《平方根》教案
教学设计思想:
平方根及算术平方根是两个重要的概念,是全章的教学重点.学生对平方根及算术平方根的概念常常混淆,因此,在教学中引导学生真正理解这两个概念的本质是什么,并能分清它们的区别与联系,这是两节课的主要教学目标.在教学设计中,力求在以下两方面突出特点:
1.引导学生建立清晰的概念系统,首先在第1课进要求学生正确理解平方根的概念的意义和平方根的表示法;其次在第2课时专门讨论算术平方根的概念及其表示.对于a表
示a的算术平方根的条件是,被开方数a表示非负数,而a本身也表示非负数,因此在教学中不能要求学生死记硬背,要向学生说明规定的合理性.为此,提出算术平方根的一种几
何解释,即面积为a的正方形(a为正数),它的边长为a(a也是正数),从而直观、形象地说明了算术平方根约定的合理性.
2.编选了有针对性的、有梯度的、形式多样的课堂练习题,让学生在练习中巩固和加深知识的理解和掌握,促使学生尽快地把新知识纳入到自己原有的认知结构中.
教学目标:
知识与技能:
1.能说出平方根和算术平方根的概念,会用根号表示一个数的平方根。
2.知道开平方与平方是互逆的运算,会利用这个互逆运算关系求某些非负数的平方根。
3a的平方根。
过程与方法:
1.通过对比体会平方根、算术平方根的联系和区别;
2.在学习开平方运算求一个数的平方根、算术平方根的过程中,体会开平方运算与平方运算之间的互逆关系.
情感态度价值观:
进一步感受到所学数学知识之间的内在联系.
教学重难点:
重点:平方根和算术平方根的概念和求法.
难点:弄清平方根与算术平方根的意义
教学方法:
探究学习
课时安排
1课时
期末检测卷 时间:120分钟 满分:100分 班级:__________ 姓名:__________ 得分:__________ 一、选择题(每小题2分,共24分) 1. 9的平方根是( ) A .±3 B .-3 C .3 D .81 2.下面所给的图形中,不是轴对称图形的是( ) A. B. C. D. 3.如图,Rt △ABC ≌Rt △DEF ,则∠E 的度数为( ) A .30° B .45° C .60° D .90° 第3题图 4.下列实数中,是无理数的是( ) A.π3 B .-0.3 C.227 D.38 5.下列各式从左到右的变形正确的是( ) A.y x =y +1 x +1 B.y x =ay ax C.y x =a 2y a 2x D.y x =(a 2+1)y (a 2+1)x 6.下列计算结果正确的是( ) A.2+5=7 B.2×5=10
C .32-2=3 D.25=510 7.如图,在数轴上表示实数 7的点可能是( ) A .点P B .点Q C .点M D .点N 第7题图 8.一个等腰三角形两边的长分别为4和9,那么这个三角形的周长为( ) A .13 B .17 C .22 D .17或22 9.如图,若∠2=30°,为了使白球反弹后能将黑球直接撞入袋中,那么击打白球时,必须保证∠1的度数为( ) A .15° B .30° C .45° D .60° 第9题图 第10题图 10.如图,在△ABC 中,AB =AC ,AD 是高,能直接判断△ABD ≌△ACD 的依据是( ) A .SSS B .SAS C .HL D .ASA 11.某工厂生产一批零件,计划20天完成.若每天多生产4个,则15天完成且还多生产10个.设原计划每天生产x 个,根据题意可列方程为( ) A.20x +10x +4=15 B.20x -10x +4 =15 C.20x +10x -4=15 D.20x -10x -4 =15 12.当x 分别取-2015、-2014、…、-2、-1、0、1、12、…、12014、12015 时,
冀教版八年级上册英语全册教案 冀教版八年级上册英语全册教案 Lesson 1 Back to School! Teaching objectives: 1. Grasp the mastery vocabulary and phrases. 2. Make the students understand the meaning of the text. 3. Learn something about an e-mail written by English. After learning this lesson, the students can write their own e-mails. Teaching Aims 1.Knowledge goals: Master the vocabulary(physics, recent, ) 2. Ability goals: (1) Useful phrases and structures (one…the other…, make friends, introduce sb. to sb., the same as) (2) Understand the meaning of the text 3. Emotion goals: Learn how to express the first day of a new term Important points: Can use phrases freely to make sentences Difficult points: Master important phrases Teaching method:Speaking, Teaching progress: Class opening: Introduce the topic of this unit. Key steps: Step 1. Ask the students to discuss the question in “Chat Show” What did you do in your summer holiday? Step 2. Dictation Dictate these words: back, be back, grade, student, pupil, class, have, have lessons /classes, more, cousin, brain Step 3. Present new sentences be back /be back home e.g. I am back. T: Ask one student “Which Grade are you in this year?” S: I am in Grade 8 this year. T: How many students are there in your school? S: There are about 900 students in my school. T: How many pupils are there in your class? S: My class has 50 pupils. Then the teacher makes the students do pair works, make sure they can
第十二章分式 1.分式与整式不同的是:分式的分母中含有字母,整式的分母中不含字母 对于任意一个分式,分母不能为零,分式有意义 对于任意一个分式,分母为零,分式无意义 4.分式的值为零含两层意思:分母不等于零;分子等于零。 5.平方差公式 a2-b2=(a+b)(a-b)两个数的平方差,等于这两个数的和与这两个数的差的积 6.完全平方公式a2+2ab+b2 = (a+b)2a2-2ab+b2=﹙a-b﹚2两个数的平方和,加上(或者减去)这两个数的积的2倍,等于这两个数的和(或者差)的平方 7.常见的恒等变形如x-y=-(y-x),(x-y)2=(y-x)2, (x-y)3= -(y-x)3. 8.约分:把一个分式中相同的因式约去的过程叫做约分 9.最简分式:如果一个分式中没有可约的因式,则为最简分式 10.通分:把几个异分母的分式分别化成与原来的分式相等的同分母的分式,叫做分式的通分 11.通分和约分都是依据分式的基本性质进行变形,其共同点是保持分式的值不变. 12分式的基本性质:分式的分子和分母乘(或除以)同一个不等于0的整式,分式值不变。 通分的关键:确定几个分式的最简公分母。通常取各分母系数的最小公倍数与字母因式的最高次幂的积作公分母,这样的公分母叫做最简公分母。求最简公分母时,首先要因式分解,将所有的表达式都化成积的形式,然后,再定最简公分母. 解分式方程的一般步骤:(1)去分母,方程两边同乘各分母的最简公分母,将分式方程转化为整式方程; (2)解整式方程;(3)验根:可把整式方程的根分别代入最简公分母,如果使最简公分母为0,那么这个根叫分式方程的增根,必须舍去;如果使最简公分母不为0,那么这个根是原分式方程的根;(4)写出方程的解. 15、用分式方程解应用题常见的等量关系 一.工程问题 1.工作效率×工作时间=工作总量工作总量÷工作效率=工作时间 工作总量÷工作时间=工作效率 设工作总量为“1”的公式:1÷单独完成的工作时间=工作效率;1÷工作效率=单独完成的工作时间。 2.完成某项任务的各工作量的和=总工作量=1 二.营销问题 1.商品总利润=商品总售价一商品总成本价= 商品单件利润×销售量 2.商品单件利润=商品单件售价一商品单件成本价 3.商品利润率=商品总利润/商品总成本价×100%=商品单件利润/商品单件成本价×100% 4.商品销售额=商品单价×商品销售量 5、折扣=实际售价÷原售价×100%(折扣<1) 三.行程问题 1.路程=速度×时间,速度=路程/ 时间 2.在航行问题中,其中数量关系是(同样适用于航空):顺水速度=静水速度+水流速度 逆水速度=静水速度-水流速度 增长率问题原来量×(1 增长率)=现在量 第十三章全等三角形 1、能够完全重合的两个三角形叫做全等三角形 2、全等三角形的性质: (1)全等三角形的对应角相等,对应边相等. (2)全等三角形中的对应线段相等.即对应的角平分线,对应的中线,对应的高线相等。
Unit 5 Buying and Selling 话题Topic 购买和销售(Buying and selling) 功能Functions 谈论筹款: How can we make money? Maybe we can work together to raise money. Maybe we can have a bake sale. 谈论购物:How much does it cost? It’s only five dollars. That’s a very low price for such a great product! 谈论商务英语:It’s short and simple English. We are in the red this month. He is a fat cat. 谈论诚信活动:Help yourself. Leave the money in the box. Give what you can. 谈论广告宣传:Go to trade shows and present your product. Push your product using samples and good deals. 谈论产品销售:She made a poster for our cookie sale. Maybe we can sell cookies in the store. 语法Grammar 宾语从句的用法 词汇和常用表达Words & expressions 1.能正确使用下列词汇(Curriculum words)(按词性排列) 名词:dollar,pocket,cent,value,gate,husband,customer 动词:pay,tie,afford,offer,shine,succeed 形容词:cheap,everyday,honest,crazy,similar 其他:sixteen,while,already 2.能正确使用下列常用表达(Useful expressions) make money,raise money,all one’s life,pay for,for sale,go over to,less than,beef up,move up,at a low price,do a good job,sell out of,push a product,get to do sth,stand out,catch one’s eye,of one’s
冀教版八年级数学上册期中试卷一.选择题 1.下列各式:,,﹣,,,其中分式共有()A.1个B.2个C.3个D.4个2.下列命题错误的是() A.对角线相等的菱形是正方形 B.位似图形一定是相似图形 C.“画一个三角形是钝角三角形”是随机事件 D.若∠A是锐角,则0<tanA<1 3.在,﹣π,0,3.14,,,中,无理数的个数有()A.1个B.2个C.3个D.4个4.下列计算中,正确的是() A.3﹣2=﹣6B.= C.a﹣1?a﹣2=a2D.= 5.如图,△ABC≌△CDA,则下列结论错误的是() A.AC=CA B.∠B=∠D C.∠ACB=∠CAD D.AB=AD 6.下列说法正确的是() A.(﹣3)2的平方根是3B.=±4 C.1的平方根是1D.4的算术平方根是2 7.若m,n为实数,(m+3)2+=0,则的值为()A.B.C.2D.4 8.下列说法正确的是() A.﹣3是﹣9的平方根B.1的立方根是±1 C.a是a2的算术平方根D.4的负的平方根是﹣2
9.下列判断正确的是() A.带根号的式子一定是二次根式 B.一定是二次根式 C.一定是二次根式 D.二次根式的值必定是无理数 10.若式子在实数范围内有意义,则x的取值范围是()A.x>1B.x>﹣1C.x≥1D.x≥﹣1 11.下列运算结果正确的是() A.=﹣3B.(﹣)2=2C.÷=2D.=±4 12.下列运算中正确的是() A.﹣=B.2+3=6 C.÷=D.(+1)(﹣1)=3 二.填空题 13.如图,数轴上点A、点B表示的数分别中1和,若点A是线段BC的中点,则点C所表示的数是. 14.计算4﹣3的结果是. 15.如图所示,将两根钢条AA′、BB′的中点O连在一起,使AA′、BB′可以绕着点O自由转动,就做成了一个测量工具,则A'B'的长等于内槽宽AB,那么判定△OAB≌OA'B'的理由是. 16.若关于x的分式方程=3的解是负数,则字母m的取值范围是.17.若分式方程2+=有增根,则k=. 三.解答题
冀教版八年级上册英语全册教案2 教师_______日期_______ Lesson 1 Presents from Canada Teacher: look-over: Teaching aims: goals: Master the vocabulary(physics, recent, ) 2. Ability goals: (1) Useful phrases and structures (one…the other…, make friends, introduce sb. to sb., the same as) (2) Understand the meaning of the text 3. Emotion goals: Learn how to express the first day of a new term Important points: Can use phrases freely to make sentences Difficult points: Master important phrases Teaching method:Speaking, Step1 2.“Free talk” Step2 1. Lead to the new lesson 2. Teach and explain the forms of key words to the tape, then finish“Let’s do it ”exercise 1 4. Go through the passage quickly and find important phrases in the text Step3 Language points (1)one…the other… (2)make friends (3)introduce sb. to sb. (4)the same as (5)the use of “look” Step4 Let’s practice togethe r Summary: Homework: lesson 1 2. Go over and recite
(冀教版)八年级数学上册(全册)单元测试汇总 第12章分式和分式方程单元测试 一、单选题(共10题;共30分) 1.化简分式bab+b2的结果为() A、1a+b B、1a+1b C、1a+b2 D、1ab+b 2.有理式①, ②, ③, ④中, 是分式的有() A、①② B、③④ C、①③ D、①②③④ 3.若x=3是分式方程的根, 则a的值是(). A、5 B、﹣5 C、3 D、﹣3 4.给出下列式子:1a、3a2b3c4、56+x、x7+y8、9x+10y, 其中, 是分式的有() A.5个 B.4个 C.3个 D.2个 5.在式子y2、x、12π、2x-1中, 属于分式的个数是() A.0 B.1 C.2 D.3 6.如果1a+1b=1, 则a-2ab+b3a+2ab+3b的值为() A.15 B.-15 C.-1 D.-3 7.学校建围栏, 要为24000根栏杆油漆, 由于改进了技术, 每天比原计划多油400根, 结果提前两天完成了任务, 请问原计划每天油多少根栏杆?如果设原计划每天油x根栏杆, 根据题意列方程为() A. = +2 B. = ﹣2 C. = ﹣2 D. = +2 8.下列分式中最简分式为() A. B. C. D. 9.小明乘出租车去体育场, 有两条路线可供选择:路线一的全程是25千米, 但交通比较拥堵, 路线二的全程是30千米, 平均车速比走路线一时的平均车速能提高80%, 因此能比走路线一少用10分钟到达.若设走路线一时的平均速度为x千米/小时, 根据题意, 得() A.25x?30(1+80%)x=1060 B.25x?30(1+80%)x=10 C.30(1+80%)x?25x=1060 D.30(1+80%)x?25x=10
Lesson 1 Presents from Canada Teacher: look-over: Teaching aims: 1.Knowledge goals: Master the vocabulary(physics, recent, ) 2. Ability goals: (1) Useful phrases and structures (one…the other…, make friends, introduce sb. to sb., the same as) (2) Understand the meaning of the text 3. Emotion goals: Learn how to express the first day of a new term Important points: Can use phrases freely to make sentences Difficult points: Master important phrases Teaching method:Speaking,
Lesson 2 Many faces, One picture Teacher: look-over: Teaching aims: 1.Knowledge goals: Master the vocabulary(perform, advise, agree, glue) 2. Ability goals: (1) Useful phrases and structures (advise sb. to do sth., be up to, agree with, put up) (2) Understand the meaning of the text 3. Emotion goals: Learn how to express people Important points: Can use phrases freely to make sentences Difficult points: Master important phrases Teaching method:Speaking,
备课本冀教版八年级上册 英语 全册教案 班级______ 教师______ 日期______
冀教版八年级上册英语全册教案 教师_______日期_______ Unit 1 Me and My class Lesson1Back to School! Teaching objectives: 1. Graspthemastery vocabulary and phrases. 2.Make the students understand the meaning of the text. 3.Learn something about an e-mail written by English. After learning this lesson,the students can write their own e-mails. Teaching Aims 1.Knowledge goals: Master the vocabulary(physics, recent, ) 2. Ability goals: (1) Useful phrases and structures (one…the other…, make friends, introduce sb. to sb., the same as) (2) Understand the meaning of the text 3. Emotion goals: Learn how to express the first day of a new term Important points: Can use phrases freely to make sentences Difficult points: Master important phrases Teaching method:Speaking, Teaching progress: Classopening:Introduce the topic of this unit. Key steps: Step1. Ask the students to disc uss the question in“Chat Show” What did you do in your summer holiday? Step2.Dictation Dictatethesewords: back, be back, grade, student, pupil, class, have, have lessons /classes, more, cousin, brain Step3. Present new sentences be back/be back home e.g. I am back. T: Ask one student “Which Grade are you in this year?” S: I am in Grade 8 this year. T:How many students are there in your school?