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深圳2012中考数学模拟试题一、选择题(每小题3分,满分24分)1.下列判断中,你认为正确的是()A.0的倒数是0B.5大于2C.π是有理数D.9的值是32.一个正多边形的每个外角都是36°,这个正多边形是()A.正六边形B.正八边形C.正十边形D.正十二边形3.函数3yx中,自变量x的取值范围是()A.3xB.3x≥C.0x≥D.3x≤4.如图,点ABC,,在O上,50A°,则BOC的度数为()A.130°B.50°C.65°D.100°5.在RtABC△中,90C°,若1sin2A,则A的度数是()A.60°B.45°C.30°D.无法确定6.同一时刻,身高2.26m的姚明在阳光下影长为1.13m;小林浩在阳光下的影长为0.64m,则小林浩的身高为()A.1.28mB.1.13mC.0.64mD.0.32m7.对于样本数据1,2,3,2,2,以下判断:①平均数为5;②中位数为2;③众数为2;④极差为2.正确的有()A.1个B.2个C.3个D.4个8.在同一直角坐标系中,二次函数22yx与一次函数2yx的图象大致是()二、填空题(每小题3分,满分24分)9.6.18的绝对值是.10.已知y是x的反比例函数,当4x时,2y.则y与x的函数关系式是.11.ABC△中,ABAC,36A°,则B的度数是.12.如图,天平盘中每个小球的重量用x克表示,砝码每个5克,那么x克.13.已知5mn,3mn,则22mnmn.yx2oAyxoByx2oCyxoD22(第12题图)(第4题图)ABOC14.在等边三角形、正方形、矩形、菱形中,是轴对称图形但不是中心对称图形的是.15.如图,ABC△中,DEF,,分别是ABBCAC,,上的点,已知DFBC∥,EFAB∥,请补充一个条件:,使ADFFEC△≌△.16.调查某小区内30户居民月人均收入情况,制成如下的频数分布直方图,收入在1200~1240元的频数是.三、解答题(本大题共10个小题,解答应写出文字说明、证明过程或演算步骤,请将解答过程写在答题卡相应的位置上,满分72分)17.(本题满分6分)计算:042tan45(π6)°.18.(本题满分6分)先化简,再求值:2(2)(2)(2)4xyxyxyxy;其中2009x,1y.19.(本题满分6分)某物体的三视图如右图:(1)此物体是体;(2)求此物体的全面积.(第15题图)ADFECB0(户)15105374111120116012001360132012801240元(第16题图)2020404020主视图左视图俯视图20.(本题满分6分)解不等式组,并将解集在数轴上表示出来.53643xxx①②21.(本题满分6分)如图,BCE,,是同一直线上的三个点,四边形ABCD与四边形CEFG都是正方形,连结BGDE,.(1)观察图形,猜想BG与DE之间的大小关系,并证明你的结论;(2)若延长BG交DE于点H,求证:BHDE.22.(本题满分6分)解方程:404012xx.23.(本题满分8分)小明练习100米短跑,训练时间与100米短跑成绩记录如下:时间(月)1234成绩(秒)15.615.415.215(1)请你为小明的100米短跑成绩y(秒)与训练时间x(月)的关系建立函数模型;(2)用所求出的函数解析式预测小明训练6个月的100米短跑成绩;(3)能用所求出的函数解析式预测小明训练3年的100米短跑成绩吗?为什么?ADGHFECB24.(本题满分8分)小亮看到路边上有人设摊玩“有奖掷币”游戏,规则是:交2元钱可以玩一次掷硬币游戏,每次同时掷两枚硬币,如果出现两枚硬币正面朝上,奖金5元;如果是其它情况,则没有奖金(每枚硬币落地只有正面朝上和反面朝上两种情况).小亮拿不定主意究竟是玩还是不玩,请同学们帮帮忙!(1)求出中奖的概率;(2)如果有100人,每人玩一次这种游戏,大约有人中奖,奖金共约是元,设摊者约获利元;(3)通过以上“有奖”游戏,你从中可得到什么启示?25.(本题满分10分)如图,AB是O的直径,CD是弦,CDAB于点E,(1)求证:ACECBE△∽△;(2)若8AB,设OEx(04x),2CEy,请求出y关于x的函数解析式;(3)探究:当x为何值时,3tan3D.26.(本题满分10分)如图,在平面直角坐标系中,四边形OABC为矩形,3OA,4OC,P为直线AB上一动点,将直线OP绕点P逆时针方向旋转90°交直线BC于点Q;(1)当点P在线段AB上运动(不与AB,重合)时,求证:OABQAPBP;(2)在(1)成立的条件下,设点P的横坐标为m,线段CQ的长度为l,求出l关于m的函数解析式,并判断l是否存在最小值,若存在,请求出最小值;若不存在,请说明理由;(3)直线AB上是否存在点P,使POQ△为等腰三角形,若存在,请求出点P的坐标;若不存在,请说明理由.CBEODAyAPBQCOx数学试卷参考答案及评分标准一、选择题(本题共8个小题,每小题3分,满分24分)1.B2.C3.B4.D5.C6.A7.D8.C二、填空题(本题共8个小题,每小题3分,满分24分)9.6.1810.8yx11.72°12.1013.1514.等边三角线15.AFFC或DFEC或ADFE或F为AC中点或DF为中位线或EF为中位线或DEAC∥等16.14三、解答题(本大题共10个小题,满分72分)17.(本题满分6分)解:042tan45(π6)°2211·································································································4分221····································································································5分1··············································································································6分18.(本题满分6分)解:2(2)(2)(2)4xyxyxyxy222244(4)4xxyyxyxy··································································3分22224444xxyyxyxy22y··········································································································4分当2009x,1y时,原式22212y··················································································6分19.(本题满分6分)(1)圆柱·····································································································2分(2)220π402π10··············································································4分1000π······································································································6分20.(本题满分6分)解:不等式①的解集2x··············································································2分不等式②的解集3x······················································································4分不等式组的解集23x···············································································5分在数轴上表示(略)························································································6分21.(本题满分6分)(1)猜想:BGDE····················································································1分BCDC90BCGDCE°CGCEBCGDCE△≌△(SAS)··········································································3分(2)在BCG△与DHG△中由(1)得CBGCDE·············································································4分CGBDGH··························································································5分90DHBBCG°BHDE·································································································6分22.(本题满分6分)解:方程两边同乘以(2)xx,得······································································1分40(2)40(2)xxxx···············································································2分整理得22800xx···················································································3分10x或8x··························································································5分经检验10x,8x都是原方程的根.···························································6分23.(本题满分8分)(1)设ykxb依题意得··············································································1分15.615.42kbkb······························································································2分解答0.21
本文标题:最新深圳2012中考数学模拟试题
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