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2013陕西中考数学一、选择题（共10小题，每小题3分，计30分）1、下列四个数中最小的数是（ ）A. B. 0 C. D. 52、如图，下面的几何体是由一个圆柱和一个长方体组成的，则它的俯视图是（ ）3、如图，ABCD，CED= ，AEC= ,则D的大小为（ ）A. B. C. D. 4、不等式组 ，的解集为（ ）A. B. C. D. 5、我省某市五月份第二周连续七天的空气质量指数分别为：111,96,47,68,70,77,105.则这7天空气质量指数的平均数是（ ）A. 71.8 B. 77 C. 82 D. 95.7 6、如果一个正比例函数的图像经过不同象限的两点A(2，m)、B（n，3），那么一定有（ ）A. m0，n0 B. m0,n0 C. m0 D. m0，n”,“=”或“ 14、 15、2416、10.5三、解答题17、解： 18、证明： 19、解：（1）抽样调查的学生人数为：3630%=120（名）（2分） （2）B的人数：12045%=54（名） C的百分比： D的百分比： 补全两幅统计图如图所示。（5分）（略）（4） 对“节约教育”内容“了解较多”的学生人数为： 180045%=810（名）（7分）20、解： 即 解之，得 路灯高CD约为6.1.（8分）21、解：设OA段图像的函数表达式为 当=1.5时，=90； 1.5 =90. =60. 当=0.5时，=600.5=30. 行驶半小时时，他们离家30千米，（3分）（2）设AB段图像的函数表达式为 （4分）A(1.5，90)，B(2.5，170)在AB上， 解之，得 （6分）（3）当=2时，=80230=130.170130=40.他们出发2小时后，离目的地还有40千米。（8分）22、解：设A,B,C,D,E分别表示大拇指，食指，中指，无名指，小拇指，列表如下：乙甲ABCDEAAAABACADAEBBABBBCBDBECCACBCCCDCEDDADBDCDDDEEEAEBECEDEE由表格可知，共有25种等可能的结果。（1）由上表可知，甲伸出小拇指取胜有1种可能。P（甲伸出小拇指取胜）= （3分）（2）由上表可知，乙取胜有5种可能。P(乙取胜)= （8分）23、（1）证明：EF是O的直径， EAF= ， ABC+ACB=.（3分）(2)解：连接OD,则ODBD。（4分） 过点E作EHBC, 垂足为点H， EH/OD. EF/BC.OE=OD, 四边形EODH是正方形（6分） EH=HD=OD=5. 又BD=12，BH=7。在RtBEH中，tanBEH= ,而ABC+BEH=,ABC+ACB=,ACB=BEH.tanACB= （8分）24、解：（1）二次函数图像的对称轴为直线 （2分） （2）设二次函数的表达式为 （3分） 当时，; 当时，. 点C坐标为（0，），顶点D坐标为（2，） OC= 又A(1，0)B(2，0) OA=1，EB=1，DE= （5分） 当AOC与DEB相似时，假设OCA=EBD,可得 （7分）假设OCA=EDB,可得 此方程无解（8分）综上所述，所求二次函数的表达式为 或（10分）25、（1）如图所示（2分） （2）如图，连接AC、BD相交于点O，作直线OM分别交AD、BC于P、Q两点，过点O作OM的垂线分别交AB、CD于E、F两点，则直线OM、EF将正方形ABCD的面积四等分（4分）理由如下：点O是正方形的对称中心.AP=CQ,EB=DF.在AOP和EOB中，AOP=AOE,BOE=AOE,AOP=BOE.OA=OB,OAP=EBO= ,AOPEOB.AP=BE=DF=CQ.AE=BQ=CF=PD. （6分）设点O到正方形ABCD一边的距离 . 直线EF、OM将正方形ABCD面积四等分（7分）（3）存在.当BQ=CD= 时，PQ将四边形ABCD面积二等分（6分）理由如下：如图，延长BA到点E,使AE=,延长CD到点F，使DF= ，连接EF. ,BE=BC= ，四边形EBCF是菱形，连接BF交AD于点M，则MABMDFAM=DMP、M两点重合P点是菱形EBCF对角线的交点（10分）在BC上截取BQ=CD=,则CQ=AB=设点P到菱形EBCF一边的距离为，则 当BQ=时，直线PQ将四边形ABCD的面积分成相等的两部分（12分）（第25题图） （第25题图） （第25题图） 笔试部分IV单选（共10 小题计10分）( 第一页)21 Its very important for us to learn by_. A ourselves B itself C myself D themselves 22 When you _ at a restaurant , please order just enough food .A ate B will eat C eat D have eaten 23 Mary called and asked her husband _ home at once , because she locked their daughter in the home .A to leave B leave C go D to go 24 To keep healthy , many people _ every day . A take a shower B take pride C take a look D take exercise 25 Which of the two subjects do you like , art pr music -_ . They are really interesting .A Neither B Both C None D All26 Go downstairs ,_stand in line on the playground as soon as possible .A and B but C so D or 27 - Its one of the _ things in the world to stay with friends .-I agree . It always makes us relaxed.A worst B happiest C busiest D hardest 28 The mobile phone has influenced peoples life a lot since it _A invents B invented C is invented D was invented29 What a nice paper fish ! Can you show us _ you make it ?A whether B how C why D what 30 We are planning to have a surprise party _ her fifteen birthday .A at B in C for D with （ 第二页）V 完形填空 （ 10小题， 计10分）阅读下面一篇短文， 理解大意， 然后从各小题的四个选项中选出一个最佳答案， 使短文连贯完整。 Jenny, form Germany , spent some time traveling in India . While she was there , she stayed with her Indian friend , Leela. However , there was a language barrier (障碍) for her there . It was very 31_,for her to communicate in the new environment, which was very different from 32 of her own country . One day , together with Leela , Jenny went to 33 an orphanage(孤儿院) 。 All the children there were very young. At first , Jenny was not sure if she could have a way to communicate with them . She went over to the children 34 and sat beside them . After some time , one of the children 35 her . She felt a little relaxed and smiled back . Then she went close to the child . She slowly put her are around the child and started 36 a song in German .The child kept smiling and started repeating the words after her . The words that came from the little mouth were different from those that Jenny sang, but the rhythm(节奏)was the same . Jenny sang a little more and the child followed her again . Wanting to join in the 37 another child went up to Jenny and started singing the rhythm . Then more children joined . They 38 many smiles together .From the other side of the hall , Leela was smiling and watching them . Noticing Leelas 39 on her , Jenny had an exciting feeling from her Heart :“ See, I dont have any language barriers here. We 40 speak and communicate!” At that moment , she understand : We are all simply human （ 第三页）and we have ability to connect each other .31 A nice B dangerous C difficult D easy32 A these B those C this D that 33 A show B visit C build D improve 34 A slowly B early C hardly D easily 35 A looked at B laughed at C shouted at D smiled at 36 A singing B writing C saying D playing 37 A club B talk C fun D dance 38 A forgot B remembered C shared D missed 39 A hands B eyes C influence D question 40 A can B must C need D should VI 阅读理解（ 共15小题， 计20分）第一节阅读下列一篇短文， 判断下列句子是否符合短文内容， 符合的用A 表示， 不否合的用B表示。（ 5小题， 5分） AHawaii has always been a magic name to people who like traveling. PeopleFrom all over the world dream of seeing the beautiful islands in the middle of the ocean. Its always one of their dreams to watch the sun going down .The sun drops like a ball of bright fire into the sea , and it drops so quickly that you can event see it move . About two thousand years ago , the first people went Hawaii in a very small boat . They found the beautiful white sand beaches and the waving palm trees, But it was difficult for people to go to Hawaii at that time . And there （第三页） were no big hotels like the ones today . Now people can get to Hawaii in different ways . More and more people go to Hawaii . So lots of nice big hotels have been built in recent years . However , the scenery （自然景色） in Hawaii hasnt changed much . The white sand beaches and the waving palm tress are still there . People often have a peaceful time , taking a walk along the water in the morning . At night , they get toghter to hold parties , chatting and dancing . So if youre thinking about relaxing yourself , Hawaii is surely the first place for you to choose .41 The sun in Hawaii drops too quickly for people to see it move ._42 In Hawaii , a large number of nice big hotels have been built in recent years ._43 The scenery in Hawaii is quite different from what it was many years ago ._44 According to the passage , Its common for people to hold parties in Hawaii at night ._45 The passage mainly tells us the first people who came to Hawaii. 第二节 阅读下面三篇短文， 从各小题中所给的四个选项中选出能回答所提问题或完成所个句子的一个最佳答案。（ 共10题，15分） To protect the environment , we are on the way , Here are a few things we can do .Unwanted gifts ? Give them away !Have you ever received a gift that you didnt like ? Did you throw it away ? If so , you can have anot