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1、2010汕头中考数学试卷(含答案)2010年广东省汕头市初中毕业生学业考试 数 学 一、选择题(本大题8小题，每小题4分，共32分)在每小题列出的四个选项中，只有一个是正确的，请把答题卡上对应题目所选的选项涂黑( 1(,3的相反数是(A) 11A(3 B( C(,3 D( ,332.下列运算正确的是(C) A A(3 B( 2a，3b,5ab，22a,b,4a,b1C D 22222C( D( ，a，ba,b,a,b，a，b,a，b(E B 3(如图，已知?1 = 70，如果CD?BE，那么?B的度数为(C) 第3题图 A(70 B(100 C(110 D(120 4(某学习小组7位同学，为玉
2、树地重灾区捐款，捐款金额分别为5元，10元，6元，6元，7元，8元，9元，则这组数据的中位数与众数分别为(B) 6，6 B(7，6 C(7，8 D(6，8 A(5(左下图为主视图方向的几何体，它的俯视图是(D) A( B( C( D( 主视方向 第4题图 6(如图，把等腰直角?ABC沿BD折叠，使点A落在边BC 上的点E处。下面结论错误的是(B) A(AB=BE B(AD=DC C(AD=DE D(AD=EC 2x,5x，4,07. 已知方程的两跟分别为?与?的半径，且OO=3,那么两圆的位置关1212C) 系是(A .相交 B.外切 C.内切 D.相离 2y,8. 已知一次函数的图像与反比例
3、函数的图像的一个交点坐标为(2，1)，y,kx,1x那么另一个交点的坐标是( B ) A.(-2,1) B.(-1,-2) C.(2,-1) D.(-1,2) 二、填空题(本大题5小题，每小题4分，共20分)请将下列各题的正确答案填写在答题卡相应的位置上( 9(据中新网上海6月1日电:世博会开园一个月来，客流平稳，累计至当晚19时，参观者development in order to protect a host of attractions and historical sites, as well as to maintain the economic vitality of the do
4、wntown area. Figure 5.1-5 figure 5.1.4 Washington mass transit network to support implementation of effective transport demand management policies to reduce urban traffic congestion and public transport priority was in the early 1960 of the 20th century by the planners first proposed in Paris, Franc
5、e, and in Europe and other major cities to operate has been the formation of the rich content system. Public transport priority consists of two aspects: one is on the bus to help. . 5.1-7 Park and ride systems 5.1.5 typical case Hong Kong-Japan Sapporo, Sapporo is a Japan Hokkaido central parts of c
6、ities, Japans fifth largest city. Area of 1121km2 in the city, a population of 1.921 million. In addition is the administrative center of Hokkaido, Sapporo is Hokkaidos industrial and commercial center, in 1972, hosted the 11th Winter Olympic Games. 3 JR Sapporo rail transit line 3 metro and 3 tram
7、lines, Sapporo in the urban development process combined with Center of construction of subway construction and residential development, and support the development of the region. Prior to 1971, Sapporo, Japan Hokkaido local Centre in the urban development process, in response to the rapid growth of
8、 the city centre traffic demand, building trams. 1981 years ago for holding the winter Olympic Games as an opportunity to start building connected to the venue and the city centre 6 已超过8000000人次(试用科学记数法表示8000000=810( 2xA 10( 分式方程的解= 1 ( ,1xx，1411( 如图，已知Rt?ABC中，斜边BC上的高AD=4，cosB=， 5B C D 则AC= 5 ( 第11题
9、图 12( 某市2007年、2009年商品房每平方米平均价格分别为4000元、5700元，假设2007年后的两年内，商品房每平方米平均价格的年增长率都为(试列出关于的方xx程: . 13( 如图(1)，已知小正方形ABCD的面积为1，把它的各边延长一倍得到新正方形ABCD;把正方形ABCD边长按原法延长一倍得到正方形ABCD(如图(2);111111112222以此下去?，则正方形ABCD的面积为 625 ( 4444C 2 C1 C1 D D C 1D C D B12 A B D A B B 12B 1 A 1 A1 A 2 第13题图(1) 第13题图(2) 三、解答题(一)(本大题5小题
10、，每小题7分，共35分) 10,114( 计算:( ，4，(,),2cos60:，2,21解:原式 ,，,，,2221422x，4x，42,，x，2x215( 先化简，再求值:，其中=. xx，221解:原式= = x216( 如图，方格纸中的每个小方格都是边长为1个单位的正方形，Rt?ABC的顶点均在个点上，在建立平面直角坐标系后，点A的坐标为(,6，1)，点B的坐标为(,3，1)，点C的坐标为(,3，3)( (1)将Rt?ABC沿x轴正方向平移5个单位得到Rt?ABC，试在图上画出的图形Rt?111ABC，并写出点A的坐标; A的坐标为(-1，1) 11111(2)将原来的Rt?ABC绕点
11、B顺时针旋转90?得到Rt?ABC，试在图上画出Rt?ABC222222的图形( y A2 y C1C C 1A1 C B 2A B 1B A 2B 11-1O-1Ox x development in order to protect a host of attractions and historical sites, as well as to maintain the economic vitality of the downtown area. Figure 5.1-5 figure 5.1.4 Washington mass transit network to support i
12、mplementation of effective transport demand management policies to reduce urban traffic congestion and public transport priority was in the early 1960 of the 20th century by the planners first proposed in Paris, France, and in Europe and other major cities to operate has been the formation of the ri
13、ch content system. Public transport priority consists of two aspects: one is on the bus to help. . 5.1-7 Park and ride systems 5.1.5 typical case Hong Kong-Japan Sapporo, Sapporo is a Japan Hokkaido central parts of cities, Japans fifth largest city. Area of 1121km2 in the city, a population of 1.92
14、1 million. In addition is the administrative center of Hokkaido, Sapporo is Hokkaidos industrial and commercial center, in 1972, hosted the 11th Winter Olympic Games. 3 JR Sapporo rail transit line 3 metro and 3 tram lines, Sapporo in the urban development process combined with Center of constructio
15、n of subway construction and residential development, and support the development of the region. Prior to 1971, Sapporo, Japan Hokkaido local Centre in the urban development process, in response to the rapid growth of the city centre traffic demand, building trams. 1981 years ago for holding the win
16、ter Olympic Games as an opportunity to start building connected to the venue and the city centre 第16题(1)答案 第16题(2)答案 17( 如图，PA与?O相切于A点，弦AB?OP，垂足为C，OP与?O相交于D点，已知OA=2，OP=4( (1)求?POA的度数; B (2)计算弦AB的长( O C (1)答:60? D (2)答: AB,23P A 第17题图 18( 分别把带有指针的圆形转盘A、B分成4等份、3等份的扇形区域，并在每一小区域内标上数字(如图所示)(欢欢、乐乐两人玩转盘游戏，
17、游戏规则是:同时转动两个转盘，当转盘停止时，若指针所指两区域的数字之积为奇数，则欢欢胜;若指针所指两区域的数字之积为偶数，则乐乐胜;若有指针落在分割线上，则无效，需重新转动转盘( (1)试用列表或画树状图的方法，求欢欢获胜的概率; (2)请问这个游戏规则对欢欢、乐乐双方公平吗,试说明理由( 55 (1)答:欢欢获胜的概率 1 93 3 1 52 (2)答:不公平。因为欢欢获胜的概率是; 2 9转盘A 转盘B 4乐乐获胜的概率是。 第18题图 9219( 已知二次函数的图象如图所示，它与x轴的一个交点坐标为(,1，0)，y,x，bx，c与y轴的交点坐标为(0，3)( (1)求出b，c的值，并写出
18、此二次函数的解析式; (2)根据图象，写出函数值y为正数时，自变量x的取值范围( y 2(1)答: bcyxx,，2323，A E ,13x(2)答: 3 D F O ,1 x B C 第20题图 第19题图 development in order to protect a host of attractions and historical sites, as well as to maintain the economic vitality of the3 downtown area. Figure 5.1-5 figure 5.1.4 Washington mass transit n
19、etwork to support implementation of effective transport demand management policies to reduce urban traffic congestion and public transport priority was in the early 1960 of the 20th century by the planners first proposed in Paris, France, and in Europe and other major cities to operate has been the
20、formation of the rich content system. Public transport priority consists of two aspects: one is on the bus to help. . 5.1-7 Park and ride systems 5.1.5 typical case Hong Kong-Japan Sapporo, Sapporo is a Japan Hokkaido central parts of cities, Japans fifth largest city. Area of 1121km2 in the city, a
21、 population of 1.921 million. In addition is the administrative center of Hokkaido, Sapporo is Hokkaidos industrial and commercial center, in 1972, hosted the 11th Winter Olympic Games. 3 JR Sapporo rail transit line 3 metro and 3 tram lines, Sapporo in the urban development process combined with Ce
22、nter of construction of subway construction and residential development, and support the development of the region. Prior to 1971, Sapporo, Japan Hokkaido local Centre in the urban development process, in response to the rapid growth of the city centre traffic demand, building trams. 1981 years ago
23、for holding the winter Olympic Games as an opportunity to start building connected to the venue and the city centre20( 如图，分别以Rt?ABC的直角边AC及斜边AB向外作等边?ACD、等边?ABE(已知?BAC=30，EF?AB，垂足为F，连结DF( (1)试说明AC=EF; (2)求证:四边形ADFE是平行四边形( 解: 333(1)提示: ACABEFAEABACAE,，222000(2)提示:，AD?EF且AD=EF ，,，,，DAFEFA60309021( 某学校组织
24、340名师生进行长途考察活动，带有行李170件，计划租用甲、乙两种型号的汽车10辆(经了解，甲车每辆最多能载40人和16件行李，乙车每辆最多能载30人和20件行李( (1)请你帮助学校设计所有可行的租车方案; (2)如果甲车的租金为每辆2000元，乙车的租金为每辆1800元，问哪种可行方案使租车费用最省, 解: 甲甲甲甲:4:5:6:7,(1)四种方案，分别为: 或或或,乙乙乙乙:6:5:4:3,甲:4,(2) 最便宜，费用为18800元。 ,乙:6,五、解答题(三)(本大题3小题，每小题12分，共36分) 22( 已知两个全等的直角三角形纸片ABC、DEF，如图(1)放置，点B、D重合，点F
25、在BC上，AB与EF交于点G(?C=?EFB=90，?E=?ABC=30，AB=DE=4( (1)求证:?EGB是等腰三角形; (2)若纸片DEF不动，问?ABC绕点F逆时针旋转E 最小_30_度时，四边形ACDE成为以ED为底的梯形E (如图2)(求此梯形的高( G A B A G 解: 0D ？,GEGB(1)提示: F ，,，,EBGE30B(D) C C F 第22题图(1) 第22题图(2) 3(2)梯形的高3-2 23( 阅读下列材料: 112 = (123,012)， 3development in order to protect a host of attractions a
26、nd historical sites, as well as to maintain the economic vitality of the downtown area. Figure 5.1-5 figure 5.1.4 Washington mass transit network to support implementation of effective transport demand management policies to reduce urban traffic congestion and public transport priority was in the ea
27、rly 1960 of the 20th century by the planners first proposed in Paris, France, and in Europe and other major cities to operate has been the formation of the rich content system. Public transport priority consists of two aspects: one is on the bus to help. . 5.1-7 Park and ride systems 5.1.5 typical c
28、ase Hong Kong-Japan Sapporo, Sapporo is a Japan Hokkaido central parts of cities, Japans fifth largest city. Area of 1121km2 in the city, a population of 1.921 million. In addition is the administrative center of Hokkaido, Sapporo is Hokkaidos industrial and commercial center, in 1972, hosted the 11
29、th Winter Olympic Games. 3 JR Sapporo rail transit line 3 metro and 3 tram lines, Sapporo in the urban development process combined with Center of construction of subway construction and residential development, and support the development of the region. Prior to 1971, Sapporo, Japan Hokkaido local
30、Centre in the urban development process, in response to the rapid growth of the city centre traffic demand, building trams. 1981 years ago for holding the winter Olympic Games as an opportunity to start building connected to the venue and the city centre 123 = (234,123)， 3134 = (345,234)， 3由以上三个等式相加
31、，可得 112，23，34= 345 = 20( 3读完以上材料，请你计算下列各题: 1(1) 12，23，34，?，1011(写出过程); ,，,10111244031(2) 12，23，34，?，n(n，1) = ; ，nnn(1)(2)32.正弦：(3) 123，234，345，?，789 = 1260 ( 周 次日 期教 学 内 容24( 如图(1)，(2)所示，矩形ABCD的边长AB=6，BC=4，点F在DC上，DF=2(动点M、N分别从点D、B同时出发，沿射线DA、线段BA向点A的方向运动(点M可运动到DA的延长线上)，当动点N运动到点A时，M、N两点同时停止运动(连接FM、FN，
32、当F、N、M不在同一直线时，可得?FMN，过?FMN三边的中点作?PWQ(设动点M、N的速度都是1个单位/秒，M、N运动的时间为x秒(试解答下列问题: tan1(1)说明?FMN?QWP; (1)三角形的外接圆: 经过一个三角形三个顶点的圆叫做这个三角形的外接圆.(2)设0?x?4(即M从D到A运动的时间段)(试问x为何值时，?PWQ为直角三角形,当x在何范围时，?PQW不为直角三角形, 4、初步学会应用加减法解决生活中简单问题，感受数学在日常生活中的作用,感受加减法与日常生活的密切联系,同时获得一些初步的数学活动经验，发展解决问题和运用数学进行思考的能力。(3)问当x为何值时，线段MN最短,
33、求此时MN的值( F F D D C C (2)扇形定义:一条弧和经过这条弧的端点的两条半径所组成的图形叫做扇形.P W W P M Q A A B B N N Q M 6、增加动手操作的机会，使学生获得正确的图形表象，正确计算一些几何形体的周长、面积和体积。第24题图(1) 第24题图(2) 圆内接四边形的性质: 圆内接四边形的对角互补;解: (1)提示:?PQ?FN，PW?MN ?QPW =?PWF，?PWF =?MNF ?QPW =?MNF 同理可得:?PQW =?NFM或?PWQ =?NFM ?FMN?QWP 定理：在同圆或等圆中,相等的圆心角所对的弧相等、所对的弦相等、所对的弦心距相
34、等。4(2)当时，?PQW为直角三角形; xx,或4344当0?x，x4时，?PQW不为直角三角形。 3394.234.29加与减（二）4 P49-56223，(3) development in order to protect a host of attractions and historical sites, as well as to maintain the economic vitality of the5 downtown area. Figure 5.1-5 figure 5.1.4 Washington mass transit network to support imp
35、lementation of effective transport demand management policies to reduce urban traffic congestion and public transport priority was in the early 1960 of the 20th century by the planners first proposed in Paris, France, and in Europe and other major cities to operate has been the formation of the rich
36、 content system. Public transport priority consists of two aspects: one is on the bus to help. . 5.1-7 Park and ride systems 5.1.5 typical case Hong Kong-Japan Sapporo, Sapporo is a Japan Hokkaido central parts of cities, Japans fifth largest city. Area of 1121km2 in the city, a population of 1.921
37、million. In addition is the administrative center of Hokkaido, Sapporo is Hokkaidos industrial and commercial center, in 1972, hosted the 11th Winter Olympic Games. 3 JR Sapporo rail transit line 3 metro and 3 tram lines, Sapporo in the urban development process combined with Center of construction
38、of subway construction and residential development, and support the development of the region. Prior to 1971, Sapporo, Japan Hokkaido local Centre in the urban development process, in response to the rapid growth of the city centre traffic demand, building trams. 1981 years ago for holding the winter Olympic Games as an opportunity to start building connected to the venue and the city centre