海南中学2020届高三第二次月考试题 (答案)
2020年上海市海南中学高三英语月考试卷及答案解析
2020年上海市海南中学高三英语月考试卷及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AIn his 402nd anniversary year, Shakespeare is still rightly celebrated as a great language master and writer. But he was not the only great master of play writing to die in 1616, and he is certainly not the only writer to have left a lasting influence on theater.While less known worldwide, Tang Xianzu is considered one of Chinas greatest playwrights and is highly spoken of in that country of ancient literary and dramatic traditions.Tang was born in 1550 inLinchuan,Jiangxiprovince. Unlike Shakespeare's large body of plays,poems and sonnets (十四行诗), Tang wrote only four major plays: The Purple Hairpin, Peony Pavilion (《牡丹亭》), A Dream under the Southern bough, and Dream of Handan. The latter three were constructed around a dream narrative, a way through which Tang unlocked the emotional dimension of human desires and ambitions and explored human nature beyond the social and political limits of that time.Similar to Shakespeare, Tang's success rode the wave of a renaissance (复兴) in theater as an artistic practice. As in Shakespeare'sEngland, Tang's works became hugely popular inChinatoo. During Tang'sChina, his plays were enjoyed performed, and changed. Kunqu Opera, a form of musical drama, spread from southernChinato the whole nation and became a symbol of Chinese culture. Combining northern tune and southern music, kunqu Opera was known for its poetic language, music, dance movements and gestures. Tang's works benefited greatly from the popularity of kunqu Opera, and his plays are considered classics of kunqu Opera.While Tang and Shakespeare lived in a world away from each other, there are many things they share in common, such e humanity of their drama, their heroic figures, their love for poetic language, a lasting popularity and the anniversary during which we still celebrate them.1. Why is Shakespeare mentioned in the first paragraph?A. To describe Shakespeare's anniversary.B. To introduce the existence of Tang Xianzu.C. To explain the importance of Shakespeare.D. To suggest the less popularity of Tang Xianzu.2. What's possibly one of the main theme of Tang's works?A. Social reality.B. Female dreams.C. Human emotions.D. Political environment.3. What does the author mainly tell us in Paragraph 4?A. The influence of Kunqu Opera on Tang's works.B. Tang's success in copying Shakespeare's styles.C. The way Kunqu Opera became a symbol of Chinese culture.D. Tang's popularity for his poetic language and music.BChimps use loud calls and gestures to make their feelings known but until now, the exact meaning for individual movements has remained a mystery. Now researchers believe they have translated the key gestures used in the chimp community and identified their intentions for the first time.From 4,351 gestures, experts were able to identify 66 that are used for 19 specific message meanings, including showing a foot to tell a child they can climb on their back. The researchers were able to narrow down these 66 gestures to 36 that are used intentionally to achieve 15 purposes. The translations were made by Dr Catherine Hobaiter and her colleagues at St Andrews University in Scotland.Dr Hobaiter used behavior sampling and filmed all recorded cases of gestural communication. Other gestures include stomping their feet to ask another chimp to stop what they are doing, and slapping objects together to ask another to follow them. Of the 19 meanings,17 encouraged interactions to start, or to develop, such as “move closer,” and “change play”. Some of the gestures were found to have more than one meaning. and only 10 of the 66 gestures were used for only a single meaning.Researchers collected a total of 471 video clips from two social groups of chimps at a shelter near Kinshasa, Democratic Republic of Congo. As well as identifying what the gesture means, they also discovered the technique needed to increase the chances of success.“Human children use gestures to communicate before they produce their first words, and their earliest gestures typically appear around 10 months of age,” explained the researchers. “In great apes, there is good evidence that language-trained individuals are capable of acquiring and understanding signals, but this is far less clear in their natural communication. ”4. Chimps slap the objects to____________.A. tell others to stop what they are doingB. ask others chimps to join themC. gather other chimps to move closerD. encourage interactions to start5. What did researchers find after studying 471 video clips?A. Chimps trained in language are good at understanding signals.B. Two social groups of chimps live at a shelter near Kinshasa.C. Language-trained individuals do well in natural communication.D. Chimps’earliest gestures appear around 10 months of age.6. How is the last paragraph developed?A. By analyzing causes.B. By examining differences.C By making comparisons. D. By following time order.7. What can be a suitable title for the text?A A New Research on Chimps B. Human Children and ChimpsC. Getting the Chimps Trained for LanguageD. Translating the Sign Language of ChimpsCWe are in lack of enough sleep, according to Arianna Huffington, the co-founder and editor-in-chief of The Huffington Post. And thishas great consequences on our health, our job performance, our relationships and our happiness. What is needed, she ly declares, is nothing short of a sleep revolution. Only by renewing our relationship with sleep can we take back control of our lives.In her bestseller Thrive, Arianna wrote about our need to redefine success through wellbeing, wisdom, wonder, and giving. Her discussion of the importance of sleep as a gateway to this more fulfilling way of living struck such a powerful chord (弦) that she realized the mystery and transformative power of sleep called for a fuller investigation (调查).The result is a scientifically sweeping and personal exploration of sleep from all angles, from the history of sleep, to the role of dreams in our lives, to the consequences of sleep deprivation (剥夺), and the new golden age of sleep science that is showing the vital role sleep plays in our every waking moment and every aspect of our health — from weight gain, diabetes, and heart disease to cancer and Alzheimer’s.In The Sleep Revolution, Arianna shows how our cultural removal of sleep as time wasted damages our health and our decision-making and our work lives and shortens our personal lives. She explores all the latest science on what exactly is going on while we sleep and dream. She decides the dangerous sleeping pill industry, and all the ways of our addiction to technology disturb our sleep. She also offers a range of recommendations and tips from leading scientists on how we can get better and more restorative sleep.In today’s fast-paced, always-connected and sleep-deprived world, our need for a good night’s sleep is moreimportant than ever. The Sleep Revolution both sounds the alarm on our worldwide sleep crisis and provides a detailed road map to the great sleep awakening that can help transform our lives, our communities, and our world.8. What is the first paragraph mainly about?A. The importance of sleep.B. The necessity of improving sleep.C. The way to improve our sleep.D. The effect of sleep on health.9. What can be inferred about Arianna’s attitude to success?A. She thinks good sleep is more important.B. She doesn’t think much of becoming successful.C. She thinks it wrong to sacrifice health to success.D. She is concerned about the nature of success.10. What can be said about Arianna’s investigation?A. It is really of great value.B. It is scientific and historical.C. It costs Arianna’s sleep in practice.D. It covers all necessary aspects scientifically,11. What influence does TheSleep Revolution have on society?A. It helps to slow down the pace of modern life.B. It warns people against taking sleeping pills.C. It warns the harm of inadequate sleep of people.D. It helps to stress the value of sleep to success.DA teenager in Georgia will no longer have to walk 7 miles to work after school thanks to one woman’s act of kindness.Jayden Sutton, a high school senior, went on foot each day from school to his job at a restaurant and then back home. Sutton was determined to work and make enough money to eventually buy his own vehicle.Sutton said he’d leave school at 3:30 pm, then walk miles to his job at the restaurant. After his work, which usually lasted six to eight hours, he walked home, sometimes not arriving back until almost midnight.That all changed when Myers saw him walking down the road in the rain in December. “The young man was insistently in a rush walking to work, saying ‘I can’t be late,’” Myers said. “He begged me to give him a ride. I toldhim I could take him as far as I was going. I began to create small talk along the way. It wasrevealedto me that his name was Jayden, 12th grader, worked 40 hours a week, walked 5 miles to work immediately after school, got off at 10:30 pm at night and walked back home another 5 miles if co-workers didn’t offer a ride.”After dropping Sutton off, Myers said his heart and determination filled her with tears. “He was smiling in good spirits and that’s a child worth blessing,” she told Fox News. So, Myers shared Sutton’s story on the GoFundMe page, which raised more than $ 9, 000 from 186 donors.She surprised Sutton with a new car after she managed to convince the general manager to drop the price of the vehicle to meet the budget.12. Why did Sutton work so hard in his spare time?A. To gain working experience.B. To pay for his education.C. To own a car.D. To support his family.13. What difficulty did Sutton have in his work at the restaurant?A. He worked longer than other workers.B. His work was too tiring.C. His job was much less paid.D. He had to walk to work.14. What does the underlined word “revealed” in paragraph 4 mean?A. Known.B. Attached.C. Believed.D. Limited.15. What do we know about the money donated online?A. It could buy more than a new car.B. It was not enough to buy a new car.C. It was given to Myers to buy herself a new car.D It mainly came from a car sales manager.第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020届海南省定安县定安中学高三上学期第二次月考物理试题 (解析版)
2020届海南省定安县定安中学高三上学期第二次月考物理试题 （解析版）一、单项选择题（本题包括6小题，每小题4分，共24分。
每小题只有一个选项是符合题意的。
） 1.一辆汽车以速度v 匀速行驶了全程的一半，以2v行驶了另一半，则全程的平均速度为（ ） A.2vB.23v C. 32v D. 3v【答案】B 【解析】设全程为2s ，前半程的时间为：1s t v=．后半程的运动时间为：222s st v v ==．则全程的平均速度为：1222 3s vv t t ==+．故B 正确，ACD 错误．故选B. 2.做自由落体运动的甲乙两物体所受的重力之比为 2：1， 下落高度之比为 1：2，则（ ） A. 下落过程中的加速度之比为 2：1 B. 下落时间之比为 1：2 C. 落地速度之比1D. 若甲乙同时下落，在甲落地前，两者间的距离越来越近 【答案】C 【解析】 【分析】自由落体运动的加速度相等，结合位移时间公式，通过下落的高度之比得出下落的时间之比．根据速度位移公式求出落地的速度之比；【详解】A 、自由下落的物体，加速度相等，与质量无关，均为g ，故A 错误； B 、根据212h gt =得t =1:2，则下落的时间之比为B 错误；C、根据v 1:2，则落地的速度之比为1:C 正确； D 、若甲乙同时下落，下落的快慢程度相同，在甲落地前，两者间的距离不变，故D 错误； 故选C 。
【点睛】关键知道自由落体运动的特点，结合运动学公式灵活求解。
3.下列几个关于力学问题的说法中正确的是（ ）A. 米、千克、牛顿等都是国际单位制中的基本单位B. 加速度大的物体，速度变化一定快C. 摩擦力的方向总是与物体的运动方向相反D. 马拉车加速前进说明马拉车的力大于车拉马的力【答案】B【解析】【详解】米、千克都是国际单位制中的基本单位、牛顿是导出单位，选项A错误；加速度大的物体，速度变化一定快，选项B正确；摩擦力的方向总是与物体的相对运动方向相反，选项C错误；马拉车加速前进，马拉车的力与车拉马的力是一对相互作用力，则马拉车的力等于车拉马的力，选项D错误；故选B.4.如图甲、乙所示, 倾角为 的固定斜面上分别有一个滑块M,图甲中滑块上表面水平,图乙中滑块的上表面平行斜面,在滑块M上分别有一个质量为m的物块,现在M和m相对静止,一起沿斜面匀速下滑,下列说法正确的是( )A. 图甲中物块m受摩擦力,方向水平向左B. 图甲中物块M受5个力C. 图乙中物块m受摩擦力,方向平行斜面向上D. 图乙中物块M受6个力【答案】C【解析】【详解】A.图甲中以m为研究的对象。
2020届海南省海南中学高三第二次月考数学试题(解析版)
2020届海南省海南中学高三第二次月考数学试题一、单选题 1．设集合M ＝{x|x ＝2k ×180°＋45°，k ∈Z}，N ＝{x|x ＝4k×180°＋45°，k ∈Z}，那么( ) A ．M ＝N B ．N ⊆MC ．M ⊆ND ．M∩N ＝∅【答案】C【解析】变形表达式为相同的形式，比较可得． 【详解】由题意可{|18045}{|2145}2kM x x k Z x x k k Z ==⋅︒+︒∈==+⋅︒∈得，（），，即M 为45︒的奇数倍构成的集合， 又{|18045}{|145}4kN x x k Z x x k k Z ==⋅︒+︒∈==+⋅︒∈，（），，即N 为45︒的整数倍构成的集合，M N ∴⊆， 故选C ． 【点睛】本题考查集合的包含关系的判定，变形为同样的形式比较是解决问题的关键，属基础题． 2．我国古代数学名著《算法统宗》中有如下问题：“远望巍巍塔七层，红光点点倍加增，共灯三百八十一，请问尖头几盏灯？”意思是：一座7层塔共挂了381盏灯，且相邻两层中的下一层灯数是上一层灯数的2倍，则塔的顶层共有灯 A ．1盏 B ．3盏 C ．5盏 D ．9盏【答案】B 【解析】【详解】设塔顶的a 1盏灯，由题意{a n }是公比为2的等比数列， ∴S 7=()711212a --=381，解得a 1=3． 故选B ．3．钱大姐常说“便宜没好货”，她这句话的意思是：“好货”是“不便宜”的（ ） A ．充分条件B ．必要条件C ．充分必要条件D ．既非充分也非必要条件【答案】A【解析】分别判断充分性和必要性得到答案. 【详解】便宜没好货，故“好货”一定“不便宜”， “不便宜”不一定是“好货”. 故选：A . 【点睛】本题考查了充分条件，意在考查学生的推断能力.4．相关变量,x y 的散点图如图所示，现对这两个变量进行线性相关分析，方案一：根据图中所有数据，得到线性回归方程11y b x a =+，相关系数为1r ；方案二：剔除点(10,21)，根据剩下数据得到线性回归直线方程：22y b x a =+，相关系数为2r .则（ ）A ．1201r r <<<B ．2101r r <<<C ．1210r r -<<<D ．2110r r -<<< 【答案】D【解析】根据相关系数的意义：其绝对值越接近1，说明两个变量越具有线性相关，以及负相关的意义作判断. 【详解】由散点图得负相关，所以12,0r r <，因为剔除点()10,21后，剩下点数据更具有线性相关性，r 更接近1，所以2110r r -<<<.选D. 【点睛】本题考查线性回归分析，重点考查散点图、相关系数，突显了数据分析、直观想象的考查.属基础题.5．下列函数中，既是奇函数，又在0,2π⎛⎫⎪⎝⎭上单调递增的是（）A ．2sin x y x =-B ．122xx y ⎛⎫=- ⎪⎝⎭C ．sin y x x =-D ．cos y x x =-【答案】B【解析】由奇函数的定义先可排除选项A,D 再利用函数单调性判断B,C ，即可得选项. 【详解】由奇函数的定义()()f x f x -=-，可知A,D 不满足奇函数的定义，排除A,D ；由2xy =与12x y ⎛⎫=- ⎪⎝⎭均为增函数，知122xx y ⎛⎫=- ⎪⎝⎭为增函数，B 正确； 对于sin y x x =-，有10y cosx -'=<，所以sin y x x =-为减函数，D 不正确. 故选B. 【点睛】本题主要考查了函数奇偶性的判断及单调性的判断，属于基础题. 6．等比数列{}n a 的前n 项和为n S ，若36=2S =18S ，，则105S S 等于( ) A ．－3 B ．5C ．33D ．－31【答案】C【解析】由等比数列的求和公式结合条件求出公比，再利用等比数列求和公式可求出105S S . 【详解】设等比数列{}n a 的公比为q （公比显然不为1），则()()61636333111119111a q S q q q S qa q q---===+=---，得2q =， 因此，()()101105510555111111233111a q S q q q S q a qq---===+=+=---，故选C. 【点睛】本题考查等比数列基本量计算，利用等比数列求和公式求出其公比，是解本题的关键，一般在求解等比数列问题时，有如下两种方法：（1）基本量法：利用首项和公比列方程组解出这两个基本量，然后利用等比数列的通项公式或求和公式来进行计算；（2）性质法：利用等比数列下标有关的性质进行转化，能起到简化计算的作用． 7．一个三位数，个位、十位、百位上的数字依次为x ，y ，z ，当且仅当y ＞x ，y ＞z 时，称这样的数为“凸数”(如243)，现从集合{1,2,3,4}中取出三个不相同的数组成一个三位数，则这个三位数是“凸数”的概率为（ ） A ．23B ．13C ．16D ．112【答案】B【解析】根据题意，分析“凸数”的定义，可得要得到一个满足三个不相同的数组成的三位“凸数”，在{1，2，3，4}的4个整数中任取3个数字，组成三位数，再将最大的放在十位上，剩余的2个数字分别放在百、个位上即可，再利用古典概型概率计算公式即可得到所求概率． 【详解】解：从集合{1,2,3,4}中取出三个不相同的数组成一个三位数共有24个结果：123,124,132,134,142,143,213,214,231,234,241,243,312,314,321,324,341,342,412,413,421,423,431,432，其中是“凸数”的是132,142,143,231,241,243,341,342，共8个结果，所以这个三位数是“凸数”的概率81243P ==， 故选：B ． 【点睛】本题主要考查古典概型的概率，关键是列举基本事件总数时不重不漏，属于基础题．8．在ABC ∆中，角A ，B ，C 的对边分别为a ，b ，c ，已知cos2cos22cos2A B C +=，则cos C 的最小值为（ ）A ．B ．2C ．12D ．12-【答案】C【解析】化简得到()2cos cos 2cos 1C A B C --=-，故()11cos 2cos 1cos A B C C-<-=-+≤，解得答案. 【详解】cos2cos22cos2A B C +=，即()()2cos cos 2cos2A B A B C +-=，即()2cos cos 2cos 1C A B C --=-，故()11cos 2cos 1cos A B C C-<-=-+≤. 解得：1cos 12C ≤<，当3A B C π===时cos C 有最小值为12. 故选：C . 【点睛】本题考查了三角恒等变换求范围，意在考查学生的计算能力和转化能力.9．函数()sin()f x A x ωϕ=+的部分图象如图中实线所示，图中圆C 与()f x 的图象交于,M N 两点，且M 在y 轴上，则下列说法中正确的是A ．函数()f x 的最小正周期是2πB ．函数()f x 的图象关于点,034⎛⎫π ⎪⎝⎭成中心对称 C ．函数()f x 在2(,)36ππ--单调递增 D ．函数()f x 的图象向右平移512π后关于原点成中心对称【答案】B【解析】根据函数的图象，求得函数()sin 23f x A x π⎛⎫=+ ⎪⎝⎭，再根据正弦型函数的性质，即可求解，得到答案． 【详解】根据给定函数的图象，可得点C 的横坐标为3π，所以1()2362T πππ=--=，解得T π=，所以()f x 的最小正周期T π=， 不妨令0A >，0ϕπ<<，由周期T π=，所以2ω=，又06f π⎛⎫-= ⎪⎝⎭，所以3πϕ=，所以()sin 23f x A x π⎛⎫=+ ⎪⎝⎭， 令2,3x k k Z ππ+=∈，解得,26k x k Z ππ=-∈，当3k =时，43x π=，即函数()f x的一个对称中心为4,03π⎛⎫ ⎪⎝⎭，即函数()f x 的图象关于点4,03π⎛⎫ ⎪⎝⎭成中心对称．故选B ． 【点睛】本题主要考查了由三角函数的图象求解函数的解析式，以及三角函数的图象与性质，其中解答中根据函数的图象求得三角函数的解析式，再根据三角函数的图象与性质求解是解答的关键，着重考查了数形结合思想，以及运算与求解能力，属于基础题． 10．已知函数(1)y f x =+的图象关于y 轴对称，且函数()f x 在(1,)+∞上单调，若数列{}n a 是公差不为0的等差数列，且418()()f a f a =，则{}n a 的前21项之和为（ ） A ．0 B ．252C ．21D ．42【答案】C【解析】由函数y ＝f （x+1）的图象关于y 轴对称，可得y ＝f （x ）的图象关于x ＝1对称，由题意可得418a a 2+=，运用等差数列的性质和求和公式，计算可得到所求和． 【详解】函数()y f x 1=+的图象关于y 轴对称，平移可得()y f x =的图象关于x 1=对称，且函数()f x 在()1,+∞上单调，由数列{}n a 是公差不为0的等差数列，且()()418f a f a =，可得418a a 2+=，所以121418a a a a 2+=+=，可得数列{}n a 的前21项和()1212121a a S 212+==.故选：C. 【点睛】本题考查函数的对称性及应用，考查等差数列的性质，以及等差数列的求和公式，考查运算能力，属于中档题．11．已知函数()cos (0)f x wx wx w =+>在区间,43ππ⎡⎤-⎢⎥⎣⎦上恰有一个最大值点和一个最小值点，则实数ω的取值范围是（ ） A ．8,73⎡⎫⎪⎢⎣⎭B ．8,43⎡⎫⎪⎢⎣⎭C ．204,3⎡⎫⎪⎢⎣⎭D ．20,73⎛⎫⎪⎝⎭【答案】B【解析】首先利用三角函数关系式的恒等变换，把函数的关系式变形成正弦型函数，进一步利用正弦型函数的性质的应用求出结果． 【详解】由题意，函数()cos 2sin()6f x x x x πωωω=+=+，令6x t πω+=，所以()2sin f x t =，在区间上,43ππ⎡⎤-⎢⎥⎣⎦恰有一个最大值点和最小值点，则函数()2sin f x t =恰有一个最大值点和一个最小值点在区间,[436]6πωππωπ+-+， 则3246232362ππωππππωππ⎧-<-+≤-⎪⎪⎨⎪≤+<⎪⎩，解答8203314ωω⎧≤<⎪⎨⎪≤<⎩，即834ω≤<，故选B ． 【点睛】本题主要考查了三角函数关系式的恒等变换，正弦型函数的性质的应用，主要考察学生的运算能力和转换能力，属于基础题型．12．若函数()f x 、()g x 分别是定义在R 上的偶函数、奇函数，且满足()()2e x f x g x -=，则( )A ．()()()231f f g -<-<-B ．()()()132g f f -<-<-C ．()()()213f g f -<-<-D ．()()()123g f f -<-<-【答案】D【解析】根据奇函数偶函数性质计算函数表达式，代入数值比较大小. 【详解】若函数()f x 、()g x 分别是定义在R 上的偶函数、奇函数，且满足()()2e xf xg x -=()()()()2e 2e x x f x g x f x g x ----=+=⇒-()4x x e e f x -+=()2x xe e g x --= 代入数值知：()()()123gf f -<-<- 故答案为D 【点睛】本题考查了根据奇偶函数性质求函数表达式，是函数性质里的常考题目.二、填空题 13．()()532xx a -+的展开式的各项系数和为32，则该展开式中4x的系数是______.【答案】5【解析】化简得到()()()()5553322x x a x a x x a -+=+-+，计算1a =，根据二项式定理计算得到答案. 【详解】()()()()5553322x x a x a x x a -+=+-+，取1x =得到()5132a +=，故1a =.()51x +的展开式的通项式为：515r rr T C x -+=，分别取1r =和4r =得到系数为：145525C C ⨯-=.故答案为：5. 【点睛】本题考查了二项式定理的应用，意在考查学生的计算能力和应用能力. 14．已知数列{}n a 满足1133,2,n n a a a n +=-=则na n的最小值为__________. 【答案】212【解析】先利用累加法求出a n ＝33+n 2﹣n ，所以331n a n n n =+-，设f （n ）331n n=+-，由此能导出n ＝5或6时f （n ）有最小值．借此能得到n an的最小值．【详解】解：∵a n +1﹣a n ＝2n ，∴当n ≥2时，a n ＝（a n ﹣a n ﹣1）+（a n ﹣1﹣a n ﹣2）+…+（a 2﹣a 1）+a 1＝2[1+2+…+（n ﹣1）]+33＝n 2﹣n +33 且对n ＝1也适合，所以a n ＝n 2﹣n +33．从而331n a n n n=+- 设f （n ）331n n =+-，令f ′（n ）23310n-=+＞，则f （n ）在)+∞上是单调递增，在(0上是递减的，因为n ∈N +，所以当n ＝5或6时f （n ）有最小值． 又因为55355a =，66321662a ==，所以n a n的最小值为62162a =故答案为 212【点睛】本题考查了利用递推公式求数列的通项公式，考查了累加法．还考查函数的思想，构造函数利用导数判断函数单调性．15． 已知函数y ＝()f x 的图像在点M (1，f (1))处的切线方程是122y x =＋，则()()1'1f f ＋＝________. 【答案】3【解析】由题意知()()115'112222f f ＝，＝＋＝， 所以f (1)＋f ′(1)＝52＋12＝3. 答案：3.16．李明自主创业，在网上经营一家水果店，销售的水果中有草莓、京白梨、西瓜、桃，价格依次为60元/盒、65元/盒、80元/盒、90元/盒.为增加销量，李明对这四种水果进行促销：一次购买水果的总价达到120元，顾客就少付x 元.每笔订单顾客网上支付成功后，李明会得到支付款的80%.在促销活动中，为保证李明每笔订单得到的金额均不低于促销前总价的七折，则x 的最大值为______. 【答案】15【解析】设购买水果的总价为y ，当120y ≥时，则()70%80%y y x ⋅≤-⋅恒成立，解得8yx ≤，得到答案. 【详解】设购买水果的总价为y ，当0120y <<时，易知成立； 当120y ≥，则()70%80%y y x ⋅≤-⋅恒成立，解得8yx ≤恒成立. 当买两盒草莓，即120y =时，8y取最小值，故x 取最大值为15. 故答案为：15. 【点睛】本题考查了不等式恒成立问题的应用，意在考查学生的应用能力.三、解答题17．已知等差数列{}n a 的前n 项和为n S ，公差0d ≠，且3550S S +=，1a ，4a ，13a成等比数列.（1）求数列{}n a 的通项公式；（2）若从数列{}n a 中依次取出第2项，第4项，第8项，…，第2n 项，…，按原来顺序组成一个新数列{}n b ，记该数列的前n 项和为n T ，求n T 的表达式.【答案】（1）21n a n =+；（2）224n n T n +=+-【解析】（1）根据题意得到181350a d +=，()()2111312a d a a d +=⋅+，解得答案，利用等差数列的通项公式可求得数列{}n a 的通项公式；（2）221nn b =⋅+，利用分组求和法计算得到答案.【详解】（1）3550S S +=，即181350a d +=；1a ，4a ，13a 成等比数列，故24113a a a =⋅，即()()2111312a d a a d +=⋅+；解得13,2a d ==，故()()1132121n a a n d n n =+-=+-=+；（2）221nn b =⋅+，故21242412nn n T n n +-=⋅+=+--.【点睛】本题考查了等差数列的通项公式，分组求和，意在考查学生对于数列公式方法的灵活运用.18．已知函数()sin(3)4f x x π=+.（1）求()f x 的单调递增区间； （2）若α是第二象限角，4()cos()cos 2354f απαα=+，求cos sin αα-的值.【答案】（1）22[,]34312k k ππππ-+，k Z ∈；（2）或． 【解析】试题分析：（1）将34x π+看作一个整体，根据正弦函数sin y x =的单调递增区间便可得()sin(3)4f x x π=+的单调递增区间.（2）将3α代入4()cos()cos 2354f απαα=+得4sin()cos()cos 2454ππααα+=+.求三角函数值时，首先考虑统一角，故利用和角公式和倍角公式化为单角α的三角函数得：4sin cos (cos sin )(cos sin )(sin cos )5αααααααα+=--+.注意这里不能将sin cos αα+约了.接下来分sin cos 0αα+=和sin cos 0αα+≠两种情况求值.试题解答：（1）22232()24243123k x k k x k k Z πππππππππ-+≤+≤+⇒-+≤≤+∈； （2）由题设得：4sin()cos()cos 2454ππααα+=+， 即4sin cos (cos sin )(cos sin )(sin cos )5αααααααα+=--+，. 若sin cos 0αα+=，则cos sin αα-= 若sin cos 0αα+≠，则241(cos sin )cos sin 5αααα=-⇒-=【考点定位】三角函数的性质、三角恒等变换三角函数的求值.19．在ABC ∆中，锐角C 满足252sin cos 232C C π⎛⎫-+= ⎪⎝⎭. （1）求角C 的大小；（2）点P 在BC 边上，3PAC π∠=，3PB =，sin 38BAP ∠=，求ABC ∆的面积.【答案】（1）3C π=；（2【解析】（1）化简得到sin 232C π⎛⎫-= ⎪⎝⎭，根据22,333C πππ⎛⎫-∈- ⎪⎝⎭得到答案. （2）根据正弦定理得到AB =根据余弦定理得到2PA =，再计算面积得到答案. 【详解】（1）252sin cos 232C C π⎛⎫-+= ⎪⎝⎭，化简得到33sin 2cos 2222C C -=.即sin 23C π⎛⎫-= ⎪⎝⎭，22,333C πππ⎛⎫-∈- ⎪⎝⎭，故233C ππ-=，3C π=.（2）易知APC ∆为等边三角形，故23APB ∠=π. 根据正弦定理：2sin sin3PB ABPABπ=∠，故AB =根据余弦定理：2222co 23sAB PA PB PA PB π=+-⋅，解得2PA =，故5BC =，2AC =.1sin 232ABC S CA CB π∆=⋅=. 【点睛】本题考查了三角恒等变换，正弦定理，余弦定理，面积公式，意在考查学生的综合应用能力.20．已知各项均不为零的数列{}n a 的前n 项和为n S ，且满足14a =，()*134n n a S n N +=+∈.（1）求数列{}n a 的通项公式；（2）设数列{}n b 满足2log n n n a b a =，数列{}n b 的前n 项和为n T ，求证：89n T <. 【答案】（1）4nn a =；（2）证明见解析【解析】（1）利用公式1n n n a S S -=-结合等比数列的定义可得出数列{}n a 的通项公式；（2）化简得到21244nn n n b n ⎛⎫== ⎪⎝⎭，利用错位相减法计算得到868994n n n T +=-⨯，得到证明. 【详解】（1）()*134n n a S n N+=+∈，当2n ≥时，134nn aS -=+，两式相减得到14n n a a +=，213416a a =+=，214a a ∴=， 所以，数列{}n a 是以4为首项，以4为公比的等比数列，故4nn a =；（2）2log n n n a b a =，即42nn b n ⋅=，故21244nn n n b n ⎛⎫== ⎪⎝⎭. 故2111242444n n T n ⎛⎫⎛⎫=⨯+⨯++ ⎪ ⎪⎝⎭⎝⎭L ，23111112424444n n T n +⎛⎫⎛⎫⎛⎫=⨯+⨯++ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭L .相减得到：23412341322222211111224444444444444n n n n n n n T ++⎛⎫=+++++-=+++++- ⎪⎝⎭L L111112122122684411434433414n n n n n n n n +++⎛⎫⨯- ⎪+⎛⎫⎝⎭=-=--=- ⎪⨯⎝⎭-， 化简整理得到：86889949n n n T +=-<⨯，得证. 【点睛】本题考查了数列的通项公式，错位相减法，证明数列不等式，意在考查学生对于数列公式方法的综合应用.21．改革开放以来，人们的支付方式发生了巨大转变．近年来，移动支付已成为主要支付方式之一．为了解某校学生上个月A ，B 两种移动支付方式的使用情况，从全校学生中随机抽取了100人，发现样本中A ，B 两种支付方式都不使用的有5人，样本中仅使用A 和仅使用B 的学生的支付金额分布情况如下：交付金额（元） 支付方式 （0,1000]（1000,2000] 大于2000仅使用A 18人 9人 3人 仅使用B 10人14人1人（Ⅰ）从全校学生中随机抽取1人，估计该学生上个月A ，B 两种支付方式都使用的概率；（Ⅱ）从样本仅使用A 和仅使用B 的学生中各随机抽取1人，以X 表示这2人中上个月支付金额大于1000元的人数，求X 的分布列和数学期望；（Ⅲ）已知上个月样本学生的支付方式在本月没有变化．现从样本仅使用A 的学生中，随机抽查3人，发现他们本月的支付金额都大于2000元．根据抽查结果，能否认为样本仅使用A 的学生中本月支付金额大于2000元的人数有变化？说明理由． 【答案】(Ⅰ) 25； (Ⅱ)见解析； (Ⅲ)见解析.【解析】(Ⅰ)由题意利用古典概型计算公式可得满足题意的概率值；(Ⅱ)首先确定X 可能的取值，然后求得相应的概率值可得分布列，最后求解数学期望即可.(Ⅲ)由题意结合概率的定义给出结论即可. 【详解】(Ⅰ)由题意可知，两种支付方式都是用的人数为：1003025540---=人，则： 该学生上个月A ，B 两种支付方式都使用的概率4021005p ==. (Ⅱ)由题意可知，仅使用A 支付方法的学生中，金额不大于1000的人数占35，金额大于1000的人数占25，仅使用B 支付方法的学生中，金额不大于1000的人数占25，金额大于1000的人数占35，且X 可能的取值为0,1,2.()32605525p X ==⨯=，()22321315525p X ⎛⎫⎛⎫==+= ⎪ ⎪⎝⎭⎝⎭，()32625525p X ==⨯=，X 的分布列为：其数学期望：()61360121252525E X =⨯+⨯+⨯=. (Ⅲ)我们不认为样本仅使用A 的学生中本月支付金额大于2000元的人数有变化.理由如下：随机事件在一次随机实验中是否发生是随机的，是不能预知的，随着试验次数的增多，频率越来越稳定于概率．学校是一个相对消费稳定的地方，每个学生根据自己的实际情况每个月的消费应该相对固定，出现题中这种现象可能是发生了“小概率事件”. 【点睛】本题以支付方式相关调查来设置问题，考查概率统计在生活中的应用，考查概率的定义和分布列的应用，使学生体会到数学与现实生活息息相关. 22．设函数()ln f x x ax =-，()x g x e ax =-，其中a 为实数.（1）若()f x 在(1,)+∞上是单调减函数，且()g x 在(1,)+∞上有最小值，求a 的取值范围；（2）若()g x 在(1,)-+∞上是单调增函数，试求()f x 的零点个数，并证明你的结论. 【答案】（1）(,)a e ∈+∞（2）当0a ≤或1a e -=时，()f x 的零点个数为1；当10a e -<<时，()f x 的零点个数为2.【解析】【详解】 （1）∵11()0ax f x a x x='-=-<，考虑到函数()f x 的定义域为(0,)+∞，故0a >，进而解得1x a ->，即()f x 在1(,)a -+∞上是单调减函数. 同理，()f x 在1(0,)a -上是单调增函数. 由于()f x 在(1,)+∞是单调减函数，故1(1,)(,)a -+∞⊆+∞，从而11a -≤，即1a ≥.令()0x g x e a '=-=，得ln x a =，当ln x a <时，()0g x '<；当ln x a >时，()0g x '>， 又()g x 在(1,)+∞上有最小值，所以ln 1a >，即a e >， 综上所述，(,)a e ∈+∞.（2）当0a ≤时，()g x 必是单调增函数；当0a >时，令()0xg x e a '=->，解得x a e <，即ln x a >，∵()g x 在(1,)-+∞上是单调函数，类似（1）有ln 1a ≤-，即10a e -<≤， 综合上述两种情况，有1a e -≤. ①当0a =时，由(1)0f =以及1()0f x x'=>，得()f x 存在唯一的零点； ②当0a <时，由于()(1)0a a a f e a ae a e =-=-<，(1)0f a =->，且函数()f x 在[,1]a e 上的图象不间断，∴()f x 在(,1)a e 是单调增函数，∴()f x 在(,1)a e 上存在零点. 另外，当0x >时，1()0f x a x'=->，则()f x 在(0,)+∞上是单调增函数，()f x 只有一个零点.③当10a e -<≤时，令1()0f x a x¢=-=，解得1x a -=. 当10x a -<<时，()0f x '>；当1x a ->时，()0f x '<. ∴1x a -=是()f x 的最大值点，且最大值为1()ln 1f a a -=--.1)当ln 10a --=，即1a e -=时，()f x 有一个零点x e =.2)当ln 10a -->，即10a e -<<时，()f x 有两个零点. 实际上，对于10a e -<<，由于11()10f e ae--=--<，1()0f a ->，且函数()f x 在11[,]e a --上的图象不间断，∴()f x 在11(,)e a --上存在零点.另外，当1(0,)x a -∈时，1()0f x a x'=->，故()f x 在1(0,)a -上是单调增函数，∴()f x 在1(0,)a -上有一个零点.下面需要考虑()f x 在(,)a+∞１上的情况，先证112()()0a f e a a e ---=-<， 为此，我们要证明：当x e >时，2x e x >，设2()xh x e x =-，则，再设()()2x l x h x e x ='=-，则()2xl x e =-'.当1x >时，()220xl x e e =->->'，∴()()l x h x '=在(1,)+∞上是单调增函数，故当2x >时，2()2(2)40x h x e x h e ''=->=->，从而()h x 在(2,)+∞上是单调增函数，进而当x e >时，22()()0x e h x e x h e e e =->=->，即当x e >时，2x e x >.当10a e -<<，即1a e ->时，11112()()0a a a f e a ae a a e -----=-=-<，又1()0f a ->，且函数()f x在11[,]a a e --的图象不间断，∴()f x 在11(,)a a e --上存在零点. 又当1x a ->时，1()0f x a x'=-<，故()f x 在1(,)a -+∞是单调减函数，所以，()f x 在1(,)a -+∞上只有一个零点.综上所述，当0a ≤或1a e -=时，()f x 的零点个数为1；当10a e -<<时，()f x 的零点个数为2. 【考点定位】本小题主要考查导数的运算及用导数研究函数的性质，考查函数、方程及不等式的相互转化，考查综合运用数学思想方法分析与解决问题及推理论证能力.。
2020届海南省海口四中高三上学期第二次月考地理试卷及答案
绝密★启用前海南省海口市第四中学2020届高三年级上学期第二次月考检测地理试题考生说明：1、考试时间：90分钟。
2、本试卷分第Ⅰ卷（单项选择题）和第Ⅱ卷（综合题），共100分。
3、请将选择题的答案涂在答题卡的相应位置上；第Ⅱ卷答案写在答题卡指定位置上，否则均不得分。
第Ⅰ卷（单项选择题20×3 = 60分）1.下面四幅图中等高距相等，坡度最陡的是：A、甲B、乙C、丙D、丁2018年3月13日，据(每日邮报》报道，天文学家在距地球200光年处发现一颗可能宜居的“超级地球”K2-155d,这颗行星围绕一颗红矮星(比太阳质量稍小、温度稍低的恒星)运转,其大小是地球的1.6倍,科学家经过模拟,推测K2-155d的大气与地球的大气还有相似成分,地表可能存在液态水,据此完成2～3题。
2.行星K2-155d所处的天体系统中,级别最低的是A.河外星系B.银河系C.太阳系D.总星系3.与地球相比,K2-155dA.与主恒星距离更近B.能自身发光发热C.对物体的引力较小 D.一定有生命存在2019年元旦北京时间7：40北京迎来了新年的第一缕曙光。
结合下图完成面4～5题。
4．据此推断当天北京时间的日落时间应为A．16：04 B．16：20C．16：36 D．16：525．此时,已进入2019年的区域约占全球面积的A．近1/3 B．近1/2 C．近2/3 D．近3/4某学校地理兴趣小组发现该校国旗旗杆正午时分的影子,在一年中位于正北的时间是正南时间的2倍。
读图,完成6～7题6.某日该校旗杆影长达到一天中最短时北京时间为13:00该地的经度为A.100°EB.105°EC.110°ED.115°E7.该地的纬度大约是A.8°NB. 32°NC.8°SD.32°S我国巴丹吉林沙漠地区年降水量在40-109mm之间,年蒸发量超过1000mm,沙漠东南部有众多起伏较大的沙山；车日格勒湖位于沙漠东南部,常年积水,湖岸东侧湖相沉积物最高处比现代湖面高出约9m。
海南省海口市第四中学2020届高三上学期第二次月考语文试卷
海口四中2019-2020学年度第一学期第二次月考高三年级语文试题命题人：曾正娟史华玮终审人：黄丽珠考生注意：本试卷时间150分钟，满分为150分。
一、现代文阅读（36分）（一）论述类文本阅读（本题共3题，9分）阅读下面的文字，完成1～3题。
中华文明的历史启示（节选）袁行霈①中华文明的历史启示之一，就是选择包容。
②包容，是中华文明固有的思想。
早在《尚书》中就有这样的话：“有容，德乃大。
”（《周书·君陈》）意思是有所包容，所成就的功德才能巨大。
《老子》也说：“容乃公，公乃王，王乃天，天乃道，道乃久。
”意思是：有所包容，就能臻于“公”，进而臻于“王”，臻于“天”，臻于“道”，臻于“久”。
这些虽然都是针对统治者而言的，但在中华文明中具有普遍的意义。
中华文明是一种包容性很强的文明，中国人常用“海纳百川”来形容一个人的气度胸襟，这四个字也可以用来形容中华文明的品格。
③越来越多的考古资料证明，中华文明的发祥地，不只是黄河流域，还包括长江流域。
越来越多的考古资料又证明，除了黄河流域和长江流域，还有许多文化遗存散布在全国各地。
中华文明的组成，既包括定居于黄河、长江流域，较早以农耕为主要生活来源的华夏民族创造的文明，也包括若干以游牧为主要生活来源的少数民族创造的文明。
中华文明的演进过程，是多种文明因素的整合。
整合的模式是以华夏文明为核心，核心向周围扩散，周围向核心趋同，核心与周围互相补充、互相吸收、互相融合。
汉族和汉族以外的少数民族，都为中华文明作出了重要的贡献。
例如：我们引为骄傲的山西应县木塔那样精美的建筑，便是契丹族所建立的辽代的杰作；蒙古族所建立的元朝，首次开辟了我国南北海运航线；满族所建立的清朝，出现了康乾盛世。
这些都为中华文明增添了精彩的一页。
④我们还可以以战国和唐代为例进一步说明中华文明的包容性。
战国时代儒家、墨家、道家、法家、名家、阴阳家等不同的学说和流派多元共存，自由争辩，这已是人所共知的事实。
海南省海口市第四中学2020届高三数学上学期第二次月考试题
海南省海口市第四中学2020届高三数学上学期第二次月考试题（满分：150分时间：120分钟）一、选择题：（每小题5分，共60分）1.已知全集U={1，2，3，4，5，6}，集合P={1，3，5}，Q={1，2，4}，则（∁U P）∪Q=（）A. B. C. 2,4, D. 2,3,4,2.已知p：（x-1）（x-2）≤0，q：log2（x+1）≥1，则p是q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3.下列命题中的假命题是（）A. ,B. ,C. ,D. ,4.以下四个命题中是真命题的是（）A. 对分类变量x与y的随机变量的观测值k来说,k越小,判断“x与y有关系”的把握程度越大B. 两个随机变量的线性相关性越强,相关系数的绝对值越接近于0C. 若数据,,,,的方差为1,则,,,,的方差为2D. 在回归分析中,可用相关指数的值判断模型的拟合效果,越大,模型的拟合效果越好．5.若b＜a＜0，则下列结论不正确．．．的是( )A. B. C. D.6.某地市高三理科学生有30000名，在一次调研测试中，数学成绩ξ～N(100，σ2)，已知P(80＜ξ≤100)＝0.45，若按分层抽样的方式取200份试卷进行成绩分析，则应从120分以上的试卷中抽取（）A. 5份B. 10份C. 15份D. 20份7.已知x＞0，y＞0，2x+y=2，则xy的最大值为（）A. B. 1 C. D.8.随机变量X的分布列如表所示，若E（X）=，则D（3X-2）=（）A. 9B. 7C. 5D. 39.将函数的图象向左平移个单位，得到函数的图象，则下列关于函数的说法正确的是A. 奇函数B. 周期是C. 关于直线对称D. 关于点对称10.当x∈R时，不等式kx2-kx+1＞0恒成立，则k的取值范围是（）A. B.C. D.11. 若，，且函数在处有极值，则的最小值为A.B.C.D.12. 已知定义域为{x |x ≠0}的偶函数f （x ），其导函数为f ′（x ），对任意正实数x 满足xf ′（x ）＞-2f （x ），若g （x ）=x 2f （x ），则不等式g （x ）＜g （1-x ）的解集是（ ）A.B.C.D.二、填空题：（每小题5分，共20分） 13. 设函数f （x ）=，则f （）的值为_________14. 设x ∈R ，向量，且，则=________15. 一正三棱柱的每条棱长都是3，且每个顶点都在球O 的表面上，则球O 的表面积为_____16. 若函数f (x )＝ln x －ax ＋1，a ∈R 有零点，则实数a 的取值范围是_______ 三、解答题（共70分） 17. (本小题12分)已知函数)2,0,0)(sin()(πϕωϕω<>>+=A x A x f的部分图象如图所示． （1）求函数f （x ）的解析式 （2）求f （x ）的单调增区间； （3）求f （x ）在区间上的最大值和最小值．18. (本小题10分)已知数列{a n }的前n 项和S n 满足4a n -3S n =2，其中n ∈N *．（Ⅰ）求证：数列{a n }为等比数列；（Ⅱ）设b n =a n -4n ，求数列{b n }的前n 项和T n ．19.(本小题12分)某大型歌手选秀活动，过程分为初赛、复赛和决赛．经初赛进入复赛的40名选手被平均分成甲、乙两个班，由组委会聘请两位导师各负责一个班进行声乐培训．下图是根据这40名选手参加复赛时获得的100名大众评审的支持票数制成的茎叶图．赛制规定：参加复赛的40名选手中，获得的支持票数不低于85票的可进入决赛，其中票数不低于95票的选手在决赛时拥有“优先挑战权”．(1)从进入决赛的选手中随机抽出2名，X表示其中拥有“优先挑战权”的人数，求X的分布列和数学期望；(2)请填写下面的2×2列联表，并判断能否在犯错误的概率不超过0.025的前提下认为进入决赛与选择的导师有关？下面的临界值表仅供参考：(参考公式：K2＝，其中n＝a＋b＋c＋d)20.(本小题12分) 如图，在四棱锥A-BCDE中，平面ABC⊥平面BCDE，∠CDE=∠BED=90°，AB=CD=2，DE=BE=1，AC=．（Ⅰ）证明：DE⊥平面ACD；（Ⅱ）求二面角B-AD-E的大小．21.(本小题12分)设椭圆C：=1（a＞b＞0），过点Q（，1），右焦点F（，0），（Ⅰ）求椭圆C的方程；（Ⅱ）设直线l：y=k（x-1）（k＞0）分别交x轴，y轴于C，D两点，且与椭圆C交于M，N两点，若，求k值，并求出弦长|MN|．22.(本小题12分)已知函数f（x）=ax2-ln x，a∈R．（Ⅰ）当a=1时，求函数f（x）在点（1，f（1））处的切线方程；（Ⅱ）是否存在实数a，使函数f（x）在区间（0，e]上的最小值为，若存在，求出a 的值，若不存在，请说明理由．海口四中2020届高三第一学期数学月考（2）答案一、选择题二、填空题13. 14.15. π21 16.]1,(-∞17.(本小题12分)解：（1）由图象知A =1， 由图象得函数的最小正周期为，则由得ω=2)2sin()(ϕ+=∴x x f 又1)62sin()6(=+⨯=ϕππf)(223Z k k ∈+=+∴ππϕπ)(26Z k k ∈+=∴ππϕ又2πϕ<6πϕ=∴)62sin()(π+=∴x x f（2）∵，∴．∴．所以f （x ）的单调递增区间为．（3）∵，∵， ∴．∴．当，即时，f （x ）取得最大值1； 当，即时，f （x ）取得最小值．18.(本小题10分)（Ⅰ）证明：因为4a n -3S n =2，①所以当n =1时，4a 1-3S 1=2，解得a 1=2；当n ≥2时，4a n -1-3S n -1=2，②…3 分 由①-②，得4a n -4a n -1-3（S n -S n -1）=0， 所以a n =4a n -1，由a 1=2，得a n ≠0，故{a n }是首项为2，公比为4的等比数列．（Ⅱ）解：由（Ⅰ），得a n =2×4n -1． 所以b n =a n -4n =4n -1-4n ，则{b n }的前n 项和T n =（40+41+…+4n -1）-4（1+2+3+…+n ）=-4×=314-n -2n 2-2n19.(本小题12分)解：(1)由题中茎叶图可知，进入决赛的选手共13名，其中拥有“优先挑战权”的选手共3名．根据题意，X 的可能取值为0,1,2.P (X ＝0)＝＝， P (X ＝1)＝＝， P (X ＝2)＝＝.X 的分布列如下：E (X )＝0×＋1×＋2×＝.(2)由茎叶图可得2×2列联表如下：K 2＝≈5.584>5.024，因此在犯错误的概率不超过0.025的前提下可以认为进入决赛与选择的导师有关． 20. (本小题12分)证明：（Ⅰ）在直角梯形BCDE 中，由DE =BE =1，CD =2，得BD =BC =，由AC =，AB =2得AB 2=AC 2+BC 2，即AC ⊥BC ，又平面ABC ⊥平面BCDE ，平面ABC ⋂平面BCDE=BC 从而AC ⊥平面BCDE ，所以AC ⊥DE ，又DE ⊥DC ，从而DE ⊥平面ACD ； （Ⅱ）21.(本小题12分)解：（Ⅰ）椭圆过点Q （，1），可得+=1，由题意可得c =，即a 2-b 2=2，解得a =2，b =，即有椭圆C 的方程为+=1；（Ⅱ）直线l ：y =k （x -1）与x 轴交点C （1，0），y 轴交点D （0，-k ）， 联立，消y 得，（1+2k 2）x 2-4k 2x +2k 2-4=0，①设M （x 1，y 1），N （x 2，y 2），则x 1+x 2=，=（x2-1，y2），=（-x1，-k-y1），由，得：x1+x2==1，解得k=±．由k＞0得k=代入①得2x2-2x-3=0，x1+x2=1，x1x2=-，可得|MN|=•=•=．22.(本小题12分)解：（Ⅰ）当a=1时，f（x）=x2-ln x，f（1）=1，，f′（1）=1，∴函数f（x）在点（1，f（1））处的切线方程为x-y=0．（Ⅱ）∵f（x）=ax2-ln x，a∈R，∴此函数的定义域为（0，+∞），=，当a≤0时，f′（x）＜0恒成立，∴f（x）在（0，e]上是减函数，∴当x=e时，f（x）取得最小值f（e）=ae2-1=，解得a=＞0与a≤0矛盾；当a＞0时，令f′（x）=0，得(舍)，，在（0，）上，f′（x）＜0，在（，+∞）上，f′（x）＞0，∴当＜e，即a＞时，函数f（x）在（0，）上是减函数，在（，e）上是增函数，∴当x=时，f（x）取得最小值，令=，得a=，符合题意．当≥e，即0＜a≤时，函数f（x）在（0，e]是减函数，∴当x=e时，f（x）取得最小值，即ae2-1=，解得a=与0＜a≤矛盾．综上，存在a=，使函数f（x）在区间（0，e]上的最小值为．。
2020届海南省海南中学高三英语月考试题及答案解析
2020届海南省海南中学高三英语月考试题及答案解析第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项AIf you are sending a text message watching TV or listening to the radio, you may stop and give this your full attention. Multitasking shrinks (使.....萎缩)the brain? research suggests.A study found that men and womenwho frequently used several types of technology at the same time had less grey matter in a key part of the brain. University of Sussex researchers said, " Using mobile phones, laptops and other media devicessimultaneouslycould be changing the structure of our brains."Worryingly, the part of the brain that shrinks is involved in processing emotion. The finding follows research which has linked multitasking with a shortened attention span, depression , anxiety and lower grades at school.The researchers began by asking 75 healthy men and women how often they divided their attention between different types of technology. This could mean sending a text message while listening to music and checking e-mail, or speaking on the phone while watching TV and surfing the Internet. The volunteers were then given brain scans which showed they had less grey matter in a region called the anterior cingu-late cortex (ACC)(前扣带皮层).Scientists have proved that brain structure can be changed on exposure to fresh environments and experience.Other studies have shown that training—such as learning to play magic tricks or taxi drivers' learning the map of London―can increase grey matter densities (密度)in certain parts.Experts have also warned of the harmful impact technology can have on our memory and attention span. The University of California team conducted a survey of more than 18,000 people aged between 18 and 99，and found 20%had problems with memory. Researchers were shocked greatly by the 14 % of 18 to 39-year-old people who also worried about their memories.Multitasking may shorten attention span, making it harder to focus and form memories, the researchers said, adding that youngsters may be particularly affected by stress.1. The underlined word " simultaneously" in Paragraph 2 means "________，"A. on one's ownB. at no timeC. at the same timeD. by accident2. All of the following are possible effects of multitasking EXCEPT________ .A. saving timeB. a shortened attention spanC. lower grades at schoolD. depression and anxiety3. Which ofthe following can be the best title of this passage?A. Media multitasking is becoming more popularB. Multitasking shrinks the brainC. Multitasking may shorten attention spanD. People are worried about their memories.BWe asked four people who watched an online talk on technology and communication by Sherry Turkle for their opinions.Fred:The talk certainly gave me plenty of food for thought about how technology is changing our behaviour. People are constantly multitasking, whether it be emailing during meetings or texting in the checkout queue. It’s as if we can’t bear to miss out on what our online friends are up to, so we juggle the real and online world. My greatest concern is that we don’t give our brains a chance to switch off. It’sthese precious momentswhen we actually process information that helps us make important decisions.Jeremy:It was a fascinating talk and the speaker really hit the nail on the head with a couple of things. Take parental influence, for instance. How can we expect teenagers not to text while doing their homework when they witness their parents posting on social media while cooking the evening meal or waiting at a red light?Kath:So much of what the speaker said rang true. I honestly believe there’s a danger that the more connected we are, the more isolated we feel. I don’t think this is such an issue for my generation who’ve lived without technology for so long. We know how to be alone. But the under 20s are another kettle of fish. They’re so busy communicating that they never experience the feeling of solitude and run the risk of not learning how to enjoy their own company.Carl:I’m not sure to what extent I agree that people are more alone, but the way we communicate has certainly evolved. The speaker makes a good point about how we’re getting used to talking with machines like Siri or robots,which are totally lack of experience of human life. But despite such limitations, we seem to be expecting more from technology and less from each other.4. What does the underlined phrase “these precious moments” in paragraph 2 refer to?A. When our brains are free.B. When we emailing during meeting.C. When we texting in the checkout queue.D. When we juggle the real and online world.5. What suggestion may Jeremy give to the parents?A. Accompany their children when they are doing homework.B. Prevent their children using phone while doing homework.C. Set a good example for their children on using phone properly.D. Stop posting on social media in face of their children.6. What does Kath worry about the under 20s generation?A. They communicate more with others.B. They use more technology.C. It’s difficult for them to find companies.D. They don’t know how to be alone.7. What is Carl’s attitude towards the use of technology in communication?A. Favorable.B. Intolerant.C. Doubtful.D. Indifferent.CAccording to Oxford Dictionaries, morality means: “Principles concerning the distinction between right and wrong or good and bad behavior.” Though morality is a rather subjective subject, there are some principles that are universal across all cultures found by an Oxford University study: “help your family, help your group, return favors, be brave, obey superiors, divide resources fairly, and respect others’ property”. The fact that these morals are found across 60 cultures from around the world demonstrates that morality, though subjective, is the cornerstone of keeping our societies together. Here are some reasons to be moral: without morality, a social life is almost impossible to maintain; having a good reputation and having a clear conscience is psychologically healthy; and most philosophies regard unselfish and principled behavior as important.There is no doubt that without morals, a society cannot function effectively. A confused situation would appear, According to the Society of Morality, “We are social animals, and the actions we take-the things we do and the things we don’t do-have consequences on our environments and on the others around us. As a result, we need to be able to govern our behavior in the near term so as not to injure ourselves or our community in the long term. This system of controlling our actions and our thoughts in order to operate in a community is what we often refer to as morality”. Therefore, we need a set of morals in order to operate within a social circle and a socialenvironment. Acting immoral usually results in being excluded from social activities or being avoided by a society based on laws and cultural standards. Besides acting moral having a sociological need, it also has a psychological basis. Most people are concerned to some extent about their reputation. According to PsyPost, “A lot of economic models of human behavior assume that people are only rational (理性的) when they narrowly pursue their own self-interest, but history shows us that people are also tremendously concerned with being and appearing moral”. So, the fear of one’s reputation being damaged is often a strong motivator to be moral. And if someonehas been immoral,most people go out of their way to make sure no one finds out, or to correct the behavior in order to not be caught. This goes in line with conscience as well. People generally feel in a better psychological state if they feel that their conscience is clean. A dirty conscience can result in a lack of sleep, anxiety, internal stress, and even illness.On the side of philosophy, the study of ethics (伦理) comes into play. Most philosophers agree that one should rationally choose a set of standards of behavior in order to function. Though there is moral relativism, there are universal anthropological (人类学的) morals, as mentioned in the introduction. By the nature of our societies and cultures, we choose what we believe is right and wrong. But surprising, this rational behavior comes to a general agreement on morals. So, there is a fine line between moral relativism and moral absolutism. But the main thing to take away from this discussion is that philosophers generally believe that each individual has the right to rationally come up with a set of ethics to live by, and that it is healthy to do so.8. The author discusses morality (paragraph 1) in order to ________.A. explain the relationship between morality and cultureB. describe the moral rules found all around the worldC. contrast the distinction between right and wrongD. introduce the definition, principles and reasons of morality9. It can be inferred from the passage that ________.A. acting moral allows us to fit into group betterB. morality brings the system of controlling behaviorC. contrast the distinction between right and wrongD. introduce the definition, principles and reasons of morality10. Which of the following is the psychological basis for acting moral?A pursuit of self-interest. B. a clean conscience.C. The concern about reputation.D. a dirty conscience.11. What does the author advise us to do according to the last paragraph?A. To reach a general agreement on morals based on ethics.B. to carve one’s own sense of ethics to operate in this world.C. To choose between moral relativism and moral absolutism.D. To exclude philosophers’ beliefs and solution as well.DOlder adults with a better sense of smell may live longer than thosewho have a poor sense of smell, a new study suggests. The study was a project of researchers in theUnited Statesthat was ongoing for over 13 years. They asked nearly 2,300 men and women to identify 12 common smells. All the subjects were from 71 to 82 years of age. The researchers gave the adults scores, from 0 to as high as 12, based on how many smells they identified correctly.During the years of follow-up investigation, over 1,200 of the subjects died. When the study was launched, none of the adults were weak. They could walk a little under half a kilometer, climb 10 steps and independently complete daily activities. In the latest findings, the researchers noted that those with a weak nose were 30 percent more likely to die than people with a good sense of smell. The findings were reported last month in the scientific publication Annals of Internal Medicine.Honglei Chen, a doctor withMichiganStateUniversityinEast Lansing,Michigan, was the lead writer of a report on the study. He said the connection between a poor sense of smell and an increased risk of dying was limited to adults who first reported good-to-excellent health. This suggests that a poor sense of smell is an early and sensitive sign for worsening health before it is recognizable in medical tests. With a poor sense of smell, people are more likely to die of brain and heart diseases, but not of cancer or breathing disorders.The results also suggest that a poor sense of smell may be an early warning for poor health in older age that goesbeyond dementia or other neurodegenerative(神经变性的) diseases. These often signal the beginning of a weakening of the mind or body.12. What do you know about the study mentioned?A. The study involved researchers from the world.B. All the participants were of different ages.C. The study began to be performed about 13 years ago.D. 2 ,300 men and women were young and healthy.13. What was the situation like at the beginning of the study?A. More than 1,200 of the participants passed away.B. Many of the subjects were found with health problems.C. All the subjects were independent of others when walking.D. One third of the participants had a poor smell sense.14. What can be inferred from the last two paragraphs?A. People with a poor sense of smell have heart disease.B. You should be careful with your health if you smell poorly.C. People with a poor sense of smell won't suffer from cancer.D. Most of the elder people may have the dementia disease.15. Which is the best title for the passage?A. Strong Sense of Smell May Be Linked to Longer LifeB. Old People Tend to Have a Poor Sense of SmellC. A Number of Factors Result in Longer LifeD. Being Ill Means Losing the Sense of Smell第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020届海南省海南中学高三英语月考试卷及参考答案
2020届海南省海南中学高三英语月考试卷及参考答案第一部分阅读（共两节，满分40分）第一节（共15小题；每小题2分，满分30分）阅读下列短文，从每题所给的A、B、C、D四个选项中选出最佳选项A4 Best Drive--In Movie Theaters in the USColorado: Holiday Twin Drive--InAddress: 2206 S Overland Trail, Fort Collins, CO 80526, USAPhone: +1 970-221-1244The theater, open since 1968 and currently the most popular drive-in in the US, provides various special foods. The menu there even amazes meat-free customers. But please remember the outside food is forbidden here. Besides, the Rocky Mountains provide a pastoral (田园式的) backdrop to screenings, and sunsets usually don’t disappoint either. It also offers lots of unique events that go beyond the big screen.North Carolina: Hound’s Drive--InAddress: 114 Raven Cir, Kings Mountain, NC 28086, USAPhone: +1 704-739-4424Having only opened in 2016, it’s one of the newest theaters on the block. The drive-in features newer equipment and digital projection. People can bring their animal friends along.Florida: Fort Lauderdale Swap ShopAddress: 3291 W Sunrise Blvd, Fort Lauderdale, FL 33311, USAPhone: +1 954-791-7927The Florida favorite offers plenty ofways to have fun. With 14 screens, the self-proclaimed (自称的) world’s largest drive-in equals any indoor cinema in terms of capacity and programming. It also includes an 88-acre flea (跳蚤) market and a free Ferrari museum. It’s best to book tickets on the Internet ahead of time if you don’t want to wait in line.California: Mission Tiki Drive -InAddress: 10798 Ramona Ave, Montclair, CA 91763, USAPhone: +1 909-628-0511Let’s have fun in the old-school outdoor cinema in Montclair, California. Remember tickets are available at the ticket office only. It alternates (交替) up to eight new releases on four screens and hosts almost daily swapmeets where people can exchange things they no longer need. It also organizes classic car and lowrider meet-ups.1.What can people do in Holiday Twin Drive-In?A.Participate in somespecial activities.B.Enjoy the film with the latest equipment.C.Learn about the benefits of being meat free.D.Share home-made cookies while watching the film.2.Which of the following theaters is friendly to visitors with pets?A.Hound’s Drive- In.B.Mission Tiki Drive-In.C.Holiday Twin Drive-In.D.Fort Lauderdale Swap Shop.3.What do Fort Lauderdale Swap Shop and Mission Tiki Drive-In have in common?A.Both feature old-fashioned styles.B.Both allow booking tickets online.C.Both provide free museum exhibitions.D.Both offer chances to trade second-hand goods.BYellowstoneNational ParkbecameAmerica's first national park in 1872. The National Park Service was formed 44 years later in 1916.Yellowstone, which is mostly in the state of Wyoming, is considered an example of the success of the National Park System.Humans have been present in Yellowstone for more than 11,000 years.Yellowstone contains beautiful mountains, deep canyons(峡谷), lakes and rivers.The nameYellowstonecomes from the river running through the area. At first known as Rock Yellow River, it became known as theYellowstoneRiver.Yellowstoneis host to many different species of plants. However, the park is most distinctive because of what lies underneath it. It sits on top of an ancient super volcano, known as The Yellowstone Caldera. The caldera is 48 by 72 kilometers. And it remains an active volcano.It is believed that the last time the volcano erupted was one half million years ago. The area has had three major eruptions in the last three million years.Experts say it may erupt again in another 1,000 to 10,000 years. But each year, there are thousands of earthquakes atYellowstone. Most are too small to be felt by people visiting the park.Yellowstoneis filled with the beauty of many hot water springs. hot water and gasses are trapped under the earth. they rush to the surface in the form of hot water and steam.Old Faithful is The most famous one .Iteruptsabout every hour or hour and a half. The eruption can last from one and a half minutes up to 5 minutes. The amount of hot water it expels（排出）in that time can be as much as 31,000 liters or more.In addition to its beauty and wonder, Yellowstone is an animal sanctuary（保护区）. It is home to the largest group of wild animals in theUnited States. As you travel through the park, you can sometimes see them in their natural habitat and hear their calls .4. What wasYellowstonenamed after?A. RockYellow RiverB. The amazing mountains.C. The stones with yellow color1D. The first discovery inwyoming.5. What makesYellowstonequite unique?A. The scenery is beautiful.B. There are a lot of explorers.C. It’s home to many plants.D. Its location is very special.6. What does the underlined word“It”in Paragraph 5 refer to?A. The earth.B. Yellowstone.C.Old Faithful.D. TheYellowstoneCaldera.7. What can we infer from the text?A. The Yellowstone Caldera has been dead for years.B. Yellowstone is a shelter for the protected wildlife.C. Big earthquakes happen frequently atYellowstone.D.YellowstoneNational Parkhas attracted visitors for centuries.CEvery racehorse has different abilities．Like humans，some are short- distance runners，while others are marathoners．Figuring out which is which and how to pace them can be the difference between failure in the finish and taking the award home．Jockeys（赛马骑师）and trainers have traditionally relied on centuries of experience and data from previous races to plan their races．Amandine Aftalion，a mathematician in Paris，thought she could add to that．Since 2013，she has been analyzing the performances of world champion runners like Usain Bolt．She has found that short-distance runners tend to win when they start strong and gradually slow down toward the finish line．Butin medium-distance races，runners perform better when they start strong，settle down，and finish with a burst of speed．Her model shows how those winning strategies maximize the energy output of muscles reliant on two different pathways：powerful aerobic（有氧的）ones that require oxygen，which can be in limited supply duringa race，and anaerobic ones，which don't need oxygen but build up waste products that lead to tiredness．Aftalion wondered which strategy would be best for horses．So she and Quentin Mercier，anothermathematician，took advantage of a new GPS tracking tool inserted in French racing saddles（马鞍）．The two studied patterns in many races at the Chantilly racetracks north of Paris and developed a model that accounted for winning strategies for three different races：a short one(1，300 meters)，a medium one (1,900 meters)，and a slightly longer one (2,100 meters)，all with different starting points on the same track．The model takes into account not just different race distances，but also the size or friction fromthe track surface．The results might surprise jockeys who hold horses back early for bursts of energy in the last finish．Instead，a strong start leads to a better finish，the team found．“That doesn't mean those jockeys are wrong，though．If the start is too strong，it can bedevastatingas well，leaving the horse tired by the end，” Aftalion says．8. What should a runner do to get an award according to the text?A. Make a good start．B. Plan for the race early．C. Run slowly on the starting line．D. Try runningquickly all the time．9. What formed the basis for Aftalion's studying horse race?A The experience and data from previous horse races．B. The benefit of knowing horses' different abilities．C. The success in studying runners' winning strategies．D. The performance of horses on different race distances．10. What does the underlined word“devastating”in the last paragraph mean?A. Boring．B. Damaging．C. Astonishing．D. Puzling．11. What can we infer from the text?A. Runners have the same energy output of muscles．B. Aftalion's findings may help horses to win the race．C. What Jockeys and trainers do makes no sense to horses．D. World champion runners made a contribution to the study．DThe beach may seem like an inviting place to run on a cool summer morning, but is running on the sand good for your body? It can be, but it’s important to be aware of the challenges that some beach runners experience before you get ready.Running on the beach can be a good thing. It’s certainly different from running on a track or a pavement. Forstarters, sand can be a challenge because it has an uneven (不平坦的) surface. As you push off, you’re going to lose some of your push as the sand moves. So, you’re not going to be able to push yourself forward as you would on a track or a pavement. But this unevenness has anupside: It gives your body an extra workout, forcing you to exercise muscles that don’t get as much use during runs on firm surfaces. For example, your feet, ankles and lower back might feel sorer and more tired than usual after a beach run just because the surface is constantly moving and changing step to step.You also might feel sore afterward because beaches tend to slope (倾斜) down to the water. If you’re going for a long run on the beach, you might notice that one side of your body might feel sorer because you’re putting more pressure on it due to the slope.Some beach runners prefer to run barefoot — not wearing anything on feet. However, if you’re not used to barefoot running, start slowly and don’t run long distances at first. That’s because running barefoot uses more different muscles than running with shoes does, and it’s important to strengthen these muscles and adapt your feet. If you want to run barefoot and as long as you run carefully enough into it, go for it!Running on the sand can be a smart choice for you, because running on softer ground surfaces can reduce muscle damage.12. Why is it difficult to run on the beach for starters?A. The soft surface makes people fall over easily.B. People need to run carefully on its smooth surface.C. Running on its uneven surface takes much effort.D. It’s hard to keep one’s balance on its hard surface.13. Which of the following best explains “upside” underlined in Paragraph 2?A. Advantage.B. Reason.C. Character.D. Challenge.14. What’s the author’s attitude to barefoot running?A. Critical.B. Supportive.C. Doubtful.D. Uncaring.15. The passage can probably be found in ______.A. A primary school textbookB. A tourist guideC. A sports magazineD. A scientific report第二节（共5小题；每小题2分，满分10分）阅读下面短文，从短文后的选项中选出可以填入空白处的最佳选项。
2020届海南省定安县定安中学高三上学期第二次月考化学试题(解析版)
海南省定安县定安中学2020届高三上学期第二次月考一、选择题（本题共8小题，每小题2分，共16分。
在每小题给出的四个选项中，只有一项十符合题目要求的。
）1.下列分离和提纯的实验操作中，正确的是()A. 蒸发B. 过滤C. 蒸馏D. 分液『答案』D『详解』A．蒸发需要的仪器为蒸发皿，不能选烧杯，A错误；B．过滤需要玻璃棒引流，图中缺少玻璃棒，B错误；C．蒸馏时温度计测定馏分的温度、冷却水下进上出，则温度计的水银球应在支管口处，冷却水应下口进水，C错误；D．利用分液漏斗分离分层的液体混合物，图中分液操作装置合理，D正确；故选D。
2.下列离子方程式书写正确的是（）A. 氢氧化铁溶于氢碘酸中：Fe(OH)3+3H+=Fe3++3H2OB. 次氯酸钙溶液中通入过量的CO2：Ca2++2ClO-+H2O+CO2=CaCO3↓+2HClOC. 向100mL0.1mol·L-1的FeBr2溶液中通入0.015mol的Cl2：2Fe2++4Br-+3Cl2=2Fe3++2Br2+6Cl-D. 向明矾溶液逐滴加入Ba(OH)2溶液至铝离子刚好沉淀完全：Al3++SO42-+Ba2++3OH-=BaSO4↓+Al(OH)3↓『答案』C『详解』A．氢氧化铁溶于氢碘酸中的离子反应为2Fe(OH)3+2I-+6H+═2Fe2++I2+6H2O，故A错误；B．次氯酸钙溶液中通入过量的CO2 的离子反应为ClO-+H2O+CO2═HCO3-+HClO，故B错误；C．向100 mL 0.1 mol•L-1的FeBr2溶液中通入0.015 mol的Cl2 的离子反应为2Fe2++4Br-+3Cl2═2Fe3++2Br2+6Cl-，故C正确；D．向明矾溶液逐滴加入Ba(OH)2溶液至铝离子刚好沉淀完全的离子反应为2Al3++3SO42-+3Ba2++6OH-═3BaSO4↓+2Al(OH)3↓，故D错误；故答案为C。
3.已知2MO y x－+5S2－+16H+=2M2++5S↓+8H2O，则MO y x－中的x的值为（）A. 1B. 2C. 3D. 4『答案』A『解析』试题分析：根据电子的得失守恒可知5×2＝2×n，解得n＝5，即MO y x－在反应中得到5个电子，所以化合价是＋7价。
【月考试卷】海南省海口市2020届高三上学期第二次月考语文试卷(含答案)
2019-2020学年度第一学期第二次月考高三年级语文试题考生注意：本试卷时间150分钟，满分为150分。
一、现代文阅读（36分）（一）论述类文本阅读（本题共3题，9分）阅读下面的文字，完成1～3题。
中华文明的历史启示（节选）袁行霈①中华文明的历史启示之一，就是选择包容。
②包容，是中华文明固有的思想。
早在《尚书》中就有这样的话：“有容，德乃大。
”（《周书·君陈》）意思是有所包容，所成就的功德才能巨大。
《老子》也说：“容乃公，公乃王，王乃天，天乃道，道乃久。
”意思是：有所包容，就能臻于“公”，进而臻于“王”，臻于“天”，臻于“道”，臻于“久”。
这些虽然都是针对统治者而言的，但在中华文明中具有普遍的意义。
中华文明是一种包容性很强的文明，中国人常用“海纳百川”来形容一个人的气度胸襟，这四个字也可以用来形容中华文明的品格。
③越来越多的考古资料证明，中华文明的发祥地，不只是黄河流域，还包括长江流域。
越来越多的考古资料又证明，除了黄河流域和长江流域，还有许多文化遗存散布在全国各地。
中华文明的组成，既包括定居于黄河、长江流域，较早以农耕为主要生活来源的华夏民族创造的文明，也包括若干以游牧为主要生活来源的少数民族创造的文明。
中华文明的演进过程，是多种文明因素的整合。
整合的模式是以华夏文明为核心，核心向周围扩散，周围向核心趋同，核心与周围互相补充、互相吸收、互相融合。
汉族和汉族以外的少数民族，都为中华文明作出了重要的贡献。
例如：我们引为骄傲的山西应县木塔那样精美的建筑，便是契丹族所建立的辽代的杰作；蒙古族所建立的元朝，首次开辟了我国南北海运航线；满族所建立的清朝，出现了康乾盛世。
这些都为中华文明增添了精彩的一页。
④我们还可以以战国和唐代为例进一步说明中华文明的包容性。
战国时代儒家、墨家、道家、法家、名家、阴阳家等不同的学说和流派多元共存，自由争辩，这已是人所共知的事实。
我想强调的是，中华文明的包容性不只体现在统治者的包容性上，也体现在整个社会的包容性上。
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记事件C为“从样本仅使用A的学生中随机抽取1人，该学生上个月的支付金额大于
1000元”，事件D为“从样本仅使用B的学生中随机抽取1人，该学生上个月的支付
金额大于1000元”．
由题设知，事件C，D相互独立，且
P(C )
93 30
0.4,
P(D) 14 1 0.6 ． 25
所以 P( X 2) P(CD) P(C)P(D) 0.24 ，
ad1
3 2
∴an＝a1＋(n－1)d＝3＋2(n－1)＝2n＋1，
即 an＝2n＋1......................................................................................................5 分 (2)由已知，得 bn＝ a2n ＝2×2n＋1＝2n＋1＋1， ∴Tn＝b1＋b2＋…＋bn＝(22＋1)＋(23＋1)＋…＋(2n＋1＋1) ＝411－－22n＋n＝2n＋2－4＋n...... .....................................................................10 分
则由上个月的样本数据得 P(E)
1 C330
1 4060
．
答案示例1：可以认为有变化． 理由如下： P（E）比较小，概率比较小的事件一般不容易发生．一旦发生，就有理由认为本 月的支付金额大于2000元的人数发生了变化，所以可以认为有变化． 答案示例2：无法确定有没有变化．理由如下： 事件E是随机事件，P（E）比较小，一般不容易发生， 但还是有可能发生的，所以无法确定有没有变化．........................................12 分
2
34
3 12
所以 f (x) 的单调递增区间为[ 2k , 2k ] （ k Z ）................5 分 3 4 3 12
（2）由已知，有 sin( ) 4 cos( ) cos 2
45
4
所以 sin cos cos sin 4 (cos cos sin sin )(cos 2 sin 2 )
13．答案：5
14. 答案： 21 2
15. 答案：3
16.答案：15 .
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）
解析：(1)依题意，得
3a1
3 2 2
d
5a1
54 2
d
50, 解得
(a1 3d )2 a1(a1 12d )
34Tn＝24＋422＋423＋424＋…＋42n－42nn＋1＝2
(
1 4
1 42
1 43
1 44
1 4n
)
－ 2n . 4n＋1
＝2×
1 4
(1
1 4n
1 1
)
－ 2n ＝2－ 2 － 2n ＝2－ 6n＋8 ， 4n＋1 3 3×4n 4n＋1 3 3×4n＋1
4
2
海南中学 2020 届高三第二次月考数学试题
g(x) ex ax 在 (1,) 上是单调增函数，无最小值，不合；若 a e ，则
g(x) ex ax 在 (1, ln a) 上是单调减函数，在 (ln a,) 上是单调增函数，
g(x)min g(ln a) ，满足，故 a 的取值范围 a e ................................................4 分
4
4
当 sin cos 0 时，有 (cos sin )2 5 ， 4
1
海南中学 2020 届高三第二次月考数学试题
命题教师：康天策 审核: 屈 韬
由 是第二象限角，知 cos sin 0 ，此时 cos sin 5 ． 2
综上， cos sin
4
2 或 cos sin
5 ................12 分 2
19.(本小题满分 12 分)
解析：（1）2sin2
C
cos
2C
3
5 2
，1
cos
2C
cos
2C
3
5 2
cos 2C 1 cos 2C 2
3 2
18.（本小题满分 12 分）
解析：（1）因为函数 y sin x 的单调增区间为[ 2k , 2k ], k Z ，
2
2
由 2k 3x 2k （ k Z ） 2k x 2k （ k Z ）
2
4
（2）
在
上恒成立, 则
a
ex
,
a
1 e
,
f
( x)
1ห้องสมุดไป่ตู้x
a
1 ax x
(x
0)
①若
,令
得增区间为
；令
得减区间为
,
当
时,
；当
时,
；
当
时,
,当且仅当
时取等号.
故:
时,
有 个 零点；当
时,
有 个零点.
②若 a 0, 则 f (x) ln x, 易得 f (x) 有 1 个零点；
③若 a 0 ，则 f (x) 1 a 0 在 (0,) 上恒成立，即： f (x) ln x ax 在 (0,) x
上是单调增函数，当 x 0 时， f (x) ；当 x 时， f (x) ，此时，
f
(x)
有
1
个零点.综上所述：当
a
1 e
或
a
0
时，
f
(
x)
有
1
个零点；当
0
a
1 e
时， f (x) 有 2 个零点.
.........................................................12 分
P(X 1) P(CD CD) P(C)P(D) P(C)P(D)
0.4 (1 0.6) (1 0.4) 0.6 0.52 ，
P( X 0) P(CD) P(C)P(D) 0.24 ．
所以 X 的分布列为
X
0
1
2
P
0.24 0.52 0.24
故 X 的数学期望 E( X ) 0 0.24 1 0.52 2 0.24 1．.........................................................8 分 （3）记事件E为“从样本仅使用A的学生中随机抽查3人，他们本月的支付金额都 大于2000元”． 假设样本仅使用A的学生中，本月支付金额大于2000元的人数没有变化，
海南中学 2020 届高三第二次月考数学试题
命题教师：康天策 审核: 屈 韬
海南中学 2020 届高三第二次月考
数学试题
（参考答案）
一. 选择题（共 12 小题，每小题 5 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。请将答案填到答题卡，答在本试卷上无效。)
BBADB
DBCBC BD
二、填空题(本大题共 4 个小题，每小题 5 分，共 20 分)
sin
2C
3 2
，
cos
2C
6
3， 2
又 2C 7 C .
6
66
3
................................6 分
（2）由（1）可知 APC 为等边三角形，且 APB 2 ，
3
在APB中， PB
sin BAP
所以从全校学生中随机抽取 1 人，该学生上个月 A，B 两种支付方式都使用的概
40 0.4 率估计为 100 ．
................................................................................4 分
（2）X 的所有可能值为0，1，2．
3
海南中学 2020 届高三第二次月考数学试题
命题教师：康天策 审核: 屈 韬
22.（本小题满分 12 分）
解析：（1）
f
( x)
1 x
a
0
在
(1,)
上恒成立，则
a
1 x
,
x
(1,)
，故
a 1 . g(x) ex a ，若1 a e ，则 g(x) ex a 0 在 (1,) 上恒成立，此时，
3
53 2
20.（本小题满分 12 分）
..............................................................12 分
解析： (1)∵an＋1＝3Sn＋4，∴an＝3Sn－1＋4(n≥2)， 两式相减，得 an＋1－an＝3an，即 an＋1＝4an 又 a2＝3a1＋4＝16＝4a1， ∴数列{an}是首项为 4，公比为 4 的等比数列， ∴an＝4n.............................................................................................................6 分 (2)证明：∵anbn＝log2an，∴bn＝24nn ，∴Tn＝421＋442＋463＋…＋24nn ， 14Tn＝422＋443＋464＋…＋42nn＋1，两式相减得，