上海市复旦附中2016年高一上学期开学考英语试题

考点05 代词人称、物主、反身、指示和疑问代词1．Being a parent is not always easy, and being the parent of a child with special needs often carries with _______ extra stress.A．it B．themC．one D．him2．-- There is still a copy of the book in the library. Will you go and borrow ________ ?---No, I’d rather buy __________ on the internet.A．it; one B．one; oneC．one; it D．it; it3．Isn’t it amazing how the human body heals ____ after an injury?A．himself B．himC．itself D．it4．Those who smoke heavily should remind __________of health, the bad smell and the feelings of other people.A．theirs B．themC．themselves D．oneself5．The quality of education in this small school is better than ______ in some larger schools. A．that B．oneC．it D．this6．The information on the Internet gets around much more rapidly than in the newspaper.A．it B．thoseC．one D．that7．--- Silly me! I forget what my luggage looks like.--- What do you think of_____over there?A．the one B．it C．that D．this8．The English spoken in the United States is only slightly different fromspoken in England. A．which B．what C．that D．the one9．Professional skills are tools like a knife or a hammer. You need ______ to complete the things you want to do.A．it B．that C．them D．ones不定代词10．It was hard for him to learn English in a family, in which _____ of the parents spoke the language.A．none B．neither C．both D．each11．Jim sold most of his things.He has hardly___left in the house.A．anything B．everythingC．nothing D．something12．My brother would like to buy a good watch but _______ was available from that shop. A．nothing B．noneC．no one D．neither13．A study shows the students who are engaged in after-school activities are happier than_________who are not.A．ones B．thoseC．these D．them14．I think Mrs. Stark could be _______ between 50 and 60 years of age.A．anywhere B．anybodyC．anyhow D．anythingit用法15．I’d appreciate ________ if you could let me know in advance whether or not you will come. A．it B．youC．one D．this16．No matter where he is, he makes ________ a rule to go for a walk before breakfast. A．him B．thisC．that D．it17．How would you like ________ if you were watching your favorite TV program and someone came into the room and just shut it off without asking you?A．them B．oneC．those D．it18．This is not my story, nor ______ the whole story. My story plays out differently.A．is there B．there isC．is it D．it is19．I like this house with a beautiful garden in front, but I don’t have enough money tobuy__________.A．one B．it C．this D．that20．It has been proved______eating vegetables in childhood helps to protect you against serious illnesses in later life.A．if B．because C．when D．that21．The employment rate has continued to rise in big cities thanks to the efforts of the local govenments to increase.A．then B．those C．it D．that22．—Who’s that at the door?—is the milkman.A．He B．It C．This D．That1.【2020·全国新课标I】Data about the moon’s composition, such as how much ice and other treasures it contains, could help China decide whether 70． (it) plans for a future lunar (月球的) base are practical.2.【2020·全国新课标I改错】＂Not that way，＂ my mom tried to stop us but failed.3.【2020·全国新课标2改错】Best of luck with yours learning kung fu in China.4.【2020·全国新课标3改错】But he insists on us eating healthy food.5．〔2015·重庆高考真题〕The meeting will be held in September, but ______ knows the date for sure. A．everybody B．nobodyC．anybody D．somebody6．〔2012·四川省高考真题〕New technologies have made ____ possible to turn out new products faster and at a lower cost.A．that B．this C．one D．it7．〔2012·山东省高考真题〕It doesn’t matter ________ you pay by cash or credit card in this store. A．how B．whetherC．what D．why8．〔2012·全国高考真题〕Larry asks Bill and Peter to go on a picnic with him, butof them wants to, because they have work to do.A．either B．anyC．neither D．none9．〔2012·福建省高考真题〕一 Have you figured out how much the trip will cost?—$4,000, or like that.A．anything B．everything C．something D．nothing10．〔2014·山东〕Susan made______ clear to me that she wished to make a new life for herself.A．that B．thisC．it D．her11．〔2015·福建〕The research group produced two reports based on the survey, but _________ contained any useful suggestions.A．all B．noneC．either D．neither12．〔2011·陕西省高考真题〕-Would you get me a bar of chocolate from the kitchen,dear?-one?A．Other B．Every C．Another D．More13．〔2016·浙江省高考真题〕In many ways, the education system in the US is not very different from ________ in the UK.A．that B．thisC．one D．it1．〔2020·某某耀华中学高一月考〕The goods ________ from the Internet are cheaper than ________ we buy in shops.A．be bought; thatB．bought; thoseC．bought; thatD．were bought; the ones2．〔2020·江苏省扬州中学高三月考〕--- The Captain is definitely a touching movie, ______ adapted from a true story.--- Exactly. Captain Liu puts the safety of passengers in the first place.A．one that B．which C．the one D．one3．〔2020·某某理工大学附属中学高一月考〕We thought _______ strange that Tony Stark should come. A．that B．it C．this D．what4．〔2020·江苏省苏州实验中学高三月考〕In public places, improved child-care facilities will benefit ________ genders, not just women.A．both B．all C．either D．other5．〔2020·某某高三二模〕Though reasons for learning Chinese vary, a common was enthusiasm for the country’s rich culture.A．one B．it C．that D．this6．〔2020·江苏省高三二模〕See things in a negative light and you will find faults everywhere and problems where there are really _______.A．none B．no one C．something D．nothing7．〔2020·天水市第一中学高一开学考试〕I would appreciate ______ if you could give me a reply as soon as possible.A．you B．it C．that D．them8．〔2020·河北承德第一中学高一月考〕 ______ has been decided that the 2020 Tokyo Olympic Games will be put off to 2021.A．It B．What C．As D．Which9．〔2020·某某四中高二期中〕The exchange student from Kenya often shares with us the news of his country and ____of his neighbouring countries.A．those B．that C．it D．the one10．〔2020·某某高三月考〕—What do you think of the information from books?— It is easier to forget than ________ from life itself.A．the one B．itC．that D．those11．〔2020·汉中市龙岗学校高一期末〕The old couple preferred a flat in a small town to ______ in so large a city as Chongqing．A．this B．it C．that D．one12．〔2020·某某市静海区大邱庄中学高三月考〕--- Silly me! I forget what my luggage looks like. --- What do you think of_____over there?A．the one B．it C．that D．this13．〔2020·江苏省天一中学高三月考〕What Chinese lawmakers begin to consider is a proposed revision to the country’s Food Safety Law,_______ include s mandatory (强制性) labeling of GM food. A．one B．the one which C．one that D．the one that14．〔2020·江苏省南京师大附中高三一模〕If you see things in a negative light, you will find faults everywhere and problems where there are really ________．A．none B．someC．many D．nothing15．〔2019·江苏省淮阴中学高三月考〕More overseas students are returning home to make contributions to our country, a large proportion of _____ reported to have received first-class education. A．whom B．which C．them D．whoever16．〔2019·黑龙江省哈九中高三月考〕You are really ! I heard marvelous news that you set a new world record.A．anything B．nothing C．something D．everything17．〔2019·黑龙江省哈九中高三月考〕When you go by train, make sure you take an express,___________stops only at big stations.A．one B．one that C．that D．what18．〔2020·某某静海一中高三月考〕“Made in China 2025〞 aims to transform China from a product-making factory into a product-making power, ______________ driven by innovation and emphasizing quality over quantity.A．the one that B．one thatC．one D．the one19．〔2020·江苏省高三开学考试〕“Made in Ch ina 2025〞 initiative aims to transform China from a manufacturing giant into a world manufacturing power, ________ driven by innovation and emphasizes quality over quantity.A．the one that B．one that C．one D．the one20．〔2020·黑龙江省黑龙江实验中学高三开学考试〕He is rich and brave. __________ is no wonder he is popular with girls.A．There B．That C．It D．What21．〔2019·某某曹杨二中高一月考〕I had to buy _____ of these books because I didn’t know which one was the best.A．both B．none C．neither D．all22．〔2020·江西省高一期末〕—I wonder how often you will clean up your room by yourself.—________ other day.A．In B．Every C．For D．Each23．〔2020·黑龙江省哈尔滨三中高二期中〕People were dressed in elegant costumes, all of _____ suitable for a multicultural parade.A．which B．whom C．them D．who24．〔2019·某某市静海区独流中学高二月考〕Praise is like sunlight to the human spirit; without _______ we cannot flower and grow.A．them B．it C．that D．which25．〔2019·某某复旦附中高二期末〕The autobiography(自传) of the happiest man would not be a record of sensational or exciting experiences, but ________ composed of simple and plain incidents or routines.A．it is B．which is C．one that D．one考点练1．A【解析】考查代词的用法。

专题5 追击相遇问题一、匀速与变速类追击相遇问题1．甲、乙两个质点沿同一直线运动，其中质点甲以3m/s的速度做匀速直线运动，质点乙做初速度为零的匀变速直线运动，它们的位置x随时间t的变化如图所示。

已知t=3s时，甲、乙图线的斜率相等。

下列判断正确的是（）A．最初的一段时间内，甲、乙的运动方向相反-B．t=3s时，乙的位置坐标为15.5mt=时，两车相遇C．10sD．乙经过原点的速度大小为/s2．（2022·重庆一中高一期末）无线蓝牙耳机可以在一定距离内与手机等设备实现无线连接。

已知无线连接的最远距离为10m，甲和乙两位同学做了一个有趣实验。

甲佩戴无线蓝牙耳机，乙携带手机检测，如图（a）所示，甲、乙同时分别沿两条平行相距6m的直线轨道向同一方向运动，甲做匀速直线运动，乙从静止开始先做匀加速直线运动，再做匀速直线运动，其速度v随时间t的关系如图（b）所示，则在运动过程中，手机检测到蓝牙耳机能被连接的总时间为（）A．4s B．9s C．13s D．17s3．（2022·湖南·高一期中）（多选）无线蓝牙耳机摆脱了线材束缚，可以在一定距离内与手机等设备实现无线连接。

为了研究在运动过程中无线连接的最远距离，甲和乙两位同学做了一个有趣的实验。

乙佩戴无线蓝牙耳机，甲携带手机检测，乙站在甲正前方10m处，二人同时沿同一直线向正前方运动，各自运动的v t-图像如图所示，结果手机检测到蓝牙耳机能被连接的时间为4s。

则下列判断正确的是（）A ．3s 时甲乙相距最远B ．6s 时甲乙相距最近C ．甲减速加速度大小为21m /sD ．5s 时两者距离为7.5m4．（2020·广东·化州市第一中学高一阶段练习）（多选）在平直公路上，自行车与同方向行驶的一辆汽车在t =0时同时经过某一个路标，它们的位移x （m ）随时间t （s ）变化的规律为：汽车为21104x t t =-，自行车为x =6t ，则下列说法正确的是（ ）A ．汽车做匀减速直线运动，且汽车经20s 停止B ．在t =8s 时两车速度相等，自行车第一次追上了汽车C ．在t =0至t =16s 时间内，两车间距离先增大后减小D ．当自行车追上汽车时，它们距路标96m5．甲、乙两车在平直公路上比赛，某一时刻，乙车在甲车前方111m L =处，乙车速度60m/s v =乙，甲车速度50m/s v =甲，此时乙车离终点线尚有2600m L =，如图所示。

上海国际学校招生计划国际学校(英语：International School)是提供中等或以下程度的教育，并拥有相当比例的外籍学生，而且实施外国学制的学校。

以下是关于上海国际学校招生计划，希望大家认真阅读!1闵行区民办德闳学校学校性质：面向中国学生的十二年制国际学校学校地址：闵行区曙光路1935号学校概况：学校在实施上海市二期课改课程的基础上，通过国外教育专家的指导，为中国学生提供更多融合了国际先进教育理念和实践经验的国际课程。

招生情况：2017年开始招生2星河湾中学学校性质：完全中学学校概况：学校在区政府、颛桥镇领导和市委的大力支持下建立，旨在建成“主打双语特色，走国际化道路”的完全中学。

招生情况：预计2017年开始招生，预计学生数超过2000人的中学，规划初中24个班(每年级6个，每班40人)、高中24个班(每年级8个，每班45人)3人大附中上海分校学校性质：小学到高中十二年寄宿制学校地址：奉贤海湾旅游区学校概况：中国人民大学附属中学创办于1950年，是一所享誉中外的著名中学。

人大附中上海分校是一所寄宿制民办学校，包括小学、初中和高中，占地规模为130亩，计划于2016年下半年开工建造。

人大附中是“三高”足球训练基地，培养“道德水平高、文化素质高、运动水平高”的足球后备人才。

为此，未来的上海分校也将一并引入“三高”项目，奉贤区提供两片专业足球场用于日常训练，使之成为奉贤区乃至上海市校园足球训练和培训中心。

据悉，上海分校将采用上海教材，但在办学理念和学校管理等方面全面引入人大附中的优质资源。

学校资产归奉贤区政府，由区教育行政部门管理。

招生情况：拟定2018年开始招生，学校拟定为48个班，其中，小学20个班，初中16个班，高中12个班。

面向全市招生，在同等条件下优先招收奉贤区学生。

4位育中学(闵行校区)学校性质：初中学校地址：莘庄工业区(中春路东面，颛盛路南面)招生情况：预计将于2018年竣工，招生计划暂时还未出5嘉定中科院上海实验学校开学时间：2017年/2018年学校概况：中国科学院上海实验学校是经中国科学院批准，隶属于嘉定区教育局的公办学校，学校地处嘉定菊园新区，设一个初中部和一个小学部。

上海师范大学附属中学 2022-2023学年高一上学期期中考试英语试卷学校:___________姓名：___________班级：___________考号：___________一、用单词的适当形式完成短文Directions: After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Charlotte Whitehead was born in England in 1843, and moved to Montreal, Canada at the age of 5 with her family. While ___1___ (take) care of her ill elder sister throughout the years, Charlotte discovered she had an interest in medicine. At 18 she married and started a family. Several years later, Charlotte said she wanted to be a doctor. Her husband supported her decision. Unfortunately, Canadian medical schools did not accept women students at the time. Therefore, Charlotte went to the United States ___2___(study) medicine at the Women’s Medical College in Philadelphia. ___3___ took her five years to earn her medical degree.Upon graduation, Charlotte returned to Montreal and set up a private clinic. Three years later, she moved to Winnipeg, Manitoba, ___4___ she was once again a busy doctor. Many of her patients were from the nearby timber and railway camps. Charlotte found herself operating on damaged limbs and setting broken bones, ___5___ delivering all the babies in the area.But Charlotte had been practising without a license. She had applied for a doctor’s license in both Montreal and Winnipeg, ___6___ was refused. The Manitoba College of Medicines, ___7___ all-male organization, wanted her to complete her studies at a Canadian medical college! Charlotte refused to leave her patients to spend time studying ___8___ she already knew. So in 1887, she appealed to the Manitoba Legislature to issue a license to her but they, too, refused. Charlotte continued to practise ___9___ a license until 1912. She died four years later at the age of 73.In 1993, 77 years after her death, a medical license was issued to Charlotte. This decision ____10____(make) by the Manitoba Legislature to honour “this courageous and pioneering woman”.Directions: After reading the passage below, fill in the blanks to make the passage coherentand grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.My Volunteer Experience in GhanaIt is not quite six in the morning. I am half asleep in a van that in the United States would seat maybe six people. Here in Ghana though, its insides have been replaced with wooden benches that can accommodate twelve of us. I use the term “accommodate” loosely; we are squeezed so tight in together ___11___ sometimes my arm goes numb (麻木的).This goes on for two hours every morning, from Monday to Friday, so that I ___12___ get to the slum town school where I teach.___13___ (arrive) at the destination always fills me with fear. The school originally functioned as a daycare type service free to the children of single mothers. ___14___ the children got older, the coordinator took it upon herself to set up a space to teach them. Into this tiny space they squeeze anywhere between 80 and 120 children under the age of six. It is literally so full of children that you have to move them out of the way by shoving (推开) them with your feet ___15___ (avoid) stepping on them.Within days, I have already learned most of their names. There are the troublemakers who spend their time ___16___(hit) one another and causing chaos in hopes that their negative behavior will attract attention to themselves. All of my child psychology classes tell me to ignore the behavior ___17___ responding to it may reinforce the behavior.Then there are the ones that make your heart bleed. The five-year-old girl who ___18___ (sit) in the front row, is ready to learn whatever knowledge we can throw her way. She learns whatever we teach her, at a pace ___19___ takes my breath away. She far outpaces any Western five-year-old I’ve ever worked with, and she’s learning in English when her family only knows and speaks Twi, a local language.I look at this decrepit (破旧的) classroom and these children in their ragged clothes, and think of ____20____ different this is from the American classrooms I’ve known.二、选用适当的单词或短语补全短文Directions: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.The digital revolution has had a huge impact on every aspect of our society. For content creators, life looks nothing like it did just a couple of decades ago. Back then, all you had to do is to take the tape off the camera and put it on your ___21___ player. At most, you had to read an article to understand the difference between HS and Betamax. Video was only consumed in two ways: television or cinema. Nowadays, you’ll probably run out of fingers ___22___ how many video formats (格式) there are out there, let alone the number of platforms and devices on which video is played. Understanding what each video format is and does is no child’s play. In fact, it is a “must” if you want your work to look the best regardless of where and how it is played. If, for example, you want to ___23___ a video website, the type of file you’ll need to use will most likely to be different from the one you’ll have to create for your social media accounts. In order to make this whole process a lot easier, we have put together a list of the most common video formats and which ones you should use for each purpose.So what’s the best video format?___24___, there isn’t a cure-all when it comes to video sharing. The good thing is that it’s actually really easy to ___25___ between video formats. If you do so, be sure to always save the original file in order to avoid ___26___ of image quality due to file compression(压缩).Here are three of the most common video uses and the ___27___ formats for each of them:●Social media: MP4 is supported by Facebook, Twitter, Instagram, IGTV, and YouTube. Facebook also___28___ MOV, while YouTube accepts most video formats.●TV and computers: A VI, MOV, and MKV ___29___ the highest quality image which makes them great options for big screen streaming.●Website: WEBM and HTML5 are the video formats meant for your account. However, using tools such as Wix Video will allow you to work with almost any file ____30____, as well as offer you much more control over your work.Directions: Complete the following passage by using the words in the box. Each word canonly be used once. Note that there is one word more than you need.The value of upcyclingRecycling is a well-known idea that refers to reusing waste materials in any way possible. But what about “upcycling”? It’s a new word, even though it’s something that has been going on since human ____31____ began. It means reusing waste materials so that they have greater value. Throughout history, people have always done creative things with “trash”. For example, they’ve used straw and dead leaves to make roofs, skin from dead animals to make leather goods, and wood from ____32____ trees to make boats. So why is there a new word for it now?One answer to this question is that we reuse fewer and fewer things, and so have become a (n) “____33____” society. This has raised huge questions about waste: Where can we____34____ it all? Will it pollute the environment? Could it be ____35____ to our health? The evidence is everywhere—even in the Pacific Ocean, where billions of bits of broken____36____ float near the surface. Fish eat them, and then we eat the fish.So upcyclers have adopted this new word to focus people’s attention on how waste cannot simply be reused, but be reused ____37____. In fact, upcyclers don’t like the idea of waste and prefer to call it an “asset”, something of value. Nowadays, there are lots of organizations that ____38____ products with upcycled material. Some artists and designers have upcycled things like denim from old jeans to make rugs, and wood from old houses to make furniture. Others have even used candy wrappers to make handbags! Sometimes they’ll add a(n) ____39____ element to their products, such as a beautiful mosaic (马赛克) made with broken dishes. With a (n) _____40_____ supply of “assets”, it seems that upcycling has a great future.三、完形填空Deliverance(解救) for Delivery Drivers?ZOOOOOOOOM A gust of air, the hum of spinning wheels, and a flash of color whizzing past. I’m sure that we have all stepped into the crosswalk, at one time or another, and experienced this sudden, heart-stopping ___41___. I am, of course, referring to deliverydrivers ___42___ through crossroads to deliver takeaway food.Over the past few years, delivery drivers have been criticized, fined, and even ___43___ for breaking traffic laws across China. Delivery drivers often ___44___ red lights, disregard speed limits, and pay little attention to pedestrian crossings. But they also often pay the___45___ price — each year, it seems like fatal injuries involving delivery drivers are increasing. ___46___, since delivery drivers are usually poorly paid, how much blame do they really deserve for running against the clock?Well, it ___47___ to be a complicated issue. Recently an article titled “Delivery Drivers, Stuck in the System” was shared widely on social media. According to the article, ___48___ between delivery services Ele.me and Meituan has caused each app to take increasingly extreme measures to out-do(超过) the other. This has included the shortening of delivery time windows. It has been ___49___, in part, through a combination of rewards for early delivery and severe punishments for late delivery. Over time, the platforms have only increased these ___50___ on drivers. As a result, drivers find themselves in a dilemma(左右两难的困境)：break traffic laws or, in some cases, lose hundreds of yuan in earnings for late deliveries.According to surveys and reactions online, ___51___ care much whether their deliveries are a few minutes late, while most believe that it is not worth risking someone’s life for. In response, Ele.me and Meituan have added a combination of features to ___52___ delivery times for slow elevators or bad weather conditions.Although these new ___53___ cannot solve the underlying problems of intense competition or the inherent dangers of driving, they should, in some measure, start reducing some of the pressure on drivers. In the meantime, as ___54___, we can help to make life for delivery riders safer and easier. ___55___, be a considerate person and don’t leave them waiting for too long. If you see a food delivery guy rushing toward you on an escalator or into a door, consider standing back and letting him go first. After all, they are putting their lives on the line just to deliver our food.41．A．fright B．delight C．pain D．sorrow 42．A．running B．walking C．rushing D．wandering 43．A．arrested B．fired C．blamed D．praised 44．A．destroy B．ignore C．observe D．interrupt 45．A．everlasting B．dramatic C．slight D．final 46．A．However B．Namely C．Indeed D．Surprisingly47．A．decides B．refuses C．turns out D．takes turns 48．A．comparison B．contrast C．competition D．cooperation 49．A．adapted B．achieved C．adopted D．assumed 50．A．motivations B．advantages C．pressures D．skills 51．A．some B．few C．many D．we 52．A．reduce B．expand C．narrow D．extend 53．A．actions B．behaviors C．features D．conditions 54．A．humans B．consumers C．friends D．taxpayers 55．A．In one word B．As a result C．For example D．On the contrary四、阅读理解Who is a genius? This question has greatly interested humankind for centuries.Let’s state clearly: Einstein was a genius. His face is almost the international symbol for genius. But we want to go beyond one man and explore the nature of genius itself. Why is it that some people are so much more intelligent or creative than the rest of us? And who are they?In the sciences and arts, those praised as geniuses were most often white men, of European origin. Perhaps this is not a surprise. It’s said that history is written by the victors, and those victors set the standards for admission to the genius club. When contributions were made by geniuses outside the club—women, or people of a different color or belief—they were unacknowledged and rejected by others.A study recently published by Science found that as young as age six, girls are less likely than boys to say that members of their gender(性别)are “really, really smart.” Even worse, the study found that girls act on that belief: Around age six they start to avoid activities said to be for children who are “really, really smart.” Can our planet afford to have any great thinkers become discouraged and give up? It doesn’t take a genius to know the answer: absolutely not.Here’s the good news. In a wired world with constant global communication, we’re all positioned to see flashes of genius wherever they appear. And the more we look, the more we will see that social factors(因素)like gender, race, and class do not determine the appearance of genius. As a writer says, future geniuses come from those with “intelligence, creativity, perseverance(毅力), and simple good fortune, who are able to change the world.”56．What does the author think of victors’ standards for joining the genius club? A．They’re unfair.B．They’re conservative.C．They’re objective.D．They’re strict.57．What can we infer about girls from the study in Science?A．They think themselves smart.B．They look up to great thinkers.C．They see gender differences earlier than boys.D．They are likely to be influenced by social beliefs58．Why are more geniuses known to the public?A．Improved global communication.B．Less discrimination against women.C．Acceptance of victors’ concepts.D．Changes in people’s social positions.59．What is the best title for the text?A．Geniuses Think Alike B．Genius Takes Many Forms C．Genius and Intelligence D．Genius and LuckFor many travelers these days, finding a way to make travel more meaningful has become a top priority. They are increasingly pursuing journeys that include time to volunteer, work on a conservation project, protect endangered animals or to do other activities that allow for giving back while exploring a new part of the world. Here are some opportunities that combine travel with doing good deeds.The AzoresThe trips offer the opportunity to work on carefully selected projects with famous scientists while also enjoying meetings with some of the world’s most attractive sea creatures in water. It allows participants to join a research team in the Azores that’s studying the animals to support future protection of the species. Advanced diving experience is required.Red Sea, EgyptCombining an opportunity for world-class diving with being part of an important research effort conducted by Hurghada Environmental Protection and Conservation Association. The seven-night trip includes learning how to gather water data with the latest scientific equipment and conducting onboard and underwater experiments.AustraliaExplore Queensland, Australia, while also supporting a registered charity that rescues farm animals from abuse, neglect, and situations where they’re in danger. Participants help with daily cleaning of barns (牲口圈) and cages, feeding, health checks, light repair, monitoring animals’ movements, and intensive care of ill, old and baby animals. The experience includes free accommodations with WiFi and a swimming pool.RomaniaWork with bears at Romania’s largest bear sanctuary (庇护所), a place that was created as a heaven for bears that have been treated in a cruel way. Located in the Carpathian Mountains, the sanctuary needs volunteers to help with preparing food, monitoring animal health and leading conservation tours. The sanctuary is home to 84 bears, with 20 more due to be rescued.60．What do the first two trips have in common?A．Both involve underwater activities.B．Both provide free accommodations.C．Both require advanced diving experience.D．Both teach how to use scientific equipment.61．Which place best suits a girl who likes horses?A．The Azores.B．Red Sea.C．Australia.D．Romania. 62．Why are the bears adopted by the sanctuary in Romania?A．They have no food.B．They are badly treated.C．They should be monitored.D．They need to live in mountains. 63．Where does the passage most probably appear?A．In a fashion magazine.B．In a shopping guide.C．In a travel brochure.D．In a biography.My son, Toby, 17 months old, has just tested positive for COVID-19. He is the first in our household to test positive, and all the information provided for people in this situation is designed for adults who are(or should be) concerned about protecting their families. Toby, obviously, cannot comprehend such advice. He cannot keep a distance from everybody else, or eat and wash in a separate room. We called 911, and the medic we spoke to agreed that the official guidance didn’t really apply to our situation.Indeed. Not much we can do. So, here we are, trapped within our four walls with a little baby infected with COVID-19, who continues to climb on us, spit in our faces, love us and hug us. It seems inevitable that we, and our elder son, are going to get COVID now. Not much we can do.My first reaction, after absorbing his diagnosis, was to cook sausages. I didn’t even know that was my comfort food of choice. Perhaps an afternoon crisis would have caused a different cooking desire? Anyway, a full stomach helped me take stock. Yes, it may now be inevitable that we’re going to contract the very virus we’ve spent a year avoiding, but as long as we don’t contract it at the same time, then, hopefully, one other of us will be available to look after our kids (thus answering my five-year-old’s most pressing concern: “…but who will make the pudding?”).So, to minimise transmission, we’ve opened all the windows. And we’ve decided to wear face coverings whenever we are with Toby. This decision has been insignificant to him—I imagine he literally cannot remember life before masks—but for me, it’s distressing. I’ve become accustomed to wearing masks in supermarkets and coffee shops, of course, but to actually walk around with half my face covered in my own house is quite another matter—it is telling me that my home has been infected, That it’s no longer a safe space.And so it was, when I sat down to write this column, that I ended up writing about COVID, which is probably the last thing you wanted to read. Sorry about that. COVID has coloured my thoughts today, even though I know that my wife and children will be fine, and that really we should just be grateful we haven’t passed it on to my grandmother.I predict there will be more sausages in the morning.64．By repeating the sentence “Not much we can do” in paragraph 2, the writer implies that ________.A．he feels inspired B．he is really helplessC．he wants professional support D．he needs to keep a distance from Toby 65．According to the writer, what did sausages bring to him?A．Appetite.B．Concern.C．Relief.D．Sadness. 66．Why did wearing masks at home distress the writer?A．It discourages him from writing about COVID．B．It brings him back to the days before COVID-19C．It makes him feel at a loss for how to help his son.D．It is a reminder of what is happening to his family.67．What can be concluded from the passage?A．The diagnosis leaves the writer’s family in a tough spot.B．Being infected with COVID-19 leaves Toby in a bad mood.C．The writer is sure that his other kids won’t contract the virus.D．Sausages have long been considered by many to be comfort foodHong Kong isn’t the first place you’d expect to find a peaceful island. But in a quiet corner of Sai Kung district (西贡区), a tiny green island offers a rare glimpse into the past.Nicknamed “Ghost Island,” Yim Tin Tsai (盐田仔) was once home to a flourishing Hakka (客家) community. They settled on the empty island and built salt pans (盐田) to earn a living. When the salt pans were shut down more than 100 years ago, most residents turned to farming and fishing.In the 1960s, more and more families moved to other places. The last of the villagers on the island had moved abroad by the 1990s, and, in the following years, Yim Tin Tsai lay empty.If travelers had visited Yim Tin Tsai a decade ago, they would have found nothing but overgrown weeds (野草) and crumbling houses. That’s exactly what villager Colin Chan saw when he returned to the island after 40 years. But, for him, the island represented something special — a unique side of Hong Kong’s history and culture that shouldn’t be forgotten.“I came back here hoping to recover something I felt I had lost,” Colin said. “I found the island was in ruins and I was very sad. This is the place I grew up. This is my father’s home and his father’s home.”In 1999, Colin was elected as village representative and began what would become a lifelong mission: to make the island come alive. Together with about 10 former villagers, Colin raised money to build a visitor center for travelers. In 2004, a charitable foundation donated funds to renovate the island’s historical chapel (小教堂). In 2005, UNESCO (联合国教科文组织) Asia-Pacific Heritage Awards for Cultural Heritage Conservation honored the chapel with an award of merit (优异奖).Motivated by this, the villagers organized a regular ferry schedule to enable travelers to reach the island, and set out to showcase the village’s unique history. They built a heritage trail, repaired Hakka ancestral homes, created a museum, and even started an organic farmthat sits at the foot of the church.68．According to the article, the Hakka community________.A．all moved to other countries in the 1990sB．settled on Yim Tin Tsai about 100 years agoC．made a living by salt mining, farming and fishing on Yim Tin TsaiD．found Yim Tin Tsai to be a fertile place when they had first arrived there69．The word “crumbling” in paragraph 4 could probably be replaced by “______.”A．frightened B．broken C．disappearing D．decreasing 70．Which of the following is NOT a reason why Colin Chan came back to Yim Tin Tsai? A．Because he wanted to recover the special feeling of the place where he grew up. B．Because as village representative, he had the duty to bring the village back to life. C．Because he didn’t want to see the hometown of his father and grandfather in ruins. D．Because he wanted to preserve Hong Kong’s history and culture mirrored in the island. 71．We can learn from the article that _______.A．UNESCO honored Yim Tin Tsai with an award of merit in 2005.B．If travelers visit Yim Tin Tsai today, they will find it a lush, green island full of life. C．Colin Chan raised money to build a museum to showcase the village’s unique history. D．the villagers on Yim Tin Tsai want to restore the salt pans which were closed more than 100 years ago.五、六选四A selection from the trolleyThe trolley problem used to be a popular question in philosophical ethics(伦理学).It runs as follows: a trolley, or a train, is speeding down a track towards a junction(三叉路口). Some evildoer has tied five people to the track ahead, and another person to the branch line. You are standing next to a lever(操纵杆) that controls the junction. Do nothing, and the five people will be killed. Pull the lever, and only one person dies. What is the ethical course of action?_____72_____ A truly self-driving car, after all, will have to be given ethical instructions of some sort by its human programmers. That has led to a boom for the world’s professional ethicists, who suddenly find themselves in hot demand.In a paper just published in Nature, a team of psychologists and computer scientists, led by Edmond Awad of the Massachusetts Institute of Technology (MIT), describe a different approach. _____73_____They created a website which presents visitors with a series of choices about whom to save and whom to kill. The website proved a hit. In the end it gathered nearly 40m decisions.The strongest preferences, expressed by respondents from all over the world, were for saving human lives over animal ones, preferring to save many rather than few and prioritising children over the old. _____74_____Iyad Rahwan, a computer scientist at MIT and one of the paper’s authors, says that many people dismiss the trolley problem as pointless as it is unlikely to arise in real life. He is unconvinced. The specific situations described by the website may hardly ever occur, he says. _____75_____ He gives the example of overtaking cyclists: “If you stay relatively near to the cycle lane, you’re increasing the chance of hitting a cyclist, but reducing the chance of hitting another car in the next lane over,” he says.A．But all sorts of choices made by the firms producing self-driving cars will affect who lives and who dies in indirect ways.B．Rather than asking philosophers for their thoughts, they decided instead to ask the public. C．That seems to conflict with most people’s moral preferences.D．The preference for saving women, for instance, was stronger in places with higher levels of gender equality.E．There were weaker preferences for saving women over men, pedestrians over passengers in the car and for taking action rather than doing nothing.F．The excitement around self-driving cars, though, has made the problem famous.六、汉译英（整句）76．从长远来看，回收包装对环境有积极的影响。

第01讲 空间直线与平面（核心考点讲与练）一、空间间位置关系的集合语言集合的语言来描述点、直线和平面之间的关系：点A 在直线l 上，记作：A l ∈；点A 不在直线l 上，记作A l ∉； 点A 在平面α内，记作：A α∈；点A 不在平面α内，记作A α∉； 直线l 在平面α内（即直线上每一个点都在平面α内），记作l α⊂； 直线l 不在平面α内（即直线上存在不在平面α内的点），记作l α⊄； 直线l 和m 相交于点A ，记作{}lm A =，简记为lm A =；平面α与平面β相交于直线a ，记作a αβ=．二、平面的三个公理及推论1.公理一：如果一条直线上的两点在一个平面内，那么这条直线上所有的点都在这个平面内．图形语言表述：如右图： αBlA符号语言表述：,,,A l B l A B l ααα∈∈∈∈⇒⊂ 用途：证明“点在面内”、“线在面内”.2.公理二：经过不在同一条直线上的三点，有且只有一个平面，也可以简单地说成，不共线的三点确定一个平面．图形语言表述：如右图，αCBA符号语言表述：,,A B C 三点不共线⇒有且只有一个平面α，使,,A B C ααα∈∈∈． 用途：证明“两平面重合”、“多点共面”、“点线共面”.3.公理三：如果不重合的两个平面有一个公共点，那么它们有且只有一条过这个点的公共直线．图形语言表述：如右图： Aαaβ符号语言表述：,A a A a αβαβ∈⇒=∈．考点考向用途：证明“多点共线”、“多线共点”.如果两个平面有一条公共直线，则称这两个平面相交，这条公共直线叫做两个平面的交线．4.推论推论1：经过一条直线和直线外的一点，有且只有一个平面．推论2：经过两条相交直线，有且只有一个平面．推论3：经过两条平行直线，有且只有一个平面．三、空间中的平行关系1.平行直线(1)平行公理过直线外一点有且只有一条直线和已知直线平行.(2)基本性质4(空间平行线的传递性)平行于同一条直线的两条直线互相平行.(3)定理如果一个角的两边与另一个角的两边分别对应平行，并且方向相同，那么这两个角相等. 2.直线与平面平行(1)直线与平面平行的定义直线l与平面α没有公共点，则称直线l与平面α平行.(2)判定定理与性质定理文字语言图形表示符号表示判定定理平面外一条直线与此平面内的一条直线平行，则该直线平行于此平面a⊄α，b⊂α，a∥b⇒a∥α性质定理一条直线和一个平面平行，则过这条直线的任一平面与此平面的交线与该直线平行a∥α，a⊂β，α∩β＝b⇒a∥b3.(1)平面与平面平行的定义没有公共点的两个平面叫做平行平面.(2)判定定理与性质定理文字语言图形表示符号表示判定定理一个平面内的两条相交直线与另一个平面平行，则这两个平面平行a⊂α，b⊂α，a∩b＝P，a∥β，b∥β⇒α∥β性质定理两个平面平行，则其中一个平面内的直线平行于另一个平面α∥β，a⊂α⇒a∥β如果两个平行平面同时和第三个平面相交，那么它们的交线平行α∥β，α∩γ＝a，β∩γ＝b⇒a∥b四、空间中的垂直关系1.直线与平面垂直(1)直线与平面垂直的定义如果一条直线和一个平面相交于点O，并且和这个平面内过交点(O)的任何直线都垂直，就说这条直线和这个平面互相垂直.(2)直线与平面垂直的判定定理及其推论文字语言图形语言符号语言判定定理如果一条直线与平面内的两条相交直线垂直，则这条直线与这个平面垂直⎭⎪⎬⎪⎫a⊂αb⊂αa∩b＝Ol⊥al⊥b⇒l⊥α推论1如果在两条平行直线中，有一条垂直于平面，那么另一条直线也垂直于这个平面⎭⎪⎬⎪⎫a∥ba⊥α⇒b⊥α推论2如果两条直线垂直于同一个平面，那么这两条直线平行⎭⎪⎬⎪⎫a⊥αb⊥α⇒a∥b2.(1)定义：一条斜线和它在平面内的射影所成的角叫做斜线和平面所成的角，一条直线垂直于平面，则它们所成的角是直角；一条直线和平面平行或在平面内，则它们所成的角是0°的角.(2)范围：⎣⎢⎡⎦⎥⎤0，π2.3.二面角(1)定义：从一条直线出发的两个半平面所组成的图形叫做二面角；(2)二面角的平面角：在二面角的棱上任取一点，以该点为垂足，在两个半平面内分别作垂直于棱的两条射线，这两条射线所构成的角叫做二面角的平面角. (3)二面角的范围：[0，π]. 4.平面与平面垂直 (1)平面与平面垂直的定义如果两个相交平面的交线与第三个平面垂直，又这两个平面与第三个平面相交所得两条交线互相垂直，就称这两个平面互相垂直.(2)平面与平面垂直的判定定理与性质定理文字语言图形语言 符号语言判定定理 如果一个平面过另一个平面的一条垂线，则这两个平面互相垂直⎭⎪⎬⎪⎫l ⊥αl ⊂β⇒α⊥β性质定理 如果两个平面互相垂直，那么在一个平面内垂直于它们交线的直线垂直于另一个平面⎭⎪⎬⎪⎫α⊥βl ⊂βα∩β＝a l ⊥a⇒l ⊥α1.异面直线的判定方法2.求异面直线所成的角的三步曲方法技巧3．线面平行的证明方法（1）定义法：一般用反证法；（2）判定定理法：关键是在平面内找(或作)一条直线与已知直线平行，证明时注意用符号语言叙述证明过程；（3）性质判定法：即两平面平行时，其中一个平面内的任何直线都平行于另一个平面．4．构造平行直线的常用方法（1）构建三角形或梯形的中位线：可直接利用线段的中点、等腰三角形三线合一或利用平行四边形对角线的交点找中点，从而构建中位线；（2）构建平行四边形：可以利用已知的平行关系(如梯形的上下底边平行)或构建平行关系(如构造两条直线同时平行于已知直线)，从而构建平行四边形．应用线面平行的性质定理时，关键是过已知直线作辅助平面与已知平面相交，所得交线与已知直线平行，还可以利用交线判断已知平面内的直线与已知直线的位置关系，即在已知平面内所有和交线平行的直线都与已知直线平行，所有和交线相交的直线都与已知直线异面．5.判定平面与平面平行的4种方法（1）面面平行的定义，即证两个平面没有公共点(不常用)；（2）面面平行的判定定理(主要方法)；（3）利用垂直于同一条直线的两个平面平行(客观题可用)；（4）利用平面平行的传递性，两个平面同时平行于第三个平面，那么这两个平面平行(客观题可用)．利用线面平行或面面平行的性质，可以实现与线线平行的转化，尤其在截面图的画法中，常用来确定交线的位置．对于线段长或线段比例问题，常用平行线对应线段成比例或相似三角形来解决．6.证明直线和平面垂直的常用方法：①判定定理；②垂直于平面的传递性(a∥b，a⊥α⇒b⊥α)；③面面平行的性质(a⊥α，α∥β⇒a⊥β)；④面面垂直的性质．7.利用判定定理证明平面与平面垂直的一般方法先从现有的直线中寻找平面的垂线，若这样的垂线存在，则可通过线面垂直来证明面面垂直；若这样的垂线不存在，则需通过作辅助线来证明平面及其基本性质1．（2022·上海民办南模中学高二开学考试）“平面内有一条直线，则这条直线上的一点必在这个平面内”用符号表述是（ ）A ．a A A a αα⊂⎫⇒⊂⎬⊂⎭B ．a A A a αα⊂⎫⇒∈⎬∈⎭C ．a A A a αα∈⎫⇒∈⎬⊂⎭D ．a A A a αα∈⎫⇒⊂⎬∈⎭2．（2022·上海·华师大二附中高二期末）设1234P P P P 、、、为空间中的四个不同点，则“1234P P P P 、、、中有三点在同一条直线上”是“1234P P P P 、、、在同一个平面上”的（ ） A ．充分非必要条件 B ．必要非充分条件 C ．充要条件D ．既非充分又非必要条件3．（2021·上海·复旦附中高二期中）若A ∈面α，B ∉面α，C ∉面α，则平面ABC 与平面α的位置关系_________．4．（2021·上海市大同中学高二阶段练习）已知111BAC B AC ∠=∠，11//AB A B ，则AC 与11A C 的位置关系是__________.直线与直线间的位置关系1．（2022·上海市建平中学高二阶段练习）不同在任何一个平面上的两条直线的位置关系是_________直线与平面间的位置关系1．（2021·上海奉贤区致远高级中学高二阶段练习）设m ，n 是两条不同的直线，α表示平面，下列说法正确的是（ ）A ．若m //α，n ⊂α，则m //nB ．若m //α，m ⊥n ，则n ⊥αC ．若m ⊥α，m ⊥n ，则n //αD ．若m ⊥α，n //α，则m ⊥n2．（2021·上海·高二专题练习）若a 、b 是异面直线，则下列命题中的假命题为（ ） A ．过直线a 可以作一个平面并且只可以作一个平面α与直线b 平行 B ．过直线a 至多可以作一个平面α与直线b 垂直 C ．唯一存在一个平面α与直线a 、b 等距 D ．可能存在平面α与直线a 、b 都垂直3．（2021·上海奉贤区致远高级中学高二阶段练习）Rt ABC △的直角边AB 在平面α内，顶点C 在平面α外，则直角边BC 、斜边AC 在平面α上的射影与直角边AB 组成的图形是（ ）A ．线段或锐角三角形B ．线段或直角三角形C ．线段或钝角三角形D ．线段、锐角三角形、直角三角形或钝角三角形 二、填空题4．（2020·上海市七宝中学高二期末）平面α外的直线a 与平面α所成的角是θ，则θ的取值范围是______. 5．（2021·上海市七宝中学高二期中）在三棱锥P ABC -中，已知PA ⊥平面ABC ，BC AC ⊥，则以P ，A ，B ，C 为顶点的直角三角形的个数为________.6．（2021·上海奉贤区致远高级中学高二阶段练习）若2AB =，线段AB 所在直线和平面α成30°角，且αA ∈，则点B 到平面α的距离=___________7．（2021·上海·位育中学高二阶段练习）如图，在直角ABC 中，2C π=，20BC =，40AB =，现将其放置在平面α的上面，其中点A ，B 在平面α的同一侧，点C ∈平面α，BC 与平面α所成的角为6π，则点A 到平面α的最大距离是___________.5．（2021·上海·华师大二附中高二阶段练习）在120°的二面角α－l －β的两个面内分别有点A ，B ，A ∈α，B ∈β，A ，B 到棱l 的距离AC ，BD 分别是2，4，且线段AB ＝10.(1)求C ，D 间的距离；(2)求直线AB 与平面β所成角的正弦值．平面与平面间的位置关系1．（2022·上海·复旦附中高二期中）已知a ，b 是两条不重合的直线，α，β是两个不重合的平面，给出下列命题：①//a α，////b a b α⇒；②//a b ，////b a αα⇒；③//αβ，a α⊂，//b a b β⊂⇒．其中假命题．．．的序号是______．（写出所有假命题．．．的序号） 2．（2021·上海南汇中学高二阶段练习）异面直线a ，b 成60°角，P 是a ，b 外一定点，若过P 点有且只有两条直线与a ，b 所成的角相等且等于θ，则θ的范围为___________.3．（2021·上海市金山中学高二期中）已知斜坡平面与水平面成30°的二面角，一条公路与坡脚成45°的角，沿公路前进100米，则路基升高了________米．4．（2020·上海师范大学第二附属中学高二期中）将边长为1的正方形ABCD 沿对角线AC 折叠，使得点B 和D 的距离为1，则二面角B AC D --的大小为______.异面直线间的距离1．（2021·上海·复旦附中高二期中）已知菱形ABCD 的边长为a ，3A π∠=．将菱形ABCD 沿对角线折成二面角θ，若2,33ππθ⎡⎤∈⎢⎥⎣⎦，则异面直线AC 与BD 距离的最大值为（ ）A ．32aB ．34aC ．34aD ．32a 2．（2022·上海·复旦附中高二期中）棱长为1的正方体中，异面直线1A D 与11B C 之间的距离为______． 3．（2016·上海·位育中学高二期末）若RtΔABC 的斜边AB =5，BC =3，BC 在平面α内，A 在平面α内的射影为O ，AO =2，则异面直线AO 与BC 之间的距离为___________．题型一：点、直线、平面之间的位置关系一、单选题1．（2021·上海师范大学第二附属中学高二期中）已知异面直线a 、b 所成角为80︒，P 为空间一定点，则过P 点且与a 、b 所成角都是50︒的直线有且仅有（ ）条． A ．2B ．3C ．4D ．62．（2022·上海市控江中学高二期末）如图，已知正方体1111ABCD A B C D -，点P 是棱1CC 的中点，设直线AB 为a ，直线11A D 为b ．对于下列两个命题：①过点P 有且只有一条直线l 与a 、b 都相交；②过点P 有且只有两条直线l 与a 、b 都成75︒角．以下判断正确的是（ ）能力拓展A ．①为真命题，②为真命题B ．①为真命题，②为假命题C ．①为假命题，②为真命题D ．①为假命题，②为假命题3．（2021·上海·位育中学高二阶段练习）已知菱形ABCD ，60DAB ∠=︒，E 为边AB 上的点（不包括A B ，），将ABD △沿对角线BD 翻折，在翻折过程中，记直线BD 与CE 所成角的最小值为α，最大值为β（ ） A ．αβ，均与E 位置有关B ．α与E 位置有关，β与E 位置无关C ．α与E 位置无关，β与E 位置有关D ．αβ，均与E 位置无关4．（2021·上海·高二专题练习）三条直线两两异面，有几条直线同时与这三条直线相交（ ） A ．一条B ．两条C ．无数条D ．没有5．（2021·上海·高二专题练习）如图两正方形ABCD ，CDFE 所在的平面垂直，将EFC ∆沿着直线FC 旋转一周，则直线EC 与AC 所成角的取值范围是（ ）A ．5,1212ππ⎡⎤⎢⎥⎣⎦B ．7,1212ππ⎡⎤⎢⎥⎣⎦C ．,122ππ⎡⎤⎢⎥⎣⎦D ．,62ππ⎡⎤⎢⎥⎣⎦6．（2021·上海·高二专题练习）设123l l l 、、为空间中三条互相平行且两两间的距离分别为4、5、6的直线，给出下列三个结论：①存在()123i i A l i ∈=，，，使得123A A A △是直角三角形； ②存在()123i i A l i ∈=，，，使得123A A A △是等边三角形； ③三条直线上存在四点()1234i i A l i ∈=，，，，使得四面体1234A A A A 为在一个顶点处的三条棱两两互相垂直的四面体，其中，所有正确结论的个数是 A ．0B ．1C ．2D ．37．（2021·上海·格致中学高二期中）从正方体八个顶点的两两连线中任取两条直线a ，b ，且a ，b 是异面直线，则a ，b 所成角的余弦值的所有可能取值构成的集合是（ ）A ．1320,,,,1232⎧⎫⎪⎪⎨⎬⎪⎪⎩⎭； B ．13260,,,,2323⎧⎫⎪⎪⎨⎬⎪⎪⎩⎭C ．1260,,,223⎧⎫⎪⎪⎨⎬⎪⎪⎩⎭； D ．1320,,,232⎧⎫⎪⎪⎨⎬⎪⎪⎩⎭． 二、填空题8．（2021·上海市复兴高级中学高二期中）已知两条异面直线a 与b 所成角为30，P 是空间一点，若过点P 与a 和b 所成角都是θ的直线有4条，则θ的范围是___________9．（2021·上海市甘泉外国语中学高二期中）若直线a 、b 是平面α上的两条直线，且a 、b 均在平面β外，则“//a β，//b β”是“//αβ”的 ____条件.（填“充分非必要”、“必要非充分”、“充要”、“既非充分又非必要”） 10．（2021·上海·格致中学高二阶段练习）直线m 和平面α所成角为6π，则直线m 和平面α内任意直线所成角的取值范围是_____11．（2022·上海长宁·高二期末）如图是一个边长为2的正方体的平面展开图，在这个正方体中，则下列说法中正确的序号是___________.①直线AF 与直线CN 垂直；②直线BM 与直线CN 相交；③直线ME 与直线CN 平行；④直线AB 与直线CN 异面；12．（2022·上海长宁·高二期末）已知平面α和两条不同的直线,a b ，则下列判断中正确的序号是___________. ① 若a ∥,b α∥α，则a ∥b ； ② 若,a b αα⊥⊥，则a ∥b ； ③ 若,//a b b α⊥，则a α⊥； ④ 若a ∥,b b α⊥，则a α⊥；13．（2021·上海奉贤区致远高级中学高二阶段练习）若两异面直线a 、b 所成的角为60，过空间内一点P 作与直线a 、b 所成角均是60的直线l ，则所作直线l 的条数为_________．14．（2021·上海市大同中学高二阶段练习）空间四边形SABC 中，23AB AC BC ===25SA SB SC ===，E 、F 分别为AC 、SB 的中点，平面α过点A ，//α平面SBC ，α平面=ABC l ，则异面直线l 和EF 所成角的余弦值为_______.15．（2021·上海·华东师范大学第三附属中学高二阶段练习）刍甍，中国古代算数中的一种几何形体，《九章算术》中记载：“刍甍者，下有袤有广，而上有袤无广.刍，草也，甍，屋盖也.”翻译为“底面有长有宽为矩形，顶部只有长没有宽为一条棱.刍甍字面意思为茅草屋顶.”如图为一个刍瓷的五面体，其中四边形ABCD 为矩形，ADE 和BCF △都是等腰三角形，2AE ED BF CF AD ====，//EF AB ，若3AB EF =，且2AD EF =，则异面直线AE 与CF 所成角的大小为______.16．（2021·上海市奉贤区奉城高级中学高二阶段练习）如图∶已知A 是BCD △所在平面外一点，AD BC =，E 、F 分别是AB 、CD 的中点，若异面直线AD 与BC 所成角的大小为θ，AD 与EF 所成角的大小为_______________．17．（2021·上海市进才中学高二阶段练习）空间给定不共面的A ，B ，C ，D 四个点，其中任意两点间的距离都不相同，考虑具有如下性质的平面α：A ，B ，C ，D 中有三个点到的距离相同，另一个点到α的距离是前三个点到α的距离的2倍，这样的平面α的个数是___________个18．（2021·上海·高二专题练习）已知两个不同平面α，β和三条不重合的直线a ，b ，c ，则下列命题： （1）若//a α，b αβ=，则//a b（2）若a ，b 在平面α内，且c a ⊥，c b ⊥，则c α⊥（3）若α，β分别经过两异面直线a ，b ，且⋂=c αβ，则c 必与a 或b 相交（4）若a ，b ，c 是两两互相异面的直线，则存在无数条直线与a ，b ，c 都相交其中正确的命题是________．（请写上正确命题的序号）三、解答题19．（2021·上海市洋泾中学高二期中）如左图所示，在直角梯形ABCD 中，//BC AD ，AD CD ⊥，2BC =，3AD =，3CD =AD 上一点E 满足1DE =.现将ABE △沿BE 折起到1A BE 的位置，使平面1A BE ⊥平面BCDE ，如右图所示.(1)求证：1A C BE ⊥；(2)求异面直线1A C 与BE 的距离；(3)求平面1A BE 与平面1A CD 所成锐二面角的余弦值.20．（2022·上海市控江中学高二期末）如图，在长方体1111ABCD A B C D -中，11,2DD DA AB ===，点E 在棱AB 上运动．(1)证明：11B C D E ⊥；(2)当E 为棱AB 的中点时，求直线AB 与平面1DEC 所成角的正弦值；(3)AE 等于何值时，二面角1A DE C --的大小为150︒？题型二：直线、平面平行的判定与性质一、单选题1．（2021·上海市洋泾中学高二期中）已知m 、n 是两条不同的直线，α、β是两个不同的平面，则以下命题正确的是（ ）A ．若m 、n 平行于同一平面，则m 与n 平行B ．若α、β垂直于同一平面，则α与β平行C ．若m 、n 不平行，则m 与n 不可能垂直于同一平面D ．若α、β不平行，则在α内不存在与β平行的直线2．（2021·上海市吴淞中学高二阶段练习）已知空间直线l 不在平面α内，则“//l α”是“直线l 上有两个点到平面α的距离相等”的（ ）A ．充分非必要条件B ．必要非充分条件C ．充要条件D ．非充分非必要条件 3．（2021·上海市洋泾中学高二阶段练习）如图，在矩形ABCD 中，2AB =，1BC =，E 、N 分别为边AB 、BC 的中点，沿DE 将ADE ∆折起，点A 折至1A 处（1A 与A 不重合），若M 、K 分别为线段1A D 、1A C 的中点，则在ADE ∆折起过程中（ ）A ．DE 可以与1A C 垂直B ．不能同时做到//MN 平面1A BE 且//BK 平面1A DEC ．当1MN AD ⊥时，MN ⊥平面1A DED ．直线1AE 、BK 与平面BCDE 所成角分别为1θ、2θ，1θ、2θ能够同时取得最大值二、填空题4．（2021·上海市吴淞中学高三期中）与不共面的四点等距离的平面有___________个.5．（2021·上海·华师大二附中高二阶段练习）给出下列4个命题：①过平面外一点，与该平面成θ角的直线一定有无穷多条；②一条直线与两个相交平面都平行，则它必与这两个平面的交线平行；③过空间任意一点有且只有一个平面与两条异面直线都平行；④与确定的两条异面直线所成的角相等的平面有无数个．其中正确命题的序号有_____（请把所有正确的序号都填上）．6．（2021·上海·位育中学高二期中）已知四边形ABCD 为矩形, 24AB AD ==,M 为AB 的中点,将ADM ∆沿DM 折起,得到四棱锥1A DMBC -,设1A C 的中点为N ,在翻折过程中,得到如下有三个命题:①//BN 平面1A DM ，且BN 5②三棱锥N DMC -22； ③在翻折过程中，存在某个位置，使得1DM AC ⊥. 其中正确命题的序号为__________．（写出所有正确结论的序号）三、解答题7．（2021·上海市徐汇中学高二期中）如图，几何体ABCDE 中，ABC 是正三角形，AE 和CD 都垂直于平面ABC ，且2EA AB ==， 1,,DC F G =分别为EB 和AB 的中点.(1)求证：FD ∥平面ABC ；(2)求二面角B FC G --的正切值.8．（2022·上海·高三专题练习）如图，将边长为2的正方形ABCD 沿对角线BD 折叠，使得平面ABD 与平面CBD 所成二面角为直角，AE ⊥平面ABD ，且2AE =.（1）求证：直线EC 与平面ABD 没有公共点；（2）求点C 到平面BED 的距离.题型三：直线、平面垂直的判定与性质一、单选题1．（2021·上海市市西中学高二期中）在下列命题中，假命题是（ ）A ．若平面α内的一条直线垂直于平面β内的任一直线，则α⊥βB ．若平面α内任一直线平行于平面β，则α∥βC ．若平面α⊥平面β，任取直线l ⊂α，则必有l ⊥βD ．若平面α∥平面β，任取直线l ⊂α，则必有l ∥β二、填空题2．（2021·上海市南洋模范中学高二期中）在正方体1111ABCD A B C D -中，M 是棱AB 的中点，过1A ，M ，C 三点的平面交棱11C D 于点N ，则11A B 与平面1A MCN 所成角的正弦值是___________.3．（2021·上海师大附中高二期中）如图，已知,,60,1AP BP AP PC ABP ACP BAC PA ⊥⊥∠=∠=∠=︒=，D 是BC 中点，则点B 到平面APD 的距离是___________.4．（2021·上海师范大学第二附属中学高二期中）在长方体1111ABCD A B C D -中，4AB =，3BC =，12BB =，那么BC 到平面11ADD A 的距离为______.5．（2021·上海·华东师大附属枫泾中学高二期中）如图，在正方体1111ABCD A B C D -中，2AB =，则直线1AA 到平面11BB D D 的距离为___________.6．（2022·上海·复旦附中高二期中）在矩形ABCD 中，AB ＝2，23BC =，沿对角线AC将矩形折成直二面角D －AC －B ，则线段BD 的长为______．7．（2021·上海市进才中学高二期中）在Rt ABC 中，已知12BC =，5AC =，D 是斜边AB 上任意一点，如图沿直线CD 将ABC 折成直二面角B CD A --.若折叠后A ，B 两点间的距离为d ，则d 的最小值为___________.三、解答题8．（2022·上海金山·高二期末）如图，在正方体1111ABCD A B C D -中，E 是棱1DD 的中点.(1)试判断直线1BD 与平面AEC 的位置关系，并说明理由；(2)求证：直线1BD ⊥面1AB C .9．（2021·上海市大同中学高二阶段练习）如图，正方体1111ABCD A B C D -中，1AA a =.（1）求证：平面11//AB D 平面1C BD ；（2）求两平面11AB D 与1C BD 之间的距离.10．（2021·上海市南洋模范中学高二期中）已知，如图P 是平面α外一点，PA 是平面α的斜线，交α于点A ，过点P 作平面α的垂线PO ，垂足是O ，直线OA 是PA 在平面α上的投影.求证：对平面α上任一直线a ，a OA ⊥是a PA ⊥的充要条件.一、单选题1．（2021·上海奉贤区致远高级中学高二期中）如图，在下列四个正方体中，A ，B 为正方体的两个顶点，M ，N ，Q 为所在棱的中点，则在这四个正方体中，直线AB 与平面MNQ 不平行的是（ ）．A ．B ．C ． D ． 2．（2022·上海·复旦附中高二期中）已知a 、b 是平面α的两条斜线，则“a 、b 与平面α所成角相等”是“//a b ”的（ ）条件A ．充分非必要B ．必要非充分C ．充分必要D ．既非充分又非必要巩固练习3．（2021·上海奉贤区致远高级中学高二阶段练习）正方体1111ABCD A B C D -的八个顶点中，平面α经过其中的四个顶点，其余四个顶点到平面α的距离都相等，则这样的平面α的个数为（ ）A ．6B ．8C ．12D ．164．（2021·上海奉贤区致远高级中学高二阶段练习）在正方形123SG G G 中，E 、F 分别是12G G 及23G G 的中点，D 是EF 的中点．现在沿SE 、SF 及EF 把这个正方形折成一个空间四边形，使1G 、2G 、3G 三点重合，重合后的点记为G ，那么，在空间四边形S EFG -中必有（ ）A ．SG EFG △⊥所在平面B ．SD EFG ⊥所在平面C ．GF SEF ⊥所在平面D ．GD SEF ⊥所在平面二、填空题 5．（2022·上海市建平中学高二阶段练习）正方体1111ABCD A B C D -的棱长为1，异面直线11A B 与1BC 的距离是_________6．（2021·上海·西外高二期中）空间中两条直线的位置关系有___________.7．（2021·上海市宝山中学高二期中）如图，正三角形ABC 的边长为2，P 是三角形ABC 所在平面外一点，PA ⊥平面ABC ，且1PA =，则P 到BC 的距离为___________.8．（2021·上海·位育中学高二期中）在30°二面角的一个面内有一个点，它到另一个面的距离是10cm ，则这个点到二面角的棱的距离为___________.9．（2021·上海市控江中学高二期中）两个平面最多可以将空间分为___________部分.10．（2021·上海市洋泾中学高二期中）在棱长为a 的正方体中，与AD 成异面直线且距离等于a 的棱共有_____________条.11．（2021·上海市吴淞中学高二阶段练习）一个山坡面与水平面成120°的二面角，坡脚的水平线（即二面角的睨）为AB ，甲沿山坡自P 朝垂直于AB 的方向走30m ，同时乙沿水平面自Q 朝垂直于AB 的方向走30m ，P ､Q 都是AB 上的点，若10m PQ =，这时甲､乙两个人之间的距离为___________.12．（2021·上海奉贤区致远高级中学高二阶段练习）如图，已知PA ⊥平面ABC ，AC BC ⊥，2AB =，2BC =，PB =6，则二面角P BC A --的大小为________三、解答题13．（2022·上海浦东新·高二期末）如图，在正方体1111ABCD A B C D -中.(1)求异面直线1A B 和1CC 所成的角的余弦值；(2)求证：直线1//A B 平面11DCC D .14．（2021·上海南汇中学高二阶段练习）已知正方体1111ABCD A B C D -中，P ､Q 分别为对角线BD ､1CD 上的点，且123CQ BP QD PD ==. (1)作出平面PQC 和平面11AA D D 的交线（保留作图痕迹），并求证：//PQ 平面11A D DA ；(2)若R 是AB 上的点，当AR AB的值为多少时，能使平面//PQR 平面11A D DA 请给出证明.15．（2021·上海奉贤区致远高级中学高二阶段练习）如图，已知1111ABCD A B C D -是底面为正方形的长方体，1160D A A ∠=，14AD =，点P 是1AD 上的动点（1）试判断不论点P 在1AD 上的任何位置，是否都有平面BPA 垂直于平面11AA D D ，并证明你的结论（2）当P 为1AD 的中点时，求异面直线1AA 与1B P 所成角的余弦值; （3）求1PB 与平面11AA D 所成角的正切值的最大值。

上海徐汇国际小学招生条件上海国际学校众多，招生要求也各不相同，对此我们整理汇总了上海2022年主流国际学校最新的招生要求，供家长们参考。

看文字太麻烦，可以直接咨询菠萝老师哦~上中国际上海中学国际部成立于1993，现有来自60多个不同国家和地区的约3000名学生。

1995年，上中国际加入了IB国际文凭组织。

上中国际同时也是由College Board授权的AP、SAT和PSAT的考试中心和由ETS授权的托福考试中心。

2014 年上中国际成为国际AS& A-Level学校，2018年通过美国AdvancED (COGNIATM)认证。

课程体系：美高+AP、A-level招生年级：•浦西校区：1-5年级(小学)；6-8年级( 初中 )；9-12年级(高中)。

•浦东校区：1-5年级（小学）招生范围:在上海工作的外国人或港澳台人士的子女。

考试要求：汉语、英语、数学（申请10年级及以上年级加试物理和化学；所有科目活动均包括笔试和面试）。

学费：1-5年级（小学）: 5万元/学期；6-8年级（初中）：5.3万元/学期；9-12年级（高中）: 5.5万元/学期。

WLSAWLSA上海学校(WLSAShanghaiAcademy)，是世界名中学联盟于2012年9月在上海复旦附中进修学校开设的国际高中课程项目。

WLSA上海学校的WLSA即为世界名中学联盟（World Leading Schools Association）的缩写，其为“英国政治家的摇篮”伊顿公学、北京四中、哈佛西湖中学、“上海四校之一”复旦附中等世界知名的51所中学联合发起成立的组织。

课程体系：AP、A-level招生年级：初三或高一在读学生招生范围：国内在读学生，户籍不限。

考试要求：需通过学校的笔试（英语+数学）、多邻国英语能力测试和英文面试。

学费：美高课程/A-level：17.2万元/年。

WLSA入学考试英语测试卷WLSA入学考试英语测试卷，需要的同学↓↓↓↓世外中学上海市世界外国语中学（以下简称世外中学），创办于1996年，是一所在上海市具有优秀学术声誉和社会声誉的民办中学。

1复旦附中2024学年第一学期高一年级数学开学考2024.09一、填空题（本大题共有12题,满分54分,第1-6题每题4分,第7-12题每题5分） 1．用列举法表示《沁园春·长沙》前三句的意象所组成的集合________．2．设高一（5）班全体学生的集合为A （A 中有17名男生，23名女生），高一（5）班全体女生的集合为B ，则A ________B ． 3．用区间法表示实数集R =________．4．已知集合{}0,1,2A =，集合{}|23x B x =>，则AB =________．5．已知集合{}1,2A =，{}532|24670B x x x x x =−+++=，则A B =________．6．已知集合{}1,2,3,4A =、{}1,2B =，满足A C BC =的集合C 有________个．7．已知集合()(){}2|10,x x x x a x R −−+=∈中的所有元素之和为1，则实数a 的取值集合为________．8．设集合{}2,0,1M =−，{}|1N x x a =−<，若M N 真子集个数为1，则正实数a 的取值范围为________． 9．关于的方程221x k xx x x−=−−的解集中只含有一个元素，则k 的所有可能值组成的集合 是________．10．设集合{}{}123,,,,1,2,3,,107n A a a a a =⊆，且A 中任意两数之和不能被5整除，则n 的最大值为________．11．已知集合A 满足若n A ∈且n Z ∈，则1A n∈，小张同学迅速得出3个结论：（1）0A ∉（2）集合A 不可能是单元素集（3）当n 取遍可以取的所有数时，集合元素的个数一定是偶数，其中错误结论的序号为________． 12.若规定集合{}0,1,2,,E n =的子集{}123,,,,m a a a a 为E 的第k 个子集，其中23122222m a a a a k =++++，则E 的第211个子集的真子集个数为________．二、选择题（4题共18分，13~14每题4分，15~16每题5分）13．必要的习题训练，也是数学训练的必须。

我是⼀位上海妈妈，有⼀个⼋岁的⼥⼉，她正在处于6-9岁的转折点，下⾯我就分享⼀下我⼥⼉6-9岁的三个转折点是如何渡过的。

⼥⼉今年三年级，是⼀个认真、内向、独⽴并且有着丰沛想象⼒的孩⼦。

如果在另⼀个语境中评论的话，她⼜是⼀个胆⼩、散漫、固执且尚未被⼤⼈思路所束缚的孩⼦。

⼥⼉出⽣后，我看了很多育⼉书，也许是70后这⼀代从⼩做惯了“乖⼩囡”从⽽对“⾃由”特别渴望的缘故，我对⼥⼉⼀直本着“理解”的态度。

现在想起来，我的价值观对⼥⼉后来的表现有着⾮常直接的影响。

⼀直到上⼩学前，我对⾃⼰这个育⼉观念还是⾮常⾃信的，⼩学前，⾯对诸多“幼⼩衔接”的培训班，我们⼀个也没去过，我也没有给她教过识字、拼⾳、算术或英语。

她感兴趣的是做实验、玩各种破玩具以及所有的户外活动。

第⼀个转折：幼升⼩“择校” 进⼩学，对于我这样的⽗母来说，只是后⾯漫漫长路的开始。

由于对⼝学校是所谓的“菜场⼩学”，我和⼥⼉开始了懵懵懂懂的幼升⼩征战。

别说⼥⼉是“考试菜鸟”（她连⼀堂正规的课也没有上过），我们⾃⼰也是“菜鸟⽗母”，所以也就随⼤流既去考了上海北区的“XX附⼩”，也去浦东与3000多⼤军参与了10年⼀贯制⼩学的考试。

记得当时看着⼥⼉⼩⼩的圆滚滚的⾝体⼀个⼈挂着牌⼦找考试教室并且还要上机考试（她以前从未使⽤过计算机），隐隐觉得随着进⼩学后， “⾃由”也许是越来越奢侈的事情。

在门⼝等她的时候，听到⾝边的⽗母在交流经验，越听越汗，普通的拼⾳学习、英语学习根本不算什么，思维训练正正经经学了3年的⼤有⼈在。

“不然考什么考，考了也是⽩考。

”有的家长说。

在⾯试环节，学校⽼师甚⾄和家长明说：“如果⽗母之间没有⼀个能‘全职’陪伴孩⼦学习，建议还是不要来读我们学校，吃不消的。

”幼升⼩考了4所学校，最后双向选择了徐汇⼀所以艺术教育和快乐教育著称的私校，⼩学⽣活就这样开始了。

⼀年级⼀开学，⽴马就给颜⾊看了，由于不识字，考卷上的题⽬都看不懂，语⽂考试只考了六⼗⼏分。

202X上海徐汇区小学盘点202X上海徐汇区小学盘点作为上海的传统教育大区，徐汇也是大家公认教育质量最好的区，拥有全市最好的高中上海中学，拥有全市数一数二的初中华育中学，简直令人羡慕！下面一起来看看202X上海徐汇区热门小学盘点。

徐汇有且仅有这4所民办小学，就算拿到全市，这几所民办小学都是综合实力排名前列的，同时，学费比其他区那些双语学校廉价的多，性价比可想而知。

世界外国语小学——徐汇四大民办之首，在全市绝对是数一数二的名校。

升学成绩、杯赛成绩亮出来都有鲜明的优势，使之称为沪上最热门的民办小学之一。

进世外的孩子都是千挑万选出来的，资质好、家境好，“牛蛙+牛爹”配置。

英语是世外强项。

从近几年招生情况看，对学生的外语能力要求也越来越高，前几年还要求英语跟读，开始要判断多国语言了，对六国语言都要有所了解，语感要强。

世外小学前110左右大概率能进入世外中学，也有近30人去上外120和华育，小升初占绝对优势。

这也是造成它年年幼升小报名火爆，开分校也能迅速招生的重要原因。

盛大花园小学是目前上海最热门的民办小学之一。

一是他本身的办学成绩喜人；二是他是徐汇区里唯一一所全市招生的民办小学，而且区内外招生人数各占一半（区外招生人数全市第4位）；三是他招收第二志愿学生，有众多抱着万一的态度第二志愿填报了盛大花园，但其实二志愿录取凤毛麟角。

盛大学生毕业择校越来越多元，华育、世外、华二、上宝、张江、西南模范、西南位育等都是盛大学子的择校方向。

而且据在读家长称，盛大的可贵之处，在于其中下游的学生大都也能有个好去向，这是其他很多公办学校无法比的。

逸夫小学曾经有“杯赛最强者”之称号，偏重数理思维，其数学成绩有目共睹，在杯赛场上，成绩可观，以被禁的四大杯赛来说，xx年的获奖人数位列全市第一：中环18人、小机灵22人、亚太11人、走美15人！逸夫小学最大的优势就是去华育的概率比拟大，每年都有30~40人考进华育。

考逸夫的牛蛙，为了小升初能进华育或其他好学校，都是目标明确且愿意为此付出时间、精力、金钱，且能够为之努力好几年。