2020年浙江省杭州市中考冲刺易错题练习(二)
〖精选4套试卷〗杭州市2020年中考数学第二次押题试卷
2019-2020学年数学中考模拟试卷一、选择题1.下列图案是用长度相同的火柴按一定规律拼搭而成,图案①需8根火柴,图案②需15根火柴,…,按此规律,图案⑩需几根火柴棒( )A .71B .72C .74D .782.如图,平面直角坐标系中,在边长为1的菱形ABCD 的边上有一动点P 从点A 出发沿A→B→C→D→A 匀速运动一周,则点P 的纵坐标y 与点P 走过的路程S 之间的函数关系用图象表示大致是( )A .B .C .D .3.平方根和立方根都是本身的数是( ) A .0B .1C .±1D .0和±14.如图圆O 直径AB 上一点P ,AB =2,∠BAC =20°,D 是弧BC 中点,则PD+PC 的最小值为( )A .3B .1C .5D .25.下列四个命题中:①若,则;②反比例函数,当时,y 随x 的增大而增大;③垂直于弦的直径平分这条弦; ④平行四边形的对角线互相平分,真命题的个数是( ) A.1个 B.2个C.3个D.4个6.据统计,截止2019年2月,长春市实际居住人口约4210000人,4210000这个数用科学记数法表示为( ) A.542.110⨯B.54.2110⨯C.64.2110⨯D.74.2110⨯7.下列运算正确的是( ) A .x 8÷x 2=x 4B .(x 2)3=x 5C .(﹣3xy)2=6x 2y 2D .2x 2y•3xy=6x 3y 28.如图,直线y =mx+n 与两坐标轴分别交于点B ,C ,且与反比例函致y =2x(x >0)图象交于点A ,过点A 作AD ⊥x 轴,垂足为D ,连接DC ,若△BOC 的面积是6,则△DOC 的面积是( )A .5﹣25B .5+25C .415﹣6D .﹣3+159.如图,正方形ABCD 的边长为8,M 在DC 上,且DM 2=,N 是AC 上一动点,则DN MN +的最小值为( )A .6B .8C .10D .1210.某校对部分参加研学旅行社会实践活动的中学生的年龄(单位:岁)进行统计,结果如表: 年龄 12 12 14 15 16 人数12231A .15,14B .15,13C .14,14D .13,1411.不等式12x-≥1的解集在数轴上表示正确的是( ) A .B .C .D .12.﹣π的绝对值是( ) A .﹣π B .3.14 C .π D .1π二、填空题13.如图,O 是等边△ABC 内一点,OA =6,OB =8,OC =10,将线段BO 以点B 为旋转中心逆时针旋转60°得到线段BO',下列结论:①△BO'A 可以由△BOC 绕点B 逆时针旋转60°得到;②点O 与O'的距离为8;③四边形AOBO'的面积为3; ④∠AOB =150°;⑤s △AOC+S △AOB =3,其中正确的结论是_____.14.如图,在△ABC 中,AC =BC =4,∠ACB =90°,若点D 是AB 的中点,分别以点A 、B 为圆心,12AB 长为半径画弧,交AC 于点E ,交BC 于点F ,则图中阴影部分的周长是_____.15.如图,AB 为⊙O 的直径,弦CD ⊥AB 于点E ,已知CD =6,EB =2,则⊙O 的半径为_____.16.分解因式a 3﹣a 的结果是_____. 17.将数1个1,2个12,3个13,…,n 个1n (n 为正整数)顺次排成一列:1、12、12、13、13、13、…、1n 、1n …,记123111,,,22a a a ===…,11S a =,212S a a =+,3123S a a a =++,…,12...n n S a a a =+++,则S 2019=______.18.如图,在□ABCD 中,AB=3,AD=4,∠ABC=60°,过BC 的中点E 作EF ⊥AB ,垂足为点F ,与DC 的延长线相交于点H ,则△DEF 的面积是 .三、解答题19.某校学生会发现同学们就餐时剩余饭菜较多,浪费严重,于是准备在校内倡导“光盘行动”,让同学们珍惜粮食,为了让同学们理解这次活动的重要性,校学生会在某天午餐后,随机调查了部分同学这餐饭菜的剩余情况,并将结果统计后绘制成了如图所示的不完整的统计图.(1)这次被调查的同学共有人;(2)补全条形统计图,并在图上标明相应的数据;(3)校学生会通过数据分析,估计这次被调查的所有学生一餐浪费的食物可以供50人食用一餐.据此估算,该校18000名学生一餐浪费的食物可供多少人食用一餐.20.如图,大楼AC的一侧有一个斜坡,斜坡的坡角为30°.小明在大楼的B处测得坡面底部E处的俯角为33°,在楼顶A处测得坡面D处的俯角为30°.已知坡面DE=20m,CE=30m,点C,D,E在同一平面内,求A,B两点之间的距离.(结果精确到1m,参考数据:3≈1.73,sin33°≈0.54,cos33°≈0.84,tan33°≈0.65)21.(1)阅读理解利用旋转变换解决数学问题是一种常用的方法.如图1,点P是等边三角形ABC内一点,PA=1,PB=3,PC=2.求∠BPC的度数.为利用已知条件,不妨把△BPC绕点C顺时针旋转60°得△AP′C,连接PP′,则PP′的长为_____;在△PAP′中,易证∠PAP′=90°,且∠PP′A的度数为_____,综上可得∠BPC的度数为_____;(2)类比迁移如图2,点P是等腰Rt△ABC内的一点,∠ACB=90°,PA=2,PB=2,PC=1,求∠APC的度数;(3)拓展应用如图3,在四边形ABCD中,BC=3,CD=5,AB=AC=12AD.∠BAC=2∠ADC,请直接写出BD的长.22.如图,1为水平地面,测角仪高1米,将测角仪放置在点D处,且垂直于地面1,测得仰角∠ACG=45°,将测角仪平移至EF处,测得仰角∠AEG=60°,已知DF=3米,求树AB的高度.23.如图,BC是半⊙O的直径,A是⊙O上一点,过点的切线交CB的延长线于点P,过点B的切线交CA 的延长线于点E,AP与BE相交于点F.(1)求证:BF=EF;(2)若AF=32,半⊙O的半径为2,求PA的长度.24.一般轮船在A、B两个港口之间航行,顺流需要4个小时,逆流需要5个小时,已知水流通度是每小时2千米,求轮船在静水中的速度.25.某校为了预测本校九年级男生毕业体育测试达标情况,随机抽取该年级部分男生进行一次测试(满分50分,成绩均记为整数分),并按测试成绩m(单位:分)分类:A类(45<m≤50),B类(40<m≤45),C类(35<m≤40),D类(m≤35)绘制出如图所示的不完整条形统计图,请根据图中信息解答下列问题:(1)a=,b=,c=;成绩等级人数所占百分比A类(45 10 20%B类22 44%C类 a bD类 c(3)若该校九年级男生有600名,D类为测试成绩不达标,请估计该校九年级男生毕业体育测试成绩能达标的有多少名?【参考答案】***一、选择题题号 1 2 3 4 5 6 7 8 9 10 11 12 答案 A A A B B C D D C A A C13.①②④⑤.14.8422π-+15.13 416.a(a+1)(a﹣1).17.403564(或36364)18.3三、解答题19.(1)1000,(2)答案见解析;(3)900.【解析】【分析】(1)结合不剩同学的个数和比例,计算总体个数,即可。
杭州市2020中考化学易错易混200题精粹word含答案
杭州市2020中考化学易错易混200题精粹word含答案一、填空题1.小红同学在学习盐酸的化学性质时,归纳出了盐酸与其它物质相互反应的关系,如图(图中“﹣”表示相连的两种物质能发生反应).(1)若X是与其它三种不同类别的化合物,则X可以是(填化学式,只填一种即可).(2)根据如图所示物质间的关系,写出①反应的化学方程式:.(3)当X是单质时,请写出X与稀盐酸反应的化学方程式:(只写出一个即可).2.下述描述生活中物质化学性质的是(_______)A.瓷碗易碎 B.轮胎能炸 C.饭菜会馊 D.____________3.下图为干电池的结构示意图,请利用所学知识完成下列问题。
(1)碳棒(主要成分是石墨)用作干电池的正极是利用了石墨的______性。
(2)干电池的材料很多可以回收利用,例如双氧水与回收的二氧化锰可用于实验室制取氧气。
写出该反应的化学方程式:;(3)黄铜是铜与锌的合金,其硬度(填“大于”或“小于”)纯铜。
将足量的锌片放入硫酸铜溶液中,观察到的现象,说明锌比铜活泼。
4.右图是甲、乙两种固体物质的溶解度曲线。
(1)℃时,甲、乙两种物质的溶解度相等。
(2)t2℃时,将等质量的甲、乙两种物质加水溶解配制成饱和溶液,所得溶液质量的大小关系为:甲乙(填“>”、“<”或“=”)。
(3)把甲物质的不饱和溶液变为饱和溶液,下列有关说法正确的是(填序号)A.溶剂的质量一定变小 B.溶质的质量可能不变 C.溶液的质量一定变大D.溶质的质量分数一定变大 E.该饱和溶液还可以溶解其它物质(4)在实验室用固体甲配制一定溶质质量分数的甲溶液,需用到的仪器有:托盘天平(带砝码盒)、烧杯和。
(填序号)A.酒精灯 B .药匙 C.玻璃棒 D.漏斗 E.铁架台 F.量筒 G 胶头滴管5.(1)化学用语是我们学习和研究化学的重要语言工具。
现有H、C、O、N、Na五种常见的元素,请选用其中的元素写出符合下列要求的物质各一种(用化学式表示):①最简单的有机物___;②空气中含量最多的气体___;③人体中含量最多的物质是___;④炉具清洁剂中的碱___。
人教版2019-2020学年度浙江省杭州市中考冲刺易错题练习(二)
人教版2019-2020浙江省杭州市中考冲刺易错题练习(二)一、语法填空A.语法填空单句练习1.Letters of recommendation have different levels __________importance, __________(depend)on the views of college or university and many other things.2.You can also download a map from the London __________(underground)website().3.It’s not the shortest route here, but I think it is ___________(simple).4.The underground staff will __________(sure) help you.5.When I finished my job, I heard my manager ask the “tin man” about what the was going to do_________those tins he had collected.6.I never even thought about this kind of question, __________I always assumed that “tin man” would take those tins to the recycling center. ___________(unexpected), “tin man” answered: “I will give these tins to my neighbor. He has epilepsy(癫痫)and cannot work.” I was so shocked _________(hear) that, so I asked him: “You mean you collect all those thins just to help your neighbor?”7.I’ve always wanted to try rock climbing, but never had the time or money for it. But I’ve discovered a way to experience the __________(excite) of climbing rock. Indoor climbing is ___________way to get a taste of rock climbing.8.___________indoor climbing is safer and simpler than real rock climbing, you should still be careful.9.Try to get under a doorway or another area of the building ___________is held up by strong beams(梁).10.Do not rush to lifts, because it is far___________(safe) to stay where you are.11.After an earthquake, many buildings are less strong, although they appear safe. If you stay indoors, move people from the building so that the building quickly and help disabled or injured people. Once outdoors, move well away _________ the building so that if it falls down, you will not___________(hurt).12.By planning ahead and keeping calm during ___________earthquake, you can greatly increase your chances of survival without injury.13.___________(thank)to fitness apps and gadgets(小机械), people can measure every step they take.14.All of __________(they)friends can see where they have run, what activities they ___________(do) or what they have had for lunch.15.My friend, Anna Palmer, is always __________(use) the fitness gadgets(小机械).16.Proper nutrition(营养)is important for good health. Your body cannot work well _________it receives the proper kindof “fuel(燃料)”.17.Vegetables and fruits are very important because they provide necessary vitamins and minerals. However, don’t overeat. __________is not helpful to be overweight.B.语法填空语篇练习(recommendation 推荐;resume 简历;)二、完形填空(一)Just before September, Miller was hit by a car and lost his right __4__. I went to see him after he had come back from hospital. He looked very __5__, but he didn’t cry at all.That season, I __6__all of Miller’s records while he watched the games from the bench at home. We beat the other team 10-1 in the final match and I was named the most valuable player, __7__I often had crazy dreams in which I was to blame for Miller’s accident.One afternoon, while i was crossing the filed to go home, I saw Miller was stuck going over a fence-which wasn’t __8__ to climb if you had both arms. I’m sure I was the __9__person in the world he wanted to accept help from. But even that challenge he accepted.4. A. leg B. foot C. arm D. hand5. A. pale B. calm C. relaxed D. ashamed6. A. held B. broke C. set D. tired7. A. and B. then C. but D. so8. A. easy B. hard C. fun D. fit9. A. first B. second C. next D. last(二)Getting the proper amount of __6__is also important. If you don’t get enough sleep, you will feel tired and __7__get angry. You have no energy. Over a long period of time a little amount of sleep __8__even result in a change personality(个性). Be sure to allow __9__seven to nine hours of sleep each night. If you do, your body will feel __10__and easily get refreshed, your mind will be active.6. A. food B. sleep C. energy D. exercise7. A. hardly B. clearly C. easily D. gradually8. A. must B. may C. have to D. need9. A. ourselves B. myself C. yourself D. themselves10. A. weak B. tired C. strong D. nervous(三)The research team __4__27men who didn’t like doing sports regularly for 12 weeks. They put the men into __5__ groups. One group did short, intense physical exercise or training on a bicycle three times a week. __6__group rode a bicycle for about 50 minutes, three times a week. The last group did nothing.The researchers found __7__that they did not think would happen. The group that exercised for only 10 minutes each time was just as healthy after 12 weeks as the __8__that exercised for 50 minutes each time. That is because of the __9__ the researchers planned the activities.4. A. tired B. decided C. followed D. pointed5. A. two B. three C. four D. five6. A. Another B. Other C. The other D. Others7. A. nothing B. anything C. something D. everything8. A. that B. those C. ones D. one9. A. idea B. way C. mind D. result三、阅读理解(一)Sitting among the cheering fans of the Chinese Womens Volleyball Team in Rio de Janeiro, a Polish fan caught a lot of attention. It is not because he is not Chinese, but because he has followed the team closely from the very beginning.The 60-year-old Jozef fell in love with the Chinese Women's Volleyball Team at the first sight when he watched the girls at the London Olympics on TV in 2012. The Polish man was crazy about the performances of the young team, especially by its core player Hui Ruoqi. Before that, Jozef was a loyal fan of his home team the Polish men’s volleyball.Since then, Jozef has become crazy about the team and has kept track of almost all their international competitions. Back in the 2013 Montreux Volley Masters of Switzerland, the Polish man, for the first time, came to cheer up for the team on site. He also drove all the way from Poland to ltaly to lend support for the girls during the 2014 Womens World Volleyball Championship.The hardcore fan traveled hundreds of miles from Poland to Brazil, and booked tickets for all matches of the Chinese Womens Volleyball. This time, Jozef was interviewed by TV and has been recognized by not just fans, but millions of Chinese TV audiauce.The "Polish grandpa" was a nickname given by Chinese volleyball fans. He has 18,000 followers on Sina Weibo, China's answer to Twitter, where Jozef has been sharing his obsession with Chinese internet users since 2013.22. What has Jozef been doing on Sina Weibo?A. Giving support to the Polish team.B. Sharing his love for the Chinese team.C. Answering questions about playing volley ball.D. Booking tickets for matches of the Chinese team.(二)Few people could forget the tragedy that happened on Nov 27, when Chinese-Canadian model and actor Godfrey Gao,35, died from cardiac arrest (心跳骤停) while filming a reality TV show in Ningbo, Zhejiang.Shocked by his sudden death, people discussed how we should deal with incidents like these. Experts suggested that people should learn first aid so that they can help heart attack victims.In China, 550,000 people suffer from sudden cardiac arrest every year, according to the National Center for Car diovascular Diseases. Only about I percent are saved.To deal with this problem, a draft of the Basic Medical Treatment and Health Promotion Law was submitted to the Standing Committee of the National People's Congress for its fourth review in December 2019. It suggests that public places should be equipped with necessary first aid equipment.One of these pieces of equipment is called an automated external defibrillator(AED, 自动体外除颤器). It can save people from sudden cardiac arrest. However, few of these devices(i#)can be found in public places.According to a CCTV report, there are 394 AEDs for every 100.000 people in Japan and 317 for every 100,000 residents in the United States. The figure(数字) is just 0.2 when it comes to the Chinese mainland. Inaddition, more people should be taught how to do first aid experts said.According to the National Health Commission, less than 1 percent of Chinese adults know how to performCPR(心肺复苏术). The most they can do during an emergency is call I20. In such situations, the “golden period” for saving someone's life -the first four minutes of a heart attack- is of little use even if first aid equipment is available, said China Daily writer Wang Yiqing.People are encouraged to receive first aid training and learn how to perform first aid in public places, ChinaDaily reported. People should-earn mrst aidt-shile-sa they can help people in need.23.The writer mentioned Godfrey Gao to _________.A. warn famous people that cardiac arrest is deadlyB. point out how dangerous cardiac arrest isC. show us how unhealthy people areD. describe how hard celebrities work24.The new draft in Paragraph 4 suggests that ________.A. more AEDs should be provided in public placesB. equipment should be invented to save more livesC. it is important to teach people how to find AEDsD. more laws are needed to save people from cardiac arrest25. The National Health Commission points out that _________.a. first aid equipment in China is much cheaper than that in the USb. more people in China should learn how to perform CPRc. the first four minutes of a heart attack are the best time to do first aidd. EDs are of little use if people don' t know how to do CPRA. abcB. bcdC. acdD. abd26. What's the writer s purpose of writing this passage?A. To ask us to help people who have heart attack.B. To tell us to learn first aid to help people in needC. To make us save more people if we canD. To tell us to know how to perform CPR correctly四、单词拼写根据下列句子及所给单词的首字母,写出各个单词的完全形式(每空限填一词)1. A j________is a person who decides who will be the winner of a competition.2.You say'I beg your p________?'when you want someone to repeat what they have just said because you have not heard or understood it.3.I prefer the subject g_________which is the study of the countries of the world and of such things as the land, seas, climate, towns, and population.4. We will visit my c________ house every summer who is the child of my uncle and has a very big farm in Hangzhou.5. Yesterday was an important day but unfortunately I was a________from school because of illness.6.If I were ill, I would choose Chinese traditional m_________. Although it tastes bitter, it is less harmful to us. Western one can be bad for our health, you may develop another problem.7.The first three m_______of the year 2002were the warmest globally since records began in 1860 and probably the warmest in 1,000 years, according to a new study by British scientists.8.City Park is not far away from here. It’s only ten m________ walk. You can’t miss it.9.Next week is my grandpa’s n________ birthday, we’re havinga big party.10. “I didn't lose the gold. I won the silver.”Edward said p_______ to his teacher with a big smile on his face.11.Sammy hates waiting in long lines. I think he’s just not very p__________.12.Jenny is a__________in class. She often answers and asks questions13.He gets all his k___________about politics from watching the television.14.He is very h___________. He always tells funny stories to make people laugh.plete the sentences with the c__________forms of the verbs in the box.16.Baby pandas usually very tiny. An adult pandas w__________many times more than a baby panda.17.They all had a great time yesterday, i___________Sam, though he is a quiet and shy boy.18.Many people like Zhong Wei r___________with great interest how their hometowns have changed.19.The tea art p___________show how to make a perfect cup of tea with beautiful tea sets.20. It is almost 23 years since Hong Kong r__________to China in 1997.语法填空:1.of; depending;2.underground’s;3.simplest;4.surely;5.with;6.because; unexpectedly; to hear;7.excitement;8.Although;9.which/that; 10.safer; 11.from; be hurt; 12.an; 13.Thanking; 14.their; have done; ing; 16.unless; 17.it;1.are written;2.achievements;3.Since;4.from;5.carefully;6.takes;7.to decide;rmation;9.better; 10.an;完形填空:CABCBD BCBCC AACCCB阅读理解:BABB单词拼写:1.judge; 2.pardon; 3.geography; 4.cousin’s; 5.absent; 6.medicine; 7.months; 8.minutes’; 9.ninetieth; 10.proudly;11.patient; 12.active; 13.knowledge; 14.humorous; 15.correct; 16.weighs; 17.including; 18.regard; 19.performance;20.returned;。
浙江省2020年中考冲刺测试卷数学
浙江省2020年中考冲刺测试卷数学一、选择题〔此题共10个小题,每题3分,总分值30分.每题只有一个正确答案〕 1.2-的倒数为〔 〕 A .2-B .2C .12D .12-2.以下讲法正确的选项是〔 〕A .9的平方根是3. B.将点(23)--,向右平移5个单位长度到点(22)-, C .38是无理数D .点(23)--,关于x 轴的对称点是(23)-,3、〝神舟七号〞宇航员翟志刚把足迹留在了茫茫太空,令国人深感自豪,他身穿的舱外航天服造价3000万元,用科学记数法表示3000万元为〔 〕元A 、3×103B 、0.3×108C 、3×107D 、3×1084抛物线2)8(2+--=x y 的顶点坐标是〔 〕A 、〔2,8〕B 、〔8,2〕C 、〔—8,2〕D 、〔—8,—2〕5、如图1是由六个边长为1个单位的小正方体搭成的几何体。
小立方体A 沿着它所在的水平线上以每秒1个单位移动,在它的移动过程中,不改变几何体的〔 〕A 、主视图B 、俯视图C 、左视图D 、三种视图6、如图2直角三角形纸片ABC 的两直角边BC =6,AC =8,沿DE 折叠使点A 与B 重合,那么tan ∠CBE 的值是〔 〕 A 、247 B 、 73 C 、724 D 、137、如图3,扇形OAB 是圆锥的侧面展开图,假设小正方形方格的边长均为1厘米,那么那个圆锥的底面半径为〔 〕厘米. A .21B .22 C .2 D .228.某函数的图象关于直线x=1对称,其中一部分图象如图,点A(x 1,y 1),B(x 2,y 2)在函数图象上,且-2<x 1<x 2<-1,那么y 1与y 2的大小关系为( ) A. y 1>y 2 B. y 1<y 2 C.y 1=y 2 D. 无法确定9. 甲、乙两名同学在一次用频率去估量概率的实验中统计了某一结果显现的频率,绘出的统计图如下图,那么符合这一结果的实验可能是〔 〕A .掷一枚正六面体的骰子,显现4点的概率B .从一个装有4个白球和2个红球的袋子中任取一球,取到红球C .抛一枚硬币,显现反面的概率D .任意写一个整数,它能被2整除的概率 10、二次函数c bx ax y ++=2 的图象大致如图,在b a bc +2,,30%40% 20% 10% 频率图1A图2图3y222222)(,,)(c b a a b b c a -+--+中,值为正数的有( )A.1B.2C.3D.4 二、填空题〔此题共6个小题,每题4分,总分值24分〕. 11、要使2a 为有理数,请写出一个符合条件的实数a :___________12、在函数15-=x y 中,自变量x 的取值范畴是_____________________ 13、依据图中信息,可得出x ﹤14x的解是 .14、校园内有一个半径为4米的圆形草坪,一些学生为走〝捷径〞,在草坪内走出了一条小路AB ,如下图∠AOB =120°,这些学生踩坏了花草,而仅仅为了少走___________步〔假设2步为1米,结果保留整数〕. 15、如图,平行四边形ABCD 中,E 是边BC 上的点,AE 交BD 于点F ,假如E 是BC 的中点,那么△BEF 与平行四边形ABCD 的面积之比是16、如图,将半径为1、圆心角为︒60的扇形纸片AOB ,在x 轴正半轴上向右作无滑动的连续滚动,点A 依次落在A 1,A 2,A 3,…的位置,那么A 2018的横坐标为__________三、解答题〔此题有8小题,第17~19题每题6分,第20、21题每题8分,第22、23题10分,第24题12分,共66分〕17.〔此题6分〕 (1)22)12(45sin 301-+-+︒-- 〔2〕解不等式组⎪⎩⎪⎨⎧+≥+<+4134)2(3x x x x 18.(此题6分)如图过正方形ABCD 的顶点D 作直线a ,过A 、C 分不作a 的垂线,垂足分不为BA︒60第16题图第13题第14题A 2B 1B 3O 3A 3OE第15题AFB(O 2) A 1 O 1xyBAO4 120DFG EPO AB C点E 、F .①求证:△AED ≌△DFC②假设AE =2,CF =1,正方形ABCD 的周长是 .19(此题6分)在元旦联欢会上,有一个开盒有奖的游戏,取三只外观一样的盒子,一只内有奖品,另两只空盒子,游戏规那么为:每次游戏时混合后拿出这三只盒子,参加游戏的同学随机打开其中一只,假设有奖品,就获得该奖品,假设是空盒子,就表演一个节目.〔1〕一个人参加游戏,获奖的概率是______,〔2〕两个人参加游戏,两个人都表演节目的概率是多少?并用树状图或列表验证你的结果.20、(此题8分)如图,方格纸中的每个小方格差不多上边长为1个单位的正方形,在建立平面直角坐标系后,△ABC 的顶点均在格点上,点B 的坐标为〔1,0 ①画出△ABC 关于x 轴对称的△A 1B 1C 1,②画出将△ABC 绕原点O 按逆时针旋转90°所得的△A 2B 2C 2,③△A 1B 1C 1与△A 2B 2C 2成轴对称图形吗?假设成轴对称图形,画出所有的对称轴;21.〔8分〕为了降低能源消耗,减少环境污染,国务院办公厅下发了〝关于限制生产销售使用塑料购物袋的通知〞〔简称〝限塑令〞〕,并从2008年6月1日起正式实施.小宇同学为了了解〝限塑令〞后使用购物袋的情形,6月8日到某集贸市场对部分购物者进行了调查,据了解该市场按塑料购物袋的承重能力提供了0.1元,0.2元,0.3元三种质量不同的塑料袋.下面两幅图是这次调查得到的不完整的统计图〔假设每人每次只使用一个购物袋〕,请你依照图中的信息,回答以下咨询题:〔1〕这次调查的购物者总人数是 ▲ ;〔2〕请补全条形统计图,并讲明扇形统计图中0.2元部分所对应的圆心角是 ▲ 度.0.3元部分所对应的圆心角是 ▲ 度;〔3〕假设6月8日到该市场购物的人数有3000人次〔假设每人每次只使用一个购物袋〕,请估量该市场销售塑料购物袋的个数及金额.22 〔此题总分值10分〕〝假日旅乐园〞中一种新型水上滑梯如图,其中线段PA 表示距离水面〔x 轴〕高度为5m 的平台〔点P 在y 轴上〕。
2020年浙江杭州市中考数学冲刺模拟试卷
2020年浙江杭州市中考数学冲刺模拟试卷一、选择题:本大题共10个小题,每小题4分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的.1.抛物线y=﹣2(x﹣3)2+5的顶点坐标是()A.(3,﹣5)B.(﹣3,5)C.(3,5)D.(﹣3,﹣5)2.在Rt△ABC中,∠C=90°,sin A=,BC=6,则AB=()A.4 B.6 C.8 D.103.将抛物线y=x2﹣2x+3向上平移2个单位长度,再向右平移3个单位长度后,得到的抛物线的解析式为()A.y=(x﹣1)2+4 B.y=(x﹣4)2+4 C.y=(x+2)2+6 D.y=(x﹣4)2+6 4.关于反比例函数y=﹣,下列说法正确的是()A.图象过(1,2)点B.图象在第一、三象限C.当x>0时,y随x的增大而减小D.当x<0时,y随x的增大而增大5.已知抛物线y=ax2+bx+c(a<0)过A(﹣2,0)、B(0,0)、C(﹣3,y1)、D(3,y)四点,则y1与y2的大小关系是()2A.y1>y2B.y1=y2C.y1<y2D.不能确定6.如图,△ABC中,D为BC中点,E为AD的中点,BE的延长线交AC于F,则为()A.1:5 B.1:4 C.1:3 D.1:27.一次函数y=ax+b和反比例函数y=在同一个平面直角坐标系中的图象如图所示,则二次函数y=ax2+bx+c的图象可能是()A.B.C.D.8.已知二次函数y=ax2+bx+c(a≠0)的图象如图所示,并且关于x的一元二次方程ax2+bx+c ﹣m=0有两个不相等的实数根,下列结论:①b2﹣4ac<0;②abc>0;③a﹣b+c<0;④m>﹣2,其中,正确的个数有()A.1 B.2 C.3 D.49.如图,在等腰Rt△ABC中,∠C=90°,AC=6,D是AC上一点,若tan∠DBA=,则AD的长为()A.2 B.C.D.110.如图,正方形ABCD的边长为2cm,动点P,Q同时从点A出发,在正方形的边上,分别按A→D→C,A→B→C的方向,都以1cm/s的速度运动,到达点C运动终止,连接PQ,设运动时间为xs,△APQ的面积为ycm2,则下列图象中能大致表示y与x的函数关系的是()A.B.C.D.二、填空题(本大题共4小题,每题5分,满分20分,将答案填在答题纸上)11.若,则=.12.如图所示,点A是反比例函数y=(x<0)的图象上一点,过点A作AB⊥y轴于点B,点P在x轴上,若△ABP的面积是2,则k=.13.将一副三角尺如图所示叠放在一起,则的值是.14.如图,平面直角坐标系中,矩形ABOC的边BO,CO分别在x轴,y轴上,A点的坐标为(﹣8,6),点P在矩形ABOC的内部,点E在BO边上,满足△PBE∽△CBO,当△APC是等腰三角形时,P点坐标为.三、解答题:本大题共2小题,每小题8分,满分16分.15.计算:.16.如图,在平面直角坐标系中,△ABC的三个顶点坐标分别为A(2,1),B(1,4),C(3,2).请解答下列问题:(1)画出△ABC关于y轴对称的图形△A1B1C1,并直接写出C1点的坐标;(2)以原点O为位似中心,位似比为1:2,在y轴的右侧,画出△ABC放大后的图形△A2B2C2,并直接写出C2点的坐标;(3)如果点D(a,b)在线段BC上,请直接写出经过(2)的变化后对应点D2的坐标.四、解答题:本大题共2小题,每小题8分,满分16分.17.如图,一次函数y=kx+b与反比例函数的图象交于A(m,6),B(3,n)两点.(1)求一次函数的解析式;(2)根据图象直接写出的x的取值范围;(3)求△AOB的面积.18.如图,在锐角三角形ABC中,点D、E分别在边AC、AB上,AG⊥BC 于点G,AF⊥DE于点F,∠EAF=∠GAC.(1)求证:△ADE∽△ABC;(2)若AD=BE=4,AE=3,求CD的值.五、解答题:本大题共2小题,每小题10分,满分20分.19.为加快城乡对接,建设全域美丽乡村,某地区对A、B两地间的公路进行改建.如图,A、B两地之间有一座山,汽车原来从A地到B地需途经C地沿折线ACB行驶,现开通隧道后,汽车可直接沿直线AB行驶.已知BC=80千米,∠A=45°,∠B=30°.(1)开通隧道前,汽车从A地到B地大约要走多少千米?(2)开通隧道后,汽车从A地到B地大约可以少走多少千米?(结果精确到0.1千米)(参考数据:≈1.41,≈1.73)20.通过学习锐角三角比,我们知道在直角三角形中,一个锐角的大小与两条边长的比值是一一对应的,因此,两条边长的比值与角的大小之间可以相互转化.类似的,可以在等腰三角形中建立边角之间的联系.我们定义:等腰三角形中底边与腰的比叫做底角的邻对(can),如图(1)在△ABC中,AB=AC,底角B的邻对记作canB,这时canB=,容易知道一个角的大小与这个角的邻对值也是一一对应的.根据上述角的邻对的定义,解下列问题:(1)can30°=;(2)如图(2),已知在△ABC中,AB=AC,canB=,S△ABC=24,求△ABC的周长.六、解答题:本题满分12分.21.如图,已知二次函数y=﹣x2+bx+c的图象经过A(﹣2,﹣1),B(0,7)两点.(1)求该抛物线的解析式及对称轴;(2)当x为何值时,y>0?(3)在x轴上方作平行于x轴的直线l,与抛物线交于C,D两点(点C在对称轴的左侧),过点C,D作x轴的垂线,垂足分别为F,E.当矩形CDEF为正方形时,求C点的坐标.七、解答题:本题满分12分.22.草莓是云南多地盛产的一种水果,今年某水果销售店在草莓销售旺季,试销售成本为每千克20元的草莓,规定试销期间销售单价不低于成本单价,也不高于每千克40元,经试销发现,销售量y(千克)与销售单价x(元)符合一次函数关系,如图是y与x的函数关系图象.(1)求y与x的函数解析式(也称关系式);(2)设该水果销售店试销草莓获得的利润为W元,求W的最大值.八、解答题:本题满分14分.23.如图,在Rt△ABC中,∠ACB=90°,AC=5cm,∠BAC=60°,动点M从点B出发,在BA边上以每秒2cm的速度向点A匀速运动,同时动点N从点C出发,在CB边上以每秒cm的速度向点B匀速运动,设运动时间为t秒(0≤t≤5),连接MN.(1)若BM=BN,求t的值;(2)若△MBN与△ABC相似,求t的值;(3)当t为何值时,四边形ACNM的面积最小?并求出最小值.2020年中考数学模试卷参考答案与试题解析一、选择题:本大题共10个小题,每小题4分,共40分.在每小题给出的四个选项中,只有一项是符合题目要求的.1.抛物线y=﹣2(x﹣3)2+5的顶点坐标是()A.(3,﹣5)B.(﹣3,5)C.(3,5)D.(﹣3,﹣5)【解答】解:∵抛物线的解析式为y=﹣2(x﹣3)2+5,∴抛物线的顶点坐标为(3,5).故选:C.2.在Rt△ABC中,∠C=90°,sin A=,BC=6,则AB=()A.4 B.6 C.8 D.10【解答】解:在Rt△ABC中,∠C=90°,sin A==,BC=6,∴AB===10,故选:D.3.将抛物线y=x2﹣2x+3向上平移2个单位长度,再向右平移3个单位长度后,得到的抛物线的解析式为()A.y=(x﹣1)2+4 B.y=(x﹣4)2+4 C.y=(x+2)2+6 D.y=(x﹣4)2+6 【解答】解:将y=x2﹣2x+3化为顶点式,得y=(x﹣1)2+2.将抛物线y=x2﹣2x+3向上平移2个单位长度,再向右平移3个单位长度后,得到的抛物线的解析式为y=(x﹣4)2+4,故选:B.4.关于反比例函数y=﹣,下列说法正确的是()A.图象过(1,2)点B.图象在第一、三象限C.当x>0时,y随x的增大而减小D.当x<0时,y随x的增大而增大【解答】解:∵k=﹣2<0,所以函数图象位于二四象限,在每一象限内y随x的增大而增大,图象是轴对称图象,故A、B、C错误.故选:D.5.已知抛物线y=ax2+bx+c(a<0)过A(﹣2,0)、B(0,0)、C(﹣3,y1)、D(3,y)四点,则y1与y2的大小关系是()2A.y1>y2B.y1=y2C.y1<y2D.不能确定【解答】解:∵抛物线过A(﹣2,0)、O(0,0)两点,∴抛物线的对称轴为x==﹣1,∵a<0,抛物线开口向下,离对称轴越远,函数值越小,比较可知C点离对称轴远,对应的纵坐标值小,即y1>y2,故选A.6.如图,△ABC中,D为BC中点,E为AD的中点,BE的延长线交AC于F,则为()A.1:5 B.1:4 C.1:3 D.1:2【解答】解:过D作BF的平行线,交AC边于G,如下图所示:∵D为BC中点,DG∥BF∴∠CGD=∠CFB又∵∠C=∠C∴△CDG∽△CBF∴==,即:CG=CF=FG又E为AD的中点,BE的延长线交AC于F,DG∥BF同理可得:△AEF∽△ADG∴==,即:AF=AG=FG∴AF=FG=GC∴===1:2故选:D.7.一次函数y=ax+b和反比例函数y=在同一个平面直角坐标系中的图象如图所示,则二次函数y=ax2+bx+c的图象可能是()A.B.C.D.【解答】解:观察函数图象可知:a<0,b>0,c<0,∴二次函数y=ax2+bx+c的图象开口向下,对称轴x=﹣>0,与y轴的交点在y轴负半轴.故选:A.8.已知二次函数y=ax2+bx+c(a≠0)的图象如图所示,并且关于x的一元二次方程ax2+bx+c ﹣m=0有两个不相等的实数根,下列结论:①b2﹣4ac<0;②abc>0;③a﹣b+c<0;④m>﹣2,其中,正确的个数有()A.1 B.2 C.3 D.4【解答】解:如图所示:图象与x轴有两个交点,则b2﹣4ac>0,故①错误;∵图象开口向上,∴a>0,∵对称轴在y轴右侧,∴a,b异号,∴b<0,∵图象与y轴交于x轴下方,∴c<0,∴abc>0,故②正确;当x=﹣1时,a﹣b+c>0,故此选项错误;∵二次函数y=ax2+bx+c的顶点坐标纵坐标为:﹣2,故二次函数y=ax2+bx+c向上平移小于2个单位,则平移后解析式y=ax2+bx+c﹣m与x 轴有两个交点,此时关于x的一元二次方程ax2+bx+c﹣m=0有两个不相等的实数根,故﹣m<2,解得:m>﹣2,故④正确.故选:B.9.如图,在等腰Rt△ABC中,∠C=90°,AC=6,D是AC上一点,若tan∠DBA=,则AD的长为()A.2 B.C.D.1【解答】解:作DE⊥AB于E,如图,∵∠C=90°,AC=BC=6,∴△ACB为等腰直角三角形,AB=AC=6,∴∠A=45°,在Rt△ADE中,设AE=x,则DE=x,AD=x,在Rt△BED中,tan∠DBE==,∴BE=5x,∴x+5x=6,解得x=,∴AD=×=2.故选:A.10.如图,正方形ABCD的边长为2cm,动点P,Q同时从点A出发,在正方形的边上,分别按A→D→C,A→B→C的方向,都以1cm/s的速度运动,到达点C运动终止,连接PQ,设运动时间为xs,△APQ的面积为ycm2,则下列图象中能大致表示y与x的函数关系的是()A.B.C.D.【解答】解:①当0≤x≤2时,∵正方形的边长为2cm,∴y=S△APQ=AQ•AP=x2;②当2≤x≤4时,y=S△APQ=S正方形ABCD﹣S△CP′Q′﹣S△ABQ′﹣S△AP′D,=2×2﹣(4﹣x)2﹣×2×(x﹣2)﹣×2×(x﹣2)=﹣x2+2x所以,y与x之间的函数关系可以用两段二次函数图象表示,纵观各选项,只有A选项图象符合.故选:A.二、填空题(本大题共4小题,每题5分,满分20分,将答案填在答题纸上)11.若,则=.【解答】解:∵,∴==,12.如图所示,点A是反比例函数y=(x<0)的图象上一点,过点A作AB⊥y轴于点B,点P在x轴上,若△ABP的面积是2,则k=﹣4 .【解答】解:设反比例函数的解析式为y=.∵△AOB的面积=△ABP的面积=2,△AOB的面积=|k|,∴|k|=2,∴k=±4;又∵反比例函数的图象的一支位于第二象限,∴k<0.∴k=﹣4.故答案为:﹣4.13.将一副三角尺如图所示叠放在一起,则的值是.【解答】解:设AC=BC=x,则CD===x,∵∠BAC=∠ACD=90°,∴∠BAC+∠ACD=180°,∴AB∥CD,∴△ABE∽△DCE,∴===,故答案为:14.如图,平面直角坐标系中,矩形ABOC的边BO,CO分别在x轴,y轴上,A点的坐标为(﹣8,6),点P在矩形ABOC的内部,点E在BO边上,满足△PBE∽△CBO,当△APC是等腰三角形时,P点坐标为(﹣,)或(﹣4,3).【解答】解:∵点P在矩形ABOC的内部,且△APC是等腰三角形,∴P点在AC的垂直平分线上或在以点C为圆心AC为半径的圆弧上;①当P点在AC的垂直平分线上时,点P同时在BC上,AC的垂直平分线与BO的交点即是E,如图1所示:∵PE⊥BO,CO⊥BO,∴PE∥CO,∴△PBE∽△CBO,∵四边形ABOC是矩形,A点的坐标为(﹣8,6),∴点P横坐标为﹣4,OC=6,BO=8,BE=4,∵△PBE∽△CBO,∴=,即=,解得:PE=3,∴点P(﹣4,3);②P点在以点C为圆心AC为半径的圆弧上,圆弧与BC的交点为P,过点P作PE⊥BO于E,如图2所示:∵CO⊥BO,∴PE∥CO,∴△PBE∽△CBO,∵四边形ABOC是矩形,A点的坐标为(﹣8,6),∴AC=BO=8,CP=8,AB=OC=6,∴BC===10,∴BP=2,∵△PBE∽△CBO,∴==,即:==,解得:PE=,BE=,∴OE=8﹣=,∴点P(﹣,);综上所述:点P的坐标为:(﹣,)或(﹣4,3);故答案为:(﹣,)或(﹣4,3).三、解答题:本大题共2小题,每小题8分,满分16分. 15.计算:.【解答】解:=3+2×﹣3+1﹣1=3+1﹣3+1=2.16.如图,在平面直角坐标系中,△ABC的三个顶点坐标分别为A(2,1),B(1,4),C(3,2).请解答下列问题:(1)画出△ABC关于y轴对称的图形△A1B1C1,并直接写出C1点的坐标;(2)以原点O为位似中心,位似比为1:2,在y轴的右侧,画出△ABC放大后的图形△A2B2C2,并直接写出C2点的坐标;(3)如果点D(a,b)在线段BC上,请直接写出经过(2)的变化后对应点D2的坐标.【解答】解:(1)如图所示,△A1B1C1即为所求,C1(﹣3,2);(2)如图所示,△A2B2C2即为所求,C2(6,4);(3)∵原点O为位似中心,位似比为1:2,∴点D(a,b)的对应点D2的坐标为(2a,2b).四、解答题:本大题共2小题,每小题8分,满分16分.17.如图,一次函数y=kx+b与反比例函数的图象交于A(m,6),B(3,n)两点.(1)求一次函数的解析式;(2)根据图象直接写出的x的取值范围;(3)求△AOB的面积.【解答】解:(1)分别把A(m,6),B(3,n)代入得6m=6,3n=6,解得m=1,n=2,所以A点坐标为(1,6),B点坐标为(3,2),分别把A(1,6),B(3,2)代入y=kx+b得,解得,所以一次函数解析式为y=﹣2x+8;(2)当0<x<1或x>3时,;(3)如图,当x=0时,y=﹣2x+8=8,则C点坐标为(0,8),当y=0时,﹣2x+8=0,解得x=4,则D点坐标为(4,0),所以S△AOB=S△COD﹣S△COA﹣S△BOD=×4×8﹣×8×1﹣×4×2=8.18.如图,在锐角三角形ABC中,点D、E分别在边AC、AB上,AG⊥BC 于点G,AF⊥DE于点F,∠EAF=∠GAC.(1)求证:△ADE∽△ABC;(2)若AD=BE=4,AE=3,求CD的值.【解答】(1)证明:AG⊥BC,AF⊥DE,∴∠AFE=∠AGC=90°,∴∠AEF+∠EAF=90°,∠GAC+∠ACG=90°,∵∠EAF=∠GAC,∴∠AEF=∠ACG,∵∠EAD=∠CAB,∴△ADE∽△ABC;(2)解:∵△ADE∽△ABC,∴=,∵AD=BE=4,AE=3,∴AB=BE+AE=4+3=7,∴=,解得:AC=,∴CD=AC﹣AD=﹣4=.五、解答题:本大题共2小题,每小题10分,满分20分.19.为加快城乡对接,建设全域美丽乡村,某地区对A、B两地间的公路进行改建.如图,A、B两地之间有一座山,汽车原来从A地到B地需途经C地沿折线ACB行驶,现开通隧道后,汽车可直接沿直线AB行驶.已知BC=80千米,∠A=45°,∠B=30°.(1)开通隧道前,汽车从A地到B地大约要走多少千米?(2)开通隧道后,汽车从A地到B地大约可以少走多少千米?(结果精确到0.1千米)(参考数据:≈1.41,≈1.73)【解答】解:(1)过点C作AB的垂线CD,垂足为D,∵AB⊥CD,sin30°=,BC=80千米,∴CD=BC•sin30°=80×(千米),AC=(千米),AC+BC=80+40(千米),答:开通隧道前,汽车从A地到B地要走80+40千米;(2)∵cos30°=,BC=80(千米),∴BD=BC•cos30°=80×(千米),∵tan45°=,CD=40(千米),∴AD=(千米),∴AB=AD+BD=40+40≈40+40×1.73=109.2(千米),∴汽车从A地到B地比原来少走多少路程为:AC+BC﹣AB=136.4﹣109.2=27.2(千米).答:汽车从A地到B地比原来少走的路程为27.2千米.20.通过学习锐角三角比,我们知道在直角三角形中,一个锐角的大小与两条边长的比值是一一对应的,因此,两条边长的比值与角的大小之间可以相互转化.类似的,可以在等腰三角形中建立边角之间的联系.我们定义:等腰三角形中底边与腰的比叫做底角的邻对(can),如图(1)在△ABC中,AB=AC,底角B的邻对记作canB,这时canB=,容易知道一个角的大小与这个角的邻对值也是一一对应的.根据上述角的邻对的定义,解下列问题:(1)can30°=;(2)如图(2),已知在△ABC中,AB=AC,canB=,S△ABC=24,求△ABC的周长.【解答】解:(1)过点A作AD⊥BC于点D,∵∠B=30°,∴cos∠B==,∴BD=AB,∵△ABC是等腰三角形,∴BC=2BD=AB,故can30°==;(2)过点A作AE⊥BC于点E,∵canB=,则可设BC=8x,AB=5x,∴AE==3x,∵S△ABC=24,∴BC×AE=12x2=24,解得:x=,故AB=AC=5,BC=8,从而可得△ABC的周长为18.六、解答题:本题满分12分.21.如图,已知二次函数y=﹣x2+bx+c的图象经过A(﹣2,﹣1),B(0,7)两点.(1)求该抛物线的解析式及对称轴;(2)当x为何值时,y>0?(3)在x轴上方作平行于x轴的直线l,与抛物线交于C,D两点(点C在对称轴的左侧),过点C,D作x轴的垂线,垂足分别为F,E.当矩形CDEF为正方形时,求C点的坐标.【解答】解:(1)∵二次函数y=﹣x2+bx+c的图象经过A(﹣2,﹣1),B(0,7)两点.∴,解得:,∴y=﹣x2+2x+7,=﹣(x2﹣2x)+7,=﹣[(x2﹣2x+1)﹣1]+7,=﹣(x﹣1)2+8,∴对称轴为:直线x=1.(2)当y=0,0=﹣(x﹣1)2+8,∴x﹣1=±2,x=1+2,x2=1﹣2,1∴抛物线与x轴交点坐标为:(1﹣2,0),(1+2,0),∴当1﹣2<x<1+2时,y>0;(3)当矩形CDEF为正方形时,假设C点坐标为(x,﹣x2+2x+7),∴D点坐标为(﹣x2+2x+7+x,﹣x2+2x+7),即:(﹣x2+3x+7,﹣x2+2x+7),∵对称轴为:直线x=1,D到对称轴距离等于C到对称轴距离相等,∴﹣x2+3x+7﹣1=﹣x+1,解得:x1=﹣1,x2=5(不合题意舍去),x=﹣1时,﹣x2+2x+7=4,∴C点坐标为:(﹣1,4).七、解答题:本题满分12分.22.草莓是云南多地盛产的一种水果,今年某水果销售店在草莓销售旺季,试销售成本为每千克20元的草莓,规定试销期间销售单价不低于成本单价,也不高于每千克40元,经试销发现,销售量y(千克)与销售单价x(元)符合一次函数关系,如图是y与x的函数关系图象.(1)求y与x的函数解析式(也称关系式);(2)设该水果销售店试销草莓获得的利润为W元,求W的最大值.【解答】解:(1)设y与x的函数关系式为y=kx+b,根据题意,得:,解得:,∴y与x的函数解析式为y=﹣2x+340,(20≤x≤40).(2)由已知得:W=(x﹣20)(﹣2x+340)=﹣2x2+380x﹣6800=﹣2(x﹣95)2+11250,∵﹣2<0,∴当x≤95时,W随x的增大而增大,∵20≤x≤40,∴当x=40时,W最大,最大值为﹣2(40﹣95)2+11250=5200元.八、解答题:本题满分14分.23.如图,在Rt△ABC中,∠ACB=90°,AC=5cm,∠BAC=60°,动点M从点B出发,在BA边上以每秒2cm的速度向点A匀速运动,同时动点N从点C出发,在CB边上以每秒cm的速度向点B匀速运动,设运动时间为t秒(0≤t≤5),连接MN.(1)若BM=BN,求t的值;(2)若△MBN与△ABC相似,求t的值;(3)当t为何值时,四边形ACNM的面积最小?并求出最小值.【解答】解:(1)∵在Rt△ABC中,∠ACB=90°,AC=5,∠BAC=60°,∴∠B=30°,∴AB=2AC=10,.由题意知:BM=2t,,∴,∵BM=BN,∴,解得:.(2)分两种情况:①当△MBN∽△ABC时,则,即,解得:.②当△NBM∽△ABC时,则,即,解得:.综上所述:当或时,△MBN与△ABC相似.(3)过M作MD⊥BC于点D,则MD∥AC,∴△BMD∽△BAC,∴,即,解得:MD=t.设四边形ACNM的面积为y,∴y===.∴根据二次函数的性质可知,当时,y的值最小.此时,.。
浙江省2020届中考语文冲刺第二次模拟考试(含答案)
浙江省2020届中考冲刺第二次模拟考试语文注意事项:1.本试卷共8页,总分120分,考试时间120分钟。
2.答卷前将密封线左侧的项目填写清楚。
3.答案须用黑色字迹的钢笔、签字笔或圆珠笔书写。
一、积累(20分)阅读下面的文字,完成1—3题。
◆《醉翁亭记》中欧阳修所描绘的是一个犹如世外桃源般的世界,春夏花朵娉.()婷而立,秋冬流水风霜高洁,四时各有其美。
向四周□(tiào)望,也许还能看到山中无人豢.()养却四肢矫健的飞禽走兽。
除了美景,在文中欧阳修也写下了字字□(zhēn)言:“醉翁之意不在酒,在乎山水之间也。
”或许只有如此心无旁□(wù)之人,才能创作出流传千古的佳作。
◆登亭台楼阁,观湖光山色,游目骋怀,纵情山水,可以让人感受自然之关,领略历史文化的底蕴。
古人往往在山水名胜中寄托自己的政治理想、志趣抱负。
1.根据拼音,在词语空缺处填写汉字。
(3分)(1)□(tiào)望(2)□(zhēn)言(3)心无旁□(wù)2.给下列加点字注音。
(2分)(1)娉.(____)婷而立(2)无人豢.(____)养3.下列对语段中画横线的词语理解不正确的一项是(2分)A.“流传”与“留传”区别在于“流传”既指时间的传承,又指空间的扩散。
而“留传”只指时间的传承。
B.“游目骋怀”在句中是指纵目四望,开阔心胸。
C.句中的“领略”也可换成“领悟”。
D.“抱负”在句中意思为志向、理想、愿望。
4.古诗文名句填空。
(5分)中华诗文,“酒”香四溢,“酒”情斑斓。
陆游蛰居山阴老家,“①,②”,陶醉于农村的丰收年景;范仲淹戍守边疆,“③,④”,浊酒一杯,寄托浓浓的乡愁;辛弃疾借酒消愁,“⑤,梦回吹角连营”,回想往昔,感叹壮志难酬。
5.下列各句中,所引古诗文句不符合语境的一项是(3分)A.对于分隔两地的亲人们来说,“但愿人长久,千里共婵娟”是一种美好的祝愿。
B.窗边的花被不断刮来的风吹得七零八落,空荡荡的房间里不时传来“呼呼”的风声,正应了“山雨欲来风满楼”,想来倾盆大雨也即将到来吧。
2020年浙江省杭州市中考数学模拟冲刺试卷附解析
2020年浙江省杭州市中考数学模拟冲刺试卷 学校:__________ 姓名:__________ 班级:__________ 考号:__________注意事项:1.答题前填写好自己的姓名、班级、考号等信息2.请将答案正确填写在答题卡上一、选择题1.如图,小亮要测量一电线杆 AB 的高度,他站在该电线杆的影子上前后移动,直到他本身影子的顶端正好与电线杆影子的顶端重叠,此时同伴测量出小亮距离电线杆9m ,小亮的影子长 5m ,若小亮的身高为 1.7m ,则电线杆 AB 的高度是( )A .4.7mB .4.76mC .3.6mD .2.9m2.已知函数c bx ax y ++=2的图象如图所示,则下列结论正确的是( )A .a >0,c >0B .a <0,c <0C .a <0,c >0D .a >0,c <03.由表格中信息可知,若使2y ax bx c =++,则下列 y 与x 之间的函数关系式正确的是( ) x- 1 0 1 ax1 ax 2+bx+c8 3 A .43y x x =-+ B .34y x x -=+ C .233y x x =-- D .248y x x =-+4.下面四个语句:①内错角相等;②OC 是∠AOB 的角平分线吗?③两条直线互相垂直,则所成的角等于直角;④π不是有理数.其中是真命题的个数为( )A .1个B .2个C .3个D .4个5.样本容量为140,最大、最小值的差为23,确定组距为4,某小组的频数为42,则组数和这个小组的频率是( )A .6,3B .6,0.3C .6,0.5D .5.5,0.26.下列命题中,是假命题的为 ( )A .任何多边形的外角和都为360°B .若△ABC 中,E ,F 分别在AB ,AC 上,且EF=12BC ,则EF ∥BCC .能单独镶嵌平面的正多边形只有正三角形,正方形,正六边形D .若在△ABC 所在的平面上有一点P ,满足PA=PB=PC ,则点P 是AABC 三边中垂线的交点7.设7的小数部分为b ,那么(4+b )b 的值是( )A .1B .是一个有理数C .3D .无法确定8.某市出租车的收费标准是:起步价 5 元(即行驶距离不超过 3 km 都预付 5 元车费),超过3 km 后,每增加 1km 加收 2 元(不足1km 按1km 计).某人乘出租车从A 地到B 地共付车费 19 元,那么A 地到B 地的路程是( )A .9.5kmB .10 kmC .至多 10 kmD .至少9 km 9.不等式4(2)2(35)x x -≥-的正整数解的个数为( ) A .0个 B .1个C .2 个D .3 个 10.计算:53x x ÷=( ) A .2xB .53x C .8x D .1 11.将x y xy x 332-+-分解因式,下列分组方法不当的是( )A .)3()3(2xy y x x -+-B .)33()(2x y xy x -+-C .y x xy x 3)3(2+--D .)33()(2y x xy x +-+- 12.用代入法解方程组342(1)25(2)x y x y +=⎧⎨-=⎩ ,使得代入后化简比较容易的变形是( ) A .由①得243y x -=B . 由①得234x y -=C . 由②得53y x +=D . 由②得25y x =-13.如果2(1)()23x x a x x -+=+-,那么 a 的值是( )A .3B .-2C .2D .3 14.下列式子中正确的是( ) A .x-(y-z )=x-y-z B .-(x-y+z ) =x-y-zC .x+2y-2z=x-2(y+z )D .-a+c+d-b=-(a+b )+(c+d )15.世纪联华超市出售的三种品牌的大米包装袋(标准质量为 50千克)上,分别标有(50± 0.2),(50±0.3),(50±0.25)的字样. 则从超市中任意拿出两袋大米,其质量与标准质量最多相差( )A . 0.4B .0.55C . 0.5D . 0.6二、填空题16.从1 00张分别写上1~1 00的数字卡片中,随意抽取一张是7的倍数的概率为 .17.当m 取 时,232(3)mm y m x -+=-是二次函数. 18.如果一个角的两边分别与另一个角的两边平行,并且这两个角相差 90°,那么这两个角的度数分别是 .19.某班a 名同学参加植树活动,其中男生b 名(b<a ),若只由男生完成,每人需植树15棵;若只由女生完成,则每人需植树_________棵.20.为了交通方便,在一块长为am ,宽为bm 的长方形稻田内修两条道路,横向道路为矩形,纵向道路为平行四边形,道路的宽均为1m(如图),则余下可耕种土地的面积是_. 21.若方程6=+ny mx 的两个解是⎩⎨⎧==11y x ,⎩⎨⎧-==12y x 则=m ,=n . 22.若m ,n 为实数,且满足2|2|(28)0m n m n +++-+=,则 mn= .23.一 只蜘蛛有 8 条腿,n 只蜘蛛有 条腿.24.如果 -22 元表示亏损 22 元,那么 45 元表示 .三、解答题25.如图,反比例函数y =kx的图象与一次函数y =mx +b 的图象交于A((1,3),B(n ,-1)两点.(1)求反比例函数与一次函数的解析式;(2)根据图象回答:当x 取何值时,反比例函数的值大于一次函数的值.26.某服装商店出售一种优惠购物卡,花 200 元买这种卡后,凭卡可以在这家商店按 8 折购物,什么情况下买卡购物合算?27.填空.已知:AB ∥CD ,(1)如图①,∠B+∠=∠BEC .理由如下:解:过点E 作EF ∥AB ,O y xA B则∠l=∠B( ).∵EF∥AB,AB∥CD( ),∴EF∥CD( ),∴∠2=∠C( ).∵∠BEC=∠l+∠2,∴∠BEC=∠B+∠C( ).(2)图②中,∠B,∠E,∠G,∠F,∠C的数量关系是;(3)图③中,∠B,∠E,∠F,∠G,∠H,∠M,∠C的数量关系是.28.“五·一”期间,某商场搞优惠促销,决定由顾客抽奖确定折扣.某顾客购买甲、乙两种商品,分别抽到七折和九折,共付款386元,这两种商品原销售价之和为500元.这两种商品的原销售价分别是多少元?29.请根据下列数据制作统计表:我国l980年人口总数为98705万人,1985年为l05851万人,1990年为ll4333万人,1995年为121121万人,1999年为l25909万人.30.某体育场的环形跑道长 400米,甲、乙二人在跑道上,练习长跑,甲平均每分钟跑250米,乙平均每分钟跑290米,现在两人同时从同一起跑线同向出发,起跑后经过多长时间两人才能第一次相遇?【参考答案】学校:__________ 姓名:__________ 班级:__________ 考号:__________注意事项:1.答题前填写好自己的姓名、班级、考号等信息2.请将答案正确填写在答题卡上一、选择题1.B2.D3.A4.B5.B6.B7.C8.C9.B10.A11.C12.D13.D14.D15.D二、填空题16.50717.18.135°、45°19.15ba b20.ab-a-b+1 21.4,222.-823.8n24.盈利 45 元三、解答题25.(1)∵A(1,3)在y=kx的图象上,∴k=3,∴y=3x又∵B(n,-1)在y=3x的图象上,∴n=-3,即B (-3,-1)313m b m b =+⎧⎨-=-+⎩,解得:m =1,b =2,∴反比例函数的解析式为y =3x , 一次函数的解析式为y =x +2.(2)从图象上可知,当x<-3或0<x<1时,反比例函数的值大于一次函数的值. 26.超过1000元27.(1)略 (2)∠B+∠G+∠C=∠E+∠F (3)∠B+∠F+∠H+∠C=∠E+∠G+∠M 28.320元和180元.29.略30.设起跑后经过x 分钟两人第一次相遇,则甲跑过的路程是250x 米,乙跑过的路程为290x 米.根据题意,得290250400x x -=,解得10x =.答:起跑后经过10分钟两人第一次相遇.。
〖加21套中考模拟卷〗浙江省杭州市拱墅区重点名校2020年中考冲刺卷英语试题含解析
浙江省杭州市拱墅区重点名校2020年中考冲刺卷英语试题Ⅰ. 单项选择1、—Would you mind my opening the door?—_____. It’s so hot in the classroom.A.Certainly B.Of course not C.Better not2、—I don’t like rainy or windy weather. What about you?—__________. I can’t do any outdoor activit ies.A.Me too B.So do I C.Neither do I D.Nor I do3、I looked down to the river, a silver stream _______ one mile below me.A.lonely B.nearly C.properly D.recently4、Aunt Judy ________ eats out with her friends, about once or twice a week.A.always B.sometimes C.hardly ever D.never5、---I hear you gave your mother a big surprise on Mother’s Day?--- Yes, a big bunch of flowers. I think my mum is always giving she has to me.A.which B.that C.what D.all what6、-Why didn't you cry for help when you were robbed (被抢劫)?-If I opened my mouth, they might find my four gold teeth. That would be ______!A.bad B.much worseC.worst D.the worst7、--- I hear that The Wondering Earth is popular now. I have never watched it. What about you? --- __________, but I am very busy this week. How about seeing it together next week?A.I don’t agree with you B.Me tooC.Me neither D.I’m afraid so8、Spud Webb has influenced me most. His stories give me much to face all kinds of difficulties. A.luck B.wealth C.courage D.decision9、—Summer vacation is coming! Could you tell me ?—Xi’an, I really want to visit the Terracotta Army.A.where are you going B.where you are going C.how you are going10、— Could you please tell me yesterday?— In the bookshop nearby.A.Where you bought the book B.Where you buy the bookC.Where did you buy the book D.Where do you buy the bookⅡ. 完形填空11、阅读下列短文,从每小题所给的A、B、C、D 四个选项中选出最佳选项。
〖加21套中考模拟卷〗浙江省杭州市拱墅区重点名校2020年中考冲刺卷英语试题含解析
浙江省杭州市拱墅区重点名校2020年中考冲刺卷英语试题Ⅰ. 单项选择1、—Would you mind my opening the door?—_____. It’s so hot in the classroom.A.Certainly B.Of course not C.Better not2、—I don’t like rainy or windy weather. What about you?—__________. I can’t do any outdoor activit ies.A.Me too B.So do I C.Neither do I D.Nor I do3、I looked down to the river, a silver stream _______ one mile below me.A.lonely B.nearly C.properly D.recently4、Aunt Judy ________ eats out with her friends, about once or twice a week.A.always B.sometimes C.hardly ever D.never5、---I hear you gave your mother a big surprise on Mother’s Day?--- Yes, a big bunch of flowers. I think my mum is always giving she has to me.A.which B.that C.what D.all what6、-Why didn't you cry for help when you were robbed (被抢劫)?-If I opened my mouth, they might find my four gold teeth. That would be ______!A.bad B.much worseC.worst D.the worst7、--- I hear that The Wondering Earth is popular now. I have never watched it. What about you? --- __________, but I am very busy this week. How about seeing it together next week?A.I don’t agree with you B.Me tooC.Me neither D.I’m afraid so8、Spud Webb has influenced me most. His stories give me much to face all kinds of difficulties. A.luck B.wealth C.courage D.decision9、—Summer vacation is coming! Could you tell me ?—Xi’an, I really want to visit the Terracotta Army.A.where are you going B.where you are going C.how you are going10、— Could you please tell me yesterday?— In the bookshop nearby.A.Where you bought the book B.Where you buy the bookC.Where did you buy the book D.Where do you buy the bookⅡ. 完形填空11、阅读下列短文,从每小题所给的A、B、C、D 四个选项中选出最佳选项。
2020年浙江省杭州市中考三轮复习语法词汇易错题练习
2020年中考三轮复习易错题练习一、语法填空1. My sister Alice and I sat down in front of the fire and wrote a letter to Father Christmas, __________ (tell) him about the presents we wanted.2. When Christmas Eva came, the whole family finished__________(decorate)the house.3. When Christmas Eva came, the whole family helped__________(decorate)the house.4. We tired to keep awake as long as possible to see Father Christmas. __________, the next thing we knew was on Christmas morning.5. This is the time of the Thai New Year. People go on the streets _________(throw) water at each other.6. They wish you could carry along ___________our best wishes and fly with happiness.7. The happiest people enjoy ___________each age gives them without wasting their time in useless regrets.8. ___________a child grows up, he can no longer expect others to pay for his food, clothes, room and many other things.9. And he has to work if he wants to live __________(comfortable).10. On thanksgiving day, about 88 percent of Americans eat turkey. But one_________(luck) turkey not only survives but also becomes famous!11. Benjamin franklin even wanted the turkey, __________of the bald eagle, to be America’s icon(象征).12. Turkeys don’t have ears. They hear ___________a snood(肉垂)above their beaks.13. In Britain, some people say they would do anything if a famous person they loved__________(ask) them to!14. Those who had strong feelings for a famous person were likely to be lonely and __________(worry).15. Worshipping(崇拜) famous people is not____________(necessary) a bad thing.16. How do you enter a room full of strangers? Do you walk right in full of confidence? Or do you try to slip in ___________being noticed?17. Now I’ll tell you some useful ways that help you become a___________(confident) person.二、单词拼写1. The development of the app Wechat can make s___________be friends.2. The old man treats everyone with kindness and warmth, s__________love and joy everywhere he goes.3. Behind gifts and Christmas trees l____________the true meaning of Christmas.4. On Fridays, students e___________to go back home earlier.5. Her parents had been d___________for ten years and she had to live alone.6. N___________, a great number of tall buildings have appeared in the new neighborhood.7. My father has r___________ the World Cup with great interest for many years.8. We have already c___________ out a lot of things from our bedroom for the yard sale.9. We are faced with lots of s___________problems today, such as low pay and unemployment.10. Was it really f___________to this boy to ask him to do all the work?11. I l__________several records to John but he never returned them.12. The hotel p____________tourists with great environment and nice service.13. After all, it is a w____________of time to play computer games.14. He is enjoying all the s_____________of being a father. His daughter is everything to him.15. Joyce c_____________up with a good idea and solved the problem.16. The question was simple. I finished it without any d____________.17. Learn l___________every day and you will learn a lot in a few years.18. Please p___________the apples before you eat them.19. We need a b___________to make the milk shake.20. Without practice, you will n__________be perfect.21. Our head teacher i____________the new classmate Tony to us just now.三、词语填空(根据语义填入恰当的词语,每空限填一词,不限定词性)1. Dad is a l liar, certainly. He never tells the truth about anything__________, or anything that he thinks is bad to me, even though I have told him that I don’t mind __________these things.2. Dad is a miser(吝啬鬼), undoubtedly. I hardly see Dad wear _________clothes.3.It is very important to be polite and friendly to other people, as it makes life more pleasant for everyone. And it’s not d___________to be polite! It makes a big d____________if we just remember to say “could you”, “please”.4. Nowadays, people often feel tired and s__________, and don’t have enough time to do everything that we need to do. We should try to remember to be polite and friendly to others, as it will help us feel happier and less stressed.5. Before Cardona could even ___________her door, the car moved ahead. Cardona jumped into the driver’s seat and reached for the handbrake(手闸). She couldn’t find the brake, and she _______________the car as it moved down...四、改写句子1. Hurry up! The movie has already began.Hurry up! The movie __________ already ___________ ___________ for ten minutes.2. They have become friends.They ___________ ___________friends since they met in Shanghai.3. I have left my hometown. I really miss it!I ___________ ___________ ___________ ___________ for a long time. I really miss it!4. Unluckily, the man we are looking for has died.Unluckily, the man we are looking for ___________ ___________ ___________for a long time.5. The old couple has married.The old couple ___________ ___________ ___________ for 20 years.参考答案一、1.telling; 2.decorating; 3.decorate; 4.However; 5.throwing; 6.with; 7.what; 8.When; fortably; 10.lucky;11.instead; 12.with; 13.asked; 14.worried; 15.necessarily; 16.without; 17.more confident;二、1.strangers; 2.spreading; 3.lies; 4.expect; 5.dead; 6.Nowadays; 7.regarded; 8.cleaned; 9.social; 10.fair; 11.lent;12.provides; 13.waste; 14.satisfaction; 15.came; 16.difficulty; 17.little; 18.peel; 19.blander; 20.never;21.introduced;三、1.bad; hearing; 2.new; 3.difficult; difference; 4.stressed; 5.close; go out of;四、1.has; been on; 2.have been; 3.have been away from; 4.has been dead; 5.has been/got married;。
【中考冲刺】2020年浙江省杭州市下城区中考数学模拟试卷(二)附答案
【点睛】
本题考查了由实际问题抽象出一元一次方程,找准等量关系,正确列出一元一次方程是解题的关键.
7.A
【解析】
【分析】
根据周角的定义求出扇形k的圆心角度数,然后根据各部分圆心角的大小解答即可.
【详解】
扇形k的圆心角度数为:360°﹣60°﹣120°﹣45°=135°.
∵s+t ,选项A正确;
∵∠AOC=90°+∠A=4∠B,∴∠A=30°.
∵OA=OC=4,∴OH OA=2,∴AH= ,∴AB= .
故答案为 .
【点睛】
本题考查了垂径定理,勾股定理,三角形的外角的性质等知识,解题的关键是学会添加常用辅助线,属于中考常考题型.
15. 或 <x<2
【解析】
【分析】
先将M(m,1),N(n,﹣2)代入y2 ,求出m、n的值,再分别求出y1>﹣4,y2<4时x的取值范围,画出函数y1=x﹣1和函数y2 的图象,根据图象找出函数y1=x﹣1在函数y2 图象的下方且y1>﹣4,y2<4时x的取值范围即可.
C.∵△CDO∽△BAO,且没有相等的对应边,∴无法证出△CDO≌△BAO,故选项C错误;
D.∵△AOC与△COD同高,∴ .
∵△CDO∽△BAO,∴ .
∵AD平分∠CAB,∴∠CAD=∠BAD.
∵CD∥AB,∴∠CDA=∠BAD,∴∠CAD=∠CDA,∴AC=CD.
∵AC=BC,∴CD=BC,∴ ,故选项D正确.
【详解】
用科学记数法表示23000为2.3×104.
故选C.
【点睛】
本题考查了科学记数法的表示方法.科学记数法的表示形式为a×10n的形式,其中1≤|a|<10,n为整数,表示时关键要正确确定a的值以及n的值.
2020年浙江省杭州市数学中考基础冲刺训练(含答案)
2020年浙江省杭州市数学中考基础冲刺训练一.选择题(每题3分,满分30分)1.下列计算中结果最小的是()A.1+B.1﹣C.1×D.12.在平面直角坐标系中,点A的坐标为(1,﹣3),则点A关于y轴对称点的坐标是()A.(﹣1,﹣3)B.(﹣3,1)C.(1,3)D.(﹣1,3)3.如图,AB、AC、BD是⊙O的切线,切点分别是P、C、D.若AB=5,AC=3,则BD的长是()A.4 B.3 C.2 D.14.小明早晨上学时,每小时走5千米,中午放学沿原路回家时,每小时走4千米,结果回家所用的时间比上学所用的时间多15分钟,问小明家离学校多远?设小明家离学校有x 千米,那么所列方程是()A.B.C.D.5.测试五位学生的“一分钟跳绳”成绩,得到五个各不相同的数据,在统计时,出现了一处错误:将最高成绩写得更高了,计算结果不受影响的是()A.方差B.标准差C.中位数D.平均数6.如图,△ABC中,∠ABD=∠C,若AB=4,AD=2,则CD边的长是()A.2 B.4 C.6 D.87.如图,在△ABC中,∠ACB=100°,∠A=20°,D是AB上一点,将△ABC沿CD折叠,使B点落在AC边上的B′处,则∠ADB′等于()A.40°B.20°C.55°D.30°8.如图,四个一次函数y=ax,y=bx,y=cx+1,y=dx﹣3的图象如图所示,则a,b,c,d的大小关系是()A.b>a>d>c B.a>b>c>d C.a>b>d>c D.b>a>c>d9.如图,在平地上种植树木时,要求株距(相邻两树间的水平距离)为4m.如果在坡度为1:2的山坡上种树,也要求株距为4m,那么相邻两树间的坡面距离为()A.4m B.2m C.m D.8m10.已知二次函数y=ax2+bx+c(a≠0)图象上部分点的坐标(x,y)的对应值如下表所示:x…0 100 400 …y… 2 ﹣2 2 …则方程ax2+bx+4=0的根是()A.x1=x2=200 B.x1=0,x2=400C.x1=100,x2=300 D.x1=100,x2=500二.填空题(每题4分,满分24分)11.分解因式:9m2﹣n2=.12.某招聘考试成绩由笔试和面试组成,笔试占成绩的60%,面试占成绩的40%.小明笔试成绩为95分,面试成绩为85分,那么小明的最终成绩是.13.如图,粮仓的顶部是圆锥形状,这个圆锥底面圆的半径长为3m,母线长为6m,为防止雨水,需在粮仓顶部铺上油毡,如果油毡的市场价是每平方米10元,那么购买油毡所需要的费用是元(结果保留一位小数).14.在Rt△ABC中,∠ACB=90°,AB=3,BC=1,那么∠A的正弦值是.15.已知一个函数,当x>0时,函数值y随着x的增大而减小,请写出这个函数关系式(写出一个即可).16.如图,矩形ABCD中,点P为AD上一个动点,以PB为对称轴将△APB折叠得到△EPB,点A的对称点为点E,射线BE交矩形ABCD的边于点F,若AB=4,AD=6,当点F为矩形ABCD边的中点时,AP的长为.三.解答题17.(6分)计算:﹣.18.(8分)某家电销售商店1﹣6周销售甲、乙两种品牌冰箱的数量如图所示(单位:台):(1)分别求该商店这段时间内甲、乙两种品牌冰箱周销售量的平均数和方差;(2)根据计算结果及折线统计图,对该商店今后采购这两种品牌冰箱的意向提出建议,并说明理由.19.如图,在△ABC中,AD⊥BC且BD=DE,EF垂直平分AC,交AC于点F,交BC于点E.(1)若∠BAE=32°,求∠C的度数;(2)若AC=6cm,DC=5cm,求△ABC的周长.20.(10分)小明家饮水机中原有水的温度为20°C,通电开机后,饮水机自动开始加热(此过程中水温y(°C)与开机时间x(分)满足一次函数关系),当加热到100℃时自动停止加热,随后水温开始下降[此过程中水温y(°C)与开机时间x(分)成反比例关系,当水温降至20C时,饮水机又自动开始加热…,重复上述程序(如图所示),根据图中提供的信息,解答下列问题:(1)当0≤x≤8时,求水温y(°C)与开机时间x(分)的函数关系式;(2)求图中t的值;(3)若小明上午八点将饮水机在通电开机(此时饮水机中原有水的温度为20°C后即外出散步,预计上午八点半散步回到家中,回到家时,他能喝到饮水机内不低于30°C的水吗?请说明你的理由.21.(10分)(1)正方形ABCD,E、F分别在边BC、CD上(不与端点重合),∠EAF=45°,EF与AC交于点G①如图(i),若AC平分∠EAF,直接写出线段EF,BE,DF之间等量关系;②如图(ⅱ),若AC不平分∠EAF,①中线段EF,BE,DF之间等量关系还成立吗?若成立请证明;若不成立请说明理由(2)如图(ⅲ),矩形ABCD,AB=4,AD=8.点M、N分别在边CD、BC上,AN=2,∠MAN=45°,求AM的长度.参考答案一.选择1.解:A、原式=1,B、原式=,C、原式=,D、原式=3,故选:C.2.解:∵点A的坐标为(1,﹣3),∴点A关于y轴的对称点的坐标是(﹣1,﹣3),故选:A.3.解:∵AC、AP为⊙O的切线,∴AC=AP=3,∵BP、BD为⊙O的切线,∴BP=BD,∴BD=PB=AB﹣AP=5﹣3=2.故选:C.4.解:设小明家离学校有x千米,根据题意,可列方程:+=,即,故选:A.5.解:因为中位数是将数据按照大小顺序重新排列,代表了这组数据值大小的“中点”,不受极端值影响,所以将最高成绩写得更高了,计算结果不受影响的是中位数,故选:C.6.解:∵∠ABD=∠C,∠A=∠A,∴△ABD∽△ACB,∴,AC=AD+DC,∴,∴DC=6.答:DC边的长为6.故选:C.7.解:∵∠A+∠B+∠ACB=180°,∠ACB=100°,∠A=20°,∴∠B=60°,根据翻折不变性可知:∠CB′D=∠B=60°,∵∠DB′C=∠A+∠ADB′,∴60°=20°+∠ADB′,∴∠ADB′=40°,故选:A.8.解:由图象可得:a>0,b>0,c<0,d<0,且a>b,c>d,故选:B.9.解:如图,∵AB的坡度为1:2,∴=,即=,解得,AC=2,由勾股定理得,AB===2(m),故选:B.10.解:由抛物线经过点(0,2)得到c=2,因为抛物线经过点(0,2)、(400,2),所以抛物线的对称轴为直线x=200,而抛物线经过点(100,﹣2),所以抛物线经过点(300,﹣2),所以二次函数解析式为y=ax2+bx+2,方程ax 2+bx +4=0变形为ax 2+bx +2=﹣2,所以方程ax 2+bx +4=0的根理解为函数值为﹣2所对应的自变量的值, 所以方程ax 2+bx +4=0的根为x 1=100,x 2=300. 故选:C . 二.填空11.解:原式=(3m )2﹣n 2=(3m +n )(3m ﹣n ), 故答案为:(3m +n )(3m ﹣n ).12.解:根据题意得:小明的最终成绩是95×60%+85×40%=91(分). 故答案为:91.13.解:根据题意得:π×3×6×10≈565.2(元), 则购买油毡所需要的费用是565.2元, 故答案为:565.214.解:∵∠ACB =90°,AB =3,BC =1, ∴∠A 的正弦值sin A ==,故答案为:.15.解:函数关系式为:y =﹣x +2,y =,y =﹣x 2+1等; 故答案为:y =﹣x +216.解:如图1中,当点F 是AD 的中点时,∵四边形ABCD 是矩形, ∴∠A =90°,AB =6,AF =3, ∴BF ===5,由翻折可知:AB =BE =4,设PA =PE =x ,则PF =3﹣x ,EF =5﹣4=1, 在Rt △PEF 中,∵PE 2+EF 2=PF 2,∴x2+12=(3﹣x)2,∴x=,∴PA=如图2中,当点F是CD的中点时,延长AD交BF的延长线于H.∵∠C=90°,BC=6,CF=DF=2,∴BF==2,∵DH∥BC,∴∠H=∠FBC,∵∠DFH=∠BFC,DF=FC,∴△DHF≌△CBF(AAS),∴DH=BC=6,FH=BF=2,∵AB=BE=4,∴EF=2﹣4,EH=2﹣4+2=4﹣4,设PA=PE=y,则PD=6﹣y,PH=6﹣y+6=12﹣y,在Rt△PEH中,∵PE2+EH2=PH2,∴y2+(4﹣4)2=(12﹣y)2,∴y=,∴PA=,综上所述,PA的长为或.故答案为或.三.解答17.解:原式=+==18.解:(1)甲品牌的销售量分别为7、10、8、10、12、13,则甲品牌冰箱周销售量的平均数为=10(台),方差为×[(7﹣10)2+(10﹣10)2+(8﹣10)2+(10﹣10)2+(12﹣10)2+(13﹣10)2]=(台2),乙品牌的销量分别为9、10、11、9、12、9,则乙品牌冰箱周销售量的平均数为=10(台),方差为×[(9﹣10)2+(10﹣10)2+(11﹣10)2+(9﹣10)2+(12﹣10)2+(9﹣10)2]=(台2);(2)甲、乙两种品牌冰箱周销售量的平均数相同,乙品牌冰箱周销售量的方差较小,说明乙品牌冰箱周销售量比较稳定,可选择采购乙品牌的冰箱;从折线图来看,甲品牌冰箱的月销售量呈上升趋势,进货时也可多进甲品牌冰箱.19.解:(1)∵AD⊥BC,BD=DE,EF垂直平分AC∴AB=AE=EC∴∠C=∠CAE,∵∠BAE=32°∴∠AED=(180°﹣32°)=74°;∴∠C=∠AED=37°;(2)由(1)知:AE=EC=AB,∵BD=DE,∴AB+BD=EC+DE=DC,∴△ABC的周长=AB+BC+AC,=AB+BD+DC+AC,=2DC+AC=2×5+6=16(cm).20.解:(1)当0≤x≤8时,设水温y(℃)与开机时间x(分)的函数关系式为y=kx+b(k≠0),将(0,20)、(8,100)代入y=kx+b中,,解得:,∴当0≤x≤8时,水温y(℃)与开机时间x(分)的函数关系式为y=10x+20.(2)当8≤x≤t时,设水温y(℃)与开机时间x(分)的函数关系式为y=(m≠0),将(8,100)代入y=中,100=,解得:m=800,∴当8≤x≤t时,水温y(℃)与开机时间x(分)的函数关系式为y=.当y==20时,x=40,∴图中t的值为40.(3)当x=30时,.答:小明上午八点半散步回到家中时,不能喝到饮水机内不低于30°C的水.21.解:(1)①如图(i),∵四边形ABCD是正方形,∴∠BAC=∠CAD=45°,∵∠EAF=45°,AC平分∠EAF,∴∠BAE=∠EAG=∠DAF=∠FAG=22.5°,∵AB=AD,∠B=∠D=90°,∴△ABE≌△ADF(ASA),∴BE=DF,AE=AF,∴∠AEF=∠AFE,∴AC⊥EF,∴∠AGE=∠AGF=90°,∵AE平分∠BAC,∴BE=EG,DF=GF,∴EF=BE+DF;②,①中线段EF,BE,DF之间等量关系还成立:EF=BE+DF;如图(ⅱ),延长CD到点H,截取DH=BE,连接AH,在△AEB与△AHD中,∵,∴△AEB≌△AHD(SAS),∴AE=AH,∠BAE=∠HAD,∵∠EAF=45°,∠BAD=90°,∴∠BAE+∠DAF=45°,∴∠DAF+∠DAH=45°.即∠EAF=∠HAF,在△EAF与△HAF中,∵,∴△EAF≌△HAF(SAS),∴EF=HF=DF+DH=BE+DF,(2)解法一:如图,取AD,BC的中点P,Q,连接QP,连接NH,∵AD=8,AB=4,∴AP=AB=BQ=PQ=4,∠B=90°,∴四边形ABQP是正方形,Rt△ABN中,AB=4,AN=2,∴BN==2,∴NQ=4﹣2=2,∵∠NAH=45°,由(1)同理得:NH=BN+PH,设PH=x,则NH=x+2,QH=4﹣x,Rt△NHQ中,NH2=QH2+NQ2,∴(2+x)2=22+(4﹣x)2,x=,∵P是AD的中点,PH∥DM,∴AH=HM,∴DM=2PH=,由勾股定理得:AM===;解法二:如图(iii),延长AN,DC交于点G,过M作MP⊥AG于点P,∵四边形ABCD是矩形,∴∠B=90°,Rt△ABN中,AB=4,AN=2,∴BN=2,CN=8﹣2=6,∵AB∥CG,∴△ABN∽△GCN,∴=,∴NG=6,∵∠MAN=45°,∠APM=90°,∴AP=PM,设AP=x,则PM=2x,PG=2x,∵AG=2+6=x+2x,x=,∴AM=x=.。
2020-2021杭州历年中考数学易错题汇编-平行四边形练习题
2020-2021杭州历年中考数学易错题汇编-平行四边形练习题一、平行四边形1.在图1中,正方形ABCD的边长为a,等腰直角三角形FAE的斜边AE=2b,且边AD和AE在同一直线上.操作示例当2b<a时,如图1,在BA上选取点G,使BG=b,连结FG和CG,裁掉△FAG和△CGB 并分别拼接到△FEH和△CHD的位置构成四边形FGCH.思考发现小明在操作后发现:该剪拼方法就是先将△FAG绕点F逆时针旋转90°到△FEH的位置,易知EH与AD在同一直线上.连结CH,由剪拼方法可得DH=BG,故△CHD≌△CGB,从而又可将△CGB绕点C顺时针旋转90°到△CHD的位置.这样,对于剪拼得到的四边形FGCH (如图1),过点F作FM⊥AE于点M(图略),利用SAS公理可判断△HFM≌△CHD,易得FH=HC=GC=FG,∠FHC=90°.进而根据正方形的判定方法,可以判断出四边形FGCH是正方形.实践探究(1)正方形FGCH的面积是;(用含a, b的式子表示)(2)类比图1的剪拼方法,请你就图2—图4的三种情形分别画出剪拼成一个新正方形的示意图.联想拓展小明通过探究后发现:当b≤a时,此类图形都能剪拼成正方形,且所选取的点G的位置在BA方向上随着b的增大不断上移.当b>a时(如图5),能否剪拼成一个正方形?若能,请你在图5中画出剪拼成的正方形的示意图;若不能,简要说明理由.【答案】(1)a2+b2;(2)见解析;联想拓展:能剪拼成正方形.见解析.【解析】分析:实践探究:根据正方形FGCH的面积=BG2+BC2进而得出答案;应采用类比的方法,注意无论等腰直角三角形的大小如何变化,BG永远等于等腰直角三角形斜边的一半.注意当b=a时,也可直接沿正方形的对角线分割.详解:实践探究:正方形的面积是:BG2+BC2=a2+b2;剪拼方法如图2-图4;联想拓展:能,剪拼方法如图5(图中BG=DH=b)..点睛:本题考查了几何变换综合,培养学生的推理论证能力和动手操作能力;运用类比方法作图时,应根据范例抓住作图的关键:作的线段的长度与某条线段的比值永远相等,旋转的三角形,连接的点都应是相同的.2.已知Rt△ABD中,边AB=OB=1,∠ABO=90°问题探究:(1)以AB为边,在Rt△ABO的右边作正方形ABC,如图(1),则点O与点D的距离为.(2)以AB为边,在Rt△ABO的右边作等边三角形ABC,如图(2),求点O与点C的距离.问题解决:(3)若线段DE=1,线段DE的两个端点D,E分别在射线OA、OB上滑动,以DE为边向外作等边三角形DEF,如图(3),则点O与点F的距离有没有最大值,如果有,求出最大值,如果没有,说明理由.【答案】(1)、5;(2)、622+;(3)、3212++.【解析】【分析】试题分析:(1)、如图1中,连接OD,在Rt△ODC中,根据OD=22OC CD+计算即可.(2)、如图2中,作CE⊥OB于E,CF⊥AB于F,连接OC.在Rt△OCE中,根据OC=22OE CE+计算即可.(3)、如图3中,当OF⊥DE时,OF的值最大,设OF交DE于H,在OH上取一点M,使得OM=DM,连接DM.分别求出MH、OM、FH即可解决问题.【详解】试题解析:(1)、如图1中,连接OD,∵四边形ABCD是正方形,∴AB=BC=CD=AD=1,∠C=90°在Rt△ODC中,∵∠C=90°,OC=2,CD=1,∴OD=2222215OC CD+=+=(2)、如图2中,作CE⊥OB于E,CF⊥AB于F,连接OC.∵∠FBE=∠E=∠CFB=90°,∴四边形BECF是矩形,∴BF=CF=12,3在Rt△OCE中,222231122OE CE⎛⎫⎛⎫+=++⎪ ⎪⎪⎝⎭⎝⎭62+(3)、如图3中,当OF⊥DE时,OF的值最大,设OF交DE于H,在OH上取一点M,使得OM=DM,连接DM.∵FD=FE=DE=1,OF ⊥DE , ∴DH=HE ,OD=OE ,∠DOH=12∠DOE=22.5°, ∵OM=DM , ∴∠MOD=∠MDO=22.5°, ∴∠DMH=∠MDH=45°, ∴DH=HM=12, ∴DM=OM=22, ∵FH=223DF DH -=, ∴OF=OM+MH+FH=2132++=321++. ∴OF 的最大值为321++. 考点:四边形综合题.3.已知正方形ABCD 中,E 为对角线BD 上一点,过E 点作EF ⊥BD 交BC 于F ,连接DF ,G 为DF 中点,连接EG ,CG .(1)请问EG 与CG 存在怎样的数量关系,并证明你的结论;(2)将图①中△BEF 绕B 点逆时针旋转45°,如图②所示,取DF 中点G ,连接EG ,CG .问(1)中的结论是否仍然成立?若成立,请给出证明;若不成立,请说明理由. (3)将图①中△BEF 绕B 点旋转任意角度,如图③所示,再连接相应的线段,问(1)中的结论是否仍然成立?(请直接写出结果,不必写出理由)【答案】(1)证明见解析(2)证明见解析(3)结论仍然成立【解析】【分析】(1)利用直角三角形斜边上的中线等于斜边的一半,可证出CG =EG .(2)结论仍然成立,连接AG ,过G 点作MN ⊥AD 于M ,与EF 的延长线交于N 点;再证明△DAG ≌△DCG ,得出AG =CG ;再证出△DMG ≌△FNG ,得到MG =NG ;再证明△AMG ≌△ENG ,得出AG =EG ;最后证出CG =EG .(3)结论依然成立.【详解】(1)CG=EG.理由如下:∵四边形ABCD是正方形,∴∠DCF=90°.在Rt△FCD中,∵G为DF的中点,∴CG=12FD,同理.在Rt△DEF中,EG=12FD,∴CG=EG.(2)(1)中结论仍然成立,即EG=CG.证法一:连接AG,过G点作MN⊥AD于M,与EF的延长线交于N点.在△DAG与△DCG中,∵AD=CD,∠ADG=∠CDG,DG=DG,∴△DAG≌△DCG(SAS),∴AG=CG;在△DMG与△FNG中,∵∠DGM=∠FGN,FG=DG,∠MDG=∠NFG,∴△DMG≌△FNG (ASA),∴MG=NG.∵∠EAM=∠AEN=∠AMN=90°,∴四边形AENM是矩形,在矩形AENM中,AM=EN.在△AMG与△ENG中,∵AM=EN,∠AMG=∠ENG,MG=NG,∴△AMG≌△ENG(SAS),∴AG=EG,∴EG=CG.证法二:延长CG至M,使MG=CG,连接MF,ME,EC.在△DCG与△FMG中,∵FG=DG,∠MGF=∠CGD,MG=CG,∴△DCG≌△FMG,∴MF=CD,∠FMG=∠DCG,∴MF∥CD∥AB,∴EF⊥MF.在Rt△MFE与Rt△CBE中,∵MF=CB,∠MFE=∠EBC=90°,EF=BE,∴△MFE≌△CBE∴∠MEF=∠CEB,∴∠MEC=∠MEF+∠FEC=∠CEB+∠CEF=90°,∴△MEC为直角三角形.∵MG=CG,∴EG=12MC,∴EG=CG.(3)(1)中的结论仍然成立.理由如下:过F作CD的平行线并延长CG交于M点,连接EM、EC,过F作FN垂直于AB于N.由于G为FD中点,易证△CDG≌△MFG,得到CD=FM,又因为BE=EF,易证∠EFM=∠EBC,则△EFM≌△EBC,∠FEM=∠BEC,EM=EC∵∠FEC+∠BEC=90°,∴∠FEC+∠FEM=90°,即∠MEC=90°,∴△MEC是等腰直角三角形.∵G为CM中点,∴EG=CG,EG⊥CG【点睛】本题是四边形的综合题.(1)关键是利用直角三角形斜边上的中线等于斜边的一半解答;(2)关键是利用了直角三角形斜边上的中线等于斜边的一半的性质、全等三角形的判定和性质解答.4.如图,正方形ABCD的边长为8,E为BC上一定点,BE=6,F为AB上一动点,把△BEF沿EF折叠,点B落在点B′处,当△AFB′恰好为直角三角形时,B′D的长为?【答案】4655或22【解析】【分析】分两种情况分析:如图1,当∠AB′F=90°时,此时A、B′、E三点共线,过点B′作B′M⊥AB,B′N⊥AD,由三角形的面积法则可求得B′M=2.4,再由勾股定理可求得B′N=3.2,在Rt△CB′N中,由勾股定理得,B′D=2222+DN= 3.2 5.6B N'+;如图2,当∠AFB′=90°时,由题意可知此时四边形EBFB′是正方形,AF=2,过点B′作B′N⊥AD,则四边形AFB′N为矩形,在Rt△CB′N中,由勾股定理得,B′D=2222+DN=22B N'+;【详解】如图1,当∠AB′F=90°时,此时A、B′、E三点共线,∵∠B=90°,∴AE=2222AB BE=86++=10,∵B′E=BE=6,∴AB′=4,∵B′F=BF,AF+BF=AB=8,在Rt△AB′F中,∠AB′F=90°,由勾股定理得,AF2=FB′2+AB′2,∴AF=5,BF=3,过点B′作B′M⊥AB,B′N⊥AD,由三角形的面积法则可求得B′M=2.4,再由勾股定理可求得B′N=3.2,∴AN=B′M=2.4,∴DN=AD-AN=8-2.4=5.6,在Rt△CB′N中,由勾股定理得,B′D=2222+DN= 3.2 5.6B N'+ =4655;如图2,当∠AFB′=90°时,由题意可知此时四边形EBFB′是正方形,∴AF=2,过点B′作B′N⊥AD,则四边形AFB′N为矩形,∴AN=B′F=6,B′N=AF=2,∴DN=AD-AN=2,在Rt△CB′N中,由勾股定理得,B′D=2222+DN=22B N'+ =22;综上,可得B′D的长为4655或22.【点睛】本题主要考查正方形的性质与判定,矩形有性质判定、勾股定理、折叠的性质等,能正确地画出图形并能分类讨论是解题的关键.5.如图,在平面直角坐标系中,直线DE交x轴于点E(30,0),交y轴于点D(0,40),直线AB:y=13x+5交x轴于点A,交y轴于点B,交直线DE于点P,过点E作EF⊥x轴交直线AB于点F,以EF为一边向右作正方形EFGH.(1)求边EF的长;(2)将正方形EFGH沿射线FB的方向以每秒10个单位的速度匀速平移,得到正方形E1F1G1H1,在平移过程中边F1G1始终与y轴垂直,设平移的时间为t秒(t>0).①当点F1移动到点B时,求t的值;②当G1,H1两点中有一点移动到直线DE上时,请直接写出此时正方形E1F1G1H1与△APE 重叠部分的面积.【答案】(1)EF=15;(2)①10;②120;【解析】【分析】(1)根据已知点E(30,0),点D(0,40),求出直线DE的直线解析式y=-43x+40,可求出P点坐标,进而求出F点坐标即可;(2)①易求B(0,5),当点F1移动到点B时,1010=10;②F点移动到F'的距离是10t,F垂直x轴方向移动的距离是t,当点H运动到直线DE上时,在Rt△F'NF中,NFNF'=13,EM=NG'=15-F'N=15-3t,在Rt△DMH'中,43MHEM'=,t=4,S=12×(12+454)×11=10238;当点G运动到直线DE上时,在Rt△F'PK中,PKF K'=13,PK=t-3,F'K=3t-9,在Rt△PKG'中,PKKG'=31539tt--+=43,t=7,S=15×(15-7)=120.【详解】(1)设直线DE的直线解析式y=kx+b,将点E(30,0),点D(0,40),∴30040k bb+=⎧⎨=⎩,∴4340kb⎧=-⎪⎨⎪=⎩,∴y=﹣43x+40,直线AB与直线DE的交点P(21,12),由题意知F(30,15),∴EF=15;(2)①易求B(0,5),∴BF=1010,∴当点F1移动到点B时,t=101010÷=10;②当点H运动到直线DE上时,F点移动到F'10,在Rt△F'NF中,NFNF'=13,∴FN=t,F'N=3t,∵MH'=FN=t,EM=NG'=15﹣F'N=15﹣3t,在Rt △DMH'中, 43MH EM '=, ∴41533t t =-, ∴t =4, ∴EM =3,MH'=4,∴S =1451023(12)11248⨯+⨯=; 当点G 运动到直线DE 上时,F 点移动到F'10,∵PF =10∴PF'10t ﹣10,在Rt △F'PK 中,13PK F K =', ∴PK =t ﹣3,F'K =3t ﹣9,在Rt △PKG'中,PK KG '=31539t t --+=43, ∴t =7,∴S =15×(15﹣7)=120.【点睛】本题考查一次函数图象及性质,正方形的性质;掌握待定系数法求函数解析式,利用三角形的正切值求边的关系,利用勾股定理在直角三角形中建立边之间的联系,准确确定阴影部分的面积是解题的关键.6.(问题情境)在△ABC 中,AB =AC ,点P 为BC 所在直线上的任一点,过点P 作PD ⊥AB ,PE ⊥AC ,垂足分别为D 、E ,过点C 作CF ⊥AB ,垂足为F .当P 在BC 边上时(如图1),求证:PD+PE =CF .证明思路是:如图2,连接AP ,由△ABP 与△ACP 面积之和等于△ABC 的面积可以证得:PD+PE =CF .(不要证明)(变式探究)(1)当点P在CB延长线上时,其余条件不变(如图3),试探索PD、PE、CF之间的数量关系并说明理由;请运用上述解答中所积累的经验和方法完成下列两题:(结论运用)(2)如图4,将长方形ABCD沿EF折叠,使点D落在点B上,点C落在点C′处,点P为折痕EF上的任一点,过点P作PG⊥BE、PH⊥BC,垂足分别为G、H,若AD =16,CF=6,求PG+PH的值.(迁移拓展)(3)在直角坐标系中,直线l1:y=-43x+8与直线l2:y=﹣2x+8相交于点A,直线l1、l2与x轴分别交于点B、点C.点P是直线l2上一个动点,若点P到直线l1的距离为2.求点P的坐标.【答案】【变式探究】证明见解析【结论运用】8【迁移拓展】(﹣1,6),(1,10)【解析】【变式探究】连接AP,同理利用△ABP与△ACP面积之差等于△ABC的面积可以证得;【结论运用】过点E作EQ⊥BC,垂足为Q,根据勾股定理和矩形的性质解答即可;【迁移拓展】分两种情况,利用结论,求得点P到x轴的距离,再利用待定系数法可求出P的坐标.【详解】变式探究:连接AP,如图3:∵PD⊥AB,PE⊥AC,CF⊥AB,且S△ABC=S△ACP﹣S△ABP,∴12AB•CF=12AC•PE﹣12AB•PD.∵AB=AC,∴CF=PD﹣PE;结论运用:过点E作EQ⊥BC,垂足为Q,如图④,∵四边形ABCD是长方形,∴AD=BC,∠C=∠ADC=90°.∵AD=16,CF=6,∴BF=BC﹣CF=AD﹣CF=5,由折叠可得:DF=BF,∠BEF=∠DEF.∴DF=5.∵∠C=90°,∴DC2222106DF CF-=-8.∵EQ⊥BC,∠C=∠ADC=90°,∴∠EQC=90°=∠C=∠ADC.∴四边形EQCD是长方形.∴EQ=DC=4.∵AD∥BC,∴∠DEF=∠EFB.∵∠BEF=∠DEF,∴∠BEF=∠EFB.∴BE=BF,由问题情境中的结论可得:PG+PH=EQ.∴PG+PH=8.∴PG+PH的值为8;迁移拓展:如图,由题意得:A(0,8),B(6,0),C(﹣4,0)∴AB2210,BC=10.68∴AB=BC,(1)由结论得:P1D1+P1E1=OA=8∵P1D1=1=2,∴P1E1=6 即点P1的纵坐标为6又点P1在直线l2上,∴y=2x+8=6,∴x=﹣1,即点P1的坐标为(﹣1,6);(2)由结论得:P2E2﹣P2D2=OA=8∵P2D2=2,∴P2E2=10 即点P1的纵坐标为10又点P1在直线l2上,∴y=2x+8=10,∴x=1,即点P1的坐标为(1,10)【点睛】本题考查了矩形的性质与判定、等腰三角形的性质与判定及勾股定理等知识点,利用面积法列出等式是解决问题的关键.7.(1)(问题发现)如图1,在Rt△ABC中,AB=AC=2,∠BAC=90°,点D为BC的中点,以CD为一边作正方形CDEF,点E恰好与点A重合,则线段BE与AF的数量关系为(2)(拓展研究)在(1)的条件下,如果正方形CDEF绕点C旋转,连接BE,CE,AF,线段BE与AF的数量关系有无变化?请仅就图2的情形给出证明;(3)(问题发现)当正方形CDEF 旋转到B ,E ,F 三点共线时候,直接写出线段AF 的长.【答案】(1)2AF ;(2)无变化;(3)AF 313.【解析】试题分析:(1)先利用等腰直角三角形的性质得出2 ,再得出BE=AB=2,即可得出结论;(2)先利用三角函数得出2CA CB =,同理得出2CF CE =△ACF ∽△BCE ,进而得出结论;(3)分两种情况计算,当点E 在线段BF 上时,如图2,先利用勾股定理求出2,6,即可得出62,借助(2)得出的结论,当点E 在线段BF 的延长线上,同前一种情况一样即可得出结论.试题解析:(1)在Rt △ABC 中,AB=AC=2,根据勾股定理得,22,点D 为BC 的中点,∴AD=122, ∵四边形CDEF 是正方形,∴2,∵BE=AB=2,∴2AF ,故答案为2AF ;(2)无变化;如图2,在Rt △ABC 中,AB=AC=2,∴∠ABC=∠ACB=45°,∴sin ∠ABC=22CA CB =, 在正方形CDEF 中,∠FEC=12∠FED=45°, 在Rt △CEF 中,sin ∠FEC=22CF CE =, ∴CF CA CE CB=, ∵∠FCE=∠ACB=45°,∴∠FCE ﹣∠ACE=∠ACB ﹣∠ACE ,∴∠FCA=∠ECB ,∴△ACF∽△BCE,∴BE CBAF CA= =2,∴BE=2AF,∴线段BE与AF的数量关系无变化;(3)当点E在线段AF上时,如图2,由(1)知,CF=EF=CD=2,在Rt△BCF中,CF=2,BC=22,根据勾股定理得,BF=6,∴BE=BF﹣EF=6﹣2,由(2)知,BE=2AF,∴AF=3﹣1,当点E在线段BF的延长线上时,如图3,在Rt△ABC中,AB=AC=2,∴∠ABC=∠ACB=45°,∴sin∠ABC=22 CACB=,在正方形CDEF中,∠FEC=12∠FED=45°,在Rt△CEF中,sin∠FEC=22CFCE=,∴CF CACE CB=,∵∠FCE=∠ACB=45°,∴∠FCB+∠ACB=∠FCB+∠FCE,∴∠FCA=∠ECB,∴△ACF∽△BCE,∴BE CBAF CA= =2,∴BE=2AF,由(1)知,CF=EF=CD=2,在Rt△BCF中,CF=2,BC=22,根据勾股定理得,BF=6,∴BE=BF+EF=6+2,由(2)知,BE=2AF,∴AF=3+1.即:当正方形CDEF旋转到B,E,F三点共线时候,线段AF的长为3﹣1或3+1.8.如图1,在正方形ABCD中,AD=6,点P是对角线BD上任意一点,连接PA,PC过点P 作PE⊥PC交直线AB于E.(1)求证:PC=PE;(2)延长AP交直线CD于点F.①如图2,若点F是CD的中点,求△APE的面积;②若ΔAPE的面积是21625,则DF的长为(3)如图3,点E在边AB上,连接EC交BD于点M,作点E关于BD的对称点Q,连接PQ,MQ,过点P作PN∥CD交EC于点N,连接QN,若PQ=5,MN=723,则△MNQ的面积是【答案】(1)略;(2)①8,②4或9;(3)5 6【解析】【分析】(1)利用正方形每个角都是90°,对角线平分对角的性质,三角形外角等于和它不相邻的两个内角的和,等角对等边等性质容易得证;(2)作出△ADP和△DFP的高,由面积法容易求出这个高的值.从而得到△PAE的底和高,并求出面积.第2小问思路一样,通过面积法列出方程求解即可;(3)根据已经条件证出△MNQ是直角三角形,计算直角边乘积的一半可得其面积.【详解】(1) 证明:∵点P在对角线BD上,∴△ADP≌△CDP,∴AP=CP, ∠DAP =∠DCP,∵PE⊥PC,∴∠EPC=∠EPB+∠BPC=90°,∵∠PEA=∠EBP+∠EPB=45°+90°-∠BPC=135°-∠BPC,∵∠PAE=90°-∠DAP=90°-∠DCP,∠DCP=∠BPC-∠PDC=∠BPC-45°,∴∠PAE=90°-(∠BPC-45°)= 135°-∠BPC,∴∠PEA=∠PAE,∴PC=PE;(2)①如图2,过点P分别作PH⊥AD,PG⊥CD,垂足分别为H、G.延长GP交AB于点M.∵四边形ABCD 是正方形,P 在对角线上,∴四边形HPGD 是正方形,∴PH=PG,PM ⊥AB,设PH=PG=a,∵F 是CD 中点,AD =6,则FD=3,ADF S n =9,∵ADF S n =ADP DFP S S +n n =1122AD PH DF PG ⨯+⨯, ∴1163922a a ⨯+⨯=,解得a=2, ∴AM=HP=2,MP=MG-PG=6-2=4,又∵PA=PE,∴AM=EM,AE=4,∵APE S n =1144822EA MP ⨯=⨯⨯=, ②设HP =b,由①可得AE=2b,MP=6-b,∴APE S n =()121626225b b ⨯⨯-=, 解得b=2.4 3.6或,∵ADF S n =ADP DFP S S +n n =1122AD PH DF PG ⨯+⨯, ∴11166222b DF b DF ⨯⨯+⨯=⨯, ∴当b=2.4时,DF=4;当b =3.6时,DF =9,即DF 的长为4或9;(3)如图,∵E 、Q 关于BP 对称,PN ∥CD,∴∠1=∠2,∠2+∠3=∠BDC=45°,∴∠1+∠4=45°,∴∠3=∠4,易证△PEM ≌△PQM, △PNQ ≌△PNC,∴∠5=∠6, ∠7=∠8 ,EM=QM,NQ=NC,∴∠6+∠7=90°,∴△MNQ 是直角三角形,设EM=a,NC=b 列方程组222252372 3a b a b ⎧+=⎪⎪⎨⎛⎪+= ⎪⎝⎭⎩, 可得12ab=56, ∴MNQ 56S V =, 【点睛】本题是四边形综合题目,考查了正方形的性质、等腰直角三角形的判定与性质、全等三角形的判定与性质等知识;本题综合性强,有一定难度,熟练掌握正方形的性质,证明三角形全等是解决问题的关键.要注意运用数形结合思想.9.△ABC 为等边三角形,AF AB =.BCD BDC AEC ∠=∠=∠.(1)求证:四边形ABDF 是菱形.(2)若BD 是ABC ∠的角平分线,连接AD ,找出图中所有的等腰三角形.【答案】(1)证明见解析;(2)图中等腰三角形有△ABC,△BDC,△ABD,△ADF,△ADC,△ADE.【解析】【分析】(1)先求证BD∥AF,证明四边形ABDF是平行四边形,再利用有一组邻边相等的平行四边形是菱形即可证明;(2)先利用BD平分∠ABC,得到BD垂直平分线段AC,进而证明△DAC是等腰三角形,根据BD⊥AC,AF⊥AC,找到角度之间的关系,证明△DAE是等腰三角形,进而得到BC=BD=BA=AF=DF,即可解题,见详解.【详解】(1)如图1中,∵∠BCD=∠BDC,∴BC=BD,∵△ABC是等边三角形,∴AB=BC,∵AB=AF,∴BD=AF,∵∠BDC=∠AEC,∴BD∥AF,∴四边形ABDF是平行四边形,∵AB=AF,∴四边形ABDF是菱形.(2)解:如图2中,∵BA=BC,BD平分∠ABC,∴BD垂直平分线段AC,∴DA=DC,∴△DAC是等腰三角形,∵AF∥BD,BD⊥AC∴AF⊥AC,∴∠EAC=90°,∵∠DAC=∠DCA,∠DAC+∠DAE=90°,∠DCA+∠AEC=90°,∴∠DAE=∠DEA,∴DA=DE,∴△DAE是等腰三角形,∵BC=BD=BA=AF=DF,∴△BCD,△ABD,△ADF都是等腰三角形,综上所述,图中等腰三角形有△ABC,△BDC,△ABD,△ADF,△ADC,△ADE.【点睛】本题考查菱形的判定,等边三角形的性质,等腰三角形的判定等知识,属于中考常考题型,熟练掌握等腰三角形的性质是解题的关键.10.定义:我们把三角形被一边中线分成的两个三角形叫做“友好三角形”.性质:如果两个三角形是“友好三角形”,那么这两个三角形的面积相等.理解:如图①,在△ABC中,CD是AB边上的中线,那么△ACD和△BCD是“友好三角形”,并且S△ACD=S△BCD.应用:如图②,在矩形ABCD中,AB=4,BC=6,点E在AD上,点F在BC上,AE=BF,AF 与BE交于点O.(1)求证:△AOB和△AOE是“友好三角形”;(2)连接OD,若△AOE和△DOE是“友好三角形”,求四边形CDOF的面积.探究:在△ABC中,∠A=30°,AB=4,点D在线段AB上,连接CD,△ACD和△BCD是“友好三角形”,将△ACD沿CD所在直线翻折,得到△A′CD,若△A′CD与△ABC重合部分的面积等于△ABC面积的,请直接写出△ABC的面积.【答案】(1)见解析;(2)12;探究:2或2.【解析】试题分析:(1)利用一组对边平行且相等的四边形是平行四边形,得到四边形ABFE是平行四边形,然后根据平行四边形的性质证得OE=OB,即可证得△AOE和△AOB是友好三角形;(2)△AOE和△DOE是“友好三角形”,即可得到E是AD的中点,则可以求得△ABE、△ABF的面积,根据S四边形CDOF=S矩形ABCD-2S△ABF即可求解.探究:画出符合条件的两种情况:①求出四边形A′DCB是平行四边形,求出BC和A′D推出∠ACB=90°,根据三角形面积公式求出即可;②求出高CQ,求出△A′DC的面积.即可求出△ABC的面积.试题解析:(1)∵四边形ABCD是矩形,∴AD∥BC,∵AE=BF,∴四边形ABFE是平行四边形,∴OE=OB,∴△AOE和△AOB是友好三角形.(2)∵△AOE和△DOE是友好三角形,∴S△AOE=S△DOE,AE=ED=AD=3,∵△AOB与△AOE是友好三角形,∴S△AOB=S△AOE,∵△AOE≌△FOB,∴S△AOE=S△FOB,∴S△AOD=S△ABF,∴S四边形CDOF=S矩形ABCD-2S△ABF=4×6-2××4×3=12.探究:解:分为两种情况:①如图1,∵S△ACD=S△BCD.∴AD=BD=AB,∵沿CD折叠A和A′重合,∴AD=A′D=AB=×4=2,∵△A′CD与△ABC重合部分的面积等于△ABC面积的,∴S△DOC=S△ABC=S△BDC=S△ADC=S△A′DC,∴DO=OB,A′O=CO,∴四边形A′DCB是平行四边形,∴BC=A′D=2,过B作BM⊥AC于M,∵AB=4,∠BAC=30°,∴BM=AB=2=BC,即C和M重合,∴∠ACB=90°,由勾股定理得:AC=,∴△ABC的面积是×BC×AC=×2×2=2;②如图2,∵S△ACD=S△BCD.∴AD=BD=AB,∵沿CD折叠A和A′重合,∴AD=A′D=AB=×4=2,∵△A′CD与△ABC重合部分的面积等于△ABC面积的,∴S△DOC=S△ABC=S△BDC=S△ADC=S△A′DC,∴DO=OA′,BO=CO,∴四边形A′BDC是平行四边形,∴A′C=BD=2,过C作CQ⊥A′D于Q,∵A′C=2,∠DA′C=∠BAC=30°,∴CQ=A′C=1,∴S△ABC=2S△ADC=2S△A′DC=2××A′D×CQ=2××2×1=2;即△ABC的面积是2或2.考点:四边形综合题.11.在矩形纸片ABCD中,AB=6,BC=8,现将纸片折叠,使点D与点B重合,折痕为EF,连接DF.(1)说明△BEF是等腰三角形;(2)求折痕EF的长.【答案】(1)见解析;(2).【解析】【分析】(1)根据折叠得出∠DEF=∠BEF,根据矩形的性质得出AD∥BC,求出∠DEF=∠BFE,求出∠BEF=∠BFE即可;(2)过E作EM⊥BC于M,则四边形ABME是矩形,根据矩形的性质得出EM=AB=6,AE=BM,根据折叠得出DE=BE,根据勾股定理求出DE、在Rt△EMF中,由勾股定理求出即可.【详解】(1)∵现将纸片折叠,使点D与点B重合,折痕为EF,∴∠DEF=∠BEF.∵四边形ABCD是矩形,∴AD∥BC,∴∠DEF=∠BFE,∴∠BEF=∠BFE,∴BE=BF,即△BEF 是等腰三角形;(2)过E作EM⊥BC于M,则四边形ABME是矩形,所以EM=AB=6,AE=BM.∵现将纸片折叠,使点D与点B重合,折痕为EF,∴DE=BE,DO=BO,BD⊥EF.∵四边形ABCD是矩形,BC=8,∴AD=BC=8,∠BAD=90°.在Rt△ABE中,AE2+AB2=BE2,即(8﹣BE)2+62=BE2,解得:BE==DE=BF,AE=8﹣DE=8﹣==BM,∴FM=﹣=.在Rt△EMF中,由勾股定理得:EF==.故答案为:.【点睛】本题考查了折叠的性质和矩形性质、勾股定理等知识点,能熟记折叠的性质是解答此题的关键.12.小明在矩形纸片上画正三角形,他的做法是:①对折矩形纸片ABCD(AB>BC),使AB 与DC重合,得到折痕EF,把纸片展平;②沿折痕BG折叠纸片,使点C落在EF上的点P 处,再折出PB、PC,最后用笔画出△PBC(图1).(1)求证:图1中的PBC是正三角形:(2)如图2,小明在矩形纸片HIJK上又画了一个正三角形IMN,其中IJ=6cm,且HM=JN.①求证:IH=IJ②请求出NJ的长;(3)小明发现:在矩形纸片中,若一边长为6cm,当另一边的长度a变化时,在矩形纸片上总能画出最大的正三角形,但位置会有所不同.请根据小明的发现,画出不同情形的示意图(作图工具不限,能说明问题即可),并直接写出对应的a的取值范围.【答案】(1)证明见解析;(2)①证明见解析;②1233)3<a<3,a>3【解析】分析:(1)由折叠的性质和垂直平分线的性质得出PB=PC,PB=CB,得出PB=PC=CB即可;(2)①利用“HL”证Rt△IHM≌Rt△IJN即可得;②IJ上取一点Q,使QI=QN,由Rt△IHM≌Rt△IJN知∠HIM=∠JIN=15°,继而可得∠NQJ=30°,设NJ=x,则IQ=QN=2x、3,根据IJ=IQ+QJ求出x即可得;(3)由等边三角形的性质、直角三角形的性质、勾股定理进行计算,画出图形即可.(1)证明:∵①对折矩形纸片ABCD(AB>BC),使AB与DC重合,得到折痕EF∴PB=PC∵沿折痕BG 折叠纸片,使点C 落在EF 上的点P 处∴PB=BC∴PB=PC=BC∴△PBC 是正三角形:(2)证明:①如图∵矩形AHIJ∴∠H=∠J=90°∵△MNJ 是等边三角形∴MI=NI在Rt △MHI 和Rt △JNI 中MI NI MH NJ=⎧⎨=⎩ ∴Rt △MHI ≌Rt △JNI (HL )∴HI=IJ②在线段IJ 上取点Q ,使IQ=NQ∵Rt △IHM ≌Rt △IJN ,∴∠HIM=∠JIN ,∵∠HIJ=90°、∠MIN=60°,∴∠HIM=∠JIN=15°,由QI=QN 知∠JIN=∠QNI=15°,∴∠NQJ=30°,设NJ=x ,则IQ=QN=2x ,22=3QN NJ -x ,∵IJ=6cm ,∴3,∴33cm ).(3)分三种情况:①如图:设等边三角形的边长为b,则0<b≤6,则tan60°=3=2ab,∴a=32b,∴0<b≤632=33;②如图当DF与DC重合时,DF=DE=6,∴a=sin60°×DE=63=33,当DE与DA重合时,a=643sin603==︒,∴33<a<43;③如图∵△DEF是等边三角形∴∠FDC=30°∴DF=643 cos303==︒∴a>43点睛:本题是四边形的综合题目,考查了折叠的性质、等边三角形的判定与性质、旋转的性质、直角三角形的性质、正方形的性质、全等三角形的判定与性质等知识;本题综合性强,难度较大.13.如图,在菱形ABCD中,AB=6,∠ABC=60°,AH⊥BC于点H.动点E从点B出发,沿线段BC向点C 以每秒2个单位长度的速度运动.过点E 作EF⊥AB,垂足为点F .点E出发后,以EF为边向上作等边三角形EFG,设点E的运动时间为t秒,△EFG和△AHC的重合部分面积为S.(1)CE= (含t的代数式表示).(2)求点G落在线段AC上时t的值.(3)当S>0时,求S与t之间的函数关系式.(4)点P在点E出发的同时从点A出发沿A-H-A以每秒2个单位长度的速度作往复运动,当点E停止运动时,点P随之停止运动,直接写出点P 在△EFG内部时t的取值范围.【答案】(1)6-2t;(2)t=2;(3)当<t≤2时,S=t2+t-3;当2<t≤3时,S=-t2+t-;(4)<t<.【解析】试题分析:(1)由菱形的性质得出BC=AB=6得出CE=BC-BE=6-2t即可;(2)由菱形的性质和已知条件得出△ABC是等边三角形,得出∠ACB=60°,由等边三角形的性质和三角函数得出∠GEF=60°,GE=EF=BE•sin60°=t,证出∠GEC=90°,由三角函数求出CE==t,由BE+CE=BC得出方程,解方程即可;(3)分两种情况:①当<t≤2时,S=△EFG的面积-△NFN的面积,即可得出结果;②当2<t≤3时,由①的结果容易得出结论;(4)由题意得出t=时,点P与H重合,E与H重合,得出点P在△EFG内部时,t的不等式,解不等式即可.试题解析:(1)根据题意得:BE=2t,∵四边形ABCD是菱形,∴BC=AB=6,∴CE=BC-BE=6-2t;(2)点G落在线段AC上时,如图1所示:∵四边形ABCD是菱形,∴AB=BC,∵∠ABC=60°,∴△ABC是等边三角形,∴∠ACB=60°,∵△EFG是等边三角形,∴∠GEF=60°,GE=EF=BE•sin60°=t,∵EF⊥AB,∴∠BEF=90°-60°=30°,∴∠GEB=90°,∴∠GEC=90°,∴CE==t,∵BE+CE=BC,∴2t+t=6,解得:t=2;(3)分两种情况:①当<t≤2时,如图2所示:S=△EFG的面积-△NFN的面积=××(t)2-××(-+2)2=t2+t-3,即S=t2+t-3;当2<t≤3时,如图3所示:S=t2+t-3-(3t-6)2,即S=-t2+t-;(4)∵AH=AB•sin60°=6×=3,3÷2=,3÷2=,∴t=时,点P与H重合,E与H重合,∴点P在△EFG内部时,-<(t-)×2<t-(2t-3)+(2t-3),解得:<t<;即点P在△EFG内部时t的取值范围为:<t<.考点:四边形综合题.14.数学活动课上,老师给出如下问题:如图,将等腰直角三角形纸片沿斜边上的高AC剪开,得到等腰直角三角形△ABC与△EFD,将△EFD的直角顶点在直线BC上平移,在平移的过程中,直线AC与直线DE交于点Q,让同学们探究线段BQ与AD的数量关系和位置关系.请你阅读下面交流信息,解决所提出的问题.展示交流:小敏:满足条件的图形如图甲所示图形,延长BQ与AD交于点H.我们可以证明△BCQ≌△ACD,从而易得BQ=AD,BQ⊥AD.小慧:根据图甲,当点F在线段BC上时,我们可以验证小慧的说法是正确的.但当点F在线段CB的延长线上(如图乙)或线段CB的反向延长线上(如图丙)时,我对小慧说法的正确性表示怀疑.(1)请你帮助小慧进行分析,小敏的结论在图乙、图丙中是否成立?请说明理由.(选择图乙或图丙的一种情况说明即可).(2)小慧思考问题的方式中,蕴含的数学思想是.拓展延伸:根据你上面选择的图形,分别取AB、BD、DQ、AQ的中点M、N、P、T.则四边形MNPT 是什么样的特殊四边形?请说明理由.【答案】成立;分类讨论思想;正方形.【解析】试题分析:利用等腰直角三角形的性质结合全等三角形的判定与性质得出BQ=AD,BQ⊥AD;利用已知条件分类得出,体现数学中的分类讨论思想,拓展延伸:利用三角形中位线定理结合正方形的判定方法,首先得出四边形MNPT是平行四边形进而得出它是菱形,再求出一个内角是90°,即可得出答案.试题解析:(1)、成立,理由:如图乙:由题意可得:∠FDE=∠QDC=∠ABC=∠BAC=45°,则DC=QC,AC=BC,在△ADC和△BQC中∵,∴△ADC≌△BQC(SAS),∴AD=BQ,∠DAC=∠QBC,延长AD交BQ于点F,则∠ADC=∠BDF,∴∠BFD=∠ACD=90°,∴AD⊥BQ;(2)、小慧思考问题的方式中,蕴含的数学思想是:分类讨论思想;拓展延伸:四边形MNPT是正方形,理由:∵取AB、BD、DQ、AQ的中点M、N、P、T,∴MN AD,TP AD,∴MN TP,∴四边形MNPT是平行四边形,∵NP BQ,BQ=AD,∴NP=MN,∴平行四边形MNPT 是菱形,又∵AD⊥BQ,NP∥BQ,MN∥AD,∴∠MNP=90°,∴四边形MNPT是正方形.考点:几何变换综合题15.(本题14分)小明在学习平行线相关知识时总结了如下结论:端点分别在两条平行线上的所有线段中,垂直于平行线的线段最短.小明应用这个结论进行了下列探索活动和问题解决.问题1:如图1,在Rt△ABC中,∠C=90°,AC=4,BC=3,P为AC边上的一动点,以PB,PA为边构造□APBQ,求对角线PQ的最小值及PQ最小时的值.(1)在解决这个问题时,小明构造出了如图2的辅助线,则PQ的最小值为,当PQ最小时= _____ __;(2)小明对问题1做了简单的变式思考.如图3,P为AB边上的一动点,延长PA到点E,使AE=nPA(n为大于0的常数).以PE,PC为边作□PCQE,试求对角线PQ长的最小值,并求PQ最小时的值;问题2:在四边形ABCD中,AD∥BC,AB⊥BC,AD=1,AB=2,BC=3.(1)如图4,若为上任意一点,以,为边作□.试求对角线长的最小值和PQ最小时的值.(2)若为上任意一点,延长到,使,再以,为边作□.请直接写出对角线长的最小值和PQ最小时的值.【答案】问题1:(1)3,;(2)PQ=,=.问题2:(1)=4,.(2)PQ的最小值为..【解析】试题分析:问题1:(1)首先根据条件可证四边形PCBQ是矩形,然后根据条件“四边形APBQ是平行四边形可得AP=QB=PC,从而可求的值.(2)由题可知:当QP⊥AC 时,PQ最小.过点C作CD⊥AB于点D.此时四边形CDPQ为矩形,PQ=CD,在Rt△ABC中,∠C=90°,AC=4,BC=3,利用面积可求出CD=,然后可求出AD=,由AE=nPA可得PE=,而PE=CQ=PD=AD-AP=,所以AP=.所以=.问题2:(1)设对角线与相交于点.Rt≌Rt.所以AD=HC,QH=AP.由题可知:当QP⊥AB时,PQ最小,此时=CH=4,根据条件可证四边形BPQH为矩形,从而QH=BP=AP.所以.(2)根据题意画出图形,当AB 时,的长最小,PQ的最小值为..试题解析:问题1:(1)3,;(2)过点C作CD⊥AB于点D.由题意可知当PQ⊥AB时,PQ最短.所以此时四边形CDPQ为矩形.PQ=CD,DP=CQ=PE.因为∠BCA=90°,AC=4,BC=3,所以AB=5.所以CD=.所以PQ=.在Rt△ACD中AC=4,CD=,所以AD=.因为AE=nPA,所以PE==CQ=PD=AD-AP=.所以AP=.所以=.问题2:(1)如图2,设对角线与相交于点.所以G是DC的中点,作QH BC,交BC的延长线于H,因为AD//BC,所以.所以.又,所以Rt≌Rt.所以AD=HC,QH=AP.由图知,当AB时,的长最小,即=CH=4.易得四边形BPQH为矩形,所以QH=BP=AP.所以.(若学生有能力从梯形中位线角度考虑,若正确即可评分.但讲评时不作要求)(2)PQ的最小值为..考点:1.直角三角形的性质;2.全等三角形的判定与性质;3.平行四边形的性质;4矩形的判定与性质.。
2020年杭州中考模拟卷2(答案版)
A.x=
B.x=
C.a2﹣b2=x2
D. = +
【分析】由 PC∥AB 得
,所以
,所以 CQ=
,所以 DP+CQ=
x+
≥2 ﹣b,当 x= 时,DP+CQ 的值最小,由此即可解决问题.
【解答】解:如图,∵四边形 ABCD 是矩形, ∴AB=CD=a,AD=BC=b,AB∥CD, ∵PC∥AB,
∴
,
∴
4.某班 30 位同学在植树节这天共种植了 130 棵树苗,其中男生每人种 5 棵,女生每人种 3 棵.设男生有 x 人,女生有 y 人,根据题意,列方程组正确的是( )
A.
B.
C.
D.
【分析】设男生有 x 人,女生有 y 人,根据 30 位同学在植树节这天共种植了 130 棵树苗, 列方程组即可.
2
绩的方差. 故选:C. 【点评】此题主要考查统计的有关知识,主要包括平均数、中位数、众数、方差的意义.反 映数据集中程度的统计量有平均数、中位数、众数方差等,各有局限性,因此要对统计 量进行合理的选择和恰当的运用. 6.如图,在△ABC 中,点 D、E 分别在边 AB、AC 上,DE∥BC,F 为 BC 边上一点,连接 AF 交 DE 于点 G,下列说法不正确的是( )
∴m=3,n=﹣(﹣4),
即 m=3,n=4.
故选:B.
【点评】本题主要考查了关于 x 轴、y 轴对称的点的坐标,熟记关于 x 轴对称的点的横坐
标相同,纵坐标互为相反数,关于 y 轴对称的点的横坐标互为相反数,纵坐标相同是解
题的关键.
3.如图,P 为⊙O 外一点,PA、PB 分别切⊙O 于 A、B,CD 切⊙O 于点 E,分别交 PA、PB
备战2020中考杭州市中考二模数学试题及答案【含多套模拟】
中学数学二模模拟试卷一、选择题〔共12小题,每题3分,每题只有一个正确答案,共36分〕1.在0、1、-2、-1四个数中,最小的数是〔〕2A.-2B.-1C.0D.12 2.马大哈做题很快,但经常不仔细,所以往往错误率非常高,有一次做了四个题,但只做对了一个,他做对的是是〔〕A.a8a4a2B.a3a4a12C.a5a5a10D.2x3x22x53.以下列图形中,既是轴对称图形又是中心对称图形的是〔〕A B C D4.由吴京特别出演的国产科幻大片?流浪地球?自今年一月份放映以来实现票房与口碑的双丰收,票房有望突破50亿元。
其中50亿用科学计数法表示为〔〕A.1010B.5108C.5109D.510105.如图,直线a∥b,将一直角三角形的直角顶点置于直线b上,假设∠1=28°,那么∠2的度数为〔〕A.108°B.118°C.128°D.152°6.以下立体图形中,主视图是三角形的是〔〕A B C D7.下表来源市气象局2021年3月7号发布的全市六个监测点监测到的空气质量指数〔AQI〕数据监测点福田罗湖盐田大棚南山宝安AQI595917134638上述〔AQI〕的数据中,中位数是〔〕A.65°8.在2021-2021B.75°赛季英超足球联赛中,截止到C.85°3月12D.90°号止,蓝月亮曼城队在联赛前30场比赛中只输4场,其它场次都保持不败,共取得了74分暂列积分榜第一名。
胜一场得3分,平一场得1分,负一场得0分。
设曼城队一共获胜了x场,那么可列方程为〔〕A.3x(30x)74B.x3(30x)74C.3x(26x)74D.x3(26x)749.定义:在等腰三角形中,底边和腰长的比叫做顶角的正对,顶角A的正对记做sadA,即sadA=底边:腰。
如图,在△ABC中,AB=AC,∠A=4∠B,那么cosB×sadA=〔〕A.133 B.C.223 D.410、如图仔细观察其中的两个尺规作图痕迹,两直线相交于点O,那么以下说法中不正确的选项是〔〕A.EF是△ABC的中位线B.∠BAC+∠EOF=180°C.O是△ABC的内心D.△AEF的面积等于△ABC面积的14AB C 第9题图题图A A DE FEFB O CC 第10题图B第1211、如图,二次函数y ax2bx的图像开口向下,且经过第三象限的点P,假设点P的横坐标是-1,那么一次函数y(a b)xb的图像大致是〔〕A B C D12如图,在正方形ABCD中,以BC为边向正方形内部做底边三角形BCE,连接AE、DE,连接BD交CE于点F,以下结论正确的有〔〕个。
2020年浙江省杭州中考冲刺练习题--语法填空
2020年浙江省杭州市中考冲刺复习练习--语法填空(一)America is a mobile society. 1.__________(friend) between Americans can be close and real, but disappear soon if situations change. Neither side 2.___________(feel) hurt by this. Both may exchange Christmas greetings for a year 3._________two, perhaps a few letters for a while--then no more. 4.__________the same two people meet again by chance, even years later, they pick up 5.__________friendship. This can be quite difficult for us Chinese 6.___________(understand), because friendships between us develop 7.__________(slow) but then may become lifelong feelings, extending (延伸) sometimes deeply into both families.Americans are ready to receive us 8.__________(foreign)at their homes, share their holidays, and their home life. They will enjoy welcoming us and be pleased if we accept their hospitality (好客) easily.Another difficult point for us Chinese to understand Americans is that 9._________they include us warmly in their personal everyday lives, they don't show their 10._________(polite) to us if it requires a great deal of time. This is not usual in our country where we may be generous with our time.(二)I'm Helen Blevins. I'm very lucky because I make money by doing 1.________ I love--painting pictures.I painted my first picture when I was just four. One day, 2.________Mom was cooking I painted a summer scene(场景) on one blue wall of my bedroom, I painted myself and my dog on the grass, with red flowers around. I painted the sun above us, 3.________a big smile on its face.I 4._______(paint) when Mom walked into my room. Her mouth was open and she 5.______ (stand)there quietly, looking at the wall. “I'm in big trouble,” I thought. So I was really surprised when Mom said, “6.________ a beautiful picture, Helen!” the picture stayed on my bedroom wall and 7._________(be)still there today, 30 years later. I see it every time I go home to visit Mom.I tell this story 8._________it shows how much Mom supported my love of painting. When I was in school, she cared about my art as much as other subjects. She kept all my paintings and hung many of them on the walls of our house. She often said, “You are so 9._______ (talent). Follow your dream.”Today I'm a successful 10.________(paint). I'm happy that people love my paintings and hang them in their homes. However, I will never forget Mom's great support!(三)Calligraphy is the art of handwriting. In the old time, the Chinese considered writing1._________an important form of art. Calligraphers would practice for years to learn to write2._________(perfect), but with style. Each of over 40,0003._________(character) needed to be written correctly. And each stroke(笔画) in a character had to be written in4.__________certain order.Poetry was also an important from of art. Great poets were famous all over the country, but all educated people 5.__________(expect) to write poetry. During the Tang Dynasty, poetry was so important 6.__________writing poetry was part of the examinations 7.__________(become) a civil servant(文官)and work for the government.Chinese painting was often connected with calligraphy. It is one of 8.__________(old) artistic traditions in the world. The most 9.__________(tradition) was of Chinese painting is known as “national” or “native” painting(国画), 10._________ is quite different from Western painting. People can draw mountains, homes, birds, trees and water on it.The London Marathon 1.__________(take) place every year since 1981. At the first one, just 6,225 people completed the course, and since then it has grown into one of the most important sporting 2.__________(event)in the world. Each winner receives $ 500,000 in prize money.However, most marathon runners are not professional (专业的). They run to raise money for charities or just as a 3.__________(person) experience. Many people do fun things to make themselves stand out, 4.__________ wearing silly clothes or doing things instead of just running.For example, Tom Harrison took three days just 5._________(reach) the halfway point, as he was crawling on his hands and knees dressed 6.__________a gorilla (猩猩), trying to raise money and attention for “The Gorilla Organization”.One exciting part from this year's race was the story of Jackie and her husband, who got 7._________(marry) on the morning of the marathon. Then they both ran the race, with Jackie doing it 8.__________her wedding dress! They were running to raise money for cancer charities, as Jackie was diagnosed (诊断) with cancer three years ago.Matthew Rees was another runner to inspire (激励) people, 9._________he stopped just before the finish line to help another runner run the last 200m. They did not know each other before, but Matthew saw that David 10.__________(be) too tired to finish the race and wanted to help him finish.(五)Allen was always a trouble 1._______(make). When he was in high school, he 2._______(put) in jail(监狱) for throwing a chair to a white girl. Later on, he was put in jail 3._________second time because of fast driving. 4.__________ he was on the school basketball team, he didn't like practicing and even laughed at his coach. Because of the troubles he had made, the NBA at first didn't want him.He was a talented basketball player but with bad 5.__________(behave). Allen realized that he6._______(will)not win any championship or be the top if he didn't change himself. He looked at7._______(he) in the mirror and asked, “Who is Allen Iverson?” In this way he changed himself. Over the years, he 8._______(change) and become a leader. “If you're getting older and not getting 9.________(smart), something is wrong,” said Iverson. On November 6, he was named the Eastern Conference Players of the Week (本周东部最佳球员). Now he has become many people's idol(偶像). “I've become matured(成熟),” he said. “I'm trying 10.________(be) a better person first, and then a better player.”参考答案:1.Friendships;2.feels;3.or;4.If;5.the;6.to understand;7.more slowly/slowly;8.foreigners;9.Although; 10.politeness;1.what;2.while/when;3.with;4.was painting;5.stood;6.What;7.is;8.because;9.talented;10.painter;1.as;2.perfectly;3.characters;4.a;5.were expected;6.that;7.to become;8.the oldest;9.traditional; 10.which;1.has taken;2.events;3.personal;4.like;5.to reach;6.as;7.married;8.in;9.because; 10.was;1.maker;2.was put;3.a;4.When;5.behaviors;6.would;7.himself;8.has changed;9.smarter;10.to be。
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2020年浙江省杭州市中考冲刺易错题练习(二)一、语法填空A.语法填空单句练习1.Letters of recommendation have different levels __________importance, __________(depend)on the views of college or university and many other things.2.You can also download a map from the London __________(underground)website().3.It’s not the shortest route here, but I think it is ___________(simple).4.The underground staff will __________(sure) help you.5.When I finished my job, I heard my manager ask the “tin man” about what the was going to do_________those tins he had collected.6.I never even thought about this kind of question, __________I always assumed that “tin man” would take those tins to the recycling center. ___________(unexpected), “tin man” answered: “I will give these tins to my neighbor. He has epilepsy(癫痫)and cannot work.” I was so shocked _________(hear) that, so I asked him: “You mean you collect all those thins just to help your neighbor?”7.I’ve always wanted to try rock climbing, but never had the time or money for it. But I’ve discovered a way to experience the __________(excite) of climbing rock. Indoor climbing is ___________way to get a taste of rock climbing.8.___________indoor climbing is safer and simpler than real rock climbing, you should still be careful.9.Try to get under a doorway or another area of the building ___________is held up by strong beams(梁).10.Do not rush to lifts, because it is far___________(safe) to stay where you are.11.After an earthquake, many buildings are less strong, although they appear safe. If you stay indoors, move people from the building so that the building quickly and help disabled or injured people. Once outdoors, move well away _________ the building so that if it falls down, you will not___________(hurt).12.By planning ahead and keeping calm during ___________earthquake, you can greatly increase your chances of survival without injury.13.___________(thank)to fitness apps and gadgets(小机械), people can measure every step they take.14.All of __________(they)friends can see where they have run, what activities they ___________(do) or what they have had for lunch.15.My friend, Anna Palmer, is always __________(use) the fitness gadgets(小机械).16.Proper nutrition(营养)is important for good health. Your body cannot work well _________it receives the proper kindof “fuel(燃料)”.17.Vegetables and fruits are very important because they provide necessary vitamins and minerals. However, don’t overeat. __________is not helpful to be overweight.B.语法填空语篇练习(recommendation 推荐;resume 简历;)二、完形填空(一)Just before September, Miller was hit by a car and lost his right __4__. I went to see him after he had come back from hospital. He looked very __5__, but he didn’t cry at all.That season, I __6__all of Miller’s records while he watched the games from the bench at home. We beat the other team 10-1 in the final match and I was named the most valuable player, __7__I often had crazy dreams in which I was to blame for Miller’s accident.One afternoon, while i was crossing the filed to go home, I saw Miller was stuck going over a fence-which wasn’t __8__ to climb if you had both arms. I’m sure I was the __9__person in the world he wanted to accept help from. But even that challenge he accepted.4. A. leg B. foot C. arm D. hand5. A. pale B. calm C. relaxed D. ashamed6. A. held B. broke C. set D. tired7. A. and B. then C. but D. so8. A. easy B. hard C. fun D. fit9. A. first B. second C. next D. last(二)Getting the proper amount of __6__is also important. If you don’t get enough sleep, you will feel tired and __7__get angry. You have no energy. Over a long period of time a little amount of sleep __8__even result in a change personality(个性). Be sure to allow __9__seven to nine hours of sleep each night. If you do, your body will feel __10__and easily get refreshed, your mind will be active.6. A. food B. sleep C. energy D. exercise7. A. hardly B. clearly C. easily D. gradually8. A. must B. may C. have to D. need9. A. ourselves B. myself C. yourself D. themselves10. A. weak B. tired C. strong D. nervous(三)The research team __4__27men who didn’t like doing sports regularly for 12 weeks. They put the men into __5__ groups. One group did short, intense physical exercise or training on a bicycle three times a week. __6__group rode a bicycle for about 50 minutes, three times a week. The last group did nothing.The researchers found __7__that they did not think would happen. The group that exercised for only 10 minutes each time was just as healthy after 12 weeks as the __8__that exercised for 50 minutes each time. That is because of the __9__ the researchers planned the activities.4. A. tired B. decided C. followed D. pointed5. A. two B. three C. four D. five6. A. Another B. Other C. The other D. Others7. A. nothing B. anything C. something D. everything8. A. that B. those C. ones D. one9. A. idea B. way C. mind D. result三、阅读理解(一)Sitting among the cheering fans of the Chinese Womens Volleyball Team in Rio de Janeiro, a Polish fan caught a lot of attention. It is not because he is not Chinese, but because he has followed the team closely from the very beginning.The 60-year-old Jozef fell in love with the Chinese Women's Volleyball Team at the first sight when he watched the girls at the London Olympics on TV in 2012. The Polish man was crazy about the performances of the young team, especially by its core player Hui Ruoqi. Before that, Jozef was a loyal fan of his home team the Polish men’s volleyball.Since then, Jozef has become crazy about the team and has kept track of almost all their international competitions. Back in the 2013 Montreux Volley Masters of Switzerland, the Polish man, for the first time, came to cheer up for the team on site. He also drove all the way from Poland to ltaly to lend support for the girls during the 2014 Womens World Volleyball Championship.The hardcore fan traveled hundreds of miles from Poland to Brazil, and booked tickets for all matches of the Chinese Womens Volleyball. This time, Jozef was interviewed by TV and has been recognized by not just fans, but millions of Chinese TV audiauce.The "Polish grandpa" was a nickname given by Chinese volleyball fans. He has 18,000 followers on Sina Weibo, China's answer to Twitter, where Jozef has been sharing his obsession with Chinese internet users since 2013.22. What has Jozef been doing on Sina Weibo?A. Giving support to the Polish team.B. Sharing his love for the Chinese team.C. Answering questions about playing volley ball.D. Booking tickets for matches of the Chinese team.(二)Few people could forget the tragedy that happened on Nov 27, when Chinese-Canadian model and actor Godfrey Gao,35, died from cardiac arrest (心跳骤停) while filming a reality TV show in Ningbo, Zhejiang.Shocked by his sudden death, people discussed how we should deal with incidents like these. Experts suggested that people should learn first aid so that they can help heart attack victims.In China, 550,000 people suffer from sudden cardiac arrest every year, according to the National Center for Car diovascular Diseases. Only about I percent are saved.To deal with this problem, a draft of the Basic Medical Treatment and Health Promotion Law was submitted to the Standing Committee of the National People's Congress for its fourth review in December 2019. It suggests that public places should be equipped with necessary first aid equipment.One of these pieces of equipment is called an automated external defibrillator(AED, 自动体外除颤器). It can save people from sudden cardiac arrest. However, few of these devices(i#)can be found in public places.According to a CCTV report, there are 394 AEDs for every 100.000 people in Japan and 317 for every 100,000 residents in the United States. The figure(数字) is just 0.2 when it comes to the Chinese mainland. Inaddition, more people should be taught how to do first aid experts said.According to the National Health Commission, less than 1 percent of Chinese adults know how to performCPR(心肺复苏术). The most they can do during an emergency is call I20. In such situations, the “golden period” for saving someone's life -the first four minutes of a heart attack- is of little use even if first aid equipment is available, said China Daily writer Wang Yiqing.People are encouraged to receive first aid training and learn how to perform first aid in public places, ChinaDaily reported. People should-earn mrst aidt-shile-sa they can help people in need.23.The writer mentioned Godfrey Gao to _________.A. warn famous people that cardiac arrest is deadlyB. point out how dangerous cardiac arrest isC. show us how unhealthy people areD. describe how hard celebrities work24.The new draft in Paragraph 4 suggests that ________.A. more AEDs should be provided in public placesB. equipment should be invented to save more livesC. it is important to teach people how to find AEDsD. more laws are needed to save people from cardiac arrest25. The National Health Commission points out that _________.a. first aid equipment in China is much cheaper than that in the USb. more people in China should learn how to perform CPRc. the first four minutes of a heart attack are the best time to do first aidd. EDs are of little use if people don' t know how to do CPRA. abcB. bcdC. acdD. abd26. What's the writer s purpose of writing this passage?A. To ask us to help people who have heart attack.B. To tell us to learn first aid to help people in needC. To make us save more people if we canD. To tell us to know how to perform CPR correctly四、单词拼写根据下列句子及所给单词的首字母,写出各个单词的完全形式(每空限填一词)1. A j________ is a person who decides who will be the winner of a competition.2.You say 'I beg your p________?' when you want someone to repeat what they have just said because you have not heard or understood it.3.I prefer the subject g_________which is the study of the countries of the world and of such things as the land, seas, climate, towns, and population.4. We will visit my c________ house every summer who is the child of my uncle and has a very big farm in Hangzhou.5. Yesterday was an important day but unfortunately I was a________ from school because of illness.6.If I were ill, I would choose Chinese traditional m_________. Although it tastes bitter, it is less harmful to us. Western one can be bad for our health, you may develop another problem.7.The first three m_______ of the year 2002 were the warmest globally since records began in 1860 and probably the warmest in 1,000 years, according to a new study by British scientists.8. City Park is not far away from here. It’s only ten m________ walk. You can’t miss it.9.Next week is my grandpa’s n________ birthday, we’re havinga big party.10. “I didn't lose the gold. I won the silver.” Edward said p_______ to his teacher with a big smile on his face.11.Sammy hates waiting in long lines. I think he’s just not very p__________.12.Jenny is a__________in class. She often answers and asks questions13.He gets all his k___________about politics from watching the television.14.He is very h___________. He always tells funny stories to make people laugh.plete the sentences with the c__________forms of the verbs in the box.16.Baby pandas usually very tiny. An adult pandas w__________many times more than a baby panda.17.They all had a great time yesterday, i___________Sam, though he is a quiet and shy boy.18.Many people like Zhong Wei r___________with great interest how their hometowns have changed.19.The tea art p___________show how to make a perfect cup of tea with beautiful tea sets.20. It is almost 23 years since Hong Kong r__________to China in 1997.语法填空:1.of; depending;2.underground’s;3.simplest;4.surely;5.with;6.because; unexpectedly; to hear;7.excitement;8.Although;9.which/that; 10.safer; 11.from; be hurt; 12.an; 13.Thanking; 14.their; have done; ing; 16.unless; 17.it;1.are written;2.achievements;3.Since;4.from;5.carefully;6.takes;7.to decide;rmation;9.better; 10.an;完形填空:CABCBD BCBCC AACCCB阅读理解:BABB单词拼写:1.judge; 2.pardon; 3.geography; 4.cousin’s; 5.absent; 6.medicine; 7.months; 8.minutes’; 9.ninetieth; 10.proudly;11.patient; 12.active; 13.knowledge; 14.humorous; 15.correct; 16.weighs; 17.including; 18.regard; 19.performance;20.returned;。