张家界市中考数学试题

张家界市2009年中考数学试题及答案张家界市2009年中考数学试题及答案张家界市2009年中考数学试题及答案精选文档你我共享张家界市2009年初中毕业学业考试一试卷数学考生注意：本学科试卷共三道大题25小题，满分120分，考试时量120分钟．一、选择题（本大题共8小题，每题3分，满分24分）1．在实数0，2，1），，π中，无理数有（3A．1个B．2个C．3个D．4个2．用计算器求23值时，需接踵按“2”，“∧”，“3”，“”键，若小红接踵按“”，“2”，“∧”，“4”，“”键，则输出结果是（）A．4B．5C．6D．163．以下图所示的几何体的主视图是（）A．B．C．D．4x75(x1)4．不等式组246的解集在数轴上表示为（）2x3x06060606A．B．C．D．5．以下运算正确的选项是（）A．2ab2ab21B．tan45°sin45°1C．x2xx3D．(a2)3a56．以下不是必定事件的是（）．两直线订交，对顶角相等B．三角形的外心到三个极点的距离相等C．三角形随意两边之和大于第三边ED．两相像多边形面积的比等于周长的比7．如图，AB∥CD，且1115°，A75°，C1则E的度数是（）DA．30°B．50°ABC．40°D．60°8．为了预防“HINI”流感，某校正教室进行药熏消毒，药品焚烧时，室内每立方米的含药量与时间成正比；焚烧后，室内每立方米含药量与时间成反比，则消毒过程中室内每立方米含药量y与时间t的函数关系图象大概为（）知识改变命运精选文档你我共享yyyyOtOtOtOtA．B．C．D．二、填空题（本大题共8小题，每题3分，满分24分）A9．3的绝对值为．EFO10．如图，O是△ABC的内切圆，与边BC，CA，ABBC的切点分别为D，E，F，若A70°，则EDF．D11．张家界国际农村音乐周活动中，来自中、日、美的三名音乐家准备在同一节目中挨次演奏本国的民族音乐，若他们出场先后的时机是均等的，则按“美—日—中”次序演奏的概率是．12．将函数y3x3的图象向上平移2个单位，获得函数的图象．13．分解因式a3ab2．14．我市甲、乙两景点今年5月上旬每日招待旅客的人数如下图，甲、乙两景点日招待游客人数的方差大小关系为：S甲2S乙2．人数28002600甲24002200乙2000180012345678910日15abbaab，在此定义下，若9x55，则x的．关于正实数a，b作新定义：值为．．如图，等腰梯形ABCD中，AD∥BC，且AD1，E为AD上一点，AC与BE16BC2交于点F，若AE:DE2:1，则△AEF的面积AED．△CBF的面积F三、解答题（此题共9小题，满分72分）BC17．（本小题6分）1(53)2sin45计算11°°122知识改变命运精选文档你我共享18．（本小题6分）小明将一幅三角板如下图摆放在一同，发现只需知道此中一边的长就能够求出其余各边的长，若已知CD2，求AC的长．DBAC19．先化简，后求值（本小题6分）421a24a2此中a22a220．（本小题6分）在成立平面直角坐标系的方格纸中，每个小方格都是边长为1的小正方形，△ABC的极点均在格点上，点P的坐标为(10)，，请按要求绘图与作答1）把△ABC绕点P旋转180°得△ABC．2）把△ABC向右平移7个单位得△ABC．（3）△ABC与△ABC能否成中心对称，假如，找出对称中心P，并写出其坐标．yABCPOx21．列方程解应用题（本小题9分）“阳黄公路”开通后，从长沙到武陵源增添了一条新线路，新线路里程在原线路长360Km的基础上缩短了50Km，今有一旅旅客车和小车同时从长沙出发前去武陵源，旅旅客车走新线路，小车因故走原线路，半途逗留6分钟．若小车速度是旅旅客车速度的1.2倍，且两车同时抵达武陵源，求两车的速度各是多少？知识改变命运精选文档你我共享22．（本小题9分）如图，有两个动点E，F分别从正方形ABCD的两个极点B，C同时出发，以同样速度分别沿边BC和CD挪动，问：1）在E，F挪动过程中，AE与BF的地点和大小有何关系？并赐予证明．2）若AE和BF订交点O，图中有多少对相像三角形？请把它们写出来．DFCEOAB23．（本小题9分）我市今年初三体育考试结束后，从某县3000名参照学生中抽取了100名考生成绩进行统计剖析（满分100分，记分均为整数），获得如下图的频数散布直方图，请你依据图形达成以下问题：（1）本次抽样的样本容量是．2）请补全频数散布直方图．3）若80分以上（含80分）为优异，请你据此．估量该县本次考试的优异人数．人数403030202010352分数10024．（本小题9分）有若干个数，第1个数记为a1，第2个数记为a2，第3个数记为a3，第n个数记为an，若a11，从第二个数起，每个数都等于1与前面那个数的差的倒数．3．．．．．．．．．．．．．．．．．．．．．．．．．（1）分别求出a2，a3，a4的值．（2）计算a1a2a3a36的值．知识改变命运精选文档你我共享25．（本小题12分）在平面直角坐标系中，已知A(4，0)，B(10)，，且以AB为直径的圆交y轴的正半轴于点C(0，2)，过点C作圆的切线交x轴于点D．1）求过A，B，C三点的抛物线的分析式2）求点D的坐标3）设平行于x轴的直线交抛物线于E，F两点，问：能否存在以线段恰巧与x轴相切？若存在，求出该圆的半径，若不存在，请说明原因？A4

EF为直径的圆，yC2BDO1x知识改变命运精选文档你我共享张家界市2009年初中毕业学业考试数学试卷答案一、选择题1．B2．A3．B4．A5．C6．D7．C8．A二、填空题．310．55°．112．y3x59116113．a(ab)(ab)14．S甲2S乙215．1616．9三、解答题17．原式212121·······························3分221212212(21)··········································4分21221···········································5分······················································6分18．解：BDCD2BC222222······································2分ABx，则AC2xx2(22)2(2x)2··········································4分x26分················································534AC2AB6···············································6分319．解：原式421(a2)(a2)a2a242(a2)a2(a2)(a2)(a2)(a2)(a······················2分2)(a2)42(a2)(a2)··········································3分(a2)(a2)1······················································4分a2当a22时11a1221知识改变命运1

精选文档你我共享21···············································6分2120．注：每问2分yAABCBCPOPxBA3），0)21．解：设旅旅客车速度为xKm/h，则小车为Km/h·····················1分36013101.2x10··············································3分x解方程得x100·············································7分经查验x120是方程的根，且合题意1.2100120Km/时·················8分答：小车的均匀速度为120Km/时·····································9分22．解：（1）在正方形ABCD中，ABBC，ABCBCD90°BECF···············································1分ABE≌△BCF（SAS）······································2分EABFBC··············································3分CBFABO90°·······································4分EABABO90°在△ABO中，AOB180°(EABABO)90°AEBF···············································6分（2）有5对相像三角形·········································7分△ABO∽△BEO△ABO∽△AE△BE∽△OBF△ABE∽△BCF△AB∽△OB·······························F9分23．（1）100··············································2分2）······················································5分3）30000.61800该县优异人数约为1800人······································9分人数404030302010

20523分数39.549.559.569.579.589.5100知识改变命运精选文档你我共享24．解：（1）a211314································2分4133a3114···············································4分31144a411··············································6分431（2）a1a2a3a3614353······················9分312425．解：（1）令二次函数yax2bxc，则16a4bc0abc0·············································1分c21a23················································2分2c2过A，B，C三点的抛物线的分析式为y123·················分xx2422（2）以AB为直径的圆圆心坐标为O3，253··········································5分OCOO22CD为圆O切线OCCD····································6分OCDDCO90°COOOCO90°COODCO△OCO∽△CDOOO/OCOC/OD····························8分3/22/ODOD8238D坐标为0，·····························