八年级下册习题三

一、阅读下面名著语段，完成问题。

【语段一】秦以前是文字发生与演化的时代，字体因世因国而不同，官书虽是系统相承，民间书却极为庞杂。

到了战国末期，政治方面，学术方面，都感到统一的需要了，鼓吹的也有人了；文字统一的需要，自然也在一般意识之中。

这时候抬出一个造字的圣人，实在是统一文字的预备工夫，好教人知道“一个”圣人造的字当然是该一致的。

【语段二】这部书意在帮助人通读古书，并非只供通俗之用，和秦代及西汉的字书是大不相同的。

……这部书是文字学的古典，又是一切古典的工具或门径。

1.【语段一】中的“造字的圣人”是指_______，【语段二】中的“这部书是指《_______》。

2.为什么说“这部书是文字学的古典”？____________________________________________________________________________ ____________________________________________________________________________1.仓颉说文解字2.因为研究汉字的形音义要靠《说文解字》，而研究汉字形音义的学问即文字学。

二、阅读下面名著语段，完成问题。

【语段一】行人不至，谋事未成，财运欠通，婚姻待决，子息不旺，乃至种种疾病疑难，许多人都会去求签问卜，算命看相，可见影响之大。

讲五行的经典，现在有《尚书·洪范》；讲八卦的便是《周易》。

【语段二】商民族是用龟的腹甲或牛的胛骨卜吉凶，他们先在甲骨上钻一下，再用火灼；甲骨经火，有裂痕，便是兆象，卜官细看兆象，断定吉凶；然后便将卜的人、卜的日子、卜的问句等用刀笔刻在甲骨上。

这便是卜辞。

卜辞里并没有阴阳的观念，也没有八卦的痕迹。

卜法用牛骨最多，用龟甲是很少的。

1.上面语段出自《经典常谈》中的《_______》篇；【语段二】中，“用刀笔刻在甲骨上”的比金文更早的文字叫作_______。

冀教版八年级英语下册UNIT 3 综合测试卷听力部分Ⅰ. 听句子，选出句子中所包含的信息(共5小题；每小题1分，满分5分) ()1. A. sheep B. jeep C. sleep()2. A. mouth B. mouse C. month()3. A. in danger B. in trouble C. in return()4. A. Don't cut down this tree!B. How about cutting down this tree?C. Why are you cutting down this tree?()5. A. Don't feed the birds in the park.B. You can feed the animals at the zoo.C. Don't feed the animals at the zoo.Ⅱ. 听句子，选出该句的最佳答语(共5小题；每小题1分，满分5分) ()6. A. Yes. That's a good idea.B. It's near my home.C. The zoo is a new one.()7. A. It likes milk.B. It has long ears.C. It's from America.()8. A. Sorry, I won't.B. No Food.C. It doesn't matter.()9. A. Yes, it is.B. No, they don't.C. Yes, there is.()10. A. Yes, it is.B. Me, too.C. No, it doesn't.Ⅲ. 听对话和问题，选择正确答案(共8小题；每小题1分，满分8分)()11. Which sign is right?()12. Which animal is mentioned in the conversation?()13. Why are wild animals in danger of disappearing?A. Because people hunt and kill them.B. Because people cut down too many trees.C. Both of the above.**************************()14. What are Mike and Kate going to do this morning?A. They are going to the park.B. They are going to the zoo.C. They are going to the forest.()15. Why can't they see any pandas in their city?A. Because it's too cold in their city.B. Because their city doesn't have bamboo.C. Because people in their city don't like pandas.**************************()16. How often does Jim feed his pet?A. Once a day.B. Twice a day.C. Three times a day.()17. What is the dog house made of?A. Paper.B. Paper boxes.C. Cotton. ()18. Where does Jim walk his dog?A. In the park.B. In the street.C. At home.Ⅳ. 听短文和问题，选择正确答案(共7小题；每小题1分，满分7分) ()19. When did the girl go to the zoo?A. Last Saturday.B. Last Sunday.C. This Saturday. ()20. Whom did the girl go to the zoo with?A. Her friends.B. Her classmates.C. Her parents.()21. How did they like the visit to the zoo?A. Great and enjoyable.B. Boring.C. Just so so.**************************()22. What should you show when you buy a student's ticket?A. Your ID card.B. Your postcard.C. Your student card.()23. When can students buy half-price tickets?A. On Saturday.B. On Sunday.C. Every day. ()24. How much should you pay for a student's ticket on weekdays?A. 20 yuan.B. 20 dollars.C. 10 yuan.()25. Why can't we feed the animals?A. Because they're dangerous.B. Because they're interesting.C. Because they're important.Ⅴ. 听短文填空(共5小题；每小题1分，满分5分)笔试部分Ⅵ. 单项选择(共10小题；每小题1分，满分10分)()31. We need courage to face the difficulty, so be ____ enough!A. magicB. braveC. strangeD. clever()32. You are late again. Can you tell me the ____？A. dangerB. reasonC. centuryD. symbol()33. We should do something useful ____ just talking about the problem.A. such asB. instead ofC. thanks toD. because of()34. I heard there were ____ beautiful red leaves in the mountains, but I can't see ____ now.A. some; someB. any; anyC. any; someD. some; any()35. Bob usually goes to work early so that he can ____ the heavy traffic in the morning.A. testB. protectC. avoidD. warn()36. Blue whales are ____. We should try to protect them.A. in timeB. in needC. in dangerD. in balance()37. —Look, the light is still on in Helen's office.—Maybe she ____ her work yet.A. doesn't finishB. won't finishC. hasn't finishedD. didn't finish()38. Lily has learned how to cook in a cooking class. And now she cooks as ____as her mother.A. goodB. wellC. betterD. best()39. A number of students ____ playing on the playground. The number of them ____ more than one hundred.A. is; isB. are; isC. are; areD. is; are()40. We must do something to stop people from ____ trees.A. looking afterB. cutting downC. coming downD. turning downⅦ. 完形填空(共10小题；每小题1分，满分10分)A few years ago, I was about fourteen or fifteen years old. One __41__，my parents went out for a walk after supper. I stayed at home alone watching TV. Later I heard my cat, Aster, meowing(喵喵叫) at the __42__. She was a funny and proud cat. She was good at catching mice, and sometimes she would like to show me her “prize”.I went to __43__ the door. She ran in quickly with __44__ in her mouth. After she dropped it on the floor, I found it was a mouse, again. It __45__ died. My mother always liked to keep the floor __46__，so I had to find something to pick the mouse up and __47__ it away.When I came back, I found the mouse disappeared. I looked everywhere but couldn't find it. We had a basement(地下室) under the house, so there were so many places and holes for it to stay. I __48__ looking for it at last.But it was not the __49__ of that. About a year later, I was helping my mum clean up the basement. And can you guess what we saw? Yes, some bones(骨头) of a dead mouse. We could only believe and hope that it was the mouse that ran __50__ from the floor that night. We know that Aster made it.()41. A. morning B. noonC. eveningD. afternoon()42. A. floor B. bedC. sofaD. door()43. A. close B. openC. breakD. repair()44. A. something B. anythingC. everythingD. nothing()45. A. already B. clearlyC. seriouslyD. almost()46. A. dirty B. cleanC. crowdedD. full()47. A. throw B. giveC. washD. die()48. A. cheered up B. tried outC. gave upD. depended on ()49. A. time B. beginningC. songD. end()50. A. up B. toC. awayD. intoⅧ. 阅读理解(共15小题；每小题2分，满分30分)A()51. 8-year-old Alice and her parents are going to the zoo on May 1st. How much should they pay?A. $36.B. $43.C. $50.D. $68.()52. What can you get if you buy tickets to the zoo online?A. Free tickets.B. Longer visits.C. Cheaper train rides.D. Chances to see more animals.()53. If you take part in the drawing competition, you can ____.A. use your own drawing paperB. sit at any place of the zoo to drawC. draw anything you like in the zooD. finish your picture after leaving the zooBMary was in bed, feeling sleepy. She read the first few words of her book, “The dodo(渡渡鸟)was a bird that couldn't fly…”，and soon she fell fast asleep.Whoosh! The window blew wide open. Mary sat up, and through the window she saw a dodo, an unusual dodo, right there in her yard!“I lived over four hundred years ago，” the dodo said. “But then terrible things happened. People cut down the forests, so we had nothing to eat. We all died. ” The dodo felt sad.Suddenly, a mammoth(猛犸)rushed in. It said，“I've been looking for you, Dodo!I lived thousands of years ago，but not now. ”It added，“Scientists think the weather changed, changing the environment where we lived. We ate grass, but as the weather grew warmer, forests spread and there was less grass to eat. ”Seconds later, an elephant bird came. It said proudly, “I'm the heaviest bird that has ever lived. I weigh half a ton. But we lived on the earth over a thousand years ago. ”The animals all looked sad. Before they had time to say another word, a tiger c ame in. “My friends，”it said, showing its big teeth. “I hear what you are talking about. We tigers are lucky. Now there are some special places for us animals who are in danger. We are safe and no one can hurt us there. ”“Sounds great！” thought Mary. “Ani mals should have more of these kinds of places！”The window blew shut, and Mary woke up with a start. There was no one and nothing to see, except the book in her hand.()54. Which of the animals lived thousands of years ago?A. Dodos.B. Elephant birds.C. Tigers.D. Mammoths.()55. Why are tigers lucky?A. Because they have big teeth.B. Because they live in safe places.C. Because the environment changed.D. Because the weather grew warmer.()56. Which question could best help us find out the writer's purpose?A. Does the writer want us to have fun？B. Does the writer want us to raise animals?C. Does the writer want us to protect dodos?D. Does the writer want us to learn something?C()57. Ya Ya had lived in the U. S. for ____ years.A. 5B. 10C. 15D. 20()58. What colour are newborn pandas?A. Black and white.B. Pink.C. Yellow.D. Grey.()59. Which of the following is TRUE according to the passage?A. Ya Ya is still a young panda now.B. Shanghai Zoo is Ya Ya's final home.C. Ya Ya had a short flight coming back home.D. Ya Ya helps foreigners know more about China.()60. This passage is ____.A. a piece of newsB. an adC. a diaryD. a letterDScientists looked for paw prints(爪印) in the forests. In this way, they knew the number of pandas! “It's hard to see pandas in the wild，” said Colby, a scientist. “They hide in the thick bamboo forests. ” That's why scientists used paw prints to get the number. The number of the pandas was a surprise to scientists. They learned that more pandas lived in the wild!“We found pandas living in areas we didn't know，” said Colby. Although the news is good, pandas are in danger.Here are some fun facts of pandas:*It takes a panda more than 10 hours to eat 9 kg to 14 kg of bamboo every day.*A newborn panda weighs 90～130 grams. That is about the weight of a mouse.A panda's front paws have wrist bones(腕骨). The panda uses them to catch bamboo.The main threat to pandas is that their land is becoming smaller and smaller. Pandas lose their land when people cut down parts of the forest for wood and farming. Now, China has 13 nature reserves(保护区) for pandas. People mustn't cut down trees there. Scientists want to create more nature centres to give pandas a better chance to live.()61. Why did scientists look for paw prints in the forests?A. Because they could catch pandas in this way.B. Because they could know where pandas were in this way.C. Because they could know the number of pandas in this way.D. Because they could find pandas in this way.()62. Which of the following is NOT mentioned in the passage?A. A panda uses its front paws to catch bamboo.B. A newborn panda is nearly as heavy as a mouse.C. A panda usually sleeps for more than 10 hours every day.D. A panda's front paws have wrist bones.()63. What does the underlined word “threat” in the last paragraph mean?A. Chance.B. Courage.C. Danger.D. Warning.()64. What does the last paragraph mainly talk about?A. Fewer and fewer trees in China.B. The big problem pandas are facing.C. The number of pandas in the wild.D. The height of pandas.()65. What can we know from the passage?A. There are fewer and fewer nature reserves in China.B. People should help pandas live a happy life in the wild.C. All the pandas should live in the nature reserves.D. No one can see the pandas.Ⅸ. 任务型阅读(共5小题；每小题2分，满分10分)Many insects and animals have their special colours. Colours in them seem to be used mainly to protect themselves.Some birds like eating locusts(蝗虫), but birds cannot easily catch them. Locusts change their colours together with the change of the colours of crops. When the crops are green, locusts look green. As the harvest time comes, locusts change to the same brown colour. It is easy for the enemy to find and then eat the insects that have different colours from plants. So these insects have to go out at night.Bears，tigers and some other animals move quietly through forests. Hunters can't see them easily. This is because they have the colours much like the trees.A kind of animal in the sea can expel(喷出) a kind of black liquid(液体) when it faces danger. When its enemies cannot see it，it quickly swims away. How interesting the animal world is!66、67题完成句子；68～70题简略回答问题。

初中八年级数学下册第十六章二次根式单元检测习题三（含答案）计算))⋅=__________．66【答案】-31【解析】【分析】直接利用平方差公式得出226，再利用二次根式计算结果即可.【详解】解：原式22=6=5-36=-31.故答案为：-31.【点睛】本题主要考察了平方差公式和二次根式的运算，熟练掌握平方差公式和二次根式的运算是本题的关键.82．化简（π﹣3.14）0+|1﹣2√2|﹣√8的结果是___．【答案】0．【解析】【分析】按顺序分别进行0次幂运算、绝对值的化简、二次根式的化简，然后再按运算顺序进行计算即可.【详解】（π﹣3.14）0+|1﹣2√2|﹣√8＝1+2√2﹣1﹣2√2＝0，故答案为：0．【点睛】本题考查了实数的运算，涉及了0次幂、绝对值化简、二次根式化简等运算，熟练掌握相关运算法则是解题的关键.83．当a=______【答案】1【解析】∵是同类二次根式，∴a+2=5−2a，解得：a=1.84．若规定一种运算为a★b(b－a)，如3★5×(5－3)＝，________．－2【解析】【分析】），再进行二次根式的乘法运算．【详解】）-2．-2．【点睛】本题考查了实数的运算：先算乘方或开方，再算乘除，然后进行加减运算；有括号先算括号．85．若实数a 满足=2，则a 的值为 ． 【答案】5【解析】试题分析：根据算术平方根平方运算等于被开方数，可得关于a 的方程． 根据题意可得：a ﹣1=4．解得a=5，考点：二次根式的定义．三、解答题86．解方程：＋1)x【答案】x ＝2. 【解析】试题分析：先化简，再进行解方程.试题解析：)11x = 221x ⎡⎤-=⎢⎥⎣⎦2x =2x = 87．计算下列各式：（1） （221-【答案】（1）-（21【解析】试题分析：（1）直接将被开方数相同的二次方根合并即可；（2）先考虑绝对值里边式子的正负，然后利用绝对值的代数意义化简，去括号合并后即可得到结果.试题解析：（1）原式(2(3=--=-；（2）原式=(21)=---21=1=-点睛：此题考查了二次根式的加减混合运算，关键是熟练掌握绝对值的化简及同类二次根式的合并.88．计算: ;(2);⎛ ⎝;a>0). 【答案】(1)；(2) -(3) 4ab -；(4)(0)a ＞.【解析】试题分析：(1)被开方数与被开方数相除，结果化为最简二次根式；(2)根号外和根号内的部分分别相除，再把所得的结果相乘；(3)被开方数与被开方数相除，结果化为最简二次根式，注意符号运算；(4)逆用二次根式的除法法则.试题解析： ===；(2)3110⎛⎫=-÷⨯ ⎪⎝⎭==-；⎛= ⎝4ab ==-；()a ===＞.89．计算：(2)4(3) (4)()21-【答案】(1)；(3)-5；(4)9.【解析】【分析】（1）先化简，再加减即可；（2）先化简然后根据二次根式的乘法、除法法则运算；（3）利用平方差公式计算；（4）利用乘法公式展开，然后化简合并即可．【详解】解：(1)原式==(2)原式=4=2=(3)原式22=-38=-5=-(4)原式81=+9=+9=【点睛】本题考查了二次根式的混合运算：先把二次根式化为最简二次根式，然后进行二次根式的乘除运算，再合并即可．在二次根式的混合运算中，如能结合题目特点，灵活运用二次根式的性质，选择恰当的解题途径，往往能事半功倍．90．先化简，再求值：22x 2x 1x 1-+-÷（x 1x 1-+-x+1），其中x=2sin45°--1）0．【答案】【解析】【分析】根据分式的运算法则以及特殊角锐角三角函数值、零指数幂的意义即可求出答案．【详解】解：当x=2sin45°--1）0．即x=2×2-1 原式=()()2(x 1)x 1x 1-+-÷2x x x 1-+=x 1x 1-+•()x 1x 1x +-=1x- =【点睛】本题考查分式的运算法则和分母有理化，以及特殊角的三角函数值，解题的关键是熟练运用分式的运算法则，本题属于基础题型．。

北师大版2020-2021学年度八年级数学下册1.1等腰三角形自主学习同步练习题3（含答案）1．等腰△ABC中，它的底角∠B＝70°，则顶角∠A的度数为（）A．70°B．30°C．40°D．60°2．等腰三角形的一个内角是70°，则它顶角的度数是（）A．70°B．70°或40°C．70°或50°D．40°3．如图所示，△ABC中，AB＝AC，D是BC上一点，DE⊥AB于点E，若∠A＝50°，则∠BDE的度数是（）A．65°B．50°C．30°D．25°4．如图，△ABC中，DE垂直平分AB，垂足为D，交BC于E，若∠B＝32°，AC＝CE，则∠C的度数是（）A．52°B．55°C．60°D．65°5．等腰三角形其中两条边的长度为5和11，则该等腰三角形的周长为（）A．21B．27C．21或32D．21或276．如图，△ABC是等腰三角形，点O是底边BC上任意一点，OE、OF分别与两边垂直，等腰三角形的腰长为6，面积为15，则OE+OF的值为（）A．5B．7.5C．9D．107．如图，在等腰△ABC中，AB＝AC＝10，BC＝12，O是△ABC外一点，O到三边的垂线段分别为OD，OE，OF，且OD：OE：OF＝1：4：4，则AO的长度为（）A．10B．9C．D．第3题第4题第6题第7题8．如图，在△ABC中，D、E分别为AB、AC边上的点，DA＝DE，DB＝BE＝EC．若∠ABC＝130°，则∠C的度数为（）A．20°B．22.5°C．25°D．30°9．如图，在△ABC中，AB＝AC，点D，点E分别是BC，AC上一点，且DE⊥AD，若∠BAD＝55°，∠B＝50°，则∠DEC的度数为（）A．125°B．120°C．115°D．110°10．如图，已知∠AOB＝10°，且OC＝CD＝DE＝EF＝FG＝GH，则∠BGH＝（）A．50°B．60°C．70°D．80°11．如图，在△ABC中，AB＝AC，∠A＝30°，直线m∥n，顶点C在直线n上，直线m 交AB于点D，交AC于点E，若∠1＝150°，则∠2的度数是（）A．45°B．40°C．35°D．30°12．如图所示，△ABC中，AB＝AC，AB的垂直平分线DE交BC的延长线于E，交AC于F，连接BF，∠A＝50°，AB+BC＝16cm，则△BCF的周长和∠E分别等于（）A．16cm，25°B．8cm，30°C．16cm，40°D．8cm，25°第9题第10题第11题第12题13．等腰三角形一腰上的高与另一腰的夹角是45°，则这个三角形的底角为（）A．67°31′B．22°30′C．67°30′D．22°30′或67°30′14．如图，在△ABC中，D，E是BC边上两点，且满足AB＝BE，AC＝CD，若∠B＝α，∠C＝β，则∠DAE的度数为（）A．B．C．D．15．如图，在等腰△ABC中，顶角∠A＝44°，BD平分底角∠ABC交AC于点D，E是BC 延长线上一点，且CD＝CE，则∠E的度数为（）A．22°B．44°C．34°D．68°16．如图，在△ABC中，AB＝AC，点D，E在边BC上，∠BAD＝∠CAE，若BC＝15，DE ＝6，则CE的长为（）A．3.5B．4.5C．5D．5.5第14题第15题第16题17．如图，等腰△ABC中，点P是底边BC上的动点（不与点B，C重合），过点P分别作AB、AC的平行线PM、PN，交AC、AB于点M、N，则下列数量关系一定正确的是（）A．PM+PN＝AB B．PM+PN＝BCC．PM+PN＝2BC D．PM+PN＝AB+BC18．等腰三角形一腰上的中线把这个三角形的周长分成12cm和21cm两部分，则这个等腰三角形底边的长为（）A．17cm B．5cm C．5cm或17cm D．无法确定19．如图，在△ABC中，AC＝BC，∠C＝36°，AD平分∠BAC，则图中等腰三角形的个数是（）A．1个B．2个C．3个D．4个20．如图，在△ABC中，AB＝AC，∠A＝36°，BD，CE分别是∠ABC，∠BCD的角平分线，那么图中的等腰三角形有（）A．2个B．3个C．4个D．5个21．如图所示的正方形网格中，网格线的交点称为格点．已知A、B是两格点，若C也是图中的格点，则使得△ABC是以AB为一腰的等腰三角形时，点C的个数是（）A．8B．6C．4D．722．如图，在Rt△ABC中，∠ACB＝90°，∠CAB＝36°，以C为原点，AC所在直线为y 轴，BC所在直线为x轴建立平面直角坐标系，在坐标轴上取一点M使△MAB为等腰三角形，符合条件的M点有（）A．6个B．7个C．8个D．9个23．如图所示的方格纸中，每个方格均为边长为1的小正方形，我们把每个小正方形的顶点称为格点，现已知A、B、C、D都是格点，则下列结论中正确的是（）A．△ABC、△ABD都是等腰三角形B．△ABC、△ABD都不是等腰三角形C．△ABC是等腰三角形，△ABD不是等腰三角形D．△ABC不是等腰三角形，△ABD是等腰三角形24．等腰三角形的周长为16，且边长为正整数，则底边长为．25．如图，在△ABC中，AE＝DE＝BD，AD＝EC，∠1＝17°，则∠EBC的度数是．26．如图，在△ABC中，∠ACB＝90°，CD⊥AB于点D，CE平分∠DCB交AB于点E．（1）求证：∠AEC＝∠ACE；（2）若∠AEC＝2∠B，AD＝1，求BD的长．27．如图：E在△ABC的AC边的延长线上，D点在AB边上，DE交BC于点F，DF＝EF，BD＝CE．求证：△ABC是等腰三角形．（过D作DG∥AC交BC于G）28．在△ABC中，AD平分∠BAC，E是BC上一点，BE＝CD，EF∥AD交AB于F点，交CA的延长线于P，CH∥AB交AD的延长线于点H，①求证：△APF是等腰三角形；②猜想AB与PC的大小有什么关系？证明你的猜想．29．如图，在△ABC中，AB＝AC＝2，∠B＝40°，点D在线段BC上运动（D不与B、C 重合），连接AD，作∠ADE＝40°，DE交线段AC于E．（1）当∠BDA＝115°时，∠BAD＝°；点D从B向C运动时，∠BDA逐渐变（填“大”或“小”）；（2）当DC等于多少时，△ABD≌△DCE，请说明理由；（3）在点D的运动过程中，△ADE的形状也在改变，判断当∠BDA等于多少度时，△ADE是等腰三角形．参考答案1．解：根据题意∠C＝∠B＝70°，∴∠A＝180°﹣70°﹣70°＝40°．故选：C．2．解：本题可分两种情况：①当70°角为底角时，顶角为180°﹣2×70°＝40°；②70°角为等腰三角形的顶角；因此这个等腰三角形的顶角为40°或70°．故选：B．3．解：∵AB＝AC，∠A＝50°，∴∠B＝∠C＝65°，∵DE⊥AB，∴∠BED＝90°，∴∠BDE＝90°﹣∠B＝25°．故选：D．4．解：连结AE，∵△ABC中，DE垂直平分AB，∠B＝32°，∴∠BED＝58°，∴∠AED＝58°，∴∠AEC＝64°，∴∠C＝180°﹣64°×2＝52°．故选：A．5．解：若5为腰长，则三边为5，5，11，∵5+5＜11，∴5，5，11不能构成三角形，若11为腰长，则三边为5，11，11，∵5+11＞11，∴等腰三角形的周长为5+11+11＝27，故选：B．6．解：连接AO，如图，∵AB＝AC＝6，∴S△ABC＝S△ABO+S△AOC＝AB•OE+AC•OF＝15，∵AB＝AC，∴AB（OE+OF）＝15，∴OE+OF＝5．故选：A．7．解：连接AO，OB，OC，∵O是△ABC外一点，O到三边的垂线段分别为OD，OE，OF，且OD：OE：OF＝1：4：4，∴O在∠BAC的角平分线上，∵AB＝AC，∴AO过D，且AD⊥BC，∵BC＝12，∴BD＝CD＝6，在Rt△ADC中，由勾股定理得：AD＝＝＝8，即BD＝8，设OD＝x，则OE＝OF＝4x，∵S△ABC+S△OBC＝S△ABO+S△ACO，AB＝AC＝10，BC＝12，AD＝8，∴＝+，∴＝，解得：x＝，即OD＝，∴AO＝AD+OD＝8+＝，故选：D．8．解：设∠C＝x，根据等腰三角形的性质得∠EBC＝x，则∠DBE＝130°﹣x，根据等腰三角形的性质得∠EDB＝25°+x，根据三角形外角的性质和等腰三角形的性质得∠A＝12.5°+x，依题意有12.5°+x+x+130°＝180°，解得x＝30°．故选：D．9．解：∵AB＝AC，∴∠B＝∠C，∵∠B＝50°，∴∠C＝50°，∴∠BAC＝180°﹣50°﹣50°＝80°，∵∠BAD＝55°，∴∠DAE＝25°，∵DE⊥AD，∴∠ADE＝90°，∴∠DEC＝∠DAE+∠ADE＝115°．故选：C．10．解：∵OC＝CD，∴∠CDO＝∠O＝10°∴∠DCE＝∠O+∠CDO＝20°，∵CD＝DE，∴∠DCE＝∠CED＝20°，∴∠EDF＝∠O+∠CED＝30°，∵DE＝EF，∴∠EDF＝∠EFD＝30°，同理∠GEF＝∠EGF＝40°，∠GFH＝∠GHF＝50°，∠BGH＝60°，故选：B．11．解：∵AB＝AC，且∠A＝30°，∴∠ACB＝75°，在△ADE中，∵∠1＝∠A+∠AED＝150°，∴∠AED＝150°﹣30°＝120°，∵m∥n，∴∠AED＝∠2+∠ACB，∴∠2＝120°﹣75°＝45°，故选：A．12．解：∵在△ABC中，AB＝AC，∠A＝50°，∴∠ABC＝∠ACB＝65°，∵DE是AB的垂直平分线，∴AF＝BF，∠BDE＝90°，∴∠E＝90°﹣∠ABC＝25°，∵AB+BC＝16cm，∴△BCF的周长为：BC+CF+BF＝BC+CF+AF＝BC+AC＝BC+AB＝16cm．故选：A．13．解：有两种情况；（1）如图，当△ABC是锐角三角形时，BD⊥AC于D，则∠ADB＝90°，已知∠ABD＝45°，∴∠A＝90°﹣45°＝45°，∵AB＝AC，∴∠ABC＝∠C＝×（180°﹣45°）＝67.5°；（2）如图，当△EFG是钝角三角形时，FH⊥EG于H，则∠FHE＝90°，已知∠HFE＝45°，∴∠HEF＝90°﹣45°＝45°，∴∠FEG＝180°﹣45°＝135°，∵EF＝EG，∴∠EFG＝∠G＝×（180°﹣135°）＝22.5°，故选：D．14．解：∵BE＝BA，∴∠BAE＝∠BEA，∴α＝180°﹣2∠BAE，①∵CD＝CA，∴∠CAD＝∠CDA，∴β＝180°﹣2∠CAD，②①+②得：α+β＝360°﹣2（∠BAE+∠CAD）∴α+β＝360°﹣2[（∠BAD+∠DAE）+（∠DAE+∠CAE）]＝360°﹣2[（∠BAD+∠DAE+∠CAD）+∠DAE]＝360°﹣2（∠BAC+∠DAE），∵∠BAC＝180°﹣（α+β），∴α+β＝360°﹣2[180°﹣（α+β）+∠DAE]∴α+β＝2∠DAE，∴∠DAE＝（α+β），故选：A．15．解：∵△ABC是等腰三角形，∴AB＝AC，∴∠ABC＝∠ACB，∵∠A＝44°，∴∠ABC＝∠ACB＝＝68°，∵CD＝CE，∴∠E＝∠CDE，∵∠E+∠CDE＝∠ACB＝68°，∴∠E＝34°，故选：C．16．解：∵AB＝AC，∴∠B＝∠C，在△BAD和△CAE中，，∴△BAD≌△CAE，∴BD＝CE，∵BC＝15，DE＝6，∴BD+CE＝9，∴CE＝4.5，故选：B．17．解：∵AB＝AC，∴∠B＝∠C，∵PN∥AC，∴∠BPN＝∠C＝∠B，∴PN＝BN，∵PM∥AB，PN∥AC，∴四边形AMPN是平行四边形，∴PM＝AN，∴PM+PN＝AN+BN＝AB，故选：A．18．解：设等腰三角形的腰长是xcm，底边是ycm．根据题意，得：或，解得或．再根据三角形的三边关系知：8，8，17不能组成三角形，应舍去．所以它的底边长是5cm．故选：B．19．解：∵AC＝BC，∠C＝36°，∴△ABC是等腰三角形，∠BAC＝∠ABC＝72°，∵AD平分∠BAC，∴∠CAD＝∠BAD＝∠C＝36°∴△CAD为等腰三角形，∵∠BDA＝∠C+∠CAD＝72°＝∠B，∴△BAD为等腰三角形，∴则图中等腰三角形的个数是3个．故选：C．20．解：共有5个．（1）∵AB＝AC∴△ABC是等腰三角形；（2）∵BD、CE分别是∠ABC、∠BCD的角平分线∴∠EBC＝∠ABC，∠ECB＝∠BCD，∵△ABC是等腰三角形，∴∠EBC＝∠ECB，∴△BCE是等腰三角形；（3）∵∠A＝36°，AB＝AC，∴∠ABC＝∠ACB＝（180°﹣36°）＝72°，又BD是∠ABC的角平分线，∴∠ABD＝∠ABC＝36°＝∠A，∴△ABD是等腰三角形；同理可证△CDE和△BCD是等腰三角形．故选：D．21．解：如图，以AB为等腰△ABC其中的一条腰时，符合条件的C点有4个．故选：C．22．解：如图，①以A为圆心，AB为半径画圆，交直线AC有二点M1，M2，交BC有一点M3，（此时AB＝AM）；②以B为圆心，BA为半径画圆，交直线BC有二点M5，M4，交AC有一点M6（此时BM＝BA）．③AB的垂直平分线交AC一点M7（MA＝MB），交直线BC于点M8；∴符合条件的点有8个．故选：C．23．解：由图可得，AC＝BC＝，AD＝BD＝5，∴△ABC、△ABD都是等腰三角形，故选：A．24．解：由题意得：2x+y＝16，∵三角形的两边之和大于第三边，∴符合条件的三角形有：腰长为5，底边为6；腰长为6，底边为4；腰长为7，底边为2；∴底边长为2，4，6，故答案为：2或4或6．25．解：∵BD＝DE，∴∠DEB＝∠1＝17°，∴∠ADE＝∠1+∠DEB＝34°，∵AE＝DE，∴∠A＝∠ADE＝34°，∵BD＝AE，AD＝CE，∴AD+BD＝CE+AE，即AB＝AC，∴∠ABC＝∠C＝73°，∴∠CBE＝∠ABC﹣∠1＝56°，故答案为：56°．26．解：（1）∵∠ACB＝90°，CD⊥AB，∴∠ACD+∠A＝∠B+∠A＝90°，∴∠ACD＝∠B，∵CE平分∠BCD，∴∠BCE＝∠DCE，∴∠B+∠BCE＝∠ACD+∠DCE，即∠AEC＝∠ACE；（2）∵∠AEC＝∠B+∠BCE，∠AEC＝2∠B，∴∠B＝∠BCE，又∵∠ACD＝∠B，∠BCE＝∠DCE，∴∠ACD＝∠BCE＝∠DCE，又∵∠ACB＝90°，∴∠ACD＝30°，∠B＝30°，∴Rt△ACD中，AC＝2AD＝2，∴Rt△ABC中，AB＝2AC＝4，∴BD＝AB﹣AD＝4﹣1＝3．27．证明：过点D作DG∥AC交BC于点G，如图所示．∵DG∥AC，∴∠GDF＝∠E，∠DGB＝∠ACB．在△GDF和△CEF中，，∴△GDF≌△CEF（ASA），∴GD＝CE．∵BD＝CE，∴BD＝GD，∴∠B＝∠DGB＝∠ACB，∴△ABC是等腰三角形．28．①证明：∵EF∥AD，∴∠1＝∠4，∠2＝∠P，∵AD平分∠BAC，∴∠1＝∠2，∴∠4＝∠P，∴AF＝AP，即△APF是等腰三角形；②AB＝PC．理由如下：证明：∵CH∥AB，∴∠5＝∠B，∠H＝∠1，∵EF∥AD，∴∠1＝∠3，∴∠H＝∠3，在△BEF和△CDH中，∵，∴△BEF≌△CDH（AAS），∴BF＝CH，∵AD平分∠BAC，∴∠1＝∠2，∴∠2＝∠H，∴AC＝CH，∴AC＝BF，∵AB＝AF+BF，PC＝AP+AC，∴AB＝PC．29．解：（1）∠BAD＝180°﹣∠ABD﹣∠BDA＝180°﹣40°﹣115°＝25°；从图中可以得知，点D从B向C运动时，∠BDA逐渐变小；故答案为：25°；小．（2∵∠EDC+∠EDA＝∠DAB+∠B，∠B＝∠EDA＝40°，∴∠EDC＝∠DAB．，∵∠B＝∠C，∴当DC＝AB＝2时，△ABD≌△DCE，（3）∵AB＝AC，∴∠B＝∠C＝40°，①当AD＝AE时，∠ADE＝∠AED＝40°，∵∠AED＞∠C，∴此时不符合；②当DA＝DE时，即∠DAE＝∠DEA＝（180°﹣40°）＝70°，∵∠BAC＝180°﹣40°﹣40°＝100°，∴∠BAD＝100°﹣70°＝30°；∴∠BDA＝180°﹣30°﹣40°＝110°；③当EA＝ED时，∠ADE＝∠DAE＝40°，∴∠BAD＝100°﹣40°＝60°，∴∠BDA＝180°﹣60°﹣40°＝80°；∴当∠ADB＝110°或80°时，△ADE是等腰三角形．。

2020人教版八下同步练习册U3 Could you please clean your room?单项选择1.—Thank you so much for helping me work out this difficult math problem.—____.A. That sounds goodB. No thanksC. I’m glad to hear thatD. No problem2.—Jack, could you please answer the phone?—____. I’m washing my hair at the moment.A. That’s all rightB. No, I couldn’tC. Sorry, I can’tD. No problem3.—Where do you want to go to have dinner?—I have no idea. ____.A. Let’s goB. You’re welcomeC. It’s up to youD. No problem4.—______.—Certainly. I’d love to.A. Can you play the accordionB. Do you mind my opening the window?C. Could you take care of my dog while I am on vacationD. Do you clean your room every day?5.—I’m waiting for Jack. I don’t know if he__________.—Don’t worry. If he ________, I will let you know.A. will come, comesB. will come, will comeC. come, comesD. comes, will come6.—What will a driver do if a traffic accident___?—Try the best to keep both the driver and passengers safe if possible..A. is happeningB. happensC. happenedD. will happen7.—I sleep nine hours every day. How about you?—________. I have to spend twenty hours working every dayA. So do l.B. Neither do I.C. Yes, I do, too.D. No, I don’t.8.—What are you doing, Ben?—I’m thinking about____________next summer vacation.A. where will I goB. where I am goingC. where was I goingD. where was I going9.He asked me_______.A. if you can play the pianoB. what I was doing at that timeC. what you are doing thenD. why are you late for school10.He was reading the newspaper ____ his father came backA. whileB. whenC. asD. after11.Mom was watching TV alone __ she heard a knock on the door, which frightened her a lot.A. whenB. whileC. as soon asD. how12.—Why does Liu Sanzi drop out of school ?—Because it’s important for him ___on their farm . His family is too poor.A. workB. workingC. to workD. works13.It’s also good ___you___me so much help.A. for, to giveB. of, to giveC. for, givingD. of, giving14.You can __________this book and you can___________it for two weeks, but you mustn’t __________it toothers.A. borrow, borrow, lendB. borrow, keep, lendC. lend, keep, borrowD. lend, borrow, borrow15.—Would you please drive a bit faster, Sir? My flight is taking off.—___.A. sorry, I think it is impossibleB. I am afraid I canC. Out of question. I will do my best.D. Sure, it depends【参考答案】DCCCA BDBBB ACABC阅读理解A“All grown-ups were once children but only few of them remember it.”It’s a thoughtful sentence from a famous book, The Little Price. The bookfirst came out in 1943 and it was written by the French writer, Antoine deSaint-Exupéry(1900-1944).The main character lives on the planet B612 alone. He leaves his star totravel and meets different kinds of people from other planets such as the king, the drunk(酒鬼), the businessman and so on. During the travel, the young prince discovers that people are all looking for happiness with hardship(苦难) but they seldom have the ability to achieve it because of their so-called “business”. In the real life, we are often busy with our study and work just like a walking dead body. We grew up and threw away a lot of memories, but thanks to this book we can look back what we have forgotten.Though it is a children’s book, it’s also written for teenagers and adults. People of all ages can read this book and have their own understanding of it. The story’s true meaning is between the lines said by the fox: “One sees clearly only with heart. What is important is invisible(隐形的) to the eyes.” Other key messages are also explained by the fox, such as: “You become responsible forever for what you have tamed(驯服的).” The fox’s messages areunquestionably the book’s most famous ideas because they deal with human(人类) relationships.It is a book about life and love, and The Little Prince can make people feel warm and fresh.1. According to the article, many people can’t achieve happiness because ____.A. people are looking for happiness with hardship.B. people are often busy with their study and work.C. people don’t have a lot of memories.D. people forget they were once young.2. Why are the words from the fox important to The Little Prince?A. Because they tell the true meaning of the story.B. Because they can help you become responsible.C. Because they are explained by the fox.D. Because they speak for children and adults.3. The writer wrote this article to ____.A. say something about B612B. introduce a famous princeC. tell what human should beD. suggest reading The Little Prince【参考答案】BADBErica David loves snow. It’s a good thing, because she lives in a very snowy, windy and cold place! The temperature in winter can sometimes reach -37℃ in Wyoming.When Erica David was 11 years old, she decided to study snow for her school science project. She asked a simple question: ____.Snow fences(栅栏) are important in Wyoming, because there is a lot of snow. The fences keep snow off roads. They also protect farm animals from the wind and snow. Erica’s experiments look simple, but her results are very interesting. In her first experiments, Erica used soap powder(粉末). The dry soap was like snow. She made wind with a fan and measured(测量) the soap. After that, she made real fences and measured real snow.Every year, Erica makes new fences. During a snowstorm, she measures wind speed. Then after the snowstorm, she measures the snow on the fences.“Some kids call me crazy,” says Erica. “Days with 20-mile-per-hour(32-kilometer-per-hour) winds are my favorite snow days.”Erica introduces the research from her experiments at her school science fair. She also competes in science competitions with students from around the world. In one competition, she won $8,000 and a computer.Next, Erica is going to research sage plants(鼠尾草). These Wyoming bushes are like a natural snow fence. She’s also going to build her biggest and best snow fences ever. How can we describe Erica’s fences? Two words: very cool!1. What has Erica David done till now?○1She’s taken part in some competitions.○2She’s built her largest snow fences.○3She’s showed the research at her school.○4She’s made only one snow fence.A. ○1○2B. ○2○3C. ○3○4D. ○1○32. What is Erica probably going to use to make snow fences?A. SnowB. Soap powderC. Sage plantsD. Rock3. Which is the best sentence for the blank in the second paragraph?A. How can we make snow fences better?B. How can we finish the science project?C. Why should people build snow fences?D. What should we prepare for the project?4. What can we learn from the passage?A. Erica won $8,000 in all from the competitions.B. Fences that were built by Erica are cool but simple.C. Building Snow Fences is really useful in some ways.D. Erica built snow fences to measure wind speed.【参考答案】DCACCEmma Watson, the Harry Potter star, was seen doing something strange on the London Underground subway system the other day---she hid 100 copies of a book named Mom & Me & Mom by the US writer Maya Angelou in different places in the subway.With each book, there is a hand-written note by Watson, asking people who find the book to “take special care” of it and “when you are finished, please leave it on the subway again for someone else to find.”What Watson was doing was, in fact, part of the Books on the Underground movement. It encourages people to leave their favorite books on the subway so other passengers can enjoy them too.The movement was first started in 2012 by Hollie Belton, a woman who worked in London. She had a habit of reading on the subway on her way to work and back home. She noticed that a lot of people shared her habit and thought it would be cool if people could know what everyone else was reading. So she designed stickers(贴纸) that had her book-sharing idea printed on them, put them on the books she had finished and then left the books on the subway. Over the years, Belton has left over 2,000 books of her own on the subway, and more and more people are taking part in the movement.The movement has not only made everyday life more fun, but also gotten people to read more. “There are people who haven’t read in ages and they’ve gotten back their love of reading after picking up one of our books,” Belton said in an interview with The Culture Trip website.Watson has the same love for books, which is why she took part in the movement. In fact, Watson set up her own online book club---Our Shared Shelf---earlier this year, and Mom& Me & Mom is Watson’s November pick for the club.1. Who started the Books on the Underground movement?A. Maya Angelo.B. Emma Watson.C. Hollie Belton.D. Harry Potter.2. What does Emma Watson ask people to do by leaving a note?A. Take care of the book that you find.B. Lend the book to people who like books.C. Leave the book anywhere after reading.D. Write down some notes while reading.3. What’s the aim of the Books on the Underground movement?A. To ask more people to join in the book club.B. To introduce an America writer’s books.C. To hear your thoughts about the books.D. To encourage people to read more books.4. Which of the following about Emma Watson is TRUE according to the passage?A. She began to take part in the movement in 2012.B. She is the author of the book Mom & Me & Mom.C. She has great love for books like Hollie Belton.D. She has left over 2000 books on the subway.【参考答案】CADCD○1Do you know any 9-year-olds who have started their own museum? When Theodore Roosevelt was only nine, he and two of his cousins opened the “Roosevelt Museum of Natural History.” The museum was in his bedroom. It had a total of 12 specimens(标本). On display were a few seashells, some dead insects, and some birds’ nests. Young Roosevelt took great pride in his small museum.○2Born in New York in 1858, Theodore Roosevelt was not always healthy. “I was a sickly small and weak boy.” He once wrote. He had a health problem called asthma(哮喘). He often found it hard to breathe. Instead of playing, he observed nature and then read and wrote about it.○3Roosevelt’s interest in nature sometimes got him into trouble. Once, his mother found several dead mice in the ice box. She demanded that the mice be thrown out. When he was about 12, his father asked him to improve hisbody. Roosevelt began working out in a gym. He didn’t become strong quickly. But he did decide to face life’s challenges with a string spirit. That determination stayed with Roosevelt his whole life. And gradually his body did get strong. As an adult, he was an active, healthy person. He enjoyed adventures, and he loves the outdoors. A toy company named the teddy bear for Theodore “Teddy” Roosevelt after it was learned that Roosevelt after it was learned that Roosevelt refused to shoot a baby bear while hunting.○4Roosevelt became the 26th President of America at 42. He was the youngest leader the country had ever had.1. What is the main idea of the first paragraph?A. Roosevelt had a natural history museum in his bedroom.B. The museum had many different kinds of sea animals.C. Roosevelt opened the museum with the help of his two cousins.D. Roosevelt was a proud and brave boy.2. Which sentence best tells the main idea of the second paragraph?A. Roosevelt loved the outdoors.B. Asthma makes it hard to have fun.C. Roosevelt did not like to play.D. Roosevelt was a sickly child.3. Which sentence does not tell about Roosevelt as a boy?A. He opened his own natural history museum.B. He became President in 1901.C. He had asthma and breathed difficultly.D. He once left several dead mice in the icebox.4. In which book might you find this passage?A. Small Nature Museums.B. Living with Asthma.C. The Childhoods of America’s Presidents.D. How the Teddy Bear Got Its Name.【参考答案】ADBC任务型阅读请仔细阅读下面短文，从A到F的六个选项中选出符合各段主题的句子，完成第31-35题。

章节测试题1.【答题】如图，在△ABC中，点D，E分别是边AB，AC的中点，点F是线段DE上的一点．连接AF，BF，∠AFB＝90°，且AB＝8，BC＝14，则EF的长是（）A. 2B. 3C. 4D. 5【答案】B【分析】本题考查三角形的中位线.【解答】∵点D，E分别是边AB，AC的中点，∴DE是△ABC的中位线，∵BC＝14，∴DE BC＝7，∵∠AFB＝90°，AB＝8，∴DF AB＝4，∴EF＝DE﹣DF＝7﹣4＝3，选B．2.【答题】如图，在四边形ABCD中，P是对角线BD的中点，点E、F分别是AB、CD 的中点，AD＝BC，∠EPF＝140°，则∠EFP的度数是（）A. 50°B. 40°C. 30°D. 20°【答案】D【分析】本题考查三角形的中位线.【解答】∵P是BD的中点，E是AB的中点，∴PE是△ABD的中位线，∴PE AD，同理，PF BC，∵AD＝BC，∴PE＝PF，∴∠EFP（180°﹣∠EPF）（180°﹣140°）＝20°，选D．3.【答题】如图，在△ABF中，点C在中位线DE上，且CE CD，连接AC，BC，∠ACB＝90°，若BF＝20，则AB的长为（）A. 10B. 12C. 14D. 16【答案】D【分析】本题考查三角形的中位线.【解答】∵DE是△ABC的中位线，BF＝20，∴DE BF＝10，∵CE CD，∴CD DE＝8，∵∠ACB＝90°，∴AB＝2CD＝16，选D.4.【答题】如图，△ABC中，N是BC边上的中点，AM平分∠BAC，BM⊥AM于点M，若AB＝8，MN＝2．则AC的长为（）A. 10B. 11C. 12D. 13【答案】C【分析】本题考查三角形的中位线.【解答】延长BM交AC于D，如图所示：∵BM⊥AM于点M，∴∠AMB＝∠AMD＝90°，∵AM平分∠BAC，∴∠BAM＝∠DAM，在△BAM和△DAM中，，∴△BAM≌△DAM（ASA）．∴AD＝AB＝8，BM＝MD，∵N是BC边上的中点，∴MN为△BCD的中位线，∴DC＝2MN＝4，∴AC＝AD+DC＝8+4＝12．选C．5.【答题】如图，在△ABC中，∠A＝90°，D是AB的中点，过点D作BC的平行线交AC于点E，作BC的垂线交BC于点F，若AB＝CE，且△DFE的面积为1，则BC的长为（）A. 2B. 5C. 4D. 10【答案】A【分析】本题考查三角形的中位线.【解答】如图，过A作AH⊥BC于H.∵D是AB的中点，∴AD＝BD，∵DE∥BC，∴AE＝CE，∴DE BC，∵DF⊥BC，∴DF∥AH，DF⊥DE，∴BF＝HF，∴DF AH，∵△DFE的面积为1，∴DE•DF＝1，∴DE•DF＝2，∴BC•AH＝2DE•2DF＝4×2＝8，∴AB•AC＝8，∵AB＝CE，∴AB＝AE＝CE AC，∴AB•2AB＝8，∴AB＝2（负值舍去），∴AC＝4，∴BC．选A．6.【答题】如图，∠MAN＝90°，点C在边AM上，AC＝2，点B为边AN上一动点，连接BC，△A'BC与△ABC关于BC所在直线对称，点D，E分别为AC，BC的中点，连接DE并延长交A'B于点F，连接A'E．当△A'EF为直角三角形时，AB的长为______．【答案】或2【分析】本题考查三角形的中位线.【解答】当△A'EF为直角三角形时，存在两种情况：①当∠A'EF＝90°时，如图，∵△A'BC与△ABC关于BC所在直线对称，∴A'C＝AC＝2，∠ACB＝∠A'CB，∵点D，E分别为AC，BC的中点，∴DE是△ABC的中位线，∴DE∥AB，∴∠CDE＝∠MAN＝90°，∴∠CDE＝∠A'EF，∴∠ACB＝∠A'EC，∴∠A'CB＝∠A'EC，∴A'C＝A'E＝2，在Rt△A'CB中，E是斜边BC的中点，∴BC＝2AE'＝4，由勾股定理可得AB2＝BC2﹣AC2，∴AB；②当∠A'FE＝90°时，如图，∵∠ADF＝∠A＝∠DFB＝90°，∴∠ABF＝90°，∵△A'BC与△ABC关于BC所在直线对称，∴∠ABC＝∠CBA'＝45°，∴△ABC为等腰直角三角形，∴AB＝AC＝2．综上，AB的长为或2．故答案为或2．7.【答题】如图，在△ABC中，M，N分别是AB和AC的中点，连接MN，点E是CN的中点，连接ME并延长，交BC的延长线于点D．若BC＝4，则CD的长为______．【答案】2【分析】本题考查三角形的中位线.【解答】∵M，N分别是AB和AC的中点，∴MN是△ABC的中位线，∴MN BC＝2，MN∥BC，∴∠NME＝∠D，∠MNE＝∠DCE，∵点E是CN的中点，∴NE＝CE，∴△MNE≌△DCE（AAS），∴CD＝MN＝2．故答案为2．8.【答题】如图，△ABC的周长为16，D，E，F分别为AB，BC，AC的中点，M，N，P分别为DE，EF，DF的中点，则△MNP的周长为______．如果△ABC，△DEF，△MNP分别为第1个，第2个，第3个三角形，按照上述方法继续作三角形，那么第n个三角形的周长是______．【答案】4；【分析】本题考查三角形的中位线.【解答】∵△ABC的周长为16，D、F、E分别为AB、AC、BC的中点，∴EF、DF、DE为三角形中位线，∴EF AB，DE AC，DF BC，∴EF+DE+DF（AB+AC+BC），即△DEF的周长是△ABC周长的一半，同理，△MNP的周长是△DEF的周长的一半，即△MNP的周长＝△ABC的周长的16＝4，以此类推，第n个小三角形的周长是第一个三角形周长的16＝，故答案为4；．9.【题文】如图，在△ABC中，AB＝AC，点D是边AB的点，DE∥BC交AC于点E，连接BE，点F、G、H分别为BE、DE、BC的中点．（1）求证：FG＝FH；（2）当∠A为多少度时，FG⊥FH？并说明理由．【答案】（1）见解答；（2）当∠A＝90°时，FG⊥FH．理由见解答. 【分析】本题考查三角形的中位线.【解答】（1）证明：∵AB＝AC．∴∠ABC＝∠ACB，∵DE∥BC，∴∠ADE＝∠ABC，∠AED＝∠ACB，∴∠ADE＝∠AED，∴AD＝AE，∴DB＝EC，∵点F、G、H分别为BE、DE、BC的中点，∴FG是△EDB的中位线，FH是△BCE的中位线，∴FG BD，FH CE，∴FG＝FH；（2）解：如图，延长FG交AC于N，∵FG是△EDB的中位线，FH是△BCE的中位线，∴FH∥AC，FN∥AB，∵FG⊥FH，∴∠A＝90°，∴当∠A＝90°时，FG⊥FH．10.【题文】如图，在△ABC中，AE平分∠BAC，BE⊥AE于点E，点F是BC的中点．（1）如图1，BE的延长线与AC边相交于点D，求证：EF（AC﹣AB）；（2）如图2，△ABC中，AB＝9，AC＝5，求线段EF的长．【答案】（1）见解答；（2）2.【分析】本题考查三角形的中位线.【解答】（1）证明：在△AEB和△AED中，，∴△AEB≌△AED（ASA），∴BE＝ED，AD＝AB，∵BE＝ED，BF＝FC，∴EF CD（AC﹣AD）（AC﹣AB）；（2）解：如图，分别延长BE、AC交于点H，在△AEB和△AEH中，，∴△AEB≌△AED（ASA），∴BE＝EH，AH＝AB＝9，∵BE＝EH，BF＝FC，∴EF CH（AH﹣AC）＝2．11.【答题】如图，在中，，分别是，的中点，，是上一点，连接，，．若，则的长度为（）A. B. C. D.【答案】B【分析】本题考查的是三角形中位线定理和直角三角形的性质，掌握三角形的中位线平行于第三边，并且等于第三边的一半是解题的关键．根据直角三角形的性质求出FE，根据三角形中位线定理计算即可．【解答】，，，；，分别是，的中点，为的中位线，，选B．12.【答题】如图，的周长为，点，都在边上，的平分线垂直于，垂足为，的平分线垂直于，垂足为，若，则的长为（）A. B. C. D.【答案】C【分析】本题考查了三角形的中位线定理，解答本题的关键是判断出△BAE、△CAD是等腰三角形，利用等腰三角形的性质确定PQ是△ADE的中位线．首先判断△BAE、△CAD是等腰三角形，从而得出BA=BE，CA=CD，由△ABC的周长为32，及BC=12，可得DE=8，利用中位线定理可求出PQ．【解答】平分，，.，，，，同理，点是的中点，点是中点（三线合一），是的中位线，，，．选C．13.【答题】如图，在四边形ABCD中，已知AB＝CD，M、N、P分别是AD、BC、BD的中点∠ABD＝20°，∠BDC＝70°，则∠NMP的度数为（）A. 50°B. 25°C. 15°D. 20°【答案】B【分析】本题考查了三角形中位线定理及等腰三角形的判定和性质，解题时要善于根据已知信息，确定应用的知识．根据中位线定理和已知，易证明△PMN是等腰三角形，根据等腰三角形的性质和已知条件即可求出∠PMN的度数．【解答】在四边形ABCD中，∵M、N、P分别是AD、BC、BD的中点，∴PN，PM分别是△CDB与△DAB的中位线，∴PM AB，PN DC，PM∥AB，PN∥DC．∵AB=CD，∴PM=PN，∴△PMN是等腰三角形，∴∠PMN=∠PNM．∵PM∥AB，PN∥DC，∴∠MPD=∠ABD=20°，∠BPN=∠BDC=70°，∴∠MPN=∠MPD+∠NPD=20°+（180﹣70）°=130°，∴∠PMN25°．选B．14.【答题】已知，四边形ABCD中，AB=2，CD=3，M、N分别是AD，BC的中点，则线段MN的取值范围是（）A. 1＜MN＜5B. 1＜MN≤5C. ＜MN＜D. ＜MN≤【答案】D【分析】本题考查了三角形的中位线，解答此题的关键是根据题意作出辅助线，利用三角形的中位线定理和三角形的三边关系求解．当AB∥CD时，MN最短，利用中位线定理可得MN的最长值，作出辅助线，利用三角形中位线及三边关系可得MN的其他取值范围．【解答】连接BD，过M作MG∥AB，连接NG．∵M是边AD的中点，AB=2，MG∥AB，∴MG是△ABD的中位线，BG=GD，MG=AB=×2=1；∵N是BC的中点，BG=GD，CD=3，∴NG是△BCD的中位线，NG=CD=×3=，在△MNG中，由三角形三边关系可知MG-NG＜MN＜MG+NG，即-1＜MN＜+1，∴＜MN＜，当MN=MG+NG，即MN=时，四边形ABCD是梯形，故线段MN长的取值范围是＜MN≤．选D．15.【答题】如图，点、、分别是的边、、的中点，连接、、得，如果的周长是，那么的周长是（）A. B. C. D.【答案】B【分析】本题考查了三角形中位线定理．解题的关键是根据中位线定理得出边之间的数量关系．由于D、E分别是AB、BC中点，则DE是△ABC的中位线，那么DE=AC，同理有EF=AB，DF=BC，于是易求△DEF的周长．【解答】、分别是的边、的中点，，同理，，．选B．16.【答题】如图，中，是的中点，平分，于点，若，，则等于（）A. B. C. D.【答案】C【分析】本题考查的是三角形中位线定理、全等三角形的判定和性质，三角形的中位线平行于第三边，且等于第三边的一半．延长BD交AC于H，证明△ADB≌△ADH，根据全等三角形的性质得到AH=AB=12，BD=DH，求出HC，根据三角形中位线定理计算即可．【解答】延长交于，平分，，，，，是中点，，，选C．17.【答题】如图，在四边形中，，，，分别是，，的中点，若，，则等于（）A. B. C. D.【答案】A【分析】本题考查了三角形中位线定理和等腰三角形的判定与性质．中位线是三角形中的一条重要线段，由于它的性质与线段的中点及平行线紧密相连，因此，它在几何图形的计算及证明中有着广泛的应用．根据三角形中位线定理和等腰三角形等边对等角的性质求解即可.【解答】，，，分别是，，中点，是的中位线，是的中位线，，，，．又，，，，，，．选A．18.【答题】已知△ABC的周长为1，连接其三边中点构成第二个三角形，再连接第二个三角形的中点构成第三个三角形，以此类推，则第2012个三角形的周长为（）A. B. C. D.【答案】C【分析】本题考查相似三角形的性质.【解答】∵连接△ABC三边中点构成第二个三角形，∴新三角形的三边与原三角形的三边的比值为1：2，∴它们相似，且相似比为1：2，同理：第三个三角形与第二个三角形的相似比为1：2，即第三个三角形与第一个三角形的相似比为1：22，以此类推：第2012个三角形与原三角形的相似比为1：22011，∵周长为1，∴第2012个三角形的周长为1：22011．选C．19.【答题】如图，▱ABCD中，对角线AC、BD交于点O，点E是BC的中点．若OE＝3cm，则AB的长为（）A. 3cmB. 6cmC. 9cmD. 12cm【答案】B【分析】本题考查三角形的中位线.【解答】∵四边形ABCD是平行四边形，∴OA=OC；又∵点E是BC的中点，∴BE=CE，∴AB=2OE=2×3=6（cm），选B．20.【答题】如图，在中，，分别是，的中点，是线段上一点，连接，，若，，，则的长为______．【答案】18【分析】本题考查是三角形中位线定理、直角三角形的性质，掌握三角形的中位线平行于第三边，并且等于第三边的一半是解题的关键．根据直角三角形的性质得到DF=8，根据EF=1，得到DE=9，根据三角形中位线定理解答即可．【解答】，点是的中点，，，，、分别是，的中点，，故答案为．。

新目标八年级下册英语Unit3补全对话练习题补全对话一、从方框中选择最佳选项完成对话, 有两项多余。

A. What do you want me to help with?B. Do you hate to do chores?C. Could you help me with some chores?D. Sure, no problem.E. Then we can go to the park.F. It’s boring.G. But first you have to clean your room.A: Hello, Jenny. 1B: Well, I hate some chores, but I like other chores.A: Really? Great! Could I ask you to help me with some chores then? B: Yes. 2A: Could you please fold my clothes for me?B: I don’t want to do that. 3A: OK. Then could you please sweep the floor for me?B: 4. But could we go to the park after that?A: Sure. I’ll finish my homework while you help me sweep the floor. 5 B: Great.1．________ 2.________ 3.________ 4.________ 5.________二、从方框中选择最佳选项完成对话, 有两项多余。

A. Could you go shopping with me?B. Yes, I think so.C. When is the party going to start?D. Yes, sure.E. Can you do chores?F. What chores do you like to do?G. Where is it?A: Are you free next Sunday?B: 1Why?A: Could you please come over to my house for a party?B: 2A: Could you come early to help me do some chores?B: Of course I can. 3A: It’s going to start at 4: 30 p. m. .B: Could I get to your house at two o’clock?A: OK! 4B: Well, I like to clean the living room and sweep the floor.A: Oh, I also need to buy some drinks and snacks. 5B: Yes, I can. You know, I like shopping.A: That’s great!1．________ 2.________ 3.________ 4.________ 5.________三、从方框中选择最佳选项完成对话, 有两项多余。

给我一个支点，可以撬起整个地球。

——阿基米德第3节重力一、单选题1.一个初中学生在地球上的重力最接近（）A.5NB.50NC.500ND.5000N2.下列关于力的大小的估计，不可能的是（）A.一名中学生的体重约450NB.拿起两只鸡蛋所用的力约1NC.物理课本重约3ND.一只普通的苹果受的重力约0.1N3.下列关于重力的说法中，正确的是（）A.静止的物体不受重力B.同一地点，物体质量大，其重力也大C.物体的重心一定在物体上D.向上抛出的物体，受到的重力方向是向上的4.下列数据最符合实际的是（）A.一个中学生的正常体温是38℃B.两个鸡蛋的重约为1NC.一个中学生的体重约为50ND.一张课桌的高度约1.2m5.关于重心，下列说法正确的是（）A.物体的重心不一定在物体上B.空心的足球没有重心C.重心的位置跟质量分布无关D.物体的重心就是物体的中心6.下列物体的重力最接近500N的是（）A.一本物理书B.一辆小轿车C.一名中学生D.一瓶矿泉水7.某小组利用天平、弹簧测力计、钩码若干，探究“物体所受重力大小与物体质量的关系”的实验数据记录如下表，则下列说法不正确的是（）次数质量m/kg质量G/N重力和质量的比值/（N/kg）10.10.989.820.2 1.969.830.3 2.949.8A.小红认为本实验中多次实验的目的是为了减小误差B.小张认为利用原有器材，在月球表面可以完成本实验C.小亮处理数据时，算出每组重力与质量的比值（如上表），可得重力与质量成正比D.小明处理数据时，给出重力G与质量m的关系图（如图），可得重力与质量成正比8.下列说法正确的是（）A.物体间发生力的作用时，一定存在着施力物体和受力物体B.两个物体没有直接接触不能产生力的作用C.托起一个鸡蛋的力约1ND.用手推墙壁，人先推墙，墙再对人施力9.如图所示是水平仪放置于某桌面上时的情形，则该桌面（）A.右面高，左面低B.左面高，右面低C.左右相平，前高后低D.左右相平，前低后高10.中国的5G技术全球领先，如图所示是华为公司生产的一款5G手机，关于它受到的重力，下列选项中最合理的是（）A.0.2NB.2NC.20ND.200N二、多选题11.下列实验不能在太空舱中失重环境下进行的是（）A.探究物体间力的作用是相互的B.用液体压强计探究液体压强特点C.探究压力作用效果与受力面积的关系D.探究物体是否具有惯性12.小杰骑自行车沿斜面向下匀速直线骑行。

新目标八年级英语下册期末综合练习题（三）一．单项选择（共35题，每小题1分）( )1.Those terrible things happened ____ me again.A.toB.inC.onD.with( )2.______ of them is good at English but they both do well in Chinese.A.BothB.NeitherC.EachD.All( )3.Jack said he_______ the Chinese History Museum the next Sunday.A.visitsB.was visitingC.visitedD.would visit( )4.Look at the clouds. I think it ______.Let’s go home at once.A.has rainedB.is going to rainC.was rainingD.rained( )5.You will get wet if you_______ your umbrella or raincoat.A.don’t takeB.won’tC.aren’t talkingD. didn’t take( )6.—Could you please help me with my English?--_______A.Why not ask Tom ?B.Yes, I will.C.No, thinks.D.Yes, I’d love to.( )7.You’d better _____ football on the road , boys.A.not to playB.not playC.don’t playD.not playing( )8.Jenny got a nice skirt______ her ______ birthday.A.on, twelveB.in ,twelfthC.at ,twelveD.on ,twelfth( )9.Why don’t you_____ a mobile phone ?It won’t______ you too much money.A.buy, costB.buying, takeC.to buy, spendD.buy, pay( )10.It’s not easy____ a new teacher.So Mr Li tries his best_____ his students.A.being ,teachingB.to be, teachingC.being , to teachD.to be, teaches ( )11.There_____ a football game tomorrow afternoon.A.is going to beB.will beC.will haveD.A and B( )12.--______ nice day! Do you think so ?--Yes, the weather______ not cold or hot.A.What, isB.How, isC.What a , isD.How, was( )13.You won’t have any problem_____ a restaurant in Singapore?A.to findB.findingC.and findD.finds( )14.—I didn’t finish my homework yesterday.--_______________.A.So do IB.Neither do IC.Neither did ID.So did I( )15.There are nine_____ workers in his factory .A.thousands ofB.thousand ofC.thousandD.thousands( )16.The little boy was ____ in _____ computer games.A.interested,playingB.interested, playC.interesting, playD.interesting,playing( )17.--Why not _____ your brother for some money ?--Good indea.A.askingB.askC.to askD.asks( )18.--Would you mind_____ here ?—No , not at all.A.he smokingB.him smokeC.his smokingD.he smoke( )19.—Tom didn’t come to school yesterday, did he ?--______________.He was ill in hospital.A.Yes,he did .B.Yes, he didn’tC.No,he didD.No, he didn’t( )20.This bag isn’t______ .Please show me the white one.A.enough beautifulB.beautiful enoughC.terrible enoughD.enough terrible.( )21.Your scarf looks the same as _____.Where did you buy it?--In the shop near my home.A. /B.mineC.ID.me( )22.--How soon will he come back ?--He will come back______ three weeks.A.inB.afterC.sinceD.for( )23.My brother_______ since he was three years old.A.has been studyingB.studiedC.has studiedD.A and C( )24.The poor little girl sells flowers for a ______.A.lfieB.liveC.aliveD.living( )25.All the workers are friendly______ him and it is quite good_____ his job.A.to , atB.to ,forC.for , toD.for ,for( )26.This coat doesn’t fit him well. He has ______ a huge body and the coat is______ small.A.so, suchB.so, soC.such, suchD.such, so( )27.It’s hot outside. Let’s watch TV at home______ going shopping.A.rather thanB.but notC.intead ofD.instead( )28.Tom______ some litter and put_____ into the dustbin.A.picks up , themB.picks up, itC.picked up, itD.picked up,them( )29.Why do you _____ your homework at home again?A.forgetB.leaveC.takeD.give( )30.I _______ your parents (Whick is wrong?)A.feel like meetingB.want to meetC.would like to meetD.get to meet( )31.The _____ we plant trees, the_____ pollution there will be.A.more,lessB.more,fewerC.many, littleD.much, few( )32.Do you find_____ very difficult to improve your spoken English?A.thatB./C.thisD.it( )33.The price of vegetable is very______ .Why don’t you buy some more?A.highB.cheapC.expensiveD.low( )34.There are four people in my family.______ me.A.BesidesB.ExceptC.ForD.Without( )35.—Do you think it will be sunny tomorrow?--__________.We plan to climb the mountain.A.I hope notB.I hope soC.No, it isn’tD.I don’t think so. 二．完形填空（10分）My name is Cathy. I'm a fourteen-year-old girl from England. Now I'm 1 in a middle school. I have to say that I was not good 2 my lessons before. 3 I was always afraid of( 害怕) exams. Last week I finished my end-of-year exams. Today I got my report Card. 4 ,I did very well. My morn and dad said it was the best report I had ever had. It was 5 main subjects that the report card talked about, and I felt very 6 today. My teachers ticked ( 给......打勾) "7 to improve" "Good" or" Very good". My English teacher said my English was much better. For math and science I also got "Very good" 8 . All my teachers said I was making excellent progress. And at the end of the report card my headteacher said."A very good 9 . Well done!" I am so pleased with it, but I hope I can get a 10 report next year. I' m sure I can.( )1. A. playing B. working C. teaching D. studying( )2. A. in B. at C. to D. for( )3. A. Do B, But C. So D. Or( )4 .A. Luckily B. Badly C. Especially D. Really( )5. A. his B. my C. her D their( )6. A. strange B. seared C. upset D.happy ( )7. A. Want B. Need C. stop D.Choose( )8. A. ticks B. lessons C.teachers D.cards( )9. A. report B. lesson C.teacher D. school( )10. A. better B. good C.best D.well三．阅读理解（40分）AOnce there was a baby eagle living in a nest(巢）on a cliff(山崖). The baby eagle loved his nest. It was warm-, soft and comfortable. And even better, he had all the food and love that his mother could give. Whenever the baby eagle was hungry ,his mother would always come just in time with the delicious food he liked.He was growing happily day after day. But suddenly his world changed. His mother stopped coming to the nest. He was full of sadness and fear. He thought he would die soon. He cried,but nobody heard him.Two days later his mother appeared with some nice food, The baby cagle was wild with joy.But his mother put the food at the top of the mountain and then looked down at her baby. The baby eagle cried out, "Mum,why did you do this to me ?I'm hungry. Don' t you know I will die if I have nothing to eat ?”Here is the last meal I give you. Come and get it by yourself," his mother said. Then she flew down and pushed the baby eagle out of the nest.The baby eagle fell down, faster and faster. He looked up at his mum, Why do you abandon me?" He looked down at the earth. The ground was much closer. Then something strange happened. The air caught behind his arms and he began to fly! He wasn' t moving to the ground any more. Instead.his eyes were pointed up at the sun."You are flying! You can make it! "His mother smiled.根据材料内容选择最佳答案，将其标号填入题前括号内。

初中数学八年级下册第二十章数据的分析单元检测练习题三（含答案）英才中学为了解中考体育科目训练情况从全校九年级学生中随机抽取了部分学生进行一次中考体育科目测试(把测试结果分为四个等级．A级：优秀；B 级：良好；C级：合格；D级：不合格)，并将测试结果绘成了如下两幅不完整的统计图．请根据统计图中的信息解答下列问题：（1）求本次抽样测试的学生人数是人．（2）图2中条形统计图C级的人数是人；（3）该校九年级有学生500名，如果全部参加这次中考体育科目测试，请估计不及格的人数约有多少人？【答案】（1）40；（2）14；（3）100人．【解析】【分析】（1）用B级的人数除以B级所占的百分比，可得答案；（2）用抽测总人数乘以C及所占的比例，可得答案；（3）利用样本估计总体的方法知，全校总人数乘以D级所占的比例，可得答案．【详解】（1）本次抽样测试的学生人数是12÷30%=40(人)．故答案为：40；（2）C级的人数为40×35%=14(人)．故答案为：14；（3）根据题意得：500840⨯=100(人)答：估计不及格的人数约有100人．【点睛】本题考查的是条形统计图和扇形统计图的综合运用，读懂统计图，从不同的统计图中得到必要的信息是解决问题的关键．条形统计图能清楚地表示出每个项目的数据；扇形统计图直接反映部分占总体的百分比大小．112．珠海市水务局对某小区居民生活用水情况进行了调査．随机抽取部分家庭进行统计，绘制成如下尚未完成的频数分布表和频率分布直方图．请根据图表，解答下列问题：（1）b= ，c= ，并补全频数分布直方图；（2）为鼓励节约用水用水，现要确定一个用水量标准P（单位：吨），超过这个标准的部分按1.5倍的价格收费，若要使60%的家庭水费支出不受影响，则这个用水量标准P= 吨；（3）根据该样本，请估计该小区400户家庭中月均用水量不少于5吨的家庭约有多少户？【答案】（1）0.24，0.18；（2）5；（3）160【解析】【分析】（1）根据频数，频率，总人数之间的关系解决问题即可．（2）利用已知条件以及表格中的信息即可解决问题．（3）利用样本估计总体的思想解决问题即可．【详解】解：（1）总人数=4÷0.08=50，∴a=50-4-14-9-6-5=12，b=1250=0.24，c=950=0.18,故答案为：0.24，0.18；（2）50×60%=30，观察表格可知：这个用水量标准P=5吨，故答案为5．（3）400×96550++=160（户），答：估计该小区400户家庭中月均用水量不少于5吨的家庭约有160户．【点睛】本题考查频数分布表和频数分布直方图，样本估计总体等知识，解题的关键是熟练掌握基本知识，属于中考常考题型．113．学校开展综合实践活动中，某班进行了小制作评比，作品上交时间为5月11日至5月30日，评委们把同学们上交作品的件数按5天一组分组统计，绘制了频数分布直方图如下，小长方形的高之比为：2：5：2：1．现已知第二组的上交作品件数是20件．求：（1）此班这次上交作品共 件；（2）评委们一致认为第四组的作品质量都比较高，现从中随机抽取2件作品参加学校评比，小明的两件作品都在第四组中，他的两件作品都被抽中的概率是多少？（请写出解答过程）【答案】（1）40（2）16【解析】 解：（1）40．（2）第四组的作品的件数为14042+5+2+1⨯=（件）．设四件作品编号为1、2、3、4号，小明的两件作品分别为1、2号．从中随机抽取2件作品的所有结果为（1，2）；（1，3）；（1，4）； （2，3）；（2，4）；（3，4），小明的两件作品都被抽中的情况有1种，∴他的两件作品都被抽中的概率是16．（1）用第二小组的频数除以该小组的份数占总份数的多少即可求得总人数：520402+5+2+1÷=．（2）根据频数、频率和总量的关系求出第四组的作品的件数，分别列举出所有可能结果后用概率的公式即可求解．114．一次安全知识测验中，学生得分均为整数，满分10分，这次测验中，甲，乙两组学生人数都为5人，成绩如下（单位：分）：甲：8，8，7，8，9乙：5，9，7，10，9（1）填写下表：（2）已知甲组学生成绩的方差22=5s甲，计算乙组学生成绩的方差，并说明哪组学生的成绩更稳定.【答案】（1）甲：平均数8；乙：平均数8，中位数9；（2）甲组学生的成绩比较稳定．【解析】【分析】（1）根据平均数和中位数的定义求解可得；（2）根据方差的定义计算出乙的方差，再比较即可得．【详解】（1）甲的平均数：8878985，乙的平均数：59710985，乙的中位数：9；（2） 222222(58)(98)(78(108)(98)1655S -+-+-+-+=-=乙）.∵22S S >乙甲，∴甲组学生的成绩比较稳定． 【点睛】本题考查了求平均数，中位数与方差，方差反映了一组数据的波动大小，方差越大，波动性越大，反之也成立．115．杭州市相关部门正在研究制定居民用水价格调整方案．小明想为政府决策提供信息，于是在某小区内随机访问了部分居民，就每月的用水量、可承受的水价调整的幅度等进行调查，并把调查结果整理成图1和图2．已知被调查居民每户每月的用水量在m 3之间，被调查的居民中对居民用水价格调价幅度抱“无所谓”态度的有8户，试回答下列问题：（1）上述两个统计图表是否完整，若不完整，试把它们补全；（2）若采用阶梯式累进制调价方案（如表1所示），试估计该小区有百分之几的居民用水费用的增长幅度不超过50%？来表1：阶梯式累进制调价方案【答案】（1）频数分布直方图见解析；（2）该小区有75%的居民用水费用的增长幅度不超过50%．【解析】【分析】(1)根据扇形统计表中角度的比例关系可得出统计样本的总数，继而可补充完整两个统计表；(2)设每月每户用水量为xm3的居民调价后用水费用的增长幅度不超过50%，由表一可知分x≤15与x＞15两部分讨论，再结合图一可得出结论．【详解】（1）频数分布直方图，如图：（2）∵设每月每户用水量为xm3的居民调价后用水费用的增长幅度不超过50%当x≤15时，水费的增长幅度为2.5 1.81.8-×100%＜50%，当x＞15时，则15 2.5 3.3(15) 1.81.8x xx⨯+--≤50%，解得x≤20，∵从调查数据看，每月的用水量不超过20m3的居民有54户，5472＝75%，又∵调查是随机抽取，∴该小区有75%的居民用水费用的增长幅度不超过50%．【点睛】考查了条形和扇形统计图以及解一元一次不等式，解题的关键是：①由样本中某项数据得出样本数；②结合表一得出关于x的一元一次不等式．本题难度不大，属于基础题，解决该类型的题目需要熟悉各种统计表．116．为宣传普及新冠肺炎防治知识，引导学生做好防控.某校举行了主题为“防控新冠，从我做起”的线上知识竞赛活动，测试内容为20道判断题，每道题5分，满分100分.为了解八、九年级学生此次竞赛成绩的情况，分别随机在八、九年级各抽取了20名参赛学生的成绩.已知抽查得到的八年级的数据如下：80，95，75，75，90，75，80，65，80，85，75，65，70，65，85，70，95，80，75，80.为了便于分析数据，统计员对八年级数据进行了整理，得到了表一：八、九年级成绩的平均数、中位数、优秀率如下：（分数80分以上、不含80分为优秀）（1）根据题目信息填空：a=________，c=________，m=________；（2）八年级王宇和九年级程义的分数都为80分，请判断王宇、程义在各自年级的排名哪位更靠前？请简述你的理由；（3）八年级被抽取的20名学生中，获得A 等和B 等的学生将被随机选出2名，协助学校普及新冠肺炎防控知识，求这两人都为B 等的概率.【答案】（1）10a =，77.5c =，25m =；（2）王宇在该年级的排名更靠前，理由见解析；（3）被选中的2人都为B 等的概率为632010=.【解析】【分析】（1）直接根据抽查得到的八年级的数据即可求出a ，c 和m 的值；（2）根据王宇和程义的成绩和所在年级抽查成绩的中位数进行比较即可得出结论；（3）令3名B 等的学生分别为a ，b ，c ，2名A 等的学生分别为m ，n 画树状图为，即可求出被选中的2人都为B 等的概率．【详解】（1）由题意可得：10a =，758077.52c +==， 3b =32%100%25%5m +∴=⨯=∴25m =；（2）王宇在该年级的排名更靠前，∵八年级王宇成绩大于中位数77.5分，名次在该年级抽查的学生数的10名或10名之前，九年级程义成绩小于中位数82.5分，名次在该年级抽查的学生数的10名之后，∴王宇在该年级的排名更靠前．（3）令3名B等的学生分别为a，b，c，2名A等的学生分别为m，n 画树状图为：共有20种等可能的结果数，其中被选中的2人都为B等有6种结果，所以被选中的2人都为B等的概率为63 2010．【点睛】此题考查了频数分布表，列表法或树状图法求概率以及中位数的知识．用到的知识点为：概率=所求情况数与总情况数之比．117．每年的4月15日是我国全民国家安全教育日．某中学在全校七、八年级共800名学生中开展“国家安全法”知识竞赛，并从七、八年级学生中各抽取20名学生，统计这部分学生的竞赛成绩（竞赛成绩均为整数，满分10分，6分及以上为合格）．相关数据统计、整理如下：八年级抽取的学生的竞赛成绩：4，4，6，6，6，6，7，7，7，8，8，8，8，8，8，9，9，9，10，10．七、八年级抽取的学生的竞赛成绩统计表根据以上信息，解答下列问题：（1）填空：a＝，b＝，c＝；（2）估计该校七、八年级共800名学生中竞赛成绩达到9分及以上的人数；（3）根据以上数据分析，从一个方面评价两个年级“国家安全法”知识竞赛的学生成绩谁更优异．【答案】（1）a＝7.5，b＝8，c＝8；（2）200人；（3）八年级“国家安全法”知识竞赛的学生成绩更优异【解析】(1)根据中位数、众数的定义结合条形统计图及八年级学生成绩即可求解；(2)先算出样本40人中竞赛成绩达到9分及以上的人数所占的百分比，然后用该百分比乘以总体400，即可求解；(3)由八年级的合格率高于七年级的合格率，可得八年级“国家安全法”知识竞赛的学生成绩更优异．【详解】解：(1)由条形统计图可得七年级成绩中最中间的两个人分数为7分和8分，故中位数a＝78=7.52+，八年级成绩中最中间的两个人分数为8分和8分，故中位数b＝88=82+，八年级成绩出现次数最多的是8分，故c＝8，故答案为：7.5，8，8；(2) 40人中竞赛成绩达到9分及以上的人数所占的百分比为(5+5)÷40=25%，∴该校七、八年级共800名学生中竞赛成绩达到9分及以上的人数＝800×25%＝200(人)，故答案为：200(人)；(3)∵八年级的合格率高于七年级的合格率，∴八年级“国家安全法”知识竞赛的学生成绩更优异．故答案为：八年级学生成绩更优异．本题考查中位数、众数、平均数的意义和计算方法，理解各个概念的内涵和计算方法是解题的关键．118．为了解2012年全国中学生创新能力大赛中竞赛项目“知识产权”笔试情况，随机抽查了部分参赛同学的成绩，整理并制作图表如下：请根据以上图表提供的信息，解答下列问题：（1）本次调查的样本容量为；（2）在表中：m= ．n= ；（3）补全频数分布直方图：（4）参加比赛的小聪说，他的比赛成绩是所有抽查同学成绩的中位数，据此推断他的成绩落在分数段内；（5）如果比赛成绩80分以上（含80分）为优秀，那么你估计该竞赛项目的优秀率大约是【答案】（1）300；（2）120；0.3；（3）答案见解析；（4）80≤x＜90；（5）60%【解析】【分析】（1）利用第一组的频数除以频率即可得到样本容量：30÷0.1=300．（2）m=0.4×300=120，n=90÷300=0.3．（3）根据80≤x＜90组频数即可补全直方图．（4）根据中位数定义，找到位于中间位置的两个数所在的组即可：中位数为第150个数据和第151个数据的平均数，而第150个数据和第151个数据位于80≤x＜90这一组，故中位数位于80≤x＜90这一组．（5）将比赛成绩80分以上的两组数的频率相加即可得到计该竞赛项目的优秀率．【详解】解：（1）此次调查的样本容量为30÷0.1=300；故答案为：300；（2）n=90300=0.3；m=0.4×300=120；故答案为：120；0.3；（3）补全频数分布直方图如图：（4）中位数为第150个数据和第151个数据的平均数，而第150个数据和第151个数据位于80≤x＜90这一组，故中位数位于80≤x＜90这一组；故答案为：80≤x＜90（5）将80≤x＜90和90≤x≤100这两组的频率相加即可得到优秀率，优秀率为60%．故答案为：60%．【点睛】本题考查频数（率）分布表，频数分布直方图，频数、频率和总量的关系，中位数，用样本估计总体．119．某校对九年级400名学生进行了一次体育测试，并随机抽取甲、乙两个班各50名学生的测试成绩（成绩均为整数，满分50分）进行整理、描述和分析．下面给岀了部分信息．（用x表示成绩，数据分成5组：A：30≤x＜34，B：34≤x＜38，C：38≤x＜42，D：42≤x＜46，E：46≤x≤50）乙班成绩在D组的具体分数是：42 42 42 42 42 42 42 42 42 42 43 44 45 45甲，乙两班成绩统计表：根据以上信息，回答下列问题：（1）直接写出m、n的值；（2）小明这次测试成绩是43分，在班上排名属中游略偏上，小明是甲、乙哪个班级学生？说明理由；（3）假设该校九年级学生都参加此次测试，成绩达到45分及45分以上为优秀，估计该校本次测试成绩优秀的学生人数．【答案】（1）m＝45，n＝42；（2）小明是乙班级学生；理由见解析；（3）该校本次测试成绩优秀的学生人数为188人．【解析】【分析】（1）根据中位数、众数的意义和计算方法分别计算即可，（2）利用中位数的意义进行判断；（3）根据用样本估计总体的方法，估计总体的优秀率，进而计算出优秀的人数．【详解】解：（1）乙班的成绩从小到大排列，处在第25、26位的两个数都是42，因此中位数是42，即n＝42，甲班的中位数一定落在D组，而甲班每组人数为：A组2人，B组2人，C 组10人，D组24人，E组12人，甲班的中位数是44.5，而D组：42≤x＜46整数，因此排序后处在第25、26位的两个数分别是44，45，于是，可得甲班得45分的学生数为2+2+10+24﹣25＝13（人），是出现次数最多的，所以，甲班成绩的众数是45，即m＝45，故答案为：m＝45，n＝42；（2）∵小明的成绩为43分，且在班上排名属中游略偏上，而甲班中位数是44.5，乙班的中位数是42，∴小明是乙班级学生；（3）甲班得45分及45分以上的有：13+12＝25（人），而乙班有：2+20＝22（人），两个班的整体优秀率为：(25+22)÷100＝47%，∴400×47%＝188（人），即：该校本次测试成绩优秀的学生人数为188人．【点睛】考查中位数、众数、平均数、方差的意义和计算方法，明确各个统计量的意义是正确解答的前提.120．某校举办了一 次趣味数学竞赛，满分100分，学生得分均为整数，成绩达到60分及以上为合格，达到90分及以上为优秀这次竞赛中，甲、乙两组学生成绩如下(单位：分)．甲组：30，60，60，60，60，60，70，90，90，100乙组：50，50，60，70，70，80，80，80，90，90（1）以上成绩统计分析表中a=________分，b=_________分，c=________分；（2）小亮同学说：“这次竞赛我得了70分，在我们小组中排名属中游略偏上！”观察上面表格判断，小亮可能是甲、乙哪个组的学生？并说明理由．（3）如果你是该校数学竞赛的教练员，现在需要你选择一组同学代表学校参加复赛，你会选择哪一组？并说明理由．【答案】（1）60，72，75；（2）小亮属于甲组学生，理由见解析；（3）选甲组同学代表学校参加竞赛，理由见解析【解析】【分析】（1）根据中位数及平均数的定义进行计算即可得解；（2）根据中位数的大小进行判断即可得解；（3）根据数据给出合理建议即可.【详解】（1）∵甲组：30，60，60，60，60，60，70，90，90，100∴6060602a+==；∵乙组：50，50，60，70，70，80，80，80，90，90∴505060707080808090907210b+++++++++==；7080752c +==；（2）小亮属于甲组学生，∵甲组中位数为60,乙组的中位数为75,而小亮成绩位于小组中上游 ∴小亮属于甲组学生；（3）选甲组同学代表学校参加竞赛，由甲组有满分同学，则可选甲组同学代表学校参加竞赛.【点睛】本题主要考查了中位数及平均数的相关概念，熟练掌握中位数及平均数的计算是解决本题的关键.。