2014学年度中大附中初三年级校一模试卷

中山中学2014年中考数学模拟试卷（八）命题人：陈 琳班级 姓名 座号 分数一、精心选一选（本大题共8小题，每小题4分，共32分）1．25的平方根是（ ）A ．5B ．±5C ．－5D ．±52．已知⊙O 1与⊙O 2的半径分别为5cm 和3cm ，圆心距O 1O 2=7cm ，则两圆的位置关系为（ ）A ．外离B ．外切C ．相交D ．内切 3．在平面直角坐标系中，将A （－3，1）绕点O 按顺时针方向旋转900得到点A ′的坐标（ ） A ．（3，1） B ．（3，－1） C ．（－1，3） D ．（1，3）4．将抛物线y=(x －1)2+3向左平移1个单位，再向下平移3个单位后所得抛物线的解析式为（ ）A ．y= (x －2)2B ．y= (x －2)2+6 C ．y= x 2+6 D ．y= x 2 5．抛物线652+-=x x y 与x 轴的交点个数有（ ）A. 0个B. 1个C. 2个D. 3个6．在同一直角坐标系中，函数m mx y +=和222++-=x mx y （m 是常数，且0≠m ）的图象可能是（ ）A B C D 7．如图，在两建筑物之间有一旗杆，高15米，从A 点经过旗杆顶点恰好看到矮建筑物的墙角C 点，且俯角α为60°，又从A 点测得D 点的俯角β为30°，若旗杆底点G 为BC 的中点，则矮建筑物的高CD 为（ ） A ．20米 B ．米C ．米D ．米8．如图，P 是菱形ABCD 的对角线AC 上一动点，过P 垂直于 AC 的直线交菱形ABCD 的边于M 、N两点，设AC=2，BD=1，AP=x ，则△AMN 的面积为y ，则y 关于x 的函数图象的大致形状是（ ）A B C D第8题图二、细心填一填（本大题共8小题，每小题4分，共32分）9．如图△ABC 中，D 、E 分别为AB 、AC 的中点，若向△ABC 中随机抛掷一枚飞镖，飞镖落在阴影区域的概率是（不考虑落在线上的情形） 。

初三英语一模拟考试试卷及答案第一卷（选择题，共70分）一、听力测试（本大题共20分，每小题1分）第一节（共10小题）听下面10段短对话，每段对话后有一个小题，从题中A、B、C三个选项中选出最佳选项。

听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。

每段对话读两遍。

听第1至10段材料，回答第1至10题。

( )1. Which sport does the woman do in Harbin?A. B. C.( )2. How did Jenny go to school today?A. B.C.( )3. Where does the girl’s father work now?A. B. C.()4. What is the time now?( )5. What does the man do?A. A detective.B. A salesman.C. A student.( )6. How many maths problems has Rose finished?A. Two .B. Ten.C. Eight.( )7. Where is the man going?A. To the market.B. To the office.C. To the park.( )8. What does Mr Zhang think of Miss Yang?A. She walks too fast.B. She walks very slowly.C. She can’t walk any further.()9. How much did Mrs Green pay for the shirt?A. 20 yuan.B. 40 yuan.C. 60 yuan.( )10. What can we learn from the talk?A. Bob didn’t watch the game.B. Bob lost the game.C. Bob works hard.第二节（共10小题）听下面3段长对话和短文，每段对话和短文后有几个小题，从题中A、B、C三个选项中选出最佳选项。

2014年广州大学附属中学中考英语一模试题本试卷共五大题,9页,满分135分。

考试时间120分钟。

一、听力(共两节,满分35分)二、语言知识及运用（共两节,满分20分）第一节单项选择（共10小题；每小题1分,满分10分）从16~25各题所给的A、B、C和D项中,选出可以填入空白处的最佳选项,并在答题卡上将该项涂黑。

16.---What do you think of _________book written by Mo Yan?---It's_________good novel.A, the, the B, a, the C, the, a D, a, a17.--Must I finish_________my homework now, Mum?---No, you _________.A, doing, needn't B, to do, may not C, do, mustn't D, doing, can't18.---Mary find_________important to tell the truth.--_________honest girl she is!A, it, What an B, that, How C, this, What a D, it, How19.---There is going to _________a physical fitness test next month.--I know. And I'm always taking a _________walk every day these days.A, have, thirty-minute B, be, thirty-minute C, be, thirty minute D, have, thirty minutes' 20.I want to know if they _________the spring sports meeting next month. I must get ready for it if they_________it.A, hold, will hold B, will hold, hold C, hold, hold D, will hold21.The _________you do your homework, the _________mistakes you will make.A, more carefully, less B, more careful, less C, more carefully, fewer D, more careful, fewer 22._________Tom_________Mary are fond of watching TV.A, Not only, but also B, Both, and C, Either, or D, Neither, nor23.--Would you like to go shopping with them tomorrow?---If you don't go, _________.A, so don't I B, neither I do C, neither will I D, so I do24.---I wonder_________at this time last night.--I was writing an e-mail_________my cousin was reading.A, what you were doing , whileB, where did you go, asC, what were you doing, sinceD, what you did, when25.---I don't think she has gone to Beijing,_________.--_________. She is in Beijing now giving a speech.A, has she, Yes B, has she, No C, do I , Yes D, do I, No第二节语法选择共10分三、完型填空共10分One night a man came to my house. He told me,"There is a family with eight 1 . They have not eaten for days."After I asked him where the family was. I took some 2 with me and left.When I finally got to that family, I 3 those little children were too hungry to say 4 . There was no food to the mother. She took half of it, and then 5 . When she returned, I asked her," 6 did you go?" She gave me this simple 7 ,"To my neighbors --- they are also 8 !"I was not surprised that she gave, because poor people are always very kind. But I was surprised that she knew her 9 were hungry. Usually, when we are in trouble, we always 10 ourselves first, and we have no time for others.( )1. A. children ( )2. A. flowers ( )3. A. showed ( )4. A. a sentence ( )5. A. went out ( )6. A. When ( )7. A. question ( )8. A. ill ( )9. A. people ( )10. A. think of B. workersB. wineB. watchedB. a wordB. came backB. WhereB. decisionB. unhappyB. neighborsB. talk aboutC. farmersC. foodC. lookedC. itC. rushed inC. HowC. answerC. tiredC. familyC. laugh atD. cooksD. waterD. foundD. nothingD. hurried backD. WhyD. lieD. hungryD. childrenD. look for1-5 ACDDA 6-10 BCDDA四、阅读理解共20小题，满分40分(A)"My dream has come true. I have always wanted to be a Grand Slam (大满贯) champion." Theseare the words of Chinese tennis player Li Na after she became the first Asian woman to win a Grand Slam final in the French Open on June 4, 2011."People were saying I'm getting old. So this is a great success for such an old woman," the29-year-old girl joked.Miss Li has a tattoo (纹身). She has dyed her hair many different colors. And, at the 2008 Beijing Olympics, she told her fans to "shut up" when they got too noisy in their support.Li Na was born in Wuhan, she started to play tennis at the age of 6. She once recalled: "As a child, I felt sad because every day I had to wake up early to practice. After school I had to practice more.I didn't have time to play."Luckily, the strong girl didn't give up, thus making history for Chinese tennis time after time.Now the new champion is already thinking about winning another Grand Slam title. "When you have one title, surely you will think about another," she says, not hiding her ambition (雄心)."Chinese people are so lacking (缺乏) in confidence on the tennis court. If there is a person like me who can prove we Chinese can do it, the other young players in China will feel the same," she said.46. Li Na was born in the year of _____.A. 1982B. 1984C. 1986D. 199047. The underlined word "dyed" here means "_____" in Chinese.A. 焗油B. 洗烫C. 染色D. 梳理48. When she began to play tennis, Li Na was _____.A. happyB. sadC. excitedD. bored49. Which of the following is WRONG about Li Na?A. Li Na took part in the 2008 Beijing Olympics.B. Li Na has already won a Grand Slam champion.C. Li Na had to wake up early to practice playing tennis.D. Li Na said she lacked confidence on the tennis court.50. The passage mainly tells us _____.A. something about the tennisB. something about how to play tennisC. the Chinese people and the tennisD. the Grand Slam champion - Li Na1-5 ACBDD(B)A lot of teenagers are good at art at school, but how would you feel if people called you “the new Picasso(毕加索)” or if presidents and other famous people collected your paintings?Alexandra Nechita was ten when her paintings became famous all over the world. She visited Britain, France, Italy, Japan, Australia, New Zealand and her family's native place (祖籍) Romania where 5,000 fans came to see her at the airport. Alexandra said, “When it all started, I was moved. It was very exciting and I loved the traveling, but I got very tired. And I missed home.”Alexandra is a good student. Her studies always come first. She only starts painting after she's done her homework. She works on two or three paintings at a time. The paintings sell for thousands and Alexandra's parents have given up their jobs to work for their daughter. Life for the Nechita family is very different from what it was like a few years ago.Alexandra's father Niki left Romania for political reasons in 1985. At first he tried his best to learn English and had different kinds of low-paid jobs. In 1987, he brought his wife and Alexandra, who was then 18 months old, to America. The family was very poor. Alexandra began to draw at the age of three.She was drawing for four or five hours a day. Soon people offered to buy her paintings and she had her first art show at the age of eight. Stories about this child appeared in the newspapers and television. They now live in a large house with a swimmi ng pool. Her mother said, “We started without anything, but thanks to Alexandra, we have everything we ever dreamed of.”51. Alexandra became well-known all over the world for her paintings at the age of _______.A. 18monthsB. threeC. eightD. ten52. Which country does Alexandra live?A. America.B. Britain.C. Romania.D. France.53. Alexandra's painting _________.A. took her a lot of time at schoolB. made her drop out of schoolC. didn't influence her studies at schoolD. made her fall behind others in studies at school54. When her family arrived in America in 1987, _________.A. their life was very hardB. they lived by selling Alexandra's paintingsC. Alexandra began to draw her paintingD. her parents left their jobs and worked for her55. From the passage, we can learn ________.A. Alexandra was not interested in travellingB. Alexandra's success changed her family's lifeC. Alexandra's parents were good at EnglishD. Alexandra's stories appeared often on the radio and TVDACAB(C)Do you know of anyone who uses the truth to deceive(欺骗)? When someone tells you something that is true，but leaves out important information that should be included, he can give you a false picture.For example，someone might say, “I just won a hundred dollars on the lottery(彩票). It was great. I took that dollar ticket back to the store and turned it in for one hundred dollars!”This guy's a winner，right? Maybe，maybe not.We then discover that he bought $ 200 worth of tickets，and only one was a winner.He's really a big loser!He didn't say anything that was false，but he left out important information on purpose.That's called a half-truth.Half truths are not technically lies，but they are just as dishonest.Some politicians often use this tri ck.Let's say that during Governor Smith's last term，her state lost one million jobs and gained three million jobs.Then she seeks an other term.One of her opponents(对手)says，“During Governor Smith's term，the state lost one million jobs!” That's true.However，an honest statement would have been，“During Governor Smith's term，the state had a net gain of two m illion jobs.''Advertisers will sometimes use half—truths.It's against the law to make false statements so they try to mislead you with the truth.An advertisement might say，“Nine out of ten doctors advised their patients to take Yucky Pills to cure toothache.”It fails to mention that they only asked ten doctors and nine of them work for the Yucky Company.This kind of deception happens too often.It's a sad fact of life：Lies are lies，and sometimes the truth can 1ie as w ell.56.How much did the lottery winner lose?A.one hundred dollars.B.Two hundred dollars.C.Three hundred dollars.D.Four hundred dollars.57.We may infer that the author believes people should ________.A.buy lottery tickets if possibleB.make use of half—truthsC.be careful about what they are toldD.not trust the Yucky Company58. How many examples does the writer give to show how the truth is used to deceive?A.One.B.Two.C.Three.D.Four.59.Which of the following is true according to the passage?ing half truths is against the law.B.Technically，half truths are in fact lies.C.Yucky Pills is a very good medicine for toothache.ernor Smith did a good job during her last term.60.Which of the following best expresses the main idea of the passage?A.A winner can be a big loser!B.Sometimes the truth can lie as well.C.Advertisers will sometimes use half truths.D.It's against the law to make false statements.(D)CCBC is a famous air company which has over twenty planes carrying passengers and goods, flying along 12 fixed lines all over the world. Its service is very good but some passengers are still not satisfied with it and that is why in 2003 and 2004 the company received letters of complaints from consumers or passengers who pointed out over a dozen kinds of problems which are divided in groups in the following table. Those about passengers’ things carried by the plane are Baggage problems. Customer service refers to service work with passengers are not satisfied with. Oversales of seats are about the fact that more seats are sold and as a result the plane is too crowded to be safe. Refund problems appear when passengers fail to receive the money paid back to them because of what they have lost. Fares are problems about the price of tickets.Consumer Complaints Received By the CBCCategory 2003 2004Flight problems 20.2% 22.1%Baggage 18.3% 21.8%Customer service 3.1% 11.3%Oversales of seats 10.5% 11.8%Refund problems 10.1% 8.1%Fares 6.4% 6.0%Reservation & Ticketing 5.8% 5.6%Tours 3.3% 2.3%Smoking 3.2% 2.9%Advertising 1.2% 1.01%Credit 1.0% 0.8%Special passengers 0.9% 0.9%Others 6.0% 5.3%Total Number of Complaints 2,988 1,79261.About how many complaints about Credit were received by the CBC in 2003?A.28B.29C.30D.3162.What does the underlined word passengers mean?A, 机长B，空姐C，乘客D，技师63.By about what percent did the total number of complaints decrease from 2003 to 2004?A.40%B.60%C.75%D.100%64.If the circle graphs below show total consumer complaints for 2003, which graph shows a dark part that is about Flight problems and Refund problems together?65.From the passage we can know that .A.customers are not satisfied with CBCB.sometimes CBC sells more tickets than its plane’s fixed seatsC.CBC has more than twenty planes which fly to all the capital cities of the worldD.customers can only buy tickets with ready money五、写作满分30分第一节单词拼写66. He didn’t give me his a__________. How can I send him the letter?67. R__________to take the umbrella with you. It’s going to rain.68. The mother turned on the radio and made the baby stop c__________.69. The p__________of houses is higher and higher in cities. Many people can’t afford it.70. My bag was very h__________because of the bottles of wine.71. People enjoy many different activities and relax in their f__________time.72. Many people go to Guangzhou Library to b__________books.73. Don’t forget to take your new c__________with you when traveling, and then we can take many beautiful pictures.74. Edison was so w__________ that he invented many things.75. We shouldn’t l__________ at the people who are in trouble. Instead, we should help them.第二节完成句子共5小题每小题2分，满分10分，每空限填一词76. 他花了三个月的时间做这个实验。

大连市2014年初中毕业升学考试模拟试题（一）数学数学学科试卷1～6页,时间120分钟；满分150分。

一、选择题（本题共8小题,每小题3分，共24分。

在每小题给出的四个选项中，只有一个选项正确.请将答案填写在答题栏中）题号 12345678得分答案1。

下列给出的实数中,绝对值最大的是 A 。

2-2B 。

-2C 。

23 D. 22。

图1是由四个完全相同的正方体组成的几何体,这个几何体的主视图是3。

计算2(—2a )2的结果是A. 8a 2 B 。

—8a C. 2a 3 D 。

4a 34。

某中学进行了“学雷锋"演讲比赛。

下面是8位评委为一位参赛者的打分:9。

4,9.6,9.8，9。

9,9。

7，9.9，9。

8，9.5.若去掉一个最高分和一个最低分，这名参赛者的最后得分是 A 。

9.68 B 。

9。

70 C 。

9。

72 D 。

9.74 5. 如图2,AE ∥BD ,C 是BD 上的点，且AB =BC ,∠ACD =110°，则∠EAB =_____度. A. 20 B 。

40C. 45 D 。

706。

下列一元二次方程中，有两个相等的实数根的是 A. 012=+-x x 2 B 。

042=++x x 2 C 。

0242=-+x x 2 D 。

0242=+-x x 27。

给甲、乙、丙三个人打电话，若打电话的顺序是任意的,则第一个电话打给甲的概率为A 。

31 B 。

21 C. 61 D 。

328。

在△ABC 中，AB =12,AC =10，BC =9，AD 是BC 边上的图1AB C DE AB D图2AA高.将△ABC 按照如图3所示的方式折叠，使点A 和点D 重合,折痕为EF ，则三角形DEF 的周长为 A 。

9。

5 B. 11。

5 C 。

13。

5 D. 15。

5二、填空题（本题共8小题，每小题3分，共24分）9。

分解因式：015422++x x =________。

第一部分 选择题（共30分）一、选择题（本大题共10小题，每小题3分，满分30分.在每小题给出的四个选项中，有且仅有一项是符合题目要求的） 1.－5的绝对值是( )Ａ．5- Ｂ．5 Ｃ．51- Ｄ．512.如图，已知AB ∥CD ，∠１＝110°，则∠A 的度数是( )A ．70° B．100° C．110° D．130°3.已知21x y =⎧⎨=⎩是二元一次方程组71ax by ax by +=⎧⎨-=⎩的解，则a b -的值( )．A ．1B ．－1C ． 2D ．34.已知等腰三角形的一个内角是30°，那么这个等腰三角形顶角的度数是（ ）． A .75° B .120° C .30° D.30°或120°5.如果两圆的半径分别为6和4，圆心距为6，那么这两圆的位置关系是（ ）.A ．外切B ．内切C ．相交D ．内含 6.函数1)1(0+-=x x y 中，自变量x 的取值范围是（ ）．A ．1x -≥B ．1->xC ．1x >-且x ≠1D ．1x -≥且x ≠1 7.已知实数a 在数轴上的位置如图所示，则21a a +--1化简的结果为（ ）． ．1 B ．-1 C ．1-2a D ．0 8.给出下列各式①22242)2(y xy x y x ++=+； ②532)(m m =；③b b b =-3445；④()()22y x y x y x -=+--，其中运算错误的有 （ ）． A.1个 B.2个 C.3个 D.4个第7题图D BAC 1 第2题图ADCPB（第9题图）60°9．如图，等边ABC △的边长为3，P 为BC 上一点，且1BP =，D 为AC 上一点，若60APD ∠=°，则CD 的长为（ ）． A ．32 B ．23 C ．12 D ．3410.二次函数2y ax bx c =++的图象如图所示，则一次函数24y bx b ac =+-与反比例函数a b cyx-+=在同一坐标系内的图象大致为（ ）．第二部分 非选择题（共120分）二、填空题（本大题共6小题，每小题3分，满分18分）11.4的平方根是________________. 12.已知α∠=260，则α∠的余角是______．13.因式分解:24m n n -=____________________．14.某同学在使用计算器求20个数的时候，错将88误输入为8，那么由此求出的平均数与实际平均数的差为 ． 15.一个用正方体积木搭成的立体图形，从左面看形状是 ，从上面看形状是 ，则至少需要______块积木．16.如右图，5个正方形重叠，重叠部分的顶点正好是下面一个正方形的中心。

2014-2015学年下学期九年级模拟考试卷数 学（时间：120分钟；满分：150分）成绩_________一、选择题（10小题，每小题4分，共40分）1．在实数－2，0，2，－3中，最小的实数是（ ） A ．－2 B ．0 C ．2 D2．某几何体的三视图如图所示，则该几何体是（ ） A ．圆锥 B ．长方体 C ．圆柱 D ．三棱柱3．2014年4月21日8时我市各地域的可吸入颗粒物数值 统计如下表：该日这一时刻的可吸入颗粒物数值的众数和中位数分别是（ ） A ．0.15和0.14 B ．0.18和0.15 C ．0.18和0.14 D ．0.15和0.15 4．如图，直线AB ∥CD ，直线EF 分别交直线AB 、CD 于点 E 、F ，过点F 作FG ⊥FE ，交直线AB 于点G ，若∠1=42O ， 则∠2的大小是（ ） A ．560 B ．480 C ．460 D ．400 5．在Rt △ABC 中，∠C=90O ，若AB=4，sinA=53，则斜边上的高等于（ ） A ．3B ．4C ．516D ．5126．当x=1时，代数式m x x ++3的值是7，则当x =－1时，这个代数式的值是（ ） A ．7 B ．3 C ．1 D ．－77．如图，平行四边形ABCD 中，E 、F 是对角线BD 上的两点， 如果添加一个条件使△ABE ≌△CDF ，则添加的条件不能 是（ ） A ．AE=CF B ．BE=FD C ．BF=DE D ．∠1=∠28．如图，在Rt △ABC 中，∠ACB=90O ，AC=3，BC=4，以点C 为圆心，CA 为半径的圆与AB 交于点D ，则AD 的长为（ ）A ． B. C ．D ．9．给出下列命题及函数y=x,y=x 2和y=x1的图象，如图下列命题错误．．的是（ ） A.如果0＜a ＜1,那么a 1＞a ＞a 2； B.如果a ＞1，那么a 2＞a ＞a 1； C.如果－1＜a ＜0，那么a 1＞a 2＞a ； D.如果a ＜－1，那么a 2＞a1＞a;则（ ）10．如图（1），点E 为矩形ABCD 边AD 上一点，点P ，Q 同时从点B 出发，点P 沿BE→ED→DC运动到点C 停止，点Q 沿BC 运动到点C 停止，它们的运动速度都是1cm/s,设P ，Q 出发ts 时，△BPQ 的面积为ycm 2，已知y 与t 的函数关系的图象如图（2）则下列正确的是（ ） A.AE=6cm ； B.sin ∠EBC=54 C.当0＜t ≤10时，252t y =D.当t=12时，△BPQ 是等腰三角形二、填空题（6小题，每小题4分，共24分） 11．327= .12．据相关报道，截止到今年四月，我国已完成578万个农村教学点的建设任务，578万可用科学记数法表示为 .13．在某批次的100件产品中，有4件是不合格产品，从中任意抽取一件检验，则抽到不合格产品的概率是 .14．如图，在一块长为22米，宽为17米的矩形地面上，要修建同样宽的两条互相垂直的道路（两条道路分别与矩形的一条边平行），剩余部分种上草坪，使草坪面积为300平方米，设道路宽为x 米，根据题意可列出的方程为 .第8题图第9题图学校 九年级（ ）班 姓名_______________ 座号__________……………………………装…………………………订…………………………线……………………………九年级数学试卷共6页（本页第1页）九年级数学试卷共6页（本页第2页）（背面还有试题）15.一个圆锥的侧面积是36πcm 2,母线长12cm,则这个圆锥的底面半径是 cm.16．如图，四边形ABCD 与四边形AEFG 都是菱形，点C 在AF 上，点E ，G 分别在BC ，CD 上，若∠BAD=1350，∠EAG=750，则AEAB= . 三、解答题（10小题，共86分）17．（8分）计算：2sin 300+(－1)2－22-.18.（8分）解方程：5113--=-x xx .19．（8分）解不等式组⎩⎨⎧<-+≤+x x x x 343)1(2并将其解集在数轴上表示出来.20．（8分）某数学兴趣小组在全校范围内随机抽取了50名同学进行“舌尖上的莆田——我最喜爱的莆田美食”调查活动，将调查问卷整理后绘制成如图所示的不完整条形统计图.请根据所给信息解答以下问题：（1）请补全条形统计图； （2）若全校有2000名同学，请估计全校同学中最喜爱“扁食”的同学有多少人； （3）在一个不透明的口袋中有四个完全相同的小球，把它们分别标号为四种小吃的序号A 、B 、C 、D ，随机地摸出一个小球然后放回，再随机地摸出一个小球，请用列表或画树形图的方法，求出恰好两次都摸到“A ”的概率。

云大附中（一二一校区）2014年学业水平考试第三次模拟考九年级数学 参考答案一、选择题（每小题3分，满分24分）1．B 2．D 3．C 4．C 5．B 6．A 7．D 8．A二．填空题（每小题3分，满分18分）9．a 5 10．12 11．x ＜-1或0＜x ＜1 12．23π13．k ＞81-且k ≠0 14．（42,0）三．解答题（共9题，满分58分）15．解：原式=yx yy x y x xy y x x y x +=-+⋅--))(()()(2 ……………………2分x=3, y=1 ……………………4分 原式=41……………………5分16. 解：（1）相等. 理由如下: ……1分∵四边形ABCD 是矩形 ∴∠C=∠D=90°∴∠BEC+∠CBE=90°∵EF ⊥BE ∴∠BEF=90° ∴∠DEF+∠BEC=90°∴∠DEF=∠CBE ………3分 （2）BE=EF.理由如下:∵AE 平分∠DAB ∴∠DAE=∠BAE ∵AB ∥CD ∴∠BAE=∠DEA ∴∠DAE=∠DEA ∴AD=ED=BC ∵∠C=∠D=90° ∠DEF=∠CBE∴△DEF ≌△CBE （ASA ）∴BE=EF ………6分17．（1）……………3分 （2）D （0，5） ……………5分18.解：（1）选择长跑训练的人数占全班人数的百分比=1-60%-10%-20%=10%；训练篮球的人数=2+1+4+7+8+2=24人，∴全班人数=24÷60%=40； …………2分 （2）人均进球数= (8×2+7×1+6×4+5×7+4×8+3×2)2+1+4+7+8+2=5 …………3分（3）设参加训练前的人均进球数为x 个，由题意得：（1+25%）x=5，解得：x=4． …………4分 答：参加训练前的人均进球数为4个． …………5分19．解：（A,B ）, （A,C ）, （A,D ）,（B,A ）, （B,C ）, （B,D ）, （C,A ）, （C,B ）, （C,D ）, （D,A ）, （D,B ）, （D,C ）(列表方法略，参照给分) ……………2分由列表（或树形图）可知，所有结果共有12种，并且每一种结果出现的可能性相同。

2015届广州市中考英语模拟试卷（13）广州市广大附中2014学年第二学期初三普通班一模九年级英语试卷一、听力（略）二、语言知识及运用（共两节，满分30分）第一节单项选择（共20小题，每小题1分，满分20分）( ) 16. The room is terribly mess. It ______ cleaned yesterday.A. can't have beenB. may have beenC. can beD. may be( ) 17. ---Mr. Johnson asked me to remind you of the meeting this afternoon. Don't forget it.---No, I ______ .A. won'tB. don'tC. willD. do ( ) 18. ---With whom did you watch the 2012 World Cup Opening Ceremony?--- ______.A. A friend of mineB. A friend of meC. A friend of my sisterD. A friend of you( ) 19. ---Samuel didn't go to the concert yesterday, did he?--- ___. He practised __English for the competition all day.A. Yes, he did; speakingB. No, he did; speakC. Yes, he didn't; speakD. No, he didn't; speaking( ) 20. ---Why are you in such a hurry, Mike?---There ______ an NBA basketball game in ten minutes.A. will haveB. will beC. is going to haveD. are going to be( ) 21. She asked ______?A. what was the matter with his computerB. what the matter was with his computerC. his computer was what matterD. what wrong was his compute( ) 22. After a ___, you can see ____ tree at the side of the road.A. 10-minutes bike ride; an 18-metres-tallB. 10 minutes' bike ride; a 18-metre-tallC. 10-minute bike ride; an 18-metre-tallD. 10-minute bike ride, an 18metres tall( ) 23. ---Because of the rainy day, students can't focus in the class these days.--- ______.A. Neither can IB. Neither I canC. So they canD. So can they( ) 24. In my opinion, the Summer Palace is ______ than the Forbidden City.A. far much attractiveB. far more attractiveC. far much attractivelyD. far more attractively( ) 25. ---How wonderful the iPod is! Is it ______?--- I wish so. But it's ______.A. you; MikeB. your; Mike'sC. you; Mikes'D. yours; Mike's( ) 26. ---It's too hot. Would you mind my ______the window?--- ______. Do it as you like, please.A. to open; OKB. opening; Certainly notC. opening; Of courseD. open; Good idea( ) 27. Lucy, with her brothers, ______to the library every day.A. goesB. goC. goingD. went ( ) 28. Ma Ling was suddenly ill at school and ______to the hospital at once.A. had been sentB. has been sentC. sentD. was sent( ) 29. ---Mum, I'd like ______something, but I don't feel like ______ meat.---Oh, don't worry! I've cooked some vegetables.A. to eat; eatingB. eating; eatingC. to eat; to eatD. eating; to eat( ) 30. --- ______good time we had at the party last night!---Yes. It was ______ exciting party that I would never forget it.A. What; soB. How; suchC. What a; such anD. How a; so an( ) 31. It's very strange ______her to wear a fake moustache.A. withB. forC. toD. of( ) 32. ---I'm very tired these days because of studying for physics.---Why not ______music? It can make you ______.A. listen to; relaxedB. to listen to; to relaxC. listening to; relaxD. listen to; relaxing( ) 33. ______all the audience ______ is the most difficult task for comedy actors.A. Make; laughingB. Make; laughC. Making; laughD. Making; to laugh( ) 34. Whenever he was late, he could find plenty of excuses______ sounded reasonable.A. whoB. whereC. whenD. which( ) 35. Mike will arrive _____Pairs _____ the morning of July 19.A. to; onB. in; onC. in; inD. at; in第二节语法选择(共10小题，每小题1分，满分10分)The Secrets of HappinessMost people want to be happy, but few know 36 happiness. Money and success alone do not bring lasting happiness. Aristotle, a Greek thinker, said, "Happiness depends upon ourselves." In other words, we make our own happiness. Here 37 some advice to help you be happier.The first secret of happiness is to enjoy the simple things in life. Too often, we spend so much time 38 the future ---- for example, getting into college or getting a good job ---- so that we fail 39 the present. You 40 enjoy life's simple pleasures, such as reading a good book, 41 your favorite music, or spending time 42 close friends. People who have several close friends live happier and healthier lives.Another secret to 43 a happy life is to be active, and have hobbies 44 you forget your problems. Many people experience this dancing or playing a sport, such as skating or soccer. You can forget about your problems, and only think about the activity.Finally, many people find happiness in helping others. According to studies, people feel good when they volunteer their time helping others. If you want to feel 45 ,do something nicefor someone. You can help a friend with his or her lesson, go shopping to buy food for your family member, or simply help out around the house by washing the dishes.( ) 36. A. what to find B. what they can findC. how to findD. hope can they find( ) 37. A. has B. am C. is D. are( ) 38. A. think about B. thinking aboutC. thinkD. thinking( ) 39. A. enjoys B. enjoyed C. to enjoy D. enjoying( ) 40. A. ought B. need C. would D. should( ) 41. A. listen to B. hear C. listening to D. hearing( ) 42. A. in B. on C. with D. for( ) 43. A. lead B. leading C. led D. being led( ) 44. A. that B. those C. which D. where( ) 45. A. happy B. happier C. good D. well三、完型填空（共10小题，每小题1分，满分10分）"I can't believe what I'm hearing!" I thought to myself. Jeff was the last candidate (候选人) for president of Student Council. My best friend Tony came to me and said. "I'm sorry, Mike. I really thought you should be 46 ."Later that day, I happened to pass Jeff in the dining room. I offered him a 47 "Congratulations" and walked to my usual table. To my surprise, Jeff put his plate beside mine."I'm, er- I'm just wondering if you would…consider coming to work on my team," he s aid 48 . "You are really smart, and you would be a great manager.""I don't think so," I replied, feeling unsure."Well, if you change your mind, we are meeting tomorrow," he said before moving to another table. All that night, I thought about the 49 from Jeff. Maybe being a part of the election process would give me a chance to make important changes at our school. I decided to join them.My first goal was to design a catchy advertisement. Within a few days, we designed a poster with Jeff's pictures showing him in a number of activities. No one could walk through any hallway 50 passing Jeff's smiling face.My next step was to 51 which new activities students would like to have at our school. Many of them wanted a chess club and a volleyball team. With the information I had collected, Jeff met with the headmaster. The headmaster 52 to add these activities to our school program. With my help, Jeff and our ideas were well 53 at school.An eighth grader said, "It'll be like attending a new school with Jeff as president."Hearing these words made my heart filled with 54 . I had wanted to become president of Student Council to make a difference. I achieved that and more by working as a member of Jeff's team. He became the most popular candidate and I was large part ofhis 55 . The fact that it has made a difference in other people's lives is the real prize.What a great feeling!( ) 46. A. heard B. chosen C. invited D. followed( ) 47. A. polite B. loud C. hot D. cheerful( ) 48. A. proudly B. quickly C. nervously D. regretfully( ) 49. A. advice B. chance C. message D. offer( ) 50. A. for B. from C. with D. without( ) 51. A. carry out B. try out C. work out D. find out( ) 52. A. agreed B. wanted C. expected D. asked( ) 53. A. allowed B. received C. introduced D. required( ) 54. A. pride B. surprise C. patience D. hope( ) 55. A. luck B. spirit C. life D. success四、阅读理解（共20小题，每小题2分，满分40分）AWe may know some good health habits, but we don't realize how much difference they can make. In the 1970s, scientists at the University of California-Los Angeles asked 7,000 people about their health habits. Then they followed these people to see how long they lived.The scientists discovered that seven habits were closely linked with a longer life.▲Eating breakfast every day.▲Avoiding eating snacks between meals.▲Keeping a good weight----not too heavy or too thin.▲Exercising regularly.▲Sleeping seven or eight hours every night----not more or less.▲Do not smoke.▲Drink fewer alcoholic drinks.The researchers found that these habits had a powerful effect on health. People in this study who had three or fewer of these habits lived another 21.6 years. People who had six or seven could expect to live another 33 years!But how do you change your habits? Make one small change every week. And be patient. It takes about 21 days to form a new habit.( ) 56. The underlined word "they" (Paragraph 1) refers to____ .A. scientistsB. good habitsC. universitiesD. 7,000 people( ) 57. One of the habits closely linked with a longer life is___ .A. taking regular exerciseB. drinking less water every dayC. sleeping more than eight hours every nightD. eating fruit between meals( ) 58. The idea "these habits had a powerful effect on health" is supported with_____ .A. guessesB. storiesC. experiencesD. facts( ) 59. In which section of a newspaper can you most probably read this passage?A. ADB. HealthC. BusinessD. Sports( ) 60. The passage is written mainly to tell people_______.A. to keep a good weightB. to avoid eating to muchC. to form good health habitsD. to keep away from dangerBJolie Ray was watching TV alone at home when the program suddenly stopped. "Sorry to interrupt the program. Here's an important notice from the police. At about 9 p.m., a lady was robbed and killed by a man in brown. If you know anything about the man, please call the police. Thank you." The terrible news made Jolie frightened. She couldn't help looking around, but didn't see anyone in her kitchen or on the balcony. But all of a sudden, a man appeared and stood in front of her. Hewas wearing brown! Jolie didn't know what to do!"Calm down, young lady. Put your jewelry and cash on the table," said the robber. "I'll stay up here for the night. If you dare to call the police, you are just asking for trouble."That made Jolie even more frightened, but she tried to calm herself. Just then came the sound of a police car. In a little while, someone rang the doorbell. The robber said, with a gun pointed against Jolie's back, "Open the door and say that you have gone to bed. Do not let anyone in."But Jolie had an idea. She opened the door."Good evening, Miss Ray. I'm Sergeant Collins. Is there anything unusual here?""No," she said loudly, "only my brother and I are in the room.""OK. Good night," Collins replied.A few minutes later, the police car went away."Good," the robber said with a smile. Just at this moment, some policemen broke the window and hurried into the room from the balcony. They quickly caught the robber."You really did a good job, Miss Ray. When you said that your brother was in the room, I knew there was something unusual," said Sergeant Collins, "because we knew that your brother had been killed in a robbery half a year ago."( ) 61. When Jolie Ray was watching TV one night, the program suddenly stoppedbecause_______ .A. the electricity went offB. something was wrong with the TVC. a robber was nearbyD. there was an important notice( ) 62. _______ made Jolie frightened.A. That she was alone at homeB. That a man was robbed and killedC. The notice from the policeD. The robber in her kitchen( ) 63. Sergeant Collins is probably a_______ .A. guardB. neighbourC. police officerD. news reporter( ) 64. We can learn from the story that_______ .A. the police knew many details of what the robber looked likeB. Sergeant Collins believed Jolie's words and left her homeC. the police got into Jolie's home through the balconyD. Jolie's brother was a robber and had been killed half a year before( ) 65. From the story we know that Jolie Ray is a(n) _______ lady.A. brave and smartB. careful and kindC. honest and confidentD. friendly and helpfulCSince the beginning of history, man has been fascinated by the idea of living forever, of winning the fight against death and disease. So far, this has only remained a dream, though a very powerful one. Many people have wondered whether it would be possible to find a way to preserve human bodies, and what would be the best way to preserve human bodies.It has long been known that meat of fruit can be kept fresh for long periods by freezing; in ancient China, for example, food was stored with ice to keep it fresh. This method could also be useful for preserving humans and in fact many people have explored this possibility.However, most living beings that exist under warm conditions die when frozen. This is because of the harmful effects of freezing ice crystals, which are not only larger than the volumeof the water originally in the cells, but also form sharp cutting shapes that harm the cells.In the 1940s Dr B.J. Luyet and a group of scientists in England were working on the problem of freezing cells without damaging them. Since the harm caused by ice crystals was the main cause of damage, Luyet suggested removing some or all of the water fromthe cells before freezing them.Using living cells from chicken, Luyet and his assistants discovered that they could partly dry the chicken cells, using a mixture of the white part of an egg and glycerin, a clear thick liquid made chiefly from fats and oils. Some success was obtained. The chicken cells were dried, frozen for a period of time, and then carefully unfrozen. Almost all the cells recovered when they reached normal temperatures. Since then, the cooling of whole animals to a temperature very much below freezing point for later unfreezing has become more of a possibility, and the glycerin method would probably be used to accomplish this. When this can be done completely and successfully, science willhave moved much closer to its aim of freezing and storing incurable patients until the daythey can be cured.( ) 66. It seems that the idea of preserving human bodies_______ .A. is importantB. comes from that of storing meat and fruit fresh by freezingC. is quite funD. doesn't make any sense( ) 67. From the fact that most living things existing under warn conditions die whenfrozen, the scientist realize that_______ .A. living things cannot be frozen actuallyB. it is impossible for them to freeze human beingsC. the water from the living cells should be removedD. cells cannot recover when they are carefully unfrozen( ) 68. Glycerin can be used_______ .A. to remove water from living cellsB. to unfreeze living cellsC. to freeze living cellsD. to change the shape of crystals( ) 69. What is the passage mainly about?A. The harmful effects of freezing food.B. How to preserve food.C. How to remove water from living cells.D. The exploration of preserving human bodies.( ) 70. What is the most probable meaning of the underlined word "fascinated"?A. attractedB. freedC. afraidD. sadDYou probably know you should say "please" and "thank you" at restaurants. You probably know the rules of a library. You know you should respect and be nice to your classmates. But do you have music manners?Keep It Down! You have to notice the volume of your music. You should not play your music so loud that everyone around you can hear it. Some people might even get angry. Usually, whenyou play the music loud on an MP3 player, other people can't hear the words of the song. They just hear a loud sound. Not one wants to listen to this. Very loud music can also be bad for your ears. So even if you are alone when listening to our MP3 player, you shouldn't have it turned up too high.Take Them off! You need to know when to turn your MP3 player off and put it away.Libraries and schools don't allow MP3 players. There are other places, like museums, that don't have rules, but is would be rude to have your MP3 player on. Sometimes, it doesn't make sense to listen your MP3 player at event. Why would you listen to music at a play, a movie or a sporting event? Youwould miss what is going on and others would wonder why you even came.Take One Out! Once is a while it's okay just to take out one earphone and not other.Imagine you are listening your MP3 player when someone asks you the way. It would not be rude to take out one earphone, tell him the way, and put back the earphone and continue listening. You can also do this when you order food at a fast-food restaurant or when you answer the telephone and it's not for you.It's Your Choice! There are times when you need to decide what is best. For example, some people canlisten to music on their MP3 Players when reading books, while others think it is disturbing. In cases like this, you need to do what seems right for you.( ) 71. The underlined word "volume" in Paragraph Two probably means_______ .A. the type of musicB. the amount of a soundC. the length of a songD. the color of and MP3 player( ) 72. No one wants to listen to from others' MP3 player_______.A. a loud soundB. sad storiesC. a long movieD. the words of a song( ) 73. What will happen if we listen to our MP3 player at a play?A. The theater won't allow it.B. The actors will get angry.C. Others won't hear the play well.D. We will miss part of the play.( ) 74. Which of the followings will not be rude if we just take out one earphone?A. Shoeing others the way.B. Talking to friends on the phone.C. Watching a sporting event.D. Having dinner with our parents.( ) 75. What can be the best title of this passage?A. Music LoversB. Music MannersC. MP3 PlayersD. MP3 Earphones五、写作（共四节，满分35分）第一节单词拼写（共10小题，每小题1分，满分10分）76. In order to protect the environment, we 'd better use the products that f ______to it.77. The post office is o ______ (to) the station.78. They had no c ______, but to agree to what they suggested.79. Health is above w ______.80. She m ______ to make herself understood in English. 80、managed81. Track events, such as running, test a person's s ______.82. She can't do the work, because she has no a ______ in that kind of work.83. Americans use forks and knives to eat with, while our Chinese use c ______.84. We should show our r ______ to others.85. On April Fools' Day, people often make j ______ about others.第二节完成句子（共5小题，每小2分，满分10分）86. 我们对你的事情不感兴趣。

2014年广东佛山中大附中初三一模数学试卷一、选择题（共10小题；共50分）1. 的绝对值为A. B. C. D.2. 如图，已知，，则的度数是A. B. C. D.3. 已知是二元一次方程组的解，则的值为A. B. C. D.4. 已知等腰三角形的一个内角是，那么这个等腰三角形顶角的度数是A. B. C. D. 或5. 如果两圆的半径分别为和，圆心距为，那么这两圆的位置关系是A. 内含B. 内切C. 相交D. 外切6. 函数的取值范围是A. B.C. 且D. 且7. 已知实数在数轴上的位置如图，则化简的结果为A. 1B. -1C. 1-2aD. 08. 给出下列各式：①；②；③；④，其中运算错误的有A. 个B. 个C. 个D. 个9. 如图，等边的边长为，为上一点，且，为上一点，若，则的长为A. B. C. D.10. 二次函数的图象如图所示，则一次函数与反比例函数在同一坐标系内的图象大致为A. B.C. D.二、填空题（共6小题；共30分）11. 的平方根是______．12. 已知，则的余角是______．13. 因式分解： ______．14. 某同学在使用计算器求个数的时候，将误输入为，那么由此求出的平均数与实际平均数的差为______．15. 一个用正方体积木搭成的立体图形，从左面看形状是，从上面看形状是，则至少需要______ 块积木．16. 如图，个正方形重叠，重叠部分的顶点正好是下面一个正方形的中心．若每个正方形的边长都是，则整个图形的周长是______．三、解答题（共9小题；共117分）17. 解方程：．18. 如图，在平行四边形中，点是的中点，连接并延长，交的延长线于点．求证：．19. 已知是关于的一元二次方程的根，求代数式的值．20. 为开展“学生每天锻炼小时”的活动，我市某中学根据学校实际情况，决定开设A：毽子，B：篮球，C：跑步，D：跳绳四种运动项目．为了了解学生最喜欢哪一种项目，随机抽取了部分学生进行调查，并将调查结果绘制成如下统计图．请结合图中信息解答下列问题：（1）该校本次调查中，共调查了多少名学生?（2）计算本次调查学生中喜欢“跑步”的人数和百分比，并请将两个统计图补充完整；（3）在本次调查的学生中随机抽取人，他喜欢“跑步”的概率有多大?21. 为响应漳州市市政府“创建国家森林城市”的号召，某小区计划购进A，B 两种树苗共棵，已知 A 种树苗每棵元，B种树苗每棵元．（1）若购进A，B 两种树苗至少用去元，且购进B种树苗不少于棵，问有几种购进方案?（2）若购买B 种树苗的数量不多于A 种树苗的数量的倍，请你给出一种费用最省的方案，并求出该方案所需费用．22. 已知圆锥的底面半径为，高，现在有一只蚂蚁从底边上一点出发．在侧面上爬行一周又回到点，求蚂蚁爬行的最短距离．23. 如图1，在底面积为平方厘米、高为厘米的长方体水槽内放入一个长方体烧杯，以恒定不变的水流速度先向烧杯中注水，注满烧杯后，继续注水，直至注满水槽为止，此过程中，烧杯本身的质量、体积忽略不计，烧杯在水槽中的位置始终不改变．水槽中水面上升的高度（厘米）与注水时间（秒）之间的关系如图 2．（1）图 2 中点______ 表示烧杯刚好注满水，点 ______ 表示水槽中水面恰与烧杯中水面齐平．（2）求烧杯的底面积．24. 如图，在平面直角坐标系中，抛物线与轴交于点，与轴交于，两点，点的坐标为，直线恰好经过，两点．（1）求抛物线的解析式及顶点的坐标；（2）求抛物线的对称轴直线，并用尺规作图在对称轴直线上作出点，使；（3）在（2）的条件下求点的坐标．25. 如图，为的直径，，为上一点，过点作的弦，设．（1）已知，求的值，及，的度数各是多少?（2）当时，是否存在正实数，使弦最短?如果存在，求出的值，如果不存在，说明理由；（3）在（1）的条件下，且，求弦的长．答案第一部分1. B2. A3. B4. D5. C6. C7. D8. D9. B 10. B第二部分11.12.13.14.15.16.第三部分17. 去分母得去括号得解得检验：当时，，所以，是原分式方程的解．18. 四边形是平行四边形，，．，．在和中，．．．19. 把代入得：，，原式20. （1）该校本次一共调查了（人）；（2）喜欢跑步的人数（人），喜欢跑步的人数占被调查学生数的百分比，补全统计图，如图：（3）在本次调查中随机抽取一名学生他喜欢跑步的概率．21. （1）设购进 A 种树苗棵，则购进B种树苗棵，解得：有三种购进方案分别为：A 种树苗棵，B 种树苗棵；A 种树苗棵，B 种树苗棵；A 种树苗棵，B 种树苗棵；（2）设购进 A 种树苗棵，则购进 B 种树苗棵，，解得：．设购买树苗总费用为，，随的减小而减小，当时，有最小值（元）．答：购进 A 种树苗棵、B 种树苗棵，费用最省；最省费用是元．22. 设扇形的圆心角为，圆锥的顶点为，，．由勾股定理可得母线，而圆锥侧面展开后的扇形的弧长为，．即是等腰直角三角形，由勾股定理得：．答：蚂蚁爬行的最短距离为．23. （1）；（2）设烧杯的底面积为，则由题意得：，解得：．答：烧杯的底面积为平方厘米．24. （1）恰好经过，两点，，，解之得，抛物线的解析式为．，顶点．（2）如图1，点是外接圆圆心．（3）如图2，过作于点，连接，设直线交轴于点．，为等腰直角三角形，，，又，，在中，，故，，．故坐标为或．25. （1）由解得经检验，是原方程的解．如图，连接，．是的直径，，；又，，，．（2）如图，连接．，，，则，解得，．要使最短，则于点，，；，；；．故存在这样的值，且．（3）如图，连接，．，，，；，，．，，；，，；同理．，③，由得，由得；，在中，，，．由，得；．。

2014一模24、25题汇编2014从化压轴24．（本小题满分14分）如图10，抛物线的顶点为A ，与y 轴交于点B ． （1）求点A 、点B 的坐标．（2）若点P 是x 轴上任意一点，求证：．（3）当最大时，求点P 的坐标． 24．解：（1）抛物线与y 轴的交于点B ， 令x=0得y=2．∴B （0，2） …………………………………2分∵∴A （—2，3）………………………………4分（2）当点P 是 AB 的延长线与x 轴交点时，．…………………………………6分当点P 在x 轴上又异于AB 的延长线与x 轴的交点时， 在点P 、A 、B 构成的三角形中，．综合上述： …………………………………………………………9分 （3）解法一：作直线AB 交x 轴于点P ，由（2）可知：当PA —PB 最大时，点P 是所求的点 …10分 作AH ⊥OP 于H ． ∵BO ⊥OP ， ∴△BOP ∽△AHP ∴ AH∥BO ∴…………………………………………………………………………12分 由（1）可知：AH=3、OH=2、OB=2，∴OP=4，故P （4，0） ……………………………………………………………14分 解法二：2124y x x =--+PA PB AB -≤PB PA -2124y x x =--+22112(2)344y x x x =--+=-++AB PB PA =-AB PB PA <-PA PB AB -≤AH HPBO OP=设直线AB 所在解析式为y kx b =+，图象经过(2,3),(0,2)A B -，………………10分得方程组232k b b -+=⎧⎨=⎩，解得122k b ⎧=-⎪⎨⎪=⎩ …………………………………………12分∴122y x =-+；当0y =时，4x =∴点P 坐标为（4，0）．………………………………………………………………14分25．（本小题满分14分）如图11，射线AM BN ∥，∠A ＝∠B ＝90°，点D 、C 分别在AM 、BN 上运动（点D 不与A 重合、点C 不与B 重合），E 是AB 边上的动点（点E 不与A 、B 重合），在运动过程中始终保持DE EC ⊥,且AD DE AB a +==． （1）求证：△ADE ∽△BEC ；（2）设AE m =，请探究：△BEC 的周长是否与m 值有关，若有关，请用含有m 的代数式表示△BEC 的周长；若无关，请说明理由．25.（1）证明：DE EC ∵⊥，90DEC ∠=∴，90AED BEC ∠+∠=∴ ………………………………………2分又90A B ∠=∠=∵，90AED EDA ∠+∠=∴，BEC EDA ∠=∠∴…………4分 ∴△ADE ∽△BEC …………………………………………6分（2）解法一：△AED 的周长AE AD DE a m =++=+，BE a m =-设AD x =，则DE a x =- ……………………………………7分ＢD∵90A ∠= 22D E A E AD =+∴即22222a ax x m x -+=+ 222a m x a-=∴ ……………………………………………9分由（1）知△ADE ∽△BEC∵2222a m ADE AD a ma BEC BE a m a -+===-△的周长△的周长……………………11分∴△BEC 的周长22a ADE a a m==+△的周长…………………13分∴△BEC 的周长与m 的值无关 …………………………14分解法二：同解法一求出BE a m =-，222a m AD a-= …………………………9分∵△ADE ∽△BEC A ED E A D B CC E B E==∴22()22AE BE m a m amBC a m AD a m a-===-+∴ …………………………10分 222222()()22a m a a m DE BE a m a CE a m AD a m a---+===-+………………11分 ∴△BEC 的周长222()2am a m BE BC CE a m a a m a m+=++=-++=++……………13分∴△BEC 的周长与m 的值无关． …………………………………14分2014番禺一模压轴 24．（本小题满分１4分）如本题图1，在ABC △中，AB BC a ==，2AC b =且a >．ECD △由ABC △沿BC 方向平移得到，连接BE 交AC 于点O ，连接AE ．（1）判断四边形ABCE 是怎样的四边形，并说明理由；（2）如本题图2，P 是线段BC 上一动点（不与点B C 、重合），连接PO 并延长交线段AE 于点Q ，再作QR BC ⊥于R ．试探究：点P 移动到何处时，PQR △与AOB △相似？24．解：（1）四边形ABCE 是菱形. …………1分证明：ECD △是由ABC △沿BC 平移得到的，EC AB ∴∥，且EC AB =，…………3分∴四边形ABCE 是平行四边形，…………4分又AB BC =，∴四边形ABCE 是菱形．……5分(2)四边形ABCE 是菱形,AC BE ∴⊥，AO OC b ==,BO OE =.……6分如图2，当点P 在BC 上运动，使PQR Rt △与AOB Rt △相似时，2∠是OBP △的外角，23ABO ∴∠>∠=∠，……8分第24题图1B第24题图2AEOBC DQP R 第24题图2F123 G 42∴∠不与ABO ∠对应，2∴∠与4∠ 对应，即必有24∠=∠，……9分〖方法一〗：又,41AB BC =∴∠=∠,故有21∠=∠，OP OC b ∴== ……10分 过O 作OG BC ⊥于G ，则G 为PC 的中点，2PC PG =. 在Rt POGC △和Rt ABO △中，cos 2,cos 4,PG AOOP AB∴∠=∠= 24∠=∠,2,PG AO AO OP b PG OP AB AB a ⨯∴=∴==……13分222222.b a b BP BC PC BC PG a a a -∴=-=-=-⨯=22220a b,a b >∴->，P 在BC 上.即222a b BP a-=时，PQR △∽AOB △.……14分〖方法二〗：设BP x =，由对称性QE x =. 过E 作EH BD ⊥于F ,则//,AE BD QR BC ⊥,则四边形RFEQ 为矩形，QR EF ∴=，RF x =,2BF x PR ∴=+.…………① ……10分又AB BC a ==，BO ∴2BE BO ==由菱形ABCE 的面积12s AC BE BC QR =⨯=⨯得：2QR a =……11分PQR △∽AOB △， ,QR BOPR AO ∴=22AO b PR QR BO a∴=⨯=. ……12分 又BEF Rt △∽BCO Rt △,BF OB EF OC ∴=,得2222a b BF a-=. ……13分代入①得222a b BP a-=，〖下同方法一〗。