高二下复习题
第2章 微粒间相互作用与物质性质 复习题-高二下学期化学鲁科版(2019)选择性必修2
第2章《微粒间相互作用与物质性质》复习题一、单选题1．下列说法正确的是A ．分子中σ键一定比π键牢固B ．所有共价键都有方向性C ．根据等电子体原理判断，1molNO +2离子含有π键的数目为2N AD ．原子半径越小，形成的共价键键能就一定越大 2．下列关于物质结构和化学用语的说法正确的是 A ．BF 3、CCl 4中所有原子均达到8电子稳定结构 B ．78gNa 2O 2晶体中所含离子数目为3N A C ．18gH 2O 或D 2O 的质子数均为10N A D ．34gH 2O 2含有极性键的数目为3N A3．纳米TiO 2是一种应用广泛的催化剂，其催化的一个实例如图所示，下列说法正确的是A ．化合物甲、乙均为手性分子B ．化合物甲中最多有8个原子共平面C ．化合物乙中采取sp 3杂化的原子只有N 、CD ．化合物甲的沸点明显高于化合物乙4．设A N 为阿伏伽德罗常数的值。
下列说法正确的是 A ．标准状况下，2.24L 24C H 中，约含有233.0110⨯个σ键B ．18g 182O 和183O 的混合气体中含有的中子数为A 8NC ．用1L0.1mol/L 的3FeCl 溶液制备()3Fe OH 胶体，胶粒数目为A 0.1ND ．6.4gCu 与S 完全反应，转移的电子数为A 0.2N5．X 、Y 、Q 、W 、Z 是原子序数依次增大的短周期主族元素，其中Y 原子最外层电子数是其内层电子数的2倍，W 与Y 位于同一主族，X 、Y 、Z 三种元素可组成用于隐形飞机中吸收微波的物质R(结构如图)，Q 元素单质可用作铝热反应的引燃剂。
下列说法正确的是A ．同一周期中，第一电离能比Q 小的只有一种B ．电负性：Y>W>XC ．物质R 吸收微波时，分子内的σ键会断裂D ．简单气态氢化物的还原性：W>Y6．向CuSO 4溶液中加入少量氨水时生成蓝色沉淀，继续加入过量氨水时沉淀溶解，得到深蓝色透明溶液，最后向该溶液中加入一定量乙醇，析出[Cu(NH 3)4]SO 4·H 2O 晶体。
高二下学期期末联考语文复习题
高二下学期期末联考语文复习题高二下学期期末联考语文复习题一、现代文阅读（9分，每小题3分）阅读下面的文字，完成1—3题。
诗歌起源的探讨同艺术起源的探讨一样，曾困扰着一代又一代的学者。
时至今日，用思维与文化的眼光重新考虑这一课题，似可区分出诗歌的二重起源——圣诗与俗诗，分别加以探讨，可以避免许多纠缠不清的死结，使问题逐步明朗化。
简单地讲，圣诗指服务于宗教信仰和礼仪活动的诗歌唱词，如祭祀歌词、咒词、祝祷之词、招魂曲词等等。
圣诗起源较早，当与人类法术思想的成熟和语言的发生同步。
各大文明初始时期被各种宗教奉为“经”的诗歌作品，如古印度《吠陀》和《薄伽梵歌》、古伊朗的《阿维斯塔》、希伯来《圣经》中的诗篇、古埃及的《亡灵书》中的诗作、苏美尔和巴比伦文明中的颂神诗与创世史诗《艾努玛·艾利什》、古希腊文明中大部失传了的诗体启示录等，便都是因及时见诸文字记载而保存至今的圣诗。
俗诗是相对圣诗而言的，泛指一切与宗教信仰并无直接关联的民间歌谣、韵语唱词等。
俗诗的起源从理论上讲，当与圣诗不相上下，同样以人类语言能力的发生为前提。
但由于二者在初民意识形态中的重要性及地位大不相同，所以早期的俗诗大都因为无法及时记录为文字而湮没无闻了。
《诗经》中的“颂”与“风”，大致相当于这里所说的“圣诗”与“俗诗”，而“雅”则介乎二者之间。
圣诗与俗诗虽同样古老，但其内容和形式却各具特色，相互之间既有影响作用，又明显地属于不同的思维和文化的产物。
圣诗的溯源研究实际上必然属于宗教文化的范畴。
俗诗的根源则在于世俗文化，尤其是民间的文化。
随着从原始到文明的演进，许多本来作为宗教信仰对象的圣诗逐渐向世俗化方向转变，也就是从固定于仪式场合演唱的歌诗向非信仰的、文学性的说唱诗转变。
我国境内许多少数民族现存的具有史诗性质的作品——以创世神话和祖先事迹为主题的长叙事诗，似可看作由仪式性的圣诗脱胎而来的产物，但它们同世俗的抒情歌诗并不同源。
安德鲁·兰的看法是，应区分民歌与史诗的不同来源，他说：“民歌有长时期和普遍的流传是可以证明的；这些歌，是从民众嘴里和心里出来的，同那些艺术诗，由于贵族为得到一种只有他们能有的那种史诗而生的，可以说是正相反。
河北省武邑中学2020-2021学年高二英语下学期6月期末复习试题2
河北省武邑中学2020-2021学年高二英语下学期6月期末复习试题2第一部分阅读理解 AI want you all to know that I’ve quit social media, and my life has gotten so much better. I mean, it’s only been 15 minutes but I can already tell I’m a different person. Fifteen minutes ago, I stopped using Facebook and Twitter. Within seconds, I noticed I am happier, less irritable, more contemplative (深思熟虑的) and balanced. I’m spending more time on activities that matter. Just in the past two minutes, I’ve looked at a book on my bo okshelf and briefly pondered opening it.I’m truly changing. This is going to sound crazy, but since quitting social media—now, let’s see, 16 minutes ago—all of my senses are enhanced. My eyesight is clearer. Food tastes better. I just smelled the first tulips of spring. I am jolted by a burst of energy. Every morning I am going to meditate or at least lie in my bed and consider meditating.What purpose does social media serve, anyhow? The academics tell us it’s making us miserable—the constant updates from friends with their expensive vacations and gossips about celebrities. If you think about it, the Internet was really only supposed to be for one thing: ordering socks from J. Crew. Then people started posting photographs of their dogs in Halloween costumes, and we all began sending Happy Birthday wishes to classmates we’d lost touch with since fifth grade, and the whole thing became the nightmare.Social media ruins perfectly good human beings. There are people I lovein real life and hate on social media. Worst still, social media stifles( 抑制) creativity. They’ve studied this in rats, you know. Scientists made rats quit using Facebook, and when they came back in a few hours, all of the rats were writing really solid debut novels.It’s been 17 minutes. I have a feeling that my quitting social media is having a physical effect. All I did was quit looking at my phone 900 times a day. I’ll tell them the secret. Quit social media. All of life’s annoying problems will be over. Your relationships will improve. Y ou’ll never feel down. You’ll never get stuck in traffic.Do I miss it? Thanks for asking. I don’t even know why I thought it was so important. I do not need to see the 800th photo from my co-worker’s trip.I have no idea how a hot topic is going on. And i t’s OK. I can’t imagine going back. I’ve quit social media. It’s only been 18 minutes, but I’m pretty sure I’m going to make it a full twenty.1. What was the Internet originally used to do according to the passage?A. To read digital books.B. To do shopping online.C. To make some new friends.D. To share holiday experience.2. The author keeps counting the time in order to ______.A. show how fantastic it is to quitB. prove it a struggling process to quitC. remind himself of the time in quittingD. make a record for his study of quitting3. What is the tone of this article?A. Official.B. Serious.C. Humorous.D. Plain.4. Which of the following would be the best title for the passage?A. How I Made an Important DecisionB. Why We Can’t Live Without the InternetC. The Influence of Social Media: Pros & ConsD. Quitting Social Media Will Save Your LifeBMost people have been taught that losing weight is a matter of simple math. Cut calories—specifically 3,500 calories, and you’ll lose a pound. But as it turns out, experts are learning that this decades-old strategy is actually pretty misguided. “This idea of ‘a calorie in and a calorie out’ when it comes to weight loss is not only outdated, it’s just wrong,” says Dr. Fa tima Cody Stanford, an obesity specialist at Harvard Medical School. The truth is that even careful calorie calculations don’t always yield(产生) uniform results.How your body burns calories depends on a number of factors. Three factors affect how your body processes calories.Your gut microbiome (肠道微生物). Trillions of organisms live in your gut, and the important types may influence how many calories your body absorbs from food. This may occur because some types of organisms are able to break down and use more calories from certain foods than other types of organisms. Researchers have found that people who are naturally thin have different typesof organisms living inside them than those who are overweight.Your metabolism (新陈代谢). Each body has a “set point” that governs weight, says Dr. Stanford. This set point reflects several factors, including your genes, your environment, and your behaviors. A region at the base of your brain stands guard to keep your body weight from dipping below that set point—which is not really a bonus if you’re trying to lose weight.The type of food you eat. Your food choices may also influence your calorie intake, and not just because of their specific calorie content. One 2019 study published in Cell Metabolism found that eating processed foods seems to spur people to eat more calories compared with eating unprocessed foods.If counting calories isn’t a dependable way to manage your weight, what can you do to shed extra pounds? Dr.Stanford recommends the following.Focus on diet quality. When planning your meals, focus on choosing unprocessed foods, including lean meats, whole grains, and lots of fruits and vegetables in their natural form.Exercise regularly. Aim to get at least 150 minutes of moderate-intensity exercise each week. Moderate exercise is done at a level where you can talk, but not sing.Consult a professional. “A lot of people believe it’s a moral failing if they are unable to lose weight,” says Dr. Stanford. But it’s not. As with other medical conditions, many people will need help from a doctor. Successful weight loss may require more than just diet and exercise. “Only 2% of peoplewho meet the criteria for the use of anti-obesity medications actually get them. This means that 98% of people who could be treated are n’t,” she says, “Don’t be afraid to seek help if you need it.”5. What can we infer from Paragraph 1?A. Old theories actually mislead us.B. Losing weight lies in losing calorie.C. Calorie calculations lead to good results.D. Losing weight by losing calorie is outdated.6. The processing of calories is affected by how you ______.A. choose the types of food you consumeB. focus on the quality of your dietC. adjust your brain to the “set point”D. reduce the organisms living in your gut7. T he underlined word “shed” in Paragraph 6 means “______”.A. weighB. produceC. loseD. cost8. It is implied in the passage that ______.A. cutting calories is essential for weight lossB. losing weight can be double-edgedC. healthy eating keeps you losing weightD. a healthy lifestyle is key to weight loss七选五How to pass an important testWhether it's a first grade science test or College Entrance Exam, all tests have one thing in common: you have to pass. 9 . Stuck in a situationwhere you don't know what to do? This article can help.Tips★Once you get the study guide, make plans right away to study as soon as possible. No excuses! Killing time with friends isn't worth it, since you can always hang out with them any other day.★Get plenty of rest. 10 . If you walk into the classroom sleepily, you'll most likely not finish the test because you are so tired.★Eat a good meal for breakfast. 11 . Some healthy breakfast suggestions are oatmeal (燕麦片), high fibre food, and grapefruit with the fresh fruit salad.★Bring all necessary materials. 12 . Bring pencils, pens, pencil sharpeners, snacks (if allowed), erasers, the calculator (if allowed) and anything else you'll need for the test.★ 13 . Showing up late cuts back the time you'll have to take for the test if it's already testing hours. You'll probably miss any important information needed in completing the test. In some tests, late comers are not allowed to take the test.A. The exam tests vocabulary, reading and maths skills.B. One piece of cheese probably won't last until test time.C. Don't forget to set your alarm clock and show up on the test day on time.D. Studies show that if you get enough sleep, your brain will be much more efficient.E. Showing up without something as simple as a pencil can make a big effecton your test.F. Failing the test won't help you in the long run, so it's important toknow how to prepare to pass that big test.G. This test is a challenging one and every year many students are unableto qualify just because of lack of guidance.二、完形填空When I tried out for the football team during the summer before 9th grade,I never imagined how important this sport would become in my life. Footballis a 1 sport, at times almost painful, and practices really 2 a team’s physical and mental limits. Without trust in my own ability and a strong sense of commitment (投入), I would never have managed to continue after years of hard work as a player, and with countless 3 .In the first year, I played on the defensive line. This was an amazing 4 that gave me a great sense of achievement. But in the last game of the season,I was seriously injured. I was prohibited from any physical activities for six months. After going 5 a series of physical treatments, I returned to the field as a team captain. I practiced harder than ever to make up for my6 time.In September, during my junior year, my name was mentioned in the local newspaper as the key defensive linemen on the team. After playing a fantastic season, I was given the 7 of Most Valuable Player.8 , my skills in football do not magically extend to other sports. During the winter break, I went on a snowboarding trip and seriously injured my right shoulder. I had to have four 9 . Since I could not use my right arm for two months, I had to learn how to write and eat using my left hand.10 life must go on. I knew that my own present efforts would decide m y f u t u r e,s o I11 the strict training program to build strength and improve flexibility in my 12 . After an eight-month recovery, I was back out on the field playing football, the sport I 13 .In this sense, the world of football has taught me an important life lesson: 14and commitment make what seems impossible 15 . This lesson from football is one that I know translates through every part of life.1. A. tough B. popular C. typical D. dynamic2. A. set B. control C. test D. require3. A. mistakes B. adventures C. accidents D. injuries4. A. performance B. position C. moment D. advantage5. A. with B. over C. through D. into6. A. valuable B. lost C. extra D. regular7. A. pride B. choice C. name D. honor8. A. Unfortunately B. Similarly C. Happily D. Gradually9. A. practices B. tryouts C. seasons D.operations10. A. But B. Or C. So D. And11. A. examined B. changed C. provided D. completed12. A. shoulder B. hand C. leg D. foot13. A. explore B. avoid C. love D. support14. A. Knowledge B. Belief C. Experience D. Opinion15. A. enjoyable B. possible C. sensible D. responsible三、应用文写作假定你是李华, 你的美国笔友 Jim 对你校社团的近期活动非常感兴趣。
高二下学期文科数学期末复习试题含答案
高二文科数学期末复习一、填空题：1.若复数z 满足()12i 34i z +=-+（i 是虚数单位），则=z . 答案：i 21+.2.设全集=U Z ，集合2{|20=--≥A x x x ，}∈x Z ，则U=A （用列举法表示）.答案：{0，1}.3.若复数z 满足i iz 31+-=（i 是虚数单位），则=z .i +4.已知A ，B 均为集合{=U 2，4，6，8，10}的子集，且}4{=⋂B A ，}10{)(=⋂A B C U ，则=A .答案：{4，10}5.已知全集R U =，集合=A {32|≤≤-x x }，=B {1|-<x x 或4>x }，那么集合⋂A （UB ）等于 .答案：{x|－1≤x≤3}解析：主要考查集合运算.由题意可得，UB ＝{x|－1≤x≤4}，A ＝{x|－2≤x≤3}，所以(⋂A U)B ＝{x|－1≤x≤3}．6.已知集合},3,1{m A =，}4,3{=B ，且}4,3,2,1{=B A ，则实数m = . 答案：27.命题“若b a >，则b a 22>”的否命题为 . 答案：若b a ≤，则ba22≤8.设函数()⎩⎨⎧=x xx f 2log 2 11>≤x x ，则()[]=2f f .答案：2 9.函数)23(log 5.0-=x y 的定义域是 .答案：]1,32(10.已知9.01.17.01.1,7.0log ,9.0log ===c b a ，则c b a ,,按从小到大依次为 .答案：c a b <<11.设函数)(x f 是定义在R 上的奇函数.若当),0(∞+∈x 时，x x f lg )(=，则满足0)(>x f 的x 的取值范围是 .答案：),1()0,1(∞+-12.曲线C ：x x y ln =在点M （e ，e ）处的切线方程为 . 答案：e x y -=213.已知函数211)(xx f -=的定义域为M ，)1(log )(2x x g -=（1-≤x ）的值域为N ，则（RM ）N ⋂等于 .答案：{x|x≥1}解析：考查定义域求解.可求得集合M ＝{x|－1<x<1}，集合N ＝{g （x ）|g （x ）≥1}，则RM ＝{x|x≤－1或x≥1}，∴（RM ）N ⋂＝{x|x≥1}.14.设⎪⎩⎪⎨⎧+--=,11,2|1|)(2x x x f 1||1||>≤x x ，则)]21([f f 等于 .答案：134解析：本题主要考查分段函数运算. ∵232|121|)21(-=--=f ，∴134)23(11)23()]21([2=-+=-=f f f .15.已知函数)1ln()(2++=x x x f ，若实数a ，b 满足0)1()(=-+b f a f ，则b a +等于 .答案：1解析：考查函数奇偶性.观察得)(x f 在定义域内是增函数， 而)1ln()(2++-=-x x x f )(11ln2x f x x -=++=，∴)(x f 是奇函数，则)1()1()(b f b f a f -=--=，∴b a -=1，即1=+b a .16.若函数)(log )(3ax x x f a -=（0>a ，1≠a ）在区间（21-，0）上单调递增，则a 的范围是 .答案：143<≤a解析：本题考查复合函数单调性，要注意分类讨论.设ax x x u -=3)(，由复合函数的单调性，可分10<<a 和1>a 两种情况讨论：①当10<<a 时，ax x x u -=3)(在（21-，0）上单调递减，即03)('2≤-=a x x u 在（21-，0）上恒成立，∴43≥a ，∴143<≤a ；②当1>a 时，ax x x u -=3)(在（21-，0）上单调递增，即03)('2≥-=a x x u 在（21-，0）上恒成立，∴0≤a ，∴a 无解.综上，可知143<≤a .17.已知()f x 为偶函数，且)3()1(x f x f -=+，当02≤≤-x 时，xx f 3)(=，则=)2011(f . 答案：3118.函数221x xy =+的值域为 .答案：)1,0(19.已知函数)(x f 的定义域为A ，若其值域也为A ，则称区间A 为)(x f 的保值区间.若()ln g x x m x =++的保值区间是[,)e +∞ ，则实数m 的值为 .答案：1-20.若不等式0122<-+-m x mx 对任意]2,2[-∈m 恒成立，则实数x 的取值范围是 .答案：)213,217(+-21.直线1=y 与曲线a x x y +-=2有四个交点，则实数a 的取值范围是 . 答案：)45,1(22.已知函数0)(3(log 2≠-=a ax y a 且)1±≠a 在]2,0[上是减函数，则实数a 的取值范围是 . 答案：)23,1()0,1( -二、解答题： 1.已知函数132)(++-=x x x f 的定义域为A ，函数)1()]2)(1lg[()(<---=a x a a x x g 的定义域为B . （1）求A ；（2）若A B ⊆，求实数a 的取值范围. 解：（1）由0132≥++-x x ，得011≥+-x x ，∴1-<x 或1≥x ， ……4分即),1[)1,(+∞--∞= A ； ……6分 （2）由0)2)(1(>---x a a x ，得0)2)(1(<---a x a x .∵1<a ，∴a a 21>+.∴)1,2(+=a a B . ……8分 ∵A B ⊆，∴12≥a 或11-≤+a ，即21≥a 或2-≤a . ……12分而1<a ，∴121<≤a 或2-≤a .故当A B ⊆时，实数a 的取值范围是)1,21[]2,( --∞. ……14分2.已知命题p ：函数)2(log 25.0a x x y ++=的值域为R ，命题q ：函数x a y )25(--= 是减函数.若p 或q 为真命题，p 且q 为假命题，求实数a 的取值范围.解：对命题p ：∵函数)2(log 25.0a x x y ++=的值域为R ，∴1)1(222-++=++a x a x x 可以取到),0(+∞上的每一个值，∴01≤-a ，即1≤a ； ……4分命题q ：∵函数xa y )25(--=是减函数，∴125>-a ，即2<a . ……8分 ∵p 或q 为真命题，p 且q 为假命题，∴命题p 与命题q 一真一假，若p 真q 假，则1≤a 且2≥a ，无解， ……10分 若p 假q 真，则21<<a ， ……12分 ∴实数a 的取值范围是)2,1( ……14分3.某摩托车生产企业，上年度生产摩托车的投入成本为1万元/辆，出厂价为2.1万元/辆，年销售量为1000辆.本年度为适应市场需求，计划提高产品档次，适度增加投入成本.若每辆车投入成本增加的比例为)10(<<x x ，则出厂价相应提高的比例为x 75.0，同时预计年销售量增加的比例为x 6.0.已知年利润=（出厂价–投入成本）⨯年销售量.（1）写出本年度预计的年利润y 与投入成本增加的比例x 的关系式；（2）为使本年度的年利润比上年有所增加，问投入成本增加的比例x 应在什么范围内？ 解：（1）由题意得)10)(6.01(1000)]1(1)75.01(2.1[<<+⨯⨯+⨯-+⨯=x x x x y ，…5分 整理得 )10( 20020602<<++-=x x x y ；……7分（2）要保证本年度的利润比上年度有所增加，当且仅当⎩⎨⎧<<>⨯--.10,01000)12.1(x y …10分即⎩⎨⎧<<>+-.10,020602x x x 解不等式得 310<<x . ……13分答：为保证本年度的年利润比上年度有所增加，投入成本增加的比例x 应满足33.00<<x .…14分 4.已知命题p ：指数函数xa x f )62()(-=在R 上单调递减，命题Q ：关于x 的方程012322=++-a ax x 的两个实根均大于3.若p 或q 为真，p 且q 为假，求实数a 的取值范围．解：若p 真，则f （x ）＝（2a －6）x在R 上单调递减，∴0<2a －6<1，∴3<a<72，若q 真，令f （x ）＝x 2－3ax ＋2a 2＋1，则应满足⎩⎪⎨⎪⎧Δ＝ －3a 2－4 2a 2＋1 ≥0－－3a2>3f 3 ＝9－9a ＋2a 2＋1>0，∴⎩⎪⎨⎪⎧a ≥2或a ≤－2a>2a<2或a>52，故a>52，又由题意应有p 真q 假或p 假q 真．①若p 真q 假，则⎩⎪⎨⎪⎧3<a<72a ≤52，a 无解．②若p 假q 真，则⎩⎪⎨⎪⎧a ≤3或a ≥72a>52，∴52<a ≤3或a ≥72.故a 的取值范围是{a|52<a ≤3或a ≥72}．5.已知函数)(x f 满足对任意实数y x ,都有1)()()(+++=+xy y f x f y x f ，且2)2(-=-f .（1）求)1(f 的值；（2）证明：对一切大于1的正整数t ，恒有t t f >)(；（3）试求满足t t f =)(的所有的整数t ，并说明理由.解：（1）令0==y x ，得1)0(-=f ；令1-==y x ，得2)1()1()2(+-+-=-f f f ，又2)2(-=-f ，∴2)1(-=-f ； 令1,1-==y x ，得)1()1()0(-+=f f f ，∴1)1(=f . ……4分 （2）令1=x ，得2)()1(+=-+y y f y f ①∴当N y ∈时，有0)()1(>-+y f y f ，由1)1(),()1(=>+f y f y f 知对*N y ∈有0)(>y f ，∴当*N y ∈时，111)(2)()1(+>+++=++=+y y y f y y f y f ，于是对于一切大于1的正整数t ，恒有t t f >)(. ……9分 （3）由①及（1）可知1)4(,1)3(=--=-f f ； ……11分下面证明当整数4-≤t 时，t t f >)(，∵4-≤t ，∴02)2(>≥+-t 由① 得0)2()1()(>+-=+-t t f t f ，即 0)4()5(>---f f ，同理0)5()6(>---f f ， ……，0)2()1(>+-+t f t f ，0)1()(>+-t f t f ， 将以上不等式相加得41)4()(->=->f t f ，∴当4-≤t 时，t t f >)(， ……15分 综上，满足条件的整数只有2,1-=t . ……16分6.如下图所示，图1是定义在R 上的二次函数)(x f 的部分图象，图2是函数)(log )(b x x g a +=的部分图象．（1）分别求出函数)(x f 和)(x g 的解析式；（2）如果函数)]([x f g y =在区间[1，m ）上单调递减，求实数m 的取值范围. 解：（1）由题图1得，二次函数)(x f 的顶点坐标为（1，2）， 故可设函数2)1()(2+-=x a x f ，又函数)(x f 的图象过点（0，0），故2-=a ， 整理得x x x f 42)(2+-=.由题图2得，函数)(log )(b x x g a +=的图象过点（0，0）和（1，1），故有⎩⎨⎧=+=1)1(log 0log b b aa ，∴⎩⎨⎧==12b a ，∴)1(log )(2+=x x g （1->x ）．（2）由（1）得)142(l og )]([22++-==x x x f g y 是由t y 2log =和1422++-=x x t 复合而成的函数，而t y 2log =在定义域上单调递增，要使函数)]([x f g y =在区间[1，m ）上单调递减，必须1422++-=x x t 在区间[1，m ）上单调递减，且有0>t 恒成立．由0=t 得262±=x ，又因为t 的图象的对称轴为1=x .所以满足条件的m 的取值范围为2621±<<m .7.已知1212)3(4)(234+-++-=x x m x x x f ，R m ∈.（1）若f 0)1('=，求m 的值，并求)(x f 的单调区间；（2）若对于任意实数x ，0)(≥x f 恒成立，求m 的取值范围.解：（1）由f ′（x ）＝4x 3－12x 2＋2（3＋m ）x －12，得f ′（1）＝4－12＋2（3＋m ）－12＝0，解得m ＝7.………2分所以 f ′（x ）＝4 x 3－12x 2＋20x －12＝4（x －1）（x 2－2x ＋3） .方程x 2－2x ＋3＝0的判别式Δ＝22－3×4＝－8＜0，所以x 2－2x ＋3＞0. 所以f ′（x ）＝0，解得x ＝1.……………………………4分由此可得f （x ）的单调减区间是（－∞，1），f （x ）的单调增区间是（1，＋∞）.…8分（2）f （x ）＝x 4－4x 3＋（3＋m ）x 2－12x ＋12＝（x 2＋3）（x －2）2＋（m －4）x 2. 当m ＜4时，f （2）＝4（m －4）＜0，不合题意；……………12分当m≥4时，f （x ）＝（x 2＋3）（x －2）2＋（m －4）x 2≥0，对一切实数x 恒成立. 所以，m 的取值范围是［4，＋∞）.……………16分。
高二下学期期中复习测试题
高二下学期期中复习测试题（时间：120分钟,满分：135分）Ⅰ. 语言知识及应用(共两节,满分45分)第一节完形填空(共15小题；每小题2分,满分30分)Fiona Famous was a very popular girl at school. She felt 1 as no other girl had so many friends at school and in the neighborhood.But everything 2 on National Friendship Day. On that day in class everyone had to make three presents to give to their three best friends. Fiona 3 the task of choosing three from all the dozens of her friends. However, she was the only one in her class who did not 4 a present! She felt terrible, and spent hours 5 . Everyone came and comforted her for a while.But each one only stayed for a short time before leaving.This was 6 what Fiona had done so many times to others.She 7 that she was a good companion and acquaintance (泛泛之交), but she had not been a true friend to anyone. She had tried to be close to everyone, but now she found that was not enough to create8 friendships.When she got home that night, Fiona told her mother about the whole thing. Her mother said, "You can't be a close friend to everybody.It's only 9 to have a few true friends.The others will just be playmates or acquaintances.”Hearing this, Fiona decided to change her way so that she could finally have some true friends. That night, in 10 , she thought about what she could do to get them. She thought about her mother. Her mother was always willing to 11 her, she put up with all of Fiona's dislikes and 12 , she always forgave her, she loved her a great deal ... That was what makes a 13 ！And Fiona 14 , realizing that she already had the best friend that anyone could 15 .She fell asleep and had a good dream.1.A.tired B.lucky C.strange D.surprised2.A.mattered B.developed C.changed D.appeared3.A.enjoyed B.improved C.failed D.ruined4.A.receive B.show plete D.make5.A.remaking B.thinking C.crying D.checking6.A.especially B.gradually C.briefly D.exactly7.A.forgot B.realized C.doubted plained8.A.new B.true C.long D.smart9.A.possible B.fair C.important D.natural10.A.chair B.bed C.school D.table11.A.correct B.follow C.help D.find12.A.dreams B.ideas C.stories D.problems13.A.playmate B.parent C.friend D.mother14.A.smiled B.suffered C.screamed D.hesitated(犹豫)pare B.protect C.remember D.want第二节语法填空(共10小题；每小题1.5分,满分15分)I enjoy doing physical training in my free time. Yesterday, when I was working out at a gym on my lunch hour, I saw 16 elderly lady there riding on a bike. She couldn't walk very well, 17 she had a cane (手杖) near her, but she was still there18 (work) hard.After I finished my exercising, I told her that I was going to wait for her 19 she got done and that I would walk her out to her car. It was a little far to her car and it was a 20 (fog) day yesterday in Missouri. I walked her to the car and opened the car door for her, 21 won me her big smile and gratitude.I know 22 is a small thing, but I felt so good inside for helping her. 23 my help, she could have fallen so 24 (easy) out in the wet parking lot, and no one would have known she had fallen. I 25 (know) she needed my help, and her smile was enough to make my day.Ⅱ. 阅读(共两节, 满分50分)第一节阅读理解(共20小题；每小题2分，满分40分)AArthur Miller was born on October 17th, 1915 and died on February 10th, 2005.Over the course of seven decades(十年)of literature career(文学生涯), Arthur Miller created some of the most memorable stage plays(舞台剧)in American Literature. He is the author of Death of a Salesman and The Crucible. Born and raised in Manhattan, Miller went through the best and the worst of American society.Arthur Miller's childhood：His father was a productive shop-keeper and clothin g manufacturer(制造商) until the Great Depression(大萧条时期) dried up nearly all business opportunities.Yet, despite being faced with poverty, Miller made the best of his childhood. He was a very active young man, in love with such sports as football and baseball. When he wasn't playing outside, he enjoyed reading adventure stories. He was also kept busy by his many boyhood jobs. He often worked alongside his father. During other times in his life, he delivered bakery goods and worked as a clerk in a car parts warehouse.College life: In 1934, Miller left the east coast to attend the University of Michigan. He was accepted into their school of journalism. His experiences during the Depression made him skeptical (怀疑的) about religion. Politically, he began leaning towards the "Left”.And since the theater was the cutting edge way for socio-economic liberals (自由主义者) to express their views, he decided to enter the Hopwood Drama competition. His first play, No Villain, received an award from the university.It was an impressive beginning for the young playwright; he had never studied plays or playwriting, and he had written his play in just five days!Miller's later years: In 1987, his autobiography was published. Many of his later plays dealt with personal experience. In particular, his final play, Finishing the Picture mirrors the last days of his marriage to Marilyn Monroe.In 2005,Arthur Miller passed away at the age of 89.26.What can we know about Arthur Miller from Paragraph 2?A.He was born into a poor family.B.His father wasn't good at business.C.He couldn't adjust himself to poverty.D.He had to do lots of jobs to make a living.27.Arthur Miller began to write plays ________.A.when he was in collegeB.when he was a small boyC.because his father encouraged him to do soD.because it was one of his school assignments(作业)28.We can infer from Paragraph 3 that ________.A.the University of Michigan is on the east coast of the USAler's university education made him doubt religionler learned playwriting all by himselfD.socio-economic liberals were probably not politically "left”29.Which of the following plays tells the story of Arthur Miller and Marilyn Monroe?A.Death of a Salesman.B.The Crucible.C.No Villain.D.Finishing the Picture.30.The passage is intended to________.A.introduce Arthur Miller's playsB.tell us about Arthur Miller's childhoodC.explain how Arthur Miller started to write playsD.give us a brief introduction to Arthur Miller's lifeBTabb doesn't look like a typical music teacher. But every weekday evening in the French Quarter New Orleans, he beats out the rhythm on his music stand as students play their chosen instruments.“I'm doing my best to take young people away from harmful things,” said Tabb. His program, "The Roots of Music”, offers free music education to more than 100 students. He struggles to keep young people on the straight and narrow in the city with the nation's highest murder rate(凶杀率).Tabb chose to target 9-to14-year-olds with his program. “That's a very important time in your life,” he said. “If I catch them then, I can hold onto them for at least four or five years and guide them the way that will lead them to success.”Students meet from 4 pm to 7 pm every weekday, all year round. They work with tutors(助教) on schoolwork, practice their music and eat a hot meal before heading home. With the money provided by some people, Tabb's group is able to provide bus transportation, instruments and food for free. He calls it his “no excuse” policy. “You have no excuse why you're not here,” Tabb said. Tabb owes the success in part to the nature of music. “You're always learning something new,”he said. “That's what keeps the kids coming back every day.”But the program isn't only about fun. “Music is about discipline (纪律),”said Tabb. He insists on good behavior and keeps kids in order with threatsof sit-ups(仰卧起坐), pushups(俯卧撑) or tasks like picking up grains of rice —but these measures aren't just punishment. Tabb wants young people to realizethat music can help th em build a better future. “I don't say that I'm saving lives,” he said. “I say I'm giving life —a whole different life of music.”31.The underlined phrase "keep young people on the straight and narrow” may mean ________.A.keep young people standing straightB.keep young people on the correct life track(道路)C.keep young people busy performing musicD.keep young people away from the dangerous parts of the city32.Which of the following kids may NOT be included in Tabb's program “ The Roots of Music”？A.Jack, 8 years old.B.Tom, 9 years old.C.John, 11 years old.D.Linda, 13 years old.33.What attracts children to join in the program to learn music?A.The free food and transportation.B.The famous music teacher.C.The chance to learn new things.D.The strict discipline rules.34.By saying “music is about discipline”, Tabb means ________.A.keeping discipline is more important than learning musicB.obeying(遵守) rules is important in playing music wellC.music is also connected with kids' gradesD.kids can learn how to behave through music35.What is the main idea of this passage?A.Tabb's program offers young people help.B.Kids improve grades through music learning.C.Tabb offers kids free food to learn music.D.Tabb performs music for street children.CThe United States of America is the most culturally diverse(多样化) country in the world in terms of culture religion, ethnicity(种族) and sexual orientation. As a combination of various races and cultures, America is home to all. The culture here is so unique that citizens can be just as proud of their original cultural heritage(遗产) as they are to be American.What is now the US was initially inhabited(居住) by native people until the land was settled by various European groups and African slaves. Since the 20th century, the country has become a heaven for people from all over the globe(全球).The arrival of immigrants(移民) has shifted populations from rural(农村的) areas into cities because immigrants tend to settle in urban areas. At present, 81 percent of the inhabitants in the US live in cities.Cultural and ethnic diversity adds a unique flavor to cities that is expressed through distinct(独特的)neighborhoods, restaurants, places of worship, museums, nightlife and multicultural learning environments.Unique musical forms, such as jazz, rock and roll, Chicano music, and the blues, grow in the US by mixing a variety of culturally distinct musical traditionsto create a new form.At the executive (行政的) level, the country is headed by a mixed-race president; two posts(职位) on the Supreme Court are held by members of the country's two largest minorities.There is also diversity in state and local governments.Without its rich mixture of races and cultures, America would not be the nation that it is today. Founded upon the basis of equality and freedom, America acts as a stage where different cultures not only co-exist peacefully, but develop well.36.According to the passage, America is a country________.A.that welcomes people from all over the worldB.where citizens take more pride in their original cultureC.that is mostly settled by Europeans and AfricansD.where 81% of the population are immigrants37.Where did most people live before many immigrants came to America?A.In the urban areas.B.In the rural areas.C.In the southern part of America.D.In the northern part of America.38.We can learn from the sixth paragraph that________.A.diversity(多样化) has existed in America in almost every aspect(方面)B.most posts in American state governments are held by mixed-race peopleC.equality and freedom make America a fair countryD.diversity has greatly affected the American political field39.What's the best title for this passage?A.The effects of culture and diversity on America.B.The influence of globalization on America.C.The political development of America.D.The bright future of America.40.We would most probably read this passage in a book about________.A.scienceB.historyC.cultureD.amusementDDo you know what your child is going to do when the school bell rings at the end of the day? More than 14 million students leave school every afternoon and have nowhere to go, since they do not have access to(使用) affordable after-school opportunities. According to the National Youth Violence Prevention Resource Center (NYVPRC), 90% of the Americans think all youths should haveaccess to after-school programs(课外活动项目), but two-thirds of parents say they have trouble finding programs locally. The bad news is that the situation may be getting worse.After-school hours are the peak time for juvenile crimes and risky behaviors, including alcohol(酒精) and drug(药物) use. NYVPRC states that children who do not spend any time in after-school activities are 49 percent more likely to use drugs and 37 percent more likely to become a teen parent. Kids are also at the highest risk of becoming a victim of violence after school, particularly between the hours of 2 p.m. and 6 p.m. The highest amount of juvenile crime occurs between 3 p.m. and 4 p.m., when most children are dismissed from school(放学).The NYVPRC defines after-school programs as safe and structured activities that offer children opportunities to learn new skills. The skills students learn can range from technology and math to reading and art. Some programs also offer opportunities for internship (实习), community service, or mentoring. These programs have been shown to improve academic achievement, as well as relieve the stresses(减压) on working families. A report by the U.S. Department of Education and the U.S Department of Justice shows that students in after-school programs have fewer behavioral problems and more self-confidence, and can handle conflicts better than students who are not involved with these programs. In addition, according to the Harvard Family Research Project, after-school programs help students from low income families overcome the inequities (不公平) they face in the school system.41.Which of the following is TRUE according to the first paragraph?A.Most parents don't believe in after-school programs.B.Students are not willing to attend after-school programs.C.It's difficult for parents to find after-school programs for their kids.D.Parents don't care about where their children go after school.42.The underlined word “juvenile” in Paragraph 2 has a similar meaning t o “_____”.A.studentB.teenagerC.adultD.campus43.We learn from the second paragraph that________.A.the teachers should watch over kids after schoolB.children are dismissed from school too lateC.after-school hours are a risky time for childrenD.children should go home immediately school is over44..The author of the passage probably________.A.fully supports after-school programsB.doubts the effects of after-school programsC.believes structured activities are useless for childrenD.thinks students today are too stressed45.What is the theme of the passage?A.Prevention of juvenile crimes.B.Risks kids face after school.C.A research report on the stresses of the students.D.The benefits of after-school programs.第二节信息匹配(共5小题；每小题2分，满分10分)首先，请阅读以下专家的解答：A.First, let' s talk about your boyfriend.If he' s laughing at you about it and won' t stop (even after you've talked to him about the fact that it hurts and annoys you) then you might need to stop being friends with him. If he really doesn't care about how he is hurting you, then he's not good enough to be your boyfriend. Second, if that girl is bothering you and threatening to beat you up you really need to turn to an adult for help. If you can't feel safe at school, youcan't concentrate and will get poor grades, which will affect your future.B.It' s true that your first year in high school is important. It's a fresh startwith your grades and it affects the rest of your high school years, but if you just stay calm, optimistic, and focused, you'll do fine. There's really no need to worry about grades as long as you work hard. Try to stay happy and confident. I think a good way to get an extra confidence boost is to wear your favorite clothes.C.You' re already on the right track by knowing what you want to change about yourself and why you feel the way you do. Understanding yourself is a big step! One good thing to do is to hang out with people a lot like you. If you have more in common with someone, then it is much easier to talk to them. Usually when you feel comfortable around a group of people, your confidence increases a lot.D.What I've discovered from my years of school changing is that confidence is the key to a good first day. Make sure you're not too threatening to your new classmates in any way, and it usually helps to be twice as nice as usual. Just smile and try to have fun. Also, about the clothes, wear something cute with bright colors. Then you'll look good, but you won' t have too many eyes on you all at once. Good luck and have fun!ually it helps your grades if your family life is less of a challenge. If you get better grades and quit running up high phone bills, you would get along better with your parents. Getting along with your parents is pretty important.They've been through a lot and are usually good people to go to for help. So try your best to get along with your family.F.If you don't feel pretty, remember that everyone looks different. There are different kinds of "pretty”, believe it or not. Some people have great smiles, some have great hair, and some have nice eyes. Pay more attention to the parts of you that you like and pay less attention to what you don't like.阅读下列人物的困惑，然后匹配相应的专家解答：46.I am in eighth grade and am about to start high school.I am super nervous about going to high school and afraid that I won' t fit in and get good grades. It is all I think about nowadays and it is ruining my life. What should I do? Please help me!47.I had a fight with a girl at school and ended up almost getting forced to leave school. Everybody makes fun of me and now my boyfriend is joining in with them. I have told him that it hurts my feelings, but he says that it is just a joke and that he may do it again. I feel scared to go to school, because I knocked her down at school and she'll get all her friends to beat me up the next time she sees me. I run as fast as I can to attend classes. Please help me!48.My dad and mom always get me mad. I have bad grades.My cell phone's bill is quite high. I think it' s because of my anger at my dad and mom. What should I do to get along well with my family?49. My family will move to a new city and I will have to start a new school. I'm really nervous about being a new kid. I don' t know what kids wear in a completely new school, how they act, or anything else. I don't want to make a bad impression on my first day. Oh, I will be in 10th grade and I've never changed schools before.50.When I was eight my parents divorced(离婚).I used to be willing to do something and talk to someone I didn't know without being nervous. After thedivorce I switched(转变) to many different schools and got really shy.My problem is that I'm shy around boys. I have to get to know them a lot to open up more and I think I might have ruined it a couple of times. I want my old self back. How do I open up even more without feeling scared?第II卷(共两节)II.读写任务（25分）阅读下面的短文，然后按照要求写一篇150词左右的英语作文。
高二数学期末复习题库
高二数学期末复习题库一、选择题1. 若函数f(x) = 2x^3 - 3x^2 + 5x - 7，求f(1)的值。
A. -3B. 0C. 2D. 52. 已知等差数列的首项a1=3，公差d=2，求第10项a10的值。
A. 23B. 25C. 27D. 293. 圆的方程为(x-3)^2 + (y-4)^2 = 25，求圆心坐标和半径。
A. 圆心(3,4)，半径5B. 圆心(4,3)，半径5C. 圆心(3,4)，半径3D. 圆心(4,3)，半径34. 已知三角形ABC的三边长分别为a=5，b=7，c=8，求其面积。
A. 12B. 15C. 18D. 205. 函数y = sin(x) + cos(x)的周期是多少？A. πB. 2πC. 3πD. 4π二、填空题6. 已知直线l1: 2x + 3y - 6 = 0与直线l2: x - 4y + 8 = 0，求它们的交点坐标。
交点坐标为：________。
7. 求函数y = x^2 - 4x + 4的顶点坐标。
顶点坐标为：________。
8. 已知向量a = (1, 2)，b = (3, 4)，求向量a与向量b的点积。
点积为：________。
9. 已知方程x^2 - 6x + 9 = 0，求它的根。
根为：________。
10. 已知正弦函数y = sin(ωx + φ)，其中ω = 2，φ = π/4，求函数的周期。
周期为：________。
三、解答题11. 证明：对于任意实数x，等式e^x ≥ x + 1恒成立。
12. 已知椭圆的方程为x^2/a^2 + y^2/b^2 = 1（a > b > 0），求椭圆的焦点坐标。
13. 解不等式：|x - 2| + |x + 3| ≥ 5。
14. 已知函数f(x) = x^3 - 3x^2 + 2，求其导数f'(x)。
15. 利用向量的知识证明勾股定理。
四、应用题16. 某工厂生产产品的成本函数为C(x) = 100 + 30x，其中x为生产数量。
广东省清远市英德市第五中学2020-2021学年高二下学期物理粤教版选修3-2第一章电磁感应复习题
电磁感应复习题一、单选题1．高频焊接原理示意图如图所示，线圈通以高频交流电，金属工件的焊缝中就产生大量焦耳热，将焊缝融化焊接，要使焊接处产生的热量较大，下列措施不可采用是（）A．减小焊接缝的接触电阻B．增大焊接缝的接触电阻C．增大交变电流的电压D．增大交变电流的频率2．如图所示，在粗糙绝缘水平面上，固定两条相互平行的直导线，导线中通有大小和方向都相同的电流，在两条导线的中间位置放置一正方形线框，导线、线框均关于虚线对称，当导线中电流发生变化时，线框始终静止。
已知导线周围某点的磁感应强度与导线中的电流大小成正比，与到导线的距离成反比。
则下列对导线中电流变化后线框所受摩擦力的方向的判断正确的是（）A．a、b中电流同步增加，摩擦力方向向左B．a、b中电流同步减小，摩擦力方向向左C．a中电流减小，b中电流增大，摩擦力方向向右D．a中电流减小，b中电流不变，摩擦力方向向左3．如图所示，用轻绳将一条形磁铁竖直悬挂于O点，在其正下方的水平绝缘桌面上放置一铜质圆环。
现将磁铁从A处由静止释放，经过B、C到达最低处D，再摆到左侧最高处E，圆环始终保持静止，则磁铁（）A．从B到C的过程中，圆环中产生逆时针方向的电流（从上往下看）B．摆到D处时，圆环给桌面的压力小于圆环受到的重力C．从A到D和从D到E的过程中，圆环受到摩擦力方向相同D．在A、E两处的重力势能相等4．如图甲所示，一个匝数为n的圆形线圈（图中只画了2匝），面积为S，线圈的电阻为R，在线圈外接一个阻值为R的电阻和一个理想电压表，将线圈放入垂直纸面向里的磁场中，磁感应强度随时间变化规律如图乙所示，下列说法错误的是（）A ．0~t 1时间内P 端电势高于Q 端电势B ．0~t 1时间内电压表的读数为101n B -B St （）C ．t 1~t 2时间内R 上的电流为121S2-nB t t R（）D ．t 1~t 2时间内P 端电势低于Q 端电势5．如图，导体轨道OPQS 固定，其中PQS 是半圆弧，Q 为半圆弧的中点，O 为圆心.轨道的电阻忽略不计.OM 是有一定电阻、可绕O 转动的金属杆，M 端位于PQS 上，OM 与轨道接触良好.空间存在与半圆所在平面垂直的匀强磁场，磁感应强度的大小为B .现使OM 从OQ 位置以恒定的角速度逆时针转到OS 位置并固定(过程Ⅰ)；再使磁感应强度的大小以一定的变化率从B 增加到B ′(过程Ⅰ).在过程Ⅰ、Ⅰ中，流过OM 的电荷量相等，则'B B等于( )A ．54B ．32C ．74D ．2二、多选题6．图甲和图乙是演示自感现象的两个电路图，L 1和L 2为电感线圈，A 1、A 2、A 3都是规格相同的灯泡。
高二下册政治世界的物质性复习题及答案
高二下册政治世界的物质性复习题及答案一、单项选择题1.物质的唯一特性是客观实在性。
这里的“客观实在”是( )A.世界上万事万物的总和B.所有有形的物体C.万事万物共同的属性和本质特征D.高山、河流等自然事物[答案]C2.人类能够创造出自然界里本来没有的东西，如计算机、电冰箱、宇宙飞船等。
这表明( )A.人类能够创造物质B.人类能够改变自然物的具体形态C.人工化的自然物不再具有客观实在性D.自然界不是物质的[答案]B3.“树欲静而风不止”这句话反映了( )A.客观事物的存在与发展不以人的意志为转移B.世界上一切事物都是物质的C.自然物有自己的起源和发展史D.物质就是指树、风等自然物[答案]A4.马克思主义哲学认为人类社会在本质上是一个客观的物质体系，这是因为( )①地理环境是客观的②人口因素是客观的③人类社会的发展是完全自发的④生产方式是客观的A.①②③B.②③④C.①②④D.①③④[答案]C5.下列对哲学上的物质认识正确的是( )A.它是不依赖于人的意识，并能为人的意识所反映的客观实在B.它概括的是自然界中一切客观存在着的事物和现象的共同本质C.它可以被人创造的D.它看得见、摸得着，具有客观实在性[答案]A6.马克思主义哲学认为：“世界的真正统一性在于它的物质性。
”下列能够说明材料中观点的是( )①自然界是物质的②人类社会是物质世界长期发展的产物，劳动创造了人类社会③人的意识一开始就是社会的产物④从构成要素来看，人类社会在本质上是一个客观的物质体系A.①②③B.①②④C.①③④D.①②③④[答案]D二、非选择题7.《尚书•洪范》一书中指出，水、火、木、金、土是世界的本原。
培根认为，万物的基础是原始物质，是基本元素。
恩格斯说：“世界的统一性在于它的物质性。
”(1)恩格斯所说的“物质”与其他两种观点的“物质”有何不同?(2)请谈谈你对辩证唯物主义的物质概念的认识。
[答案](1)恩格斯所说的“物质”是世界上万事万物的共同属性和本质特征;而《尚书•洪范》一书和培根所讲的“物质”实际上是具体的物质形态。
2-3期未复习题(二)(高二(下)数学同步测试题)
高二数学期未复习题（二）一、选择题：本大题共12小题，在每小题给出的四个选项中，只有一项符合题目要求。
1.已知随机变量X ～B(6,0.4),则当η=-2X+1时,D(η)=( ). A.-1.88B.-2.88C.5.76D.6.762．已知一次考试共有60名同学参加,考生成绩X ～N(110,52),据此估计,大约有57人的分数所在的区间为( ).A.(90,100]B.(95,125]C.(100,120]D.(105,115] 3．满足条件|z |＝|3＋4i|的复数z 在复平面上对应点的轨迹是( )． A ．一条直线 B ．两条直线 C ．圆 D ．椭圆 4. 求曲线y ＝x 2与y ＝x 所围成图形的面积，其中正确的是( )A ．S ＝⎠⎛01(x 2－x)d xB ．S ＝⎠⎛01(x －x 2)d xC ．S ＝⎠⎛01(y 2－y)d xD ．S ＝⎠⎛01(y －y)d y5．样本中共有五个个体，其值分别为0,1,2,3，m .若该样本的平均值为1，则其方差为( ) A.105 B.305C. 2 D ．2 6．曲线y ＝13x 3－2在点(－1，－53)处切线的倾斜角为( )A ．30°B ．45°C ．135°D ．150°7．我国古代数学名著《九章算术》有“米谷粒分”题：发仓募粮，所募粒中秕不百三则收之(不超过3%)，现抽样取米一把，取得235粒米中夹秕n 粒，若这批米合格，则n 不超过( )A ．6粒B ．7粒C ．8粒D ．9粒8.某校高二年级共有六个班级，现从外地转入4名学生，要安排到该年级的两个班级且每班安排2名，则不同的安排方案种数为（ ）Ａ．60 Ｂ．90 Ｃ．120 Ｄ．1809.一个电路如图所示， C 、D 、E 、F 为4个开关，其闭合的概率都是12，且是相互独立的，则灯亮的概率是( )A. 916B. 716C. 1316D. 31610．若0<x<π2，则2x与3sin x的大小关系( )．A．2x>3sin x B．2x<3sin x C．2x＝3sin x D．与x的取值有关11. 设随机变量X～N(μ，σ2)且P(X<1)＝12，P(X>2)＝p，则P(0<X<1)的值为( )A.12p B．1－p C．1－2p D.12－p12. 设某大学的女生体重y(单位：kg)与身高x(单位：cm)具有线性相关关系，根据一组样本数据(x i，y i)(i＝1,2，…，n)，用最小二乘法建立的回归方程为y^＝0.85x－85.71，则下列结论中不正确的是( )A．y与x具有正的线性相关关系 B．回归直线过样本点的中心(x，y) C．若该大学某女生身高增加1 cm，则其体重约增加0.85 kgD．若该大学某女生身高为170 cm，则可断定其体重必为58.79 kg二、填空题：本大题共4小题，每小题5分，共20分。
2020-2021学年高二数学下学期期末专项复习2.1 坐标平面上的直线解析版
专题2.1 坐标平面上的直线【章节复习专项训练】【考点1】 ：直线的方程例题1．（2020·上海师大附中高二期末）直线方程20x y m -+=的一个方向向量d 可以是（ ） A ．(2,1)- B ．(2,1) C ．(1,2)- D ．(1,2)【答案】D【分析】先根据直线方程得直线的一个法向量，再根据法向量可得直线的方向向量. 【详解】解：依题意，()2,1-为直线的一个法向量，∴方向向量为()1,2， 故选：D .【变式1】（2021·上海市奉贤中学高二期末）如图，平面上过点P (1，2)的直线与x 轴正半轴交于点A ，与y 轴正半轴交于点B .过点P 分别作直线垂直于x 轴与y 轴，垂足分别为M ，N .则满足2020PAMPBNS S-=的直线有（ ）条A ．0B ．1C ．2D ．3【答案】B【分析】设直线AB 为y =k (x -1)+2()0k <，分别令x =0，y =0，求得点A ，B 的坐标， 然后由2020PAMPBNSS-=求解.【详解】因为过点P (1，2)，且斜率存在， 设直线AB 为y =k (x -1)+2()0k <， 令x =0，y =2-k ； 令y =0，x =2k k- 2(,0),(0,2)k A B k k-∴-， 2,2,AM PM BN k k∴=-==-，2020PAMPBNSS-=，121()21()202022k k ∴⨯-⨯-⨯⨯-=， 即2404040k k --=，0k <，所以k 的取值只有一个， 故这样的直线有一条. 故选：B【变式2】（2021·上海高二期末）直线1123x y l -+=:的一个方向向量可以是（ ） A ．(2，3) B ．(2-，3)C ．(3，2)D ．(3-，2)【答案】A【分析】将直线方程转化为()3112y x +=-，求得斜率即可. 【详解】直线1123x y l -+=:可化为：()3112y x +=-，所以直线的斜率为32k， 所以直线的一个方向向量可以是(2,3) 故选：A【变式3】（2020·上海曹杨二中高二期末）已知直角坐标系xOy 平面上的直线1x ya b+=经过第一、第二和第四象限，则,a b 满足（ ） A ．0,0a b >> B ．0a >，0b < C ．0a <，0b < D ．0a <，0b <【答案】A【分析】求出直线与坐标轴的交点，即可得出答案. 【详解】令0x =，则y b =；令0y =，则x a = 所以(0,),(,0)b a 在直线1x ya b+=上因为直线1x ya b+=经过第一、第二和第四象限 所以0,0a b >> 故选：A【点睛】本题主要考查了由直线所过象限求参数范围，属于基础题.例题2．（2020·上海市建平中学高二期末）过点()1,2C ，且与直线20x y --=垂直的直线方程为______. 【答案】30x y +-=【分析】先由垂直关系求出所求直线的斜率，再利用点斜式可求出直线方程 【详解】解：因为所求直线与直线20x y --=垂直， 所以所求直线的斜率为1-， 因为所求直线过点()1,2C ，所以所求直线方程为2(1)y x -=--，即30x y +-=， 故答案为：30x y +-=【点睛】此题考查两直线的位置关系，考查直线方程的求法，属于基础题【变式1】（2020·上海曹杨二中高二期末）过点()3,2P -且与直线210x y ++=垂直的直线方程是______. 【答案】270x y --=【分析】根据直线的垂直关系，设出所求直线方程，将()3,2P -代入方程，即可求解. 【详解】所求直线与直线210x y ++=垂直， 设该直线方程为20x y c -+=，()3,2P -代入上式方程得7c =-，所以所求的直线方程为270x y --=. 故答案为：270x y --=.【点睛】本题考查直线的位置关系求方程，利用直线的位置关系合理设方程是解题的关键，属于容易题. 【变式2】（2020·上海市控江中学高二期末）经过点()1,0，且以()2,5d =为一个方向向量的直线l 的方程为_____.【答案】5250x y --=【分析】求出直线l 的斜率，可得出直线l 的点斜式方程，化为一般式即可. 【详解】直线l 的斜率为52k =，所以，直线l 的方程为()512y x =-，即5250x y --=. 故答案为：5250x y --=.【点睛】本题考查直线的方程，考查直线的方向向量与斜率的关系，考查计算能力，属于基础题. 【变式3】（2020·上海高二期末）已知点()1,2A ,()3,0B ,则线段AB 的垂直平分线的方程是_____． 【答案】10x y --=【分析】先求出AB 的中点M 的坐标,再求出直线AB 的斜率,根据两直线垂直时斜率乘积为1-得到垂直平分线的斜率,最后用点斜式公式即可求出直线方程. 【详解】解:设M 的坐标为(),x y ， 则1322x,2012y,所以()2,1M . 因为直线AB 的斜率为120113k , 所以线段AB 垂直平分线的斜率2111k , 则线段AB 的垂直平分线的方程为112y x 化简得10x y --=. 故答案为：10x y --=【点睛】本题考查求线段AB 的垂直平分线:即要求垂直平分线线上一点与直线的斜率，根据中点坐标公式求出AB 的中点M 的坐标利用A 与B 的坐标求出直线AB 的斜率根据两直线垂直时斜率乘积为1-得到垂直平分线的斜率根据M 的坐标和求出的斜率写出AB 的垂直平分线的方程即可.【变式4】（2020·上海高二期末）若直线l 过点3(2,)A -且平行于向量(6,5)d =，则直线l 的点方向式方程是___________. 【答案】2365x y -+= 【分析】利用直线l 的点方向式方程即可得出． 【详解】由已知可得：直线l 的点方向式方程是2365x y -+=．故答案为：2365x y -+=． 【点睛】本题考查直线的点方向式方程，考查推理能力与计算能力，属于基础题．【变式5】（2021·上海市松江二中高二期末）若关于x 、y 的二元一次方程组42mx y m x my m +=+⎧⎨+=⎩无解，则实数m =________ 【答案】2-【分析】根据方程组无解，得到直线42+=+mx y m 与直线+=x my m 平行，根据两直线平行的充要条件，即可求出结果.【详解】因为关于x 、y 的二元一次方程组42mx y m x my m +=+⎧⎨+=⎩无解，所以直线42+=+mx y m 与直线+=x my m 平行，所以24024m m m m ⎧-=⎪⎨+≠⎪⎩，解得：2m =-.故答案为：2-【点睛】本题主要考查由方程组无解求参数，熟记直线与直线平行的判定条件，灵活运用转化与化归的思想即可，属于常考题型.【变式6】（2020·上海师大附中高二期末）直线10x y -+= 上一点P 的横坐标是3，若该直线绕点P 逆时针旋转90°得直线l ，则直线l 的方程是____________． 【答案】70x y +-=【详解】(,3,4)P l 的倾斜角为4590135,tan1351k ︒-︒=︒=︒=-， 则其方程为43y x -=-+，即70x y +-=. 故答案为：70x y +-=.【变式7】（2021·上海市奉贤中学高二期末）数学家欧拉在1765年提出定理；三角形的外心､重心､垂心依次位于同一直线上，且重心到外心的距离是重心到垂心距离的一半，这条直线被后人称之为三角形的欧拉线.已知ABC 的顶点A (4，0)，B (0，2)，AC BC =，则ABC 的欧拉线所在直线方程为___________.【答案】2x -y -3=0【分析】根据题意求出线段AB 的垂直平分线即可求解. 【详解】线段AB 的中点为(2，1)，201042AB k -==--， 线段AB 的垂直平分线为：y =2(x -2)+1，即2x -y -3=0 AC =BC ，∴三角形的外心､重心､垂心依次位于AB 的垂直平分线上，因此ABC 的欧拉线方程为2x -y -3=0. 故答案为：2x -y -3=0.【变式8】（2020·华东师范大学附属周浦中学高二期末）直线l 经过点(3,5)P -，且(1,2)n =是直线l 的一个法向量，则直线l 的一般式方程是________. 【答案】270x y ++=【分析】由直线的法向量可得直线的方向向量，进而可得直线的斜率，由直线方程的点斜式即可得出结果. 【详解】直线的法向量为(1,2)n =，则直线的方向向量为(2,1)m =-，直线的斜率为12k =- 由点斜式可得：1(5)(3)2y x --=--，即270x y ++= 故答案为：270x y ++=【变式9】（2020·上海市三林中学高二期末）过点()1,0且与直线20x y +=垂直的直线的方程______. 【答案】210x y --=【分析】方法一，利用两条直线互相垂直，斜率之积等于-1，求出垂线的斜率，再求垂线的方程； 方法二，根据两条直线互相垂直的关系，设出垂线的方程，利用垂线过某点，求出垂线的方程. 【详解】方法一，直线20x y +=的斜率是-2， 则与这条直线垂直的直线方程的斜率是12， ∴过点()1,0且与直线20x y +=垂直的直线方程为()1012y x -=-， 即210x y --=；方法二，设与直线20x y +=垂直的直线方程为20x y a -+=， 且该垂线过过点()1,0，∴11200a ⨯-⨯+=，解得1a =-，∴这条垂线的直线方程为210x y --=. 故答案为：210x y --=.【点睛】本题考查了直线方程的求法与应用问题，也考查了直线垂直的应用问题，是基础题目.例题3．（2021·上海高二期末）已知直线l 与直线250x y +-=平行，并且直线l 与两坐标轴围成的三角形的面积为4，求直线l 的一般式方程. 【答案】240x y ++=或240x y +-=【分析】设所求直线方程为()205x y C C ++=≠-，求出直线l 与两坐标轴的交点坐标，结合已知条件可得出关于C 的方程，进而可求得直线l 的方程.【详解】由于直线l 与直线250x y +-=平行，设直线l 的方程为()205x y C C ++=≠-， 在直线l 的方程中，令0x =，可得y C =-；令0y =，可得2Cx =-. 所以，直线l 交x 轴于点,02C ⎛⎫-⎪⎝⎭，交y 轴于点()0,C -. 由于直线l 与两坐标轴围成的三角形的面积为4，则214224C C C ⨯-⨯-==，解得4C =±. 因此，直线l 的方程为240x y ++=或240x y +-=.【变式1】（2020·上海高二期末）已知直线1:220l x y +-=和2:10l mx y -+=. (1)当12l l //时，求m 的值； (2)当1l 与2l 的夹角为4π时，求m 的值. 【答案】(1)2-；(2)3或13-. 【分析】（1）直接利用线线平行的充要条件的应用求出结果． （2）直接利用夹角公式的应用求出结果．【详解】（1）直线1:220l x y +-=和2:10l mx y -+=． 所以20m --=，解得：2m =-．（2）由于1:220l x y +-=的斜率12k =-，2:10l mx y -+=的斜率2=k m ．所以2112tan||141k kk kπ-==+，解得3m=或13-．【点睛】本题考查的知识要点：线线平行的充要条件的应用，夹角公式的应用，主要考查学生的运算能力和转换能力及思维能力，属于基础题型．【考点2】：直线的倾斜角和斜率例题1．（2020·上海市杨浦高级中学高二期末）直线210x y+-=的倾斜角为（）.A．arctan2B．arctan2-C．()arctan2π--D．arctan2π-【答案】D【分析】先根据所给直线的斜率-2，直线的斜率是倾斜角的正切，得到[)tan=20ααπ-∈，，，根据倾斜角的范围和正切的反三角函数的值域确定结果.【详解】因为直线210x y+-=的斜率2k=-，所以[)tan=20ααπ-∈，，，所以=arctan2απ-.所以直线210x y+-=的倾斜角为arctan2π-.故选：D【点睛】求斜率的方法：①定义法：()tan90kαα=≠；②两点法求斜率：()212121y yk x xx x-=≠-；③由直线方程求斜率；④由直线的方向向量求斜率.【变式1】（2020·上海高二期末）下图中的直线1l、2l、3l的斜率分别为1k、2k、3k,则（）A．123k k k<<B．312k k k<<C．321k k k<<D．132k k k<<【答案】D【分析】根据斜率与直线倾斜角的关系判断即可.【详解】由图可知：10k <,20k >,30k >,且直线3l 的倾斜角小于直线2l 的倾斜角,所以32k k <,综上可知：132k k k <<.故选：D ．【点睛】本题主要考查了直线斜率与倾斜角的关系,属于基础题.【变式2】（2020·上海高二期末）已知l 过定点()4,5的直线的一个方向向量是()2,3d =-，则直线l 的点方向式方程可以为（ ） A ．()()3425x y -=- B ．45=23x y --- C ．()()34250x y -+-= D ．45=32x y -- 【答案】B【分析】利用直线的点向式方程可以直接得到所求的方程． 【详解】因为直线l 的方向向量为()2,3d =-且经过点()4,5， 故直线l 的点向式方程为45=23x y ---． 故选：B ．【点睛】本题考查直线的点向式方程，注意点向式方程的标准形式，此题属于基础题．【变式3】．（2021·上海市建平中学高二期末）直线l 的倾斜角为θ，则直线l 关于直线y =x 对称的直线l '的倾斜角不可能为（ ） A ．θ B ．2θπ- C ．πθ-D ．32πθ- 【答案】C【分析】可分类讨论求出对称直线l '的倾斜角，然后判断． 【详解】当[0,]2πθ∈时，直线l '的倾斜角为2θπ-，当,2πθπ⎛⎫∈ ⎪⎝⎭时，直线l '的倾斜角为32πθ-，当4πθ=时，直线l '的倾斜角为4πθ=，因此ABD 均可能，只有C 不可能．实际上当直线l '倾斜角为πθ-时，直线l '与直线l 关于和x 轴垂直的直线对称． 故选：C ．【变式4】．（2020·上海市洋泾中学高二期末）若直线0ax by c 的一个法向量()3,1n =-，则该直线的倾斜角为（ ） A ．6πB ．3πC ．23π D ．56π 【答案】B【分析】根据直线的方程可得直线的法向量，结合题设条件可得,a b 的关系，从而可求直线的斜率进而得到直线的倾斜角.【详解】由直线的方程为0ax by c可得直线的法向量为(),m a b =，故,m n 共线，所以()1b a ⨯-=，即ab-=，设直线的倾斜角为[)()0,θθπ∈，则tan θ=3πθ=.故选：B.例题2．（2020·上海市进才中学高二期末）直线210x y -+=的倾斜角为________． 【答案】1arctan2【分析】根据直线方程求出直线的斜率，从而求出倾斜角. 【详解】直线210x y -+=的斜率12k =， 所以直线的倾斜角是1arctan 2. 故答案为：1arctan2. 【变式1】（2020·上海高二期末）直线40x my 的倾斜角为4π,则m 的值是_____． 【答案】1【分析】由直线的倾斜角求出斜率,再由斜率列式求得m 值. 【详解】解：直线40x my 的倾斜角为4π. 所以该直线的斜率为tan 14π=,所以11m=,解得：1m =. 故答案为：1.【点睛】本题考查直线的斜率与倾斜角的关系,是基础题.【变式2】（2020·上海市七宝中学）直线l 的倾斜角范围是__________； 【答案】0,【分析】由直线的倾斜角定义来确定. 【详解】由直线倾斜角的定义：x 轴正向与直线向上方向之间所成的角叫直线的倾斜角.特别地，当直线与x 轴平行或重合时，我们规定它的倾斜角为0度. 范围：倾斜角的取值范围是0°≤α＜180°. 故答案为：0,【点睛】本题主要考查了直线倾斜角的定义及范围，还考查了理解辨析的能力，属于基础题. 【变式3】（2020·上海高二期末）若直线l 的倾斜角的范围为,43ππ⎡⎫⎪⎢⎣⎭，则l 的斜率的取值范围是__________.【答案】【分析】利用直线斜率与倾斜角的关系、三角函数的单调性即可得出． 【详解】直线l 的倾斜角,43θππ⎡⎫⎪⎢∈⎣⎭，则l 的斜率tan [1θ∈．故答案为：．【点睛】本题考查直线斜率与倾斜角的关系、三角函数的单调性，考查推理能力与计算能力，属于基础题． 【变式4】（2020·上海复旦附中高二期末）一个方向向量为(1,3d =的直线的倾斜角的大小是__________． 【答案】60︒【分析】根据直线的方向向量可得直线的斜率，然后可求直线的倾斜角.【详解】因为直线的方向向量为(1,3d =，所以直线的斜率为k = 所以直线的倾斜角的大小是60︒. 故答案为：60︒.【点睛】本题主要考查直线的倾斜角，明确直线的方向向量与直线的斜率间的关系是求解的关键，侧重考查数学运算的核心素养.【变式5】（2020·上海市金山中学高二期末）直线l ：4y =+的倾斜角的大小为______.【答案】3π；【分析】由直线的斜率与倾斜角的关系可得tan θ=. 【详解】解：设直线的倾斜角为θ，由直线l 的方程为：4y =+可得tan θ= 又[)0,θπ∈， 所以3πθ=，故答案为：3π.【点睛】本题考查了直线的斜率与倾斜角的关系，属基础题.【变式6】（2021·上海市松江二中高二期末）若直线l 的参数方程是2,()12x t t y t =+⎧∈⎨=--⎩R ，则l 的斜率为________． 【答案】-2【分析】把参数方程消参化为斜截式方程即可求出斜率．【详解】由2,()12x t t y t =+⎧∈⎨=--⎩R ，消去参数t 可得23y x =-+， 所以直线的斜率2k =- 故答案为2-【点睛】本题考查直线的参数方程与一般方程的互化，属于基础题．【变式7】（2021·上海市奉贤中学高二期末）直线23y x =-+的倾斜角是___________(结果用反三角表示). 【答案】arctan 2π-【分析】根据斜率公式tan k α=化简即可.【详解】解：由题意得tan 2,arctan 2k ααπ==-∴=- 故答案为：arctan 2π-.【变式8】（2021·上海高二期末）直线1:10l x y +-=与直线2:20l x y -+=夹角的大小为___________. 【答案】2π 【分析】根据直线方程求得两直线的斜率，进而可求得倾斜角，即可求得答案.【详解】直线1:10l x y +-=的斜率为-1，因为倾斜角[0,)απ∈，即tan 1α=-，所以1l 的倾斜角为34π， 同理直线2:20l x y -+=的斜率为1，所以2l 的倾斜角为4π， 所以直线1l 与2l 的夹角为3442πππ-=. 故答案为：2π 【变式9】（2021·上海曹杨二中高二期末）若直线l 的倾斜角为34π，则l 的一个方向向量d 可以是______.(只需填写一个) 【答案】()1,1-【分析】利用直线倾斜角确定直线斜率，进而确定方向向量的横纵坐标之比，写出方向向量. 【详解】直线l 的倾斜角为34π，故直线的斜率3tan 14k π==-， 故方向向量的横纵坐标之比为1-， 故d 可以是()1,1-， 故答案为：()1,1-.【变式10】（2020·上海曹杨二中高二期末）设()1,2A ，()3,1B -，若直线2y kx =-与线段AB 有公共点，则实数k 的取值范围是______. 【答案】(][),14,-∞-+∞【分析】画出图象求出定点与A 、B 两点连线的斜率，即可求出实数k 的取值范围．【详解】解：直线2y kx =-恒过定点()0,2-，由题意平面内两点()1,2A ，()3,1B -，直线2y kx =-与线段AB 恒有公共点，如图求出定点与A 、B 两点连线的斜率，()122410k --==-．()212130k --==---，所以直线2y kx =-与线段AB 恒有公共点，则实数k 的取值范围是(][),14,-∞-+∞，故答案为：(][),14,-∞-+∞【点睛】本题考查直线斜率的求法，考查数形结合的思想的应用，考查计算能力．【变式11】（2020·上海高二期末）已知直线l 的一个方向向量是(1,2)，则它的斜率为______________. 【答案】2【分析】根据直线方向向量与直线斜率关系求斜率即可. 【详解】直线l 的一个方向向量是(1,2)，则直线的斜率为：2=21故答案为：2【点睛】本题考查直线方向向量以及直线斜率，考查基本分析求解能力，属基础题. 【变式12】（2020·上海高二期末）直线210x y +-=的倾斜角为________． 【答案】arctan 2π-【分析】先求直线210x y +-=的斜率,进而用反三角函数转化为倾斜角即可. 【详解】直线210x y +-=的斜率为2k =-,设倾斜角为α,所以tan 2α,则arctan 2απ-= 故答案为：arctan 2π-【点睛】本题关键是倾斜角以及反三角函数的问题,考查计算能力．【变式13】（2020·上海市控江中学高二期末）若不垂直于x 轴的直线10kx y -+=与直线20x y -=所成的角的大小为25，则实数k 的值为_____.【答案】34【分析】设直线20x y -=的倾斜角为α，记β=k 的方程，进而可求得实数k 的值.【详解】设直线20x y -=的倾斜角为α，记β=，则tan 2α=，cos 5β=，sin 5β=，1tan 2β=，由题意可得tan 21tan 1tan 122k k k k αβα--===++，解得34k =.故答案为：34. 【点睛】本题主要考查直线夹角公式的应用，涉及两角差的正切公式的应用，考查计算能力，属于基础题. 【变式14】．（2020·上海交大附中高二期末）直线223x ty t =+⎧⎨=+⎩（参数t R ∈）的倾斜角为_________.【答案】12arctan【分析】代入消参，将参数方程化为普通方程，再根据斜率求得倾斜角. 【详解】由3y t =+可得3t y =-，代入22x t =+，可得()223x y =+- 整理得：直线的一般式方程为240x y -+= 则直线的斜率为12k =，设其倾斜角为θ，[)0,θπ∈ 故12arctanθ=. 故答案为：12arctan. 【点睛】本题考查将直线的参数方程化为普通方程，以及由直线斜率求解倾斜角，属基础题.例3．（2019·上海高二期末）已经直线:1l y kx =-与两点()()1,5,4,2.A B - （1）若l 与直线AB 平行，求它们之间的距离以及l 的倾斜角；（2）若l 与线段AB 无公共点，求k 的取值范围. 【答案】（1）d =；3arctan 5θπ=-；（2）36,4⎛⎫- ⎪⎝⎭【分析】（1）由两点连线斜率公式可求得AB k ，即k ，从而得到直线l 方程及tan θ、直线AB 方程；根据反三角函数可求得倾斜角θ，利用平行直线间距离公式可求得所求距离d ；（2）首先确定直线恒过定点()0,1C -，可知临界状态为,AC BC ，利用两点连线斜率公式求得,AC AB k k ，可知(),AC AB k k k ∈，从而得到结果. 【详解】（1）由,A B 坐标可得：523145AB k -==--- ∴直线AB 方程为：()3245y x -=--，即35220x y +-= l 与直线AB 平行 35AB k k ∴==- 3:15l y x ∴=--，即3550x y ++=设直线l 倾斜角为θ 3tan 5θ∴=- 3arctan 5θπ∴=-直线l 与直线AB之间距离34d ==（2）由题意知，直线l 恒过点()0,1C -51610AC k +∴==---，213404BC k +==- l 与线段AB 无公共点 (),AC AB k k k ∴∈，即36,4k ⎛⎫∈- ⎪⎝⎭【点睛】本题是对直线部分知识的综合考查，涉及到直线斜率与倾斜角的关系、两条直线平行的位置关系的应用、平行直线间距离公式、根据直线与线段交点情况求解斜率范围的问题，属于基础题. 【考点3】 ：两条直线的位置关系例题1．（2020·上海高二期末）直线210x y ++=与直线36100x y 的位置关系是（ ） A ．相交 B ．重合C ．平行D ．垂直【答案】C【分析】根据直线的一般方程满足111222A B C A B C =≠,则两直线平行. 【详解】解: 直线210x y ++=与直线36100x y ,满足1213610, 故直线210x y ++=与直线36100x y 平行. 故选:C【点睛】本题考查直线与直线的位置关系,若两直线满足111222A B C A B C =≠,则两直线平行. 【变式1】．（2020·上海市金山中学高二期末）已知两条直线1l 与2l 不重合，则“1l 与2l 的斜率相等”是“1l 与2l 的平行”的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件 D ．既不充分也不必要条件【答案】A【分析】“1l 与2l 的平行”则有“1l 与2l 的斜率相等”或“1l 与2l 的斜率均不存在”两种情况，再判断即可得解. 【详解】解：因为两条直线1l 与2l 不重合，由“1l 与2l 的斜率相等”可得“1l 与2l 的平行”； 由“1l 与2l 的平行”则可得“1l 与2l 的斜率相等”或“1l 与2l 的斜率均不存在”， 即“1l 与2l 的斜率相等”是“1l 与2l 的平行”的充分不必要条件， 故选：A.【点睛】本题考查了两直线平行的充分必要条件，重点考查了直线的斜率，属基础题. 【变式2】．（2020·上海市嘉定区封浜高级中学高二期末）14a =是“直线(1)310a x ay +++=与直线(1)(1)30a x a y -++-=相互垂直”的（ ）.A ．充分而不必要条件B ．必要而不充分条件C ．充要条件D ．既不充分也不必要条件【答案】A【分析】对a 分类讨论，利用两条相互垂直的直线与斜率之间的关系即可得出． 【详解】解：对于：直线(1)310a x ay +++=与直线(1)(1)30a x a y -++-=， 当0a =时，分别化为：10x +=，30x y -+-=，此时两条直线不垂直，舍去；当1a =-时，分别化为：310y -+=，230x --=，此时两条直线相互垂直，因此1a =-满足条件； 当1a ≠-，0时，两条直线的斜率分别为：13a a +-，11a a -+，由于两条直线垂直，可得11131a aa a +--⨯=-+，解得14a =或1-（舍去）． 综上可得：两条直线相互垂直的充要条件为：14a =或1-． ∴14a =是“直线(1)310a x ay +++=与直线(1)(1)30a x a y -++-=相互垂直”的充分而不必要条件． 故选：A ．【点睛】本题考查了两条相互垂直的直线与斜率之间的关系，考查了分类讨论思想、推理能力与计算能力，属于中档题．例题2．（2021·上海闵行中学高二期末）过点()3,5与直线y x m =+垂直的直线方程是___________. 【答案】80x y +-=【分析】设与y x m =+垂直的直线方程为y x n =-+，利用过的点，求出n 即可. 【详解】设所求直线为y x n =-+ 过点()3,5，故8n = 直线方程为80x y +-= 故答案为：80x y +-=【变式1】．（2021·上海位育中学高二期末）已知直线1:230l ax y a ++=与直线2:3(1)70l x a y a +-+-=互相垂直，则a =________ 【答案】25【分析】利用两条直线垂直的等价条件可得()3210a a +-=，解方程即可求a 的值. 【详解】因为直线1:230l ax y a ++=与直线2:3(1)70l x a y a +-+-=互相垂直， 所以()3210a a +-=，解得：25a =， 故答案为：25.【变式2】．（2021·上海市进才中学高二期末）若直线1:210l ax y ++=与2:(1)10l x a y +++=互相垂直，则a 的值为_________. 【答案】23-【分析】根据两个直线垂直的公式代入计算. 【详解】因为12l l ⊥，所以2(1)0a a ++=，得23a =-. 故答案为：23-【变式3】．（2021·上海市复兴高级中学高二期末）已知直线220x y +-=和10x y -+=的夹角为______. 【答案】arctan 3【分析】求出两直线的斜率，利用相交两直线的夹角公式求解而得. 【详解】直线220x y +-=和10x y -+=的斜率分别为k 1=-2，k 2=1， 设直线220x y +-=和10x y -+=的夹角为(0)2πθθ<≤，而两直线不垂直，由夹角公式得：121221tan ||||311(2)1k k k k θ---===++-⋅，所以arctan 3θ=. 答案为：arctan 3【变式4】．（2020·上海闵行中学高二期末）已知直线1:10l ax y -+=，2:10l x ay --=，且12l l ⊥，则实数a =_________. 【答案】0【分析】依据两条直线垂直充要条件12120A A B B +=直接计算即可. 【详解】因为12l l ⊥，所以()()1100a a a ⨯+-⨯-=⇒= 故答案为：0【变式5】．．（2020·上海高二期末）已知直线1:42l mx y m +=+，2:l x my m +=，若12//l l ，则实数m =________．【答案】2-【分析】根据直线互相平行的判定公式得到结果. 【详解】直线1:42l mx y m +=+，2:l x my m +=， 若12//l l ，则24102m m -⨯=⇒=±，当2m =时，1l 和2l 化简为：1:22l x y +=，2:22l x y +=，此时，1l 与2l 重合，故2m =时不符合题意当2m =-时，1l 和2l 化简为：1:20l x y -=，2:220l x y -+=，此时，1l 与2l 不重合且平行，故2m =-时符合题意 故答案为：2-.【点睛】这个题目考查了已知两直线的位置关系求参数的应用，属于基础题.【变式6】．（2020·上海高二期末）直线10x y ++=与直线30x y -+=的夹角大小等于___________. 【答案】2π【分析】算出两条直线的斜率，根据它们的乘积为1-可得它们的夹角． 【详解】设两条直线的夹角为θ，直线10x y ++=的斜率为11k =-，直线30x y -+=的斜率为21k =， 因为121k k =-，所以两条直线垂直，所以2πθ=．故答案为：2π． 【点睛】本题考查直线的夹角，注意先判断它们是否垂直，如果不垂直，则利用夹角公式1212tan 1k k k k θ-=+来计算，本题属于容易题．【变式7】．（2020·上海市洋泾中学高二期末）已知直线1:220++=l x ay 与直线2:(1)310l a x y -++=平行，则实数a 的值为__________ 【答案】2-或3【分析】根据两直线平行，直接列式求解. 【详解】12//l l ，22131a a ∴=≠-，解得：2a =-或3a =. 故答案为：2-或3【变式8】．（2020·上海高二期末）直线1:210l x y -+=与直线2:210l x y ++=的夹角为______________. 【答案】90︒【分析】先利用斜率之积为1-，判定两直线垂直，即可得解.【详解】由直线1:210l x y -+=与直线2:210l x y ++=的方程可知，两直线的斜率分别为：1212,2k k ==-，∴121k k =-，∴12l l ⊥,∴两直线的夹角为90︒. 故答案为：90︒.【点睛】本题考查两直线的夹角的求法，关键根据两直线的方程求得斜率，根据斜率是否乘积为1-，从而判定两直线是否垂直是关键点.【变式9】．（2020·上海格致中学高二期末）若直线1:2310l x y +-=的方向向量是直线2:20l ax y a -+=的法向量，则实数a 的值等于__________. 【答案】32【分析】由题意结合直线方向向量、法向量的概念可得12l l ⊥，再由直线垂直的性质即可得解. 【详解】直线1l 的方向向量是直线2l 的法向量，∴12l l ⊥，∴230a -=，解得32a =. 故答案为：32. 【点睛】本题考查了直线方向向量、法向量概念的应用，考查了直线垂直的性质，属于基础题.【变式10】．（2020·上海高二期末）已知直线1l ：210ax y -+=、2l ：()130x a a y ++-=，若12l l ⊥，则实数a =_________.【答案】0或12- 【分析】若直线1l ：1110A x B y C ++=与直线2l ：2220A x B y C ++=垂直，则12120A A B B +=，代入数据计算即得. 【详解】直线1l ：210ax y -+=、2l ：()130x a a y ++-=，且12l l ⊥，()()1+210a a a ∴⨯-⨯+=,即220a a +=，解得0a =或12a =-. 故答案为：0a =或12a =-. 【点睛】本题考查直线的位置关系，属于基础题.【变式11】．（2020·上海市三林中学高二期末）已知直线1l ：()6180x t y +--=，直线2l ：()()46160t x t y +++-=，若1l 与2l 平行，则t =______.【答案】-5【分析】由平行关系可得()()()6641t t t ⨯+=+-，解方程验证排除重合可得.【详解】由题意可得()()()6641t t t ⨯+=+-，解方程可得5t =-或8t =，经验证8t =时直线重合，应舍去故当5t =-时，两直线平行.故答案为：-5.【点睛】本题考查直线的一般式方程和平行关系，属基础题.【变式12】．（2021·上海市奉贤中学高二期末）已知直线()()1:3410l k x k y -+-+=与()2:23230l k x y --+=平行，则k 的值是____．【答案】3或5【分析】由两直线平行得出()()()23243k k k --=--，解出k 的值，然后代入两直线方程进行验证. 【详解】直线()()1:3410l k x k x y -+-++=与()2:23230l k x y --+=平行，()()()23243k k k ∴--=--，整理得()()350k k --=，解得3k =或5.当3k =时，直线1:10l y +=，23:02l y -=，两直线平行； 当5k =时，直线1:210l x y -+=，23:202l x y -+=，两直线平行. 因此，3k =或5.故答案为3或5.【点睛】本题考查直线的一般方程与平行关系，在求出参数后还应代入两直线方程进行验证，考查运算求解能力，属于基础题.例题3．（2020·上海高二期末）已知二元一次方程组()()32232120k x y k x k y k ⎧--=⎪⎨++++=⎪⎩无解，求k 的值： 【答案】32k 【分析】根据题意知两直线平行,根据直线与直线平行的关系建立方程,求解验证即可.【详解】解:因为二元一次方程组()()32232120k x y k x k y k ⎧--=⎪⎨++++=⎪⎩无解, 则()322k x y k --=与()32120x k y k ++++=平行, 由3223212k k k k ---=≠++，解得：32k ． 经过验证满足题意． 32k ∴=时方程组无解． 【点睛】本题考查两直线平行,求参数,是基础题.【考点4】 ：点到直线的距离例题1．（2020·上海市七宝中学）直线l 经过点()2,1P -，且点()1,2--A 到l 的距离为1，则直线l 的方程为______．【答案】2x =-或4350x y ++=【分析】当直线l 斜率存在时，设出点斜式并利用点到直线的距离公式算出l 的方程为4350x y ++=；当直线与x 轴垂直时，l 方程为2x =-也符合题意．由此即可得到此直线l 的方程．【详解】设直线l 的方程为()12y k x -=+，即210kx y k -++=∵点()1,2--A 到l 的距离为1，1=，解之得43k =-， 得l 的方程为4350x y ++=．当直线与x 轴垂直时，方程为2x =-，点()1,2--A 到l 的距离为1，∴直线l 的方程为2x =-或4350x y ++=．故答案为：2x =-或4350x y ++=【点睛】本题主要考查求经过定点，且到定点的距离等于定长的直线l 方程，着重考查了直线的方程、点到直线的距离公式等知识，属于基础题．【变式1】．（2020·上海高二期末）若O 为坐标原点，P 是直线20x y -+=上的动点，则||OP 的最小值为______________.【分析】线段OP 的最小值，就是原点到已知直线的距离，根据点到直线的距离公式即可得出．【详解】解：原点到直线的距离d==故||OP【点睛】本题考查了点到直线的距离公式、转化方法，属于基础题．【变式2】．（2020·上海高二期末）已知点()4,1P,点Q的坐标(),x y满足212x y=,则点P与点Q距离的最小值为_____．【分析】先将212x y=转化为直线220x y--=,再求点P到直线220x y--=的距离即可.【详解】解: 点Q的坐标(),x y满足212x y=,则点Q在直线220x y--=上,则点P与点Q距离的最小值即为点P到直线220x y--=的距离:d===故点P与点Q故答案为:【点睛】本题考查二阶行列式的运算,考查点到直线的距离公式,是基础题.【变式3】．（2019·上海市进才中学高二期末）圆22240x y x y+-+=的圆心到直线3450x y+-=的距离等于________。
2024学年山西省吕梁育星中学化学高二下期末复习检测试题(含解析)
2024学年山西省吕梁育星中学化学高二下期末复习检测试题注意事项：1．答卷前，考生务必将自己的姓名、准考证号、考场号和座位号填写在试题卷和答题卡上。
用2B铅笔将试卷类型（B）填涂在答题卡相应位置上。
将条形码粘贴在答题卡右上角"条形码粘贴处"。
2．作答选择题时，选出每小题答案后，用2B铅笔把答题卡上对应题目选项的答案信息点涂黑；如需改动，用橡皮擦干净后，再选涂其他答案。
答案不能答在试题卷上。
3．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新答案；不准使用铅笔和涂改液。
不按以上要求作答无效。
4．考生必须保证答题卡的整洁。
考试结束后，请将本试卷和答题卡一并交回。
一、选择题（每题只有一个选项符合题意）1、四种短周期元素X、Y、Z和W在周期表中的位置如图所示，其中W元素的原子最外层电子数是内层电子数的2倍。
下列说法正确的是A．原子半径大小：W>Y>ZB．X的氢化物与Z的氢化物可以发生反应C．氧化物对应水化物的酸性：Z>Y>WD．氢化物的稳定性：Y>Z2、图A 图B 图C 图DA．除去CO中的CO2B．苯萃取碘水中的I2分出水层后的操作C．配制0.10 mol·L－1NaOH溶液D．记录滴定终点读数为12.20mL3、下列说法正确的是A．天然油脂的分子中含有酯基，属于酯类B．煤经处理变为气体燃料的过程属于物理变化C．棉、麻、丝、毛完全燃烧都只生成CO2和H2OD．可以用加热的方法分离提纯蛋白质4、当H原子和F原子沿z轴结合成HF分子时，F原子中和H原子对称性不一致的轨道是( )A．1s B．2s C．2p x D．2p zClH C表示的有机物中，能发生消去反应的共有（）5、组成和结构可用63A．10种B．16种C．20种D．25种6、下列指定反应的离子方程式正确的是（）A．金属钠和水反应：Na+2H2O=Na++2OH-+H2↑B．硫酸铵溶液和氢氧化钡溶液反应：Ba2++SO42-=BaSO4↓C．用氢氧化钠溶液吸收少量二氧化碳气体：CO2+OH-= HCO3-D．澄清石灰水与盐酸的反应 OH﹣+H+===H2O7、用固体样品配制一定物质的量浓度的溶液，需经过称量、溶解、转移溶液、定容等操作。
第八章立体几何初步综合复习题-2021-2022学年高二下学期数学人教A版(2019)必修第二册
第八章立体几何初步综合复习题一、选择题1.已知空间中不过同一点的三条直线l，m，n．则“l，m，n共面”是“l，m，n两两相交”的( )A．充分不必要条件B．必要不充分条件C．充分必要条件D．既不充分也不必要条件2.如果PA，PB，PC两两垂直，那么点P在平面ABC内的投影一定是△ABC( )A．重心B．内心C．外心D．垂心3.给出下列命题：（1）若一条直线与两条直线都相交，那么这三条直线共面；（2）若三条直线两两平行，那么这三条直线共面；（3）若直线a与直线b异面，直线b与直线c异面，那么直线a与直线c异面；（4）若直线a与直线b垂直，直线b与直线c垂直，那么直线a与直线c平行；其中正确的命题个数有( )A．0个B．1个C．2个D．3个4.如图，网格纸上小正方形的边长为1，粗线画出的是某几何体的三视图，则该几何体的体积为( )A．9πB．22π3C．28π3D．34π35.若正四棱锥的侧面积等于12√34，底面边长为6，则棱锥的高等于( )A．4B．5C．6D．76.下列四个正方体中，A，B，C为正方体所在棱的中点，则能得出平面ABC∥平面DEF的是( )A．B．C．D．7.如图，平面α∩平面β=l，A，B∈α，C∈β，C∉l，直线AB∩l=D，过A，B，C三点确定的平面为γ，则平面γ，β的交线必过( )A．点A B．点BC．点C，但不过点D D．点C和点D8.若一个四面体的四个侧面是全等的三角形，则称这样的四面体为“完美四面体”，现给出四个不同的四面体A k B k C k D k(k=1,2,3,4)，记△A k B k C k的三个内角分别为A k，B k，C k，其中一定不是“完美四面体”的为( )A．A1:B1:C1=3:5:7B．sinA2:sinB2:sinC2=3:5:7C．cosA3:cosB3:cosC3=3:5:7D．tanA4:tanB4:tanC4=3:5:7二、多选题9.下列说法正确的是( )A．一个棱锥至少有四个面B．如果四棱锥的底面是正方形，那么这个四棱锥的四条侧棱都相等C．五棱锥只有五条棱D．用与底面平行的平面去截三棱锥，得到的截面三角形和底面三角形相似10.a，b，c是空间中的三条直线，下列说法中正确的是( )A．若a∥b，b∥c，则a∥cB．若a与b相交，b与c相交，则a与c也相交C．若a，b分别在两个相交平面内，则这两条直线可能平行、相交或异面D．若a与c相交，b与c异面，则a与b异面11.在正方体ABCD−AʹBʹCʹDʹ中，过体对角线BDʹ的一个平面交AAʹ于E、交CCʹ于F，则以下结论中正确的是( )A．四边形BFDʹE一定是平行四边形B．四边形BFDʹE有可能是正方形C．四边形BFDʹE有可能是菱形D．四边形BFDʹE在底面的投影一定是正方形12.如图，在正四棱锥S−ABCD中，E，M，N分别是BC，CD，SC的中点，动点P在线段MN（不包含端点）上运动时，下列四个结论中恒成立的为( )A．EP⊥AC B．EP∥BDC．EP∥平面SBD D．EP⊥平面SAC三、填空题13.如图所示，已知多面体ABCDEFG中，AB，AC，AD两两互相垂直，平面ABC∥平面DEFG，平面BEF∥平面ADGC，AB=AD=DG=2，AC=EF=1，则该多面体的体积为．14.已知三棱锥P−ABC的侧棱PA，PB，PC两两垂直，且长度均为1，若该棱锥的四个顶点都在球O的表面上，则球O的表面积为．15.我国古代数学名著《九章算术》中将底面为矩形且有一侧棱垂直于底面的四棱锥称为“阳马”，现有一“阳马”如图所示，PA⊥平面ABCD，PA=4，AB=√3，AD=1，则该“阳马”外接球的表面积为．16.已知a，b为异面直线，且a，b所成的角为40∘，过空间一点作直线c，直线c与a，b均异面，且所成的角均为θ．若这样的直线c共有四条，则θ的取值范围为．三、解答题17.已知P是平面ABC外一点，PA⊥平面ABC，AC⊥BC，求证：PC⊥BC．18.如图，AB是⊙O的直径，PA垂直于⊙O所在的平面，C是圆周上的一点，且PA=AC，求二面角P−BC−A的大小．19.如图，已知在棱长为a的正方体A1B1C1D1−ABCD中，M，N分别是棱CD，AD的中点．求证：(1) 四边形MNA1C1是梯形；(2) ∠DNM=∠D1A1C1．20.如图，正方形ABCD所在平面与三角形CDE所在平面相交于CD，AE⊥平面CDE，且AE=1，AB=2．(1) 求证：AB⊥平面ADE；(2) 求凸多面体ABCDE的体积．21.如图，四边形ABCD是平行四边形，平面AED⊥平面ABCD，EF∥AB，AB=2，BC=EF=1，AE=√6，DE=3，∠BAD=60∘，G为BC的中点．(1) 求证：FG∥平面BED；(2) 求证：平面BED⊥平面AED；(3) 求直线EF与平面BED所成角的正弦值.22.如图，在四棱锥P−ABCD中，底面ABCD为菱形，∠BAD=60∘，Q为AD的中点，(1) 若PA=PD，求证：平面PQB⊥平面PAD；(2) 点M在线段PC上，PM=tPC，试确定实数t的值，使得PA∥平面MQB；(3) 在（2）的条件下，若平面PAD⊥平面ABCD，PA=AD=PD=2，求二面角M−BQ−C的大小．。
2012-2013学年高二下学期英语复习题(第05周)选修七Unit 3 Under the sea
2012-2013学年高二下学期英语复习题（第05周）姓名：______________ 成绩：_______________Unit3 Under the sea1. health n. __________ adj. __________ adv.2. sugar n. vt. __________ adj.3. __________ n. curious adj. __________ adv.4. __________n. weak adj. __________ v.5.__________ n. __________ vt. strong adj.6. digest vt. __________ n. __________ adj.7. benefit v.& n. __________ adj.【练习】用括号内所提供词的适当形式填空。
1). Y ou look much ________ (health) than before.2). The boy had burning ________ (curious) about what was going on.3). The government decided to take some measures to _________ (strength) the economy.4). Fresh air is ________ (benefit) to one’ s health.5). Mike was the ________ (strength) boy in his class.6). It’ s that ________ (sugar) smile of hi s that I can’ t bear - it makes me want to puke!7). It’ s important to know your own strengths and ________ (weak).8). V egetables are usually cooked to aid ________ (digest).1. disability n.无能；残疾disabled adj.伤残的able adj.能干的；能够的2. ambition n.野心，雄心ambitious adj.有雄心的，野心勃勃的3.beneficial adj.有益的benefit v.&n.受益；利益，好处4. independent adj.独立的independence n.独立depend v.依靠，依赖5.encouragement n.鼓励encourage v.鼓励courage n.勇气，精神【练习】根据句子结构，用括号内所提供词的适当形式填空1)The ______ girl swims well in spite of her _______.(disable)2) Robert is a very _______ man and one of his ______ is to travel in Antarctica. (ambition)3) If you want to be a _______, you should work hard at ______ and care for ______ situations. (politics)4) It is known to all that fresh air is _______ to our health and the new park ______ us all, so we should keep it clean.(benefit)5) The boy who used to ______on his parents now wants the ______ from them and is learning to be _______.(depend)6) Praise acts as an ______ to the players, and therefore they will feel ______ and get the _______to continue and improve their performance.(encourage)7) My brother ______ from a well-known American university. My parents attended his _______ ceremony yesterday.(graduate)8) When someone ______ others on their success, he or she usually says “_______”.(congratulate)9) This concert was _______ by a famous _______ from V ienna. (conduct)一、语言要点I 单元要点预览（旨在让同学整体了解本单元要点）II 词语辨析 (旨在提供完形填空所需材料)1). shore/seaside/beach/coast/bank n.海边，海岸【练习】选择shore/seaside/beach/coast 或bank 并用其适当的形式填空 1) Last summer we spent all our holiday at the _______. 2) I enjoy lying on the _______ with sunglasses in the sun.3) It’s dangerous for children to play on the _______ of the river. 4) We often see many ships on the sea about several miles off the ______. 5) The land is barren on the east ______.2). flee/escape v.逃避, 逃跑, 逃走【练习】选择flee 或escape ，并用其适当的形式填空 1) The enemy ______ in disorder.2) Citizens were forced to ______ the besieged city. 3) He narrowly _________ death. 3) deep/deeply adv.深深地；【练习】选择deep 或deeply 并用其适当的形式填空1) The police found out the lost child _______ in the woods at last. 2) All of us were _______ shocked at the bad news.III 词性变化 （旨在提供语法填空所需材料）【练习】根据句子结构，用括号内所提供词的适当形式填空1) The lake is over 20 meters in _____ so we were all moved ______ by the man who dived _______ into the lake to save the little boy. (deep)2) I ____ remember the girl dressed in ______ color he drew in the exhibition.(vivid)3) Anyone who launches a war is ______ and is _______ by people who love peace all around the world. (awe) 4) The _______ of energy will help us research the way to save and _______ the energy. (conserve) 5) Though the soup is _______, I’ve lost my sense of ______ and it ____just like ______water.(taste)词汇 部分词语 辨析1.shore/seaside/beach/coast/bank2.flee/escape3. deep/deeply 词形 变化1. _________ n. _________ adv. deep adj.& adv.2. conserve v. _________ v.3.vivid adj._________ adv. 4. _________ adj. _________ n. awe vt.5. _________ adj.taste v.n_________ adj. 重点 单词 1. annual adj. witness n. accommodation n. abandon vt. 2. reflect vt. aware adj. scare vt. 重点 词组sort out help out throw oneself out of upside down重点句型1. It was a time when the killer whales, or “killers” as they were then called, helped the whalers catch the baleen whales that were on their annual migration.2. I had already heard that George didn’t like being kept waiting, so even though I didn’t have theright clothes on, raced after him. 3. I’m sitting in the warm night air with a cold drink in my hand and reflect ing on the day-a day of pure magic!重点语法 被动语态（II ）(见语法专题)VI 重点句子（旨在提供句子结构等所需材料）1. It was a time when the killer whales, or “killers” as they were th en called, helped the whalers catch the baleen whales that were on their annual migration.1) It was a time when motorcars were rare.2) It was a time when she could not bear the pain and wanted to kill herself.[练习] 汉译英1)曾经没人能理解我的计划和雄心。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
两个计数原理
一、选择题
1．把4张同样的参观券分给5个代表，每人最多分一张，参观券全部分完，则不同的分法共有（）
A. 120
B. 1024种
C. 625种
D. 5种
2．3科老师都布置了作业，在同一时刻4名学生都做作业的可能情况有（）
A. 43种
B. 34种
C. 4×3×2种
D. 1×2×3种
3．将甲、乙、丙、丁四名学生分配到三个不同的班，每个班至少一名，则不同分法的种数为（）
A. 18
B. 24
C. 36
D. 72
4．某2017年夏令营组织5名营业员参观北京大学、清华大学等五所大学，要求每人任选一所大学参观，则有且只有两个人选择北京大学的不同方案共有（）
A. 240种
B. 480种
C. 640种
D. 1280种
5．5位同学报名参加两个课外活动小组，每位同学限报其中的一个小组，则不同的报名方法共有（）
A. 10种
B. 20种
C. 25种
D. 32种
6．张、王两家夫妇各带1个小孩一起到动物园游玩，购票后排队依次入园，为安全起见，首尾一定要排两位大人，另外，两个小孩一定要排在一起，则这6人的入园顺序排法种数共有( )
A. 144
B. 124
C. 72
D. 36
7．某人有3个电子邮箱，他要发5封不同的电子邮件，则不同的发送方法有（）
A. 8种
B. 15种
C. 种
D. 种
8．完成一项工作，有两种方法，有5个人只会用第一种方法，另外有4个人只会用第二种方法，从这9个人中选1人完成这项工作，一共有多少种选法？
A. 20
B. 9
C. 5
D. 4
9．4名同学分别报名参加数、理、化竞赛，每人限报其中的1科，不同的报名方法种数（）A. 24 B. 4 C. D.
10．有不同颜色的四件上衣与不同颜色的三条长裤，如果一条长裤与一件上衣配成一套，则不同的配法种数()
A. 7
B. 64
C. 12
D. 81
11．甲组有5名男同学，3名女同学；乙组有6名男同学、2名女同学。
若从甲、乙两组中各选出2名同学，则选出的4人中恰有1名女同学的不同选法共有( )
A. 150种
B. 180种
C. 300种
D. 345种
12．大数据时代出现了滴滴打车服务，二胎政策的放开使得家庭中有两个小孩的现象普遍存在，某城市关系要好的四个家庭各有两个小孩共8人，准备使用滴滴打车软件，分乘甲、乙两辆汽车出去游玩，每车限坐4名（乘同一辆车的4名小孩不考虑位置），其中户家庭的孪生姐妹需乘同一辆车，则乘坐甲车的4名小孩恰有2名来自于同一个家庭的乘坐方式共有A. 种 B. 种 C. 种 D. 种
13．8把椅子摆成一排，4人随机就座，任何两人不相邻的坐法种数为（）
A. 144
B. 120
C. 72
D. 24
二、解答题
14．现有5幅不同的国画，2幅不同的油画，7幅不同的水彩画.
（1）从中任选一幅画布置房间，有几种不同的选法？
（2）从这些国画、油画、水彩画中各选一幅布置房间，有几种不同的选法？
（3）从这些画中选出两幅不同种类的画布置房间，有几种不同的选法？
15．个人排成一排，在下列情况下，各有多少种不同排法？
（1）甲不排头，也不排尾，
（2）甲、乙、丙三人必须在一起
（3）甲、乙之间有且只有两人，
16．用0，1，2，3，4，5可以组成多少个无重复数字的比2 000大的四位偶数？
三、填空题
17．5位同学报名参加两个课外活动小组，每位同学限报其中一个小组，则不同的报名方法共有_______种.
18．6名同学争夺3项冠军，获得冠军的可能性有种。