【英语】重庆市第一中学2018-2019学年高二下学期期中考试试题
2018-2019学年重庆市第一中学高二下学期期中考试数学试题(文)

重庆市第一中学2018-2019学年高二下学期期中考试(文) 注意事项:1. 答卷前,考生务必将自己的姓名、准考证号码填写在答卷上。
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第Ⅰ卷(选择题,共60分)一、选择题(本题共12小题,每小题5分,共60分. 在下列各题的四个选项中,只有一个选项是符合题意的)1.已知集合{}=1,0,1,2M -,{}230N x x x =-<,则MN =( ) A .{}0,1 B .{}1,0- C .{}1,2 D .{}1,2-2.当1m <时,复数2(1))m i i +-(为虚数单位在复平面内对应的点位于( ) A .第一象限 B .第二象限 C .第三象限 D .第四象限3.已知命题p q ∨为真,p ⌝为真,则下列说法正确的是( )A .p 真q 真B .p 假q 真C .p 真q 假D .p 假q 假4.设函数()241,0,log ,0x x f x x x ⎧-≤=⎨>⎩则12f ⎛⎫= ⎪⎝⎭( ) A .1- B .1 C .12-D .22 5.设,x R ∈则2x ≤“”是11x +≤“”的( ) A .充分而不必要条件 B .必要而不充分条件C .充分必要条件D .既不充分也不必要条件6.根据如下样本数据: x1 2 3 4 5 y 1a - 1- 0.5 1b + 2.5得到的回归方程为,y bx a =+若样本点的中心为(3,0.1),则b 的值为( )A .0.8B .0.8-C .2.3D . 2.3-7.已知双曲线()222210,0x y a b a b -=>>的渐近线与圆()2224a x a y ++=相切,则双曲线的离心率等于( )A .2B .3C .2D .233 8.下列函数中,既是奇函数,又在0+∞(,)上是增函数的是( ) A .()sin f x x = B .()x x f x e e -=+ C .3()f x x x =+ D. ()ln f x x x = 9.如右图所示是某几何体的三视图,则该几何体的体积为( )A .6432π+B .6464π+C .25664π+D .256128π+ 10.已知函数1,0(=2,0x x x f x x +<⎧⎨≥⎩())(),则不等式2(2)(34)f x x f x -<-的解集为( ) A .(1,2) B .(1,4) C .(0,2) D .4(1,]311.函数()f x 对于任意实数,都有()()f x f x -=与(1)(1)f x f x +=-成立,并且当01x ≤≤时,2()f x x =.则方程()02019x f x -=的根的个数是( ) A .2020 B .2019 C .1010 D .1009 12.已知函数()g x 满足121()(1)(0),2x g x g e g x x -'=-+且存在实数0x 使得不等式021()m g x -≥成立,则m 的取值范围为( )A .[0,)+∞B .[1,)+∞C .2∞(-,] D . 3∞(-,] 第Ⅱ卷(非选择题,共90分)二、填空题(本题共4小题,每小题5分,共20分)13.若函数()f x 的定义域为[2,3],-则函数(2)f x 的定义域是__________.14.若函数3()(1)2f x a x x a =+-+为奇函数,则曲线()y f x =在点(1,(1))f 处的切线方程为__________.15. 直线(1)y k x =-与抛物线24y x =交于,A B 两点,若4,AB =则弦AB 的中点到抛物线的准线的距离为__________.16.在正三棱锥P ABC -中,,,PA PB PC 两两垂直,且2,PA PB PC ===则正三棱锥P ABC -的内切球的半径为__________.解答题;共70分.解答应写出文字说明、证明过程或演算步骤.第17~21题为必考题,每个试题考生都必须作答.第22、23题为选考题,考生根据要求作答.17.(本小题满分12分)已知函数21lg(43)x y x x x-=+-+的定义域为M . (1)求M ;(2)当[0,1]x ∈时,求()42x x f x =+的最小值.18.(本小题满分12分)某校开展了知识竞赛活动.现从参加知识竞赛活动的学生中随机抽取了100名学生,将他们的比赛成绩(满分为100分)分为6组:[)40,50,[)50,60,[)60,70,[)70,80,[)80,90,[]90,100,得到如右图所示的频率分布直方图.(1)求a 的值;(2)在抽取的100名学生中,规定:比赛成绩不低于80分为“优秀”,比赛成绩低于80分为“非优秀”.请将下面的22⨯列联表补充完整,并判断是否有99.9%的把握认为“比赛成绩是否优秀与性别有关”?(结果精确到0.001) 优秀 非优秀 合计 男生40 女生 50合计100 参考公式及数据:22(),()()()()n ad bc K n a b c d a b c d a c b d -==+++++++19.(本小题满分12分)如右图所示,直三棱柱111ABC A B C -中,D 是BC 的中点,四边形11A B BA 为正方形.(1)求证:1A C //平面1AB D ;(2)若ABC ∆为等边三角形, 4BC =,求点B 到平面1AB D 的距离.20.(本小题满分12分)已知椭圆C 的中心在坐标原点,焦点在x 轴上,离心率为12,椭圆C 上的点到焦点距离的最大值为3.(1)求椭圆C 的标准方程;(2)斜率为12的直线l 与椭圆C 交于不同的两点,A B ,且线段AB 的中垂线交x 轴于点P ,求点P 横坐标的取值范围.21.(本小题满分12分)已知215(),(=122x f x e g x x x =--)(为自然对数的底数). (1)记()ln (),F x x g x =+求函数()F x 在区间[]1,3上的最大值与最小值;(2)若,k Z ∈且()()0f x g x k +-≥对任意x R ∈恒成立,求k 的最大值.选考题:共10分.请考生在第22、23题中任选一题作答,如果多做,则按第一题计分.22.(本小题满分10分)选修4—4:坐标系与参数方程已知在平面直角坐标系xOy 中,直线14:23x t l y t=--⎧⎨=+⎩(t 为参数),以原点为极点,轴的非负半轴为极轴,且取相同的单位长度建立极坐标系,曲线C 的极坐标方程为22sin().4πρθ=+ (1)求直线l 的普通方程及曲线C 的直角坐标方程;(2)设点P 的直角坐标为(1,2),-直线l 与曲线C 交于,A B 两点,求PA PB ⋅的值.23.(本小题满分10分)选修4—5:不等式选讲已知函数()21f x x a x =+--(1)当1a =时,求不等式()0f x >的解集;(2)若0a >,不等式()1f x <对x R ∈都成立,求a 的取值范围.。
重庆市第一中学校2023-2024学年高一上学期期中考试英语试题

重庆市第一中学校2023-2024学年高一上学期期中考试英语试题学校:___________姓名:___________班级:___________考号:___________一、阅读理解Paris is one of the most-visited destinations in the world. There are lots to explore and there’s delicious food on every comer. A relaxing trip to Paris takes a little bit of planning. Here are some tips for you to make your trip smooth.Planning your tripHave a valid passport for international travel. A passport costs $ 110 and takes 6-8 weeks to arrive after you apply.Booking FlightsThe cheapest period to fly is during the Spring time, especially if you can leave on the first three days of the week. You’ll save even more money by booking around 90 days in advance. In the summer months, tickets will be more expensive no matter when you book.Enjoying Your TimeVisit the Eiffel Tower.The Eiffel Tower is the most recognizable symbol of Paris. To avoid the crowds, go to the Eiffel Tower early in the morning. It costs €25 to go to the top, or €10 to climb to the first 2 levels on foot. See the Notre Dame Cathedral.At present, the Notre Dame Cathedral is not accessible to tourists due to the fire that ruined parts of the cathedral. However, you can still visit the outside of the cathedral.\ Go to the Louvre to world-famous art.The Louvre hosts the Mona Lisa along with 35, 000 other pieces of art. If you’re pressed for time, visit the highlights. The Louvre costs €15 at the museum or €17 in advance (to skip most of the line).Take a day trip to Versailles.If you have a day to spare, head to the palace of Versailles, around 14 miles southwest of the city. Take a tour to see King Louis XVI’s palace and gardens. It costs e 20 to visit the palace and grounds.1.How can one save the most money if booking plane tickets ahead of time?A.If he leaves on a Monday in June.B.If he leaves on a Wednesday in December.C.If he leaves on a Tuesday in May.D.If he leaves on a Thursday in March.2.Which tourist attraction is not open to visitors at the moment?A.The Notre Dame Cathedral.B.The Eiffel Tower.C.The Louvre.D.Versailles.3.Where is the text probably taken from?A.A course plan.B.A research paper.C.A travel brochure.D.An encyclopedia.My son loves hockey (曲棍球). As his supportive fan, I watched him paying in all the matches across half of USA this year, and I’ve learned that losing maybe best for kids.In his third season in 2022, my son’s team never lost more than three straight games. There was happiness, boasting, celebration, pizza. In short, it was a typically good youth hockey season. He improved as a player, but did not much change as a person.However, what happened the next year added its story to the legends of sporting inability. Not only weak but prettily bad, this team lost 40 of their first 50 games, most of the defeats coming in the course of two losing streaks (倒霉的时刻). For a time, I worried that these streaks would kill my child’s love of the game.But that’s not what happened. As bad as it got, the losing was clarifying. It kept out the kids who were in it less for the game than the glory, leaving just the die-hards behind. What started as a list of 17 of the team was cut down to 12. It was especially instructive for the kids. It taught him a great truth of the world: For everyone good, there is someone better.What more, the kids were learning the game in a way that only losing can teach. Each player got to play everywhere, to learn and appreciate the role of every position on the ice. They kept an eye on the payers from the other team too, studying and applying the tricks of success. In an effort to break the streak, they went back to basics, accepted the intelligence of the hockey ancients: If playing like a team, they can defeat a collection of all-stars; If doing small and unimportant tasks well, they can get the goal.This new team had personalities and could never be listed, no matter the score. They had learned the most important lesson: You can lose without being beaten. They squeaked into the state game, then made it all the way to the final, where the winner was decided in overtime(超时赛). When they lost that game and went into the handshake line, it was not as runners-up but as a team that had been made into winners in the only way that will stick — by losing.4.What does the author think about his son’s team in the third season in 2022?A.The team succeeded as a result of good luck.B.The team had an extremely impressive performance.C.The team didn’t live up to the author’s expectations.D.The team behaved rather badly in three straight games.5.What does the underlined word “clarify” refer to?A.The losing improved their teamwork.B.The losing made them better understand hockey.C.The losing helped them learn a great truth of the world.D.The losing kept true players instead of those for the glory.6.What can we infer from the last two Paragraphs?A.They became the winner finally.B.They didn’t start their training as beginners.C.They have personalities that can be counted.D.They applied themselves to improving their skill.7.According to the author, what have the son’s team learned?A.Falls seven times, stand up eight.B.The hardest fight is to fight oneself.C.God helps those who help themselves.D.Hope for the best, but prepare for the worst.Once I was chatting with some friends about the fact that we all have accents (口音), most of them replied proudly, “Well, I speak perfect English or Chinese.” But this kind of reply is nowhere near the point.More often than not, what we mean when we say someone “has an accent” is that their accent is different from the local one, or that their pronunciations are different from our own. But this understanding of accents is limiting and could cause prejudice (偏见). Funnily enough, in the language study, every person speaks with an accent. It is the regular differences in how we produce sounds that decide our accents. Even if you don’t hear ityourself, you speak with some sort of accent. In this sense, it’s pointless to point out that someone “has an accent”. We all do!Every person speaks a dialect (方言), too. In the field-of language study, a dialect is a version of a language that is characterized by its variations of structure, phrases and words. For instance, “You got eat or not?” (meaning “Have you eaten?”) is an acceptable and understood question in Singapore Oral English. The fact that this expression would cause a standard American English speaker to stop for a while doesn’t mean that Singapore Oral English is “wrong” or “ungrammatical”. The sentence is well-formed and clearly communicative, according to native Singapore English speakers’ system of grammar. Why should it be wrong just because it’s different?We need to move beyond a narrow understanding of accents and dialects-for the good of everyone. Language differences like these provide insights into people’s cultural experiences and backgrounds. In a global age, the way one speaks is a special part of who they are. Most people would be happy to talk about the cultures behind their speech. We’d learn more about the world we live in and make friends along the way.8.What does the author think of his friends’ reply?A.It suggests their impoliteness.B.It shows their language levels.C.It reflects their self-confidence. D.It misses the real meaning of accents. 9.Why does the author mention Singapore Oral English?A.To prove dialects are acceptable B.To correct a grammatical mistake.C.To show different types of English.D.To encourage more changes tolanguages.10.What is the last paragraph mainly about?A.We should be pround of our cultures.B.We should make friends more in the futureC.We should speak with our local dialect smote.D.We should treasure the value of accents and dialects.A.cultural researcher B.public speakerC.Chinese learner D.magazine editorsuggests smell is important in human relations, too. There is also evidence that human beings can lead to close relationship, deduce (推断) emotional states and even detect disease via the sense of smell.Now, Inbal Ravreby of the Weizmann Institute of Science in Israel has gone a step further. He think he has been able to prove, admittedly in a fairly small sample of individuals, that friends actually smell alike. He has also shown that with people picking friends at least partly on the basis of body odour (气味), rather than the body odours of people who become friends afterwards forming.But why? To cast light on whether friendship causes a similarity in smell, or a similarity in smell causes friendship, Dr Ravreby investigated whether e-nose (electronic nose) measurements could predict positive interactions between strangers (new friendships often start from being strangers). To achieve this goal they gathered 17 volunteers, gave them T-shirts to wear to collect their body odours, ran these odours past the e-nose and then asked the participants to play a game.That game involved silently mirroring another individual’s hand movements. Participants were paired up at random (随机) and their reactions were recorded. After each interaction, they show how close they felt to their fellow gamer by overlapping (部分重叠) two circles (one representing themselves, the other their partner) on a screen. The more similar the two smells were which are brought about by e-nose, the greater the overlap.But why body odour might play a role in helping to form friendships remains unclear. Dr Rav re by theorizes that there may be “an evolutionary advantage in having friends that are genetically similar to us”. Body odour is known to be linked to genetic makeup. Smelling others may thus allow hidden connections about genetic similarity to be drawn.12.What does the underlined sentence mean in Paragraph 1?A.People will sniff their friends in private.B.People will close their eyes when sniffing.C.Sniffing their friends is not allowed when they meet.D.Sniffing their friends is uncommon when they meet.13.According to Dr Ravreby, which comes first, friendship or similarity of smell?A.Friendship.B.Similarity of smell.C.It remains unclear.D.It depends.14.What can we learn from the experiment?A.It involves participants who are friends already.B.The e-nose can help predict a possible friendship.C.The overlap part shows the two smell alike.D.It aims to find out how close two people can be.15.What is the best title for the text?A.Genetic similarity — the start of our friendship.B.Dog’s sniff — the origin of our friendship.C.Body odour — the connection of our friendship.D.E-nose — the measurement of our friendship.Scientists at the University of Massachusetts(UMass) announced recently that they have worked out how to design a biofilm (生物膜) that collects the energy in evaporation (蒸发) and changes it to electricity. This biofilm, which was announced in Nature, has the ability to change the world of wearable electronics, powering everything from personal medical sensors (感应器) to personal electronics.“This is a very impressive technology,” says Li Xiumeng, a graduate student in electrical and computer energy, “and unlike other so-called ‘green-energy’ sources, its production is absolutely green.”That is because this biofilm—which is a sheet of bacterial cells (细菌细胞) and as thin as a sheet of paper—is produced naturally by an improved version of the bacterium Geo. Geo is known to produce electricity and has been used before in “microbial batteries” to power electrical equipment. But such batteries require that Geo be properly cared for and fed a continuous diet. By contrast, this new biofilm, which can supply as much energy as a battery of the similar size, works continuously, because it is dead. And because it is dead, it doesn’t need to be fed.The secret behind this new biofilm is that it makes energy from the moisture (水分) on your skin. While we daily read stories about solar power (太阳能), at least 50%of the solar energy reaching the earth goes toward evaporating water. “This is a huge, undiscovered source of energy,” says Ye Xun, professor of electrical and computer engineering at UMass, and the paper’s one senior author. Since the surface of our skin is always wet with sweat, the biofilm can make use of it and change the energy locked in evaporation into enough energy topower small equipment. “Our next step is to increase the size of our film to power more smarter wearable electronics,” says Ye, and Li points out that one of the goals is to power entire electronic systems, rather than single equipment.16.Which can biofilm do according to Paragraph 1?A.Invent wearable electronics.B.Get power from evaporation.C.Supply energy to microbial batteries.D.Produce more electricity than before.A.it is relatively thinner B.it is environmentally friendlyC.it applies a rare energy source D.it decreases the cost in usage 18.What do Ye and Li think of the future of the biofilm?A.Doubtful.B.Bright.C.Unclear.D.Harmful. 19.What is the purpose of the text?A.To introduce us to a new biofilm.B.To describe the disadvantages of the biofilm.C.To compare the new biofilm with others.D.To change people’s view on the new biofilm.二、七选五Signs That You Are GrowingGrowing is a lifelong process. Here are the signs that show that you are actually growing and not getting stuck in the process.20Often, we see how badly people look when they get overly upset due to unimportant things. So the first sign of maturity (成熟) is letting the small things go and not getting angry over a tiny detail that didn’t go as you planned.You start forgiving and understanding other peopleWhen we are young, we are often unforgiving. As we mature, we are better able to understand the world beyond black and white. 21 . It enables us to look beyond the obvious and let go of simple judgments. We begin to understand better that others have complex (复杂的) lives and personalities, and so we become more willing to forgive their mistakes.You always complete things that matterImmature people don’t know when to commit (承诺) themselves and their energy or resources are always not well employed. 22 . In this way, they can often keep their promises and honor their commitments.You accept the possibility of being wrong23 . They are always able to accept the possibility that they are wrong, that they don’t know something, because there is always more to learn.Being mature is knowing that you are always growing up. You are never done learning and developing. This means that you don’t set yourself up as the highest authority.24 .A.You follow the crowdB.You let the small things goC.Instead, mature people focus on completing things that matterD.Immature and mature people can both have plans for their livesE.Rather, you open your mind to other ideas and new possibilitiesF.Becoming more understanding is a sign of strength, not weaknessG.Mature people appear more confident, however, they are not overconfident三、完形填空I embarked on an overnight bus journey from Kolhapur to Aurangabad in India. Thethe discomfort of the 10-hour journey. Because I was travelling on a student bus pass I had no34 .Just then, something 35 happened. Our observer stood up and offered his seat to another standing man. All of a sudden, we had unexpectedly caused a chain reaction: almost all the standees got a(n) 36 to be seated. More surprisingly, people even started chatting with each other while exchanging their positions, and soon began sharing jokes. Needless to say, the rest of the journey was quite 37 .The bus reached its destination the next morning. I stood in the early morning light, waving goodbye to the groups, who went their separate routines. But this extraordinary experience has stayed with me after all the years. I am always 38 of an important life lesson—that we can all 39 what we have, including our burdens, and help our co-passengers in the journey of life.25.A.narrowed B.packed C.advanced D.delayed 26.A.standing B.sitting C.lying D.moving 27.A.applied for B.made up C.added to D.worked out 28.A.rain B.water C.tears D.sweat 29.A.gave B.held C.supplied D.sensed 30.A.company B.help C.contact D.attention 31.A.advice B.seat C.hand D.instruction 32.A.frightened B.surprised C.awkward D.confident 33.A.take back B.set up C.cut in D.give out 34.A.adventure B.conversation C.deal D.exchange 35.A.confusing B.powerful C.magical D.positive 36.A.challenge B.goal C.arrangement D.chance 37.A.enjoyable B.glorious C.shocking D.admirable 38.A.warned B.reminded C.freed D.affected 39.A.throw B.deliver C.share D.track四、用单词的适当形式完成短文阅读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式。
重庆市第一中学校2018-2019学年高一上学期期末考试物理试题+Word版含答案

重庆一中高2021届(一上)期末考试物理测试试题卷2019.1一、单项选择题:本题共10小题,每小题3分,共30分。
在每小题给出的四个选项中,只有一项符合题目要求,选对得3分,选错得0分1.在国际单位制中,力学的三个基本单位是A.牛顿、厘米、秒B.千克、米、秒C.千克、秒、焦耳D.牛顿、秒、米/秒2.最早将实验和逻辑推理(包括数学演算)和谐地结合起来,从而发展了人类的科学思维方式和科学研究方法的科学家是()A.亚里士多德B.爱因斯坦C.笛卡尔D.伽利略3.一起严重的交通事故中,一辆越野车与一辆面包车迎面相撞,面包车车头凹陷、变形,几乎报废,而越野车仅前保险杠稍微变形。
关于此次碰撞,下列说法正确的是()A.越野车发生形变使面包车受到作用力B.越野车对面包车的作用力大于面包车对越野车的作用力C.越野车撞击面包车的时间比面包车撞击越野车的时间长D.越野车对面包车的作用力和面包车对越野车的作用力是一对平衡力4.下列有关惯性的说法中正确的是(A.物体仅在静止和匀速直线运动状态时才具有惯性B.汽车速度越大越不容易停下来,是因为速度越大惯性越大C.在月球上举重比在地球上容易,所以质量相同的物体在月球上比在地球上惯性小D.歼击机战斗前抛掉副油箱是为了减小惯性5.如图所示,在平原上空水平匀速飞行的轰炸机,每隔1s投放一颗炸弹,若不计空气阻力,下列说法正确的是A.落地前炸弹排列在同一条抛物线B.炸弹落地时速度大小方向都相同C.相邻炸弹落到水平面上时距离逐渐增大D.相邻炸弹在空中的距离保持不变6.如图,在光滑水平面上,质量分别为M和m的物体A和B相互接触,已知M>m,第一次用水平力F由左向右推A,物体间的相互作用力为F1;第二次用同样大小的水平力F由右向左推B,物体间的相互作用力为F2,则()A.F I=F2B.F I<F2C. F1>F2D.无法确定7.甲、乙两物体同时同地沿同一方向做直线运动的D-图像如图所示,则A.甲、乙两次相遇的时刻为10s末和第40s末B.在第50s末,甲在乙的前方C.甲、乙两次相遇的时刻为20s末和第60s末D.经20s后乙开始返回8.如图所示,位于水平地面上的质量为M的木块,在方向与水平面成a角、大小为F的拉力作用下,沿地面做匀加速直线运动,若木块与地面间的动摩擦因数为,则木块的加速度为()A.错误!未找到引用源。
四川省遂宁市第一中学2023-2024学年高二下学期4月期中考试英语试题

四川省遂宁市第一中学2023-2024学年高二下学期4月期中考试英语试题一、阅读理解Babysitter(保姆) WantedI am seeking a babysitter for my 6-month-old son. A few hours on Saturdays and Sundays to help me and then other times as needed. He or she should be over 18, responsible, loving, warm, and have some experience in caring for babies. This position also suits a college student with experience looking for a part-time job. The pay is $10 an hour.Ifthissoundslikeagoodjobtoyou,***************************************-4964.Office Manager WantedOur company is looking for a full-time experienced manager to run the business. Strong skills in organization and business management are required for this position. The office manager will be responsible for keeping financial (财务的) records, so he or she should be familiar with computers.************************************************-6978 to apply.Waiter/ Waitress WantedA restaurant is looking for an experienced waiter / waitress. Knowledge of wines and experience in dining are necessary. Must work well under pressure and understand the basics (基本要素) of fine dining and customer service.If you’re interested, please contact us at job-tkupe-********************************.This is a part-time job.Office Cleaner WantedLooking for a Part-time job? A position in the Mississauga area needs an office cleaner! Part-time 4 hours a day from 10:00 am - 2:00 pm.Duties include:●Cleaning the washrooms●Cleaning the furniture●Sweeping the floors●Other general cleaning experience is necessary. Pay: $15 per hourReply to:job-p3b7u-**********************************-8197.1.Which of the following position is a full-time job?A.Babysitter.B.Office manager.C.Waiter / waitress.D.Office cleaner.2.If a college girl with some experience caring for children wants to apply for a job, where should she send an email?A.job-p3b7u-*************************B.job-tkupe-*************************C.**************************D.*****************3.Which of the following is necessary for a waiter / waitress?A.Being familiar with computers.B.Having knowledge of wines.C.Knowing more about menus.D.Working well with others.Sitting in the classroom I felt confused, for I couldn’t read the blackboard. Then Mum took me to the hospital. Within a few days, I was diagnosed (诊断) with a severe visual impairment (视力障碍). In fact, I was practically blind. Amazingly, I’d managed to reach the age of 13 without anyone realizing, not even me! “It all makes sense now,” Mum said. As a kid living on a farm, I was forever falling over things. I was known as the clumsy (笨拙) one to my parents and four sisters. But now, I was being told that I saw the world differently — I could only make out the outlines of things. I was given reading glasses but they didn’t help much.Refusing to let my diagnosis hold me back, I continued doing everything I loved. As long as everything was in its place, I could feel my way around.Later I got married to Lance and had amazing kids. I could change nappies (尿布) and dress the kids fine — it just took a little longer as I relied on touch to work out where things were. Cooking, on the other hand, was not my forte. I was terrible — always mixing up sugar and salt!Nowadays, my grandkids have all been brought up not to leave toys on the floor or movechairs away from the table. “We don’t want Grandma tripping,” Lance will say.Over the year, I’ve enjoyed lovely family holidays, but sometimes felt like Lance or the kids were too protective of me. So I was thrilled when I booked myself on a trip to the Gold Coast with people who were just like me in a travel company. I’m not missing out — my life is beautiful. I’m so lucky to have a wonderful family and lots of experiences.Life is precious — you don’t need to “see” that.4.What can we know from the first paragraph?A.The reading glasses got the problem fixed.B.She always tripped because she was awkward.C.She got severe visual impairment at the age of 13.D.Nobody realized her sight was poor until she was 13.5.What does the underlined word “forte” in Paragraph 3 mean?A.Weakness.B.Favourite.C.Strength.D.Business.6.What can we know about the author?A.She is able to see things clearly now.B.She led a lonely and hopeless life.C.She could help care for the kids.D.She went to the Gold Coast all by herself.7.What can we learn from the author’s story?A.We need to go to travel frequently on our own.B.We should always turn to the family for help.C.Everyone should pay special attention to the blind people.D.Everyone can enjoy the beauty of life with a positive mind.Dog owners walked about 23minues longer each day than non-dog owners In a new study, dog owners took 2,760 additional seps—compared to people who didn’t have a dog at home. Bu here’s the real good news: That extra exercise was done at a moderate(适度的)pace, which means it could help adults meet their recommended weekly totals for physical activity.The research, published in BMC Public Health, focused on adults 65 and older, who tend to be less active than younger people. The study included 43 dog owners and 43 non-dog owners, allof whom were monitored continuously for three week-long periods. When they compared the two groups, the researchers found that dog ownership was associated with a large, potentially health-improving effect.Dog owners walked about 23 minutes longer each day than non-dog owners, 119 minutes versus 96 minutes on average. They also took an additional 2,760 steps, and had eight fewer continuous periods of sitting down. Most of that extra walking was done at moderate pace, defined as 100 or more steps a minute. Dog owners walked at this pace for 32 minutes a day, versus just 11 minutes a day for non-dog owners.The World Health Organization(WHO)recommends that adults get at least 150 minutes of physical activity a week. This increased walking time alone could just about satisfy that requirement, say the researchers—so it makes total sense that 87 percent of dog owners in the study met these guidelines, versus just 47 percent of non-dog owners.Co-author Nancy Gee says that pet ownership may help older adults get more activity or maintain their current activity level for a longer period of time. “This could improve their chances of a better quality of life, improved or maintained cognition(认知), and perhaps, even overall longevity(寿命),”she said.Here at Health, we’ ll add that caring for pets has been shown to have plenty of other physical and mental health benefits, as well. As animal lovers ourselves, we’ re happy to add one more to the list.8.What can we learn about the research?A.It was targeted on old people.B.It was sponsored by the WHO.C.It had an undesirable effect on dog owners.D.It took the mental health of dog owners into consideration.9.What does the author intend to do in Paragraph 3?A.To present the results of the research.B.To show the guidelines of the research.C.To describe the process of doing the research.D.To explain the reasons for conducting the research.10.What does Nancy Gee think of owning a dog?A.It is too expensive.B.It is time-consuming.C.It enables older adults to live a healthy life.D.It helps young adults to keep a healthy routine.11.What is the best title for the text?A.Non-pet owners enjoy more pleasureB.Animal lovers are more generousC.Young people walk less todayD.Dog owners walk way moreThe Amazon rainforest is as undisturbed a place as most people can imagine, but even there, the effects of a changing climate are playing out. Now, research suggests that many of the region’s most sensitive bird species are starting to evolve in response to warming.Birds are often considered sentinel (哨兵) species — meaning that they indicate the overall health of an ecosystem — so scientists are particularly interested in how they’re responding to climate change. In general, the news has not been good. For instance, a 2019 report by the National Audubon Society found that more than two-thirds of North America’s bird species will be in danger of extinction by 2100 if warming trends continue on their current course.For the new study, researchers collected the biggest database so far on the Amazon’s resident birds, representing 77 non-migratory species and lasting the 40 years from 1979 to 2019. During the study period, the average temperature in the region rose, while the amount of rainfall declined, making for a hotter, dryer climate overall. According to the report on November 12 in the journal Science Advances, 36 species have lost substantial weight, as much as 2 percent of their body weight per decade since 1980. Meanwhile, all the species showed some decrease in average body mass, while a third grew longer wings.Because of the study’s long time series and large sample sizes, the authors were able to show the morphological (形态学的) effects of climate change on resident birds. However, the researchers themselves are unsure and wonder what advantage the wing length changes give the birds, but suppose smaller birds may have an easier time keeping cool. In general, smaller animals have a larger rate of surface area to body size, so they dissipate more heat faster than a biggeranimal. Less available food, such as fruit or insects, in dryer weather might lead to smaller body size.12.Why are scientists fond of doing research on birds?A.They have small body sizes.B.They are sensitive to hot weather.C.They are ecological balance indicators.D.They live in an undisturbed rainforest. 13.What can we learn from the new study?A.Two-thirds of species showed a considerable decrease in weight.B.About 26 species responded to climate change with longer wings.C.36 species lost 2% of their body weight every year from 1979 to 2019.D.A third of species have been extinct for a decade due to the hotter climate.14.What does the underlined word “dissipate” in the last paragraph mean?A.Put off.B.Give off.C.Put away.D.Give away. 15.What would probably the researchers further study?A.Why it is easier for smaller animals to keep cool.B.Why the Amazonian birds have lost substantial weight.C.Whether bird species in Amazon will be extinct in 2100.D.What effects the wing length changes have on birds.In the modern busy life, there are a large number of immigrants (移民) who have been willing to have a comfortable life in other nations. Many advocate that people should follow the local customs and traditions when they settle in a new country. 16 People will face problems and enjoy benefits from local customs.There are two important reasons why new comers should bring themselves into the local culture in the host country. Firstly, the refusal to adapt to host environment would create a cultural barrier for immigrants. 17 The loneliness in turn has negative influences on people’s life.Secondly, it is true that limited knowledge of local customs may result in some illegal actions in the host country and make local people unpleased. For instance, Singapore is one of the cleanest countries in Asia. 1819 One is that if immigrants behave in agreement with the local norms (规范), they will be accepted easily by local people. As a result, they can easily gain respect as well as helpfrom the local. For example, when a company wants to expand its production in a new country, it must be aware of business practices there, which provides it with useful information to maximize profits. Another benefit is that newcomers might gain the richness of knowledge through the local customs and traditions. 20 In many festivals, people are able to join freely and feel harmonious like their own country.A.It also creates social loneliness.B.Visitors are asked to clean the street.C.Personally, I strongly agree with this idea.D.They will be appreciated and offered a good job.E.It enables them to join in the activities of the community.F.Anyone who leaves rubbish in public is considered ill-mannered.G.Newcomers can gain some benefits if they adopt the customs of a new country.二、完形填空I’ve been having a really hard time lately with the very recent loss of my father and work-related stress. I went back to 21 after taking one day off and was having a very 22 , tear-filled day.My job took me around the city. As I was 23 a busy street, I saw a homeless man who 24 himself with a blanket(毛毯). His feet were sticking out with no shoes. A 25 wind was sweeping through the street. I rushed to a shop without thinking, and bought him some 26 and gloves. I left them beside him to find when he woke up. Then he could at least be a little warmer.The next day I came back to the street, still feeling sad, still 27 , when two ladies 28 me to ask if I was the girl who left socks and gloves to that homeless man yesterday. I said yes and they 29 told me how they 30 to buy him a big warm jacket after seeing me and then another person give him some warm and 31 clothes. One of the ladies said I was a 32 . Now as she meets with me in that 33 , she greets(问候)me “Hey, my hero!”I think what I did meant nothing, but I hope it made that man’s day a little better and a little34 . At least, he could stay warm. Those ladies really filled my heart with 35 on the winter day.21.A.school B.work C.hospital D.sleep 22.A.common B.boring C.difficult D.funny 23.A.walking down B.looking for C.thinking of D.coming across 24.A.shared B.covered C.provided D.filled25.A.hot B.cool C.calm D.cold 26.A.socks B.shoes C.jackets D.trousers 27.A.wondering B.improving C.struggling D.pretending 28.A.cheated B.stopped C.pushed D.punished 29.A.shyly B.painfully C.secretly D.excitedly 30.A.failed B.needed C.offered D.refused 31.A.comfortable B.big C.formal D.old 32.A.buyer B.guest C.teacher D.hero 33.A.way B.street C.shop D.year 34.A.longer B.safer C.easier D.harder 35.A.wealth B.credit C.spirit D.warmth三、语法填空阅读下面短文,在空白处填入1个适当的单词或括号内单词的正确形式。
2022-2023学年重庆市第一中学高二下学期期中数学试题

2023年重庆一中高2024届高二下期期中考试数学测试试题卷注意事项:1.答题前,考生务必用黑色碳素笔将自己的姓名、准考证号、考场号、座位号在答题卡上填写清楚.2.作答时,务必将答案写在答题卡上,写在本卷或者草稿纸上无效.3.考试结束后,请将本试卷和答题卡一并交回.满分150分,考试用时120分钟. 一、选择题:本题共8小题,每小题5分,共40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. 设命题:,,则为( )p R x ∀∈e 1xx ≥+p ⌝A. , B. , R x ∃∈e 1x x ≥+R x ∀∈e 1x x <+C. ,D. ,R x ∃∈e 1x x <+R x ∀∈e 1≤+x x 2. 设,则( )9290129(12)x a a x a x a x -=++++ 1a =A. B. C. D.2-18-2183. 下图是根据某班学生体育测试成绩画出的频率分布直方图,由直方图得到的中位数为( )A. B. C.D.6572.57321534. 某学校为举行校园艺术节活动,共有个节目,要求节目不排在最后且节目相6A ,C D 邻,则节目安排的方法总数为( ) A.B.C.D.48961922405. 已知抛物线,直线交该抛物线于两点.若线段的中点坐标为2:4G y x =l ,A B AB ,则直线斜率为()()3,2l A.B.C. D.1214126. 已知函数有两个极值点, 则实数的取值范围是( ) ()2ln f x k x x x =-+k A.B.C.D.1,8⎛⎫-∞ ⎪⎝⎭1,8⎛⎫+∞ ⎪⎝⎭(),1-∞-10,8⎛⎫ ⎪⎝⎭7. 已知,则的最小值是( )0x y >>222x y xy y +-A. B.2+2+C.D.228. 已知随机变量的分布列服从,记X ()~,X B n p ()()(),1f n p P X n P X n ==-+=,在上的最大值为,若正整数满足,则(),f n p 10,2p ⎡⎤∈⎢⎥⎣⎦()F n ,a b 2003a b >>和的大小关系是( )()F a ()F b A. B. ()()F a F b <()()F a F b =C.D. 无法确定()()F a F b >二、选择题:本题共4小题,每小题5分,共20分.在每小题给出的选项中,有多项符合题目要求.全部选对的得5分,部分选对的得2分,有选错的得0分.9. 下列结论中,所有正确的结论是( )A. 当 0x >2≥B. 若时,a b <a b <C. 若,则 ,0x y z x y z <<++=xz yz >D. 当时,的最小值为 3x >-13y x x =++1-10. 下列说法中,正确的命题有( ) A. 已知随机变量服从正态分布,,则ξ()2N 2,δ(4)0.84P ξ<=(24)0.16P ξ<<=B. 以模型去拟合一组数据时,为了求出回归方程,设,求得线性回归方e kx y c =ln z y =程为,则 的值分别是和0.3 ˆ0.34zx =+,c k 4e C. 8个完全相同的球放入编号为1,2,3的三个空盒中,要求放入后3个盒子均不空且数量均不同,则有12种放法D. 若样本数据的方差为2,则数据,,的方差为129,,,x x x 1132x +2132x +91...,32x +411. 已知某一物品的单件回收费为,根据以往回收经验可得,随机变量0,,2X a =02a <<的分布列如图所示,其中结论正确的是( )X X 0a2 P1214bA 14b =B. 若该物品4件,其中2件单件回收费为2的概率为9256C. 若该物品4件,单件回收费不为0的件数为,则 Y ()2E Y =D. 当时,取得最小值 23a =()D X 12. 小明与小兵两位同学计划去科技博物馆参加活动.小明在如图的街道E 处,小兵在如图的街道F 处,科技博物馆位于如图的G 处,则下列说法正确的是( )A. 小明到科技博物馆选择的最短路径条数为126条B. 小兵到科技博物馆选择的最短路径条数为4条C. 小明到科技博物馆在选择的最短路径中,与到F 处和小兵会合一起到科技博物馆的概率为1021D. 小明与小兵到科技博物馆在选择的最短路径中,两人约定在科技博物馆门口汇合,事件A :小明经过F ;事件B :从F 到科技博物馆两人的路径没有重叠部分(路口除外),则()29P B A =三、填空题:本题共4小题,每小题5分,共20分.13. 一个袋子中装有大小和质地均相同的3个黑球和和2个白球,则从中摸出2个球恰好是1个黑球和1个白球的概率为________.14. 若随机变量,且,则的值是________. (),0.8X B n ()4E X =()1P X =15. 有两个分类变量和,其中一组观测值为如下的列联表:x y 22⨯1y2y 总计1xa10a -102x10a -20a +30 总计103040其中均为大于的整数,则________时,在犯错误的概率不超过0.01的前提,10a a -3=a 下为“和之间有关系”.附: x y ()()()()()22n ad bc K a b c d a c b d -=++++()2P K k ≥ 0.10 0.05 0.025 0.0100.005k 2.706 3.841 5.024 6.6357.87916. 某靶场有两种型号的步枪可供选用,其中甲使用两种型号的步枪的命中率分,A B ,A B 别为.现在两把步枪中各装填3发子弹,甲打算轮流使用两种步枪进行射1,314,A B ,A B 击,若击中标靶,则继续使用该步枪,若未击中标靶,则改用另一把步枪,甲首先使用A 种型号的步枪,若出现连续两次子弹脱靶或者其中某一把步枪的子弹打光耗尽的现象便立刻停止射击,记为射击的次数,则________.X ()5P X ==四、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. 已知集合和非空集合 {}2870A x x x =-+≤{}121B x m x m =+≤≤-(1)若,求;5m =A B ⋂(2)若“”是“”的必要不充分条件,求实数的取值范围. x A ∈x B ∈m 18. 根据国家统计局统计,我国2018—2022年的新生儿数量如下:年份编号 x 12345年份2018 2019 2020 2021 2022新生儿数量(单位:万人) y 1523 1465 1200 1062 956(1)由表中数据可以看出,可用线性回归模型拟合新生儿数量与年份编号的关系,请y x 用相关系数说明相关关系的强弱;(,则认为与线性相关性很强) r 0.751r ≤≤y x (2)建立关于的回归方程,并预测我国2025年的新生儿数量. y x 参考公式及数据:rn∑i =1x i y i ‒nx ⋅yb n∑i =1x i y i ‒nx ⋅ya y ‒bx ,5∑i =1y i=6206,5∑i =1y i =6206, i ≈1564.19. 已知双曲线,焦点为,其中一条渐近线的倾斜角为()2222:10,0x y C a b a b-=>>12,F F ,点在双曲线上,且.30 M 12MF MF -=(1)求双曲线的标准方程;C (2)若直线交于两点,若,求正实数的值. :l y x m =+C ,A B AOB m 20. 已知正项数列满足:;为数列为的前项{}n a 22111230,3n n n n a a a a a ++--==n T {}n b n 和,,对任意的自然数,恒有. 222b a =-n 23n n T nb n =+(1)求数列的通项公式及其前项和;{}n a n n S(2)证明:数列是等差数列,并求其通项公式.{}n b 21. 在全球抗击新冠肺炎疫情期间,我国医疗物资生产企业加班加点生产口罩、防护服、消毒水等防疫物品,保障抗疫一线医疗物资供应,在国际社会上赢得一片赞誉.我国某口罩生产厂商在加大生产的同时,狠抓质量管理,不定时抽查口罩质量.该厂质检人员从某日生产的口罩中随机抽取了100个,将其质量指标值分成以下五组:,[)100,110,,, ,得到如下频率分布直方图.规定:口[)110,120[)120130,[)130140,[]140,150罩的质量指标值越高,说明该口罩质量越好,其中质量指标值低于130的为二级口罩,质量指标值不低于130的为一级口罩.(1)将上述质量检测的频率视为概率,现从该工厂此类口罩生产线上生产出的大量口罩中,采用随机抽样方法每次抽取1个口罩,抽取8次,记被抽取的8个口罩中一级口罩个数为.若每次抽取的结果是相互独立的,求的方差;ξξ(2)现从样本口罩中利用分层抽样的方法随机抽取8个口罩,再从中抽取3个,记其中一级口罩个数为,求的分布列及数学期望;ηη(3)在2023年“五一”劳动节前,甲、乙两人计划同时在该型号口罩的某网络购物平台上分别参加两店各一个订单“秒杀”抢购,其中每个订单由个该型号口,A B ()2,Nn n n *≥∈罩构成.假定甲、乙两人在 两店订单“秒杀”成功的概率分别为,,记,A B 2πnπ2cosn n甲、乙两人抢购成功的口罩总数量为,求当的数学期望取最大值时正整数X X ()E X n 的值.22. 已知函数. ()()()3211e R ,e 23axx f x x a g x x mx =+∈=-+(1)讨论函数在上的单调性;()f x ()0,∞+(2)若,当时,判断函数的零点个数.()()()h x f x g x =-1,0a m =≥()h x2023年重庆一中高2024届高二下期期中考试数学测试试题卷一、选择题:本题共8小题,每小题5分,共40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. 设命题:,,则为( )p R x ∀∈e 1xx ≥+p ⌝A. , B. , R x ∃∈e 1x x ≥+R x ∀∈e 1x x <+C. , D. ,R x ∃∈e 1x x <+R x ∀∈e 1≤+x x 【答案】C2. 设,则( )9290129(12)x a a x a x a x -=++++ 1a =A. B. C. D.2-18-218【答案】B3. 下图是根据某班学生体育测试成绩画出的频率分布直方图,由直方图得到的中位数为( )A. B. C.D.6572.5732153【答案】D4. 某学校为举行校园艺术节活动,共有个节目,要求节目不排在最后且节目相6A ,C D 邻,则节目安排的方法总数为( ) A. B.C.D.4896192240【答案】C5. 已知抛物线,直线交该抛物线于两点.若线段的中点坐标为2:4G y x =l ,A B AB ,则直线斜率为()()3,2l A.B.C. D.121412【答案】C6. 已知函数有两个极值点, 则实数的取值范围是( )()2ln f x k x x x =-+k A. B.C.D.1,8⎛⎫-∞ ⎪⎝⎭1,8⎛⎫+∞ ⎪⎝⎭(),1-∞-10,8⎛⎫ ⎪⎝⎭【答案】D7. 已知,则的最小值是( ) 0x y >>222x y xy y+-A. B.2+2+C. D.22【答案】C8. 已知随机变量的分布列服从,记X ()~,X B n p ()()(),1f n p P X n P X n ==-+=,在上的最大值为,若正整数满足,则(),f n p 10,2p ⎡⎤∈⎢⎥⎣⎦()F n ,a b 2003a b >>和的大小关系是( )()F a ()F b A. B. ()()F a F b <()()F a F b =C. D. 无法确定()()F a F b >【答案】A二、选择题:本题共4小题,每小题5分,共20分.在每小题给出的选项中,有多项符合题目要求.全部选对的得5分,部分选对的得2分,有选错的得0分.9. 下列结论中,所有正确的结论是( )A. 当 0x >2≥B. 若时,a b <a b <C. 若,则 ,0x y z x y z <<++=xz yz >D. 当时,的最小值为 3x >-13y x x =++1-【答案】AD10. 下列说法中,正确的命题有( ) A. 已知随机变量服从正态分布,,则ξ()2N 2,δ(4)0.84P ξ<=(24)0.16P ξ<<=B. 以模型去拟合一组数据时,为了求出回归方程,设,求得线性回归方e kx y c =ln z y =程为,则 的值分别是和0.3 ˆ0.34zx =+,c k 4e C. 8个完全相同的球放入编号为1,2,3的三个空盒中,要求放入后3个盒子均不空且数量均不同,则有12种放法D. 若样本数据的方差为2,则数据,,的方差为129,,,x x x 1132x +2132x +91...,32x +4【答案】BC11. 已知某一物品的单件回收费为,根据以往回收经验可得,随机变量0,,2X a =02a <<的分布列如图所示,其中结论正确的是( )X X 0a2 P1214bA. 14b =B. 若该物品4件,其中2件单件回收费为2的概率为9256C. 若该物品4件,单件回收费不为0的件数为,则 Y ()2E Y =D 当时,取得最小值 23a =()D X 【答案】ACD12. 小明与小兵两位同学计划去科技博物馆参加活动.小明在如图的街道E 处,小兵在如图的街道F 处,科技博物馆位于如图的G 处,则下列说法正确的是( )A. 小明到科技博物馆选择的最短路径条数为126条B. 小兵到科技博物馆选择的最短路径条数为4条C. 小明到科技博物馆在选择的最短路径中,与到F 处和小兵会合一起到科技博物馆的概率为1021D. 小明与小兵到科技博物馆在选择的最短路径中,两人约定在科技博物馆门口汇合,事件A :小明经过F ;事件B :从F 到科技博物馆两人的路径没有重叠部分(路口除外),则()29P B A =【答案】ACD三、填空题:本题共4小题,每小题5分,共20分.13. 一个袋子中装有大小和质地均相同的3个黑球和和2个白球,则从中摸出2个球恰好是1个黑球和1个白球的概率为________. 【答案】## 350.614. 若随机变量,且,则的值是________. (),0.8X B n ()4E X =()1P X =【答案】## 46250.006415. 有两个分类变量和,其中一组观测值为如下的列联表:x y 22⨯1y2y 总计1xa10a -102x10a -20a +30 总计103040其中均为大于的整数,则________时,在犯错误的概率不超过0.01的前提,10a a -3=a 下为“和之间有关系”.附: x y ()()()()()22n ad bc K a b c d a c b d -=++++()2P K k ≥ 0.10 0.05 0.025 0.0100.005k 2.706 3.841 5.024 6.6357.879【答案】616. 某靶场有两种型号的步枪可供选用,其中甲使用两种型号的步枪的命中率分,A B ,A B 别为.现在两把步枪中各装填3发子弹,甲打算轮流使用两种步枪进行射1,314,A B ,A B 击,若击中标靶,则继续使用该步枪,若未击中标靶,则改用另一把步枪,甲首先使用A 种型号的步枪,若出现连续两次子弹脱靶或者其中某一把步枪的子弹打光耗尽的现象便立刻停止射击,记为射击的次数,则________. X ()5P X ==【答案】772四、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. 已知集合和非空集合 {}2870A x x x =-+≤{}121B x m x m =+≤≤-(1)若,求;5m =A B ⋂(2)若“”是“”的必要不充分条件,求实数的取值范围. x A ∈x B ∈m 【答案】(1){}67A B x x ⋂=≤≤(2) []2,4【解析】【分析】(1)解集合A 中的不等式,得到集合A ,求出时集合B ,再求; 5m =A B ⋂(2)问题转化为是的真子集,由此列不等式组求出实数m 的取值范围. B A 【小问1详解】不等式解得,则有, 2870x x -+≤17x ≤≤{}17A x x =≤≤当时,,. 5m ={}69B x x =≤≤{}67A B x x ∴⋂=≤≤【小问2详解】因为“”是“”的必要不充分条件,故是的真子集,x A ∈x B ∈B A 则有,由于等号不能同时成立,故,21111217m m m m -≥+⎧⎪+≥⎨⎪-≤⎩24m ≤≤所以实数的取值范围.m []2,418. 根据国家统计局统计,我国2018—2022年的新生儿数量如下:年份编号 x 12345年份2018 2019 2020 2021 2022新生儿数量(单位:万人) y 1523 1465 1200 1062 956(1)由表中数据可以看出,可用线性回归模型拟合新生儿数量与年份编号的关系,请y x 用相关系数说明相关关系的强弱;(,则认为与线性相关性很强) r 0.751r ≤≤y x (2)建立关于的回归方程,并预测我国2025年的新生儿数量. y x 参考公式及数据:rn∑i =1x i y i ‒nx ⋅yb n∑i =1x i y i ‒nx ⋅ya y ‒bx ,5∑i =1y i =6206,5∑i =1y i =6206, i ≈1564.【答案】(1)答案见解析;(2),472.7万人. 153.71702.3y x =-+【解析】【分析】(1)求出相关系数即得解;(2)利用最小二乘法求出关于的回归方程,再预测我国2025年的新生儿数量. y x 【小问1详解】,15370.981564r -=≈≈-,故与的线性相关性很强..0.75r > y x 从而可以用线性回归模型拟合与的关系. y x 【小问2详解】,()51111123453,62061241.2555i i x y y ==++++===⨯=∑.52222222215123455310ii xx =-=++++-⨯=∑故, 51522151537ˆ153.7105i ii ii x y xybxx ==--===--∑∑所以, ()ˆˆ1241.2153.731702.3ay bx =-=--⨯=所以关于的回归方程为,y x 153.71702.3y x =-+将2025年对应的年份编号代入回归方程得 8x =153.781702.3ˆ472.7y=-⨯+=所以我国2025年的新生儿数量约为472.7万人.19. 已知双曲线,焦点为,其中一条渐近线的倾斜角为()2222:10,0x y C a b a b-=>>12,F F ,点在双曲线上,且.30M 12MF MF -=(1)求双曲线的标准方程;C (2)若直线交于两点,若,求正实数的值.:l y x m =+C ,A B AOB m 【答案】(1)2213x y -=(2)2【解析】【分析】(1)利用双曲线的定义和渐近线方程即可求得双曲线的标准方程. (2)联立双曲线和直线方程,利用韦达定理表示出弦长,即可得出答案. 【小问1详解】 由条件知,,2tan 30b a a ==︒=故.1a b ==即双曲线标准方程为.2213x y -=【小问2详解】设,到直线的距离为,()()1122,,,A x y B x y O l h 联立得,2213x y y x m ⎧-=⎪⎨⎪=+⎩2226330x mx m +++=由,解得, ()2223683312240m m m ∆=-+=->22m >又,故,0m>m >而又由,21212333,2m x x m x x ++=-=故弦长,AB ==h 又12AOB S AB h == 解得,, 42280m m --=24m =又,故.m >2m =20. 已知正项数列满足:;为数列为的前项{}n a 22111230,3n n n n a a a a a ++--==n T {}n b n 和,,对任意的自然数,恒有. 222b a =-n 23n n T nb n =+(1)求数列的通项公式及其前项和;{}n a n n S(2)证明:数列是等差数列,并求其通项公式. {}n b 【答案】(1) 1133,322nn n n a S +==⨯-(2)证明见解析, 41n b n =-【解析】【分析】(1)由题目条件可得,即可得是以为首项,公()()1130n n n n a a a a ++-+={}n a 3比为3的等比数列,代入公式即可求得通项公式和前项和;n n S (2)由利用等差中项性质即可得,即可得数列是23n n T nb n =+212n n n b b b --+={}n b ,公差的等差数列,所以.13b =4d =41n b n =-【小问1详解】由题意可知,,且()()1130n n n n a a a a ++-+=0n a >即可得,即 13n n a a +=13n na a += 所以是首项为,公比为3的等比数列, {}n a 13a =所以,即数列的通项公式为111333n n n n a a q--==⨯={}n a ,3N n n a n +=∈由等比数列前项和公式可得; n ()13131331322nn n S +⨯-==⨯--【小问2详解】在中,令得,,又23n n T nb n =+1n =13b =2227b a =-=由得: 23n n T nb n =+()()112131,2n n T n b n n --=-+-≥两式相减得:()1213n n n b nb n b -=--+即 ()()()1213,2n n n b n b n --=--≥⋅⋅⋅⋅⋅⋅①当时,由①可得: 3n ≥()()12323,n n n b n b ---=--⋅⋅⋅⋅⋅⋅② 可得对任意的都成立, ①-②212n n n b b b --+=3n ≥ 故是等差数列,首项是,公差是{}n b 13b =214d b b =-=从而,11(41)n b n b n d +-=-=所以数列的通项公式为{}n b 41,N n b n n +-∈=21. 在全球抗击新冠肺炎疫情期间,我国医疗物资生产企业加班加点生产口罩、防护服、消毒水等防疫物品,保障抗疫一线医疗物资供应,在国际社会上赢得一片赞誉.我国某口罩生产厂商在加大生产的同时,狠抓质量管理,不定时抽查口罩质量.该厂质检人员从某日生产的口罩中随机抽取了100个,将其质量指标值分成以下五组:,[)100,110,,, ,得到如下频率分布直方图.规定:口[)110,120[)120130,[)130140,[]140,150罩的质量指标值越高,说明该口罩质量越好,其中质量指标值低于130的为二级口罩,质量指标值不低于130的为一级口罩.(1)将上述质量检测的频率视为概率,现从该工厂此类口罩生产线上生产出的大量口罩中,采用随机抽样方法每次抽取1个口罩,抽取8次,记被抽取的8个口罩中一级口罩个数为.若每次抽取的结果是相互独立的,求的方差;ξξ(2)现从样本口罩中利用分层抽样的方法随机抽取8个口罩,再从中抽取3个,记其中一级口罩个数为,求的分布列及数学期望;ηη(3)在2023年“五一”劳动节前,甲、乙两人计划同时在该型号口罩的某网络购物平台上分别参加两店各一个订单“秒杀”抢购,其中每个订单由个该型号口,A B ()2,Nn n n *≥∈罩构成.假定甲、乙两人在 两店订单“秒杀”成功的概率分别为,,记,A B 2πnπ2cosn n甲、乙两人抢购成功的口罩总数量为,求当的数学期望取最大值时正整数X X ()E X n 的值.【答案】(1)1.5 (2)分布列见解析,34(3)6 【解析】【分析】(1)由题可知,抽到一级口罩的频率为0.25,且,根据二项分布(8,0.25)B ξ 的方差公式,计算结课;(2)根据题意知,可能的值有,计算对应概率,写出分布列和期望即可; η0,1,2(3)设甲乙抢购成功的订单总量为,由题可知,可能为,计算出对应概率,求Y Y 0,1,2出,结合,化简,最后用导数找出最大值,求解即可. ()E Y X nY =()E Y 【小问1详解】(1)由题知,抽到一级口罩的频率为,则, ()0.020.005100.25+⨯=(8,0.25)B ξ 故. ()(1)80.250.75 1.5D np p ξ=-=⨯⨯=【小问2详解】按分层抽样抽取8个口罩,则其中一级、二级口罩个数分别为,0.2582⨯=,()10.2586-⨯=故可能的取值为0,1,2,η,,,306238C C 5(0)C 14P η===21623815(1)28C C P C η===1262383(2)28C C P C η===的分布列为 η η012P 514 1528 328. 15()0114533228284E η+⨯⨯+⨯==【小问3详解】设甲乙抢购成功的订单总数量为,由题知,可能的取值为0,1,2,Y Y , 2232cos2cos 2cos(0)(1)(11ππππππn n n P Y n n n n n ==--=--+, 22232cos2cos 2cos 4cos(1)(1(1)ππππππππn n n n P Y n n n n n n n ==-+-⋅=+-,32cos(2)ππn P Y n ==所以232332cos2cos 2cos 4cos 2cos ()0(1)1(2ππππππππππn n n n n E X nn n n n n n =⨯--++⨯+-+⨯,2π2cos πn n n=+因为,所以, X nY =22cos()()()2cos ππππn E X nE Y n nn n n==+=+令,设, 11(0,]2t n =∈()2cos f t πt πt =+则,()()E X f t =因为, 1()2sin 2(sin )2f t πππt ππt '=-=-所以当时,;当时,; 10,6t ⎛⎫∈ ⎪⎝⎭()0f t '>11,62t ⎛⎫∈ ⎪⎝⎭()0f t '<所以在上单调递增,在上单调递减, ()f t 10,6⎛⎫ ⎪⎝⎭11,62⎛⎫ ⎪⎝⎭故当,即时,取最大值, 16t =6n =()f t 所以,所以取最大值时,正整数. ()max 1π66f t f ⎛⎫==⎪⎝⎭()E X 6n =22. 已知函数. ()()()3211e R ,e 23axx f x x a g x x mx =+∈=-+(1)讨论函数在上的单调性; ()f x ()0,∞+(2)若,当时,判断函数的零点个数.()()()hx f x g x =-1,0a m =≥()h x 【答案】(1)答案见解析;(2)只有1个零点. 【解析】【分析】(1)求出,再对分和两种情况讨论得解; ()f x 'a 0a ≥a<0(2)求出,再对分三种情况讨论,得到每一种情(),()h x h x 'm 111,,0222m m m =>≤<况下,在上都只有1个零点,综合即得解. ()h x R 【小问1详解】,因为()f x '()e e e 1ax ax axax ax =+=+0x >故当时,在上恒成立,所以函数的增区间为;0a ≥()0f x ¢>()0,∞+()f x ()0,∞+当时,令得,令得, a<0()0f x ¢>1x a<-()0f x '<1x a>-综上当时,的增区间为;当时,的增区间为,减0a ≥()f x ()0,∞+a<0()f x 10,a ⎛⎫-⎪⎝⎭区间为. 1,a ∞⎛⎫-+ ⎪⎝⎭【小问2详解】,定义域为.()()()()32111e 32x h x f x g x x x mx =-=-+-+R()h x '()2e 2e 2x xx x mx x x m =+-=+-令,()e 2xt x x m =+-当时,,故在上单调递增, 12m =()e 1,xt x x =+-()e 10x t x '=+>()t x R 又()00e 010t =+-=故当时, 恒成立,0x >()e 10,xt x x =+->()(e 1)0x h x x x '=+->当时, 恒成立,且0x <()e 10,xt x x =+-<()(e 1)0x h x x x '=+->()00h '=综上,在上单调递增, ()h x R 又,故在上只有1个零点 ()()11010,1023h h =-+=()h x R 当时,在上单调递增,12m >()e 2x t x x m =+-R()()0120,e m t m t m m =-<=-令,则在上恒成立()x φ1e ,2xx x =->()x φ'e 10x =->12x >所以在上单调递增,故,故 ()x φ1,2⎛⎫+∞ ⎪⎝⎭1()()2x φφ>102=->()0t m >所以存在唯一,使得,即 ()10,x m ∈()10t x =()10h x '=当时,,故, 0x <()0t x >()(e 2)0x h x x x k '=+->当时,,故 10x x <<()0t x <()(e 2)0x h x x x k '=+-<当时,,故,1x x >()0t x >()(e 2)0x h x x x k '=+->所以在上单调递增,在上单调递减,在上单调递增 ()h x (),0∞-()10,x ()1,x +∞因为 ()()()()3111010,331e 022m h x h h m m <=-+=-+所以当时,在上只有1个零点, 12m >()h x R当时,在上单调递增102m ≤<()e 2xt x x m =+-R 因为()()10120,1120t m t e m -=->-=--<所以存在唯一,使得,即 ()21,0x ∈-()20t x =()20h x '=当时,,故 2x x <()0t x >()(e 2)0x h x x x k '=+->当时,,故 20x x <<()0t x <()(e 2)0x h x x x k '=+-<当时,,故,0x >()0t x >()(e 2)0x h x x x k '=+->所以在上单调递增,在上单调递减,在上单调递增 ()h x ()2,x -∞()2,0x ()0,∞+因为 ()()111010,10232h h m =-+=-+所以当时,恰有1个零点, ()0,x ∈+∞()h x 当时, (),0x ∈-∞()()()2322222max 111e 32xh x h x x x mx ==-+-+,令,解得:2()h x '22222e 2x x x mx =+-2()0h x '=22e 2x x m +=所以 ()()()222322322222222e 11111e 22e 132223x x x x h x x x x x x x +⎡⎤=-+-⋅+=--++-⎢⎥⎣⎦令,则 ()()()23122e 1,1,03x x x x x x φ=-++-∈-()x φ'()2e 10x x =+≥所以在上单调递增, 故 ()x φ()1,0-()(1)x φφ>-5154154e 10e 3e 33e -=--=-=>所以()20h x <故当时,无零点(),0x ∈-∞()h x 当时,在上只有1个零点 102m ≤<()h x R 综上,当时,函数在上只有1个零点1,0a m =≥()h x R 【点睛】方法点睛:利用导数研究函数的零点问题,常用的方法是:(1)方程法,直接解方程得解;(2)图象法,直接画出函数的图象分析得解;(3)方程+图象法,令()f x 得到,再画出函数的图象分析得解. ()0f x =()()g x h x =(),()g x h x。
重庆市第一中学校2020-2021学年八年级下学期期中考试英语试题(答案+解析)

学校:___________姓名:___________班级:___________考号:___________
一、单选题
1.---Look, _______ emperor in his new clothes is coming to us.
6.As soon as the movie Peter Rabbit _______, children all over the world fell in love with this little cute rabbit.
A.found outB.handed outC.came outD.gave out
When Lisa started in eighth grade with new classmates, she thought she was not going to have a wonderful school life. She only had three friends. And she was13afraid to speak in front of class. She had a lot of negative(消极的) ideas when she noticed people14her. She was always thinking about if people liked her or if15thought she was cool.
A.offerB.needC.practiceD.enjoy
9.People were completely shocked at the news that _______ of the two towers were taken down by terrorists.
重庆市北碚区2018-2019学年七年级下学期期末英语试题(解析版)

A. GreatB. Not badC. TerribleD. Pretty good
【答案】C
【解析】
试题分析:句意:--近段一切好吗?--真糟糕,我的英语书找不到了。A. rible糟糕;D. Pretty good非常好。根据I can’t find my English book.可知故选C。
听下面一段材料,回答第15和16小题
15. Why does Lisa want to eat out?
A. Because it’s her birthday today.
B. Because her parents aren’t at home.
C. Because she likes Thai food.
【答案】B
【解析】
【详解】句意:——你好。你是谁?——我是彼得。我可以和艾米通话吗?
考查电话用语。电话用语中,“我”用this表示,“你”用that表示。回答:This is Peter我是彼得,可以推测出问的是:你是谁:Who’s that…。故选B。
完形填空。根据短文内容,从A、B、C、D四个选项中选出一个能填入相应空格内的最佳答案,并把答题卡上对应题目的答案标号涂黑。
13. Where did the man go?
A. To the mountain. B. To the countryside. C. To a bank.
14. What did the man do on Dragon Boat Festival?
A. Joined in the boat race. B. Planted trees. C. Ate zongzi.
重庆市第一中学校2018-2019学年八年级上学期期末考试数学试题

2018-2019学年八年级上学期期末考试数学试题一、选择题:(本大题共12个小题,每小题4分,共48分)1.下列各数中,是无理数的是()A.B.C.﹣2 D.0.32.下列图形中,既是轴对称图形,又是中心对称图形的是()A.B.C.D.3.计算(﹣xy2)2的结果是()A.2x2y4B.﹣x2y4C.x2y2D.x2y44.分式有意义,则x的取值范围是()A.x>3 B.x<3 C.x≠3 D.x≠﹣35.△ABC三边长分别为a、b、c,则下列条件不能判断△ABC是直角三角形的是()A.a=3,b=4,c=5 B.a=4,b=5,c=6C.a=6,b=8,c=10 D.a=5,b=12,c=136.下列命题是假命题的是()A.两直线平行,同位角相等B.全等三角形面积相等C.直角三角形两锐角互余D.若a+b<0,那么a<0,b<07.估计(2+)•的值应在()A.3和4之间B.4和5之间C.5和6之间D.6和7之间8.如果直线y=3x+b与两坐标轴围成的三角形面积等于2,则b的值是()A.±3B.3C.D.29.如图,直线y=﹣x﹣1与y=kx+b(k≠0且k,b为常数)的交点坐标为(﹣2,l),则关于x的不等式﹣x﹣1<kx+b的解集为()A.x>﹣2 B.x<﹣2 C.x>1 D.x<l10.如图,把Rt△ABC放在平面直角坐标系中,点B(1,1)、C(5,1),∠ABC=90°,AC =4.将△ABC沿y轴向下平移,当点A落在直线y=x﹣2上时,线段AC扫过的面积为()A.B.C.D.11.如图,Rt△ABC的两边OA,OB分别在x轴、y轴上,点O与原点重合,点A(﹣3,0),点B(0,3),将Rt△AOB沿x轴向右翻滚,依次得到△1,△2,△3,…,则△2020的直角顶点的坐标为()A.(673,0)B.(6057+2019,0)C.(6057+2019,)D.(673,)12.已知整数k使得关于x、y的二元一次方程组的解为正整数,且关于x的不等式组有且仅有四个整数解,则所有满足条件的k的和为()A.4 B.9 C.10 D.12二、填空题:(本大题6个小题,每小题4分,共24分)13.因式分解:5x2﹣2x=.14.+(π﹣3.14)0﹣(﹣)﹣2=.15.一次函数y=kx+b的图象经过点(0,3),且与直线y=﹣x+1平行,则该一次函数解析式为.16.若m,n为实数,且m=+8,则m+n的算术平方根为.17.甲、乙两人在同一直线道路上同起点、同方向、同时出发,分别以不同的速度匀速跑步1800米,当甲第一次超出乙300米时,甲停下来等候乙.甲、乙会合后,两人分别以原来的速度继续跑向终点,先到终点的人在终点休息.在整个跑步过程中,甲、乙两人之间的距离y(米)与乙出发的时间x(s)之间的关系如图所示则当甲到达终点时,乙跑了米.18.A、B、C、D、E、F六人按顺序围成一圈做游戏,每人抽一个数,已知每人按顺序抽到数字的两倍与其他五个人的平均数之差分别为9、10、13、15、23、30,则C抽到的数字是.三、解答题(本大题2个小题,每小题8分,共16分)19.解下列方程组或者不等式组(1)解方程组:(2)解不等式组:20.作图题:(不要求写作法)如图,在平面直角坐标系中,△ABC的三个顶点的坐标分别为A(﹣3,4),B(﹣3,1),C(﹣1,3).(1)作图:将△ABC先向右平移4个单位,再向下平移3个单位,则得到△A1B1C1,求作△A1B1C1;(2)求△BCC1面积.四、解答题:(本大题4个小题,每小题10分,共40分)21.重庆一中田径代表队在2018年重庆市青少年田径锦标赛上勇夺金牌8枚,银牌4枚,铜牌8枚,喜讯再次点燃了同学们热爱运动的热情为了解学生参与运动的情况,学校随机抽查了部分学生每日运动时间的情况,并将调查学生每日运动时间情况条形统计图学生每日运动时间情况扇形统计图.(1)被抽查的学生总数是人,并在图中补全条形统计图;(2)写出每日运动时间的中位数是小时,众数是小时;(3)求这批被调查学生平均每日运动的时间.22.如图,直线AB:y=2x+6与直线AC:y=﹣2x+2相交于点A,直线AB与x轴交于点B,直线AC与x轴交于点D,与y轴交于点C.(1)求交点A的坐标;(2)求△ABC的面积.23.为了满足学生的需求,重庆一中mama超市准备购进甲、乙两种绿色袋装食品.其中甲乙两种绿色袋装食品的进价和售价如表:已知:超市购进200袋甲种袋装食品或者购进300袋乙种袋装食品所用金额相等(1)求n的值;(2)要使购进的甲、乙两种绿色袋装食品共1200袋的总利润(利润=售价﹣进价)不少于6400元,且不超过6420元,问该mama超市有哪几种进货方案?要获得最大利润该如何进货?(请写出具体方案)24.在△ABC中,AB=AC,点D为BC的中点,连接AD.(1)如图1,H为线段CB延长线上的一点,连接AH,若∠ACB=60°,∠AHC=45°,AH =2,求HC;(2)如图2,点E为AD上任意一点,过点E作EF⊥AD交AC于点F,连接BF,取BF中点M,连接MD和ME,求证:ME=MD.五、解答题:(本大题2个小题,25题10分,26题12分,共22分)25.阅读下列材料:对于一个任意四位正整数,若其千位数字与百位数字组成的两位数是它的十位数字与个位数字组成的两位数的两倍,则称这样的四位正整数为“双倍数”,如6231,其千位数字与百位数字组成的两位数为62,其十位数字与个位数字组成的两位数是31,62是31的两倍,则称6231为“双倍数”(1)猜想任意一个“双倍数”能否被67整除,并说明理由;(2)若一个双倍数的各个数位数字分别加上1组成一个新的四位正整数,这个新的四位正整数能被7整除,求所有满足条件的“双倍数”.26.如图,平面直角坐标系中直线l1:y=x与直线l2:y=﹣x+8相交于点A,直线l2与x轴相交于点B,与y轴相交于点C,点D(﹣6,0),点F(0,6),连接DF.(1)如图1,求点A的坐标;(2)如图1,若将△ODF向x轴的正方向平移a个单位,得到△O′D′F′,点D与点B 重合时停止移动,设△O′D′F′与△OAB重叠部分的面积为S,请求出S与a的关系式,并写出a的取值范围;(3)如图2,现将△ODF向x轴的正方向平移12个单位得到△O1D1F1,直线O1F1与直线l2交于点G,再将△O1GB绕点G旋转,旋转角度为α(0°≤α≤360°),记旋转后的三角形为△O1′GB′,直线O1′G与直线l1的交点为M,直线GB′与直线l1的交点为N,是否存在△GMN为等腰三角形?若存在请直接写出MN的值;若不存在,请说明理由.参考答案与试题解析一.选择题(共12小题)1.下列各数中,是无理数的是()A.B.C.﹣2 D.0.3【分析】无理数就是无限不循环小数.理解无理数的概念,一定要同时理解有理数的概念,有理数是整数与分数的统称.即有限小数和无限循环小数是有理数,而无限不循环小数是无理数.由此即可判定选择项.【解答】解:A.是无理数;B.是分数,属于有理数;C.﹣2是整数,属于有理数;D.0.3是有限小数,即分数,属于有理数;故选:A.2.下列图形中,既是轴对称图形,又是中心对称图形的是()A.B.C.D.【分析】根据轴对称图形与中心对称图形的概念求解.【解答】解:A、不是轴对称图形,也不是中心对称图形,故此选项错误;B、不是轴对称图形,是中心对称图形,故此选项错误;C、是轴对称图形,也是中心对称图形,故此选项正确;D、是轴对称图形,不是中心对称图形,故此选项错误.故选:C.3.计算(﹣xy2)2的结果是()A.2x2y4B.﹣x2y4C.x2y2D.x2y4【分析】根据积的乘方和幂的乘方运算法则计算可得.【解答】解:(﹣xy2)2=x2y4,故选:D.4.分式有意义,则x的取值范围是()A.x>3 B.x<3 C.x≠3 D.x≠﹣3【分析】本题主要考查分式有意义的条件:分母≠0,即x﹣3≠0,解得x的取值范围.【解答】解:∵x﹣3≠0,∴x≠3.故选:C.5.△ABC三边长分别为a、b、c,则下列条件不能判断△ABC是直角三角形的是()A.a=3,b=4,c=5 B.a=4,b=5,c=6C.a=6,b=8,c=10 D.a=5,b=12,c=13【分析】如果三角形的三边长a,b,c满足a2+b2=c2,那么这个三角形就是直角三角形.【解答】解:A.∵32+42=52,∴△ABC是直角三角形;B.∵52+42≠62,∴△ABC不是直角三角形;C.∵62+82=102,∴△ABC是直角三角形;D.∵122+42=132,∴△ABC是直角三角形;故选:B.6.下列命题是假命题的是()A.两直线平行,同位角相等B.全等三角形面积相等C.直角三角形两锐角互余D.若a+b<0,那么a<0,b<0【分析】根据平行线的性质对A进行判断;根据全等三角形的性质对B进行判断;根据互余的定义对C进行判断;利用反例对D进行判断.【解答】解:A、两直线平行,同位角相等,所以A选项的命题为真命题;B、全等三角形面积相等,所以B选项的命题为真命题;C、直角三角形两锐角互余,所以C选项的命题为真命题;D、当a=﹣3,b=1,所以D选项的命题为假命题.故选:D.7.估计(2+)•的值应在()A.3和4之间B.4和5之间C.5和6之间D.6和7之间【分析】直接利用二次根式乘法运算法则化简,进而估算无理数的大小即可.【解答】解:(2+)•=2+2,∵2<2<3,∴4<2+2<5.故选:B.8.如果直线y=3x+b与两坐标轴围成的三角形面积等于2,则b的值是()A.±3B.3C.D.2【分析】设直线y=3x+b与x轴交于点A,与y轴交于点B,利用一次函数图象上点的坐标特征可得出点A,B的坐标,利用三角形的面积公式结合△AOB的面积为2,可得出关于b的一元二次方程,解之即可得出结论.【解答】解:设直线y=3x+b与x轴交于点A,与y轴交于点B.当x=0时,y=3x+b=b,∴点B的坐标为(0,b);当y=0时,3x+b=0,解得:x=﹣.∵S△AOB=OA•OB=2,∴×|b|×|﹣|=2,∴b=±2.故选:C.9.如图,直线y=﹣x﹣1与y=kx+b(k≠0且k,b为常数)的交点坐标为(﹣2,l),则关于x的不等式﹣x﹣1<kx+b的解集为()A.x>﹣2 B.x<﹣2 C.x>1 D.x<l【分析】根据题意知,直线y=kx+b位于直线y=﹣x﹣1上方的部分符合题意.【解答】解:如图,直线y=﹣x﹣1与y=kx+b(k≠0且k,b为常数)的交点坐标为C (﹣2,l),所以关于x的不等式﹣x﹣1<kx+b的解集为x>﹣2.故选:A.10.如图,把Rt△ABC放在平面直角坐标系中,点B(1,1)、C(5,1),∠ABC=90°,AC =4.将△ABC沿y轴向下平移,当点A落在直线y=x﹣2上时,线段AC扫过的面积为()A.B.C.D.【分析】根据题意,可以求得点A的坐标,然后根据平移的特点,可知线段AC扫过的图形是平行四边形,再根据点A落在直线y=x﹣2上时,从而可以求得线段AC平移的距离,进而求得线段AC扫过的面积.【解答】解:∵点B(1,1)、C(5,1),∠ABC=90°,AC=4,∴BC=4,∴AB==4,∴点A的坐标为(1,5),将x=1代入y=x﹣2得,y=﹣,∴线段AC扫过的面积为:|5﹣(﹣)|×(5﹣1)==,故选:D.11.如图,Rt△ABC的两边OA,OB分别在x轴、y轴上,点O与原点重合,点A(﹣3,0),点B(0,3),将Rt△AOB沿x轴向右翻滚,依次得到△1,△2,△3,…,则△2020的直角顶点的坐标为()A.(673,0)B.(6057+2019,0)C.(6057+2019,)D.(673,)【分析】在翻滚的过程中,每翻滚三次就重复出现原来的形状,可将这样的翻滚称为三循环,那么2020÷3=673.…1,所以△2020的形状如同△4,即直角顶点的纵坐标为0,再求出△ABC的周长的673倍即为横坐标.【解答】解:∵2020÷3=673. (1)∴△2020的形状如同△4∴△2020的直角顶点的纵坐标为0而OB1+B1A2+A2O2=3+6+3=9+3∴△2020的直角顶点的横坐标为(9+3)×673=6057+2019故选:B.12.已知整数k使得关于x、y的二元一次方程组的解为正整数,且关于x的不等式组有且仅有四个整数解,则所有满足条件的k的和为()A.4 B.9 C.10 D.12【分析】解方程组得,得到k=4,6;解不等式组得到k=4,5,6,于是得到所有满足条件的k的和=4+6=10.【解答】解:解方程组得,∵方程组的解为正整数,∴,∴k=4,6;解不等式组得,,∵不等式组有且仅有四个整数解,∴1<≤2,∴3<k≤6,∴k=4,5,6,∴所有满足条件的k的和=4+6=10,故选:C.二.填空题(共6小题)13.因式分解:5x2﹣2x=x(5x﹣2).【分析】提取公因式x即可得.【解答】解:5x2﹣2x=x(5x﹣2),故答案为:x(5x﹣2).14.+(π﹣3.14)0﹣(﹣)﹣2=﹣10 .【分析】直接利用零指数幂的性质以及负指数幂的性质、立方根的性质分别化简得出答案.【解答】解:原式=﹣2+1﹣9=﹣10.故答案为:﹣10.15.一次函数y=kx+b的图象经过点(0,3),且与直线y=﹣x+1平行,则该一次函数解析式为y=﹣x+3 .【分析】设一次函数解析式为y=kx+b,先把(0,3)代入得b=3,再利用两直线平行的问题得到k=﹣,即可得到一次函数解析式;【解答】解:设一次函数解析式为y=kx+b,把(0,3)代入得b=3,∵直线y=kx+b与直线y=﹣x+1平行,∴k=﹣,∴一次函数解析式为y=﹣x+3.故答案为y=﹣x+3.16.若m,n为实数,且m=+8,则m+n的算术平方根为 3 .【分析】根据二次根式的被开方数是非负数求得n=1,继而求得m=8,然后求m+n的算术平方根.【解答】解:依题意得:1﹣n≥0且n﹣1≥0,解得n=1,所以m=8,所以m+n的算术平方根为:==3.故答案是:3.17.甲、乙两人在同一直线道路上同起点、同方向、同时出发,分别以不同的速度匀速跑步1800米,当甲第一次超出乙300米时,甲停下来等候乙.甲、乙会合后,两人分别以原来的速度继续跑向终点,先到终点的人在终点休息.在整个跑步过程中,甲、乙两人之间的距离y(米)与乙出发的时间x(s)之间的关系如图所示则当甲到达终点时,乙跑了1380 米.【分析】先由图象和已知条件求出甲乙的速度,进而求出两人相距300米时甲跑的路程以及离终点的距离和从会和到终点甲所用的时间,从而求出乙跑420秒的路程,最后求出乙跑的总路程.【解答】解:由题意得乙的速度:1800÷1200=1.5(米/秒),甲的速度:1.5+300÷300=2.5 (米/秒),∴两人相距300m时,甲跑的路程是 2.5×300=750(米),此时离终点距离为1800﹣750=1050(米),∴从会合到终点甲的用时是 1050÷2.5=420(秒)乙从会合点跑420秒路程是 420×1.5=630(米),∴当甲到终点时,乙跑的总路程是 750+630=1380(米).故答案为:1380.18.A、B、C、D、E、F六人按顺序围成一圈做游戏,每人抽一个数,已知每人按顺序抽到数字的两倍与其他五个人的平均数之差分别为9、10、13、15、23、30,则C抽到的数字是15 .【分析】设A、B、C、D、E、F六人抽到的数分别为:a,b,c,d,e,f,由题意列出方程组,可求c的值.【解答】解:设A、B、C、D、E、F六人抽到的数分别为:a,b,c,d,e,f,由题意可得解得:c=15故答案为:15三.解答题(共8小题)19.解下列方程组或者不等式组(1)解方程组:(2)解不等式组:【分析】(1)利用加减消元法求解可得;(2)分别求出各不等式的解集,再求出其公共解集即可.【解答】解:(1)整理得①﹣②得7y=﹣1,解得y=﹣,把y=﹣代入②得x+=2,解得x=,所以方程组的解为;(2)解不等式①得,x≤4;解不等式②得x>﹣5,不等式组的解集为﹣5<x≤4.20.作图题:(不要求写作法)如图,在平面直角坐标系中,△ABC的三个顶点的坐标分别为A(﹣3,4),B(﹣3,1),C(﹣1,3).(1)作图:将△ABC先向右平移4个单位,再向下平移3个单位,则得到△A1B1C1,求作△A1B1C1;(2)求△BCC1面积.【分析】(1)依据平移动方向和距离,即可得到△A1B1C1;(2)利用割补法进行计算,即可得到△BCC1面积.【解答】解:(1)如图所示,△A1B1C1即为所求;(2)如图,△BCC1面积为:6×3﹣×1×6﹣×2×2﹣×3×4=18﹣3﹣2﹣6=7.21.重庆一中田径代表队在2018年重庆市青少年田径锦标赛上勇夺金牌8枚,银牌4枚,铜牌8枚,喜讯再次点燃了同学们热爱运动的热情为了解学生参与运动的情况,学校随机抽查了部分学生每日运动时间的情况,并将调查学生每日运动时间情况条形统计图学生每日运动时间情况扇形统计图.(1)被抽查的学生总数是100 人,并在图中补全条形统计图;(2)写出每日运动时间的中位数是40 小时,众数是40 小时;(3)求这批被调查学生平均每日运动的时间.【分析】(1)根据题意列式计算,补全条形统计图即可;(2)根据条形统计图中的数据即可得到结论;(3)根据平均数的计算公式即可得到结论.【解答】解:(1)被抽查的学生总数是10÷10%=100人,每日运动时间为1.2小时的学生人数为100×20%=20人,补全条形统计图如图所示;故答案为:100;(2)每日运动时间的中位数是40小时,众数是40小时;故答案为:40,40;(3)这批被调查学生平均每日运动的时间=×(0.2×10+0.5×15+1×40+1.2×20+1.6×10+2×5)=0.995小时.22.如图,直线AB:y=2x+6与直线AC:y=﹣2x+2相交于点A,直线AB与x轴交于点B,直线AC与x轴交于点D,与y轴交于点C.(1)求交点A的坐标;(2)求△ABC的面积.【分析】(1)联立直线AB,AC的解析式成方程组,通过解方程组即可求出点A的坐标;(2)设直线AB与y轴交于点E,利用一次函数图象上点的坐标特征可求出点B,C,E的坐标,利用三角形的面积公式结合S△ABC=S△BOE﹣S△BOC﹣S△ACE,即可求出△ABC的面积.【解答】解:(1)联立直线AB,AC的解析式成方程组,得:,解得:,∴交点A的坐标为(﹣1,4).(2)设直线AB与y轴交于点E,如图所示.当x=0时,y=2x+6=6,y=﹣2x+2=2,∴点E的坐标为(0,6),点C的坐标为(0,2),∴OE=6,OC=2,CE=4.当y=0时,2x+6=0,解得:x=﹣3,∴点B的坐标为(﹣3,0),OB=3.∴S△ABC=S△BOE﹣S△BOC﹣S△ACE,=×3×6﹣×3×2﹣×4×1,=4.23.为了满足学生的需求,重庆一中mama超市准备购进甲、乙两种绿色袋装食品.其中甲乙两种绿色袋装食品的进价和售价如表:已知:超市购进200袋甲种袋装食品或者购进300袋乙种袋装食品所用金额相等(1)求n的值;(2)要使购进的甲、乙两种绿色袋装食品共1200袋的总利润(利润=售价﹣进价)不少于6400元,且不超过6420元,问该mama超市有哪几种进货方案?要获得最大利润该如何进货?(请写出具体方案)【分析】(1)根据“购进200袋甲种袋装食品或者购进300袋乙种袋装食品所用金额相等”列出方程并解答;(2)设购进甲种绿色袋装食品x袋,表示出乙种绿色袋装食品(1200﹣x)袋,然后根据总利润列出一元一次不等式组解答;【解答】解:(1)依题意得:200(n+2)=300(n﹣2),解得:n=10,(2)设购进甲种绿色袋装食品x袋,表示出乙种绿色袋装食品(1200﹣x)袋,根据题意得,,解得:≤x≤270,∵x是正整数,270﹣266.7+1=4,∴共有4种方案;∵甲的利润大于乙的利润,要获得最大利润该应该进货时甲最大才行,即甲进货270袋,乙进货1200﹣270=930袋.24.在△ABC中,AB=AC,点D为BC的中点,连接AD.(1)如图1,H为线段CB延长线上的一点,连接AH,若∠ACB=60°,∠AHC=45°,AH=2,求HC;(2)如图2,点E为AD上任意一点,过点E作EF⊥AD交AC于点F,连接BF,取BF中点M,连接MD和ME,求证:ME=MD.【分析】(1)证明△ABC是等边三角形,得出BC=AB,∠ABC=∠BAC=60°,AD⊥BC,CD =BD=BC,∠BAD=30°,证明△ADH是等腰直角三角形,得出AD=DH=AH=2,由含30°角的直角三角形的性质得出AD=BD=2,求出CD=BD=,即可得出HC=DH+CD =2+;(2)延长FE、DM交于点G,证出∠DEG=90°,EF∥BC,由平行线的性质得出∠G=∠BDM,证明△BDM≌△FGM(AAS),得出DM=GM,再由直角三角形斜边上的中线性质即可得出结论.【解答】(1)解:∵AB=AC,∠ACB=60°,∴△ABC是等边三角形,∴BC=AB,∠ABC=∠BAC=60°,∵点D为BC的中点,∴AD⊥BC,CD=BD=BC,∠BAD=30°,∵∠AHC=45°,AH=2,∴△ADH是等腰直角三角形,∴AD=DH=AH=2,∵∠BAD=30°,∴AD=BD=2,∴CD=BD=,∴HC=DH+CD=2+;(2)证明:延长FE、DM交于点G,如图2所示:∵EF⊥AD,AD⊥BC,∴∠DEG=90°,EF∥BC,∴∠G=∠BDM,∵M为BF的中点,∴BM=FM,在△BDM和△FGM中,,∴△BDM≌△FGM(AAS),∴DM=GM,∴EM=DG=MD.25.阅读下列材料:对于一个任意四位正整数,若其千位数字与百位数字组成的两位数是它的十位数字与个位数字组成的两位数的两倍,则称这样的四位正整数为“双倍数”,如6231,其千位数字与百位数字组成的两位数为62,其十位数字与个位数字组成的两位数是31,62是31的两倍,则称6231为“双倍数”(1)猜想任意一个“双倍数”能否被67整除,并说明理由;(2)若一个双倍数的各个数位数字分别加上1组成一个新的四位正整数,这个新的四位正整数能被7整除,求所有满足条件的“双倍数”.【分析】(1)根据已知条件,将数字表示成67的倍数即可;(2)根据已知条件,表示出已知数字,即可求出已知数的满足条件,写出已知数即可.【解答】解:设正整数m=D4D3D2D1,其中D4、D3、D2、D1表示各个位置上的数字,且为0到9之间的整数(D4≠0),根据“双倍数”的定义,有10D4+D3=2(10D2+D1).(1)假设m=D4D3D2D1是“双倍数”,则有m=1000D4+100D3+10D2+D1=100(10D4+D3)+10D2+D1,根据“双倍数”定义,有m=100×2(10D2+D1)+10D2+D1=2010D2+201D1=201(10D2+D1),则==3(10D2+D1)=30D2+3D1为整数,由此可见,任意一个“双倍数”都能被67整除;(2)由题意,新组成的四位正整数可表示为:1000(D4+1)+100(D3+1)+10(D2+1)+D1+1=201(10D2+D1)+1111因为=N,也就是2010D2+201D1+1111可以整除7,而1111÷7=158……5,所以需要“双倍数”(2010D2+201D1)÷7=n……2才可以整除7故所有满足这样条件的“双倍数”(用排除法)有:2613,502526.如图,平面直角坐标系中直线l1:y=x与直线l2:y=﹣x+8相交于点A,直线l2与x轴相交于点B,与y轴相交于点C,点D(﹣6,0),点F(0,6),连接DF.(1)如图1,求点A的坐标;(2)如图1,若将△ODF向x轴的正方向平移a个单位,得到△O′D′F′,点D与点B重合时停止移动,设△O′D′F′与△OAB重叠部分的面积为S,请求出S与a的关系式,并写出a的取值范围;(3)如图2,现将△ODF向x轴的正方向平移12个单位得到△O1D1F1,直线O1F1与直线l2交于点G,再将△O1GB绕点G旋转,旋转角度为α(0°≤α≤360°),记旋转后的三角形为△O1′GB′,直线O1′G与直线l1的交点为M,直线GB′与直线l1的交点为N,是否存在△GMN为等腰三角形?若存在请直接写出MN的值;若不存在,请说明理由.【分析】(1)由两直线解析式组成方程组,解方程组即可得到交点A的坐标;(2)△DOF向右水平移动时,与△AOB重叠的图形在0<a≤6时为直角三角形,用a表示出两直角边即可求出面积的函数关系式,当6<a<24时,重叠部分为四边形,S四边形SHO′D′=S﹣S△F′SH.△F′O′D′(3)存在,在△GO1B绕点G逆时针旋转过程中,等腰△MNG只有两种情况:①∠MGN=60°,②∠MGN=120°;分类进行计算.【解答】解:(1)由题意得,解得,∴A(6,).(2)在y=﹣x+8中,令y=0,得﹣x+8=0,∴x=24∴B(24,0),令x=0,y=,∴C(0,),在Rt△BOC中,tan∠BCO===,∴∠BCO=60°,在Rt△DOF中,tan∠DFO===,∴∠DFO=30°.分两种情况:①当0≤a≤6时,如图1,F′O′交直线l1于点E,则O′(a,0),∴y=a,∴E(a,a),即EO′=a,OO′=a,∴S=OO′•EO′==,②当6<a≤30时,如图2,OO′=a,∴H(a,)F′H=﹣()=∵F′O′∥OC,∴∠BHO′=∠BCO=60°∵∠D′F′O′=∠DFO=30°,∴∠F′SH=90°,∴SH=F′H=(),F′S=SH=(),∴S=S△F′O′D′﹣S△F′HS=F′O′•D′O′﹣F′S•SH=×6×6﹣×()×()=∴.(3)存在,MN=8或24.∵F1O1∥y轴,∴∠BGO1=∠BCO=60°,∴△GMN为等腰三角形时,∠MGN=60°或120°,分两种情况:①当∠MGN=60°时,△GMN必为等边三角形,如图3,此时旋转角α=30°或90°或270°,∵OO1=12,∴BO1=12,∴BG===8,AB=OB cos∠OBC=24cos30°=12,∴AG=AB﹣BG=12﹣8=4,∴MN=NG===8,②当∠MGN=120°时,△GMN为等腰三角形,∴∠MNG=∠NMG=30°,如图4,此时旋转角α=120°或300°,MN=2AN===24.。
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重庆市第一中学2018-2019学年高二下学期期中考试英语试题第一部分听力(共两节,满分30分)第一节(共5小题,每小题1.5分,满分7.5分)听下面5段对话。
每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。
听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What does the woman suggest?A. They don’t have to go to the concert.B. His brother will let them use the car.C. The bus is fine for them.2. What do we know about the match?A. It can’t be much fun.B. It must be exciting.C. It may be put off.3. What is wrong with the printer?A. It doesn’t flash.B. There isn’t ink.C. It’s broken.4. What is the woman interested in?A. Sports.B. Fashion.C. Politics.5. What are the two speakers mainly talking about?A. New dictionaries.B. Language forms.C. The development of languages.第二节(共15小题;每小题1.5分,满分22.5分)听下面5段对话或独白。
每段对话或独白后面有2至4个小题,从题中所给的A、B、C三个选项中选出最佳选项,并标在试卷的相应位置。
听每段对话或独白前,你将有5秒钟的时间阅读各个小题;听完后,各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料,回答第6、7题。
6. What’s wrong with the man?A. He is very tired and sleepy.B. He is worried about his text.C. He is ill because of hard work.7. What did the man do last night?A. He studied in the library.B. He went to a party.C. He prepared for a big text.听第7段材料,回答第8至10题8. How did the two speakers get to their destination?A. By bike.B. By car.C. By taxi.9. What are the two speakers going to watch?A. A film.B. A game.C. A car race.10. Why did the two speakers arrive early?A. To find Peter.B. To meet the players.C. To get a good place.听第8段材料,回答第11至13题。
11. Who is Jimmy?A. A policeman.B. A passer-by.C. Another truck driver.12. What time was it when the accident happened?A. At 2:45.B. At 2:54.C. At 4:25.13. Who or what was to blame for the accident?A. The truck driver.B. The driver of the blue Ford.C. The traffic lights.听第9段材料,回答第14至16题。
14. Where do the two speakers work?A. In a plant in Chicago.B. In a large company.C. In an office in Atlanta.15. Who has risen to a higher position?A. Jim.B. Martha.C. Both Jim and Martha.16. Why does the woman want to remain in the company office?A. She is fond of writing notices.B. She is still new in her position.C. She hopes to be with the top leaders.听第10段材料,回答第17至20题。
17. Whom is the speaker speaking to?A. Students.B. Teachers.C. Reporters.18. How often does The V oice come out each week?A. Every other day.B. Every day.C. On weekdays.19. What’s the best reason for taking the job according to the speaker?A. To learn to type.B. To enjoy oneself.C. To make some money.20. When are volunteers expected to start working?A. Tomorrow.B. Immediately.C. Next week.第二部分阅读理解(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,从每题所给的四个选项(A、B、C和D)中,选出最佳选项。
AThrough your childhood and, let’s be honest, most of your adult life, you may have wondered ⸺ how do you get to Sesame Street? After 50 years, the answer has finally been revealed.New York City’s Official Sesame StreetIn the past, there was guessing about the true location of the street, like Harlem or Alphabet City since both neighborhoods resembled Sesame Street in appearance and population makeup. Recently, in honor of the children’s television show’s 50th anniversary, New York City Mayor Bill de Blasio declared that West 63rd Street between Central Park West and Broadway will now officially be known as Sesame Street, close to the Sesame Workshop office.A Year-long Celebration for the 50th AnniversarySince 1969, the children’s television show Sesame Street has been a pioneering force in media and education, dealing with issues like racism, loss, poverty and living with a disability. With a mission to help kids everywhere grow smarter, stronger, and kinder, Sesame Street has brought the life-changing benefits of early learning to children across the globe for 50 years. Today, we reach kids in 150 countries and 70 languages ⸺ and we’re celebrating our landmark anniversary with fans and families all year long!Events and Activities Throughout 2019Fans and families around the world can join their favorite furry friends in celebrating Sesame Street’s past, present, and future, with:⸺ A 50th television season which focuses on the power of possibilities, empowering kids to take safe risks and learn from their mistakes.⸺ A nationwide road trip where Sesame Street characters and friends host community events in ten cities around the country.⸺ A research report that will explore an important issue facing kids and families today.⸺ Celebrity and fan-fueled social media campaigns showcasing favorite Sesame Street memories.⸺ New corporations across fashion, lifestyle, and themed entertainment for fans of all ages.⸺ A November star-studded prime-time special, whose contents include new takes on classic scenes and visits from Sesame Street icons.21. Where is the official Sesame Street?A. In Harlem or Alphabet City.B. Around the corner of the West 63rd Street.C. At the Sesame Workshop office.D. Between Central Park West and Broadway.22. What benefits are children able to get from the television show?A. They can learn to solve all life problems in the childhood.B. They will definitely become smarter, stronger and kinder.C. They may get positive help meaning much to their later life.D. They are likely to make friends with kids from 150 countries.23. Which of the following is not an event or activity to celebrate the 50th anniversary?A. A new season of the television show.B. A 10-city journey for lucky fans.C. A special TV program in November.D. A report good for kids and families.BWhen Sir Ector saw Arthur pulled the sword out of the stone and then pushed it back, he rubbed his eyes. “I can’t believe it!” he cried. Then he fell on his knees before Arthur. “Father, please do not kneel before me. Tell me what you mean!” Arthur said with great confusion.“Listen, then,” said Sir Ector. “Years ago the wise magician, Merlin, carried a baby in his arms. That baby was you. Merlin told me to bring you up as my own son. Now I can guess. You must be the late king ⸺ King Uther’s son. Who else could have pulled out the sword? Arthur, we must let all England know you are qualified to be the new king.”“I would rather be your son than be a king!” cried Arthur.“On Christmas the Bishop(主教) will give everyone a chance to pull the sword. You must take your turn and show everyone that you are the only person who can pull the sword out.”On Christmas Day the great crowd of knights(骑士) and lords gathered before the church. They pulled and pushed, but no one could make the sword move.Down the street came Merlin. Behind him came Sir Ector with Arthur. “Who are these men?” asked the Bishop. “Here is one who will try the sword,” said Merlin. He laid his hand on Arthur’s shoulder. “Here, lords of England, is the true son of King Uther!” Arthur stepped upon the stone and laid his hand on the sword. Smoothly and easily he pulled it out. He held it high so all could see.So Arthur became King of all England. Some of the lords did not want him, and he had to fight them. As the years went by, he became stronger and greater. Knights came from all lands to be in his court. At Camelot Arthur started the famous Knights of the Round Table. These were the greatest of all the knights. They made their names famous for all time.24. Sir Ector fell on his knees before Arthur because ______.A. Sir Ector wanted to ask for forgiveness from the new kingB. Merlin told Sir Ector to respect Arthur as if he were the KingC. Arthur pulled the sword out and Sir Ector knew who he wasD. Arthur was so powerful that Sir Ector admired him very much25. Arthur found it ______ when Sir Ector said he was qualified to be the new king.A. believableB. unacceptableC. enjoyableD. unchangeable26. What did Arthur do as King of all England according to the passage?A. Fighting the foreign countries.B. Making the famous table.C. Developing the national economy.D. Gathering the greatest knights.27. What is the best title for the passage?A. Arthur Becomes KingB. Arthur Trains KnightsC. Arthur Defeats EnemiesD. Arthur Loves SwordsCIn recent years more and more Chinese schoolchildren are required to wear uniforms at school. Do American children wear school uniforms? In fact, American schoolchildren often wear uniforms if they attend religious or other private schools. Most public schools do not require uniforms. But over the last ten years or so, more of them have moved in that direction, including high schools. Another option is that students may just have to dress alike — for example, white shirts and dark colored pants or skirts. Even schools that do not require uniforms generally have a dress rule about what they consider acceptable. Schools commonly forbid clothing that shows images or words causing displeasure, or simply too much skin. Hats may be forbidden because, for example, different colors may be connected with bad guys.Some parents like the idea of uniforms. Some say it means they do not have to spend much on clothing for their kids. Others, though, argue that uniforms represent an unnecessary cost.There are also debates about whether uniforms or other dress rules go against civil rights. Students and parents have taken legal action against school dress requirements. Several years ago, a middle school was asked to stop its dress rule unless families had a way out of it. The American Civil Liberties Union of Northern California brought the case for the families of several students who had been punished by the school. Most attention centered on a girl who wore socks with the Tigger character from Winnie the Pooh. The school said its clothing policy, including no picturesof any kind, was needed to control a growing problem with gangs. The families argued that the policy went against free speech rights as protected by the United States and California constitutions.The United States Supreme Court says student expression is protected as long as it does not harm the work and the rule of a school. But some educators believe dressing alike helps improve student learning. They believe that uniforms help create a sense of unity and reduce the risk of fights. They also say uniforms make it easier for security reasons to tell if someone belongs to the school or not.28. According to the passage there is a trend in the USA that ______.A. most public schools do not require uniformsB. most public schools move in the direction of requiring uniforms at churchC. most schools require the students to be dressed in white shirts and dark colored pantsD. more and more schools have a dress rule about what are suitable for schoolchildren29. Which of the following is NOT a reaction mentioned to the dress rule?A. Some parents like the rule which means they could spend less on clothing for the kids.B. Some parents think the rule has nothing to do with them.C. Some parents say that uniforms are an extra cost for them.D. Some others argue that uniforms or other dress rules go against civil rights.30. What is the girl’s problem?A. She brought her pet called Tigger to school.B. She put Tigger into her socks in class.C. She wore socks with pictures.D. She had a problem with some gangs.31. School dress requirements can benefit schools and students except to help ______.A. the court protect student expressionB. students focus on their studiesC. make a united effort to avoid fightsD. strengthen campus securityDWhen one tried to unify gravity with quantum mechanics(量子力学), one had to introduce the idea of ‘imaginary’ time. If one can go forward in imaginary time, one ought to be able to turn round and go backward. This means that there can be no important difference between the forward and backward directions of imaginary time. Yet there is a big difference between the forward and backward directions of ‘real time’ in ordinary life. Imagine a cup of water falling off a table and breaking into pieces on the floor. If you take a film of this, you can easily tell whether it is being run forward or backward. You can tell that the film is being run backward because this kind of behavior is never observed in ordinary life.The explanation that is usually given as to why we don’t see broken cups gathering themselves together off the floor and jumping back onto the table is that it is forbidden by the second law of thermodynamics(热力学). This says that in any closed system disorder, or entropy(熵), always increases with time. In other words, it is a form of Murphy’s law: things always tend to go wrong! An intact cup on the table is a state of high order, but a broken cup on the floor is a disordered state. One can go readily from the cup on the table in the past to the broken cup on the floor in the future, but not the other way round.The increase of disorder or entropy with time is one example of what is called an arrow of time, something that tells the past from the future, giving a direction to time. There are at least three different arrows of time. First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropy increases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, the direction in which we remember the past but not the future. Finally, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.32. How does ‘imaginary time’ differ from ‘real time’ according to the passage?A. Imaginary time is more important than real time in science.B. Directions mean less to imaginary time than to real time.C. One can go backward in real time but can’t in imaginary time.D. It is harder to tell directions of real time than of imaginary time33. What’s the purpose of writing about a cup of water falling off a table?A. To define the forward and backward directions of real time.B. To tell the backward direction from the forward direction of real time.C. To show real time is more scientific than imaginary time in ordinary life.D. To prove there’s a big difference between the directions of real time.34. Why don’t we see broken cups gathering themselves together off the floor and jumping back onto the table?A. It doesn’t agree with the second law of thermodynamics.B. Things will quickly go wrong for entropy increases with time.C. There is an interchange between a state of high order and a disordered stateD. All above.35. The underlined word in the last paragraph is closest in meaning to ______.A. universalB. physicalC. technologicalD. geographical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。