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2010年云南高中(中专)招生统一考试数学(全卷三个大题,共23个小题,共6页;满分120分,考试用时120分钟)注意事项:1.本卷为试题卷,考生必须在答题卷上解题作答,答案书写在答题卷相应位置上,在试题卷、草稿纸上作答无效.2.考试结束后,请将试题卷和答题卷一并交回.一、选择题(本大题共7小题,每小题只有一个正确先项,每小题3分,满分21分)1.下列结论错误的是A.42B.方程240x的解为2xC.22()()abababD.22xyxy2.下列图形是轴对称图形的是[来源:学,科,网Z,X,X,K]3.下列运算正确的是A.235xxx·B.222()ababC.235()aaD.235aaa4.下列事件中是必然事件的是A.一个直角三角形的两个锐角分别是40°和60°B.抛掷一枚硬币,落地后正面朝上C.当x是实数时,20x≥D.长为5cm、5cm、11cm的三条线段能围成一个三角形5.某物体的三视图如图1所示,那么该物体的形状是A.圆柱B.球C.正方体D.长方体6.如图2,ABCD∥,EFAB于E,EF交CD于F,已知230°,则1是A.B.C.D.图1图2A.20°B.60°C.30°D.45°7.二次函数2yaxbxc的图象如图3所示,则下列结论正确的是A.200040abcbac,,,B.200040abcbac,,,C.200040abcbac,,,D.200040abcbac,,,二、填空题(本大题共8小题,每小题3分,满分24分)8.3的相反数是__________.9.计算:0(3)1__________.10.分解因式:234abab__________.11.如图4,上海世博会的中国馆建筑外观以“东方之冠,鼎盛中华,天下粮仓,富庶百姓”为构思主题,建筑面积4.6457万平方米,保留两个有效数字是__________万平方米.12.不等式1302x≤的解集为_________.13.如图5,O⊙的弦8AB,M是AB的中点,且OM为3,则O⊙的半径为_________.14.如果两个相似三角形的一组对应边分别为3cm和5cm,且较小三角形的周长为15cm,则较大三角形的周长为__________cm.15.某种火箭被竖直向上发射时,它的高度(m)h与时间(s)t的关系可以用公式2515010htt表示.经过________s,火箭达到它的最高点.三、解答题(本大题共8小题,满分75分)16.(7分)先化简再求值:239242xxxx,其中5x.图3图4图517.(8分)如图6,ABCD的两条对角线AC、BD相交于点O.(1)图中有哪些三角形是全等的?(2)选出其中一对全等三角形进行证明.18.(8分)水是生命之源,水是希望之源,珍惜每一滴水,科学用水,有效节水,就能播种希望.某居民小区开展节约用水活动,3月份各户用水量均比2月份有所下降,其中的20户、120户、60户节水量统计如下表:户数2012060节水量(立方米/每户)22.53(1)节水量众数是多少立方米?(2)该小区3月份比2月份共节约用水多少立方米?(3)该小区3月份平均每户节约用水多少立方米?19.(9分)全球变暖,气候开始恶化,中国政府为了对全球气候变暖负责任,积极推进节能减排,在全国范围内从2008年起,三年内每年推广5000万只节能灯.居民购买节能灯,国家补贴50%购灯费.某县今年推广财政补贴节能灯时,李阿姨买了4个8W和3个24W的节能灯,一共用了29元,王叔叔买了2个8W和2个24W的节能灯,一共用了17元.求:(1)该县财政补贴50%后,8W、24W节能灯的价格各是多少元?(2)2009年我省已推广通过财政补贴节能灯850万只,预计我省一年可节约电费2.3亿元左右,减排二氧化碳43.5万吨左右,请你估算一下全国一年大约可节约电费多少亿元?大约减排二氧化碳多少万吨?(结果精确到0.1)[来源:Z.xx.k.Com]图620.(8分)小颖为学校联欢会设计了一个“配紫色”的游戏;下面是两个可以自由转动的转盘,每个转盘被分成面积相等的几个扇形,游戏者同时转动两个转盘,如果转盘A转出了红色,转盘B转出了蓝色,那么他就赢了,因为红色和蓝色在一起配成了紫色.(1)利用树状图或列表的方法表示出游戏所有可能出现的结果;(2)游戏者获胜的概率是多少?21.(10分)云南2009年秋季以来遭遇百年一遇的全省性特大旱灾,部分坝塘干涸,小河、小溪断流,更为严重的情况是有的水库已经见底,全省库塘蓄水急剧减少,为确保城乡居民生活用水,有关部门需要对某水库的现存水量进行统计,以下是技术员在测量时的一些数据:水库大坝的横截面是梯形ABCD(如图7所示),ADBC∥,EF为水面,点E在DC上,测得背水坡AB的长为18米,倾角30B°,迎水坡CD上线段DE的长为8米,120ADC°.(1)请你帮技术员算出水的深度(精确到0.01米,参考数据31.732≈);(2)就水的深度而言,平均每天水位下降必须控制在多少米以内,才能保证现有水量至少能使用20天?(精确到0.01米)A盘B盘图722.(11分)在如图8所示的方格图中,每个小正方形的顶点称为“格点”,且每个小正方形的边长均为1个长度单位,以格点为顶点的图形叫做“格点图形”,根据图形解决下列问题:(1)图中格点ABC△是由格点ABC△通过怎样变换得到的?(2)如果建立直角坐标系后,点A的坐标为(5,2),点B的坐标为(50),,请求出过A点的正比例函数的解析式,并写出图中格点DEF△各顶点的坐标.23.(14分)如图9,已知直线l的解析式为6yx,它与x轴、y轴分别相交于A、B两点,平行于直线l的直线n从原点O出发,沿x轴正方向以每秒1个单位长度的速度运动,运动时间为t秒,运动过程中始终保持nl∥,直线n与x轴,y轴分别相交于C、D两点,线段CD的中点为P,以P为圆心,以CD为直径在CD上方作半圆,半圆面积为S,当直线n与直线l重合时,运动结束.(1)求A、B两点的坐标;(2)求S与t的函数关系式及自变量t的取值范围;(3)直线n在运动过程中,①当t为何值时,半圆与直线l相切?②是否存在这样的t值,使得半圆面积12ABCDSS梯形?若存在,求出t值,若不存在,说明理由.[来源:Zxxk.Com]图8图9(1)图9(2)备用图2010云南中考数学答案一、选择题:1.D2.B3.A4.C5.D6.B7.D二、填空题:8.39.210.(34)aba11.4.612.6x≤13.514.2515.15三、解答题:16.解:239242xxxx232249xxxx·322(2)(3)(3)xxxxx·12(3)x····································································································5分当5x时,原式112(53)4·································································7分17.解:(1)AOBCOD△≌△、AODCOB△≌△、ABDCDB△≌△、ADCCBA△≌△·························································································4分(2)以AOBCOD△≌△为例证明,四边形ABCD是平行四边形,OAOCOBOD,.在AOB△和COD△中,OAOCAOBCODOBOD,,.AOBCOD△≌△.······················································································8分18.解:(1)节水量的众数是2.5立方米.·························································2分(2)该小区3月份比2月份共节约用水:2202.5120360520(立方米).·······················································5分(3)该小区3月份平均每户节约用水:2202.51203602012060x2.6(立方米).··················································8分19.解:(1)设8W节能灯的价格为x元,24W节能灯的价格为y元.···················1分则43292217xyxy,①.②··················································································2分解之3.55xy,.································································································4分答:该县财政补贴50%后,8W节能灯的价格为3.5元,24W节能灯的价格为5元.···················································································································5分(2)全国一年大约可节约电费:2.3500013.5850≈(亿元)·································7分大约减排二氧化碳:43.55000255.9850≈(万吨)·············································9分20.解:(1)用树状图表示:···············································································································4分[来源:学+科+网]所有可能结果:(红、黄),(红、绿),(红、蓝),(白、黄),(白、绿),(白、蓝)····6分(或)用列表表示:黄绿蓝红(红,黄)(红,绿)(红,蓝)白(白,黄)(白,绿)(白,蓝)(2)P(获胜)=16.···················································································8分21.解:分别过A、D作AMBC于M、DNBC于N,·····························1分在RtABM△中,30B°,192AMAB.ADBCAMBCDNBC∥,,,9AMDN.························································································2分DNBC,DNAD,90ADN°.1209030CDNADCADN°°°.延长FE交DN于H.在RtDHE△中,cosHDEDHDE,cos308DH°,A盘B盘38432DH,·················································································6分943941.7322.07HNDNDH≈.(米)··········
本文标题:2010年云南省中考数学试卷及答案(word版)
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