
Liu Min is an English teacher. These days, herfamily are experiencing a different life of working and studying. They get upand do morning exercises at 6:30 in the living room. After breakfast, theystart their work and study. Her husband turns on his computer in the study (书房), reading his e-mails andmaking a list of today’s work.

In ourdaily lives, we are often given some boring or tiring tasks. What’s in yourmind when your mom tells you to clean the floor? Have you ever wanted tocomplain(抱怨)? I think most people have.

Apassenger told an air hostess(空姐)that he needed a cup of water to take hismedicine when the plane just took off. She told him that she would bring himthe ___11___ in ten minutes.

The boy named Li Banghua is from Hefei. AnhuiProvince. He made the plane completely by himself. The plane is 0.6 meterswide, has a wingspan (翼展) of 4.4 meters and weighs about 40 kilograms.According to a local report, Li just finished his high-school entrance exam ayear ago and got good grades.

Parents and children often face the challengesof money. Common topics include setting pocket money, learning to save, anddeciding to buy expensive things. The goal of most parents is to teach theirkids how to deal with money wisely. The goal of most kids is getting money tospend. How can families achieve these goals?

Every month, Julia and her cousins would go forthe big family meal at their grandparents’ house. On each visit, their grandpawould give them a few coins. Then all the children would run off to buy sweets.One day, he gathered the children together.

Du, 23,is a student from Shanghai University. He won third place at the ninth IOIO (国际折纸奥林匹克) in February this year. A total of 803 competitors from 59countries and areas took part in this year’s event.

At 9 a.m. , he drives to primary schools and middle schools in Xi’an, ShaanxiProvince, to teach students about Shaanxi kuaiban. It is a traditional Chineseform of storytelling to the rhythm(节奏) of bamboo clappers(响板), whichthe art form is named after. Sometimes, he helps students prepare forcompetitions. Usually, his classes run until about 6. p.m. , and then hereturns home to prepare classes for the next day.

Flying kites Kites have quite a long history. The earliest kites were made ofwood, instead of paper. Nowadays, the three most famous kites are the Beijingkite, Tianjin kite, and Weifang kite. And they are quite different from eachother. For example, the swallow-shaped kite is a well-known Beijing style.

ThreeRiver-Source National Park on the Qinghai-TibetPlateau(青藏高原),is the largest national park in China. Because it is home to the sources of theYangtze, Yellow and Lancang rivers, people call it “China’s water tower”.

Antarctica is a continent (大陆) of ice. There is hardlyany rain in Antarctica, so the Antarctic Desert becomes the driest desert inthe world. It is also the world’s largest desert by area.

When youand your friends turn to each other to talk about problems or troubles, yougive each other advice and help. One important thing of our growth is to makedecisions to help our friends and learn to support each other. This requires usto learn what it means to help friends and how to help them in right ways.

Everyone knows how similar chimpanzees (黑猩猩)are to humans. So it’s no surprise that their greetings are also close to ours.The most common ways of greeting between chimpanzees are hand touching andhugging. Sometimes they also kiss each other. Some chimpanzees can even learnsimple sign language.

Raden Roro Hendarti, nearly 50 years old, is alibrarian in Muntang village. She started a “trash library”, hoping to makechildren read more as well as make them realize the importance of environmentprotection. Each weekday, Raden puts all kinds of books on the back of herthree-wheeler (三轮车)and rides to Muntang village. There, children line up to exchange plastic cups,bags and other trash for books from Raden’s mobile library. After finishing theexchange, Raden carries back all the trash.

Each ofthem has their own experience- two people with synesthesia may both “feel”music, but they almost never feel the music in the same way. For example, onemay feel the music of the violin lightly brushing his face; the other may feelit on her ankle (脚踝). And one’s experience of synesthesia is alwaysthe same. If they see the number 5 in the color blue, then 5 is blue every timethey see it.

Slowlybut surely, Amy and her grandparents were making progress. Boxes of all sizeswere placed on top of each other throughout the house. Amy’s grandparents hadlived in the house for years and they had collected many things.

As thegovernment encourages the renaissance (复兴) of traditional culture,Hanfu is getting more and more popular with the teenagers. Every year, we canenjoy different Hanfu shows around the cities. And now quite a few Hanfu clubshave been set up in universities. Members usually wear Hanfu at theirgraduation ceremonies or during holidays. Some even wear Hanfu on regular days,too. And these fans created a special day—China Haniu Day to celebratetraditional Chinese clothing. It falls on the third day of the third month inChinese lunar calendar (阴历).

一、情境导学我国著名数学家吴文俊先生在《数学教育现代化问题》中指出:“数学研究数量关系与空间形式,简单讲就是形与数,欧几里得几何体系的特点是排除了数量关系,对于研究空间形式,你要真正的‘腾飞’,不通过数量关系,我想不出有什么好的办法…….”吴文俊先生明确地指出中学几何的“腾飞”是“数量化”,也就是坐标系的引入,使得几何问题“代数化”,为了使得空间几何“代数化”,我们引入了坐标及其运算.二、探究新知一、空间直角坐标系与坐标表示1.空间直角坐标系在空间选定一点O和一个单位正交基底{i,j,k},以点O为原点,分别以i,j,k的方向为正方向、以它们的长为单位长度建立三条数轴:x轴、y轴、z轴,它们都叫做坐标轴.这时我们就建立了一个空间直角坐标系Oxyz,O叫做原点,i,j,k都叫做坐标向量,通过每两个坐标轴的平面叫做坐标平面,分别称为Oxy平面,Oyz平面,Ozx平面.

本节课选自《2019人教A版高中数学选择性必修第一册》第二章《直线和圆的方程》,本节课主要学习抛物线及其标准方程在经历了椭圆和双曲线的学习后再学习抛物线,是在学生原有认知的基础上从几何与代数两 个角度去认识抛物线.教材在抛物线的定义这个内容的安排上是:先从直观上认识抛物线,再从画法中提炼出抛物线的几何特征,由此抽象概括出抛物线的定义,最后是抛物线定义的简单应用.这样的安排不仅体现出《课程标准》中要求通过丰富的实例展开教学的理念,而且符合学生从具体到抽象的认知规律,有利于学生对概念的学习和理解.坐标法的教学贯穿了整个“圆锥曲线方程”一章,是学生应重点掌握的基本数学方法 运动变化和对立统一的思想观点在这节知识中得到了突出体现,我们必须充分利用好这部分教材进行教学

∵在△EFP中,|EF|=2c,EF上的高为点P的纵坐标,∴S△EFP=4/3c2=12,∴c=3,即P点坐标为(5,4).由两点间的距离公式|PE|=√("(" 5+3")" ^2+4^2 )=4√5,|PF|=√("(" 5"-" 3")" ^2+4^2 )=2√5,∴a=√5.又b2=c2-a2=4,故所求双曲线的方程为x^2/5-y^2/4=1.5.求适合下列条件的双曲线的标准方程.(1)两个焦点的坐标分别是(-5,0),(5,0),双曲线上的点与两焦点的距离之差的绝对值等于8;(2)以椭圆x^2/8+y^2/5=1长轴的端点为焦点,且经过点(3,√10);(3)a=b,经过点(3,-1).解:(1)由双曲线的定义知,2a=8,所以a=4,又知焦点在x轴上,且c=5,所以b2=c2-a2=25-16=9,所以双曲线的标准方程为x^2/16-y^2/9=1.(2)由题意得,双曲线的焦点在x轴上,且c=2√2.设双曲线的标准方程为x^2/a^2 -y^2/b^2 =1(a>0,b>0),则有a2+b2=c2=8,9/a^2 -10/b^2 =1,解得a2=3,b2=5.故所求双曲线的标准方程为x^2/3-y^2/5=1.(3)当焦点在x轴上时,可设双曲线方程为x2-y2=a2,将点(3,-1)代入,得32-(-1)2=a2,所以a2=b2=8.因此,所求的双曲线的标准方程为x^2/8-y^2/8=1.当焦点在y轴上时,可设双曲线方程为y2-x2=a2,将点(3,-1)代入,得(-1)2-32=a2,a2=-8,不可能,所以焦点不可能在y轴上.综上,所求双曲线的标准方程为x^2/8-y^2/8=1.
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