2020.1高一上学期期末试卷
2020年高一语文上学期期末考试试题

第一学期期末考试高一语文试卷注意事项:1.答卷前,考生务必将自己的姓名、考号填写在答题卡上。
2.考试结束,将答题卡交回。
一、基础知识(21分,每小题3分)1.下列各组词语中,加点字的读音错误最多的一组是(3分)A.敛裾.(jū) 猗. (yi)郁肄.(yì)业风靡.(mí)一时B.窈.(yǎo)窕相勖.(xù) 修禊.(qì) 否.(pǐ)极泰来C.愀.(qiǎo)然流觞.(shāng) 蕈菌(jūn) 放荡冶.(yé)游D.嫠.(lí)妇悼(dào)念房檩.(lǐn) 东渐.(jiān)于海2.下列各组词语中,只有一个错别字的一组是(3分)A.杀戮通缉云宵光怪陆离容有底止B.偏袒落漠苍桑终南捷迳情随事迁C.惦记风资淅沥放浪形骸汗流夹背D.怯懦些坦销弭信誓旦旦游目聘怀3.下列各句中加点的成语使用正确的一项是(3分)A.他愤愤地大谈社会的腐败,暗地里却收受贿赂,这种做法和叶公好龙....没有什么两样。
B.有些保护区把老虎放养到大自然中去,这种放虎归山....的做法是值得夫力推广的。
C.无边的细雨笼罩着金黄的油菜花,真是春风.化雨..润物无声啊,我不禁想起陆游的诗句“小楼一夜听春雨”。
D.美方代表在解决中美贸易摩擦问题吋毫无诚意,每次涉及实质问题,他们总是虚与委蛇....,顾左右而言他。
4.下列句子中,没有语病的一项是(3分)A.朱自清笔下的荷塘月色是美好的,他精雕细琢这一美景时,虽然文章的描写很细致,但没有丝毫的过分,力度把握得分毫不差。
B.这秋蝉的嘶叫,在北平可和蟋蟀耗子一样,简直像是家家户户养在家里的家虫。
C.《诗经》和《离骚》分别开创了我国古代诗歌创作的现实主义和浪漫主义的优秀传统。
D.《孔雀东南飞》是最早保存下来的一首长篇叙事诗,它与北朝的《木兰辞》被并称“乐府双璧”。
5.下面关于文学文化常识的表述,正确的一项是(3分)A.古诗文中的植物常有特殊含义,如“棠棣”常用以指兄弟,“杨柳”常用于送别,“梧桐” 是凄凉悲伤的象征,“丁香”代表的是淡雅、美丽、忧愁。
2020-2021学年高一第一学期期末考试(一)英语试卷含答案

汪清四中2020-2021学年度高一年级第一学期期末考试英语试卷(考试时间:120分钟试题总分:120分)第一部分听力(共两节,满分20分)第一节(共5小题;每小题1分,满分5分)1.What are the speakers doing?A.Seeing a doctor.B. Enjoying a concert.C. Buying some tickets.2.What will the the man do next Thursday?A.Start his new job.B. Have an interview.C. Meet Professor Green.3.What is the woman’s first lesson this morning?A.ScienceB. GeographyC. Math.4.What day is it probably today?A.MondayB. Wednesday.C. Friday5.What kind of music does the woman like best?A.Country music. B. Rock music. C. Pop music第二节(共15小题:每小题1分,满分15分)听第六段材料,回答第6、7题。
6.How old is the woman now?A.Eight years old. B.Ten years old. C. Eighteen years old.7.Where does the woman plan to go next year ?A.To Canada. B. To America. C. To France.听第七段材料,回答第8、9题。
8.How does the man feel when he sees the sandwiches?A.DisappointedB. ExcitedC. Annoyed9.What will the man order ?A.Steak B. Seafood C. Fried chicken听第八段材料,回答第10至12题。
湖北省2020学年高一数学上学期期末考试试题

第一学期高一年级期末考试试卷数学试题一.选择题(每小题5分,共60分)1.已知集合A ={x|0<x≤1},B ={x|x 2<1},则(∁R A)∩B=( ) A .(0,1) B .[0,1] C .(-1,1] D .(-1,0] 2.下列四组函数,表示同一函数的是( ) A . B ., C . D .3.函数的定义域为( ) A . B . C . D .4.已知,则m 、n 、p 的大小关系为( ) A .nmp B .npm C .pnm D .mpn5.已知()1tan 2πα+=,则sin cos 2sin cos αααα-+=( ) A .14 B .12 C .14- D .12-6.若点55,cos 66sinππ⎛⎫⎪⎝⎭在角α的终边上,则sin α=( )A .12 C .-.12- 7.如图所示,在△ABC 中,点D 、E 、F 分别是边AB 、BC 、AC 的中点,则下列结论正确的是( )A .B .=0C .D .8.函数()()sin f x A x ωϕ=+的部分图象如图所示,则此函数的解析式为( ) A .()2sin 33f x x ππ⎛⎫=-⎪⎝⎭ B .()2sin 16f x x π⎛⎫=- ⎪⎝⎭C .()2sin 3f x x π⎛⎫=-⎪⎝⎭D .()2sin 66f x x ππ⎛⎫=-⎪⎝⎭9.将函数)6sin()(π-=x x f 图像上所有点的横坐标缩短到原来的一半(纵坐标不变),再将它的图像向左平移ϕ个单位)0(>ϕ,得到了一个偶函数的,则ϕ的最小值为( )A .6π B .4π C .3π D .65π 10.已知函数是奇函数,当时,,则的解集是( ) A . B . C . D .11.函数sin y x = 的定义域为[]a b ,,值域为1⎡-⎢⎣⎦,则b a - 的最大值和最小值之差等于( ) A .53π B .56π C .2π D .π 12.已知定义在R 上的函数()f x 满足()()4f x f x +=,且(]2,2x ∈-时,()()2111,022{ 2,20x x x x x f x x x x ⎛⎫+--<≤⎪⎝⎭=-+-<≤,则()()4log g x f x x =-零点个数是( )A .4B .7C .8D .9二.填空题(每小题5分,共20分) 13.已知向量,,若向量∥,则实数________ 14.已知函数,则__________. 15.已知,则__________.16.下列说法: ①正切函数在定义域内是增函数; ②函数是奇函数;③是函数的一条对称轴方程;④扇形的周长为,面积为,则扇形的圆心角为; ⑤若是第三象限角,则取值的集合为, 其中正确的是__________.(写出所有正确答案的序号)三.解答题(共70分)17.(本小题10分)已知()()1,2,3,2a b ==-.(1)求2a b -的坐标; (2)当k 为何值时, ka b +与2a b -共线. 18.(本小题12分)计算:⑴5log 3333322log 2log log 859-+- ⑵11222134142290.064---⎛⎫+-+⨯ ⎪⎝⎭19.(本小题12分)已知二次函数()y f x =的最大值是4,且不等式()0f x >的解集为(1,3)-. (1)求()f x 的解析式;(2)若存在[2,2]x ∈-,使得()0f x m -≤成立,求实数m 的取值范围.20.(本小题12分)已知()1sin 226f x x π⎛⎫=+ ⎪⎝⎭(1)求函数()f x 的的最小正周期;(2)求函数()f x 的最大值,并写出取最大值时自变量x 的集合; (3)求函数()f x 在0,2x π⎡⎤∈⎢⎥⎣⎦上的单调区间;21.(本小题满分12分)已知点()()11,A x f x , ()()22,B x f x 是函数()()2sin f x x ωϕ=+(0ω>, 02πϕ-<<)图象上的任意两点,且角ϕ的终边经过点(1,P ,若()()124f x f x -=时, 12x x -的最小值为3π. (1)求函数()f x 的解析式; (2)求函数()f x 的单调递增区间; (3)当0,6x π⎡⎤∈⎢⎥⎣⎦时,不等式()()2mf x m f x +≥恒成立,求实数m 的取值范围.22.(本小题满分12分)对于定义域为D 的函数)(x f y =,如果存在区间D n m ⊂],[,同时满足:①)(x f 在],[n m 内是单调函数;②当定义域是],[n m 时,)(x f 的值域也是],[n m .则称],[n m 是该函数的“和谐区间”. (1)证明:]1,0[是函数)(x f y ==2x 的一个“和谐区间”.(2)求证:函数xx g y 53)(-==不存在“和谐区间”. (3)已知:函数xa x a a x h y 221)()(-+==(∈a R ,0≠a )有“和谐区间” ],[n m ,当a 变化时,求出m n -的最大值.答案1.D 2.D 3.A 4.B 5.C 6.C 7.D 8.A 9.C 10.A 11.B 12.C 1.D【解析】因为2{| 01},{| 1}A x x B x x =<≤=<, 所以(]()(),01,,1,1R A B =-∞⋃+∞=-ð,所以()(]1,0R A B ⋂=-ð,故选D.2.D 【解析】 【分析】分别判断两个函数的定义域值域、和对应法则是否一致,即可得结果. 【详解】对于,两个函数的对应法则不相同,不是同一函数;对于的定义域为,而的定义域为定义域不同,不是同一函数. 对于,两个函数的定义域不相同,不是同一函数.对于的定义域、值域为, 的定义域、值域为,两个函数的定义域、值域和对应法则相同,是同一函数, 故选D. 【点睛】本题通过判断几组函数是否为同一函数主要考查函数的定义域、值域以及对应法则,属于中档题.判断函数是否为同一函数,能综合考查学生对函数定义的理解,是单元测试卷经常出现的题型,要解答这类问题,关键是看两个函数的三要素:定义域、值域、对应法则是否都相同,三者有一个不同,两个函数就不是同一函数. 3.A 【解析】 【分析】由函数的解析式可得,化简可得 ,由此求得函数的定义域. 【详解】由函数的解析式可得, ∴,解得, 故选:A . 【点睛】本题主要考查对数函数的定义域,对数不等式的解法,属于基础题.对于函数定义域问题,首先分式要满足分母不为0,根式要求被开方数大于等于0,对数要求真数大于0,幂指数要求底数不等于0即可. 4.B【解析】解析:因为,即,又,即,故应选B.点睛:本题设置的目的是综合考查指数函数、对数函数、幂函数的图象和性质及数形结合思想等知识和方法的运用,求解的关键是准确利用所学函数的图象与单调性进行分析求解,对转化与化归的能力要求较高. 5.C【解析】由()1tan 2πα+= 得: 1tan 2α=, 所以11sin cos tan 1122sin cos 2tan 1114αααααα---===-+++,故选D.6.C【解析】由题意得5sin cos62πα==-,选C. 7.D【解析】△ABC 中,点D 、E 、F 分别是边AB 、BC 、AC 的中点,∴(+)=+,∴A 错误;+=2,∴B 错误;+++,∴C 错误; ,∴D 正确.故选D .8.A【解析】试题分析:根据题意,图像中最大值和最小值分别为2,-2,那么A=2,同时可知2(4-1)=6,是二分之一周期的长度,因此一个周期的长度为6,因此263w w ππ=∴=,然后代入点(1,0),可知,f(1)=0,则可知0=2sin(3πϕ+),那么可得033ππϕϕ+=∴=-符合题意。
吉林省2020学年高一数学上学期期末考试试题

上学期期末考试 高一数学试卷考试时间:120分钟 分值:150分 第I卷 选择题(总计60分)一、选择题(本大题共12小题,每小题5分,共60分.在每小题给出的四个选项中,只有一项是符合题目要求的)1.已知集合}3,2{}30{=≤≤∈=N x N x M ,,则M N ⋂=( ) A.{0,1} B.{3} C.{2,3} D.{1,2,3}2.已知角α的终边过点)(23,21,则=-)cos(απ( ) A. 23 B. 23- C. 21 D. 21-3.下列函数是偶函数,且在(0,)+∞上是减函数的是( ) A.1+=x y B.cos y x = C.2y x -= D.2xy = 4.已知向量(1,1),(1,2)a b =-=-,则(2)a b b +⋅=( ) A.1- B.0 C.1 D.2 5.函数xx x f 2ln )(-=的零点所在的区间为( ) A.)2,1( B.)3,2( C.)4,3( D.),4(+∞6.学校宿舍与办公室相距a m ,某同学有重要材料要送给老师,从宿舍出发,先匀速跑步3分钟来到办公室,停留2分钟,然后匀速步行10分钟返回宿舍。
在这个过程中,这位同学行走的路程是时间的函数,则这个函数图象是( )AB7.已知角α的终边在直线2y x =上,则sin cos αα=( ) A.25 B.25- C.45 D.45- 8.已知函数)sin()(ϕω+=x x f 在区间]34,0[π上单调,且1)34(,0)3(==ππf f ,则 )0(f 的值为( )A. 1-B. 21-C. 23-D. 09.设点G 是ABC ∆的重心,若13AG AB AC λ=+,则实数λ=( )A.23B.16C.13D.1210.设4log ,44tan ,251051===c b a ,则下列大小关系正确的是( )A.b a c <<B.c a b <<C.c b a <<D.b c a << 11.已知函数)(x f 是定义在R 上的偶函数,并且满足)(1)2(x f x f =+,当32≤≤x 时,x x f =)(,则=)5.105(f ( )A.21B. 23C. 23-D. 2512.已知函数12,021()23,012x x x e f x x e ⎧-≥⎪⎪+=⎨⎪-<⎪+⎩,则使不等式212(log )(log )2(2)f t f t f +<成立的t的取值范围是( )A.1(,2)2B.1(,4)4C.(2,4)D.1(,2)4第Ⅱ卷 非选择题(总计90分)二、填空题:本大题共4小题,每小题5分. 13._______9log 2log 34=⋅14.函数1sin(),[0,2]23y x x ππ=+∈的单调递增区间是__________15.函数()122100x x f x x x -⎧-≤⎪=⎨⎪>⎩,,,满足f (x )>1的x 的取值范围_________ CD16.函数2sin 21xy x x =+++的最大值与最小值之和为____ 三、解答题(本大题共6小题,共70分.解答应写出文字说明、证明过程或演算步骤) 17. (本小题满分10分)已知幂函数αx x f =)(的图象经过点)2,2(. (1)求幂函数)(x f 的解析式;(2)试求满足)3()1(a f a f ->+的实数a 的取值范围. 18.(本小题满分12分)已知34==→→b a ,,61)2()32(=+⋅-→→→→b a b a . (1)求→a 与→b 夹角θ; (2)求→→b a 2-. 19.(本小题满分12分) 已知函数)4sin()(πω+=x x f ,)0(>ω的最小正周期为π.(1)求函数)(x f 的单调递增区间;(2)说明如何由函数x y sin =的图象经过变换得到函数)(x f 的图象. 20.(本小题满分12分) 已知π<<x 0,51cos sin =+x x . (1)求x tan 的值;(2)求x x x x 22cos 3cos sin 2sin ++的值。
2020 年高一(上)期期末考试 数学试卷

2020 年高一(上)期期末考试 数学试卷一、选择题:本题共 12 小题,每小题 5 分,共 60 分.在每小题给出的四个选 项中,只有一项是符合题目要求的.1.120° 化成弧度制为( ) A .34π B .65π C .32π D .3π2.设集合 B = { x |2x − 4 x + m= 0},若1 ∈B ,则 B= ()A .{1 ,3}B .{1,0}C .{1 ,−3}D .{1 ,5}3.已知弧度数为 2 的圆心角所对的弦长也是 2,则这个圆心角所对的弧长为 ( ) A .2B .1sin 2 C .2sin 1 D .sin2 4.已知点 P(sin1050°, cos1050°) ,则 P 在平面直角坐标系中位于( )A .第一象限B .第二象限C .第三象限D .第四象限 5.函数 f ( x) = x+23+x 的零点所在区间为( ) A .( − 3, −2) B .( − 2, −1) C .( −1, 0) D .(0,1) 6.角α的终边经过点(2, −1) ,则2αsin + 3αcos 的值为( )A .55-B .55C.554-D .554 7.已知幂函数 f ( x) =nx 的图象经过点(3,3) ,则 f (9)的值为()A .3B . ±3C .21D .338.函数 x x x x f +=cos )(在[−π,π] 上的图象大致为()A .B . C. D.9.函数 y = x 2cos − sin x+1 的值域是( )A .[0 ,2]B .[2,49] C .[1 ,3]D .[0,49]10.已知 a =5log 21- , b= 27log 8, c = 51⎪⎭⎫⎝⎛e ,则 a ,b ,c 的大小关系为( )A . a > c > bB . b > a > cC . c > a > bD . a > b > c11.已知函数 f ( x) 是定义在 R 上的奇函数, f (23+ x) = f ( x −23) ,且 x ∈(23-, 0) 时, f ( x) =log (−3 x+ 1) ,则 f(2020) = ( )A .4B .7log 2C .2D .−212.已知函数 f(x) =⎩⎨⎧≥+--<-2,2)3(2,)2(log 23x x x x ,g( x) =11-+xx ,则方程 f ( g( x)) = a 的实根个数最多为( ) A .6 B .7 C .8D .9二、填空题:本题共 4 小题,每小题 5 分,共 20 分. 13、 函数 y = )1,0(32≠>+=-a a ay x的图象恒过定点,则这个定点的坐标是14.若函数)(x f = )20)(tan(πϕωϕω<>+且x 的一个单调区间为⎪⎭⎫⎝⎛-6,3ππ ,且 f(0) =33,则 )12(πf =15.若函数1++=xax y 有两个零点,则实数 a 的取值范围是16.已知 [x] 表示不超过 x 的最大整数(如[2.5] = 2) ,若函数 221)(x x x f +=,则[21)(-x f ] + [21)1(-x f ] 的值域为三、解答题:共 70 分.解答应写出文字说明、证明过程或演算步骤.17、(本小题满分 10 分)化简或求下列各式的值.(1) )4()5()2(3543132323b a b a b a ÷-⨯ ; (2)15log 4log 20lg 5lg )5(lg 222++⨯+.18、(本小题满分 12 分)计算下列各式:(1)已知2tan =θ,求)sin()cos()2cos()23sin(θπθπθπθπ--++--的值; (2)若 43tan =α,求αααcos sin 4cos 2+的值.已知集合 A = { x | a −1 < x < 2a+ 3}, B = { x | −2 ≤ x ≤ 4},全集U = R . (1)当 a = 2时,求 B A ;(2)若A B A = ,求实数 a 的取值范围. 20、(本小题满分 12 分)首届中国国际进口博览会在2018年115日−10日在上海国家会展中心举办.会议期间,某公司欲采购东南亚某水果种植基地的水果,公司刘总经理与该 种植基地的负责人陈老板商定一次性采购一种水果的采购价 y (元/ 吨)与 采购量 x (吨) 之间的函数关系的图象如图中的折线 ABC 所示(不包含端点 A ,但包含端点C) .(1)求 y 与 x 之间的函数关系式;(2)已知该水果种植基地种植该水果的成本是 2800 元/ 吨,那么刘总经理的 采购量为多少时,该水果基地在这次买卖中所获得利润 W 最大?最大利润是多 少?已知函数)2,0(),sin(2)(πϕωϕω<>+=x x f 的最小正周期为π ,且图象关于 x =3π对称. (1)求 ω和 ϕ的值;(2)将函数f(x)的图象上所有横坐标伸长到原来的4倍,再向右平移3π个单位,得到函数 g( x) 的图象,求 g( x) 的单调递增区间以及 1)(≥x g 的 x 取值范围. 22、(本小题满分 12 分)已知函数11log )(21--=x axx f 的图象关于原点对称,其中a 为常数.(1)求 a 的值;(2)当),1(+∞∈x 时, m x x f <-+)1(log )(21恒成立,求实数 m 的取值范围;(3)若关于 x 的方程)(log )(21k x x f +=在 [2,3] 上有解,求 k 的取值范围.。
2020-2021学年高一上学期期末考试数学卷及答案

2020-2021学年高一上学期期末考试数学卷及答案1.集合A和B分别表示y=x+1和y=2两个函数的图像上所有的点,求A和B的交集。
答案:A={(-∞,1]}。
B={2}。
A∩B=A={(-∞,1]}2.已知函数y=(1-x)/(2x^2-3x-2),求函数的定义域。
答案:分母2x^2-3x-2=(2x+1)(x-2),所以函数的定义域为x∈(-∞,-1/2]∪(2,∞)。
3.如果直线mx+y-1=0与直线x-2y+3=0平行,求m的值。
答案:两条直线平行,说明它们的斜率相等,即m=2.4.如果直线ax+by+c=0经过第一、第二,第四象限,求a、b、c应满足的条件。
答案:第一象限中x>0.y>0,所以ax+by+c>0;第二象限中x0,所以ax+by+c0.y<0,所以ax+by+c<0.综上所述,应满足ab<0.bc<0.5.已知两条不同的直线m和n,两个不同的平面α和β,判断下列命题中正确的是哪个。
答案:选项A是正确的。
因为如果m与α垂直,n与β平行,那么m和n的夹角就是α和β的夹角,所以m和n垂直。
6.已知圆锥的表面积为6π,且它的侧面展开图是一个半圆,求这个圆锥的底面半径。
答案:设底面半径为r,侧面的母线长为l,则圆锥的侧面积为πrl。
根据题意,πrl=6π,所以l=6/r。
而侧面展开图是一个半圆,所以底面周长为2πr,即底面直径为2r,所以侧面母线长l=πr。
将上述两个式子代入公式S=πr^2+πrl中,得到r=2.7.已知两条平行线答案:两条平行线的距离等于它们的任意一点到另一条直线的距离。
我们可以先求出l2上的一点,比如(0,7/8),然后带入l1的方程,得到距离为3/5.8.已知函数y=ax-1/(3x^2+5),如果它的图像经过定点P,求点P的坐标。
答案:点P的坐标为(1,2)。
因为当x=1时,y=a-1/8,所以a=17/8.又因为当x=2时,y=1/13,所以17/8×2-1/13=2,解得a=17/8,所以y=17x/8-1/(3x^2+5),当x=1时,y=2.9.已知a=3/5,b=1/3,c=4/3,求a、b、c的大小关系。
山东省淄博一中2020学年高一数学上学期期末考试新人教A版

2020学年高一第一学期期末考试数学试题注意事项:1.答第I卷前,考生务必将自己的姓名,准考证号,考试科目涂写在答题卡上; 2.每小题选出答案后,用铅笔把答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦干净后,再选涂其他答案标号,不能答在试题卷上.第I 卷(选择题,共60分)一、选择题(本大题共12小题,每小题5分,共60分,在每小题给出的四个选项中,只有一项是符合题目要求的).1、下列四组中()()x g x f ,表示相等函数的是 ( ) A.()()()2,x x g x x f == B.()()33,x x g x x f ==C.()()xxx g x f ==,1 D.()()x x g x x f ==, 2、点P 从()0,1出发,沿单位圆逆时针方向运动34π弧长到达Q 点,则Q 点的坐标为A .⎪⎪⎭⎫ ⎝⎛-23,21 B .⎪⎪⎭⎫ ⎝⎛--21,23 C .⎪⎪⎭⎫ ⎝⎛-21,23 D.⎪⎪⎭⎫⎝⎛--23,21 3、下列函数是偶函数,且在()0,∞-上单调递减的是 ( )A .xy 1=B .21x y -=C .x y 21-=D .x y =4、下列式子正确的是 ( )A .()03>=a a a aB .2lg 6lg 2lg 6lg -= C .()012>=-a aaD .()()[]()()5lg 3lg 53lg -+-=-⋅-5、三个数5.06 , 65.0 , 6log 5.0的大小顺序为 ( )A .5.065.065.06log <<B .65.05.05.066log << C .6log 65.05.05.06<< D .5.05.0666log 5.0<<6、为了得到函数sin(2)3y x π=-的图像,只需把函数x y 2sin =的图像( )A .向左平移3π个长度单位 B .向右平移6π个长度单位 C .向左平移6π个长度单位 D .向右平移3π个长度单位7、方程42=+x x的根所在区间为 ( )A .()0,1-B .()1,0C .()2,1D .()3,28、函数2log (1)x a y ax -=+-+1(a >0,a ≠1)的图象必经过定点 ( )A.(0,1)B.(2,1)C.(2,2)D.(2,3)9、已知向量a →、b →、c →,且满足a →+b →+c →=0→,|a →|=3,|b →|=4,|b →|=5,设a→与b →的夹角为1θ,b →与c →的夹角为2θ,a →与c →的夹角为3θ,则它们的大小关系是( ) A .123θθθ<< B .132θθθ<< C .231θθθ<< D .321θθθ<< 10、函数cos tany x x =(0x π≤≤且2x π≠)的图象为 ( )11、若316sin =⎪⎭⎫⎝⎛-απ,则⎪⎭⎫⎝⎛+απ232cos = ( ) A .97-B .31-C .31D .97 12、如下图,在△ABC 中,设AB →=a →,AC →=b →,AP 的中点为Q ,BQ 的中点为R ,CR 的中点为P ,若AP →=m a →+n b →,则m n += ( )A. 21B. 32C. 54 D. 76第II 卷(非选择题,共90分)二、填空题(每小题5分,共40分,把正确答案填写在题中的横线上,或按题目要求作答).13、已知x x x f 2)1(2-=+,则=)2(f .RQPC14、若幂函数的图象经过点(2,22),则该函数在(0,)∞+上是 函数(只填单调性).15、若集合{}R ∈==x x x A x ,32cos 3π,{}R ∈==y y y B ,12,则: A ∩B = .16、已知a →=(1,2),b →=(-2,k),若a →∥(a →+b →),则实数k 的值为 . 17、1tan151tan15+︒=-︒.18、已知一扇形所在圆的半径为10cm ,扇形的周长是45cm ,那么这个扇形的圆心 角为 弧度.19、某商场对顾客实行购物优惠活动,规定一次购物付款总额, ①如果不超过200元,则不予优惠,②如果超过200元,但不超过500元,则按标准价给予9折优惠,③如果超过500元,则其500元按第②条给予优惠,超过500元的部分给予7折优惠; 某人两次去购物,分别付款168元和423元,假设他只去一次购买上述同样的商品,则应付款是 元.20、已知函数x x x f sin cos )(=,给出下列四个说法:①若)()(21x f x f -=,则21x x -=,②点(,0)π是)(x f 的一个对称中心, ③)(x f 在区间]4,4[ππ-上是增函数,④)(x f 的图象关于直线43π=x 对称. 其中正确说法的序号是 .(只填写序号)三、解答题(本题满分50分,共4个题,解答题要求写出必要的解答过程,证明题要求写出详细的证明步骤).21、(本小题满分12分)已知|a →|=1,|b →|=2;(I)若a →.b →=22,求→a 与→b 的夹角;(II)若→a 与→b 的夹角为︒135,求|a →+b →|.22、(本小题满分12分)已知函数2()5sin cos 2f x x x x =-+,(Ⅰ)确定函数()f x 的单调增区间;(Ⅱ)当函数()f x 取得最大值时,求自变量x 的集合.23、(本小题满分12分)已知函数()()⎪⎭⎫⎝⎛<>>+=2,0,0sin πϕωϕωA x A x f 在一个周期内的部分函数图象如图所示,(I)求函数()x f 的解析式;(Ⅱ)求函数()x f 在区间[]1,0上的最大值和最小值.24、(本小题满分14分)已知C B A ,,为锐角ABC ∆的三个内角,向量m →(22sin ,cos sin )A A A =-+,n →(1sin ,cos sin )A A A =+-,且m →⊥n →.(Ⅰ)求A 的大小;(Ⅱ)求下列函数:222sin cos(2)3y B B π=+-的值域.2020学年高一第一学期期末考试21、 解: (I)设→a 与→b的夹角为θ,则21cos ==θ……4分 因[]οο180,0∈θ,所以︒=60θ,故→a 与→b 的夹角为︒60 ……6分(II)因→a 与→b 的夹角为︒135,所以1135cos -==⋅︒→a ……8分12222=+-=+⋅+=+a ρ……11分1=+ …………12分22.解:55()sin 2(1cos 2)sin 2cos 222222f x x x x x =-++=- 15(sin 2cos 2)5sin(2)223x x x π=-=-. ……6分(Ⅰ)52222321212k x k k x k πππππππππ-≤-≤+⇒-≤≤+, 所以()f x 的单调增区间为5[,],()1212k k k ππππ-+∈Z . ……9分(Ⅱ)当2232x k πππ-=+,即5{|,}12x x k k ππ=+∈Z 时,()f x 有最大值5.… 12分23、解:(1)由函数图象知2=A ……………………………………1分131342=-=T Θ ωπ22==∴T 则πω= …………………………………………3分 ()()ϕπ+=∴x x f sin 2又由1+232k ππϕπ+= ()k Z ∈得:26k πϕπ=+()k Z ∈,因为2πϕ<,所以6πϕ=……………………………………………5分故()⎪⎭⎫⎝⎛+=6sin 2ππx x f ………………………………………6分(2)法Ⅰ:10≤≤x Θ,6766ππππ≤+≤∴x …………… 9分 1)6sin(21≤+≤-∴ππx ,2)6sin(21≤+≤-∴ππx ……………………… 11分 故()x f 在区间[]1,0上的最大值为2,最小值为1-.………………12分 法Ⅱ:由函数的图象知:直线31=x 是函数()x f 的对称轴, 则()x f 在⎥⎦⎤⎢⎣⎡31,0上单调递增,在⎥⎦⎤⎢⎣⎡1,31上单调递减.…………………9分故()231max =⎪⎭⎫ ⎝⎛=f x f ()()11min -==f x f …………………11分 即()x f 在区间[]1,0上的最大值为2,最小值为1-.…………………12分24、解:(Ⅰ)Q m n ⊥u r r,∴(22sin )(1sin )(cos sin )(cos sin )0A A A A A A -+++-=………… 2分2222(1sin )sin cos A A A ⇒-=-22212cos 12cos cos 4A A A ⇒=-⇒=. … 5分ABC ∆Q 是锐角三角形,1cos 23A A π∴=⇒=.…………………6分(Ⅱ)ABC ∆Q 是锐角三角形,且3A π=, 62B ππ∴<<……8分22132sin cos(2)1cos 2cos 22322y B B B B B π∴=+-=--+ 332cos 213)123B B B π=-+=-+ ………………… 10分 2,02,0sin(2)162333B B B πππππ<<∴<-<∴<-≤Qy (1,13]∴∈+ …………… 14分。
天津市2020年高一上学期期末考试数学试题

第一学期期末考试 高一年级数学学科试卷本试卷分第I 卷(选择题)和第II 卷(非选择题)两部分共100分,考试用时100分钟.第I 卷(选择题 共40分)一.选择题:本大题共8小题,每小题5分,共40分,在每小题的4个选项中,只有一项是符合题目要求的,将答案涂在答题卡上.......... 1.105sin 15cos 75cos 15sin +等于A. 0B. 1C.23 D. 212. 把函数x y cos =的图象上的所有点的横坐标缩小到原来的一半(纵坐标不变),然后把图象向左平移4π个单位,则所得图象对应的函数解析式为 A. )421cos(πx y += B. )42cos(πx y +=C. )821cos(πx y +=D. )22cos(πx y +=3. 7.03=a ,37.0=b ,7.0log 3=c ,则c b a ,,的大小关系是A. b a c <<B. a c b <<C. a b c <<D. c a b <<4.设R ϕ∈,则“=0ϕ”是“()=cos(+)f x x ϕ()x R ∈为偶函数”的A .充分不必要条件B .必要不充分条件C .充分必要条件D .既不充分也不必要条件5.已知函数()f x 是定义在R 上的偶函数, 且在区间[0,)+∞单调递增. 若实数a 满足212(log )(log )2(1)f a f f a ≤+, 则a 的取值范围是A .[1,2]B .10,2⎛⎤ ⎥⎝⎦C .(0,2]D .1,22⎡⎤⎢⎥⎣⎦6. 在ABC ∆中,若tan tan tan A B A B ++=⋅,且sin cos B B ⋅=, 则ABC ∆的形状为A. 直角三角形B. 等边三角形C. 等边三角形或直角三角形D. 等腰直角三角形7.若02πα<<,02πβ<<-,1cos 43πα⎛⎫+= ⎪⎝⎭,cos 42πβ⎛⎫-=⎪⎝⎭,则cos 2βα⎛⎫+= ⎪⎝⎭AB. CD.- 8.已知函数22()4sin sin ()2sin 24x f x x x ωπωω=⋅+-()0ω>在区间2,23ππ⎡⎤-⎢⎥⎣⎦上是增函数,且在区间[]0,π上恰好取得一次最大值,则ω的取值范围是A .(]0,1B .30,4⎛⎤ ⎥⎝⎦ C .13,34⎡⎤⎢⎥⎣⎦ D .13,24⎡⎤⎢⎥⎣⎦第II 卷(非选择题 共60分)二.填空题:本大题共7小题,每小题4分,共28分,将答案填写在答题卡上........... 9. 求值:=-+-ππππ313cos 4tan 713cos )623sin( . 10.化简:7sin(2)cos()cos()cos()225cos()sin(3)sin()sin()2πππαπαααππαπαπαα+--------++= . 11.函数21()21x x f x -=+的值域为 .12.已知奇函数()x f 的定义域为R ,且对任意实数x 满足()()2f x f x =-,当()1,0∈x 时,()21xf x =+,则121log 15f ⎛⎫⎪⎝⎭=___________. 13.已知()()x x x f a a log log 2+-=对任意⎪⎭⎫ ⎝⎛∈21,0x 都有意义,则实数a 的取值范围是 .14.已知函数()sin()(0,0,)2f x A x A πωϕωϕ=+>><的图象与y 轴的交点为()0,1,它在y 轴右侧的第一个最高点和第一个最低点的坐标分别为()0,2x 和()02,2x π+-.则ϕ= ,0x = .15. 给出下列命题:(1)函数)32sin(4)(πx x f +=的图象关于点)0,6(π-对称; (2)函数)32sin(3)(πx x g --=在区间)125,12(ππ-内是增函数;(3)函数)2732sin()(πx x h -=是偶函数;(4)存在实数x ,使3cos sin πx x =+;(5)如果函数()3cos(2)f x x ϕ=+的图象关于点403π⎛⎫⎪⎝⎭,中心对称,那么ϕ的最小值为3π.其中正确的命题的序号是 .三.解答题:本大题共3小题,共32分,将解题过程及答案填写在答题卡上................ 16. (本小题满分10分)设函数()cos(2)22,(,)3f x x x m x R m R π=+++∈∈,(1)求函数()f x 的最小正周期及单调增区间; (2)当04x π≤≤时,()f x 的最小值为0,求实数m 的值.17.(本小题满分10分)已知]2,0[,cos sin sin )(2πx x x x x f ∈+= (1)求)(x f 的值域; (2)若65)(=αf ,求α2sin 的值。
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实验高中高一期末模块测试卷(英语)第一部分阅读理解(共两节, 满分50分)第一节(共20小题; 每小题2分, 满分40分)阅读下面短文,从每题所给的四个选项(A、B、C和D)中, 选出最佳选项,并在答题卡上将该项涂黑。
ADu Kun, a Chinese boy is called “the youngest writer in the world.” He has written three books till now. Du Kun was born in Jiangsu in 1994. When he was 7 months old, his parents started working in over 30 different cities, such as Xi'an and Shenzhen. This kind of life gave him things to think and write about. When he was 9 months old, he could speak and at the age of one, he could say five to six hundred words. At three, he could look up words in the dictionary. At four, his father taught him how to learn by himself. His parents like reading very much. So does he. At the age of 5, he began writing fairy tales. At the age of 6, he wrote a novel about his life in different cities with his parents. His fairy tales are all from his life. One day, he found many mice in the house. They not only ate their food but also hurt his mother's hand. So he thought, “If we give mice the stomach of cows, they will eat grass and they will be helpful to people.” This was his first fairy tales Change Stomach for Mice. Now he studies well in a middle school.He has written his third book. The novel called Eyes of Children. He says, “I am not different from other children, I just wrote several books.”1.Thanks to his________, Du Kun could write his books.A.motherB. fatherC.school lifeD. life in different cities2. Du Kun began to use a dictionary, ________.A. when he wrote fairy talesB. before his father taught him how to learn somethingC. after he went to schoolD. after his mother taught him how to learn something3. The underlined sentence shows us that Du Kun________.A. is different from other childrenB. doesn't tell the truthC. is the same as other childrenD. likes his books4. Which is the best title?A. Du Kun — the Youngest WriterB. How to Write a Fairy TalesC. How Clever the Boy isD. Three Books by a ChildBBonfire night(篝火之夜) is fast approaching in London. The following are the best spots to watch fireworks shows.Saturday Morden ParkThis fireworks show is perfect to take the tittle ones along to. The show will include new fire and light acts and will be set toaccompanying music. When all of the magic is over, attendees can enjoy the entertainment or pick up a refreshment(饮料) at theon-site bar.Tickets:£9 in advance £10 at the gates.Tickets can be bought here.Clissold ParkThis 20-minute show is more demure(娴静的) than other show spots due to the animals which live in the park, however, still promises a beautiful show. The show will also be accompanied(伴奏) by music.Tickets: Adults £8.75, children £3.75. Prices reduced by £l for people living in Hackney BoroughTickets can be bought here.Croydon Road Recreation GroundThis family-focused event has been running since 1946 and offers two chances to catch the excitement of the fireworks. A smaller show at 6:00pm promises reduced noise, perfect for little children, meanwhile, the main event promises a bang at 7:45pm.Tickets: Children under 11 free, over 11£5, adults£10Tickets can be bought on the gate.Alexandra PalaceThe biggest fireworks event in London, having run for 150 years, Alexandra Palace is set to excite audiences again this year with a splendid show. The grounds will also include a German-Beer festival and delicious food.Tickets: Adults £12.50, kids 11-15 £10, and kids under£2.50Tickets can be bought here.5.What do Clissold Park and Saturday Morden Park have in common?A.Neither is open to kids.B.One can enjoy coffee in a bar.C.The background music is provided.D.There are caged animals.6.What is special about Croydon Road Recreation Ground?A.It is the biggest firework show.B.It includes two shows.C.It serves delicious food.D.It is accompanied by music.7.How much would a couple with a child of 10 pay least for a show? A.£15.5. B.£18.25. C.£19.25. D.£20. 8.Where is this text most likely from?A.A textbook B.A magazine C.A website. D.A reportCMany animals recognize their food because they see it. So do humans. When you see an apple or a piece of chocolate you know that these are things you can eat. You can also use other senses when you choose your food. You may like it because it smells good or because it tastes good. You may dislike some types of food because they do not look, smell or taste very nice. Different animalsuse different senses to find and choose their food. A few animals depend on only one of their senses, while most animals use more than one sense.Although there are many different types of food, some animals spend their lives eating only one type. The giant panda eats only one particular type of bamboo. Other animals eat only one type of food even when given the choice. A kind of white butterfly will stay on the leaves of a cabbage, even though there are plenty of other vegetables in the garden. However, most animals have a more varied diet. The bear eats fruits and fish. The fox eats small animals, birds and fruits. The diet of these animals will be different depending on the season.Humans have a very varied diet. We often eat food because we like it and not because it is good for us. In countries such as France and Britain, people eat foods with too much sugar. This makes them overweight, which is bad for their health. Eating too much red meat and animal products, such as butter, can also be bad for the health. Choosing the right food, therefore, has become an area of study in modern life.9.Which of the following eats only one type of food?A. the small birdB. the white butterflyC. the bearD. the fox10. We can infer from the text that humans and animals _____.A. depend on one sense in choosing foodB. are not satisfied with their foodC. choose food in similar waysD. eat entirely different food11. Certain animals change their choice of food when _____.A. the season changesB. the food color changesC. they move to different placesD. they are attracted by different smells12. We can learn from the last paragraph that __________.A. food is chosen for a good reasonB. French and British food is goodC. some people have few choices of foodD. some people care little about healthy dietDThe importance of reading literature often seems lost on many Chinese people. Even experts in education think that the first goalof education is to encourage a love of learning. There is thereforethe possibility of something wrong with the way students are taught here.Why should they read literature? Do stories have value compared with the reading and learning of facts? Studies show clearly that the most powerful ways of learning are by experience, action and doing experiments and taking risks. Yet there are so many important things to learn that cannot be learned in these ways: feelings, problem solving, danger and relationships, for example. Research into this has shown how deep reading is a valuableexperience different to a learning of words or facts. Keen(热心的) readers of literature show a better understanding of others. Their abilities to make good decisions are raised. Young children who enjoy a parent reading stories to them show greater awareness(意识) when they reach school age.The best schools do seem to provide a limited (有限的) chance to enjoy literature, usually about the Chinese classic stories but thereis not enough "free" time for students. There are enough reading materials (材料). Chinese book shops are full of story books, and most of them are of good quality (质量) in terms of content, plot (情节) and language. Was there not a Chinese author who received a Nobel Prize for literature recently? There are moves in Chinese education to promote (提升) decision making and shared values. The value of literature is helpful to these as well as to the future of China.13.What does the author think of the way students are educated in China?A.He doesn't quite accept it. B.He is interested in it. C.He is proud of it. D.He is confident about it. 14.Which is not among the most powerful ways of learning according to paragraph 2?A.By experience. B.By taking risks.C.By doing experiments. D.By reading deeply. 15.What can be learned from the last paragraph?A.Chinese students like reading stories as they get older.B.Reading literature helps develop good values.C.Stories in Chinese bookstores are generally of poor quality. D.Chinese students have no chance to read enough materials. 16.What's the main idea of the text?A.Literature is a kind of art.B.Good reading materials are in great need.C.Reading literature should be valued.D.Something is wrong with Chinese education.EKnowing Mr I.M. Pei, and establishing the LM. Pei Foundation with his son, Didi Pei, are among the most fortunate things to ever happen to me.Like many Chinese Americans, I chose to study architecture in 1975, simply because I wanted to be the next I.M. Pei. He was the inspiration for my career and my life. Unfortunately when I applied for a job at his office after graduation in 1980, his associate partner, Kellogg Wong told me that I was too young and inexperienced, and advised me to try again after a few years.In 1984, however, I set up my own firm, James Jao Associates. It was the heyday of my firm in the late 1980s, designing about 30 percent of new residential family buildings in Queens. The joke at the time was that I.M. Pei was the biggest Chinese American architectural firm with over 2,800 employees, and James Jao with 100 was the second largest.In the summer of 1990, I had the first opportunity to pay Mr Pei a personal visit at his office. After knowing my age, he congratulated me for breaking what he thought to be the curse (诅咒) that no architect can be famous until after the age of 40. He even said that I had a greater influence than him. I was surprised by his nice words. However, I don’t think anyone, especially me, will ever be as influential as him.In November, 2018, after my 60th birthday celebrations, I met Mr Pei in his apartment discussing the establishment of the I.M. Pei Foundation, a non-profit organization to promote the philosophy of his works and, most importantly, his spirit of achieving excellence in art and culture.This morning I was deeply saddened to hear about the passing of a great architectural legend (传奇) of our time. At the age of 102, Mr Pei died with great achievements to his name.Rest in peace, Mr Pei. We will vow to carry on your torch (火炬) and your spirit because you are the one only I.M. Pei.James C Jao,May 16th. 2019 17.The writer chose to study architecture because ________. A.she wanted to make as much money as I.M. PeiB.she wanted to be a great architect(建筑师) like I.M. PeiC.she wanted to work in I.M. Pei’s officeD.she wanted to have the lessons of I.M. Pei18.The underlined word “heyday” in the third paragraph probably means ________.A.the golden period B.the weakest periodC.the darkest period D.the toughest period 19.What did I.M. Pei think of James Jao?A.She was inexperienced. B.She was too young.C.She was very beautiful. D.She was very excellent. 20.What is the purpose of writing this passage?A.To introduce I.M. PeiB.In memory of I.M. PeiC.To tell her successful experienceD.To advertise the I.M. Pei Foundation第二节(共5小题; 每小题2分, 满分10分)根据短文内容,从短文后的选项中选出能填入空白处的最佳选项。