杨浦初中补习班杨浦初中培训机构新王牌数学资料6

杨浦新王牌新王牌初中数学靳T老师知识点汇总一线段、角1）经过两点有一条直线，并且只有一条直线。

2）两点之间线段最短二相交线、平行线1）经过直线外或直线上一点，有一条而且只有一条直线与已知直线垂直2）经过已知直线外的一点，有一条直线而且只有一条直线与已知直线平行三平行四边形平行四边形两组对边分别平行平行四边形的对角相等1）平行四边形的性质平行四边形的对边相等平行四边形的对角线互相平分平行四边形是中心对称图形，两条对角线的交点是对称中心两组对边分别平行的四边形平行四边形两组对边分别相等的四边形是平行四边形2）平行四边形的判定一组对边分别相等的四边形是平行四边形对角线互相平分的四边形是平行四边形两组对角分别相等的四边形是平行四边形四菱形、矩形、正方形（具有平行四边形所有的性质）矩形的性质矩形的四个角都是直角矩形的对角线相等矩形的判定有三个角是直角的四边形是矩形对角线相等的平行四边形是矩形菱形的四条边都相等菱形的性质菱形的对角线互相垂直，且每一条对角线平分一组对角菱形的面积等于它的两条对角线的积的一半菱形的判定四条边相等的四边形是菱形对角线互相垂直的平行四边形是菱形正方形四个角是直角正方形的性质正方形的对角线相等且互相垂直平分正方形四条边相等正方形每一条对角线平分一组对角正方形的判定有一个角是直角的菱形是正方形有一组邻边相等的矩形是正方形菱形、矩形、正方形是中心对称图形，对称中心是对角线的交点五梯形等腰梯形的同一底边上的两个内角相等等腰梯形的性质等腰梯形是轴对称图形，经过两底中点的直线是它的对称轴等腰梯形的两条对角线相等等腰梯形的判定：在同一条底边上的两个内角相等的梯形是等腰梯形对角线相等的梯形是等腰梯形梯形的中位线：梯形的中位线平行于两底，并且等于两底和的一半梯形的面积：中位线×高（上底+下底）×高÷2六三角形①三角形的概念1）三角形的三个内角和等于180°2）三角形的一个外角等于和它不相邻的两个内角和3）三角形的一个外角大于任何一个和它不相邻的内角4）三角形的任何两边的和大于第三边②等腰三角形的性质：(1)等腰三角形的两腰相等(2)等腰三角形的两个底角相等. (等边对等角)(3)等腰三角形的顶角平分线、底边上的中线、底边上的高互相重合(等腰三角形三线合一.)(4)等腰三角形是轴对称图形，顶角平分线（底边上的中线、底边上的高）所在的直线是它的对称轴 .③等腰三角形的判定:(1)有两条边相等的三角形是等腰三角形.(定义)(2)有两个角相等的三角形是等腰三角形.(等角对等边)④等边三角形的性质:(1)等边三角形的三条边都相等.(2)等边三角形的三个内角都相等，并且每一个内角都等于60°(3)等边三角形是轴对称图形，有三条对称轴.⑤等边三角形的判定:(1)有三条边相等的三角形是等边三角形.(定义)(2)三个角都相等的三角形是等边三角形.(3)有一个角是60°的等腰三角形是等边三角形⑥直角三角形的性质:(1)直角三角形的两个锐角互余.(2)直角三角形斜边上的中线等于斜边的一半.(3)在直角三角形中，30°角所对的直角边等于斜边的一半.(4)在直角三角形中，如果一条直角边等于斜边的一半，那么这条直角边所对的锐角等于30° (5)勾股定理:直角三角形两条直角边的平方和等于斜边的平方.⑦直角三角形的判定:(1)有一个角是直角的三角形是直角三角形.(定义)(2)较小两边的平方和等于较大边的平方的三角形是直角三角形.(勾股定理的逆定理) 七 相似三角形 ①比例线段，若dcb a =（或a ∶b =c ∶d ），则四条线段a 、b 、c 、d 叫做比例线段. 比例基本性质：若dcb a =，则ad =bc .在比例中运用设k 法.②相似多边形，对应边成比例，对应角相等.）③相似三角形的相似比（当k =1时,得特殊的相似三角形，称为全等三角形）. ④相似三角形的判定定理：(1)如果一个三角形的两角分别与另一个三角形的两角对应相等，那么两个三角形相似；(2)如果一个三角形的两边分别与另一个三角形的两边对应成比例，并且夹角对应相等，那么两个三角形相似；(3)如果一个三角形的三条边与另一个三角形的三条边对应成比例，那么两个三角形相似； (4)如果两个直角三角形的斜边和一条直角边对应成比例，那么这两个直角三角形相似． ⑤相似三角形的性质定理：(1)若两个三角形相似，则这两个三角形的对应边成比例，对应角相等.(2)若两个三角形相似，它们对应中线的比，角平分线的比，高的比都等于相似比. (3)若两个三角形相似，它们周长比等于相似比，面积比等于相似比的平方. ⑥重心：三角形的重心与顶点的距离等于它与对边中点的距离的两倍八 圆1、 圆的定义：圆是平面上到定点的距离等于定长的点的集合。

上海杨浦区最好的补习班新王牌初一数学李G老师拓展提高work Information Technology Company.2020YEAR杨浦新王牌初一数学期中复习题型一：1. 下列语句正确的是( )A. 5-是5的一个平方根；B. 400万有7个有效数字；C. 近似数12.8和12.80表示的意义是相同的；D. 一个数的平方根与其立方根相同，则这个数是1.2. 下列语句中错误的是（ ）A.数轴上的每一个点都有一个实数与它对应；B.0.087用科学计数法可表示为2107.8-⨯；C.据报道：2007年2月18日起，整存整取的三年期定期存款的年利率为3.96%，其中3.96% 这个数是近似数；D.据统计某校7班有45名学生，其中45这个数是准确数.3．下列说法正确的是……………………………………………………（ ）(A) －81平方根是－9; (B)81的平方根是±9; (C)x x x 22=+; (D)521+-a 一定是负数.4. 一个自然数的正的平方根为m ，则下一个自然数的正的平方根为( ) A.1+m ; B.12+m ; C.m+1； D;12+m5. 下列说法正确的是（ ）A.如果两个角相等，那么这两个角是对顶角；B.经过一点有且只有一条直线与已知直线平行；C.如果两条直线被第三条直线所截，那么内错角相等；D.连接直线外一点与直线上各点的所有线段中，垂线段最短.6. 下列说法正确的是（ ）A. 一对同旁内角的平分线互相垂直；B. 垂直于同一条直线的两条直线互相垂直；C. 邻补角的平分线互相垂直；D. 过一点至少有一条直线与已知直线垂直.7. 下列结论正确的是（ ）A.过一点有且只有一条直线与已知直线平行；B.平行于同一条直线的两条直线平行；C.两条直线被第三条直线所截，同位角相等；D.不相交的两条直线必平行.8. 如图，以数轴的单位长度为边作一个正方形，以数轴的原点为圆心，正方形对角线长为半径画弧，交数轴正半轴于点A ，则点A 表示的数是（ ）A. 211； B. 1.4； C.3； D. 29. 如图，下列判断： ①∠A 与∠1是同位角；②∠A 与∠B 是同旁内角；③∠4与∠1是内错角；④ ∠1与∠3是同位角. 其中正确的个数是（ ）A. 4个；B. 3个；C. 2个；D. 1个10. 如图，图中同旁内角的对数是（）A.2对；B.3对；C.4对；D.5对11. 如图所示，把一个长方形纸片沿EF折叠后，点D、C分别落在'D、'C的位置，若∠EFB=700，则'∠等于（）AEDA.700B.650C.500D.400题型二：1.2)9(-的平方根为___________2.如果实数b在数轴上对应的点到12b= ．3.若m ，小数部分是n ，则()3m m += ．4. 如果264a =，那么13a-= ．5. 21.35=213.5=，则x ：y = ．6. 已知数轴上点A 到原点的距离为1，那么在数轴上到点A 的距离为3的点所表示的数有_________个；7.20y +=，则x y += .8. 近似数510008.2⨯精确到______位，它有_____个有效数字.9. 已知()()811=--+-b a b a ，则_______=-b a .10. 已知a a =3，b b =，c c =3，则______=++c b a11. 若732.13=，则__________30000=.12. 若01.5≈a ，则a 的取值范围为________.13. 若111+-+-=x x y ，则________20102010=+y x .14. 计算：._________5757312121312121=⎪⎪⎭⎫⎝⎛+⎪⎪⎭⎫ ⎝⎛-15. 若两条直线平行，则一对同旁内角的平分线互相 ．16. 如图，写出图中∠A 所有的内错角：___________________.17. 如图，正方形ABCD 的面积为5，正方形BEFG 的面积为4，那么△GCE 的面积是___.18. 如图，把矩形ABCD 沿EF 进行翻折，若150∠=，则AEF ∠=______度．19. 如图，把△ABC 纸片沿DE 折叠，点点A 落在四边形BCDE 内部时，则∠A 、∠1、∠2之间的数量关系是________.20. 观察：52252458522=⨯==-；1033103910271033=⨯==-； 猜想：2655-=__________;并通过类似的计算验证你的猜想. 21. 如图，AD ∥EF ∥BC ，AC ∥MF ，与∠FMB 相等的角有______个.1FE D CB A （第18题22. 按虚线剪去长方形纸片相邻的两个角，并使∠1=1300，AB⊥BC，∠2=______0.23. 如图：AB∥CD，则：∠1+∠2+∠3+∠4的度数为__________.24.如图，m∥n，若过点P作DP∥m，则∠1、∠2、∠3之间的数量关系为__________25. 如图，若过点P、2P作直线m的平行线，则∠1、∠2、∠3、∠4间的数量关系是1_______.26. 如图，m∥n，则∠1、∠2、∠3、∠4、∠5间的数量关系是_______.题型三：1. 利用幂的运算性质计算：662284÷⨯2. 利用幂的运算法则计算：4648832÷⨯.3. 已知：51=+x x ，求x x 1-的值.4. 已知a 、b 为实数，且满足233+-+-=b b a ，求b a ab ab +-⋅1的值.5. 如图，已知AB ∥CD ，分别写出下面四个图形中∠APC 和∠PAB 、∠PCD 的数量关系，再请你从所写出的四个数量关系中任选一个，说明该数量关系的正确性.数量关系：（1）____________；（2）______________；（3）____________；（4）_______________________.选择：______________说明理由：6. 如图，已知AD ∥BC.（1）找出图中所有面积相等的三角形，并选择其中一对说明理由；（2）如果BE ⊥AC ，CF ⊥BD ，垂足分别为E 、F ，43 BD AC ，求CF BE 的值.（直接写出答案）7. 已知PE ∥BA ，PE 交BC 于E ；PF ∥BC ，PF 交BA 于F ，PH ⊥BA ，垂足为H（1）如图：若∠FPH=430，则∠ABC=______0（2）若∠ABC=720，则∠FPH=______0（3）如果∠ABC 是一个钝角，那么点F 和点B 在点H 的______（填“同”或“异”）（4）当∠ABC=1500，BE=BF=3cm 时，画出图形并求出∠FPH 的大小.8. 先阅读下列的解答过程，然后再解答; 形如n m 2±的化简，只要我们找到两个正数a 、b ，使m b a =+，n ab =，使得()()m b a =+22，n b a =⋅，那么便有：()()b a b a b a n m >±=±=±22 例如：化简347+ 解：首先把347+化为1227+，这里m=7，n=12，由于4+3=7,4×3=12 即()()73422=+，1234=⋅所以347+=1227+=()32342+=+ （1）填空：_________324=-，_________549=+（2）化简：15419-9. 观察下列各式及其验证过程： 验证：322322+=； 验证：()()322122122122223232222233+=-+-=-+-==； 验证：833833+=； 验证：()()833133133133338383322233+=-+-=-+-==. （1）按照上述两个等式及其验证过程的基本思路，猜想1544的变形结果并进行验证；（2）针对上述各式反映的规律，写出用n（n为任意自然数，且n》2）表示的等式，并给出证明.11。

杨浦新王牌小班辅导教学设计教案the Indians smoking.Soon the dried leaves were sent to Europe where smoking began to catch on(变得流行).In the late 1800s, the Turks(土耳其人) made cigarettes popular.Cigarette smoking damages the lungs(肺) and therefore affects breathing and causes the heart to beat faster and increases the breathing rate.Smoking cigarettes is dangerous.The US Public Health Service declared(声明) that cigarette smoking is the cause of lung cancer(癌症)and several other deadly diseases(疾病).The US government now requires that each package of cigarettes has a special warning about the dangers of smoking.Answer the following question1.Where was tobacco first grown?________________________________________2.When did cigarettes become popular?________________________________________3.What disease is caused by cigarette smoking?________________________________________4.Who put the warning on the packages of cigarettes in America?________________________________________5.What’s the passage mainly about?________________________________________Once there lived a man in a town.He always l__1_____a lot of things,so his wife always had to say to him,’Remember this.’One day he went on a long j___2____alone.Before he went out,his wife said,’Now you have all these things.Take care of them.’He went to the station,b___3_______a ticket and went on the train with i__4____.About an hour later,the conductor came to the man and said,’Will you please s__5______me your ticket?’Theman looked for his ticket in all his pockets,but he couldn’t f___6____it.1．________ 2._________3._________4.__________5._________ 6._________参考答案：The tobacco was first grown in AmericaIn the late 1800s,cigarettes became popularLung cancer is caused by cigarette smokingThe tobacco companies put the warning on the package of cigarettes in America. The passage is mainly about the dangers of smoking cigarettes.lost journey bought it show find参考答案1.When he had lunch.2.By car./He drove his car.3.He didn’t see the red lights.4.Yes,he did.5.Any acceptable answers.since have went Japanese for would。

知识框架
（1）英国科学家牛顿在他的《普通算术》一书中，有一道关于牛在牧场上吃草的问题，即牛在牧场上吃草，牧场上的草在不断的、均匀的生长．后人把这类问题称为牛吃草问题或叫做“牛顿问题”．
（2）“牛吃草”问题主要涉及三个量：草的数量、牛的头数、时间．难点在于随着时间的增长，草也在按不变的速度均匀生长，所以草的总量不定．“牛吃草”问题是小学应用题中的难点．
（3）解“牛吃草”问题的主要依据：
草的每天生长量不变；
每头牛每天的食草量不变；
草的总量=草场原有的草量+新生的草量，其中草场原有的草量是一个固定值
新生的草量=每天生长量⨯天数．
（4）同一片牧场中的“牛吃草”问题，一般的解法可总结为：
⑴设定1头牛1天吃草量为“1”；
⑵草的生长速度=(对应牛的头数⨯较多天数-对应牛的头数⨯较少天数)÷(较多天数-较少天数)；
⑶原来的草量=对应牛的头数⨯吃的天数-草的生长速度⨯吃的天数；
⑷吃的天数=原来的草量÷(牛的头数-草的生长速度)；
⑸牛的头数=原来的草量÷吃的天数+草的生长速度．
（5）“牛吃草”问题有很多的变例，像抽水问题、检票口检票问题等等，只有理解了“牛吃草”问题的本质和解题思路，才能以不变应万变，轻松解决此类问题．
重难点。

第六讲 不等式及不等式组例1：解不等式组：⎪⎪⎩⎪⎪⎨⎧--≤++<-+232312223125x x x x 例2：⎪⎩⎪⎨⎧-+≤-+≤-3253341445x x x x x例3：解不等式组：⎪⎪⎩⎪⎪⎨⎧-+>--+≥-45833277)1(3425x x x x 例4：求不等式组⎪⎪⎩⎪⎪⎨⎧<-≥--221322x x x 的整数解.例5：若不等式组⎩⎨⎧->-<+)3(4121x x a x 的解集为一切负数，求a 的值.例6：满足31222-≥+x x 的x 的值中，绝对值不超过9的整数之和是多少？例7：一件商品售价为120元，如果按售价的九折出售，获利不超过百分之二十；如果按售价的七折出售，那么出现亏本，求商品成本价的范围。

例8：如果关于x 的不等式组⎩⎨⎧->-->63332a x x x 的整数解只有2，求a 的取值范围。

课后练习：练习1：解不等式组 ⎩⎨⎧->>-545)1(2x x 练习2：解不等式 2)23(210-<-<-x练习3：解不等式组⎪⎩⎪⎨⎧≤--≥+5)4(31)32(2)2(3x x x 练习4：解不等式组 ⎪⎪⎩⎪⎪⎨⎧--≤++<-+332312223125x x x x练习5：求使方程组⎩⎨⎧+=++=+36542m y x m y x 的解x 、y 都是正数的m 的取值范围。

练习6：求不等式组⎪⎪⎩⎪⎪⎨⎧≥-+<-+<-231)12(4)13(24322x x x x x x 的整数解。

练习:7：如果关于x 的不等式组⎩⎨⎧->->-x x a x 313)1(202的解集是a x 2>，求a 的取值范围。

练习8：某单位组织旅游，定了若干条船（不超过10条），如果每条游船坐4人，那么还余19人没安排；如果每条游船坐6人，那么有一条船人没坐满，问该单位定了多少条游船？。

杨浦补习班新王牌教学资料预初讲义Step1知识检查默写和测试另附1.玩的开心，过得愉快（三种）2.为......做准备（两种）3.我们明天去野餐吧（六种）4.足够的钱5.寒冷的天气6.结冰的水7.保持安静8.这个标志什么意思？9.让某物留在某地10.追赶兔子11.在公交站台等我12.在入口处13.在左边14.禁止吸烟15.乘公共汽车去上学16.离......远17.半小时的步行18.游客19.邀请函20.到达Step2.作业点评详见上次讲义Step3同步知识学习Module 3 Unit 10 Healthy eating 单元重点1, 词性转换Health n. --------healthy a. -------------unhealthy a.---------------healthily ad. Usual a. ---------usually ad. -----------unusual a.Eat v. -----------eating n.Favor n.----------favorite a. suggest v. ----------suggestion n.Healthy diets food pyramidShow sb sth =show sth to sbShow me your photos= show your photos to meShow sb around sp show her around our school Live in the city in the countrysideHave an unhealthy diet work in the gardenDo some exercises = have sports do some exercisesHave lunch with sb stay with sbFor a few weeks become fit and healthy One…the other…as+adj/adv+asImprove eating habit drink a lot of waterTake turns do a quizGet right/ wrong should do /should not doToo much spicy food each correct answerHave some burgers for lunch go to bedWash your hands1)we need a little sugar ----------how much sugar do you want?2)We need plenty of vegetables ---------how many vegetables do you need?How much 提问不可数名词数量how many提问可数名词数量3)Your diet is healthier than my diet = My diet is not as healthy as your dietTom is taller than Jack= Jack isn’t as tall as TomJohn is fatter than Ben=4)形容词比较级，最高级的构成直接加--er –estSoft softer softest / few fewer fewest 以e结尾加---r, ----estLarge larger largest重读闭音节双写最后一个字母，加---er, ----estThin Thinner Thinnest / wet wetter wettestHot hotter hottest/ red redder reddestFat fatter fattest / big bigger biggest辅音加y 结尾的双音节，去y加---ier,---iestPretty prettier prettiest / healthy healthier healthiest多音节在前加---more --- mostmodern more modern most moderninteresting more interesting most interestingbeautiful more beautiful most beautiful5)副词比较级，最高级的构成Slowly more slowly most slowlyQuickly more quickly most quickly6)不规则比较级，最高级的构成原级比较级最高级Good/well better bestBad/badly worse worstLittle less leastFar farther/ further farthest/ furthestMany/much more mostOld older/elder oldest/eldest（四）用法原级So good too bad very clear quite importantRather difficult old enough as often as not as/so easy as比较级Bigger than much better far more useful even earlier Still greater a little longer better and betterMore and more important the earlier you get up, the healthier you are Who works harder, ben or kitty?最高级The fastest in our class the tallest of the threeThe second longest river one of the longest rivers among the best filmsWhich is the biggest ,the sun, the earth , or the moon?形容词副词同形Early fast hard late六年级(上)6AU10练习卷一姓名一Rewrite the sentences as required (根据要求改写句子)1．Selling flowers can make a lot of money.（改为否定句）Selling flowers make money.2.I have bought a little chocolate ice-cream. （划线提问）chocolate ice-cream you ?3.The 30th Olympic Games will be hosted in London in 2012. （划线提问）he 30th Olympic Games be hosted in 2012?4.In Canada there are a lot of beautiful mountains and lakes. (保持原句意思)Canada a lot of beautiful mountains and lakes.5. My uncle’s diet is healthier than your aunt’s. (改为一般疑问句)your uncle’s diet than your aunt’s?6. He likes dumplings best. (同义句转换)is dumplings?二Fill in the blanks with the given words in their proper forms.7.Your diet is (little) healthier than my diet.三Choose the right words or expressions to complete the sentence8. Ken is (as healthy as, a little) his brother.9. I came to school (as healthy as, a little) earlier this morning.10. (What; How) did you have for lunch yesterday?11. Eating too much salt is not (healthy; unhealthy).四Choose the best answer. (选择最恰当的答案)( ) 12. There is rice left. Lets buy some.A. someB. anyC. a littleD. little( ) 13. I don’t like rice dumplings with meat. I like sweet ones.A. saltB. saltyC. healthD. healthy( )14. –Would you like to have dinner with me tonight?-- .A. Yes, I’d love toB. Thank you all the sameC. You’re welcomeD. That’s allright( ) 15. Listening is as as speaking in language learningA. importantB. more importantC. most importantD. the most important( ) 16. How many and how much do you need?A. beef; orangeB. orange; waterC. juice; milkD. oranges; fish( ) 17. –May I have hamburgers?--I’m sorry. We don’t have hamburgers here.A. some; someB. any; someC. some; anyD. any; any( )18. –Is this your shoe?--Yes, it is, but where is ?A. the othersB. other oneC. anotherD. the other one五Cloze test (完型填空)AWho Are You?(Mary is six years old. It's nine o'clock at night. Mary is going home.)Mary is w 19 home this evening. Suddenly she f 20 a girl is behind her. She runs, the girl runs. She stops, the girl stops, too. "Who are you? What are you doing?" Mary asks. There is no a 21 . Mary begins to run. "Don't run a 22 me. Go away." The girl is still after her. She shouts. "Help! Help!" Mary runs back home."Dad, h 23 me, there is a girl behind me. You see." Father takes a look and smiles."Mary, don't w 24 . The girl is you. That is your shadow."19. 20 21.22. 23. 24.BBob goes to a n 25 school. One day he c 26 back . "Bob, do you like your new teacher?" his mother asks."I don't like her, Mother. B 27 first she says that three and three is six, and then she says that two and four is six, too."25. 26. 27.六Fill in the blanks with proper forms of the given wordspack work finish listen go move talk be28. Michael often his homework before nine o’clock every evening.29. My mother in a shop. She at work now.30. –Where are Ken and Kitty?--They their things in the room. They into a new flat this Sunday.31. The teacher now. Let’s to her.32. I think they to Yinfa Home for the aged next week.六年级(上)6AU10练习卷二姓名一Rewrite the sentences as required (根据要求改写句子)1．Tom didn’t run so fast as Jim.（改为肯定句）Tom ran fast Jim.5.You shouldn’t keep the knife in your right hand.（改为祁使问）the knife in your right hand.6.Ms. Gao teaches us how to play velleyball. （保持原句意思）We how to play volleyball Ms. Gao.7.My favourite school day is Wednesday. What’s yours? (保持原句意思)I like Wednesday best. you?二Choose the best answer. (选择最恰当的答案)( ) 5. After class I have gymnastics two hours.A. withB. aboutC. forD. at( ) 6. –What did Lucy do last night?--She too many snacks.A. eatsB. drinksC. ateD. had( ) 7. They always sell their clothes at a very price.A. bigB. tallC. highD. well( ) 8. your brother and you any question?A. Do; hasB. Do; haveC. Does; haveD. Does; has三Fill in the blanks with proper forms of the given wordshave one work they want flower happyswim people familyJohnson likes 9 in a small river near his house. But then his father goes to 10 in a big city and Johnson goes with his 11 . Their new house 12 a garden, but the garden is very small. Johnson is not very glad.―Is there a river near the house?‖ he asks his father on the 13 morning .‖ No, there isn’t . But there is a big park with many 14 near here. And there’s a pool in it. ―We are going there this afternoon.‖ says his father. Johnson is15 . Johnson and his father go to the park in the afternoon. Johnson 16 to walk near the pool. But he sees a sign. His father reads it to him: ―Warning（警告）This pool is dangerous. 362 17 fell(掉) into it. ‖Johnson looks into the pool carefully, then he says ,―I can’t see18 . ‖9. 10. 11. 12.13. 14 15.16. 17. 18.五Cloze test (完型填空)AThe summer vacation is over. It's true that time 19 flies fast. During the vacation, the weather was hot and I could not do much work, but I lived happily.As the afternoon was hot,I did my work in the 20.I used to get up at 6: 30 and take a walk in the garden for 21 . After breakfast at 7 o’clock, I began reading English and Chinese and did some exercises in maths. Those took me three hours or more. 1 worked quite 22 and made good progress.I spent the afternoon outside. 1 went to swim and it was funny. I would not go home until it was about five or six o'clock. Sometimes a friend would come to see me and we would spend some hours listening to music.In this way l spent my vacation 23 . And I not only studied well but also became a good swimmer. Now I am in good health and high spirits.( )19. A. never B. some time C. always D. usual( )20.A. morning B. evening C. night D. noon( )21. A. 10 minutes B. half an hourC. an hourD. 15 minutes( )22. A. good B. well C. much D.hard( )23. A. fine B. happily C. quick D. badlyBI’m Steven. There is a big g 24 around my house. We can get a lot of honey from the garden b 25 there are a lot of flowers in it, and the bees make their honey from these flowers. We often sell the honey in the market and we can make some m 26 . Sometimes we give our honey to our neighbours. We never b 27 any honey or jam in the shops. Mum makes all our jam from the fruit in our garden. It tastes much b 28 than the jam from shops. I love it so much.24. 25. 26.27. 28CLast year l went to America. I stayed there f__29__ half a year. I found most Americans had three meals a day. They had b 30 in the morning, a light lunch at noon, and a big dinner in the evening. They often had breakfast and lunch in a hurry, but they had m 31 time for dinner. Americans usually drink a lot of w 32 ,a lot of milk, and a lot of coffee, but they don’t d 33 much tea.29. 30. 31.32. 33六年级(上)6AU10练习卷一参考答案1．mustn’t any2. How much have bought3. Where will4. has5. Is healthier6. His favourite food7. less8. as healthy as9. a little10. What11. healthy12—18. D B A A D C D19. walking 20. finds 21. answer22. after 23. help 24. worry25. new 26. comes 27. because28. finishes 29. works; is30. are packing; will move31. is talking; listen32. will go六年级(上)6AU10练习卷二参考答案1．less than 2. Don’t keep 3. learn from 4. What about 5—8. C D C B9. swimming 10. work 11. family 12. has 13. first 14. flowers 15. happy 16．Wants 17．people 18．Them19--23. D A B D B 24. garden 25. because 26. money 27. buy 28. better 29. for30. breakfast 31. much 32.water 33. drink。

一、知识精要直角三角形全等的判定：斜边与一直角边对应相等的两个直角三角形全等．（ＨＬ）直角三角形的性质定理及其推论：定理1：直角三角形的两个锐角互余；定理2：直角三角形斜边上的中线等于斜边的一半；定理2的推论：（1）在直角三角形中，如果一个锐角等于30°，则它所对的直角边等于斜边的一半;（2）在直角三角形中，如果一条直角边等于斜边的一半，那么这条直角边所对的角为30°. 轨迹：把符合某些条件的所有点的集合叫做点的轨迹。

三条基本轨迹：轨迹1 和已知线段两个端点相等的点的轨迹是这条线段的垂直平分线。

轨迹2 到已知角的两边距离相等的点的轨迹是这个角的平分线轨迹3 到定点的距离等于定长的点的轨迹是以定点为圆心，以定长为半径的圆二、热身练习1．如图1所示，AB=CD，DE⊥AC于E，BF⊥AC于F，且DE=BF，∠D=65°，则∠A=__________．2．在直角三角形ABC中，∠ACB=90度，CD是AB边上中线，图中有_______等腰三角形.3．如图2，在△ABC中，∠B=∠C=∠BAC，D、E分别是BC、AC的中点，AB=8，则△DEC的周长为。

图1 图2 4．顶角为30度的等腰三角形，若腰长为2，则腰上的高__________，三角形面积是________5．Rt△ABC中，∠C=90°，∠A=15°，AB的垂直平分线交AC于D,AB于E, 求证AD=2BC.6、已知如图在ABC∆中，AD是CB边上的高，CE是AB边上的中线，,DC BE DG CE=⊥于点G,（1）求证：G是CE的中点；（2）求证：2B BCE∠=∠三、精解名题ABCDEGA基础题例1：例3. 如图，Rt △ABC 中，∠C=90°，∠A=15°，AB 的垂直平分线交AC 于D 、AB 于E. 则AD=______BC.例2：在△ABC 中，∠ACB=90°，D 是AB 边的中点，点F 在AC 边上，DE 与CF 平行且相等。

浦东补习班新王牌初中数学孙ZC老师初一期中复习讲义一、填空题1.计算：a2, a3 = ________ __________ .2.已知圆的直径为d,用含d的代数式表示圆的面积 ______________ .3.计算：(2x-y) (-y-2x)= ________________________ .4. ______________________________ 多项式-产3 +厂+ 2兀-1是______ 次 ___________________________________ 项式，常数项是_________________ .5.把多项式ab2-2a2b+a3+3b3-l按a降幕排列________________ .6.若单项式3x?严与一丄的和是单项式，则m + n二 _____________ ・47.分解因式：2a2-8= ______________________ .&分解因式：一4兀2歹一6兀尸+2与二__________ ・9.计算：-x3• (-x) 2= ______________10.已知M l=ab16,则M二__________ •11.如果(兀一y)2+M = (x+y)2,那么M二_____________________ ・12.要使二次三项式x2-16x+m成为一个完全平方式，则m= _____________ 13•某商品原价为。

元，现价比原价降低了25%,则现价为________ 元.(用含°的代数式表示)14.已知5'=3, 5，=4,则25內二_______________ ・15.如果x2+y2-4x+6y+13=0,那么2x+3y= ____________ ・16.如杲4F+mx+9是一个完全平方式，那么常数"匸 ______________ •17.己知a—丄=4,则(Q —2)(丄+ 2)二____________ .a a18.计算：502-492+482-472+••• + 22-12= ________________ ・19 .已知Q = 2013" = 2012,则/一lab + h2-6a-^6h = _____________ ・20.已矢口：x+y = 3,兀2+)，=5,贝*J xy - ______________21.如果代数式4)，_2〉，+ 5的值是7,那么2y2-y + \的值_________________ ・4. 从边长为Q 的大正方形纸板中挖去一个边长为"的小正方形纸板后，将其裁成 四个相同的等腰梯形（如图甲），然后拼成一个平行四边形（如图乙）.那么通过 计算两个图形阴影部分的面积，可以验证成立的公式为（ ）A> cr-h 2 =(a-h)2 ；B> (d + b)? =a 2 + 2ab 4-b 1 ；C 、 (6f —Z?)2 — cr — 2cib+b~ ；D 、 cr -b 2 = (ab)(a - b)・5. 若加2 +Ax+9 = (2x-3)2 ,则 in,22、若d —丄=3,则a 2+-^ a cr二、选择题下列从左到右的变形中，（a + b ）（G-b ） = a 2 -b 2 1.A 、是因式分解的是 B 、一 2a'b + 4a'b = 2a~b(2 - a) C 、(d + 防=a 2 +2“+， D 、— 2Q — 3 = Q (a — 2) — 3 2 •下列代数式中整式有（—,2x+y, — a 2b, x 3A 、4个B 、5个 =0.5 , a 4xC 、6 个D 、7 个" 色，从第二个数开始，每一个数都等于1与它前面 71 那个数的倒数的差，若q=2,贝吒2她为（ ）A 、2007B 、1C 、 2D 、 -1 k 的值分别是（A 、m=—2, k=6, B> m=2, k=12,C 、m=4, k 二一12、D m=4, k 二 12、 三、简答题1. 计算:(x+2y) (x-2y) - (x+2y)220132-2015x2011 甲 乙(d —b)2 (3d —2) + (2 —3Q )/?23.先化简，再求值：-(3a 2 -4ab) + \_a 2 -2(2a + 2ab)],其中a = -2；四、解答题1. 已知：a+b=7 ab= 10,求 a 2+ab+b 2 的值。

张老师秋季辅导材料八Part1Listening（第一部分听力）Listen to the passage and tell whether the following statements are true or false.1.A new way to spend holidays is travel study.2.When you have a travel study,you only can see many beautiful sights.3.During the study travel,you have to speak English every day and almost everywhere.4.Traveling can help you make a lot of new friends.5.You can read all books of the past during the study travel.6.English-speaking teachers alone can help you improve English.7.You can get a chance to learn how to live by yourself during the travel study.Part2Vocabulary（第二部分词汇）I.根据音标写出单词，词性及中文词义1./'ækjurit/2./ə'meiziŋ/3./'kælkjuleit/4./kə'mju:nikeit/5./kəm'pli:t/6./di'veləp/7./in'vent/8./'liviŋ/9./'ləukəl/10./'nesisəri/11./pə'lait/12./'pauəful/13./sɔ:lt/14./'sə:vis/15./sɔlv/16./'ʃuəli/II.写出所给单词的词性及中文词义1.chain2.charge3.check4.course5.custom6.culture7.especially8.lecture9.lightning10.pack11.program12.response13.snack14.system15.wholeplete the sentences with the given words in their proper forms(用括号中所给单词的适当形式完成下列句子）1.With the(develop)of economy,China is becoming stronger and stronger.2.Who first(invention)the systems of numbers from1to9?3.On the(four)day,the sick boy came to life.4.The computer is such a machine that it can do a within seconds (calculator).5.There’s(little)than ten minutes left.Hurry up.6.It’s(near)eleven clock.You’d better go to bed.7.Scientists from all around the world want to know why all(live)things died at the end of the Cretaceous period(白垩纪）.8.Children are not allowed to use some of the(electricity)appliances.9.Please tell Jane that a classmate of is going to visit her.(she)10.The skillful of a computer is hard to learn.(operate)11.The TV news reported the celebration of the old man’s birthday.(hundred)12.Wang Damin enjoys with his big birds.(fish)13.Do you need the of a lawyer?(serve)14.I’ll have two cups of tomato cups for.(start)15.Many after-class activities make our school life much more.(enjoy)plete the following sentences.The first letter has been given.（完成下列句子，首字母已给）1.It is r to see a man over160years old.2.The store sells big ones,small ones,m ones,or what have you.3.Let’s go Dutch.We’ll both pay half of the b.4.The restaurant has a service c of ten per cent.5.The moon sank b the hills.6.She took three c:reading,writing and mathematics.7.There are only a few days1before I’m going to face mid-term examination.8.She is very f of Chinese classical literature and has spent some time reading Tang and Song poetry.Part3Writing（第三部分写作）1.Write a passage of at least60words about“Computer and My Life”.The following questions are for your reference.●What do you usually do on the computer?●Do you think the computer is becoming more and more important in your life?●Why do you think so2.Write at least60words about the topic"My Favorite Dinner Party"(以“我最喜欢的宴会”为题，写一篇不少于60词的短文）Part4Reading（第四部分阅读）1.A.energeticB.endsC.eveningD.lowE.cycleF.highG.fitH.betterI.riseDo you find getting up in the morning so difficult that it’s painful?This might be called laziness,but Dr. Kleitman has a new explanation.He has proved that everyone has a daily energy1During the hours when you labor through your work,you may say that you’re“hot”.That’s true.The time of day when you feel most2is when your cycle of body temperature is at its peak.For some people the peak comes during the forenoon.For others it comes in the afternoon or evening.No one has discovered why this is so,but it leads to such familiar monologues as,“Get up,John!You’ll be late for work again!”The possible explanation to the trouble is that John is at his temperature-and-energy peak in the3Much family quarrelling4when husbands and wives realize what these energy cycles mean,and which cycle each member of the family has.You can’t change your energy cycle,but you can learn to make your life5it better.Habit can help, Dr.Kleitman believes.Maybe you’re sleepy in the evening but feel you must stay up late anyway.Counteract(对抗）your cycle to some extent by habitually staying up later than you want to.If your energy is6in the morning but you have an important job to do early in the day,7before your usual hour.This won’t change your cycle,but you’ll get up steam and work8at your low point.Get off to a slow start which saves your energy.Get up with a leisurely yawn and stretch.Sit on the edge of the bed a minute before putting your feet on the floor.Avoid the troublesome search for clean clothes by laying them out the night before.Whenever possible,do routine work in the afternoon and save tasks requiring more energy or concentration for your sharper hours.2.Once,there was an old granny who was living alone in the mountains.She never felt lonely because she would go to the forests to see1there were any wounded animals every day.One day,she found a big tiger2on the ground shedding a lot of blood.The old granny thought：“I should do something quickly to rescue it.”So she went home to fetch medicine3Although the tiger was fatally wounded,after the careful treatment,the tiger recovered soon.The tiger decided to find a chance torepay the old lady4her kindness.One night,it had a heavy rain.The tiger came to the granny’s house5to hint(示意）with his head to ask the old granny to ride on his back.After that,the tiger ran away with the granny on his back.The old lady queered：“What is the matter?”But when she looked back,she found her house had collapsed6the erosion of the rain.She knew the tiger had come to rescue her.Later,the tiger asked many animals who had been treated by the old granny to build a big,solid house by a river.The old granny continued to rescue the wounded animals,and many animals had become her assistants.1.A.where B.why C.if D.asying B.lying C.dying D.waiting3.A.for the first time B.for the time being C.now and then D.in a hurry4.A.like B.with C.for D.from5.A.slowly B.suddenly C.frighteningly D.excitedly6.A.based on B.because of e to an end D.consist of3.The Japanese pay much attention to the lucky meanings of telephone numbers.The bathhouses,for example, like to use4626,because when read1Japanese,it has the same pronunciation as“having a good bath”.Both the clothes shops and the butcher’s like4129better than any other numbers because this number can 2be read as“good meat”or“nice clothes”.Since these numbers are3with something nice,people can remember them very easily.So they have become advertisements for the shops.4,there are also telephone numbers which are regarded as forbidden by the Japanese people.1564,for example,has the sound of“kill people”while the number4219has the5of“people die”.At present,there are about44million telephones in Japan,yet it is almost6for everyone to get a lucky number.So these numbers have become valuable and can be sold as goods.The price can reach as high as 222thousand Japanese yen.1.A.with B.about C.in D.along2.A.not B.never C.either D.even3.A.dealt B.designed C.connected D.consisted4.A.On one hand B.On the other handC.In my opinionD.In short5.A.voice B.sound C.noise D.ring6.A.possible B.changeable C.responsible D.impossible4.In almost all western restaurants you must find1table.Do not sit at a table where other people are already sitting.2there are no empty tables,wait in the area provided.It is not polite to stand behind people who are eating while you wait for them to finish.Sometimes you3wait a short time in the lobby when you first arrive,before a table is4The waiter will ask you if you prefer to sit in an area where smoking is allowed(允许）or not.Many public places in the West forbid(禁止）smoking altogether,others allow it only in one area.When you invite foreigners to dinner,always remember that foreigners do not eat the viscera(内脏)，heads and feet of pigs or chickens.Usually the waitress will5the bill when you finish,but if you want to have it quickly,do not6 or you can call softly,Miss or Sir.You can put up your hand.If one person invites the others to a restaurant,he or she will pay.Otherwise people usually divide the cost.1.A.empty B.a empty C.the empty D.an empty2.A.Since B.If C.Why D.Though3.A.have to B.can C.may D.must4.A.clean B.dirty C.busy D.free5.A.take B.bring C.carry D.put6.A.speak B.cry C.shout D.call5.We all have three people within us.One of them is a parent,the other is an adult and the third is a child.The parent:when the parent in our head controls us we c1people,we tell them how to behave as our parents told us to behave.The good side of the parent is caring for people and passing on the traditions ofs2The bad sideof the parent is giving more importance to traditions and rules than to the needs of the individual.The adult:the adult in our head looks carefully at information and tries to think of sensible ideas.Our adult is open-minded to new situations and to o3people and their feelings and opinions.The good side of the adult is thoughtfulness and openness to new ideas.The bad side of the adult is not making d4quickly and not giving importance to enjoyment,etc.The child：everybody has a child within them.The child in e5person is perhaps more important than the parent and the adult!The child gives us joy,openness,i6and activity,just like a child in a family.Unfortunately the child inside us is often not healthy and we are“childish,and silly and not“child-like”and joyful,open and creative.The good side of the child is joy,excitement,openness to new e7and creative energy.The bad side of the child is being silly,selfish,spoilt and conceited(自负的）.It is important that there is a balance of the good aspects of the parent,the adult and the child within us.In this way we can be caring,thoughtful and joyous.6.Mind Those Manners on the SubwaySo,there you are,just sitting there in the subway car,enjoying the book you just bought.Suddenly,you feel someone leaning over your shoulder reading along with you.Or,the person sitting next to you takes out a nail clipper(指甲刀）and begins cutting his or her nails.Annoying?Many of us have to spend some time every day on public transportation.We all know that some behaviors are s1unacceptable.So,to make the trip more pleasant,we suggest the following：Let passengers get off the bus or subway car before you can get on.Getting off and on in an orderlym2can save time for all.S3away from the doors when they are closing.Don’t talk loudly on a bus or subway.Chatting loudly with your friends can be annoying to o4Don’t shout into your mobile phone on a bus or subway.Don’t think your bags and suitcases(手提箱）deserve a seat of their e a tissue whenever you cough or sneeze(打喷嚏).An uncovered sneeze can s6germs(细菌),especially in crowded places.Don’t cut your nails or pick your nose on public transportation.Don’t read over other people’s shoulder.Many people do this on subways,but it’s r7annoying.It can make people uncomfortable.They might think you’re too stingy(小气的）even to buy a newspaper.Or theymight think you’re judging their behavior.7.John Chapman was born in Massachusetts about1774.He grew up to be a gardener.He planted apple trees in New York and Pennsylvania.In the e11800s,he carried apple seeds west.He walked the wilderness that would later become Michigan,Ohio,Indiana,and Illinois.When he found a good place for apple trees,he cleared the brush.He planted the seeds in rows.Then he fenced them in.At first he went back e2for more ter he got seeds from the t3he grew.He roamed through the wilderness,tending to his orchards.He traveled on f4often without shoes.He carried with him a cooking pot.When the first settlers came,Chapman sold his trees for pennies.Sometimes he traded them for used clothes. The settlers called him Johnny Appleseed.Those who moved on west told of the man who sold them the trees. The tale p5down through the generations.More tales were a6to the legend.In one tale, Johnny Appleseed slept through a storm with a bear.In another,a rattlesnake(响尾蛇）tried to bite his foot,but his skin was too tough.In books,he might be shown in clothes that are too big,wearing his pot as a hat.Some of the trees he planted still b7fruit today.。

七年级：分式综合复习（教案）教学目标：1. 掌握分式的相关概念；2. 掌握分式的加减乘除运算；3.掌握可化为一元一次方程的分式方程的解法；4. 掌握分式方程的应用及整数指数幂；教学重点：分式计算；分式方程的无解与增根问题；整数指数幂计算；教学难点：分式方程的无解与增根；知识点1：分式的定义一般地，如果A ，B 表示两个整数，并且B 中含有字母，那么式子B A 叫做分式，A 为分子，B 为分母。

知识点2：与分式有关的条件①分式有意义：分母不为0（0B ≠）②分式无意义：分母为0（0B =）③分式值为0：分子为0且分母不为0（⎩⎨⎧≠=00B A ）④分式值为正或大于0：分子分母同号（⎩⎨⎧>>00B A 或⎩⎨⎧<<00B A ） ⑤分式值为负或小于0：分子分母异号（⎩⎨⎧<>00B A 或⎩⎨⎧><00B A ） ⑥分式值为1：分子分母值相等（A=B ）⑦分式值为-1：分子分母值互为相反数（A+B=0）知识点3：分式的基本性质分式的分子和分母同乘（或除以）一个不等于0的整式，分式的值不变。

字母表示：C B C ∙∙=A B A ，CB C ÷÷=A B A ，其中A 、B 、C 是整式，C ≠0。

拓展：分式的符号法则：分式的分子、分母与分式本身的符号，改变其中任何两个，分式的值不变，即BB A B B --=--=--=A A A 注意：在应用分式的基本性质时，要注意C ≠0这个限制条件和隐含条件B ≠0。

知识点4：分式的约分定义：根据分式的基本性质，把一个分式的分子与分母的公因式约去，叫做分式的约分。

步骤：把分式分子分母因式分解，然后约去分子与分母的公因。

注意：①分式的分子与分母为单项式时可直接约分，约去分子、分母系数的最大公约数，然后约去分子分母相同因式的最低次幂。

②分子分母若为多项式，约分时先对分子分母进行因式分解，再约分。