =-<?,集合B Z =,则A B ?__________ 【答案】{}2 【解析】 【分析】利用绝对值不等式的解法化简集合A ,由交集的定义可得结果. 【详解】21x -<,即121x -<-<, 解得13x <<,即()1,3A =, 集合B Z =,则{}2A B?,故答案为{}2.【点睛】本题考查交集的求法以及绝对值不等式的解法,意在考查灵活应用所学知识解答问题的能力,是基础题,解题时要认真审题. 7.“2x <”是“24x <”的__________ 【答案】必要不充分 【解析】 【分析】根据一元二次不等式的解法化简不等式24x <,利用充分条件和必要条件的定义即可得到结论.【详解】由24x <得22x -<<,则“2x <”是“24x <”的的必要不充分条件, 故答案为必要不充分.【点睛】本题主要考查不等式的解法、充分条件与必要条件相关问题,将一元二次不等式的解法、充分条件、必要条件相关的问题联系起来,体现综合应用数学知识解决问题的能力,是基础题.8.命题“已知,x y R Î,如果2x y +?,那么0x ¹或2y ¹.”是__________命题.(填“真”或“假”) 【答案】真 【解析】 【分析】先写出原命题的逆否命题,并判断其真假 ,进而根据互为逆否的两个命题真假性一致,得到结论.【详解】命题“已知,x y R Î,如果2x y +?,那么0x ¹或2y ¹” 的逆否命题为“已知,x y R Î,如果0x =且2y =,那么2x y +=” 为真命題,故命题“已知,x y R Î,如果2x y +?,那么0x ¹或2y ¹” 是真命题,故答案为真.【点睛】本题考査的知识点是命题的真假判断与应用,其中当原命题的真假判断比较麻烦或无法证明时,常去判断其逆否命题的真假,进而根据互为逆否的两个命题真假性一致,得到结论.9.函数()f x =__________. 【答案】11,2纟ç-úçú棼 【解析】 【分析】根据分式的分母不为零,且二次根式的被开方数大于或等于零,由此建立关于x 的不等式组,解之即得函数()f x 的定义域.【详解】要使函数()f x = 则121xx -+0³,等价于()()211011210x x x x ì-+?ï?<?í+?ïî, 函数()f x =11,2纟ç-úçú棼,故答案为11,2纟ç-úçú棼. 【点睛】定义域的三种类型及求法:(1)已知函数的解析式,则构造使解析式有意义的不等式(组)求解;(2) 对实际问题:由实际意义及使解析式有意义构成的不等式(组)求解;(3) 若已知函数()f x 的定义域为[],a b ,则函数()()f g x 的定义域由不等式()a g x b #求出.10.已知()214f x x +=-,则()f x 的解析式为__________. 【答案】()223f x x x =-- 【解析】 【分析】令1x t +=,则1x t =-,求出()f t 223t t =--,从而可得结果. 【详解】因为()214f x x +=-,\令1x t +=,则1x t =-,()()()2114f x f t t \+==-- 223t t =--,\函数()f x 的解析式为()223f x x x =--.,故答案为()223f x x x =--.【点睛】本题主要考查函数解析式的求法,属于中档题.求函数的解析式常见题型有以下几种:(1)根据实际应用求函数解析式;(2)换元法求函数解析式,利用换元法一定要注意,换元后参数的范围;(3)待定系数法求函数解析式,这种方法适合求已知函数名称的函数解析式;(4)消元法求函数解析式,这种方法求适合自变量互为倒数或相反数的函数解析式.11.集合(){}(){}2,|1,,23A x y y ax B x y y x ==+==+,A B Ç的元素只有1个,则a 的取值范围是__________.【答案】10,2禳镲-睚镲铪【解析】 【分析】由A B Ç中有且仅有一个元素,可知两个方程联立得到方程是一次方程或二次方程有两个相等的根;利用分类讨论思想,可求出a 的范围.【详解】联立2123y ax y x ì=+ïí=+ïî 即2220ax x --=,A B Ç是单元素集,\分两种情况考虑:0a ¹,方程有两个相等的实数根,即0D=, 可得()2280a -+=,解得12a =- 0a =,方程220x --=只有一个根,符合题意,综上,a 的范围为10,2禳镲-睚镲铪故答案为10,2禳镲-睚镲铪. 【点睛】本题主要考查集合交集的定义与性质以及一元二次方程根与系数的关系,意在考查综合应用所学知识解答问题的能力,属于中档题. 12.若函数()()2225f x x a x =+-+在区间()4,+?上是增函数,则实数a Î__________. 【答案】[)2,-+?【解析】 【分析】根据二次函数的性质,判断出其图象是开口方向朝上,以2x a =-为对称轴的抛物线,利用[)4,+?为[)2,a -+?的子集可构造一个关于a 的不等式,解不等式即可得到实数a 的取值范围.【详解】函数()()2225f x x a x =+-+的图象是开口方向朝上, 以2x a =-为对称轴的抛物线,若函数()()2225f x x a x =+-+在区间[)4,+?上是增函数,所以[)4,+?为[)2,a -+?的子集,则24a -?,解得2a ?,故答案为[)2,-+?.【点睛】本题考査的知识点是函数单调性及二次函数的性质,属于简单题. 利用单调性求参数的范围的常见方法:① 视参数为已知数,依据函数的图象或单调性定义,确定函数的单调区间,与已知单调区间比较求参数需注意若函数在区间[],a b 上是单调的,则该函数在此区间的任意子集上也是单调的; ② 利用导数转化为不等式()'0f x £或()'0f x ³恒成立问题求参数范围,本题是利用方法 ① 求解的.13.已知函数()f x 是定义在R 上的奇函数,且当0x £时,()2f x x x =--,则()2f =__________. 【答案】2 【解析】 【分析】由()f x 为R 上的奇函数即可得出()()22f f =--,并且0x £时,()2f x xx =--,从而将2x =-代入()2f x x x =--的解析式即可求出()2f -,从而求出()2f . 【详解】()f x 是定义在R 上的奇函数,并且0x £时,()2f x x x =--,()()()()222222f f 轾\=--=-----=犏臌,故答案为2 . 【点睛】本题主要考查函数的解析式与函数奇偶性的应用,意在考查对基础知识掌握的熟练程度,属于简单题. 14.已知函数()2x g x =,且()()2g a g b ?,则ab 的最大值是__________.【答案】14【解析】 【分析】 由()()2g a g b ?可得1a b +=,由基本不等式可得2124a bab 骣+琪?琪桫,注意等号成立的条件即可.【详解】函数()2x g x =,且有()()2g a g b =,2222,1a ba b a b +\=?\+=,0a >且210,24a bb ab 骣+琪>\?琪桫, 当且即当12a b ==时,ab 取最大值14,故答案为14.【点睛】本题主要考查指数幂的运算以及利用基本不等式求最值,属于中档题. 利用基本不等式求最值时,一定要正确理解和掌握“一正,二定,三相等”的内涵:一正是,首先要判断参数是否为正;二定是,其次要看和或积是否为定值(和定积最大,积定和最小);三相等是,最后一定要验证等号能否成立(主要注意两点,一是相等时参数否在定义域内,二是多次用³或£时等号能否同时成立).15.已知关于x 的一元二次不等式20ax bx c ++>的解集为()2,3-.则关于x 的不等式0cx a +<的解集为__________.【答案】10,9轹÷ê÷ê滕 【解析】 【分析】构造解集和20ax bx c ++>是同解()2,3-的不等式,然后可得出,,a b c ,再代入求0cx a +<求解即可. 【详解】()()230x x +-<的解集为()2,3-,则260x x -++>与20ax bx c ++>是同解不等式,1,1,6a b c \=-==,则关于x 的不等式0cx a +<的解集即为610x <的解集,2610\<,即()()110<,解得109x?,故关于x 的不等式0cx a +<的解集为10,9轹÷ê÷ê滕,故答案为10,9轹÷ê÷ê滕.【点睛】本题主要考查一元二次不等式的解法,以及特值法在解题中的应用,意在考查灵活应用所学知识解答问题的能力,属于中档题.16.设3,0a b b +=>,则当a =__________时,13aa b+取得最小值【答案】32- 【解析】 【分析】需要分类讨论,当03a <<和当0a <,分别化简13aa b+,利用基本不等式即可得到结论.【详解】3,0a b b +=>,30b a \=->,即3a <, 当03a <<时,11112739999939a ab a b a a b a b a b ++=+=++?+=, 当且仅当34a =取等号 故当34a =时,13a a b+取得最小值79, 当0a <时,11112539999939a ab a b a a b a b a b ++=--=---?+-+=, 当且仅当32a =-取等号, 故当32a =-时,13a a b+取得最小值59, 综上所述a 的值为32-时, 13a a b+取得最小值,故答案为32-. 【点睛】本题主要考查基本不等式的应用,属于难题. 在利用基本不等式求最值时,要特别注意“拆、拼、凑”等技巧,使其满足基本不等式中“正”(即条件要求中字母为正数)、“定”(不等式的另一边必须为定值)、“等”(等号取得的条件)的条件才能应用,否则会出现错误.三、解答题17.已知x,y是实数,求证:.【答案】见解析【解析】利用综合法,证明不等式即可.【详解】因为,可得,,可得,所以.【点睛】本题考查不等式的证明,综合法的应用,是基本知识的考查.18.已知全集,集合,,求,.【答案】,【解析】先求出A,B,然后进行交集、并集和补集的运算即可.【详解】;;;;,;.【点睛】考查描述法表示集合的定义,,以及交集、并集和补集的运算.19.已知命题p:关于x的一元二次方程有两个不相等的实数根;命题q:关于x的一元二次方程对于任意实数a都没有实数根.若命题p为真命题,求实数m的取值范围;若命题p和命题q中有且只有一个为真命题,求实数m的取值范围.【答案】(1);(2)或.【解析】由题意可得判别式大于0,由绝对值不等式的解法可得m的范围;考虑命题q真,运用绝对值不等式的性质和判别式小于0,解不等式可得m的范围,由p,q一真一假,解不等式即可得到所求范围.【详解】命题p:关于x的一元二次方程有两个不相等的实数根,可得,解得;命题q:关于x的一元二次方程对于任意实数a都没有实数根,可得,由,可得无实数解,可得,即,命题p和命题q中有且只有一个为真命题,可得或或或,即有或.【点睛】本题考查二次方程和二次不等式的解法,注意运用判别式和绝对值不等式的性质,考查化简运算能力,属于基础题.20.已知集合,集合当时,求集合和集合B;若集合为单元素集,求实数m的取值集合;若集合的元素个数为个,求实数m的取值集合【答案】(1),;(2);(3)或【解析】(1)m=2时,化简集合A,B,即可得集合∁R A和集合B;(2)集合B∩Z为单元素集,所以集合B中有且只有一个整数,而0∈B,所以抛物线y=(1﹣m2)x2+2mx﹣1的开口向上,且与x轴的两个交点都在[﹣1,1]内,据此列式可得m=0;(3)因为A=(﹣∞,﹣1)∪(2,+∞),(A ∩B)∩Z中由n个元素,所以1﹣m2>0,即﹣1<m<1;A∩B中至少有3或﹣2中的一个,由此列式可得.【详解】集合A={x|x2﹣x﹣2≥0}={x|x≥2或x≤﹣1},集合{x|(1﹣m2)x2+2mx﹣1<0,m∈R}={x|[(1+m)x﹣1][(1﹣m)x+1]<0}(1)当m=2时,集合∁R A={x|﹣1<x<2};集合B={x|﹣1<x<};(2)因为集合B∩Z为单元素集,且0∈B,所以,解得m=0,当m=0时,经验证,满足题意.故实数m的取值集合为{0}(3)集合(A∩B)∩Z的元素个数为n(n∈N)个,A∩B中至少有3或﹣2中的一个,所以令f(x)=(1﹣m2)x2+2mx﹣1,依题意有或,解得﹣1<m<﹣或<m<1∴【点睛】本题考查了交、并、补集的混合运算属难题.21.已知集合P的元素个数为个且元素为正整数,将集合P分成元素个数相同且两两没有公共元素的三个集合A、B、C,即,,,,其中,,若集合A、B、C中的元素满足,,,2,,则称集合P为“完美集合”.若集合2,,2,3,4,5,,判断集合P和集合Q是否为“完美集合”?并说明理由;已知集合x,3,4,5,为“完美集合”,求正整数x的值;【答案】(1)见解析;(2)见解析【解析】(1)讨论集合A与集合B,根据完美集合的概念知集合C,根据ak +bk=ck,可依次判断集合P与Q是否为完美集合;(2)讨论集合AB,根据完美集合的定义,建立等式求x的值.【详解】(1)集合P=2,为“完美集合”,令A={1},B={2},C={3}.则集合A、B、C中的元素满足a k+b k=c k,集合Q=2,3,4,5,不是“完美集合”,若集合Q为“完美集合”,则C中元素最小为3,若C的最小元素为3,则a1+b1=1+2=3,a+b2=4+5=c2=6不可能成立,2若C的最小元素为4,则a1+b1=1+3=4,a+b2=2+5=c2=6不可能成立,2若C的最小元素为5,则a1+b1=1+4=5,a+b2=2+3=c2=6不可能成立,2综上可得集合Q={1,2,3,4,5,6}不是“完美集合”(2)由(1)可得x≠2,若A={1,3},4∈B,则5∈C,6∈B,x=3+6=9∈C满足“完美集合”的定义;若A={1,3},5∈B,则6∈C,5∈B,x=3+5=8∈C满足“完美集合”的定义;【点睛】这个题目考查了集合的新概念型问题,关键是读懂题意,按照题目所给的定义求解.。

2019-2020学年上海市闵行区七宝中学高一(上)期中数学试卷 (含答案解析)

2019-2020学年上海市闵行区七宝中学高一(上)期中数学试卷 (含答案解析)

2019-2020学年上海市闵行区七宝中学高一(上)期中数学试卷一、选择题(本大题共4小题,共12.0分)1. 对于α:a−1a+1>0,β:关于x 的方程x 2−ax +1=0有实数根,则α是β成立的( ) 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. 已知集合P ={0,1},Q ={−1,0,1},则( ) A. P ∈QB. P ⊆QC. P ⊇QD. Q ∈P 3. 若实数a <b <0,则下列不等式中正确的是( ) A. 1a <1bB. |b |>|a |C. a b +b a >2D. ab <b 2 4. 若函数f(x)=x−1x ,则方程f(4x)=x 的根为( ) A. −2 B. −12 C. 12 D. 2二、填空题(本大题共12小题,共36.0分)5. 已知集合A ={x|1≤x ≤2},集合B ={x|x ≥a}.若A ∪B =B ,则实数a 的取值范围是______.6. 已知集合M ={x|0≤x <2},N ={−1,0,1,2},则M ∩N =______.7. 命题“若x 2−x ≥0,则x >2”的否命题是__________.8. 在R 上定义运算⊙:a ⊙b =ab +2a +b ,则关于实数x 的不等式:x ⊙(x −2)<0的解集为______ .9. 已知函数f(x)={2x ,x >0x,x ≤0,则f(1)+f(−1)为________. 10. 若f(x)=√x(x +1),g(x)=√x ,则f(x)⋅g(x)= ______ .11. 不等式|2x −1|<x 的解集为______ .12. 已知不等式x 2+(m +1)x +m 2>0的解集为R ,则实数m 的取值范围为______ .13. 设函数f(x)=√1−lgx 的定义域为______.14. 函数y =x +1x−3(x >3)的最小值为________.15. 如果|x −1|+|x −9|>a 对任意实数x 恒成立,则a 的取值范围是______ .16. 若集合M ={0,1,2},N ={(x,y)|x −2y +1≥0,且x −2y −1≤0,y ∈M},则集合N 中元素的个数为__________.三、解答题(本大题共5小题,共60.0分)17. 已知集合A ={x|x 2−2x −8=0},B ={x|x 2+ax +a 2−12=0},且A ∪B ≠A ,求实数a 的取值范围.18.设f(x)=|x|+|x+10|.(Ⅰ)求f(x)≤x+15的解集M;(Ⅱ)当a,b∈M时,求证:5|a+b|≤|ab+25|19.为了在夏季降温和冬季取暖时减少能源消耗,业主决定对房屋的屋顶和外墙喷涂某种新型隔热材料,该材料有效使用年限为20年,已知该房屋外表喷涂一层这种隔热材料的费用为每毫米厚(0≤x≤10) 6万元,且每年的能源消耗费用H(万元)与隔热层厚度x(毫米)满足关系H(x)=403x+5设f(x)为隔热层建造费用与20年的能源消耗费用之和.(1)请解释H(0)的实际意义,并求f(x)的表达式;(2)当隔热层喷涂厚度为多少毫米时,业主所付的总费用f(x)最少?并求此时与不建隔热层相比较,业主可节省多少钱?20.已知函数f(x)=|x|+|x−4|.(1)若f(x)≥|m+2|恒成立,求实数m的最大值;(2)记(1)中m的最大值为M,正实数a,b满足a2+b2=M,证明:a+b≥2ab.21.集合A={1,2,3},B={1,2},定义集合间的运算A+B={x|x=x1+x2,x1∈A,x2∈B},则集合A+B中元素的最大值是________.-------- 答案与解析 --------1.答案:B解析:【分析】本题主要考查充分条件和必要条件的判断,求出命题的等价条件是解决本题的关键.求出α,β的等价条件,结合不等式的关系,利用充分条件和必要条件的定义进行判断即可.【解答】>0得a>1或a<−1,解:α:a−1a+1β:关于x的方程x2−ax+1=0有实数根,则判别式△=a2−4≥0,得a≥2或a≤−2,∵{a|a≥2或a≤−2}⫋{a|a>1或a<−1},∴α是β成立的必要不充分条件,故选:B.2.答案:B解析:【分析】本题考查命题真假的判断,考查集合与集合的关系等基础知识,考查推理能力与计算能力,属于基础题.利用集合与集合的关系直接求解.【解答】解:∵集合P={0,1},Q={−1,0,1},∴P⊆Q.故选:B.3.答案:C解析:【分析】本题考查了不等式的性质,考查特殊值的应用,是一道基础题.根据不等式的性质取特殊值验证即可.【解答】令b=−1,a=−2,则C正确,A,B,D错误,故选:C.4.答案:C解析:【分析】本题考查函数零点与方程根的关系,属于基础题.【解答】解:因为函数f(x)=x−1,x=x,所以f(4x)=x即为4x−14x即4x2−4x+1=0,,解得x=12故选C.5.答案:a≤1解析:因为A∪B=B,所以A⊆B,由集合A={x|1≤x≤2},集合B={x|x≥a}.所以a≤1.故填a≤1.根据A与B的子集关系,借助数轴求得a的范围.此题考查了子集及其运算,属于简单题.6.答案:{0,1}解析:【分析】本题考查了交集的定义与运算问题,是基础题.根据交集的定义计算即可.【解答】解:集合M={x|0≤x<2},N={−1,0,1,2},则M ∩N ={0,1}.故答案为:{0,1}.7.答案:若x 2−x <0,则x ≤2.解析:【分析】本题考查否命题的概念,属于基础题.注意否命题需要对条件和结论都否定.【解答】解:命题“若x 2−x ≥0,则x >2”的否命题是“若x 2−x <0,则x ≤2”.故答案为:若x 2−x <0,则x ≤2.8.答案:(−2,1)解析:解:由题意知:原不等式可化为x(x −2)+2x +x −2<0⇔x 2+x −2<0⇔(x +2)(x −1)<0⇔−2<x <1.故答案为:(−2,1).原不等式可化为x(x −2)+2x +x −2<0,解之得−2<x <1.本题借助新定义题考查了一元二次不等式的解法,根据定义把不等式转化为一元二次不等式是关键. 9.答案:1解析:【分析】本题考查了分段函数,将x 的值代入函数的解析式即可得答案.【解答】解:由函数f(x)={2x ,x >0x,x ⩽0可得f(1)+f(−1)=2−1=1, 故答案为1.10.答案:√x +1(x >0).解析:解:由题意f(x)的定义域为{x|x ≤−1或x ≥0},g(x)的定义域为{x|x >0},∴f(x)g(x)的定义域为{x|x >0},f(x)g(x)=√x +1,故答案为√x +1(x >0).确定函数的定义域,再求出函数的解析式即可.本题考查函数解析式的求解,考查学生的计算能力,比较基础.11.答案:(13,1)解析:解:由不等式|2x −1|<x 可得−x <2x −1<x ,解得13<x <1,故不等式||2x −1|<x 的解集是(13,1).故答案为:(13,1).原不等式等价于−x <2x −1<x ,由此求得不等式|2x −1|<x 的解集.本题主要考查绝对值不等式的解法,体现了等价转化的数学思想,属于中档题. 12.答案:(−∞,−13)∪(1,+∞)解析:【分析】不等式恒成立,需△<0,解出即可.本题考查函数恒成立问题、一元二次不等式的解法,考查转化思想、考查学生解决问题的能力.【解答】解:∵x 2+(m +1)x +m 2>0的解集为R ,∴△=(m +1)2−4m 2<0,解得:m <−13或m >1.故答案为:(−∞,−13)∪(1,+∞). 13.答案:(0,10]解析:解:函数f(x)=√1−lgx 的定义域为:{1−lgx ≥0x >0, 解得:0<x ≤10.∴函数f(x)=√1−lgx 的定义域为:(0,10].故答案为:(0,10].由函数f(x)=√1−lgx 的定义域为:{1−lgx ≥0x >0,解不等式组即可求出答案. 本题考查函数的定义域及其求法,考查不等式的解法,是基础题.14.答案:5解析:解:∵x >3,∴y =x +1x−3=x −3+1x−3+3≥2√1x−3⋅(x −3)+3=2+3=5,当且仅当x −3=1时,即x =4时取等号,故答案为:5.根据基本不等式即可求出.本题考查了基本不等式的应用,属于基础题.15.答案:a<8解析:解:由于|x−1|+|x−9|表示数轴上的点x到1和9对应点的距离之和,其最小值等于8,故由题意可得a<8,故答案为:a<8利用|x+1|+|x+9|表示数轴上的点x到−1和−9对应点的距离之和,其最小值等于8,从而求得a 的取值范围.本题考查绝对值的意义,绝对值不等式的解法,函数的恒成立问题,判断|x−1|+|x−9|的最小值等于8,是解题的关键.16.答案:4解析:【分析】本题考查元素和集合的关系的应用,属于基础题目.【解答】解:因为集合M={0,1,2},N={(x,y)|x−2y+1≥0,且x−2y−1≤0,x,y∈M},所以N={(0,0),(1,1),(1,0),(2,1)},所以集合N中元素个数为4.故答案为4.17.答案:解:集合A={x|x2−2x−8=0}={−2,4},B={x|x2+ax+a2−12=0},若A∪B=A,则B⊆A,可分为以下几种情况,(1)B=A,即方程x2+ax+a2−12=0的解为x=−2或x=4,解得a=−2;(2)B={−2},即方程x2+ax+a2−12=0的解为x=−2,(−2)2−2a+a2−12=0,解得:a=−2(舍)或a=4;(3)B ={4},即方程x 2+ax +a 2−12=0的解为x =4,a 2+4a +4=0,解得a =−2,此时B ={−2,4}≠{4},故需舍弃;(4)B 为空集,即方程x 2+ax +a 2−12=0无解,a 2−4(a 2−12)<0,解得a >4或a <−4. 综上可知,若B ∪A =A ,a =−2或a ≥4,或a <−4.解析:化简集合A ,若A ∪B =A ,则B ⊆A ,分类讨论,即可求实数a 的取值集合,本题考查实数的取值范围的求法,正确分类讨论是关键,是基础题.18.答案:解:( I)由f(x)=|x|+|x +10|≤x +15得:{x <−10−x −x −10≤x +15 ①,或{−10≤x ≤0−x +x +10≤x +15 ②,或{x >0x +x +10≤x +15③. 解①求得x ∈⌀,解②求得−5≤x ≤0,解③求得5≥x >0,故原不等式的解集为M ={x|−5≤x ≤5 }.( II)当a ,b ∈M 时,−5≤a ≤5,−5≤b ≤5,不等式5|a +b||≤|ab +25|,等价于25(a +b)2≤(ab +25)2,即25(a 2+b 2+2ab)≤a 2⋅b 2+50ab +625,即25a 2+25b 2−a 2⋅b 2−625≤0,等价于(a 2−25)⋅(25−b 2)≤0.而由−5≤a ≤5,−5≤b ≤5,可得a 2≤25,b 2≤25,∴a 2−25≤0,25−b 2≥0,∴(a 2−25)⋅(25−b 2)≤成立,故要证的不等式5|a +b|≤|ab +25|成立.解析:( I)把要解的不等式等价转化为与之等价的三个不等式组,求出每个不等式组的解集,再取并集,即得所求.(Ⅱ)当a ,b ∈M 时,等价转化不等式5|a +b|≤|ab +25|为(a 2−25)⋅(25−b 2)≤0,结合题意可得(a 2−25)⋅(25−b 2)≤0成立,从而得出结论.本题主要考查绝对值不等式的解法,用分析法证明不等式,属于中档题.19.答案:解:(1)H(0)=405=8,H(0)的实际意义为不使用新型隔热材料时,每年的能源消耗费用为8万元.f(x)的解析式为:f(x)=8003x+5+6x(0≤x ≤10).(2)f(x)=8003x+5+6x =8003x+5+2(3x +5)−10≥2√1600−10=70.当且仅当8003x+5=2(3x +5)即x =5时取等号.∴厚度为5mm 时,总费用最小70万元.若不使用隔热材料,则20年的能源消耗总费用为8×20=160万元,故业主可节省90万元.解析:(1)将建造费用和能源消耗费用相加得出f(x)的解析式;(2)利用基本不等式得出f(x)的最小值及对应的x 的值,与不使用隔热材料的总费用比较得出结论. 本题考查了函数解析式的求解,函数最值的计算,属于中档题.20.答案:解:(1)由已知可得f(x)={−2x +4,x ≤04,0<x <42x −4,x ≥4,所以f min (x)=4,所以只需|m +2|≤4,解得−6≤m ≤2,所以实数m 的最大值M =2;( 2)由(1)知a 2+b 2=2,又a 2+b 2⩾2ab ,∴ab ≤1,∴√ab ≤1 ①,当且仅当a =b 时取等号,又∵√ab a+b ≤12,∴ab a+b ≤√ab 2 ②,当且仅当a =b 时取等号, 由①②得ab a+b ≤12,所以a +b ≥2ab .解析:本题考查函数的最值的求法,基本不等式的应用,考查分析法与综合法的应用,考查逻辑推理能力以及计算能力.(1)求出函数的解析式,然后求解函数的最小值,通过|m +2|≤4,求解m 的范围,得到m 的最大值M .(2)综合法,利用基本不等式证明即可.21.答案:5解析:【分析】本题考查集合的 新定义,属于基础题型,理解题意 是关键.【解答】解:∵A ={1,2,3},B ={1,2},定义集合间的运算A +B ={x|x =x 1+x 2,x 1∈A,x 2∈B}, ∴A +B ={2,3,4,5}故集合A +B 中元素的最大值是5;故答案为5.。

上海市七宝中学2019-2020学年高一上学期期中数学试题

上海市七宝中学2019-2020学年高一上学期期中数学试题

绝密★启用前上海市七宝中学2019-2020学年高一上学期期中数学试题试卷副标题注意事项:1.答题前填写好自己的姓名、班级、考号等信息 2.请将答案正确填写在答题卡上第I 卷(选择题)请点击修改第I 卷的文字说明 一、单选题1.设命题甲“1x =”,命题乙“21x =”,那么甲是乙的( ) A.充分非必要条件 B.必要非充分条件 C.充要条件D.既非充分又非必要条件2.已知集合{,}P a b =,{|}Q M M P =⊆,则P 与Q 的关系为( ) A.P Q ⊆B.Q P ⊆C.P Q ∈D.P Q ∉3.若实数a 、b 、c 满足a b c >>,则下列不等式正确的是( ) A.a b c +>B.11a c b c<-- C.||||a c b c >D.222211ab a b c c <++ 4.已知a 、b 、c 为实数,2()()()f x x a x bx c =+++,2()(1)(1)g x ax cx bx =+++,记集合{|()0,}S x f x x ==∈R ,{|()0,}T x g x x ==∈R ,则下列命题为真命题的是( )A.若集合S 的元素个数为2,则集合T 的元素个数也一定为2B.若集合T 的元素个数为2,则集合S 的元素个数也一定为2C.若集合S 的元素个数为3,则集合T 的元素个数也一定为3D.若集合T 的元素个数为3,则集合S 的元素个数也一定为3第II 卷(非选择题)请点击修改第II 卷的文字说明 二、填空题5.已知集合{|2019}A x x =≤,{|}B x x a =>,且A B =R ,则实数a 的取值范围是_______ .6.若集合{1,3}M =-,2{3,21,2}N a a a =-++,若{3}M N =-I ,则实数a =_______ .7.命题:“若 不为零,则 都不为零”的逆否命题是 。

上海市闵行区七宝中学2019_2020学年高一数学上学期9月月考试题(含解析)

上海市闵行区七宝中学2019_2020学年高一数学上学期9月月考试题(含解析)

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1.点(2,3)P -关于y 轴对称的点的坐标为________ 【答案】(2,3) 【解析】 【分析】根据点关于y 轴对称点的特征,求得P 点关于y 轴的对称点.【详解】点关于y 轴对称,横坐标相反,纵坐标相同,故()2,3P -关于y 轴对称点的坐标为()2,3.故填:()2,3.【点睛】本小题主要考查点关于y 轴对称点的特征,属于基础题.2.函数y =x 的取值范围是________ 【答案】35x <≤ 【解析】 【分析】根据分母不为零,偶次方根被开方数为非负数列不等式组,解不等式组求得函数定义域. 【详解】依题意3050x x ->⎧⎨-≥⎩,解得35x <≤.故填:35x <≤.【点睛】本小题主要考查函数定义域的求法,主要考虑分式的分母、偶次方根的被开方数,属于基础题.3.已知反比例函数ky x=(0k ≠),当0x <时,y 随x 的增大而增大,那么一次函数y kx k=-的图像不经过第________象限 【答案】三 【解析】 【分析】根据反比例函数的单调性求得k 的范围,由此判断出一次函数不经过的象限. 【详解】由于函数k y x=0x <时递增,故k 0<,由()1y kx k k x =-=-可知,直线过()1,0,且斜率小于零,由此可判断一次函数y kx k =-不经过第三象限.故填:三.【点睛】本小题主要考查反比例函数的单调性,考查一次函数过定点以及一次函数经过的象限,属于基础题.4.x =-的解的集合为________ 【答案】{}1- 【解析】 【分析】先求得x 的范围,然后两边平方求得方程的解的集合.【详解】依题意0x -≥,解得0x ≤x =-两边平方得22x x +=,解得1x =-或2x =,由于0x ≤,故1x =-,所以方程的解的集合为{}1-.故填:{}1-.【点睛】本小题主要考查含有根式的方程的解法,解题过程中要注意x 的取值范围,属于基础题.5.反比例函数2y x=的图像与一次函数y x b =-+的图像在第一象限内有交点,则b 的最小值为________【答案】22【解析】【分析】联立一次函数和反比例函数的解析式,利用判别式为非负数且0b>列不等式组,解不等式组求得b的最小值.【详解】由于反比例函数2yx=过第一、三象限,一次函数y x b=-+斜率为10-<,两个函数公共点在第一象限,故0b>,由2yxy x b⎧=⎪⎨⎪=-+⎩,消去y得220x bx-+=,其判别式280b-≥,结合0b>解得22b≥,故b的最小值为22.故填:22.【点睛】本小题主要考查反比例函数、一次函数的图像交点问题,考查一元二次方程有解的条件,属于基础题.6.如图,过△ABC的重心G作BC的平行线,分别交AB、AC于点E、F,若4EF=,则BC=_______【答案】6【解析】【分析】根据三角形重心的性质列方程,解方程求得BC的长.【详解】由于G是三角形ABC的重心,且//EF BC,所以23EFBC=,所以362EFBC==. 故填:6.【点睛】本小题主要考查三角形重心的性质,考查平行线的性质,属于基础题.7.已知0x y z ++≠,a 、b 、c 均不为0,且x a y z =+,yb x z=+,z c x y =+,则111a b ca b c++=+++_______ 【答案】1 【解析】 【分析】化简已知条件,由此求得表达式的化简结果. 【详解】由xa y z=+,yb x z=+,zc x y=+得1,1,1x y z x y z x y za b c y z x z x y ++++++=+=+=++++,所以111,,111y z x z x y a x y z b x y z c x y z +++===+++++++++,所以111a b ca b c ++=+++1x y z x y z x y z x y z++=++++++. 故填:1.【点睛】本小题主要考查代数式的运算,属于中档题.8.已知点(1,1)A 和点(3,2)B ,在直线y x =-上有一个点P ,满足PA PB +最小,则PA PB +的最小值是________ 【答案】5 【解析】 【分析】根据对称性求得A 关于直线y x =-对称点的坐标'A ,由'A B 求得PA PB +的最小值.【详解】由于()1,1A 在y x =上,所以点A 关于直线y x =-的对称点为()'1,1A --,所以PA PB +的最小值为'5A B ==.故填:5.【点睛】本小题主要考查点关于直线对称点问题,考查类似将军饮马的最短距离和问题,考查数形结合的数学思想方法,属于基础题.9.已知方程|53||54|7x x ++-=,则x 的取值范围是_______ 【答案】3455x -≤≤ 【解析】 【分析】化简原方程,利用绝对值的几何意义,求得x 的取值范围. 【详解】由|53||54|7x x ++-=得347555x x ++-=,方程表示数轴上到35-和45的距离和为75的点,而35-和45的距离是75,故符合题意的x 的范围是3455x -≤≤.故填:3455x -≤≤. 【点睛】本小题主要考查利用绝对值的几何意义解方程,属于基础题.10.关于x 方程221(43|43|)2x x x x k -+--+=有两个不同的根,则k 的取值范围是_____ 【答案】(1,0)- 【解析】 【分析】根据x 的取值范围去绝对值,求得方程左边的表达式,根据方程根的个数,结合图像,求得k 的取值范围.【详解】当1x ≤或3x ≥时,方程为0k =,不符合题意.当13x <<时,方程为()()2431,3x x k x -+=∈,画出()()2431,3y x x x =-+∈的图像如下图所示,由图可知,要使方程()()2431,3x x k x -+=∈有两个不相同的根,则需()1,0k ∈-. 故填:(1,0)-.【点睛】本小题主要考查含有绝对值的方程的求解策略,考查数形结合的数学思想方法,属于中档题.11.已知集合{1,2,3,,}M n =⋅⋅⋅(1n >,*n ∈N ),则M 的所有非空子集的元素和为_______(只需写出数学表达式)【答案】22()2n n n -+⋅【解析】 【分析】求得含1个元素的子集的元素和、求得含2个元素的子集的元素和、以此类推,求得含n 个元素的子集的元素和,然后相加,求得M 所有非空子集的元素和. 【详解】含1个元素的子集的元素和为()()11112n n n C C -+++⋅-L ,含2个元素的子集的元素和为()()22112n n n C C -+++⋅-L ,……以此类推含1n -个元素的子集的元素和为()()11112n n n n n C C ---+++⋅-L ,含n 个元素的子集的元素和为()12nn n C +++⋅L .上述n 个式子相加得()()()1212111112n n n n n n n n n n C C C C C C ----+⎡⎤+++++++⎣⎦L L ()2122222n n n n n n --+=⋅=+⋅. 故填:()222n n n -+⋅.【点睛】本小题主要考查集合非空子集元素和的计算,考查等差数列前n 项和公式,考查二项式展开式的二项式系数和公式,属于中档题.12.当一个非空数集F 满足条件“若,a b F ∈,则+a b ,-a b ,ab F ∈,且当0b ≠时,aF b∈”时,称F 为一个数域,以下四个关于数域的命题: (1)0是任何数域的元素;(2)若数域F 有非零元素,则2019F ∈; (3)集合{|3,}P x x k k ==∈Z 为数域; (4)有理数集为数域;其中,真命题的编号为________(写出所有真命题的编号) 【答案】(1)(2)(4) 【解析】根据新定义数域的概念,对四个命题逐一分析,由此得出真命题的编号. 【详解】对于(1),当a b =时,0a b F -=∈,故(1)正确. 对于(2),当a b =时,1aF b=∈,所以11,21,,20181+++L 都是F 的元素,故(2)正确. 对于(3)由于33,3P P ∈∉,故P 不是数域.对于(4)有理数集满足,a b F ∈,则+a b ,-a b ,ab F ∈,且当0b ≠时,aF b∈.故(4)正确.综上所述,正确的命题编号为:(1)(2)(4). 故填:(1)(2)(4).【点睛】本小题主要考查新定义集合的理解,考查分析问题与解决问题的能力,属于中档题.二.选择题13.已知关于x 的一次函数27y mx m =+-在15x -≤≤上的函数值总是正的,则m 的取值范围是( ) A. 7m > B. 1m >C. 17m ≤≤D. 以上都不对 【答案】A 【解析】 【分析】根据一次函数的单调性列不等式组,解不等式组求得m 的取值范围.【详解】由于一次函数是单调函数,依题意有2705270m m m m -+->⎧⎨+->⎩,解得7m >,故选A.【点睛】本小题主要考查一次函数的性质,考查一元一次不等式组的解法,属于基础题.14.m 是一个完全平方数,则( ) A. 1m -一定是完全平方数 B. 1m -一定不是完全平方数 C. 2m +一定是完全平方数 D. 2m +一定不是完全平方数【答案】D【分析】对m 取特殊值,排除错误选项,从而得出正确结论.【详解】当4m =时,13m -=不是完全平方数,26m +=不是完全平方数,由此排除A,C 两个选项.当1m =时,10m -=是完全平方数,由此排除B 选项.故本小题选D. 【点睛】本小题主要考查完全平方数的特点,考查特殊值解选择题的方法,属于基础题.15.如图,反比例函数3y x=-(0x >)图像经过矩形OABC 边AB 的中点E ,交边BC 于F 点,连结EF 、OE 、OF ,则△OEF 的面积是( )A.32B.94C.73D.52【答案】B 【解析】 【分析】设出A 点坐标,求得,,B E F 的坐标,利用矩形面积减去三个直角三角形的面积,求得三角形OEF 的面积.【详解】设(),0,0A a a >,则366,,,,,2a E a B a F a a a ⎛⎫⎛⎫⎛⎫--- ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭,矩形OABC 的面积为66a a ⋅=,三个直角三角形的面积为131********222222424a a a a a a ⋅⋅+⋅⋅+⋅⋅=++=,所以三角形OEF 的面积为159644-=,故选B. 【点睛】本小题主要考查反比例函数上点的坐标的特点,考查利用割补法求三角形面积,属于基础题.16.如果不等式组9080x a x b -≥⎧⎨-<⎩的整数解有n (*n ∈N )个,那么适合这个不等式组的整数a 、b 的有序数对(,)a b 共有( )个A. 17个B. 64个C. 81个D. 72个【答案】D 【解析】 【分析】先解不等式组求得x 的取值范围,根据整数解的情况,确定有序对的个数. 【详解】由9080x a x b -≥⎧⎨-<⎩得98a bx ≤<,不妨设1n =,故a 可取1,2,3,4,5,6,7,8,9共9种可能,b 可取9,10,11,12,13,14,15,16共8种可能,可以满足整数解有1个,为1.所以有序数对(),a b 共有9872⨯=个,故选D.【点睛】本小题主要考查一元一次不等式组的解法,考查分步计数原理,考查整数的性质,考查分析与思考的能力,属于基础题.三.解答题17.求3232x x x ++-除以2x -的商式与余数. 【答案】商式23715x x =++,余式28=. 【解析】 【分析】设商为2ax bx c ++,利用()()22x ax bx c -++的展开式与3232x x x ++-比较,求得,,a b c的值,进而求得商式和余式.【详解】设商为2ax bx c ++,()()22x ax bx c -++()()32222ax b a x c b x c =+-+--,所以32121a b a c b =⎧⎪-=⎨⎪-=⎩,解得3,7,15a b c ===,()()223715x x x -++22330x x x =++-,由()32223233028x x x x x x ++--++-=可知,余式为28.【点睛】本小题主要考查多项式除法,考查化归与转化的数学思想方法,属于基础题.18.如图所示为圆柱形大型储油罐固定在U 型槽上的横截面图,已知图中ABCD 为等腰梯形(AB ∥DC ),支点A 与B 相距8m ,罐底最低点到地面CD 距离为1m ,设油罐横截面圆心为O ,半径为5m ,56D ∠=︒,求:U 型槽的横截面(阴影部分)的面积.【参考数据:sin530.8︒≈,tan56 1.5︒≈,3π≈,结果保留整数】【答案】202m【解析】【分析】利用梯形面积,减去弓形面积,求得阴影部分面积.【详解】连接,,OA OB AB ,过O 作OG CD ⊥交AB 于E ,交劣弧»AB 于F .过A 作AH CD ⊥交CD 于H ,过B 作BI CD ⊥交CD 于I .由于228AB AE BE ===,5OB OA ==,所以3,2,3OE FE OF OE EG EF FG ==-==+=,所以3AH BI ==,在直角三角形ADH 中,3tan ,tan 56,2AH D DH DH DH===o ,同理求得2CI =,所以28212CD =++=,故梯形ABCD 的面积为8123302+⨯=.在直角三角形OAE 中4sin 0.85AOE ∠==,故53,106AOE AOB ∠≈∠=o o ,所以扇形OAFB 的面积为1063522360⨯⨯≈,而三角形AOB 的面积为183122⨯⨯=,所以弓形AFB 的面积为221210-=,故阴影部分面积为2301020m -=.【点睛】本小题主要考查与圆有关的面积计算,考查梯形面积公式、扇形面积公式,考查分析与思考、解决问题的能力,属于中档题.19.如图,在边长为6的正方形ABCD 中,弧AC 的圆心为B ,过弧AC 上的点P 作弧AC 的切线,与AD 、CD 分别相交于点E 、F ,BP 的延长线交AD 边于点G .(1)设AE x =,CF y =,求y 与x 之间的函数解析式,并写出函数定义域;(2)当2AE =时,求EG 的长.【答案】(1)3666x y x -=+,(0,6)x ∈;(2)52. 【解析】【分析】(1)根据切线长定理求得,PE PF 的长,在直角三角形DEF 中利用勾股定理求得y 与x 的关系式.(2)以B 为平面直角坐标系原点,BC BA 分别为,x y 轴建立平面直角坐标系,又,E F 坐标,求得直线EF 的斜率,进而求得直线BP 的斜率,由此求得AG 长,进而求得EG 的长.【详解】(1)根据切线长定理得,PE AE x PF CF y ====,且6,6DE x DF y =-=-,直角三角形DEF 中由勾股定理得()()()22266x y x y +=-+-,化简得3666x y x -=+,由066x <-<,解得06x <<,也即函数定义域为()0,6.所以函数解析式为()()3660,66x y x x-=∈+.(2)当2AE =时,由(1)知3CF =.以B 为平面直角坐标系原点,BC BA 分别为,x y 轴建立平面直角坐标系,则()()()()0,6,6,0,2,6,6,3A C E F ,所以直线EF 的斜率为633264-=--,所以与EF 垂直的直线BG 的斜率为43,而4tan tan 3AB AGB GBC AG ∠=∠==,所以3942AB AG ==,所以95222EG AG AE =-=-=.即EG 长为52.【点睛】本小题主要考查圆的切线长定理,考查勾股定理,考查坐标法求解几何问题,属于中档题.20.对于函数()f x ,若存在0x ∈R ,使00()f x x =成立,则称点00(,)x x 为函数()f x 的不动点.(1)已知函数2()f x ax bx b =+-(0a ≠)有不动点(1,1)和(3,3)--,求a 、b ;(2)若对于任意的实数b ,函数2()f x ax bx b =+-总有两个相异的不动点,求实数a 的取值范围.【答案】(1)1a =,3b =;(2)(0,1).【解析】【分析】(1)根据不动点的定义列方程组,解方程组求得,a b 的值.(2)根据不动点的概念列式,利用一元二次方程根的个数与判别式的关系列不等式,解不等式求得a 的取值范围.【详解】(1)依题意()()11393943f a b b a f a b b a b ⎧=+-==⎪⎨-=--=-=-⎪⎩,解得1,3a b ==. (2)首先0a ≠,依题意20000()f x ax bx b x =+-=有两个不同的解,即()20010ax b x b +--=有两个不同的解,所以()2140b ab ∆=-+>,即()24210b a b +-+>对任意b R ∈都成立,所以()24240a ∆=--<,即216160a a -<,()10a a -<,解得01a <<.所以实数a 的取值范围是()0,1.【点睛】本小题主要考查新定义概念的理解和运用,考查一元二次不等式根的个数与判别式的关系,考查一元二次不等式恒成立问题的求解策略,属于中档题.21.设n 为正整数,集合12{|(,,,),{0,1}}n k A t t t t αα==⋅⋅⋅∈(1,2,,k n =⋅⋅⋅),对于集合A 中的任意元素12(,,,)n x x x α=⋅⋅⋅和12(,,,)n y y y β=⋅⋅⋅,记111122221(,)[(||)(||)(||)]2n n n n M x y x y x y x y x y x y αβ=+--++--+⋅⋅⋅++--. (1)当3n =时,若(1,1,0)α=,(0,1,1)β=,求(,)M αα和(,)M αβ的值;(2)当4n =时,设B 是A 的子集,且满足:对于B 中的任意元素α、β,当α、β相同时,(,)M αβ是奇数,当α、β不同时,(,)M αβ是偶数,求集合B 中元素个数的最大值.【答案】(1)(,)2M αα=,(,)1M αβ=;(2)4.【解析】【分析】(1)利用(,)M αβ的定义,求得(,)M αα和(,)M αβ的值.(2)当4n =时,根据α、β相同时,(,)M αβ是奇数,求得此时集合B 中元素所有可能取值,然后验证α、β不同时,(,)M αβ是偶数,由此确定集合B 中元素个数的最大值.【详解】(1)依题意(,)M αα()()()111011000022=+-++-++-=⎡⎤⎣⎦; (,)M αβ()()()110111001112=+-++-++-=⎡⎤⎣⎦. (2)当4n =时,依题意当α、β相同时,(,)M αβ()()()()1122334412x x x x x x x x =+++++++⎡⎤⎣⎦1234x x x x =+++为奇数,则1234,,,x x x x 中有“3个1和1个0”或者“1个1和3个0”.当α、β不同时:①当1234,,,x x x x 中有“3个1和1个0”时,元素为()()()()1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,1,经验证可知(,)M αβ是偶数,符合题意,集合B 最多有4个元素()()()()1,1,1,0,1,1,0,1,1,0,1,1,0,1,1,1.②当1234,,,x x x x 中有“1个1和3个0”时,元素为()()()()1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1,经验证可知(,)Mαβ是偶数,符合题意,集合B 1,0,0,0,0,1,0,0,0,0,1,0,0,0,0,1.最多有4个元素()()()()综上所述,不管是①还是②,集合B中元素个数的最大值为4.【点睛】本小题主要考查新定义概念的理解和运用,考查分析、思考与解决问题的能力,属于中档题.。

2019-2020学年上海市闵行区七宝中学高一上学期期中考试数学试卷含详解

2019-2020学年上海市闵行区七宝中学高一上学期期中考试数学试卷含详解

2019-2020学年上海市闵行区七宝中学高一(上)期中数学试卷一.填空题1.已知集合A={x|x≤2019},B={x|x>a},且A∪B=R,则实数a的取值范围是2.若集合M={1,﹣3},N={a﹣3,2a+1,a2+2},若M∩N={﹣3},则实数a=3.命题“若a•b不为零,则a,b都不为零”的否命题是.4.科技节期间,高一年级的某同学发明了一个魔术盒,当任意实数对(a,b)进入其中时,会得到一个新的实数:2a+b﹣1,如把(3,﹣2)放入其中,就会得到2×3+(﹣2)﹣1=3,现将实数对(m,﹣3m)放入其中,得到实数﹣9,则m=5.设函数,若f(x0)=3,则x0=6.已知函数,,则f(x)•g(x)=7.已知不等式|x﹣1|<m的解集中有且只有5个整数,则实数m的取值范围是8.若关于x的不等式x2﹣2x≤4﹣a在R上的解集为∅,则实数a的取值范围是9.已知函数f(x)的定义域为(﹣1,1),则函数的定义域为10.设x>0,y>0,且+=2,则2x+y的最小值为.11.已知不等式|3x﹣a|>x﹣1对任意x∈(0,2)恒成立,则实数a的取值范围是12.对于集合M,定义函数,对于两个集合M、N,定义集合M*N={x|f M(x)•f N(x)=﹣1},用Card(M)表示有限集合M所含元素的个数,若A={1,2,4,8},B={2,4,6,8,10},则能使Card(X*A)+Card(X*B)取最小值的集合X的个数为.二.选择题13.α:x=1,β:x2=1,则α是β的()A.充分非必要条件B.必要非充分条件C.充要条件D.既非充分又非必要条件14.已知集合P={a,b},Q={M|M⊆P},则P与Q的关系为()A.P⊆Q B.Q⊆P C.P∈Q D.P∉Q15.若实数a、b、c满足a>b>c,则下列不等式正确的是()A.a+b>c B.C.a|c|>b|c|D.16.已知a、b、c为实数,f(x)=(x+a)(x2+bx+c),g(x)=(ax+1)(cx2+bx+1),记集合S={x|f(x)=0,x∈R},T={x|g(x)=0,x∈R},则下列命题为真命题的是()A.若集合S的元素个数为2,则集合T的元素个数也一定为2B.若集合T的元素个数为2,则集合S的元素个数也一定为2C.若集合S的元素个数为3,则集合T的元素个数也一定为3D.若集合T的元素个数为3,则集合S的元素个数也一定为3三.解答题17.已知集合,函数的定义域为集合B,且A⊆B,求实数a的取值范围.18.若实数x、y、m满足|x﹣m|<|y﹣m|,则称x比y接近m.(1)若x2+3比4接近1,求实数x的取值集合M;(2)若a、b均属于(1)中集合M,求证:a+b比ab+1接近0.19.近年来,某企业每年消耗电费约24万元,为了节能减排,决定安装一个可使用15年的太阳能供电设备接入本企业电网,安装这种供电设备的工本费(单位:万元)与太阳能电池板的面积(单位:平方米)成正比,比例系数约为0.5.为了保证正常用电,安装后采用太阳能和电能互补供电的模式.假设在此模式下,安装后该企业每年消耗的电费C(单位:万元)与安装的这种太阳能电池板的面积x(单位:平方米)之间的函数关系是C(x)=(x≥0,k为常数).记F为该村安装这种太阳能供电设备的费用与该村15年共将消耗的电费之和.(1)试解释C(0)的实际意义,并建立F关于x的函数关系式;(2)当x为多少平方米时,F取得最小值?最小值是多少万元?20.已知M是满足下述条件的所有函数f(x)组成的集合:对于函数f(x)定义域内的任意两个自变量x1、x2,均有|f(x1)﹣f(x2)|≤2|x1﹣x2|成立.(1)已知定义域为R的函数f(x)=kx+b∈M,求实数k、b的取值范围;(2)设定义域为[﹣1,1]的函数g(x)=ax2+x,且g(x)∉M,求正实数a的取值范围;(3)已知函数的定义域为R,求证:h(x)∈M.21.对于正整数集合A={a1,a2,…,a n}(n∈N*,n≥3),如果去掉其中任意一个元素a i(i=1,2,…,n)之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合A 为“和谐集”.(1)判断集合{1,2,3,4,5}是否为“和谐集”,并说明理由;(2)求证:集合{1,3,5,7,9,11,13}是“和谐集”;(3)求证:若集合A是“和谐集”,则集合A中元素个数为奇数.2019-2020学年上海市闵行区七宝中学高一(上)期中数学试卷参考答案与试卷解析一.填空题1.【解答】解:∵A={x|x≤2019},B={x|x>a},且A∪B=R,结合数轴可知,a≤2019故答案为:(﹣∞,2019]2.【解答】解:∵集合M={1,﹣3},N={a﹣3,2a+1,a2+2},M∩N={﹣3},∴或,解得实数a=﹣2.故答案为:﹣2.3.【解答】解:先否定命题“若a•b不为零,则a,b都不为零”的题设,得到否命题的题设“若a•b为零”,再否定命题“若a•b不为零,则a,b都不为零”的结论,得到否命题的结论“至少有一个为零”,∴命题“若a•b不为零,则a,b都不为零”的否命题是:若a•b为零,则a,b至少有一个为零.故答案为:若a•b为零,则a,b至少有一个为零.4.【解答】解:根据定义直接代入2m+(﹣3m)﹣1=﹣9,解之得m=8.故答案为:8.5.【解答】解:根据题意,函数,若f(x0)=3,当x0≤1时,f(x0)=x02+1=3,解可得x0=±,又由x0≤1,此时x0=﹣;当x0>1时,f(x0)=2x0+1=3,解可得x0=1,又由x0>1,此时x0=1舍去;综合可得:x0=﹣;故答案为:﹣.6.【解答】解:,∴f(x)•g(x)=1(x>0).故答案为:1(x>0).7.【解答】解:由|x﹣1|<m,得﹣m+1<x<m+1.∵不等式|x﹣1|<m的解集中有且只有5个整数,∴,∴2<m≤3,∴m的取值范围为(2,3].故答案为:(2,3].8.【解答】解:不等式x2﹣2x≤4﹣a,即(x﹣1)2≤5﹣a,因为左边完全平方式≥0,要使不等式在R上的解集为∅,所以5﹣a<0,即a>5.故答案为:a>5.9.【解答】解:∵f(x)的定义域为(﹣1,1),∴要使g(x)有意义,则,解得1<x<2,∴g(x)的定义域为(1,2).故答案为:(1,2).10.【解答】解:∵+=2,∴2x+y=2x+y+1﹣1=(2x+y+1)•(+)﹣1=(2+2++)﹣1≥2﹣1+×2=1+2=3,当且仅当x=1,y=1时取等号,故2x+y的最小值为3,故答案为:3.11.【解答】解:|3x﹣a|>x﹣1等价于3x﹣a>x﹣1或3x﹣a<1﹣x,解得或x<,当,即a<3时,不等式解集为R,显然符合题意.当a≥3时,(0,2)⊆(﹣∞,)∪(,+∞),所以或,解得a≥7或a≤1(舍去),综上,实数a的取值范围是a≥7或a<3.故答案为:(﹣∞,3)∪[7,+∞).12.【解答】解:∵函数,f M(x)和f N(x)的可能值为1或﹣1.根据集合M、N的定义,有f M(x)=1且f N(x)=﹣1或者f M(x)=﹣1且f N(x)=1即,所以X*A中元素最少时X*A={1,2,4,8},X*B中元素最少时X*B={2,4,6,8,10}所以Card(X*A)+Card(X*B)取最小值时X的个数为{2,4,8}的子集个数23=8,故答案为:8.二.选择题13.【答案】A【解答】解:当x=1时,x2=1,即充分性成立,若x2=1,解得x=±1,即必要不充分条件,则α是β的充分不必要条件,故选:A.14.【答案】C【解答】解:因为集合P的子集有∅,{a},{b},{a,b},所以集合Q={∅,{a},{b},{a,b}},所以p∈Q.故选:C.15.【答案】B【解答】解:∵a>b>c,∴A.a+b>c错误,比如﹣4>﹣5>﹣6,得出﹣4﹣5<﹣6;B.a﹣c>b﹣c>0,∴,∴该选项正确;C.a|c|>b|c|错误,比如|c|=0时,a|c|=b|c|;D.ab2﹣a2b=ab(b﹣a),ab(b﹣a)=0时,ab2=a2b,∴,∴该选项错误.故选:B.16.【答案】D【解答】解:x2+bx+c=0,两边除以x平方,得,如果两个根不为o,x2+bx+c=0与cx2+bx+1=0的根互为倒数,f(x)=0有一个根为x=﹣a,如果a≠0,g(x)=0一定有一个根x=﹣,这两个根也是互为倒数,若f(x)有两个根x=﹣a(a≠0),另外一个根为0,则g(x)只有一个根x=﹣,故A不成立,同理B不成立,若g(x)有三个根,其中一个根为x=﹣,则a不等于0,cx2+bx+1=0有2个与﹣不同的根,其中都不为0,否则得到1=0,显然不成立,那么这三个根的倒数必然存在,且不相等,故f(x)也有三个不同的根,所以D成立,反之,根据以上分析,C 不一定成立,故选:D.三.解答题17.【解答】解:由条件知,集合A={x|2<x<3};函数f(x)的定义域为:B={x|x<a﹣1或x>a+1};∵A⊆B;∴a﹣1≥3或a+1≤2;a≥4或a≤1,∴实数a的取值范围是:(﹣∞,1]∪[4,+∞).18.【解答】解:(1)x2+3比4接近1,∴|x2+3﹣1|<|4﹣1|,即|x2+2|<3,∴﹣1<x<1,∴实数x的取值集合M={x|﹣1<x<1};(2)证明:a、b均属于(1)中集合M,即a∈(﹣1,1),b∈(﹣1,1),∴要证a+b比ab+1接近0,只需证|a+b|<|ab+1|,只需证a2+b2+2ab<a2b2+2ab+1,即证(1﹣a2)(1﹣b2)<0,∵a∈(﹣1,1),b∈(﹣1,1),∴1﹣a2<0,1﹣b2<0,∴(1﹣a2)(1﹣b2)<0成立,∴a+b比ab+1接近0.19.【解答】解:(1)C(0)的实际意义是安装这种太阳能电池板的面积为0时的用电费用,即未安装太阳能供电设备时全村每年消耗的电费…(2分)由C(0)==24,得k=2400…所以F=15×+0.5x=+0.5x,x≥0…(7分)(2)因为+0.5(x+5)﹣2.5≥2﹣2.5=57.5,…(10分)当且仅当=0.5(x+5),即x=55时取等号…(13分)所以当x为55平方米时,F取得最小值为57.5万元…(14分)20.【解答】解:(1)∵g(x)=kx+b∈M,∴使得任意x1、x2∈R,均有|g(x1)﹣g(x2)|≤2|x1﹣x2|成立.即存在|g(x1)﹣g(x2)|=|k||x1﹣x2|≤2|x1﹣x2|,所以k∈[﹣2,2],b∈R;(2)g(x)=ax2+x,x∈[﹣1,1],g(x)∉M,即存在x1、x2∈[﹣1,1],有|g(x1)﹣g(x2)|>2|x1﹣x2|成立,即|x1﹣x2||a(x1+x2)+1|>2|x1﹣x2|,由,|a(x1+x2)+1|≥a|x1+x2|+1>2,得a>,故a∈;(3)证明:的定义域为R,任意两个自变量x1、x2,只需证明|h(x1)﹣h(x2)|=||≤2|x1﹣x2|成立,根据基本不等式,,故=成立,所以h(x)∈M.21.【解答】解:(1)对于集合{1,2,3,4,5},当去掉元素2时,剩余的所有元素之和为13,不能分为两个交集为空集且这两个集合的所有元素之和相等的集合,所以集合{1,2,3,4,5}不是“和谐集”.(2)证明:设A={1,3,5,7,9,11,13},当去掉元素1时,有3+5+7+9=11+13;当去掉元素3时,有1+9+13=5+7+11;当去掉元素5时,有9+13=1+3+7+11;当去掉元素7时,有1+9+11=3+5+13;当去掉元素9时,有1+3+5+11=7+13;当去掉元素11时,有3+7+9=1+5+13;当去掉元素13时,有1+3+5+9=7+11.所以集合A={1,3,5,7,9,11,13}是“和谐集”.(3)证明:设“和谐集”A={a1,a2,…,a n}所有元素之和为M.由题可知,M﹣a i(i=1,2,…,n)均为偶数,因此a i(i=1,2,…,n)的奇偶性相同.(ⅰ)如果M为奇数,则a i(i=1,2,…,n)也均为奇数,由于M=a1+a2+…+a n,所以n为奇数.(ⅱ)如果M为偶数,则a i(i=1,2,…,n)均为偶数,此时设a i=2b i,则{b1,b2,…,b n}也是“和谐集”.重复上述操作有限次,便可得各项均为奇数的“和谐集”.此时各项之和也为奇数,集合A中元素个数为奇数.综上所述,集合A中元素个数为奇数.。

七宝中学2019学年度第一学期高一期中考试物理试卷1

七宝中学2019学年度第一学期高一期中考试物理试卷1

七宝中学2019学年度第一学期高一期中考试物理试卷(考试时间60分钟,满分100分)本卷取g=10m/s2一、选择题(共40分,1至8题每小题3分,9至12题每小题4分,每小题只有一个正确选项)1.关于质点的说法正确的是()A.只要体积很小的物体都可以看作质点B.只要质量很小的物体都可以看作质点C.质量很大或体积很大的物体都一定不能看作质点D.同一物体有时可以看作质点,有时不能看作质点2.关于力的说法正确的是()A.力是物体对物体的作用,所有只有直接接触的物体间才有力的作用B.有一定距离的磁体间有相互作用力,因此力可以离开物体而独立存在C.力是使物体发生形变或改变物体运动状态的原因D.力的大小可以用天平测量3.关于摩擦力,正确的是()A.有弹力必有摩擦力B.静止的物体受到的摩擦力一定是静摩擦力C.滑动摩擦力的方向一定和物体运动方向相反D.滑动摩擦力的大小和物体间的相对速度无关4.一物体做匀变速直线运动,则()A.物体的末速度一定与时间成正比B.物体的位移一定与时间的平方成正比C.物体的速度变化量与时间成正比D.若为匀加速运动,速度和位移都随时间增加;若为匀减速,速度和位移都随时间减小5.如图所示,为一物体运动的位移一时间图象,则物体()A.一直做匀加速直线运动B.一直做匀减速直线运动C.以某一速率做往复运动D.有时做匀加速直线运动,有时做匀减速直线运动6.若汽车的加速度方向与初速度方向一致,当加速度减小时,()A.汽车的速度一定在增大B.汽车的速度也减小C.汽车的速度可能不变D.当加速度减小到零时,汽车静止7.一物体由静止起做匀加速运动,在第7s的初速度是2.1m/s,则它的加速度是()A.0.3m/s2B.0.35m/s2C.2.1m/s2D.4.2m/s28.关于自由落体运动,正确的说法是()A.在空气中不考虑空气阻力的都是自由落体运动B.物体做自由落体运动时不受任何外力作用C.质量大的物体,受到的重力也大,落地时的速度也越大D.自由落体运动是初速度为零、加速度为重力加速度的匀加速直线运动9.物体沿直线从A点经B点运动到C点,在AB段运动速度为60m/s,在BC段运动速度30m/s,且AB=3BC,则AC段的平均速度为()A.37.5m/s B.45m/s C.48m/s D.52.5m/s10.一物体在高处以初速度20m/s竖直上抛,到达离抛出点15m处所经历的时间不可能是()A.1s B.2s C.3s D.2+√7s11.一物体做直线运动的加速度随时间变化的a-t图象如左图所示,则可能正确描述此物体运动的v-t图象是()A.B.C.D.12.某乘客用手表估测火车的加速度,他先观测3分钟,发现火车前540m,隔3分钟后又观测1分钟,发现火车前进了360m,若火车在这7分钟内做匀加速直线运动,其加速度为()A.0.03m/s2B.0.01m/s2C.0.5m/s2D.0.6m/s2二、填空题(共20分,每个空格2分)13.质点由A点出发向正东方向移动了8m后到达B点,再从B点出发向正北方向移动6m 后到达C点,则质点从A点到C点经过的路程是m,位移大小是m。

2019年七宝中学高一期中考试题

2019年七宝中学高一期中考试题

七宝中学高一期中数学试卷2019.04一. 填空题1. 函数12sin(4)y x =-的最小正周期是2. 函数cos2y x =的对称轴方程是3. 在平面直角坐标系中,已知角θ的顶点在坐标原点,始边与x 轴正半轴重合,终边在直 线3y x =上,则sin2θ=4. 若锐角α、β满足3cos 5α=,5cos()13αβ+=-,则cos β= 5. 函数2sin(2)3y x π=-的单调递减区间为6. 已知2sin 5x =-(32x ππ<<),则x = (用反正弦表示)7. 方程sin x x =的解是8. 在△ABC 中,角A 、B 、C 的对边分别为a 、b 、c ,面积为S ,且224()S a b c =+-, 则cos C = 9. 若将函数()cos()8f x x πω=-(0ω>)的图像向左平移12π个单位后,所得图像对应的 函数为偶函数,则ω的最小值是 10. 已知函数sin(2)cos(2)sin(2)cos(2)()||22x x x x f x ππππ+-=+,对任意x ∈R ,都有不等式12()()()f x f x f x ≤≤恒成立,则21||x x -的最小值为 11. 已知函数1sin()()20192019x xx f x π-=+(x ∈R ),下列命题:① 函数()f x 是奇函数;② 函数()f x 在区间[2,2]ππ-上共有13个零点; ③ 函数()f x 在区间(0,1)上单调递增; ④ 函数()f x 的图像是轴对称图形.其中真命题有 (填所有真命题的序号) 12. 已知k 是正整数,且12019k ≤≤,则满足方程sin1sin2sin sin1sin2sin k k ︒+︒+⋅⋅⋅+︒=︒⋅︒⋅⋅⋅︒的k 有 个二. 选择题13. “[,]22x ππ∈-”是“sin(arcsin )x x =”的( ) A. 充分非必要条件 B. 必要非充分条件 C. 充要条件 D. 既非充分条件又非必要条件 14. 将函数sin()12y x π=-图像上的点(,)4P t π向左平移s (0s >)个单位,得到点P ',若 P '位于函数sin 2y x =的图像上,则( )A. 12t =,s 的最小值为6πB. t =,s 的最小值为6πC. 12t =,s 的最小值为12πD. 2t =,s 的最小值为12π15. 若方程212cos sin 0x x a --+=有实数解,则实数a 的取值范围( ) A. 9(,]8-∞ B. 9[2,]8- C. 9[0,]8 D. 9[1,]8- 16. 如图,在△ABC 中,BC a =,AC b =,AB c =,O 是△ABC 的外心,OD BC ⊥于D ,OE AC ⊥于E , OF AB ⊥于F ,则::OD OE OF 等于( )A. ::a b cB. cos :cos :cos A B CC. sin :sin :sin A B CD. 111::a b c三. 解答题17. 已知7cos(23)25θπ-=,且θ是第四象限角; (1)求cos θ和sin θ的值;(2)求3cos()sin()22tan [cos()1]tan()cos()ππθθθπθπθθ--++---的值.18. 在△ABC 中,角A 、B 、C 的对边分别为a 、b 、c ,已知2a b -=,4c =,sin 2sin A B =. (1)求△ABC 的面积S ;(2)求sin(2)A B -的值.19. 已知函数()2sin 2f x x x =-. (1)求()y f x =的最小正周期和对称中心;(2)将()f x 的图像向左移α(0α>)个单位得函数()y g x =的图像,若(0,)2πα∈,()y g x =的一条对称轴为12x π=,求()y g x =,[0,]2x π∈的值域.20. 如题所示:扇形ABC 是一块半径为2千米,圆心角为60°的风景区,P 点在弧BC 上,现欲在风景区中规划三条商业街道PQ 、QR 、RP ,要求街道PQ 与AB 垂直,街道PR 与AC 垂直,直线PQ 表示第三条街道.(1)如果P 位于弧BC 的中点,求三条街道的总长度;(2)由于环境的原因,三条街道PQ 、PR 、QR 每年能产生的经济效益分别为每千米300万元,200万元及400万元,问:这三条街道每年能产生的经济总效益最高为多少?(精确到1万元)21. 给出集合{()|(2)(1)(),}M f x f x f x f x x =+=+-∈R . (1)若()sin3xg x π=,求证:函数()g x M ∈;(2)由(1)可知,()sin3xg x π=是周期函数且是奇函数,于是张三同学得出两个命题:命题甲:集合M 中的元素都是周期函数;命题乙:集合M 中的元素都是奇函数,请对此给 出判断,如果正确,请证明;如果不正确,请举出反例;(3)设P 为常数,且0P ≠,x ∈R ,求()sin h x px M =∈的充要条件并给出证明.参考答案一. 填空题 1.2π2. 2k x π=,k ∈Z3. 354. 33655. 511[,]1212k k ππππ++,k ∈Z6. 2arcsin 3π+7. 7212x k ππ=+或13212x k ππ=+,k ∈Z 8. 0 9. 3210. 38 11.②④ 12. 11二. 选择题13. B 14. A 15. B 16. B三. 解答题 17.(1)4cos 5θ=,3sin 5θ=-;(2)38.18.(1;(2)32.19.(1)T π=,(,0)122k ππ+,k ∈Z ;(2)[-.20.(1)2+;(2)1222万元.21.(1)略;(2)甲真命题,周期为6,乙假命题,如cos3xy π=;(3)略.。

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七宝高一英语期中考试(2019年11月)满分:150分I. Listening Comprehension (25%)Section ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. 5:00. B. 4:30. C. 5:30. D. 6:00.2. A. In a factory. B. In a hotel room. C. At a reception desk. D. In the hell.3. A. She doesn’t like eating the cake. B. She is trying to buy some cake.C. She is leaving to take a flight.D. She is going on a diet now.4. A. She’s a housewife. B. She’s a nurse.C. She’s a babysitter.D. She’s a teacher.5. A. Painting the room. B. Pleasure in helping others.C. Preparing for a surprise party.D. Asking Mike for help.6. A. She is working in the hospital as a doctor.B. She is a patient in the hospital.C. She is not allowed to be visited by her friends.D. She is seeing patients of injuries on the fourth floor.7. A. Nervous. B. Relaxed. C. Confident. D. Fine.8. A. He is not afraid of driving in the terrible rush hour.B. Driving is much faster than taking the bus to work.C. He has to leave the seat when the bus gets to his stop.D. He doesn’t like standing all the way on his way to work.9. A. Because she doesn’t want a good rest.B. Because she doesn’t take a bad cold seriously.C. Because she will lose her job if she does.D. Because she wants to keep on working.10. A. Her English class is interesting. B. Mr. Jackson is stricter than Mr. White.C. She wants to shout in English class.D. She doesn’t like being sleepy in class.Section BDirections: In Section B, you will hear two short passages, and you will be asked to questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. How to say and spell “horse”. B. A few simple spelling tricks.C. A comfortable pattern of numbers.D. Rules in math without a problem.12. A. He learned the spelling “rules” in high school.B. He spent hours online playing word games.C. He entered himself in competitions of all levels.D. He learned Spanish to play in another language.13. A. He was good with words in elementary school.B. He didn’t realize his talent in words until high school.C. He competed in order to win Word Game Player of the Year.D. Becoming a word game addict did harm to his life.Questions 14 through 16 are based on the following news.14. A. To take up some time. B. To plan a training.C. To learn from adventure.D. To develop leadership skills.15. A. Lectures on public relations. B. Tests on management.C. Climbing mountains.D. Long-distance running.16. A. The company decides the employees’ income according to the report.B. The employees in the company cannot handle difficult conditions.C. The employees have to ask for leave for 20 days in July for the program.D. The company provides the program as welfare for its employees.Section CDirections: I n Section C, you will hear a longer conversation. The conversation will be read twice. After you hear the conversation, you are required to answer the following questions.17. A. Their opinions about making friends online.B. Their time of going to bed at night.C. The popularity of social networks.D. Spending time in a more meaningful way.18. A. Crazy. B. Necessary. C. Interesting. D. Unreal.19. A. Making friends online is very interesting.B. He can share secrets safely with others.C. He won’t meet someone he knows online.D. He can practice his English when chatting.20. A. Come to her house.B. Get up early in the morning.C. Sleep more in the evening.D. Do some more important things.II. Grammar and vocabulary (50%)Section A (30%)Directions: fill in the blank with the proper form of the given verb.21.If you don’t come this afternoon, you ________(miss) a lot of nice things.22.A family may have a member who ________(think) of as a black sheep, a person who brings trouble.23. The glasses I thought I ________(lose) are here, right under my nose.24. Last month, an Alabama school leader suggested a dress code that ______ (ban) Capri pants (七分裤) andscarves and include restrictions on eye makeup and nail polish.25. Zootopia ___________(praise) for its sharp humor and strong message since its release.26. Amilia Earthart was the first woman ________(fly) the Atlantic Ocean alone.27. Do you have trouble ________(express) yourself in written English?28. People’s awareness of personal information protection remains ________(raise).29. The way to avoid ________(fine) is to obey the traffic rules when you drive.30. I seem ________(leave) my homework at home, so I have to do it again during the break.Directions: Read the following passage. Fill in the blanks to make the passage coherent. Fill in each blank with the proper form of the given verb. Make sure that your answers are grammatically correct.Discover new ways to travelWe’ve probably all met someone who likes to boast about how many places he or she has been to. It’s annoying but it’s true that to some people, traveling is all about the number of destinations one _____31.____(set) foot on. But fortunately, the old “been there, seen that” mode is changing.Last year’s travel trend was “experiential travel”. This is where tourists look for ways to get to know local culture and interact with local people, so they feel less like an outsider but more like a resident. So what about this year? Can thoughtful tourists get even more out of their traveling experience?Transformative travelTransformative travel is much like “experiential travel”, but takes it a step further.It usually ____32.____(go) through three phases – you go to a place that has a very different background than where you come from, you learn wisdom from the new culture and the people you meet, and finally you return home and use the knowledge in your own life and the lives of those around you. This last phase is how the “transformation” ____33.____(complete) and what ____34.____(separate) transformative travel from experiential travel.“This allows our travelers ____35.____(start) to see the world less in black and white, and to begin to appreciate how nuanced(微妙的) many issues are when ____36.____(see) from very different perspectives,” Jennine Cohen, director of US travel company GeoEx, told V ogue magazine.Go greenAccording to Rebecca Warren, managing editor at Lonely Planet, eco-friendly and sustainable travel will be one of this year’s top trends.One way to plan a low-impact trip is to travel a shorter distance, which can reduce your carbon footprint. “One trans-Atlantic flight equals a year’s worth of driving, so consider ____37.____(plan) an adventure closer to home,” suggested Warren, according to US News.Another way to involve sustainability in your travel plans is to choose a destination that ____38.____(benefit) the most from your trip. For example, places like Nepal will enjoy a boost of its local economy from the money it will make through tourism.Disappearing destinationsDestinations at risk of disappearing are also welcoming an increasing number of tourists.Everett Potter, a USA Today writer, says that the Arctic and Antarctic have become popular destinations since they ____39.____(threaten) by climate changes.Another top destination is the Great Barrier Reef in Australia. Due to pollution and global warming, it’s predicted that the reef ____40.____(damage) in just a few decades. Travelers are longing to see the coral “before it’s gone or completely changed”, Potter told US News.Section B (20%)Directions: Complete the following passages by using the words in the box. Each word can only be used once. Note that there is one word more than you need.At the end of a long day, it’s all too easy to take a hot shower, throw on some pajamas, brush your teeth, andthen jump into bed. But have you ever stopped to think about the _____41.___ of sleeping with wet hair? As it turns out, going to bed with wet hair isn’t as ____42.____ as you probably thought.The first negative result of sleeping with wet hair is purely cosmetic: you can’t predict how your wet hair is going to look in the morning. “If you try to ____43.____ your hair in the morning after sleeping on it wet, you’re probably going to have funny waves, flat sides, and crinkles,” says hairstylist Olga Gilbert of J. Russell Salon in Southern California.“When you wake up to unruly bedhead, you’re probably going to have to re-wet it again to properly dry it and regain control. This ____44.____ adds time to your morning routine,” she says.Gilbert says that sleeping with wet hair does not immediately damage your hair follicles or shaft, but it can certainly lead to hair breakage, because wet hair is weakest when wet, making it easier to break. “If you pull your wet hair up into a tight ponytail or bun, you have a much greater chance of breaking it during the night,” Gilbert says. To help with that, here’s how to repair ____45.____ hair with items you already have at home.If you absolutely must sleep with wet hair because you have to wake up early for work, there are a few easy ways to minimize the damage. First, you can change your cotton pillowcases for silk or satin ones like these. Silk has a much smoother surface, so you won’t experience as much unfortunate breakage. Not using the silk pillowcase is one of the nighttime habits that could ____46.____ your hair.Next, you can make sure to sleep with your hair down or in a(n) ____47.____ braid(辫子), instead of up in a tight bun or ponytail. In addition, you should replace your tight, elastic bands with a soft scrunchy(束发带) that isn’t going to roughly pull at night. If you’re willing, it’s also very helpful (but less comfortable) to wrap your hair in a silk scarf.Finally, if you’re going to bed with wet hair, the most important rule is never to forget to ____48.____ product! Protective serums(精华液), dry oils, and texturizing mousses are some of the best ways to ____49.____ you don’t wake up looking like an alpaca(羊驼) while protecting your precious hair from damage. Now that you know how bad sleeping with wet hair is, make sure you’re not making these hairstyle mistakes that ____50.____ your face.Heritage list on Saturday as an early _____51._____ to globalization.The decision was made at the ongoing 41st session of World Heritage Committee in Krakow, Poland, which designated Kulangsu a Historic International Settlement.____52._____ a mere 1.88 square kilometers, the island hosted settlements from 13 countries from the end of the First Opium War (1840-42) to the early 20th century.The committee found that Kulangsu was China’s major gateway in early-stage globalization and ____53.____ mixed architectural characteristics from the local, Southeast Asian and Western styles. It _____54.____ reflected cross-border communication.Today, 931 historical buildings and gardens in various styles remain, most of them former tycoons’residences, overseas companies and public institutions like hospitals. Many pioneers of Chinese modernization were born and left their former residences on Kulangsu. "The island has deep traditional Chinese culture roots and inclusiveness to embrace different values and cultures," said Song Xinchao, deputy director of the State Administration of Cultural Heritage. "It also shows a(n) ____55._____ of ancient thought and modern living concepts."Since 2014, preparations have been made for World Heritage status, Liang said. For example, a digital monitoring network was set up at the sites and a special office was opened within his committee for the ____56._____ of cultural relics."Kulangsu is not only a scenic spot, but also a community," Liang said. "We’ve tried to encourage local residentsto participate in the protection."New museums have opened on the island to better present its cultural resources. An abandoned hospital, for example, was renovated to be used as a satellite gallery of Beijing’s Palace Museum to display its _____57._____ of foreign artifacts."The central government will continue to encourage improving the quality of island residents` lives and improving visitors’experiences there," Song said. "An even more beautiful Kulangsu will be ____58.____ to the public."As a popular tourism destination, Kulangsu has had problems with crowding. Song said the daily number of visitors will be capped to meet crowd-control ____59._____ from World Heritage Committee. More measures will follow to better study and preserve historical heritage on the island.About 1,600 delegates from 107 countries and 167 international organizations attended the conference, which will continue through July 12. Delegates are judging 35 candidate World Heritage Sites from around the world and also discussing the status and protection of ____60._____ World Heritage Sites in Syria.III. Reading Comprehension (55%)Section A (15%)Directions: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Why did the ancient Maya abandon their citiesThe ancient Maya built many large cities in the Classic Period, which lasted from about 250 until about 900. Each city had its own king and _____61_____ class. The cities traded with one another but often ____62_____ with one another as well. In about 900, the Maya ___63_____ many of their cities. Archaeologists and other scientists have long puzzled over why the Maya left. They have formed theories by examining those cities carefully and studying the settlements that surround them. Researchers think that the _____64____ in some places may have been so large that people left because there was not enough ____65____ for everyone.Archaeologists studied ___66____ from one city and its surroundings to learn what had happened there. In Copan they found many tools dating from 500 to about 1000 and a few tools dating from about 1000 to 1200. They found that no new monuments had been built after 822. From studying plant remains, scientists concluded that the area around Copan had been ___67_____. Other evidence suggested that the land was overfarmed. In view of the evidence, the scientists concluded that a large population lived in Copan until about 1000. As more people farmed the land, the soil ____68____ its richness and produced few crops, which caused the Maya who lived there to ____69_____ malnutrition, as analysis of skulls show. As a result, people began to leave Copan in about 1000, but they did not completely abandon the city until about 1200.____70____ also may have caused the Maya to abandon some of their cities. For example, it is thought that a rival city, Caracol, may have once conquered Tikal. Then, after more than 100 years had passed, Tikal returned to power, and the ruling family built temples to ____71____ its victory. ____72____, by the end of the 800s, Tikal was no longer powerful. Its inhabitants left the city. Some archaeologists and historians think that war may have broken out again and caused the citizens to leave.Although we do not know for certain why many ancient Maya abandoned their cities, we may find some clues by observing today’s Maya. Modern Maya still live in the lands, including Mexico and Guatemala, that their ancestors ___73_____. Many present-day Maya ___74_____ a variety of ancient beliefs and customs, such as farming practices. Studying their beliefs and practices may ____75____ scientist to discover more about ancient Mayan culture.61.A. ruling B. living C. educating D. farming62.A. communicated B. fought C. quarreled D. bargain63.A. destroyed B. restored C. decorated D. abandoned64.A. population B. area C. family D. profit65.A. land B. water C. food D. space66.A. routes B. clues C. soil D. monuments67.A. wasteland B. ruins C. battlefield D. farmland68.A. developed B. created C. lost D. kept69.A. get rid of B. result from C. suffer from D. show sympathy for70.A. Malnutrition B. War C. Flood D. Earthquake71.A. honor B. record C. secure D. taste72.A. Otherwise B. Besides C. Therefore D. However73.A. cleared B. approached C. isolated D. occupied74.A. practice B. declare C. respect D. challenge75.A. remind B. help C. force D. forbidSection B (32%)Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.AOne Friday morning, before Michael was leaving for work he told his wife that he had finally determined to ask his boss for a salary raise. All day Michael felt nervous and anxious as he thought about the upcoming showdown. What if Mr. Duncan refused to grant his request? Michael had worked so hard in the last 18 months and brought some great benefits to Braer and Hopkins Advertising Agency. Of course, he deserved a wage increase.The thought of walking into Mr Duncan’s office left Michael weak in the knees. Late in the afternoon he was finally courageous enough to approach his superior. To his delight and surprise, the ever-frugal (一惯节省的) Rowland Duncan agreed to give Michael a raise!Michael arrived home that evenin g—despite breaking all city and state limits—to a beautiful table set with their best china, and candles lit. His wife, Cassie, had prepared a delicate meal including his favourite dishes. Immediately he thought someone from the office had tipped her off!Next to his plate Michael found a beautiful lettered note. It was from his wife. It read: “Congratulations, my love! I knew you’d get the raise! I prepared this dinner to show just how much I love you. I am so proud of your accomplishments!” He read it and stopped to think about how sensitive and caring Cassie was.After dinner, Michael was on his way to the kitchen to get dessert when he observed that a second card had slipped out of Cassie’s pocket onto the floor. He bent forward to pick it up. It read: “Don’t worry about not getting the raise! You do deserve one! You are a wonderful provider and I prepared this dinner to show you just how much I love you even though you did not get the increase.”Suddenly tears swelled in Michael’s eyes. Total acceptance! Cassie’s support for him was not conditional upon his success at work.The fear of rejection is often softened and we can undergo almost any setback or rejection when we know someone loves us regardless of our success or failure.76. What was Michael’s plan that Friday?A. To find a job with the Braer and Hopkins Advertising Agency.B. To ask for a wage increase from his boss.C. To celebrate his success.D. To ask his boss to come for dinner.77. On his way back home, Michael __________.A. felt weak in the kneesB. was punished by the traffic policemanC. was too anxious to share the news with his wifeD. couldn’t wait to enjoy a meal78. Which of the following statements about the story is FALSE?A. Michael was afraid that his request would lead to a disaster.B. Michael had worked very hard and done his part for the company.C. Michael’s boss agreed to his request.D. One of Michael’s colleagues had told his wife the good news.79.According to the passage, which of the following can best describe Michael’s wife, Cassie?A. Passionate, thoughtful and talented.B. Considerate, generous and reliable.C. Decisive, optimistic and energetic.D. Caring, tolerant and supportive.BSuppose you’re in a rush, felling tired, not paying attention to your screen, and you send an email that could get you in trouble.Realisation will probably set in seconds after you’ve clicked “send”. You freeze in horror and burn with shame.What to do? Here are four common email accidents, and how to recover.Clicking “send” too soonDon’t waste your time trying to find out if the receivers has read it yet. Write another email as swiftly as you can and send it with a brief explaining that this is the correct version and the previous version should be ignored.Writing the wrong nameThe sooner you notice, the better. Respond quickly and briefly, apologizing for your mistake. Keep the tone measured: don’t handle it too lightly, as people can be offended, especially if your error suggests a misunderstanding of their culture(i.e. incorrect ordering of Chinese names).Clicking “reply all” unintentionallyYou accidentally reveal(透露)to the entire company what menu choices you would prefer at the staff Christmas dinner, or what holiday you’d like to take. In this instance, the best solution is to send a quick, light-hearted apology to explain your awkwardness. But it can quickly rise to something worse, when everyone starts hitting “reply all” to join in a long and unpleasant conversation. In this instance, step away from your keyboard to allow everyone to calm down.Sending an offensive message to its subjectThe most awkward email mistake is usually committed in anger. You write an unkind message about someone, intending to send it to a friend, but accidentally send it to the person you’re discussing. In that case, ask to speak in person as soon as possible and say sorry. Explain your frustrations calmly and sensibly—see it as an opportunity to clear up any difficulties you may have with this person.80. After realising an email accident, you are likely to feel _______.A. curiousB. tiredC. awfulD. funny81. If you have written the wrong name in an email, it is best to ________.A. apologise in a serious mannerB. tell the receiver to ignore the errorC. learn to write the name correctlyD. send a short notice to everyone82. What should you do when an unpleasant conversation is started by your “reply all” email?A. Try offering other choices.B. Avoid further involvement.C. Meet other staff members.D. Make a light-hearted apology.83. How should you deal with the problem caused by an offensive email?A. By promising not to offend the receiver again.B. By seeking support from the receiver’s friends.C. By asking the receiver to control his anger.D. By talking to the receiver face to face.COne windy spring day, I observed young people having fun using the wind to fly their kites. Multicolored creations of varying shapes and sizes filled the skies like beautiful birds racing and dancing. As the strong winds blew against the kites, a string kept them in check.Instead of blowing away with the wind, they arose against it to achieve great heights. They shook and pulled, but the string and the tail kept them attached, facing upward and against the wind. The kites struggled and kept being dragged behind, facing upward and against the wind. As the kites struggled and trembled against the string, they seemed to say, “Let me go! Let me go! I want to be free!” They soared beautifully even as they fought the restriction of the string. Finally, one of the kites succeeded in breaking loose. “Free at last,” it seemed to say. “Free to fly with the wind.”Yet freedom from restriction simply put it at the mercy of a cruel breeze. It flew ungracefully to the ground and landed in a messed mass of weeds and string against a dead bush. “Free at last”, free to lie powerless in the dirt, to be blown helplessly along the ground, and to stop lifeless against the first obstruction.How much like kites we sometimes are. The heaven gives us misfortune and limitations, and rules to follow from which we can grow and gain strength. Restriction is a necessary companion to the winds of opposition. Some of us resist the rules so hard that we never soar to reach the heights we might have obtained. We keep part of the order and never rise high enough to get our tails off the ground.Let us each rise to the great heights, recognizing that some of the restrictions that we may be annoyed at are actually the steadying force that helps us improve and achieve.84. According to paragraph 2, “Let me go!” is said by _______.A. the kiteB. the windC. the birdD. the flyer85. Which of the following words has the meaning closest to the underlined word “obstruction” in paragraph 3?A. destructionB. miracleC. observationD. obstacle86. According to the writer, in what way is man similar to kites?A. Man will never reach the desirable height unless he breaks some rules.B. Man can be empowered by difficulties to go further and higher.C. Man desires freedom but only a few will succeed.D. Man is limited by his surroundings.87. By telling the story of kite flying, the writer wants to share the lesson that _______.A. rules are made to be brokenB. flying a kite involves skills and patienceC. sometimes difficulties can be potential blessingsD. it’s no use complaining about the difficulties we encounterDMassive rubbish dumps and sprawling landfills constitute one of the more uncomfortable impacts that humans have on wildlife. They have led some birds to give up on migration. Instead of flying thousands of miles in search of food, they make the waste sites their winter feeding grounds.Researchers in Germany used miniature GPS tags to track the migrations of 70 white storks (鹳) from different sites across Europe and Asia during the first five months of their lives. While many birds travelled along well-known routes to warmer climates, others stopped short and spent the winter on landfills, feeding on food waste, and the multitudes of insects that thrive on the dumps.In the short-term, the birds seem to benefit from overwintering(过冬) on rubbish dumps. Andrea Flack of the Max Planck Institute found that birds following traditional migration routes were more likely to die than German storks that flew only as far as northern Morocco, and spent the winter there on rubbish dumps. “For the birds it’s a very conveni ent way to get food. There are a lot of organic waste they can feed on,” said Flack. The meals are not particularly delicious, or even safe. Much of the waste is discarded(丢弃的) rotten meat, mixed in with other human debris such as plastic bags and old toys.“It’s very risky. The birds can easily eat pieces of plastic or rubber bands and they can die,” said Flack. “And we don’t know about the long-term consequences. They might eat something poisonous and damage their health. We cannot estimate that yet.”The scientists tracked white storks from different colonies in Europe and Africa. The Russian, Greek and Polish storks flew as far as South Africa, while those from Spain, Tunisia and Germany flew only as far as the Sahel.Landfill sites on the Iberian peninsula have long attracted local white storks, but all of the Spanish birds tagged in the study flew across the Sahara desert to the western Sahel. Writing in the journal, the scientists describe how the storks from Germany were clearly affected by the presence of waste sites, with four out of six birds that survived for at least five months overwintering on rubbish dumps in northern Morocco, instead of migrating to the Sahel.Flack said it was too early to know whether the benefits of plentiful food outweighed the risks of feeding on landfills. But that’s not the only uncertainty. Migrating birds affect ecosystems both at home and at their winter destinations, and disrupting the traditional routes could have unexpected side effects. White storks feed on locusts (蝗虫) and other insects that can become pests if their numbers get out of hand. “They provide a useful service,” said Flack.88. What is the impact of rubbish dumps on wildlife?A. They have forced white storks to search for safer winter shelters.B. They have seriously polluted the places where birds spend winter.C. They have accelerated the reproduction of some harmful insects.D. They have changed the previous migration habits of certain birds.89. What do we learn about birds following the traditional migration routes?A. They can multiply at an accelerating rate.B. They can better pull through the winter.C. They help humans protect insects.D. They are more likely to be at risk of dying.90. What can be inferred about the Spanish birds tagged in the study?A. They gradually lose the habit of migrating in winter.B. They prefer rubbish dumps far away to those at home.C. They are not attracted to the rubbish dumps on their migration routes.D. They join the storks from Germany on rubbish dumps in Morocco.91. What is scientists’ other concern about white storks feeding on landfills?A. The potential harm to the ecosystem.B. The genetic change in the stork species.。

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