最新江苏常州中考数学及答案优秀名师资料.doc
2011江苏常州中考数学及答案江苏省常州市二00一年初中毕业、升学统一文化考试 数学 说明:1.本试卷共6页,全卷满分120分,考试时间为120分钟,考生应将答案全部填写在答题卡相应位置上,写在本试卷上无效,考试结束全,请将本试卷和答题卡一并交回,考试时不允许使用计算器. 2.答题前,考生务必将自己的姓名、考试证号填写在试卷上,并填写好答题卡上的考生信息. 3.任图必须用2B铅笔,并请加黑加粗,描写清楚. 一、选择题(本大题共有8小题,每小题2分,共16分,在每小题所给的四个选项中,只有一项是正确的) 1. (2011江苏常州,1,2分)在下列实数中,无理数是( ) 15A.2 B.0 C. D. 3【答案】 C 2. (2011江苏常州,2,2分)下列计算正确的是( ) 22363633A.aaa, B. C.3m+3n=6mn D. xx,yyy,，【答案】D 3. (2011江苏常州,3,2分)已知某几何体的三个视图(如图),此几何体是( ) A.正三棱柱 B. 三棱锥 C. 圆锥 D. 圆柱 【答案】C 4. (2011江苏常州,4,2分)某地区有8所高中和22所初中,要了解该地区中学生的视力情况,下列抽样方式获得的数据最能反映该地区中学生视力情况的是( ) A.从该地区随机选取一所中学里的学生 B.从该地区30所中学生里随机选取800名学生 C.从该地区的一所高中和一所初中各选取一个年级的学生 D.从该地区的22所初中里随机选取400名学生 【答案】B x,25. (2011江苏常州,5,2分)若在实数范围内有意义,则x的取值范围是( ) A.x?2 B.x?2 C.x,2 D.x,2 【答案】A accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan 6. (2011江苏常州,6,2分)如图,在Rt?ABC中，?ACB=90?,CD?AB,垂足为D.若AC=,BC=2,则sin?ACD的值为( ) 525255A. B. C. D. 3325【答案】A 7. (2011江苏常州,7,2分)在平面直角坐标系中,正方形ABCD的顶点坐标分别为A(1,1),B(1,-1),C(-1,-1),D(-1,1),y轴上有一点P(0,2).作点P关于点A的对称点,作点关PP11于点B的对称点,作点关于点C的对称点,作点关于点D的对称点,作点关PPPPPP223344于点A的对称点,作点关于点B的对称点,按此操作下去,则点的坐标为PPPP5562011( ) A.(0,2) B. (2,0) C. (0,-2) D.(-2,0) 【答案】D 12yxx,，,8. (2011江苏常州,8,2分)已知二次函数,当自变量x取m时,对应的函数值大5于0,当自变量x分别取m-1,m+1时对应的函数值yy、y,则必值,y满足 ( ) 1212yyyyA. >0,y>0 B. <0,y<0 C.<0,y>0 D.>0,y<0 12121212【答案】B 二、填空题(本大题共有9小题,第9小题4分,其余8小题每小题2分,共20分,不需要写出解答过程) 0111,9. (2011江苏常州,9,2分)计算:-(-)=_;=_;=_; ,222,11,=_. ,2,accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan 11【答案】,1,-2 2222x，110. (2011江苏常州,10,2分)计算:=_;分解因式:=_. x,9，2【答案】,(x+3)(x-3) xx，2111. (2011江苏常州,11,2分)?的补角是120?,则?=_,sin=_. 3【答案】60?， 2212. (2011江苏常州,12,2分)已知关于x的方程的一个根为2,则m=_,另一xmx，,60根是_. 【答案】1，,3 13. (2011江苏常州,13,2分)已知扇形的圆心角为150?，它所对应的弧长为20cm,则此扇形的2半径是_cm面积是_cm.(结果保留) 【答案】24，240 14. (2011江苏常州,14,2分)某市2007年5月份某一周的日最高气温(单位:?)分别为:25,28,30,29,31,32,28,这周的日最高气温的平均值是_?,中位数是_?. 【答案】29 29 15. (2011江苏常州,15,2分)如图,DE是?O的直径,弦AB?DE,垂足为C,若AB=6,CE=1,则OC=_,CD=_. 【答案】4，9 16. (2011江苏常州,16,2分)已知关于x的一次函数y=kx+4k-2(k?0).若其图象经过原点,则k=_;若y随x的增大而减小,则k的取值范围是_. 1【答案】; k<0 217. (2011江苏常州,17,4分)把棱长为4的正方体分割成29个棱长为整数的正方体(且没有剩余),其中棱长为1的正方体的个数为_. 【答案】24 三、解答题(本大题花共2小题,共18分.解答应写出演算的步骤) accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan 21x1318. (2011江苏常州,18,8分) (1)计算:sin45?; (2)化简: ,，82xx,42222【答案】(1)原式=2. -2，2222xx，,xxxx，,，,2222，(2)原式= 221xx,xxx，,，222，239. (2011江苏常州,19,10分)1 (1)解分式方程:; ,xx，,22xx,，26(), (2)解不等式组: ,5(1)64(1).xx,，,【答案】(1)去分母，得2(x-2)=3(x+2) 解，x=-10 经检验:x=-10是原方程的解。 (2)解不等式?得x>-4. 得x?15 解不等式?原不等式组的解集是x?15。 四、解答题(本大题共2小题,共15分,解答应写出文字说明或演算步骤) 20. (2011江苏常州,20,7分)某中学为了解决本校学生对球类运动的爱好情况,采用抽样的方法,从足球、篮球、排球、其它等四个方面调查了若干名学生,并绘制成“折线统计图”与“扇形统计图”.请你根据图中提供的部分信息解答下列问题: (1)在这次调查活动中,一共调查了_名学生; (2) “足球”所在扇形的圆心角是_度; (3)补全折线统计图 【答案】(1)100;(2)108?;(3)略 21. (2011江苏常州,21,8分)甲、乙、丙三个布袋都不透明,甲布袋中装有1个红球和1个白球;乙布袋中装有1个红球和2个白球;丙布袋中装有2个白球,这些球除颜色外都相同,从这匹个布袋中各随机地取出1个小球. (1)取出的说个小球恰好是2个红球和1个白球概率是多少? (2)取出的说个小球恰好全是白球的概率是多少? accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan 【答案】 (1)从树状图可以看出，所有可能出现的结果共有12个，恰好是2个红球和1个白球的结21果有2种，所以这个事件的概率是=; 12641=(2)3个球恰好全是白球的概率是。 123五、解答题(本大题共2小题,共12分.解答应写出证明过程) 22. (2011江苏常州,22,5分)已知:如图,在?ABC中,D为BC上的一点,AD平分?EDC,且?E=?B,ED=DC. 求证:AB=AC 【答案】证明?AD平分?EDC,?ADE=?ADC,又DE=DC,AD=AD,?ADE?ADC, ?E=?C,又?E=?B, ?B =?C, ?AB=AC. 23. (2011江苏常州,23,7分)已知:如图,在梯形ABCD中AB?CD,BC=CD,AD?BD,E为AB中点, 求证:四边形BCDE是菱形. 【答案】证明:?AD?BD， ?ADB=90?。 11又E为AB中点，?DE=AB,BE=AB, ?DE=BE 22accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded specification for construction and acceptance of oil tank 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98 compressor, fan ? DBE =?EDB 又AB?CD, ? BDC =?EDB ?BC=CD, ?DBC =?DBC ?BC?DE. ?EB?CD ?四边形BCDE是平行四边形 ?BC=CD ?四边形BCDE是菱形。 六探究与画图(本大题共2分,共13分) 324. (2011江苏常州,24,7分)如图,在?ABO中,已知点A(,3),B(-1,-1),O(0,0),正比例y=-x的图象是直线l,直线AC?x轴交直线l于点C. (1)C点坐标为_; (2)以点O为旋转中心,将?ABO顺时针旋转角a(0?<a<180?),使得点B落在直线l上的对应点,AOBBA为,点A的对应点为,得到?. ?a=_; ,AOB; ?画出?(3)写出所有满足?DOC?AOB的点D的坐标. 3333【答案】(1)C点坐标为(-3，3);(2)?=90?略 (3)D(9,-), D(,-9). 1225. (2011江苏常州,25,6分)已知:如图1,图形?满足:AD=AB,MD=MB, ?A=72?, ?M=144?.图形?与图形?恰好拼成一个菱形(如图2).记作AB的长度为a,BM的长度为b. (1)图中?中?B=_度,图中?中?E=_度. (2)小明有两种纸片各若干张,其中一种纸片的形状及大小与图形?相同,这咱纸片称为“风筝一号”另一种纸片的形状及大小与图形?相同,这种纸片称为“飞镖一号”. ?小明仅有“,风筝一号”纸片拼成一个边长为b的正十边形,需要这种纸片_张; ?小明用若干张“风筝一号”和 “飞镖一号”纸片拼成一个“大风筝”(如图3),其中 ?P=72?, ?Q=144?,PI=PJ=a+b,IQ=JQ.请你在图中画出拼接线并保留画图痕迹.(本题中均为无重叠、无缝隙拼接) accident and the responsibility of leadership, such as concerning administrative sanctions should be dealt with by the personnel Department of the company. (3) personal injury accident occurs, the direct punishment 500-1000, who is directly responsible for the accident responsibility, give notice of criticism and 50-100 economic sanctions against them. (4) to conceal the accident, reported without undue delay or false, to inform the administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of fie
