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1、9-2013广东广州中考数学真题及答案2013年广州市初中毕业生学业考试数学 满分150分。考试用时120分钟 一、选择题: 1,21、比0大的数是( )A -1 B C 0 D 1 2、图1所示的几何体的主视图是( ) (D)正面 (C)(A)(B) 3、在66方格中，将图2?中的图形N平移后位置如图2?所示，则图形N的平移方法中，正确的是( ) A 向下移动1格 B 向上移动1格 C 向上移动2格 D 向下移动2格 236625232mn4、计算:的结果是( )A B C D mnmnmnmn，5、为了解中学生获取资讯的主要渠道，设置“A:报纸，B:电视，C:网络，D:身边的人，E:其他”
2、五个选项(五项中必选且只能选一项)的调查问卷，先随机抽取50名中学生进行该问卷调查，根据调查的结果绘制条形图如图3，该调查的方式是( )，图3中的a的值是( ) A 全面调查，26 B全面调查，24 C 抽样调查，26 D全面调查，24 6、已知两数x,y之和是10，x比y的3倍大2，则下面所列方程组正确的是( ) xy，,10xy，,10xy，,10xy，,10,A B C D ,yx,，32yx,32xy,，32xy,32,02.5aa,2.57、实数a在数轴上的位置如图4所示，则=( ) 图4a,2.52.5,aa，2.5,a2.5A B C D x8、若代数式有意义，则实数x的取值范围
3、是( ) x,1advantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted investment promotion several times. Industry-led unit and various town streets are developing detailed promotion plans, the basis of what is specific to each industry, h
4、as formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location, focus on the development of the kind of industries. Four stroke technology and science. Determinants of technology is the Countys economic development through scientific and te
5、chnological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent is the city center citys first resource, is the primary industry development, and revitalization of the social protection. So, in terms of skills: t
6、o catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research cooperation, using advanced technology to increase the added value of their products to ensure that introduction of transforming scientific and technological achievements duri
7、ng the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation of talent, efforts to increase vocational education and training and meet the basic demand of enterprise development. Then introduced a number of the
8、 county needed scarce education, health professionals, meet social development needs to invest more in machinery, pharmaceutical manufacturing research and development in higher education, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation, . .
9、Food research station platform, to the XX University to find experts A B C D x,1x,0x,0xx,01且29、若，则关于x的一元二次方程的根的情况是( ) 5200k，,xxk，,40A 没有实数根 B有两个相等的实数根 C有两个不相等的实数根 D无法判断 10、如图5，四边形ABCD是梯形，AD?BC，CA是的平分线，且，BCDABACABAD,4,6,则=( ) tanBDA1155 A B C D 232244CB 图5二(填空题(本大题共6小题，每小题3分，满分18分) 11.点P在线段AB的垂直平分线上，
10、PA=7,则PB=_ . 12.广州某慈善机构全年共募集善款5250000元，将5250000用科学记数法表示为_ . 213.分解因式:_. x，xy,yxmy,(m，2)x，1,一次函数若随的增大而增大，则的取值范围是14(2013广州)._ . Rt,ABCRt,ABC15(2013广州).如图6，的斜边AB=16, 绕点OA,Rt,ABCRt,ABCAB顺时针旋转后得到，则的斜边上的中线,CD的长度为_ . BC AO Cy 16(2013广州).如图7，在平面直角坐标系中，点O为坐B图6x,P标原点，点P在第一象限，与轴交于O,A两点，点APx,P的坐标为(6,0)，的半径为，则点P
11、的坐标为 13AO( 6, 0 )_. 图7 三(解答题(本大题共9小题，满分102分，解答应写出文字说明，证明过程或演算步骤) 17.(本小题满分9分) 2x,10x，9,0解方程:. 18(2013广州本小题满分9分)如图8，四边形ABCD是菱形，对角线AC与BD相交于O, advantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted investment promotion several times. I
12、ndustry-led unit and various town streets are developing detailed promotion plans, the basis of what is specific to each industry, has formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location, focus on the development of the kind of indu
13、stries. Four stroke technology and science. Determinants of technology is the Countys economic development through scientific and technological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent is the city cent
14、er citys first resource, is the primary industry development, and revitalization of the social protection. So, in terms of skills: to catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research cooperation, using advanced technology to i
15、ncrease the added value of their products to ensure that introduction of transforming scientific and technological achievements during the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation of talent, effort
16、s to increase vocational education and training and meet the basic demand of enterprise development. Then introduced a number of the county needed scarce education, health professionals, meet social development needs to invest more in machinery, pharmaceutical manufacturing research and development
17、in higher education, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation, . . Food research station platform, to the XX University to find experts DOACB 图8 AB=5,AO=4,求BD的长. 22xy19(2013广州本小题满分10分)先化简，再求值:，其中,x,yx,yx,1，23,y,1,23.20.(2013广州本小题满分10分)
18、 已知四边形ABCD是平行四边形(如图9)，把?ABD沿对角线BD翻折180?得到?ABD. A，1， 利用尺规作出?ABD.，要求保留作图痕迹,不写作法，; D(2)设D A 与BC交于点E，求证:?BAE?DCE. BC21.(本小题满分12分) 图9在某项针对18,35岁的青年人每天发微博数量的调查中，设一个人的“日均发微博条数”为m，规定:当m?10时为A级，当5?m,10时为B级，当0?m,5时为C级.现随机抽取30个符合年龄条件的青年人开展每人“日均发微博条数”的调查，所抽青年人的“日均发微博条数”的数据如下: 11 10 6 15 9 16 13 12 0 8 2 8 10 17
19、 6 13 7 5 7 3 12 10 7 11 3 6 8 14 15 12 (1) 求样本数据中为A级的频率; (2) 试估计1000个18,35岁的青年人中“日均发微博条数”为A级的人数; (3) 从样本数据为C级的人中随机抽取2人，用列举法求抽得2个人的“日均发微博条数”都是3的概率. 22.(2013广州本小题满分12分) 如图10， 在东西方向的海岸线MN上有A、B两艘船，均收到已触礁搁浅的船P的求救信号，已知船P在船A的北偏东58?方向，船P在船B的北偏西35?方向，AP的距离为30海里. 北(1) 求船P到海岸线MN的距离(精确到0.1海里); 东P(2) 若船A、船B分别以2
20、0海里/小时、15海里/小时的速度同时出发，匀速直线前往救援，试通过计算判断哪艘船先到达船P处. ABNM 图1023.(2013广州本小题满分12分) y如图11，在平面直角坐标系中，点O为坐标原点，正方形OABCBDC的边OA、OC分别在x轴、y轴上，点B的坐标为(2,2)，反advantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted inve数学试卷 第3页 (共5页) stment promotion
21、several times. Industry-led unit and various town streets are developing detailed promotion plans, the basis of what is specific to each industry, has formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location, focus on the development of
22、the kind of industries. Four stroke technology and science. Determinants of technology is the Countys economic development through scientific and technological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent
23、is the city center citys first resource, is the primary industry development, and revitalization of the social protection. So, in terms of skills: to catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research cooperation, using advanced
24、 technology to increase the added value of their products to ensure that introduction of transforming scientific and technological achievements during the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation o
25、f talent, efforts to increase vocational education and training and meet the basic demand of enterprise development. Then introduced a number of the county needed scarce education, health professionals, meet social development needs to invest more in machinery, pharmaceutical manufacturing research
26、and development in higher education, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation, . . Food research station platform, to the XX University to find expertsxAO图11k比例函数(x,0，k?0)的图像经过线段BC的中点D. y,x(1)求k的值; (2)若点P(x,y)在该反比例函数的图像上运动(不与点D重合)，过点P作
27、PR?y轴于点R,作PQ?BC所在直线于点Q，记四边形CQPR的面积为S，求S关于x的解析式并写出x的取值范围。 24.(2013广州本小题满分14分) 已知AB是?O的直径，AB=4，点C在线段AB的延长线上运动，点D在?O 上运动(不与点B重合)，连接CD，且CD=OA. (1)当OC=时(如图12)，求证:CD是?O的切线; 22(2)当OC,时，CD所在直线于?O相交，设另一交点为E，连接AE. 22?当D为CE中点时，求?ACE的周长; ?连接OD,是否存在四边形AODE为梯形,若存在，请说D明梯形个数并求此时AE?ED的值;若不存在，请说明理由。 ACBO (1)证明:连接OD，如
28、答图?所示( 由题意可知，CD=OD=OA= 图121 2 AB=2，OC=2 2 ， 222?OD+CD=OC 由勾股定理的逆定理可知，?OCD为直角三角形，则OD?CD， 又?点D在?O上， ?CD是?O的切线( (2)解:?如答图?所示，连接OE，OD，则有CD=DE=OD=OE， ?ODE为等边三角形，?1=?2=?3=60?; ?OD=CD，?4=?5， advantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, ta
29、rgeted investment promotion several times. Industry-led unit and various town streets are developing detailed promotion plans, the basis of what is specific to each industry, has formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location,
30、focus on the development of the kind of industries. Four stroke technology and science. Determinants of technology is the Countys economic development through scientific and technological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve l
31、eapfrog development. Talent is the city center citys first resource, is the primary industry development, and revitalization of the social protection. So, in terms of skills: to catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research
32、 cooperation, using advanced technology to increase the added value of their products to ensure that introduction of transforming scientific and technological achievements during the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must
33、strengthen the cultivation of talent, efforts to increase vocational education and training and meet the basic demand of enterprise development. Then introduced a number of the county needed scarce education, health professionals, meet social development needs to invest more in machinery, pharmaceut
34、ical manufacturing research and development in higher education, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation, . . Food research station platform, to the XX University to find experts ?3=?4+?5，?4=?5=30?， ?EOC=?2+?4=90?， 因此?EOC是含30度角的直角三角形，
35、?AOE是等腰直角三角形( 2 在Rt?EOC中，CE=2OA=4，OC=4cos30?=3 ， 在等腰直角三角形AOE中，AE= 2 OA=2 2 ， ?ACE的周长为:AE+CE+AC=AE+CE+(OA+OC)=2 2 +4+(2+2 3 )=6+2 2 +2 3 ( ?存在，这样的梯形有2个( 答图?是D点位于AB上方的情形，同理在AB下方还有一个梯形，它们关于直线AB成轴对称( ?OA=OE，?1=?2， ?CD=OA=OD，?4=?5， ?四边形AODE为梯形，?OD?AE，?4=?1，?3=?2， ?3=?5=?1， 在?ODE与?COE中， ?OEC,?OEC ?3,?5 ad
36、vantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted inve数学试卷 第5页 (共5页) stment promotion several times. Industry-led unit and various town streets are developing detailed promotion plans, the basis of what is specific to each indust
37、ry, has formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location, focus on the development of the kind of industries. Four stroke technology and science. Determinants of technology is the Countys economic development through scientific a
38、nd technological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent is the city center citys first resource, is the primary industry development, and revitalization of the social protection. So, in terms of skil
39、ls: to catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research cooperation, using advanced technology to increase the added value of their products to ensure that introduction of transforming scientific and technological achievements
40、 during the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation of talent, efforts to increase vocational education and training and meet the basic demand of enterprise development. Then introduced a number o
41、f the county needed scarce education, health professionals, meet social development needs to invest more in machinery, pharmaceutical manufacturing research and development in higher education, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation,
42、 . . Food research station platform, to the XX University to find experts?ODE?COE， 则有 OE CE , DE OE 22，?CEDE=OE=2=4( ?1=?5，?AE=CE， ?AEDE=CEDE=4( 综上所述，存在四边形AODE为梯形，这样的梯形有2个，此时AEDE=4( 25、(2013广州本小题满分14分) 2已知抛物线y=过点A(1,0)，顶点为B，且抛物线不经过第三象限。 axbxcaac，,(0,)1(1)使用a、c表示b; (2)判断点B所在象限，并说明理由; c,8b，(3)若直线y=2x+
43、m经过点B，且于该抛物线交于另一点C(),求当x?1时y的取12a值范围。 2013广州中考数学参考答案: advantages, facing the Yangtze River Delta, Pearl River Delta, Shandong peninsula, Beijing-Tianjin-Tangshan area, targeted investment promotion several times. Industry-led unit and various town streets are developing detailed promotion plans, the
44、 basis of what is specific to each industry, has formed a kind of scale, need to bring in the kind of projects each town street has the kind of resources, what location, focus on the development of the kind of industries. Four stroke technology and science. Determinants of technology is the Countys
45、economic development through scientific and technological innovation, improve product value-added and improve economic competitiveness, is the inevitable way to achieve leapfrog development. Talent is the city center citys first resource, is the primary industry development, and revitalization of th
46、e social protection. So, in terms of skills: to catch . Competitive. Encouraging enterprises to actively undertake science and technology projects, strengthening research cooperation, using advanced technology to increase the added value of their products to ensure that introduction of transforming
47、scientific and technological achievements during the year . . New research enterprises . . Home, creating innovative platforms . . Generic classifier. In: first, we must strengthen the cultivation of talent, efforts to increase vocational education and training and meet the basic demand of enterpris
48、e development. Then introduced a number of the county needed scarce education, health professionals, meet social development needs to invest more in machinery, pharmaceutical manufacturing research and development in higher education, such as the introduction of talent to meet the need. Third, we must rely on . . Post-doctoral workstation, .