最新深圳2012中考数学模拟试题

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32．一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．3xB．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．yx2oAyxoByx2oCyxoD22（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．53643xxx①②21．（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）9．6.1810．8yx11．72°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)4xyxyxyxy222244(4)4xxyyxyxy··································································3分22224444xxyyxyxy22y··········································································································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BCDC90BCGDCE°CGCEBCGDCE△≌△（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