2006年辽宁省大连西岗区初中毕业升学统一考试数学试题

2006年辽宁省大连西岗区初中毕业升学统一考试数学试题 2006年大连西岗区初中毕业升学统一考试 数 学 题号 一 二 三 四 五 附加题 总分 分数 本1,8页，共150分，考试时间120分钟。 请考生准备好圆规，直尺、三角板、计算器等答题工具，祝愿所有考生都能发挥最佳水平。 一、选择题(本题8小题，每小题3分，共24分) 阅卷人 得分 说明:将下列各题唯一正确的代号A、B、C、D填到题后的括号内。 1.,的相反数是 ( ) 2 22A. B., C. D., 2222 2.在平面直角坐标第中，点(2，,1)在 ( ) A.第一象限 B.第二象限 C.第三象限 D.第四象限 3.半径为4和2的两圆相外切，则其圆心距为 ( ) A.2 B.3 C.4 D.6 4.下列各式运算正确的是( ) 32,325,32,32,aaa，, B.aaa,, C.aaa,, D.aaa,, A. 5.为了判断甲乙两组学生英语口语测试成绩哪一组比较整齐，通常需要知道这两组成成绩的 ( ) AA.平均数 B.方差 C.众数 D.中位数 M6.如图1，直线AB、CD相交于点O，OM?AB，若?COB=135?， 则?MOD等于( ) ODCA.45? B.35? C.25? D.15? B图 1 7.将一张纸片沿图2中?、?的虚线对折得图2中的?，然后剪去一个角，展开铺平后的图形如图2中的?，则图2中的?沿虚线的剪法是( ) ???? 图 2 DBCA 28.如图3，数轴上表示1，的对应点A、B，点B关于点A的对称点为C，则点C所表示的数是( ) 22,22,A. B. BCA x02121,12,C. D. intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision 二、填空题(本题共7小题，每小题3分，共21分) 阅卷人 得分 说明:将答案直接填在题后的横线上。 AD P9.已知甲地的海拔高度为150m，乙地的海拔高度为,30m，那么 甲地比乙地高________m; CBk1图 410.反比例函数的图象过点A(,2，)，则k的值为____________; y,x2 11.在Rt?ABC中，?C=90?，AC = 3，BC = 4，则tanA的值为______________; O12.如图4，正方形ABCD的顶点都在?O上，P是弧DC上的一点， 则?BPC的度数是__________; AB13.如图5，AB是?O的切线，?O=60?，OA = 10，则?O的半径长为__________; 图 514.如图6是小亮用8根，14根、20根火柴搭的1条、2条、3条“金鱼”， 按此方法搭n 条“金鱼”需要火柴__________根。(用含n的代数式表示) y1 3条1条2条 -201图6 y 2图715.如图7是一次函数y = ax + b， y = kx + c的图象，观察图象， 12 ?0时x的取值范围____________________。 写出同时满足y?0，y21 三、解答题(本题共5小题，其中16、17题各9分，18、 阅卷人 得分 19、20题各10分，共48分) 2xx,12116.已知y,,,。当x为何值是地，y的值为; 223xxxxx,,，，211 17.如图8，ABCD中，AE?BD于E，CF?BD于F。 AD 求证:AE = CF F E CB intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision 18.当今，青少年视力水平的下降已引起全社会的关注。为了解某校初中二300名学生的视力情况，从中 随机抽查了一部分学生的视力，将其整理后，画出频数分布直方图，如图9。 ?随机抽查了_________名学生的视力; ?若视力在4.85以上属于正常，不需矫正，估计该校 22二年级300名学生中约有多少名学生的视力不需要矫正。 18?若要使该校视力正常的百分率提高到70,，估计要有 多少名学生通过矫正达到正常。 6 2 3.954.254.554.855.155.45视力 图9 A 19.如图10，已知?ABC和?A″B″C″及点O。 ?画出?ABC关于点O对称的?A′B′C′; ?若?A″B″C″与?A′B′C′关于点O′对称， OCB请确定点O′的位置; ?探究线段OO′与线段CC″之间的关系，并说明理由。 A″ C″B″ 图 10 intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision 20.小明从家到学校，开始步行，后来跑步，小明离家的路程S(m)与所用时间t (分)之间的关系如图11所示。 ?根据图象回答:小明家距学校的路及小明步行的速度。 ?若h?8,小明跑步速度为210 m/分，求小明至少需要跑几分钟。 s (m) 2100 270 t (分) 3h 图 11 四、解答题(本题共3小题，其中21题7分，22、23题各8分，共23分) 阅卷人 得分 21.如图?、?、?中，点E、D分别是正?ABC、正四边形ABCM、正五边形ABCMN中以C点为顶点的相 邻两边上的点，且BE = CD，DB交AE于P点( ?求图?中，?APD的度数; ?图?中，?APD的度数为___________，图?中，?APD的度数为___________; ?根据前面探索，你能否将本题推广到一般的正n 边形情况(若能，写出推广问题和结论;若不能，请 说明理由( A AAM NBP E DDPP BBCCCMDEE 图?图? 图? intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision 22.如图13，放在平面直角坐标系中的正方形ABCD的边长为4，现做如下实验: 抛掷一枚均匀的正四面体骰子(如图14，它有四个顶点，各顶点数分别是1、2、3、4)。 每个顶点朝上的机会是相同的，连续抛掷两次，将骰子朝上的点数作为直角坐标系中点 P的坐标(第一次的点数为横坐标，第二次的点数为纵坐标)。 ?求点P落在正方形面上(含边界，下同)的概率。 1?将正方形ABCD平移数个单位，是否存在一种平移，使点P落在正方形面上的概率为，若存在，指出其4中的一种平移方式，若不存在，说明理由。 yDA 1 2 43x CB 图 14图 13 23.如图15，?POA，?PAA，?PAA……?PAA都是等腰直角三角形，点P、P、P……P都在,11212323nn1n123n 4y,函数(x > 0)的图象上，斜边OA、AA、AA……AA都在x轴上。 ,11223n1nx y?求A、A点的坐标; 12 ?猜想A点的坐标(直接写出结果即可) n P1 P2 P3P4 OA4AAA123x 图 15 intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision 五、解答题和附加题(本题共3小题，24、25题各12分，26题10分，共34分，附加题 阅卷人 得分 5分，全卷累积不超过150分，建议考生最后答附加题) 24.某汽车经销公司经销A、B两种品牌的轿车50辆，该公司经销这50辆轿车的成本不少于1240万元，但不超过1244万元，两种轿车的成本和售价如下表。 A B 成本(万元/辆) 24 26 售价(万元/辆) 27 30 ?该公司经销这两种品牌轿车有哪几种，哪种方案获利最大,最大利润是多少, ?根据市场调查，一段时期内，B牌轿车售价不会改变，每辆A牌轿车的售价将会提高a万元(0 < a <1.2)，且所有两种轿车全部售出，哪种经销方案获利最大,(注:利润 = 售价,成本) intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision 1225.已知抛物线经过点(1，,1)和C(0，,1)，且与x轴交于A、B两点(A在B左边)，直线y,x，bx，c2 x = m (m > 0)与x轴交于点D。 ?求抛物线的解析式。 ?在第一象限内，直线x上是否存在点P，使得以P、B、D为顶点的三角形与?OBC全等，若存在，求出点P坐标，若不存在，说明理由。 ?在?的情况下，过点P作x轴的平行线交抛物线于点Q，四边形AOPQ能否为平行四边形,若能，求Q点坐标，若不能，说明理由。 x = m y AODBx C 图 16 intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision 26.如图16，以?ABC的边AB、AC为直角边向外作等腰直角?ABE和?ACD，M是BC的中点，请你探究线段DE与AM之间的关系。 说明:?如果你经历反复探索～没有找到解决问题的方法～请你把探索过程中的某种思路写出来(要求至少写 3步),?在你经历说明?的过程之后～可以从下列?、?中选取一个补充或更换已知条件～完成你的证明。 完成证明得10分,选取?完成证明得5分。 注意:选取? ?画出将?ACM绕某一点顺时针旋转180?后的图形; ??BAC = 90?(如图17) 附加题:如图18，若以?ABC的边AB、AC为直角边，向内作等腰直角?ABE和?ACD，其它条件不变，试探究线段DE与AM之间的关系。 E E ADDACAM DCBBCMMBE 图 18图 16图 17 intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision intensive development. (5) have different emphasis: for development, "with development, the emphasis on" way, from space, multiple groups from a single radiation-belt open development. Spatial structure of 2, the prominent cultural city protection elements on the development of the whole city and culture series supporting role, with natural landscapes and green for the background, according to the combined city, urban Group organization structure, set up a decentralized development patterns, building ... Three rivers: the Yangtze, jinsha River and minjiang rivers, cities in three rivers based on development along the Yangtze River, city on the River, River in the city. Multiple groups: the relatively compact area layout, each district consists of multiple groups, and the area has both integrated urban functions, and have their own characteristics and perimeter formation Li Zhuang, Li Zhuangdong characteristic tour area and Hong Kong in group, consists of 17 groups. Band: modern features gathering along the Yangtze River belt. Dvn group in the upper reaches of the jinsha River along the river continues to the East to South stream groups, layout along the city's main commercial, business, administrative, cultural and creative research and development in science and education function of modern service and port equipment manufacturing, liquor, and other features and modern industry. 2.5-2 spatial planning figure 2.6 in Yibin city, Central City urban development vision vision