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全新版大学进阶英语第二册第一单元答案

全新版⼤学进阶英语第⼆册第⼀单元答案Unit 1 Living GreenKey to ExercisesOpenerSuggested answers for reference1. There are a lot of simple things we can do to decrease energy consumption. Here are just a few examples:Use energy efficient light bulbs for our most-used lights.When we leave a room, turn off the light.Turn off our computer/laptop when we are not using it.Save water. Take quicker showers. When brushing teeth we should not leave faucet running.Use reusable cloth shopping bags that are made from plant fibers. Whenever possible, walk, bike, carpool, or use public transportation.2. Old clothes and books: Other people can reuse our unwanted clothes and books if we donate them.Old clothes can also be made into other items such as cushion covers. Old electrical equipment: Donate old electrical equipment to schools or community centers so that others can reuse them.Rechargeable batteries: Unlike regular batteries that create unnecessary waste, rechargeable batteries can be reused many times before they need to be thrown away.Jars and pots: By cleaning glass jars and small pots, we can use them as small containers to store odds and ends（零星物品）.3. Living green means reducing one’s carbon footprint, or, more generally, making as small an impact on the natural environment as possible. Yes, I have thought about it. I can take some small steps to restrict energy consumption. For example, taking shorter, cooler showers. In that way I can save energy by minimizing hot water use.Reading & InteractingI. Understanding the Text1. Text Organization2. Comprehension CheckFocusing on the main ideasAfter living in the city of Las Vegas for years, Alison Zeuschel and her family decided to move to the countryside. Their homehunting ended up in a very small town in Arizona where they purchased a house on 40 acres that was not only off the grid, but without access to any (public) utilities. Just imagine the challenges facing them, such as generating their own power and hauling their own water. However, they worked hard and succeeded in making the adjustment in a few months.In addition, they benefited a lot from living off the grid there. Most important of all, they came to know the importance of conservation and learned how to conserve power and water and how to reuse things, etc.In other words they learned how to live green.Digging into detail1. Her daughter wanted a horse. Her husband wanted property. Her sonwanted a dirt bike. The writer herself wanted her family to be moreself-sufficient.2. The property was off the grid. It was actually not connected to anyutilities — power, water or a sewer system.3. They generated electricity by wind and solar power, and stored itin 16 golf cart batteries. Water had to be hauled in from a nearby town and stored in two tanks located on the property.4. In her view, one of the greatest benefits was teaching her childrenthe importance of conservation.5. Other changes included reducing the amount of trash by recyclingand composting, growing their own organic vegetables and reusing things that they would normally toss away. Understanding difficult sentences1. A2. B3. B4. A5. BII. Focusing on Language in Context1. Key Words & Expressions1. Jack has no interest whatsoever in pursuing an acting career. Heloves writing and directing.2. The idea was to have users upload their medical records, so thatthey could be available at any time.3. Traffic jams often build up when drivers slow down to see whathappened in a crash.4. A native New Yorker, Ben is familiar with the city, its neighborhoods,and all he has connections with.5. You may have already seen your dream house. Before you put in anoffer, you can do a few more things to ensure you purchase the right property for the right price.6. Buying organic fruit and vegetables costs more, and for manyshoppers, the benefits hardly seem worth the extra expense.7. Self-sufficient living is the practice of providing for your ownneeds without outside aid or resources.8. In the interview, the writer was asked how he set about writing anovel based on a dream he once had.9. Are you thinking of becoming an insurance sales agent Take this quizto find out if this is the right career choice for you.10. The rent for the apartment is reasonable; besides, the utilitiesare included, which means you don’t have to pay anything for gas, electricity and water.11. A central heating and cooling system produces warm or cool air inone central area and distributes it throughout the building.12. We were deeply shocked and saddened when we learned of the suddendeath of our newly retired professor.13. If you know the ins and outs of something, you know all the detailsabout it and understand how it works.14. It’s long been proven that we can accomplish any project if we breakit up into small pieces and do the project one piece at a time.1. consist of2. tossed3. overall4. hauling5. went out6. in use1. If you’re in business long enough, it’s inevitable you will meetwith/face/encounter setbacks.2. Hydroelectric power plants generate electricity in a much cleanerway than coal-fired ones.3. Knowing the proper way to do laundry will help you avoid shrinkingyour sweaters and dyeing your white socks pink.4. We really appreciate the invitation to your party, but my elderlymother lives with us and we don’t like to leave her alone in the evenings.5. The hotel is OK but could make some adjustments to live up to its5-star rating.6. Most of us take electricity for granted. But do you know that aboutbillion people in this world have no access to electrical power2. Usage1. He spoke to her looking away, as though to avoid meeting her eyes.2. I hope to arrive in Hangzhou at 2:20 pm to catch the 3:10 train to Ningbo.3. Maria refused to attend a party to which Lucia was also invited.4. You may want to consider going on strike if you think you are paidunfair wages.5. I remember feeling really happy when I was told they had found ahouse that could meet our needs.6. If I fail to pass the exam on the first attempt, can I take the exam again7. The hotel and its staff are great. We really enjoyed staying thereduring our trip to Nanjing.8. It is not only your health that will improve if you give up smoking,but also the health of your family.9. Few of my friends could resist playing this computer game.10. Please remember to pay back the money to Mary the moment you receiveyour salary next month.3. Sentence Patterns1. It was the day before yesterday that they set out. / It was theythat set out the day before yesterday.2. It was by the roadside that I found the lost wallet. / It was Ithat/who found the lost wallet by the roadside. /It was the lost wallet that I found by the roadside.3. It was not until he got everything ready for the experiment thatXiao Wang left the lab.1. It took my parents half an hour to finally find their way back tothe hotel. / It took half an hour for my parents to finally find their way back to the hotel.2. It took us almost two hours to work out this difficult math problem./ It took almost two hours for us to work out this difficult math problem.3. It will take us more than three months to accomplish this art project./ It will take more than three months for us to accomplish this art project.4. Comprehensive PracticeClozeIf you want to know all the ins and outs of living green, then you should visit Backsbottom Farm. It is run by Rod and Jane, who have tried to be as self-sufficient as possible. They use a horse to haul the logs they cut from their woods. The fields are nourished by organic waste from the horse and their other animals rather than chemicals. They rely on a windmill to generate their electricity and when the wind slows down the lights go out and they have to set about looking for the candles.Jane, who was brought up in a home where constant electric power was taken for granted, admits it was hard to make the adjustment when they first arrived at the farm, but adds that overall they really appreciatetheir new way of life.Translation1. Jack is so diligent a student that he never goes anywhere withouta book.2. This is an outline of my paper; any of your suggestions will be trulyappreciated.3. Whether you’re buying or renting, you’ll need to be fully awarewhat kind of property best suits you and your lifestyle.4. It is dangerous to ride a bicycle on an icy road, so we have to usethe brake to slow it down.5. If we put all our energy and effort into this project, we willdefinitely accomplish it in a few more months.6. I am thinking about moving to a three-bedroom house located nearthe town center. In addition, it is within walking distance to the train station.7. A lot of the things we take for granted as trash, such as newspapers,magazines, old computers and cellphones, can actually be recycled or reused in one way or another.8. — What questions can I ask when inquiring about a job— You may ask if the position is still available and how long you have to wait before getting to know if you will be given an interview.Reading & ComprehendingReading 11. Comprehension Check for Reading 11. F2. T3. F4. T5. F6. F7. T8. T9. T 10. F2. Translation1. 在⼀个国际⼤都市（澳⼤利亚的悉尼）的郊区，有五周时间尝试⽆车的⽣活⽅式，有机会践⾏我们有关可持续发展和健康的价值观，这令我们激动不已。

课本知识点详解及练习：必修2Unit1(人教版)-教育文档

高一｜课本知识点详解及练习：必修2Unit1（人教版）Unit1 Cultural relics知识点详解Ⅰ. 常考单词必背1．valuable adj. 贵重的；有价值的This is one of the most valuable lessons I learned.这是我所学到的最宝贵的教训。

2．survive vi. 幸免；幸存；生还Of the four people in the car accident，only one survived.车祸中的四个人，只有一个人幸免于难。

[快速闪记](1)survive from 从……流传下来survive on 靠……活下来，靠……生存(2)survivor n．幸存者；生还者survival n．幸存；存活3．amaze vt. 使吃惊；惊讶He amazed everyone by passing his driving test.他通过了驾驶考试，这让大家很惊奇。

It is amazing that she should have said nothing about the murder.令人惊奇的是她竟然对这桩凶杀案不置一词。

[快速闪记](1)amazing adj.令人吃惊的，常用来修饰令人吃惊的人或物。

(2)amazed adj.(感到)吃惊的，常用来修饰表示人的名词或代词。

(3)amazement n．惊奇，惊愕4. select vt. 挑选；选择Which place in the world would you select as your perfect home?你选择世界上的什么地方作为你最理想的安家之地呢？5．design n．设计；图案；构思vt. 设计；计划；构思This bike is designed for children.这种自行车是为儿童设计的。

[快速闪记](1)by design＝on purpose 有意地；故意地be designed for sb/sth 为某人或某物设计be designed to do sth 设计来做某事be designed as sth 设计为(2)designer n．设计者6. belong vi. 属于；为……的一员This nice house belongs to Mr.Black.这座好房子属于布莱克先生。

高中数学必修2(人教B版)第一章集合1.2知识点总结含同步练习题及答案

描述：高中数学必修2(人教B版)知识点总结含同步练习题及答案第一章立体几何初步 1.2 点、线、面之间的位置关系一、学习任务1. 理解空间点、线、面的位置关系，会用数学语言规范地表述空间点、线、面的位置关系；了解可以作为推理依据的公理和定理，能正确地判断空间线线、线面与面面的位置关系．2. 认识和理解空间中线面平行、垂直的有关判定定理和性质定理，能用图形语言和符号语言表述这些定理，并能证明有关性质定理；能运用公理、定理和已获得的结论证明一些空间位置关系的简单命题．二、知识清单平面的概念与基本性质点、线、面的位置关系空间的平行关系空间的垂直关系点面距离三、知识讲解1.平面的概念与基本性质平面的概念生活中的一些物体通常呈平面形，课桌面、黑板面、海面都给我们以平面的形象．几何里所说的平面就是从这样的一些物体中抽象出来的，但是几何中的平面是没有厚度、无限延展的．平面的画法我们常常把水平的平面画成一个平行四边形，用平行四边形表示平面，平行四边形的锐角通常画为，且横边长等于其邻边长的倍．如果一个平面被另一个平面遮挡住，为了增强它的立体感，我们常把被遮挡的部分用虚线画出来．平面的表示为了表示平面，常把希腊字母等等写在代表平面的平行四边形的一个角上，如平面、平面；也可以用代表平面的平行四边形的四个顶点，或者相对的两个顶点的大写英文字母作为这个平面的名称，如图中的平面可以表示为平面、平面或者平面．集合符号在立体几何中的应用以点作为元素，直线和平面都是由点构成的集合．几何中许多符号的规定都是源于将图形视为点集．例如：点在平面内，记作；点不在平面内，记作．直线在平面内，记作；直线不在平面内，记作；直线与相交于点，记作；平45∘2α,β,γαβABCD AC BD A αA ∈αA αA ∉αl αl ⊂αl αl ⊄αl m A l ∩m =A例题：面与平面相交于直线，记作．平面的基本性质平面的基本性质是由三条公理描述的：公理1 如果一条直线上的两点在一个平面内，那么这条直线在此平面内．符号语言：，，且，．公理2 过不在一条直线上的三点，有且只有一个平面．推论1 经过一条直线和直线外一点，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．公理3 如果两个不重合的平面有一个公共点，那么它们有且只有一条过该点的公共直线．符号语言：，且，且．空间位置关系与几何量的基础平行公理平行于同一条直线的两条直线互相平行．等角定理空间中如果两个角的两边分别对应平行，那么这两个角相等或互补．αβaα∩β=aA∈l B∈l A∈αB∈α⇒l⊂αP∈αP∈β⇒α∩β=l P∈l用符号语言表示下列语句．（1）点在平面外，点在平面内，直线经过点，；（2）与交于，与交于．解：（1），，，．（2），．AαBαl A B平面ABD平面BCD BD平面ABC平面ADC ACa∉αB∈αA∈l B∈l平面ABD∩平面BCD=BD平面ABC∩平面ADC=AC如图所示，在四面体中，、、、分别是、、、上的点，且，求证，，三点共线．ABCD E F G H AB AD BC CDEF∩GH=PB D P2.点、线、面的位置关系证明：因为，，所以，同理，，又，所以，，而，所以，即，，三点共线．E ∈ABF ∈AD EF ⊂平面 ABD GH ⊂平面 BCD EF ∩GH =P P ∈平面 ABD P ∈平面 BCD 平面 ABD ∩平面 BCD =BD P ∈直线BD B D P 已知：如图，，，．求证：直线，，在同一平面内．证法一：（同一法）因为，所以和确定一个平面．　因为，所以．又因为，所以．同理可证．又，，所以．因此，直线，，在同一个平面内．证法二：（重合法）因为，所以，确定一个平面．因为，所以，确定一个平面．又因为，，所以．又，，所以．同理可证得，，，．所以不共线的三个点，，在平面内，又在平面内．所以平面和平面重合，即直线，，在同一平面内．∩=A l 1l 2∩=B l 2l 3∩=C l 1l 3l 1l 2l 3∩=A l 1l 2l 1l 2α∩=B l 2l 3B ∈l 2⊂αl 2B ∈αC ∈αB ∈l 3C ∈l 3⊂αl 3l 1l 2l 3∩=A l 1l 2l 1l 2α∩=B l 2l 3l 2l 3βA ∈l 2⊂αl 2A ∈αA ∈l 2⊂βl 2A ∈βB ∈αB ∈βC ∈αC ∈βA B C αβαβl 1l 2l 3结合空间想象回答下列问题：（1）个平面可以分空间为______部分；（2）个平面可以分空间为______部分；（3）正方体的各个面延伸后将空间分成______部分．解：（1），；（2），，，；（3）．对于（1）：当个平面平行时，分成部分；当两个面相交时，分成部分；对于（2）：当个平面两两平行时，分成部分；当其中两个平面平行，和另外一个平面相交或者三个平面相交于一条直线时，分成部分；当个平面两两相交且交线两两平行时，分成部分；当个平面两两相交且交线相交于一点时，分成部分；对于（3）：首先，将正方体的四个侧面延伸，可知将空间分成部分，然后，将正方体的上下底面延伸可知将之前部分分成了层，每层部分，共部分．233446782723434637389393×9=27若直线、、相交于一点，则这条直线可能确定的平面有（）A．个 B．个 C．无数个 D．个或个解：D当、、三线共面时，平面只有个；当三线不共面时，任意两条可确定一个平面，共个．a b c 30113a b c 13描述：例题：点与平面的位置关系平面内有无数个点，平面可以看成点的集合．点在平面内，记作；点不在平面内，记作．直线与直线的位置关系空间直线与直线的位置关系共有以下两种：共面直线在同一平面内的两条直线．更进一步，若这两条直线有且只有一个公共点，则称它们是相交直线，若这两条直线没有公共点，则称它们是平行直线；异面直线不同在任何一个平面内的两条直线．直线垂直如果两条直线所成的角是直角，那么我们就说这两条直线互相垂直，记作．在空间，两条直线垂直包括两种情形：共面垂直和异面垂直．直线与平面的位置关系空间直线与平面的位置关系共有以下三种：直线在平面内直线上的所有点都在平面内；直线与平面相交直线与平面有且仅有一个公共点；直线与平面平行直线与平面没有公共点．平面与平面的位置关系空间平面与平面的位置关系共有以下两种：平行两个平面没有公共点，则称这两个平面平行；相交两个平面有一条公共直线，则称这两个平面相交，此时这条公共直线称为这两个平面的交线．A αA ∈αA αA ∉αa ⊥b 如果在两个平面内分别各有一条直线，这两条直线互相平行，那么这两个平面的位置关系是（）A．平行 B．相交 C．平行或相交 D．垂直相交解：C可根据题意作图判断，如图所示，分别为两个平面平行、相交的情况．分别和两条异面直线都相交的两条直线的位置关系是（）A．相交 B．异面 C．异面或相交 D．平行解：C如图所示，可能相交，也可能异面，若两直线平行，则此两条直线确定一个平面，且原两条异面直线均在此平面内，故矛盾．描述：3.空间的平行关系空间四边形顺次连接不共面的四个点、、、所构成的图形，叫做空间四边形．这四个点中的各个点叫做空间四边形的顶点；所连接的相邻顶点间的线段叫做空间四边形的边；连接不相邻的顶点的线段叫做空间四边形的对角线．空间四边形用表示顶点的四个字母表示．例如，图中的四边形可以表示为空间四边形，线段，是它的对角线．直线与平面平行的判定定理：平面外一条直线与此平面内的一条直线平行，则该直线与此平面平行．　用符号表示：，，且．平面与平面平行的判定定理：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．用符号表示：，，，，．平面与平面平行的判定定理的推论如果一个平面内有两条相交直线分别平行于另一个平面内的两条直线，那么这两个平面平行．若直线不平行于平面，且，则（）A．内的所有直线与异面 B．内不存在与平行的直线 C．内存在唯一的直线与平行 D．内的直线与都相交解：B依题意，设直线，如图．内的直线若经过点，则与直线相交；若不经过点，则与直线是异面直线，但不可能与平行．l αl ⊄ααl αl αl αl l ∩α=A αA l A l l A B C D ABCD AC BD a ⊄αb ⊂αa ||b ⇒a ||αa ⊂βb ⊂βa ∩b =P a ||αb ||α⇒β||α例题：直线与平面平行的性质定理：一条直线与一个平面平行，则过这条直线的任一平面与此平面的交线与该直线平行．用符号表示：，，．平面与平面平行的性质定理：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．用符号表示：，，．a ||αa ⊂βα∩β=b ⇒a ||b α||βα∩γ=a β∩γ=b ⇒a ||b 下列命题（其中，表示直线，表示平面）中，正确的个数是（）①若，，则；②若，，则；③若，，则；④若，，则．A．个 B．个 C．个 D．个解：A①中缺少这一条件；②中，还有可能相交或异面；③中还有可能；④中与还有可能异面．a b αa ∥b b ⊂αa ∥αa ∥αb ∥αa ∥b a ∥b b ∥αa ∥αa ∥αb ⊂αa ∥b 0123a ⊄αa b a ⊂αa b 若平面，直线，点，则在内过点的所有直线中（）A．不一定存在与平行的直线B．只有两条与平行的直线C．存在无数条与平行的直线D．有且只有一条与平行的直线解：D直线与点确定平面，设，则唯一．α∥βa ⊂αB ∈ββB a a a a a B γβ∩γ=l l 如图，四棱锥中，底面是正方形，是棱的中点．求证：．证明：P −ABCD ABCD E P D P B ∥平面 EAC连接，与相交于点，连接．因为四边形为正方形，所以为中点．又因为为棱中点，所以．又，，故．BD AC O EO ABCD O BD E P D P B ∥EO P B ⊄平面 EAC EO ⊂平面 EAC P B ∥平面 EAC 如图所示，三棱锥被一平面所截，截面为平行四边形．求证：．证明：因为四边形为平行四边形，所以．又，，所以．而，，所以．A −BCD EF GH CD ∥EF EF GH EF ∥GH GH ⊂平面BCD EF ⊄平面BCD EF ∥平面BCD EF ⊂平面ACD 平面ACD ∩平面BCD =CD EF ∥CD 如图所示，在三棱锥中，，，分别是棱，，的中点，求证：．证明：因为，分别是棱，的中点，所以是的中位线，．因为，，所以．同理，．又因为，，，所以．S −ABC D E F AC BC SC 平面DEF ∥平面SAB D E AC BC DE △ABC DE ∥AB DE ⊄平面SAB AB ⊂平面SAB DE ∥平面SAB DF ∥平面SAB DE ∩DF =D DE ⊂平面DEF DF ⊂平面DEF 平面DEF ∥平面SAB 如图所示，已知在正方体中，，，分别是，，的中点．求证：．证明：ABCD −A 1B 1C 1D 1M N P C C 1B 1C 1C 1D 1平面 MNP ∥平面BD A 1描述：4.空间的垂直关系直线与平面垂直的判定如果直线与平面内的任意一条直线都垂直，我们就说直线与平面互相垂直．记作．直线叫做平面的垂线，平面叫做直线的垂面．直线与平面垂直时，它们唯一的公共点叫做垂足．直线与平面垂直的判定定理一条直线与一个平面内的两条相交直线都垂直，则该直线与此平面垂直．用符号表示：，，，，．平面与平面垂直的判定定理一个平面过另一个平面的垂线，则这两个平面垂直．用符号表示：，．直线与平面垂直的性质定理垂直于同一个平面的两条直线平行．用符号表示：，．平面与平面垂直的性质定理两个平面垂直，则一个平面内垂直于交线的直线与另一个平面垂直．用符号来表示：连接，，因为，分别是，的中点，所以．又因为是正方体，所以，所以．同理可得，．因为，，，，所以．B 1D 1C B 1N P B 1C 1C 1D 1PN ∥B 1D 1ABCD −A 1B 1C 1D 1∥BD B 1D 1PN ∥BD MN ∥D A 1PN ,MN ⊂平面MNP PN ∩MN =N ,BD ⊂平面BD A D A 1D ∩BD =D A 1平面 MNP ∥平面 BD A 1l αl αl ⊥αl ααl P ab ⊂αa ∩b =P l ⊥a l ⊥b ⇒l ⊥αl ⊥αl ⊂β⇒α⊥βa ⊥αb ⊥α⇒a ||b AB ⊂αAB ⊥CD ⇒AB ⊥β例题：，，，．α⊥βα∩β=CD AB⊂αAB⊥CD⇒AB⊥β下列命题中，正确的序号是______．①若直线与平面内的无数条直线垂直，则；②若直线与平面内的一条直线垂直，则；③若直线不垂直于平面，则内没有与垂直的直线；④若直线不垂直于平面，则内也可以有无数条直线与垂直；⑤过一点与已知平面垂直的直线有且只有一条．解：④⑤当直线与平面内的无数条平行直线垂直时，与不一定垂直，所以①不正确；当与内的一条直线垂直时，不能保证与平面垂直，所以②不正确；当与不垂直时，可能与内的无数条平行直线垂直，所以③不正确，④正确；过一点有且只有一条直线垂直于已知平面，所以⑤正确．故填④⑤．lαl⊥αlαl⊥αlααllααllαlαl αlαlαl α如图，三棱锥中，，底面的斜边为，为上一点．求证：．证明：因为，，所以．又，，所以．又，所以．P−ABC P A⊥平面ABC Rt△ABC AB F P CBC⊥AFP A⊥平面ABC BC⊂平面ABC P A⊥BCAC⊥BC AC∩P A=A BC⊥平面P ACAF⊂平面P AC BC⊥AF如图，已知四棱锥，底面是菱形，，，，点为的中点．求证：．证明：如图，连接，因为，，所以为等边三角形．因为是的中点，所以．因为，，所以．因为，，，所以．又，所以．P−ABCD ABCD∠DAB=60∘P D⊥平面ABCD P D=AD E AB平面P ED⊥平面P ABBD AB=AD∠DAB=60∘△ADBE AB AB⊥DEP D⊥面ABCD AB⊂平面ABCD AB⊥P DDE⊂平面P ED P D⊂平面P ED DE∩P D=D AB⊥平面P EDAB⊂平面P AB平面P ED⊥平面P ABAB⊂P AB3P C⊥AC C，求点到平面 P C⊥CD CH答案：1. 在下列命题中，不是公理的是 A ．平行于同一个平面的两个平面相互平行B ．过不在同一条直线上的三点，有且只有一个平面C ．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此平面内D ．如果两个不重合的平面有一个公共点，那么他们有且只有一条过该点的公共直线A()答案：2. 设是两条不同的直线，是两个不同的平面 A ．若，则 B ．若，则 C ．若，则 D ．若，则 Cm ,n α,β()m ∥α,n ∥αm ∥n m ∥α,m ∥βα∥βm ∥n ,m ⊥αn ⊥αm ∥α,α⊥βm ⊥β答案：3. 一定能得到结论"平面平面 "的条件是 A ．存在一条直线，使得 B ．存在一个平面，使得 C ．存在一个平面，使得 D ．存在一条直线，使得 Dα⊥β()l l ⊥α,l ⊥βγγ⊥α,γ⊥βγγ∥α,γ∥βl l ∥α,l ⊥β答案：4. 下列正方体或正四面体中，，，，分别是所在棱的中点，这四个点不共面的一个图是 A．B ．C ．D ．D P Q R S()高考不提分，赔付1万元，关注快乐学了解详情。

必修2第一单元知识清单+重点语句检索+易错点分析(新)

必修2知识清单第一单元：公民的政治生活1、国家是阶级统治的工具，阶级性是国家的根本属性。

2、国体：国体就是国家性质，是社会各阶级在国家中的地位。

国家性质是由占统治地位的阶级的性质决定的。

3、我国的国家性质（国体）：我国是工人阶级领导的，工农联盟为基础的人民民主专政的社会主义国家，其本质是人民当家作主。

人民是国家的主人。

（1）民主：在我国，人民民主具有广泛性（表现为民主主体和民主权利的广泛性）和真实性（表现为人民当家作主的权利有制度、法律、物质保障；广大人民的利益得到日益充分的实现；国家尊重保障人权；）（2）专政：依法打击极少数敌人的破坏活动，依法打击各种犯罪活动，维护社会治安和社会秩序，保障民主等。

4、人民民主专政是立国之本，政治基石，已载入宪法。

坚持人民民主专政是社会主义现代化建设的政治保证（发扬民主调动人民群众投身于社会主义现代化建设的积极性；坚持专政保障人民民主，维护国家长治久安。

）5．公民的政治权利和义务（1）依据：我国是人民当家作主的社会主义国家，公民与国家形成了新型的关系。

人民是国家的主人，国家权力来源于人民，国家通过宪法和法律规定了公民享有的政治权利和自由以及应履行政治性义务。

（2）政治权利主要有：①选举权和被选举权（是公民基本的民主权利，是公民参与管理国家和社会的基础和标志）、②政治自由（在法律允许范围内行使）、③监督权（对象：监督任何国家机关和工作人员；它包括批评权、建议权、检举权、申诉权、控告权和检举权）；（3）政治义务主要有：①维护国家统一和民族团结；（是我国顺利进行社会主义现代化建设的根本保证）；②遵守宪法和法律；（是党的主张和人民意志相统一的体现，是公民根本的行为准则）；③维护国家安全、荣誉和利益；④服兵役和参加民兵组织。

6．参与政治生活的基本原则：（1行义务，平等地适用法律；国家在保护公民的合法权利和依法实施处罚方面，对任何公民一律平等）（2识，珍惜公民权利；树立义务意识，自觉履行公民义务）（3公民个人的合法权益。

高中数学必修2第1、2章知识点+习题

第一章空间几何体1.1柱、锥、台、球的结构特征1 三视图：正视图：从前往后侧视图：从左往右俯视图：从上往下 2 画三视图的原则：长对齐、高对齐、宽相等 3直观图：斜二测画法 4斜二测画法的步骤：（1）.平行于坐标轴的线依然平行于坐标轴；（2）.平行于y 轴的线长度变半，平行于x ，z 轴的线长度不变；（3）.画法要写好。

5 用斜二测画法画出长方体的步骤：（1）画轴（2）画底面（3）画侧棱（4）成图空间几何体的表面积与体积（一）空间几何体的表面积1棱柱、棱锥的表面积：各个面面积之和2 圆柱的表面积3 圆锥的表面积2r rl S ππ+=4 圆台的表面积22R Rl r rl S ππππ+++= 5 球的表面积24R S π=（二）空间几何体的体积 1柱体的体积 h S V ⨯=底2锥体的体积 h S V ⨯=底313台体的体积 h S S S S V ⨯++=)31下下上上（4球体的体积 334R V π=第一章空间几何体一、选择题1．有一个几何体的三视图如下图所示，这个几何体可能是一个( )．222r rl S ππ+=主视图左视图俯视图 (第1题)A ．棱台B ．棱锥C ．棱柱D ．正八面体2．如果一个水平放置的平面图形的斜二测直观图是一个底角为45°，腰和上底均为1的等腰梯形，那么原平面图形的面积是( )．A ．2＋2B ．221＋ C ．22＋2 D ．2＋13．棱长都是1的三棱锥的表面积为( )． A ．3B ．23C ．33D ．434．长方体的一个顶点上三条棱长分别是3，4，5，且它的8个顶点都在同一球面上，则这个球的表面积是( )．A ．25πB ．50πC ．125πD ．都不对5．正方体的棱长和外接球的半径之比为( )． A ．3∶1B ．3∶2C ．2∶3D ．3∶36．在△ABC 中，AB ＝2，BC ＝1.5，∠ABC ＝120°，若使△ABC 绕直线BC 旋转一周，则所形成的几何体的体积是( )．A ．29π B ．27π C ．25π D ．23π 7．若底面是菱形的棱柱其侧棱垂直于底面，且侧棱长为5，它的对角线的长分别是9和15，则这个棱柱的侧面积是( )．A ．130B ．140C ．150D ．1608．如图，在多面体ABCDEF 中，已知平面ABCD 是边长为3的正方形，EF ∥AB ，EF ＝23，且EF 与平面ABCD 的距离为2，则该多面体的体积为( )．A ．29 B ．5C ．6D ．215 9．下列关于用斜二测画法画直观图的说法中，错误．．的是( )． A ．用斜二测画法画出的直观图是在平行投影下画出的空间图形 B ．几何体的直观图的长、宽、高与其几何体的长、宽、高的比例相同C．水平放置的矩形的直观图是平行四边形D．水平放置的圆的直观图是椭圆10．如图是一个物体的三视图，则此物体的直观图是()．(第10题)二、填空题11．一个棱柱至少有______个面，面数最少的一个棱锥有________个顶点，顶点最少的一个棱台有________条侧棱．12．若三个球的表面积之比是1∶2∶3，则它们的体积之比是_____________．13．正方体ABCD－A1B1C1D1 中，O是上底面ABCD的中心，若正方体的棱长为a，则三棱锥O－AB1D1的体积为_____________．14．如图，E，F分别为正方体的面ADD1A1、面BCC1B1的中心，则四边形BFD1E在该正方体的面上的射影可能是___________．15．已知一个长方体共一顶点的三个面的面积分别是2、3、6，则这个长方体的对角线长是___________，它的体积为___________．16．一个直径为32厘米的圆柱形水桶中放入一个铁球，球全部没入水中后，水面升高9厘米则此球的半径为_________厘米．三、解答题17．有一个正四棱台形状的油槽，可以装油190 L，假如它的两底面边长分别等于60 cm和40 cm，求它的深度．18 *．已知半球内有一个内接正方体，求这个半球的体积与正方体的体积之比．[提示：过正方体的对角面作截面]19．如图，在四边形ABCD中，∠DAB＝90°，∠ADC＝135°，AB＝5，CD＝22，AD＝2，求四边形ABCD绕AD旋转一周所成几何体的表面积及体积．(第19题)20．养路处建造圆锥形仓库用于贮藏食盐(供融化高速公路上的积雪之用)，已建的仓库的底面直径为12 m，高4 m，养路处拟建一个更大的圆锥形仓库，以存放更多食盐，现有两种方案：一是新建的仓库的底面直径比原来大4 m(高不变)；二是高度增加4 m(底面直径不变)．(1)分别计算按这两种方案所建的仓库的体积；(2)分别计算按这两种方案所建的仓库的表面积；(3)哪个方案更经济些？第二章直线与平面的位置关系2.1空间点、直线、平面之间的位置关系1 平面含义：平面是无限延展的2 平面的画法及表示（1）平面的画法：水平放置的平面通常画成一个平行四边形，锐角画成450，且横边画成邻边的2倍长（如图）（2）平面通常用希腊字母α、β、γ等表示，如平面α、平面β等，也可以用表示平面的平行四边形的四个顶点或者相对的两个顶点的大写字母来表示，如平面AC 、平面ABCD 等。

高中数学必修2(人教A版)第一章几何空间体1.1知识点总结含同步练习及答案

描述：例题：描述：高中数学必修2(人教A版)知识点总结含同步练习题及答案第一章空间几何体 1.1 空间几何体的结构一、学习任务认识柱、锥、台、球及其简单组合体的结构特征，能运用这些结构特征描述现实生活中简单物体的结构．二、知识清单典型空间几何体空间几何体的结构特征组合体展开图截面分析三、知识讲解1.典型空间几何体空间几何体的概念只考虑物体的形状和大小，而不考虑其他因素，那么由这些物体抽象出来的空间图形就叫做空间几何体．2.空间几何体的结构特征多面体由若干个平面多边形围成的几何体叫做多面体．围成多面体的各个多边形叫做多面体的面；相邻两个面的公共边叫做多面体的棱；棱与棱的公共点叫做多面体的顶点；连接不在同一个面上的两个顶点的线段叫做多面体的对角线．按多面体的面数可把多面体分为四面体、五面体、六面体．其中，四个面均为全等的正三角形的四面体叫做正四面体．旋转体由一个平面图形绕它所在的平面内的一条定直线旋转所形成的封闭几何体叫做旋转体．这条定直线叫做旋转体的轴．棱柱的结构特征一般地，有两个面互相平行，其余各面都是四边形，且每相邻两个四边形的公共边都互相平行，由这些面所围成的多面体叫做棱柱（prism）．棱柱中，两个互相平行的面叫做底面，简称底；其余各面叫做棱柱的侧面；相邻侧面的公共边叫做棱柱的侧棱；侧棱与底面的公共顶点叫做棱柱的用一个平行于棱锥底面的平面去截棱锥，得到两个几何体，一个是______，另一个是______．解：棱锥；棱台．⋯⋯余各面叫做棱柱的侧面；相邻侧面的公共边叫做棱柱的侧棱；侧棱与底面的公共顶点叫做棱柱的顶点．底面是三角形、四边形、五边形的棱柱分别叫做三棱柱、四棱柱、五棱柱，可以用表示底面各顶点的字母或一条对角线端点的字母表示棱柱，如下图的六棱柱可以表示为棱柱或棱柱．侧棱与底面不垂直的棱柱叫做斜棱柱；侧棱与底面垂直的棱柱叫做直棱柱；底面是正多边形的直棱柱叫做正棱柱；底面是平行四边形的棱柱叫做平行六面体；侧棱与底面垂直的平行六面体叫做直平行六面体．棱锥的结构特征一般地，有一个面是多边形，其余各面都是有一个公共顶点的三角形，由这些面所围成的多面体叫做棱锥（pyramid）．这个多边形面叫做棱锥的底面或底；有公共顶点的各个三角形面叫做棱锥的侧面；各侧面的公共顶点叫做棱锥的顶点；相邻侧面的公共边叫做棱锥的侧棱．底面是三角形、四边形、五边形的棱锥分别叫做三棱锥、四棱锥、五棱锥其中三棱锥又叫四面体．棱锥也用表示顶点和底面各顶点的字母或者用表示顶点和底面一条对角线端点的字母来表示，如下图的四棱锥表示为棱锥或者棱锥．棱锥的底面是正多边形，且它的顶点在过底面中心且与底面垂直的直线上，这个棱锥叫做正棱锥．正棱锥各侧面都是全等的等腰三角形，这些等腰三角形底边上的高都相等，叫做棱锥的斜高．⋯⋯⋯⋯ABCDEF−A′B′C′D′E′F′DA′⋯⋯⋯⋯S−ABCD S−AC棱台的结构特征用一个平行于棱锥底面的平面去截棱锥，底面与截面之间的部分，这样的多面体叫做棱台（frustum of a pyramid）．原棱锥的底面和截面分别叫做棱台的下底面和上底面；其他各面叫做棱台的侧面；相邻两侧面的公共边叫做棱台的侧棱；两底面的距离叫做棱台的高．由正棱锥截得的棱台叫做正棱台，正棱台的各个侧面都是全等的等腰梯形，这些等腰梯形的高叫做棱台的斜高．圆柱的结构特征以矩形的一边所在直线为旋转轴，其余三边旋转形成的面所围成的旋转体叫做圆柱（circular cylinder）．旋转轴叫做圆柱的轴；垂直于轴的边旋转而成的圆面叫做圆柱的底面；平行于轴的边旋转而成的曲面叫做圆柱的侧面；无论旋转到什么位置，不垂直于轴的边都叫做圆柱侧面的母线．圆锥的结构特征以直角三角形的一条直角边所在直线为旋转轴，其余两边旋转形成的面所围成的旋转体叫做圆锥（circular cone）．圆台的结构特征例题：用平行于圆锥底面的平面去截圆锥，底面与截面之间的部分叫做圆台（frustum of a cone）．棱台与圆台统称为台体．球的结构特征以半圆的直径所在直线为旋转轴，半圆面旋转一周形成的旋转体叫做球体，简称球（solid sphere）．半圆的圆心叫做球的球心，半圆的半径叫做球的半径，半圆的直径叫做球的直径．球常用表示球心的字母表示．O下列命题中，正确的是（）A．有两个面互相平行，其余各面都是四边形的几何体叫棱柱B．棱柱中互相平行的两个面叫做棱柱的底面C．棱柱的侧面是平行四边形，而底面不是平行四边形D．棱柱的侧棱长相等，侧面是平行四边形解：D如图(1)，满足 A 选项条件，但不是棱柱；对于 B 选项，如图(2)，构造四棱柱，令四边形是梯形，可知，但这两个面不能作为棱柱的底面；C选项中，若棱柱是平行六面体，则它的底面是平行四边形．ABCD−A1B1C1D1ABCD面AB∥面DCB1A1C1D1若正棱锥的底面边长与侧棱长相等，则该棱锥一定不是（）A．三棱锥 B．四棱锥 C．五棱锥 D．六棱锥解：D如下图，正六边形中，，那么正六棱锥中，，即侧棱长大于底面边长．ABCDEF OA=OB=⋯=AB S−ABCDEF SA>OA=AB描述：3.组合体简单组合体的构成有两种基本形式：一种是由简单几何体拼接而成，一种是由简单几何体截去或挖去一部分而成．如图所示的几何体中，是台体的是（）A．①② B．①③ C．③ D．②③解：C利用棱台的定义求解．①中各侧棱的延长线不能交于一点；②中的截面不平行于底面；③中各侧棱的延长线能交于一点且截面与底面平行．有下列四种说法：①圆柱是将矩形旋转一周所得的几何体；②以直角三角形的一直角边为旋转轴，旋转所得几何体是圆锥；③圆台的任意两条母线的延长线，可能相交也可能不相交；④半圆绕其直径所在直线旋转一周形成球．其中错误的有（）A．个 B．个 C．个 D．个解：D圆柱是矩形绕其一条边所在直线旋转形成的几何体，故①错；以直角三角形的一条直角边所在直线为轴，旋转一周，才能构成圆锥，②错；圆台是由圆锥截得，故其任意两条母线延长后一定交于一点，③错；半圆绕其直径所在直线旋转一周形成的是球面，故④错误．1234例题：描述：4.展开图空间形体的表面在平面上摊平后得到的图形，是画法几何研究的一项内容．描述图中几何体的结构特征．解：图（1）所示的几何体是由两个圆台拼接而成的组合体；图（2）所示的几何体是由一个圆台挖去一个圆锥得到的组合体；图（3）所示的几何体是在一个圆柱中间挖去一个三棱柱后得到的组合体．下图中的几何体是由哪个平面图形旋转得到的（）解：D）不在同一平面内的有______对．3内．解：C描述：例题：5.截面分析截面用平面截立体图形所得的封闭平面几何图形称为截面．平行截面、中截面与立体图形底面平行的截面称为平行截面，等分立体图形的高的平行截面称为中截面．轴截面包含立体图形的轴线的截面称为轴截面．球截面球的截面称为球截面．球的任意截面都是圆，其中通过球心的截面称为球的大圆，不过球心的截面称为球的小圆．球心与球的截面的圆心连线垂直于截面，并且有，其中为球的半径，为截面圆的半径，为球心到截面的距离．+=r 2d 2R 2R r d 下面几何体的截面一定是圆面的是（）A．圆台 B．球 C．圆柱 D．棱柱解：B如图所示，是一个三棱台，试用两个平面把这个三棱台分成三部分，使每一部分都是一个三棱锥．解：如图，过，，三点作一个平面，再过，，作一个平面，就把三棱台分成三部分，形成的三个三棱锥分别是，，．ABC −A ′B ′C ′A ′B C A ′B C ′ABC −A ′B ′C ′−ABC A ′−B B ′A ′C ′−BC A ′C ′如图，正方体中，，，分别是，，的中点，那么正方体中过点，，的截面形状是（）A．三角形 B．四边形 C．五边形 D．六边形ABCD −A 1B 1C 1D 1P Q R AB AD B 1C 1P QR作截面图如图所示，可知是六边形．ii）若两平行截面在球心的两侧，如图(2)所示，则解：四、课后作业（查看更多本章节同步练习题，请到快乐学）答案：1.如图，能推断这个几何体可能是三棱台的是．A ．B ．C ．D ．C ()=2,AB =3,=3,BC =4A 1B 1B 1C 1=1,AB =2,=1.5,BC =3,=2,AC =3A 1B 1B 1C 1A 1C 1=1,AB =2,=1.5,BC =3,=2,AC =4A 1B 1B 1C 1A 1C 1AB =,BC =,CA =A 1B 1B 1C 1C 1A 1答案：2. 纸制的正方体的六个面根据其方位分别标记为上、下、东、南、西、北．现在沿该正方体的一些棱将正方体剪开、外面朝上展平，得到如图所示的平面图形，则标" "的面的方位是．A ．南B ．北C ．西D ．下B △()3. 向高为的水瓶中注水，注满为止，如果注水量与水深的函数关系的图象如图所示，那么水瓶的形状是．A ．H V h ()高考不提分，赔付1万元，关注快乐学了解详情。

高中物理必修(1,2)各章节知识点及配套练习

1西 C第一章运动的描述：机械运动、参考系、质点1．两辆汽车在平直公路上，甲车内一个人看到窗外树木向东移动，乙车内一个人发现甲车没有运动，以大地为参考系，则说明 ( )A ．甲车向西运动，乙车不动：B ．乙车向西运动，甲车不动；C ．甲车向东运动，乙车向东运动；D ．甲乙两车以相同速度同时向西运动。

2．下列情况中的物体，哪些可以看作质点？（）A ．研究从北京开往上海的一列火车的运行速度B ．研究汽车后轮上一点运动情况的车轮C ．体育教练员研究百米赛跑运动员的起跑动作D ．研究地球自转时的地球时间、位移1．以下的计时数据指时间的是（）A ．天津开往德州的625次列车于13时35分从天津出发B ．某运动员用11s 跑完100mC ．中央电视台新闻联播节目每晚19时开播D ．某场足球赛开赛15min 时，甲队攻入一球 2．如图1所示，物体沿两个半径为R 的半圆弧由A 运动到C ，则它的位移和路程分别是（）A ．0，0B ．4R 向东，2πR 向东C ．4πR 向东，4RD ．4R 向东，2πR平均速度、瞬时速度1．下述各项所指的速度哪项是指瞬时速度?A ．汽车从20km/h 的速度通过大桥；B ．子弹以500m/s 的速度飞出枪口；C ．人步行的速度大约是5km/h ；D ．台风中心以25km/h 的速度向沿海海岸移动。

2．一辆汽车以速度v 1匀速行驶全程的32的路程，接着以v 2=20 km/h 走完剩下的路程，若它全路程的平均速度v =28 km/h ，则v 1应为（）A ．24 km/hB ．34 km/hC ．35 km/hD ．28 km/h加速度：描述运动物体速度变化快慢的物理量；与初速度、末速度、时间无关；大小等于单位时间内速度变化量，方向与速度变化量的方向一致。

1.关于速度和加速度，下述正确的是（） A ．物体的速度大，加速度就大 B ．物体速度的改变量大，加速度就大 C ．物体的速度改变快，加速度就大 D ．物体的速度为零时，加速度一定为零直线运动的位移、速度图象1、下列各图中，不是匀速直线运动的是2、甲、乙两个质点同时、同地向同一方向做直线运动，它们的速度——时间图像如图所示，则由图像可知（）A.甲质点比乙质点运动的快，故乙追不上甲；B.在2s 末时乙追上甲；C.在2s 末时甲、乙的位移相同；D .甲做匀速直线运动，乙做初速度为零的匀加速直线运动。

(完整word版)高中数学必修2第一章知识点习题

第一章空间几何体1.1 柱、锥、台、球的构造特点1.棱柱：有两个面相互平行，其他各面都是四边形，且每相邻两个四边形的公共边都相互平行，由这些面所围成的几何体。

几何特点：两底面是对应边平行的全等多边形；侧面、对角面都是平行四边形；侧棱平行且相等；平行于底面的截面是与底面全等的多边形。

2.棱锥：有一个面是多边形，其他各面都是有一个公共极点的三角形，由这些面所围成的几何体。

几何特点：侧面、对角面都是三角形；平行于底面的截面与底面相像。

3.棱台：用一个平行于棱锥底面的平面去截棱锥，截面和底面之间的部分几何特点：①上下底面是相像的平行多边形②侧面是梯形③侧棱交于原棱锥的极点1.2 空间几何体的三视图和直观图1.三视图：正视图：光芒从几何体的前面向后边正投影获得的投影图；侧视图：光芒从几何体的左面向右边正投影获得的投影图；俯视图：光芒从几何体的上边向下边正投影获得的投影图。

2.画三视图的原则：长对齐、高对齐、宽相等3.直观图：斜二测画法4. 斜二测画法的基本步骤：①成立适合直角坐标系②成立斜坐标系''y'' ''0（或 135x O，使xO y=45），注意它们确立的平面表示水平平面；③画对应图形，在已知图形平行于X 轴的线段，在直观图中画成平行于X‘轴，且长度保持不变；在已知图形平行于Y 轴的线段，在直观图中画成平行于Y‘轴，且长度变成本来的一半5.用斜二测画法画出长方体的步骤：（ 1）画轴（ 2）画底面（ 3）画侧棱（ 4）成图1.3 空间几何体的表面积与体积（一）空间几何体的表面积1 棱柱、棱锥的表面积：各个面面积之和2圆柱的表面积S2rl2r 23圆锥的表面积Srl r 24圆台的表面积Srl r 2Rl R25球的表面积S4 R 2（二）空间几何体的体积1 柱体的体积V S底 h3 台体的体积V 1S上 S下S下 ) h（ S上32 锥体的体积V1S底 h34 球体的体积V4R33xOy （尽可能使更多的点在座标轴上）第一章空间几何体一、选择题1．以下图是由哪个平面图形旋转获得的（）A B C D2.如图是一个物体的三视图，则此物体的直观图是()．3．有一个几何体的三视图以以下图所示，这个几何体可能是一个() ．主视图左视图俯视图A．棱台 B ．棱锥C．棱柱 D ．正八面体4. 图（ 1）为长方体积木块堆成的几何体的三视图，此几何体共由________块木块堆成图（ 1）5．假如一个水平搁置的平面图形的斜二测直观图是一个底角为45°，腰和上底均为1的等腰梯形，那么原平面图形的面积是() ．A． 2＋ 2 B ．1＋ 22＋ 2D ． 1＋ 22C．26．棱长都是1的三棱锥的表面积为() ．A． 3 B ． 2 3C．3 3 D ． 4 37．长方体的一个极点上三条棱长分别是3， 4，5，且它的8 个极点都在同一球面上，则这个球的表面积是 () ．A． 25π B ． 50πC．125π D ．都不对8．正方体的棱长和外接球的半径之比为() ．A． 3 ∶ 1 B ． 3 ∶ 2C．2∶ 3 D ． 3 ∶ 39．在△ ABC 中， AB＝ 2，BC＝，∠ ABC＝ 120°，若使△ ABC 绕直线BC旋转一周，则所形成的几何体的体积是() ．9753 A．π B ．πC．π D ．π2222 10．若底面是菱形的棱柱其侧棱垂直于底面，且侧棱长为5，它的对角线的长分别是9 和 15，则这个棱柱的侧面积是() ．A． 130 B ． 140C．150 D ． 16011．如图，在多面体ABCDEF 中，已知平面ABCD 是边长为 3 的正方形， EF ∥AB ，EF ＝3，且 EF 与平面 ABCD 的距离为 2，则该多面体的体积为() ．29( 第11题)15 A．C． 6B ． 5 D ．22 12.以下对于用斜二测画法画直观图的说法中，错误．．的是 () ．A．用斜二测画法画出的直观图是在平行投影下画出的空间图形B．几何体的直观图的长、宽、高与其几何体的长、宽、高的比率同样C．水平搁置的矩形的直观图是平行四边形D．水平搁置的圆的直观图是椭圆二、填空题1．一个棱柱起码有 ______个面，面数最少的一个棱锥有________个极点，极点最少的一个棱台有 ________条侧棱．2．若三个球的表面积之比是1∶2∶ 3，则它们的体积之比是 _____________．3．正方体 ABCD －A B C D1中， O 是上底面 ABCD 的中心，若正方体的棱长为a，111则三棱锥 O－ AB1D 1的体积为 _____________ ．4．如图， E，F 分别为正方体的面 ADD A 、面 BCC B的中心，则四边形 BFD E 在11111该正方体的面上的射影可能是___________ ．(第4题 )5．已知一个长方体共一极点的三个面的面积分别是 2 、 3 、 6 ，则这个长方体的对角线长是___________ ，它的体积为 ___________ ．6．一个直径为32 厘米的圆柱形水桶中放入一个铁球，球所有没入水中后，水面高升9 厘米则此球的半径为_________ 厘米．三、解答题1．如图，在四边形 ABCD 中，∠ DAB ＝ 90°，∠ ADC ＝ 135°， AB＝ 5，CD ＝ 2 2 ，AD ＝2，求四边形ABCD 绕 AD 旋转一周所成几何体的表面积及体积．( 第 2题 )2．以下图是一个四棱柱铁块，画出它的三视图．3.依所给实物图的形状，画出所给组合体的三视图．。

新教材人教版高中物理选择性必修第二册第一章安培力与洛伦兹力课时练习题及章末测验含解析

第一章安培力与洛伦兹力1.磁场对通电导线的作用力........................................................................................... - 1 -2.安培力的综合应用....................................................................................................... - 5 -3.磁场对运动电荷的作用力........................................................................................... - 9 -4.带电粒子在匀强磁场中的运动................................................................................. - 14 -5.质谱仪与回旋加速器................................................................................................. - 23 -第一章综合测验............................................................................................................ - 28 -1.磁场对通电导线的作用力一、单项选择题1．关于通电导线所受安培力F的方向，磁场B的方向和电流I的方向之间的关系，下列说法正确的是( )A．F、B、I三者必须保持相互垂直B．F必须垂直B、I，但B、I可以不相互垂直C．B必须垂直F、I，但F、I可以不相互垂直D．I必须垂直F、B，但F、B可以不相互垂直2．某同学画的表示磁感应强度B、电流I和安培力F的相互关系如下列选项图所示，其中正确的是( )3．如图所示，一导体棒ab静止在U形铁芯的两臂之间．电键闭合后导体棒受到的安培力方向( )A．向上 B．向下 C．向左 D．向右4.如图，等边三角形线框LMN由三根相同的导体棒连接而成，固定于匀强磁场中，线框平面与磁感应强度方向垂直，线框顶点M、N与直流电源两端相接．已如导体棒MN受到的安培力大小为F，则线框LMN受到的安培力的大小为( )A．2F B．1.5F C．0.5F D．05.在等边三角形的三个顶点a、b、c处，各有一条长直导线垂直穿过纸面，导线中通有大小相等的恒定电流，方向如图所示．过c点的导线所受安培力的方向( ) A．与ab边平行，竖直向上B．与ab边垂直，指向左边C．与ab边平行，竖直向下D．与ab边垂直，指向右边二、多项选择题6．如图所示，纸面内的金属圆环中通有电流I，圆环圆心为O、半径为R，P、Q为圆环上两点，且OP垂直于OQ，磁感应强度大小为B的匀强磁场垂直于纸面向里，则( )A．整个圆环受到的安培力大小为2πBIRB．整个圆环受到的安培力大小为0C．圆弧PQ受到的安培力大小为BIRD．圆弧PQ受到的安培力大小为2BIR7．如图甲所示，扬声器中有一线圈处于磁场中，当音频电流信号通过线圈时，线圈带动纸盆振动，发出声音．俯视图乙表示处于辐射状磁场中的线圈(线圈平面即纸面)，磁场方向如图中箭头所示，在图乙中( )A．当电流沿顺时针方向时，线圈所受安培力的方向垂直于纸面向里B．当电流沿顺时针方向时，线圈所受安培力的方向垂直于纸面向外C．当电流沿逆时针方向时，线圈所受安培力的方向垂直于纸面向里D．当电流沿逆时针方向时，线圈所受安培力的方向垂直于纸面向外8．图中装置可演示磁场对通电导线的作用．绕有导线的两铁芯之间某一水平面内固定两条平行金属导轨，L是置于导轨上并与导轨垂直的金属杆．当电磁铁线圈两端a、b，导轨两端e、f，分别接到两个不同的直流电源上时，L便在导轨上滑动，下列说法正确的是( )A．若a接正极，b接负极，e接正极，f接负极，则L向右滑动B．若a接正极，b接负极，e接负极，f接正极，则L向右滑动C．若a接负极，b接正极，e接正极，f接负极，则L向左滑动D．若a接负极，b接正极，e接负极，f接正极，则L向左滑动答案及解析1．解析：安培力F总是与磁场B方向和电流I方向决定的平面垂直，但B与I(即导线)可以垂直，也可以不垂直，通电导线受安培力时，力F与磁场及力F与导线都是垂直的，故A、C、D均错，B正确．答案：B2．解析：A图中磁场方向和电流方向平行，导线不受安培力作用，根据左手定则可知，B图中安培力的方向应垂直于磁场方向向上，C图中安培力的方向应垂直于导线向下，D图中安培力的方向垂直于导线向右．故选项D 正确．答案：D3．解析：根据图中的电流方向，由安培定则知U 形铁芯下端为N 极，上端为S 极，ab 中的电流方向由a →b ，由左手定则可知导体棒受到的安培力方向向右，选项D 正确．答案：D4．解析：设三根相同的导体棒的电阻均为R ，长度均为l ，其中ML 和LN 为串联关系，总电阻为2R . 由并联电路特点可知，通过MN 的电流为通过ML 和LN 中的电流的两倍，若MN 受到的安培力F ＝BIl ，则ML 和LN 受到的安培力的合力F 1＝BIl2，MN 受到的安培力与ML 和LN受到的安培力的合力的方向相同，故线框受到的安培力为F 合＝F ＋F 1＝1.5F ，故选B.答案：B5．解析：等边三角形的三个顶点a 、b 、c 处均有一通电直导线，且导线中通有大小相等的恒定电流．由安培定则可得：导线a 、b 的电流在c 处的合磁场方向竖直向下．再由左手定则可得：安培力的方向是与ab 边垂直，指向左边，故选B.也可以根据同向电流相互吸引，导线a 、b 对c 的引力大小相等，合力沿角平分线方向，即与ab 边垂直，指向左边．B 项正确．答案：B6．解析：根据左手定则可知，整个圆环关于圆心对称的两部分受到的安培力等大反向，受到的合力为0，选项A 错，B 对；圆弧PQ 受到的安培力大小等于直线段PQ 受到的安培力大小，为2BIR ，选项C 错，D 对．答案：BD7．解析：将线圈看作由无数小段直导线组成，由左手定则可以判断，当电流沿顺时针方向时，线圈所受安培力的方向垂直于纸面向外，选项B 正确，A 错误；当电流沿逆时针方向时，线圈所受安培力的方向垂直于纸面向里，选项C 正确，D 错误．答案：BC8．解析：若a 接正极，b 接负极，由安培定则知两铁芯间磁场方向向上、若e 接正极，f 接负极，由左手定则知L 受到的安培力向左；若e 接负极，f 接正极，L 受到的安培力向右，选项A 错误，选项B 正确．同理，若a 接负极，b 接正极，两铁芯间磁场方向向下、e 接负极，f 接正极，L 所受的安培力向左；e 接正极，f 接负极，L 所受的安培力向右，选项C 错误，选项D 正确．答案：BD2.安培力的综合应用一、单项选择题1．通有电流的导线L1、L2处在同一平面(纸面)内，L1是固定的，L2可绕垂直纸面的固定光滑转轴O转动(O为L2的中心)，各自的电流方向如图所示．下列哪种情况将会发生( )A．因L2不受磁场力的作用，故L2不动B．因L2上、下两部分所受的磁场力平衡，故L2不动C．L2绕轴O按顺时针方向转动D．L2绕轴O按逆时针方向转动2.条形磁铁固定在水平面上，其正上方有一根通电导线，电流方向向左．不考虑导线的重力，在条形磁铁磁场的作用下，关于导线运动情况的说法正确的是( )A．从上向下看逆时针转90°，同时向上运动B．从上向下看逆时针转90°，同时向下运动C．从上向下看顺时针转90°，同时向下运动D．从上向下看顺时针转90°，同时向上运动3．如图，一绝缘光滑固定斜面处于匀强磁场中，磁场的磁感应强度大小为B，方向垂直于斜面向上，通有电流I的金属细杆水平静止在斜面上．若电流变为0.5I，磁感应强度大小变为3B，电流和磁场的方向均不变，则金属细杆将( )A．沿斜面加速上滑B．沿斜面加速下滑C．沿斜面匀速上滑 D．仍静止在斜面上二、多项选择题4.如图所示，一根通有电流I的直铜棒MN，用导线挂在磁感应强度为B的匀强磁场中，此时两根悬线处于张紧状态，下列哪些措施可使悬线中张力为零( )A．适当增大电流IB．使电流反向并适当增大IC．保持电流I不变，适当增大BD．使电流I反向，适当增大B5．在某次科技活动中，有人做了一个电磁“小车”实验：如图所示，用裸露的铜导线绕制成一根长螺线管，将螺线管固定在水平桌面上．用一节干电池和两个磁铁制成一个“小车”，两磁铁的同名磁极粘在电池的正、负两极上．将这辆“小车”推入螺线管中(磁铁与电极和铜线均能良好导电)，“小车”就加速运动起来．关于“小车”的运动，以下说法正确的是( )A．图中“小车”加速度方向向右B．图中“小车”加速度方向向左C．只将“小车”上某一磁铁改为S极与电池粘连，“小车”就不能加速运动D．只将“小车”上两磁铁均改为S极与电池粘连，“小车”的加速度方向不变三、非选择题6．如图所示，两根平行、光滑的斜金属导轨相距L＝0.1 m，与水平面间的夹角为θ＝37°，有一根质量为m＝0.01 kg的金属杆ab垂直导轨搭在导轨上，匀强磁场与导轨平面垂直，磁感应强度为B＝0.2 T，当杆中通以从b到a的电流时，杆可静止在导轨上，取g＝10 m/s2.(sin 37°＝0.6，cos 37°＝0.8)(1)求此时通过ab杆的电流；(2)若保持其他条件不变，只是突然把磁场方向改为竖直向上，求此时杆的加速度．7．如图所示，在水平放置的平行导轨一端架着一根质量m＝0.04 kg的金属棒ab，导轨另一端通过开关与电源相连．该装置放在高h＝20 cm的绝缘垫块上．当有竖直向下的匀强磁场时，闭合开关，金属棒ab会被抛到距导轨右端水平距离s＝100 cm处，试求开关闭合后安培力对金属棒做的功．(g取10 m/s2)答案及解析1．解析：由右手螺旋定则可知导线L1上方的磁场的方向为垂直纸面向外，且离导线L1的距离越远的地方，磁感应强度越弱，导线L2上的每一小部分受到的安培力方向水平向右，由于O点的下方磁场较强，则安培力较大，因此L2绕轴O按逆时针方向转动，D选项对．答案：D2．解析：根据条形磁铁的磁场分布，并结合左手定则，可知通电导线左半部分受到的安培力方向垂直纸面向里，右半部分受到的安培力方向垂直纸面向外，因此通电导线从上向下看顺时针转90°，且随着转动会受到向下的安培力，即同时向下运动，故C正确．答案：C3．解析：设斜面倾角为θ，当磁场的磁感应强度大小为B ，通过金属细杆的电流为I 时，金属细杆处于静止状态．其受力分析如图所示，根据平衡条件和安培力公式可得F ＝BIL ＝mg sin θ.当磁场的磁感应强度大小变为3B ，电流变为0.5I 时，此时的安培力大小变为F ′＝3B ×0.5I ×L ＝1.5BIL ，金属细杆将沿斜面向上加速运动，故A 正确，B 、C 、D 错误．答案：A4．解析：A 、C 对：根据左手定则，判断导线受到的安培力方向向上，增大安培力，可使悬线中张力为零，根据公式F ＝BIL 知，适当增大电流I 或者保持电流I 不变，适当增大B ，可使悬线中张力为零．B 、D 错：若使电流I 反向，则安培力向下，悬线中的张力不可能为零．答案：AC5．解析：两磁极间的磁感线如答图甲所示，干电池与磁铁及中间部分线圈组成了闭合回路，在两磁极间的线圈中产生电流，左端磁极的左侧线圈和右端磁极的右侧线圈中没有电流．其中线圈中电流方向的左视图如答图乙所示，由左手定则可知中间线圈所受的安培力有向右的分力，根据牛顿第三定律有“小车”向左加速，A 错误，B 正确；如果只改变某一磁铁S 极与电池粘连，则磁感线不会向外发散，两部分受到方向相反的力，合力为零，“小车”不能加速运动，C 正确；将“小车”上两磁铁均改为S 极与电池粘连，磁感线会向里聚集，受到的力与答图中方向相反，故“小车”的加速度方向将发生改变，D 错误．答案：BC6．解析：(1)杆静止在导轨上，受力平衡，杆受到重力、导轨的支持力以及安培力，根据平衡条件得：BIL ＝mg sin θ，解得：I ＝mg sin θBL ＝0.01×10×0.60.2×0.1A ＝3 A. (2)若把磁场方向改为竖直向上，对杆受力分析，根据牛顿第二定律得：F 合＝mg sin θ－BIL cos θ＝mg sin θ－mg sin θcos θ＝ma解得：a ＝g sin θ－g sin θcos θ＝(10×0.6－10×0.6×0.8) m/s 2＝1.2 m/s 2，方向沿导轨向下．答案：(1)3 A (2)1.2 m/s 2，方向沿导轨向下7．解析：设在闭合开关到金属棒离开导轨的短时间内，安培力对金属棒做的功为W ，由动能定理得W ＝12mv 2，设平抛运动的时间为t ，则竖直方向有h ＝12gt 2，水平方向有s ＝vt ，将数据代入解得W ＝0.5 J.答案：0.5 J3.磁场对运动电荷的作用力一、单项选择题1.带电粒子(重力不计)穿过饱和蒸汽时，在它走过的路径上饱和蒸汽便凝成小液滴，从而显示粒子的径迹，这是云室的原理，如图所示是云室的拍摄照片，云室中加了垂直于照片向外的匀强磁场，图中Oa 、Ob 、Oc 、Od 是从O 点发出的四种粒子的径迹，下列说法中正确的是( )A ．四种粒子都带正电B ．四种粒子都带负电C ．打到a 、b 点的粒子带正电D ．打到c 、d 点的粒子带正电2．如图所示，方形玻璃管中有NaCl 的水溶液，沿x 轴正方向流动，沿y 轴正向加恒定的匀强磁场B .图中a 、b 是垂直于z 轴方向上玻璃管的前后两内侧面，则( )A．a处电势低于b处电势B．a处钠离子浓度大于b处钠离子浓度C．溶液上表面的电势高于下表面的电势D．溶液上表面处的氯离子浓度大于下表面处的氯离子浓度3.图中a、b、c、d为四根与纸面垂直的长直导线，其横截面位于正方形的四个顶点上，导线中通有大小相同的电流，方向如图所示．一带正电的粒子从正方形中心O点沿垂直于纸面的方向向外运动，它所受洛伦兹力的方向是( )A．向上 B．向下C．向左 D．向右4．下列有关洛伦兹力和安培力的描述，正确的是( )A．通电直导线在匀强磁场中一定受到安培力的作用B．安培力是大量运动电荷所受洛伦兹力的宏观表现C．带电粒子在匀强磁场中运动，受到的洛伦兹力做正功D．通电直导线在磁场中受到的安培力方向与磁场方向平行5．如图所示是电子射线管的示意图．电子射线由阴极沿x轴正方向射出，在荧光屏上会看到一条亮线．要使荧光屏上的亮线向下(z轴负方向)偏转，在下列措施中可采用的是( )A．加一电场，电场方向沿z轴负方向B．加一电场，电场方向沿y轴正方向C．加一磁场，磁场方向沿z轴负方向D．加一磁场，磁场方向沿y轴正方向二、多项选择题6．一带电粒子(重力不计，图中已标明粒子所带电荷的正负)进入磁场中，下列关于磁场方向、速度方向及带电粒子所受的洛伦兹力方向的标示正确的是( )7．如图所示，一质量为m、电荷量为＋q的圆环可在水平放置的足够长的粗糙细杆上滑动，细杆处于磁感应强度为B的匀强磁场中，不计空气阻力，现给圆环向右的初速度v0，在以后的运动过程中，圆环运动的v t图像可能是图中的( )8．如图所示，带电平行板中匀强电场E的方向竖直向上，匀强磁场B的方向水平(垂直纸面向里)．某带电小球从光滑绝缘轨道上的A点自由滑下，经过轨道端点P进入板间后恰好沿水平方向做直线运动．现使球从较低的B点开始滑下，经P点进入板间，则球在板间运动的过程中( )A．动能将会增大B．电势能将会增大C．所受的磁场力将会增大D．所受的电场力将会增大答案及解析1．解析：由左手定则知打到a、b点的粒子带负电，打到c、d点的粒子带正电，D正确．答案：D2．解析：A错，B对：溶液中的正负离子沿x轴正向移动，由左手定则可知运动的正离子受到沿z轴正向的洛伦兹力，运动的负离子受到沿z轴负向的洛伦兹力，故正离子都会偏向a处，负离子都会偏向b处，a处电势高于b处电势，a处钠离子浓度大于b处钠离子浓度．C、D错：正离子都会偏向a处，负离子都会偏向b处，并没有上下之分，所以溶液上表面的电势等于下表面的电势，溶液上表面处的离子浓度也等于下表面处的离子浓度．答案：B3．解析：a、b、c、d四根导线上电流大小相同，它们在O点形成的磁场的磁感应强度B的大小相同，方向如图甲所示．O点合磁场方向如图乙所示，则据左手定则可以判定由O点垂直纸面向外运动的带正电的粒子所受洛伦兹力方向向下．B选项正确．答案：B4．解析：当电流方向与磁场方向平行时，通电直导线不受安培力，故A错误；导线中定向移动的电荷受到的洛伦兹力在宏观上表现为导线受到的安培力，所以说安培力是大量运动电荷所受洛伦兹力的宏观表现，B正确；洛伦兹力的方向与电荷运动方向始终垂直，因此洛伦兹力对电荷不做功，C错误；通电直导线在磁场中受到的安培力方向与磁场方向垂直，D错误．答案：B5．解析：电子由阴极沿x轴正方向射出，要使电子的径迹向下(z轴负方向)偏转，则应使电子受到向下的力．若加一电场，由于电子带负电，所受电场力与电场方向相反，因此电场方向应沿z轴正方向；若加一磁场，根据左手定则可知，所加磁场应沿y轴的正方向(注意电子带负电，四指应指向电子运动的反方向)．故选项D正确．答案：D6．解析：A中，带负电的粒子向右运动，掌心向外，四指所指的方向向左，拇指所指的方向向下，选项A正确；B中，带正电的粒子向下运动，掌心向里，四指所指的方向向下，拇指的方向向左，选项B正确；C中，带正电粒子的运动方向与磁感线平行，此时不受洛伦兹力的作用，选项C错误；D中，带负电的粒子向右运动，掌心向外，四指所指的方向向左，拇指所指的方向向下，选项D错误．答案：AB7．解析：由左手定则可判断洛伦兹力方向向上，圆环受到竖直向下的重力、垂直杆的弹力及向左的摩擦力，当洛伦兹力初始时刻小于重力时，弹力方向竖直向上，圆环向右减速运动，随着速度减小，洛伦兹力减小，垂直杆的弹力越来越大，故做加速增大的减速运动，直到速度为零而处于静止状态，选项中没有对应图像；当洛伦兹力初始时刻等于重力时，垂直杆的弹力为零，摩擦力为零，故圆环做匀速直线运动，故选项A正确；当洛伦兹力初始时刻大于重力时，弹力方向竖直向下，圆环做减速运动，速度减小，洛伦兹力减小，垂直杆的弹力减小，在弹力减小到零的过程中，摩擦力逐渐减小到零，故做加速度逐渐减小的减速运动，摩擦力为零时，开始做匀速直线运动，故选项D正确．答案：AD8．解析：根据受力情况判断，小球带的只能是正电荷．当带电小球从A点自由滑下时，G＝F1＋F2＝qvB＋qE.小球从B点开始滑下，进入板间时的速度v′＜v，因此洛伦兹力F′1<F1，三力在竖直方向不平衡，小球在板间开始做加速曲线运动，速度将增大，从而动能将会增大，洛伦兹力也将会增大．另外，由于小球向下运动，克服电场力做功，因此电势能也将增大．答案：ABC4.带电粒子在匀强磁场中的运动一、单项选择题1．一质子在匀强磁场中运动，不考虑其他场力(重力)作用，下列说法正确的是( ) A．可能做类平抛运动B．一定做匀变速直线运动C．可能做匀速直线运动D．只能做匀速圆周运动2．两相邻匀强磁场区域的磁感应强度大小不同、方向平行．一速度方向与磁感应强度方向垂直的带电粒子(不计重力)，从较强磁场区域进入到较弱磁场区域后，粒子的( ) A．轨迹半径增大，角速度增大B．轨迹半径增大，角速度减小C．轨迹半径减小，速度增大D．轨迹半径减小，速度不变3．质量和电荷量都相等的带电粒子M和N以不同的速率经小孔S垂直进入匀强磁场，运动的半圆轨迹如图中虚线所示．下列表述正确的是( )A．M带负电，N带正电B．M的速率小于N的速率C．洛伦兹力对M、N做正功D．M的运行时间大于N的运行时间4．如图所示，某两相邻匀强磁场区域以MN为分界线，磁感应强度分别为B1、B2，磁场方向均垂直于纸面．有甲、乙两个电性相同的粒子同时分别以速率v1和v2从边界的a、c点垂直于边界射入磁场，经过一段时间后甲、乙两粒子恰好在b点相遇(不计重力及两粒子间的相互作用力)，O1和O2分别位于所在圆的圆心，其中R1＝2R2则( )A．B1、B2的方向相反B．v1＝2v2C．甲、乙两粒子做匀速圆周运动的周期不同D．若B1＝B2，则甲、乙两粒子的比荷不同5．用洛伦兹力演示仪可以观察电子在磁场中的运动径迹，如图甲是洛伦兹力演示仪的实物图，图乙是结构示意图．励磁线圈通电后可以产生垂直纸面的匀强磁场，励磁线圈中的电流越大，产生的磁场越强．图乙中电子经电子枪中的加速电场加速后水平向左垂直磁感线方向射入磁场．下列关于实验现象的分析正确的是( )A．仅增大励磁线圈中的电流，电子束径迹的半径变小B．仅升高电子枪加速电场的电压，电子束径迹的半径变小C．仅升高电子枪加速电场的电压，电子做圆周运动的周期将变小D．要使电子形成如图乙中的运动径迹，励磁线圈中应通以逆时针方向的电流6.如图所示，以O为圆心的圆形区域内，存在方向垂直纸面向外的匀强磁场，磁场边界上的A点有一粒子发射源，沿半径AO方向发射出速率不同的同种粒子(重力不计)，垂直进入磁场，下列说法正确的是( )A．速率越大的粒子在磁场中运动的时间越长B．速率越小的粒子在磁场中运动的时间越长C．速率越大的粒子在磁场中运动的角速度越大D．速率越小的粒子在磁场中运动的角速度越大二、多项选择题7.如图所示，若粒子(不计重力)能在图中所示的磁场区域内做匀速圆周运动，则可以判断( )A．粒子在运动过程中机械能不变B．若粒子带正电，则粒子沿顺时针方向运动C．在其他量不变的情况下，粒子速度越大，运动周期越大D．在其他量不变的情况下，粒子速度越大，做圆周运动的半径越大8.如图所示，截面为正方形的容器处在匀强磁场中，一束电子从孔a垂直磁场方向射入容器中，其中一部分从c孔射出，一部分从d孔射出，则下列叙述中正确的是( ) A．从两孔射出的电子速率之比v c:v d＝2:1B．从两孔射出的电子在容器中运动所用时间之比t c:t d＝1:2C．从两孔射出的电子在容器中运动时的加速度大小之比a c:a d＝2:1D．从两孔射出的电子在容器中运动时的加速度大小之比a c:a d＝2:1三、非选择题9.如图所示，一个带负电的粒子以速度v由坐标原点射入磁感应强度为B的匀强磁场中，速度方向与x轴、y轴正方向均成45°角．已知该粒子带电荷量为q，质量为m，则该粒子通过x轴和y轴的坐标分别是多少？10.一个电子(电荷量e ，质量m )以速率v 从x 轴上某点垂直x 轴进入上方匀强磁场区域，如图所示，已知上方匀强磁场的磁感应强度为B ，且大小为下方匀强磁场的磁感应强度的12，那么(1)电子运动一个周期所用的时间是多少？ (2)电子运动一个周期沿x 轴上移动的距离是多少？ 11.一个重力不计的带电粒子，电荷量为q ，质量为m ，从坐标为(0，L )的a 点平行于x 轴射入磁感应强度为B 的圆形匀强磁场区域，又从x 轴上b 点射出磁场，速度方向与x 轴正方向夹角为60°，如图所示．试求：(1)带电粒子的速度大小； (2)粒子由a 点运动到b 点的时间．12.如图所示，在长方形区域ABCD 内存在垂直纸面向外的匀强磁场，AB :BC ＝3:2.比荷相同的两个粒子a 、b 从CD 边的中点E 垂直磁场及磁场边界进入磁场．已知粒子a 从D 点射出磁场，粒子b 从B 点射出磁场，sin 37°＝0.6，cos 37°＝0.8，粒子重力不计，求：(1)粒子a 、b 进入磁场时的速率之比v a :v b . (2)粒子a 、b 在磁场中运动的时间之比t a :t b .1．解析：质子在匀强磁场中的运动形式有三种：当质子的速度方向与磁场方向平行时，质子不受洛伦兹力，做匀速直线运动；当质子的速度方向与磁场方向垂直时，质子做匀速圆周运动，洛伦兹力提供向心力；当质子的速度方向与磁场方向有一定夹角(不垂直)时，质子做螺旋运动．综上可知，本题应选C.答案：C2．解析：带电粒子在匀强磁场中做匀速圆周运动，根据洛伦兹力提供向心力，有qvB＝m v 2R ，可得R ＝mvqB，从较强磁场区域进入到较弱磁场区域后，B 减小，所以R 增大．线速度、角速度的关系为v ＝ωR ，因为洛伦兹力不做功，故线速度v 的大小不变，半径R 增大，所以角速度减小，故B 正确，A 、C 、D 错误．答案：B3．解析：根据左手定则可知，N 带正电，M 带负电，A 正确；因为r ＝mvqB，而M 的轨迹。

数学必修二第一章知识点总结+习题

人教版高中数学必修二第一章知识点总结第一章空间几何体1、空间几何体的结构：空间几何体分为多面体和旋转体和简单组合体⑴常见的多面体有：棱柱、棱锥、棱台；常见的旋转体有：圆柱、圆锥、圆台、球。

(2)简单组合体的构成形式：一种是由简单几何体拼接而成，例如课本图1.1-11中（1）（2）物体表示的几何体；一种是由简单几何体截去或挖去一部分而成，例如课本图1.1-11中（3）（4）物体表示的几何体。

练习1．下图是由哪个平面图形旋转得到的（）A B C D2、柱、锥、台、球的结构特征（1）棱柱：定义：有两个面互相平行，其余各面都是四边形，且每相邻两个四边形的公共边都互相平行，由这些面所围成的几何体。

分类：以底面多边形的边数作为分类的标准分为三棱柱、四棱柱、五棱柱等。

表示：用各顶点字母，如五棱柱'''''EDCBAABCDE 或用对角线的端点字母，如五棱柱'AD几何特征：两底面是对应边平行的全等多边形；侧面、对角面都是平行四边形；侧棱平行且相等；平行于底面的截面是与底面全等的多边形。

（2）棱锥简单组合体定义：有一个面是多边形，其余各面都是有一个公共顶点的三角形，由这些面所围成的几何体分类：以底面多边形的边数作为分类的标准分为三棱锥、四棱锥、五棱锥等表示：用各顶点字母，如五棱锥'''''E D C B A P - 几何特征：侧面、对角面都是三角形；平行于底面的截面与底面相似。

(3）棱台：定义：用一个平行于棱锥底面的平面去截棱锥，截面和底面之间的部分分类：以底面多边形的边数作为分类的标准分为三棱态、四棱台、五棱台等表示：用各顶点字母，如五棱台'''''E D C B A P -几何特征：①上下底面是相似的平行多边形 ②侧面是梯形 ③侧棱交于原棱锥的顶点练习2．一个棱柱至少有 _____个面，面数最少的一个棱锥有 ________个顶点，顶点最少的一个棱台有 ________条侧棱。

新教材人教版英语必修第二册Unit1 Cultural Heritage学案知识点考点及配套习题

Unit 1 Cultural Heritage首批公布的20个国家公园包括9个苏州古典园林，这些园林不仅以其悠久的历史，而且以其精致的景色给游客留下了深刻的印象，尤其是沧浪亭、拙政园、留园、狮子林，这四个最著名的代表了宋、元、明、清不同朝代风格的园林。

National parksThe first batch of 20 national parks include 9 Suzhou classical gardens：Zhuozheng Garden，Liu Garden，Wangshi Garden，Huanxiu Villa，Lion Grove，Yipu Garden，Ou Garden，Tuisi Garden and Canglang Pavilion.National parks refer to the famous city parks and gardens.Suzhou classical gardens are parts of China's precious cultural heritage (all the 9 gardens are on the list of World Cultural Heritage) as well as a necessary part of the life of Suzhou citizens，not to mention they are also world-famous tourism resorts.In fact，their unique historical and cultural background serves to contribute to their ranking among national parks.The earliest classical gardens in Suzhou can date back to the Song Dynasty.However，the gardens impress their visitors not only with their age-old history but also with their delicate scenes，particularly Canglang Pavilion，Zhuozheng Garden，Lion Grove and Liu Garden，the most famous four that represent different styles of dynasties of Song，Yuan，Ming and Qing.In 1978，an imitation of a Suzhou classical garden was set up by Chen Congzhou (the author of the book Suzhou Classical Gardens) in the City Museum of Art in New York，US，which was the first time ever to directly introduce Chinese ancient architecture to Westerners.[阅读障碍词]1．release v．公布2．precious adj.宝贵的3．resort n. 胜地4．imitation n. 仿造品[诱思导读]1．How many parks and gardens are selected as National Parks in the first group?[答案]20.2．Where did the first imitation of a Suzhou classical garden was set up?[答案]In the City Museum of Art in New York.Section ⅠListening and Speaking & Reading and Thinking——ComprehendingⅠ.匹配下列单词的词性及汉语意思()1.temple A．vt.保存；保护；维持n．保护区()2.former B．n.庙；寺()3.preserve C．vt.促进；提升；推销；晋级()4.promote D．n.申请(表)；用途；运用；应用(程序) ()5.application E．adj.以前的；(两者中)前者的()6.protest F．n.委员会()mittee G．vt.建立；创立()8.establish H．n.抗议v．(公开)反对；抗议()9.department I．n.文件；公文；(计算机)文档vt.记录；记载(详情)()10.document J．n.部；司；科[答案]1－5BEACD6－10HFGJIⅡ.选择下列句子中词组的汉语意思A．导致B．阻止；阻碍；阻挠C．参与(某事)；参加(某活动)D．向……求助E．让步；屈服F．保持平衡G．撞倒并碾轧H．向……捐赠……()1.They all dressed up to take part in the New Year's party.()2.The news shocked the public，leading to great concern about students' safety at school.()3.With no one to turn to in her difficult times，my mother felt bad.()4.I had meant to call on you，but I was prevented from doing so.()5.This box looks as if it's been run over by a bus.()6.They used to donate large sum of money to the Red Cross every year.()7.Our employer did not give way to our demands for higher wages.()8.It helps the tiger keep balance when running fast.[答案]1－8 CADBGHEF第一步速读——了解文章主题和段落大意速读P4教材课文，选择最佳答案What is the text mainly about?A．The Aswan Dam project.B．Economic development and society.C．The protection of cultural sites.D．The loss of cultural relics.[答案] A第二步细读——把控文章关键信息细读P4教材课文，选择最佳答案1．What's the challenge we are facing now?A．How to improve society rapidly.B．How to preserve everything from the past.C．How to keep balance between the past and the progress.D．How to find great solutions to the progress of society.2．Why was the proposal of building a new dam protested in Egypt?A．Because the Egyptian government wanted to control floods.B．Because it would probably destroy cultural relics.C．Because it would do great damage to the Nile.D．Because it would affect citizens near the dam greatly.3．How were the temples and other cultural sites saved?A．By moving them to safety.B．By taking them down.C．By asking for contributions.D．By investigating the issue.4．How long did it take to complete the new dam?A．Over 20 years.B．More than 30 years.C．Less than 20 years.D．Exactly 20 years.[答案]1－4CBAA第三步研读——能力升华接轨高考根据P4教材课文，在空白处填入1个适当的单词或括号内单词的正确形式In the 1950s，the Egyptian government would like to build a new dam across the Nile，but the proposal led to 1.protests (protest)．This was because the new dam would 2.likely (like) destroymany cultural relics.Then the government 3.established (establish) a committee to find a solution to the 4.protection (protect) of Egypt's cultural heritage.After a proposal for how the relics could 5.be saved (save) was made，the projectbegan in 1960 and ended in 1980.During those years，22 temples 6.and countless cultural relics were taken down piece by piece，moved and put back together again in a place where they were safe 7.from the water.The project was considered 8.a great success.It's believed that it was possible for different countries 9.to work (work) together to build a better tomorrow.The spirit of the Aswan Dam project is still alive today.If a problem seems too difficult for a single country，the 10.global (globe) community can sometimes provide a solution.Section ⅡListening and Speaking & Reading andThinking——Language PointsⅠ.单词拼写根据汉语或首字母提示，写出下列单词1．He has a key position in the department (部门)．2．They have accepted my application (申请) to join the club.3．The teacher recommended some really worthwhile (值得的) novels to his students.4．The committee (委员会) which was responsible for this decision would consider it over again.5．It is the overall balance (平衡) of the diet that is important.6．The tall walls are to prevent the lions from escaping from the zoo.7．The sudden loss of his money had made him very sad.8．I attempted to persuade my father to quit smoking，but in vain.9．His research has contributed greatly to our understanding of this disease.10．Both the blue and yellow dresses are pretty，but I prefer the former．Ⅱ.拓展单词根据词性和汉语提示，写出下列单词1．apply v．申请；使用→application n．申请(表)；用途；运用；应用(程序)2．contribute v．捐助；捐献→contribution n．贡献；捐款；捐赠3．appear v．出现；到场→disappear vi.消失；灭绝；消亡→disappearance n．消失；灭绝；消亡4．create v．创造，建立→creative adj.创造性的；有创造力的；有创意的→creatively adv.创造性地；有创造力地5．balance vt.使平衡n．均匀；平衡→balanced adj.保持平衡的6．propose v．提议，建议，主张→proposal n．提议；建议[寻规律、巧记忆]1v.＋ive→adj. n.＋al→adj.active adj.活跃的addictive adj.上瘾的creative adj.有创造力的environmental adj.环境的personal adj.个人的musical adj.音乐的Ⅲ.补全短语根据提示补全下列短语1．take part in参与(某事)；参加(某活动)2．give way to 让步；屈服3．keep balance 保持平衡4．lead to 导致5．make a proposal 提出建议6．turn to 向……求助7．prevent...from．.. 阻止；阻碍；阻挠8．donate...to．.. 向……捐赠……9．run over 撞倒并碾轧；驱车送；快速阅读Ⅳ.选词填空选用上述短语的适当形式填空1．In given conditions，a bad thing can lead to good results.2．I hope that all of you can take part in the sports meeting for the honour of our class. 3．The manager made a proposal for uniting the two companies last year.4．He was turned to for advice by all sorts of people in the past.5．At first he said nothing，and then his silence gave way to anger.[寻规律、巧记忆]2v.＋to→动词短语vt.＋n.＋prep.→动词短语belong to属于refer to 参阅，谈及turn to 求助于；转向take care of照顾catch sight of看见；看到do harm to对……有害背教材原句记句式结构仿写促落实1.There comes a time when the old must give way to the new，and it is notpossible to preserve everything from our past as we move towards the future.新旧更替的时代已经到来，在走向未来的过程中，我们不可能将过去的一切都保存下来。

新概念英语第二册第一单元课后练习答案

新概念英语第二册第一单元课后练习答案Lesson 1Key to Summary writingThe writer went to the theatre last week. He did not enjoy the play. A young man and a young woman were sitting behind him. They were talking loudly. The writer could not hear the actors. He turned round. ‘I can't hear a word!’ he said. ‘This is a private conversation!’ the young man said.Key to KS ExercisesAI (1) got (2) very angry (3).I (1) could not hear (2) the actors (3).I (1) turned round (2).I (1) looked at (2) the man and the woman (3) angrily (4).They (1) did not pay (2) any attention (3).In the end (6), I (1) could not bear (2) it (3).I (1) turned round (2) again (6).‘I (1) can't hear (2) a word (3)!’I (1) said (2) angrily (4).‘It (1) is (2) none of your business (3)’,the young man (1) said (2) rudely (4).‘This (1) is (2) a private conversation (3)!’B1 I enjoyed the film yesterday.2 I listened to the news carefully.3 The man played the piano well.4 The children played games quietly in their room yesterday.5 He opened the door quietly.6 He left immediately.7 He planted a tree in the corner of the garden.8 He read the letter quickly in his office before lunch.9 I borrowed a book from the library this morning.10 The cook spoilt the soup.11 We stay at home on Sundays.12 There are a lot of people at the bus stop.13 The little boy ate greedily an apple in the kitchen this morning.14 She draws beautifully.15 I like music very much.16 They built a new school in our village last year.17 The match ended at four o'clock.18 She received a letter from her brother last week.Lesson 2Key to Summary writingThe writer always gets up late on Sundays. He got up late last Sunday. Then his auntLucy telephoned. She had arrived by train. She was coming to see him. ‘I'm still having breakfast,’ he said. His aunt was very surprised. It was one o'clock.Key to KS ExercisesA1 are playing … play … is kicking … is running2 ‘What are you doing?’ my landlady asked. ‘I'm leaving, Mrs. Lynch,’ I answered. ‘Why are you leaving?’ she asked. …‘friends never come to visit me … I frequently go to bed … I rarely listen … I always feel cold …’B1 She rarely answers my letters.2 We never work after six o'clock.3 The shops always close on Saturday afternoons.4 Do you always go to work by car?5 Our teacher frequently collects our exercise books.6 We sometimes spend our holidays abroad.7 I often buy CDs.8 Do you ever buy CDs?Key to SD Exercises1 What a wonderful garden (this is)!2 What a surprise (this is)!3 What a lot of trouble he is causing!4 What wonderful actors (they are)!5 What a hard-working woman (she is)!6 What a tall building (it is)!7 What a terrible film (it is)!8 What a clever boy you are!9 What a pretty girl (she is)!10 What a strange guy (he is)!Lesson 3Key to Summary writingPostcards always spoil the writer's holidays. He spent his holidays in Italy last summer. He thought about postcards every day. He did not send any cards to his friends. He bought thirty-seven cards on the last day. He stayed in his room all day. He did not write any cards.Key to KS ExercisesA went (1.1); visited (I.2); sat (I.2); taught (1.2); lent; read (1.3); did not understand; thought (1.4); passed (1.5); did not send (1.5); made; got up (1.6); bought (1.7); spent(1.7); did not write (1.8)C …Roy died last year … left me … spent a lot of money… bought one or two… never went to the cinema … stayed at home…listened to music … often lent CDs … they kept them … lost many CDs …Key to SD Exercises1 He paid some money to the shopkeeper.2 He handed the prize to me.3 The waiter brought the man a bottle of beer.4 He sold me all his books.5 The shop assistant found me some curtain material.6 He did a big favour for me.7 She showed her new hat to her husband.8 She promised the finder a reward.9 He gave some advice to his son.10 His uncle left some money to/for him.11 He is teaching us English.12 I bought you this bunch of flowers.13 Bring me that book please.14 He offered a cigarette to me.15 Read the first paragraph to me.16 I've ordered you some soup.17 I owe a lot of money to him.18 Pass your father the mustard.Lesson 4Key to Summary writingThe writer. has just received a letter from his brother, Tim. Tim is an engineer. He has been in Australia for six months. He has already visited many places. Now he is in Alice Springs：Tim has never been abroad before. He is enjoying his trip very much. Key to KS ExercisesA1 I have just had breakfast.2 He has been in prison for six months.3 The police have not caught the thief yet.4 You have (already) asked that question three times (already).5 Have you ever been to Switzerland?6 I have never been to Switzerland.7 He is a wonderful runner. He has broken two records so far.8 I haven't seen George lately.C1 He has just left the house.2 He has just had breakfast.3 She has just written a letter.4 My sister has just turned on the radio.5 My mother has just made the bed.6 She has just bought a new hat.D1 He hasn't washed the dishes yet.2 She hasn't made the beds yet.3 He hasn't combed his hair yet.4 She hasn't swept the carpet yet.5 We haven't read ‘Macbeth’ yet.E1 Have you seen the new play at‘The Glob’ yet?2 Have you taken your holidays yet?3 Have you read this book yet?4 Have you done your homework yet?5 Have you finished your work yet?Key to SD Exercises1 received2 received3 took4 taken5 takeLesson 5Key to Summary writingMr. Scott has opened his second garage in Pinhurst. His first garage is in Silbury. Silbury is five miles away. Mr. Scott cannot get a telephone for his new garage. He has bought twelve pigeons. They carry messages from one garage to the other in three minutes.Key to KS ExercisesAWhat happened：carried (1.4); covered (1.5)What has happened：has just bought (1.1); has just bought (11.3-4); has sent (1.6); has begun (1.8)C1 What did you buy …? 5 They have already left.2 he has never lent … 6 When did you lose …?3 Have y ou burnt …?7 Did you listen … ?4 He fought …8 We have just won …Key to SD ExercisesA1 On the way 4 in this/a way2 in the way 5 in the way3 By the wayB1 There is a spare wheel in the back of the car.2 I always go on excursions in my spare time.3 ‘Have you any old clothes to spare?’ he asked.4 The guest slept in our spare room.5 ‘Spare me!’ begged the prisoner.Lesson 6Key to Summary writingThe writer has just moved to a house in Bridge Street. A beggar knocked at her dooryesterday. She sang songs. The writer gave him a meal and a glass of beer in return for this. The beggar’s name is Percy Buttons. He calls at every house once a month. Key to KS ExercisesAsome a some a a a a/some some a a a a some some an a/someCa ×a a a the ×a the the a a ×a a aD1 I found an old coin in the garden.2 I put some sugar in my tea.3 I cut some wood for the fire.4 I bought a newspaper yesterday.5 I made some coffee.6 I like the curtains in this room.Key to SD ExercisesAout over off atBknock out; knock off; knock 20% off the priceLesson 7Key to Summary writingDetectives were waiting at the airport all morning. They were expecting a valuable parcel of diamonds from South Africa. Two men took the parcel into the Customs House after the arrival of the plane. Two detectives opened it. The parcel was full of stones and sand.Key to KS ExercisesAdetectives were waiting (1.1); They were expecting (1.2); detectives were waiting (1.5); others were waiting (1.6); two detectives were keeping guard (11.7-8)B1 When the plane arrived, some of the detectives were waiting inside the main building while others were waiting on the airfield.2 When two of the detectives opened the parcel, two others were keeping guard at the door.C (sample answers)1 I was getting into my bath when you telephoned me.2 I was reading Hamlet when you saw me in the library this morning.3 I was saying that you must see the new film when you interrupted me.D1 was leaving …arrived2 worked/was working … was sitting/sat3 was walking … met4 was reading … heard5 was preparing … set/was setting6 dropped … spokeKey to SD Exercises1 He gave all his books away.2 She woke the children up early this morning.4 They cut the king's head off.5 Put your hat and coat on.7 Help me to lift this table up.8 Take your shoes off and put your slippers on.11 They have pulled the old building down.12 Make your mind up.14 She threw all those old newspapers away.Lesson 8Key to Summary writingJoe Sanders has the best garden in town. He wins ‘The Nicest Garden Competition' each year：Bill Frith also has a fine garden. Joe's is better. The writer's garden is terrible. He always wins a prize for the worst garden in the town.Key to KS ExercisesA1 Mary's handwriting is worse than Jane's.2 Caroline's handwriting is worse than Mary's and Jane's.3 Caroline's dress is/was more expensive than Jane's.4 Mary's dress is/was more expensive than Jane's and Caroline's.B… has the most beautiful garden in our town … 'The Nicest Garden Competition' … garden is larger than Joe's … works harder than Joe and grows more flowers and vegetables … garden is more interesting … for the worst garden in the town!D1 in2 of3 of4 inKey to SD ExercisesA 1 believes 2 was 3 triesB Sentences 2, 3 and 5Lesson 9Key to Summary writingWe went to the Town Hall on New Year's Eve. There were a lot of people there. The Town Hall clock would strike twelve in twenty minutes' time. It stopped at five to twelve. It refused to welcome the New Year. Then the crowd began to laugh and sing. Key to KS ExercisesA1 We went to the Town Hall on Wednesday evening/New Year's Eve.2 The clock would strike twelve in twenty minutes' time.3 The clock stopped at five to twelve.B1 in2 On3 during/in4 in5 at6 on … in7 in 8 at … in9 untilC (sample answers)1 The match will begin at2 They bought their house in 1980.3 The shop is closed from one till two.4 The children went to school in the morning.5 He'll finish school in two years' time.6 Let's go for a walk in the evening.7 He went to church on Sunday.Key to SD ExercisesA1 No, I haven't any/have no money.2 No, I didn't go anywhere/went nowhere in the.holidays.3 No, I didn't buy anything/bought nothing this morning.4 No, there wasn't anybody/was nobody present when the accident happened.BHe has no hobbies. He goes nowhere. He sees nobody. He is interested in nothing-except food!Lesson 10Key to Summary writingWe own an old clavichord. It was made in 1681. My grandfather bought the instrument many years ago. A visitor damaged it recently. She tried to play jazz on it! She broke two of the strings. A friend of my father's is repairing it now.Key to KS ExercisesA1 Our old musical instrument is called a clavichord.2 It was made in Germany.3 It is kept in the living room.4 It was bought many years ago.5 It was damaged recently.6 Two of the strings were broken.7 My father was shocked.8 We aren't allowed to touch it.9 The clavichord is being repaired.Key to SD ExercisesA1 of2 in3 fromB1 He borrowed a record of mine.2 She showed me a picture of John's.3 It was an idea of hers.4 A letter of yours was found on my desk.5 Some friends of theirs came to see me.Lesson 11I was having dinner at a restaurant. I saw Tony Steele after a while. He always borrows money from his friends. Tony sat at my table. I asked him to lend me twenty pounds. He gave me the money at once. He wanted me to pay for his dinner.Key to KS ExercisesAa he is now working (1.2)b he gets (1.3); he always borrows (1.3); never pays it back (1.4)c came in…worked (11.1-2); Tony saw (1.4); came and sat (1.4); I asked him (1.6); he gave me (1.7);Tony said (1.8)d He has never borrowed (1.5); I have never borrowed (1.7)e I was having (1.1); he was eating (1.6)C1 gets…got2 have not had3 was writing…talked/were talking4 am typing5 passed/were passingDThe Taj Mahal was built…after he became/had become ruler,his wife…died. The Taj Mahal was built in her honour. Experts were called in…The Taj Mahal, which was begun in 1632 and (was) completed in 1654, cost a fortune…it has been visited by…Key to SD ExercisesaA1 The officer ordered the men to fire at the enemy.2 He wants his wife to wear this dress.3 She wants us to explain it.4 I cannot allow him to enter the room.B (sample sentences)1 He asked me to help him.2 We preferred her to stay at home.3 He taught me to speak English.4 My mother wished me to collect the laundry.5 Do you want her to visit you?b1 salary2 lent…salary/wages3 borrowed4 wages5 wagesLesson 12Key to Summary writingWe shall meet our neighbour, Captain Charles Alison, at Portsmouth Harbour early tomorrow morning. He will be in his small boat, Topsail. He will leave at eight o'clock. We shall say goodbye to him. He will take part in an important race across the Atlantic.Key to KS ExercisesA will sail (1.1); shall meet (1.2); will be (1.3); will set out (11.4-5); shall have (1.5); shall see (1.5); shall say (1.6); will be (1.6); will take part (1.7)C I shall go to the theatre…Reg and I shall see the first performance…the producer will give a short speech. He will speak to…The play will be very… people will enjoy it very much.Key to SD Exercises1 He is not back yet. He will be back in ten minutes.2 A new play is on at the Globe Theatre.3 When the concert was over, we went home.4 They will set out/off very early tomorrow morning. (Be off is also possible.)5 You can't take the exam yet. You are not up to it.6 He will be away from home for two months.7 She swam across the English Channel and set up a new world record.Lesson 13Key to Summary writingThe Greenwood Boys are pop singers. They will be coming here tomorrow. Most of the young people in the town will be meeting them at the station. They will give five performances. The police will be trying to keep order as usual.Key to KS ExercisesAwill be arriving (1.2); will be coming (1.3); will be meeting (1.4); will be singing (1.5); will be staying (1.6);will be trying (1.8)C1 I'll be ironing the clothes.2 The train will be arriving in a few minutes.3 We'll be seeing you in the morning.4 We'll be watching the match.5 He'll be correcting exercise books.Key to SD Exercises1 It's George's.2 It's Jean's.3 It's that woman's.4 I like Keats' poetry best.5 They're the children's.6 They're the soldiers'.7 I'll leave in six hours' time.8 There was a hundred pounds' worth of damage.Lesson 14Key to Summary writingThe writer gave a lift to a young man in the south of France last year. They greeted each other in French. Apart from a few words, the writer doesn't speak any French. They sat in silence. At the end of the journey the young man asked, ‘Do you speak English?’He was English himself.Key to KS ExercisesA1 I drove on to the next town after I had left a small village.2 I said good morning to him in French as soon as he had got into the car.3 I had nearly reached the town, when the young man said,‘Do you speak English?’C1 After she had written the letter, she went to the post office.2 After he had had dinner, he went to the cinema.3 When I had fastened my seat belt, the plane took off.4 We did not disturb him until he had finished work.5 As soon as he had left the room, I turned on the radio.6 He had been very ill before he died.D1 regretted2 had begun/began3 arrivedKey to SD Exercises1 Except for2 both of3 Apart from4 asked…ask for5 either of…askedLesson 15Key to Summary writingMr. Harmsworth wanted to see me. I felt very nervous. I went into his office. He said that business was bad. The firm could not pay such large salaries. Twenty people had already left. He didn’t ask me to leave. He offered me an extra thousand pounds a year.Key to KS ExercisesB1.told would come2.said had cut3.told had never4.did say had done/would do/did5.did tell had bought6.said could not7.said had worked8.told had never written9.did say were 10.said would waitKey to SD ExercisesStudy office nervous afford irritableLesson 16Key to Summary writingTraffic police usually give you a ticket if you park your car in the wrong place. The writer found a polite note on his car during a holiday in Sweden. The traffic police wanted him to pay attention to their street signs. No one can fail to obey a polite request.Key to KS ExercisesA The word if has been used four times.C 1 rains 2 will never pass3 is4 will get5 enjoys6 isD … if I listen to the radio … If I do something wrong, do n't shout at me. If the house is untidy, don't blame me. If you want me to do something, don't forget to say ‘please’. If I am playing a nice game, don't send me to bed. If I ask for something … If it is cold don't put the cat out …Key to SD Exercises1 pay attention2 remind3 are knocking4 look after5 Remember meLesson 17Key to Summary writingMy aunt Jennifer is an actress. She is over thirty years old. She often appears on the stage as a young girl. Jennifer will act the part of a girl of seventeen in a new play soon. She never tells anyone how old she really is.Key to KS ExercisesAShe must be (1.1); Jennifer will have to take (1.3); she must appear (1.4); she had to wear (11.5-6); it must be terrible (11.7-8)C1 You must/ will have to see a doctor.2 Must you/ Do you have to make so much noise?3 She said we must/ had to/ would have to stay here.4 I must/ have to have some help.5 I've had to go out last night.Key to SD ExercisesA1 in the position of2 because3 At the time whenB1 grow2 suit3 costume4 dressLesson 18Key to Summary writingThe writer had lunch at a village pub. She could not find her bag after her meal. She could not pay the bill. The landlord soon found it for her. His dog had taken it into the garden.Key to KS ExercisesA1 I looked for my bag after I had had lunch at a village pub.2 I had left my bag on a chair beside the door.3 The landlord asked me, ‘Did you have a good meal?’4 I answered, ‘I can't pay the bill because I haven't got my bag.’5 The dog had taken the bag into the garden.CSentences 2, 3, 5, 7, 8, 10, 11.Key to SD ExercisesA1 back2 away3 in4 inB1 Besides2 besideLesson 19Key to Summary writingThe play was going to begin at any moment. I asked for two tickets. There were none left. Susan and I were disappointed. Just then, a man hurried to the ticket office. He returned two tickets. They were for next Wednesday's performance. I bought them. Key to KS ExercisesA may begin (1.1); may have begun (1.2); May I have (1.3); Can I return (1.8); Could I have (1.11); I might as well have (1.13)Key to SD Exercises1 I have not seen …2 There aren't …3 He does not … you are …4 She didn't tell … she hadn't …5 I shan't stay …6 He won't do … he's told7 When will I …8 What have you … You have broken …9 He is … He has just come …10 I can't understand … he has not …11 You must not believe …12 I was not … You were not …13 That man has been …14 They had not seen …Lesson 20Key to Summary writingFishing is the writer's favourite sport. Some unlucky fishermen catch old boots and rubbish. The writer is not so lucky. He never catches anything. He is not really interested in fishing. Sitting in a boat and doing nothing at all is the only thing that interests him.Key to KS ExercisesAFishing (1.1); catching (11.1-2); catching (1.3); having spent (1.5); fishing (1.6); fishing … sitting (1.8); doing (1.9)C1 He went out of the restaurant without paying the bill.2 She bought a pair of boots instead of getting a pair of shoes.3 She was afraid of spending the night alone.4 After hearing/having heard the news, she fainted.5 Think carefully before answering my question.6 On seeing the plane coming towards me, I dashed for cover.Key to SD Exercises1 realized2 It's … understand … its3 exciting4 interesting5 exciting6 interestedLesson 21Key to Summary writingThe writer is slowly going mad. He lives near an airport. Passing planes can be heard night and day. Most of his neighbours have left their homes. He has been offered money to leave. He is determined to stay. Everyone says he must be mad. They are probably right.Key to KS ExercisesA… passing planes can be hear d (1.2); it could not be used then (1.3); a hundred people must have been driven away (11.4-5); this house will be knocked down by a passing plane (11.6-7); I have been offered a large sum of money (1.7)C1 A message will be sent immediately.2 All these goods must be sold.3 I told you the parcel would be received in time.4 The letter has to be delivered by hand.5 Your letter must have been lost in the post.Key to SD ExercisesA(sample answers)The dog drove the sheep out of the field.The police drove the crowds back.I drove my car into the garage.B1 home2 houses3 house4 homeLesson 22Key to Summary writingJane crossed the Channel last year. She threw a bottle into the sea. It contained apiece of paper with her name and address on it. Ten months later, she received aletter from a girl in Holland. They write to each other regularly now. They send theirletters by post.1 from 9 from 17 from 25 in 33 on 41 on 49 of2 on 10 in 18 of … On26 on 34 on 42 on 50 of3 in 11 on … In19 on 27 on 35 in 43 of 51 on4 on 12 of 20 of … Of28 from 36 from 44 in 52 of5 from 13 in 21 of 29 on 37 on 45 in 53 from6from 14 on 22 of/ from 30 in 38 on 46 in 54 in7 of 15 of 23 of 31 from 39 in 47 from8 on 16 of 24 from 32 on 40 of 48 ofLesson 23My sister will come to England next year. She will get a surprise if she comes. Wehave a new house in the country. I have invited my sister to stay with us. It is a verymodern house. It has got many large rooms and a lovely garden.Key to KS ExercisesC1 wrote2 had finished3 breaks4 shall/will goD1 told … would2 told … had lost3 said … did not likeKey to SD Exercises1 It2 There3 There4 there5 It6 It7 There8 it9 there 10 itLesson 24Key to Summary writingI had just lost ￡50. I felt very upset. I told the manager about it. He could not do anything. He began to complain about this wicked world. Just then a girl came in with the money. She had found it outside my room. There is still some honesty in this world.Key to SD ExercisesA1 received6 salary11 are16 beside2 on the7 lend12 pay attention to17 It's … ex citing3 On the8 asked for13 Remember18 understand4 believes9 Apart from14 suit19 home5 of10 an irritable15 grow up20 There isB1 What a wonderful garden (this is)!2 What a lot of trouble he is causing!3 What a tall building (it is)!4 What a clever girl you are!C1 He handed the prize to me.2 The waiter brought the man a bottle of beer.3 I've ordered you some soup.4 Bring me that book please!5 She promised the finder a reward.D1 I haven't any/have no money.2 I didn't go anywhere/went nowhere in the holidays.3 There wasn't anybody/was nobody present when the accident happened. E1 It's George's.2 It's that woman's.3 I like Keats' poetry best.4 They're the children's.5 They're the soldiers'.F1 off2 back3 up4 over5 on6 awayG1 I put my hat on.2 I took my coat off.3 He put the fire out.4 They cut the king's head off.新概念英语第二册第一单元多项选择题详解Lesson 11. b选b最为正确。

成都四川省成都市中和中学小学数学二年级下册第一单元知识点总结

一、选择题1．下表是二年级学生喜欢的图书人数情况。

A.连环画B.故事书C.科技书D.其他（2）喜欢( )的人数最少。

A.连环画B.故事书C.科技书D.其他（3）喜欢故事书的人数比喜欢连环画的少( )人。

A.10B.6C.4D.8（4）喜欢连环画的和喜欢科技书的一共有( )人。

A.30B.20C.26D.12A解析：（1）A（2）D（3）B（4）C【解析】2．下表是二年级学生喜欢的图书人数情况。

A.连环画B.故事书C.科技D.其他（2）喜欢（）的人数最少。

A.连环画B.故事书C.科技书D.其他（3）喜欢故事书的人数比喜欢连环画的少（）人。

A.10B.6C.4D.8（4）喜欢连环画的和喜欢科技书的一共有( )人。

A.30B.20C.26D.12A解析：（1）A（2）D（3）B（4）C【解析】【解答】（1）因为18＞12＞8＞4，所以喜欢连环画的人数最多.（2）因为4＜8＜12＜18，所以喜欢其他的人数最少.（3）18-12=6（人）.（4）18+8=26（人）.故答案为：（1）A；（2）D；（3）B；（4）C.【分析】（1）要求喜欢哪种图书的人数最多，将喜欢四种图书的人数按从大到小排列即可；（2）要求喜欢哪种图书的人数最少，将喜欢四种图书的人数按从小到大排列即可；（3）要求喜欢故事书的人数比喜欢连环画的少几人，用喜欢连环画的人数-喜欢故事书的人数=喜欢故事书的人数比喜欢连环画的少的人数，据此列式解答；（4）要求喜欢连环画的和喜欢科技书的一共有几人，用喜欢连环画的人数+喜欢科技书的人数=喜欢连环画的和喜欢科技书的一共有几人，据此列式解答.3．心心幼儿园新进了一批玩具。

玩具个数（个）812610A. 20B. 36C. 18D. 26B解析： B【解析】【解答】解：因为8+12+6+10=36（个），所以心心幼儿园新进的玩具一共有36个。

故答案为：B。

【分析】小熊的数量+小羊的数量+小鸭子的数量+小猴的数量=新进玩具的数量。