24．（本题满分10分）
y D 如图，在直角梯形OBCD中，OB?8，BC?1，CD?10． （1）求C，D两点的坐标；
（2）若线段OB上存在点P，使PD⊥PC，求过D，P，C 三点的抛物线的表达式．
25．（本题满分12分）
C P B x O （第24题图） 如图，?O的半径均为R．
（1）请在图①中画出弦AB，CD，使图①为轴对称图形而不是中心对称图形；请在图②中画出弦．．
AB，CD，使图②仍为中心对称图形；
（2）如图③，在?O中，AB?CD?m(0?m?2R)，且AB与CD交于点E，夹角为锐角?．求四边形ACBD面积（用含m，?的式子表示）； （3）若线段AB，CD是?O的两条弦，且AB?CD?2R，你认为在以点A，B，C，D为顶点
的四边形中，是否存在面积最大的四边形？请利用图④说明理由． （第25题图①）
（第25题图②）
O O C A E D ? O B O （第25题图③） （第25题图④）
陕西省基础教育课程改革实验区2007年初中毕业学业考试
数 学
答案及评分标准
一、选择题
1．A 2．B 3．D 4．A 5．C 6．C 7．B 8．A 9．B 10．C 二、填空题
11．?x3y3 12．B 13．115°（填115不扣分） 14．（1）0.433 （2）90.6 15．21 16．21 三、解答题
17．解：当A?B时，xx?13(x?1)(x?1)xx?1?3x?12?1．
?····························································································1分 ?1．·
方程两边同时乘以(x?1)(x?1)，得
························································································2分 x(x?1)?3?(x?1)(x?1)．·
x?x?3?x?1．
x?2．·························································································································3分
22检验：当x?2时，(x?1)(x?1)?3?0．
∴x?2是分式方程的根． ····························································································4分
因此，当x?2时，A?B． ·························································································5分
18．解：（1）画图正确得4分．
D A （第18题答案图）
C? C B D? B? A?
（2）210个单位．·····································································································6分 19．解：（1）证明：∵AB∥DC，DA?AB，?B?45°， ∴?C?135°，DA?DE． ·························································································1分 又∵DE?DA，
∴?E?45°．··············································································································2分 ∴?C??E?180°．···································································································3分 ∴AE∥BC．··············································································································4分
（2）解：∵AE∥BC，CE∥AB，
··················································································5分 ∴四边形ABCE是平行四边形．·
∴CE?AB?3．
∴DA?DE?CE?CD?2．······················································································6分
∴S?ABCE················································································7分 ?CE·AD?3?2?6． ·
20．解：（1）2006年外省区市在陕投资总额为：
124?67?66?47?119?423（亿元）． ·····································································2分
（2）如图①所示．········································································································5分 2006年外省区市在陕投资金额计图 2006年外省区市
在陕投资金额使用情况统计图
140 120 100 80 60 40 20 0
金额/亿元 124 119 67 66 47 其它 68% 西安经济技术 开发区13% 西安高新技术 产业开发区19%
广东福建北京浙江其它省区 市
（第20题答案图①） （第20题答案图②）
（3）如图②所示．········································································································8分 21．解：（1）设y与x的函数关系式为y?kx?b，······················································1分
?2100k?b?1800，由题意，得? ?2800k?b?2300， ····················································································3分
5??k?，解之，得? ·······································································································5分 7?b?300．?∴y与x的函数关系式为y?57····································································6分 x?300． ·
（2）当x?5600时，y?57················································7分 ?5600?300?4300元． ·
···································································8分 ∴王老师旅游这条线路的价格是4300元． ·
22．解：（1）(?1，，···············································································3分 1)(0，0)，，(1?1)．·（2）∵在?ABCD内横、纵坐标均为整数的点有15个，
其中横、纵坐标和为零的点有3个， ·············································································6分
∴P?315?15． ············································································································8分
23．解：（1）证明：∵AC是?O的切线，AB是?O直径，
∴AB?AC．
则?1??2?90°．·······································································································1分
又∵OC?AD，
∴?1??C?90°．······································································································2分 ∴?C??2． ··············································································································3分
而?BED??2， ∴?BED??C． ········································································································4分 （2）解：连接BD． C ∵AB是?O直径，
∴?ADB?90°．
∴BD?AB?AD?2222E D A
1 2 O
（第23题答案图）
B
10?8?6． ·····································································5分
∴△OAC∽△BDA． ·································································································6分 ∴OA:BD?AC:DA．
即5:6?AC:8． ·········································································································7分
∴AC?203．···············································································································8分
24．解：（1）过点C作CE?OD于点E，则四边形OBCE为矩形．
y ∴CE?OB?8，OE?BC?1． ∴DE?CD?CE22?10?8?6．
22D 3 ∴OD?DE?OE?7．
E C 1 P 2 B x （第24题答案图）
O ∴C，D两点的坐标分别为C(8，，·····························································4分 1)D(0，7)． ·
（2）∵PC?PD，
∴?1??2?90°．
又?1??3?90°，
∴?2??3．
∴Rt△POD∽Rt△CBP．∴PO:CB?OD:BP．
即PO:1?7:(8?PO)．
∴PO?8PO?7?0． ∴PO?1，或PO?7．
2···············································································6分 ∴点P的坐标为(1，0)． ·0)，或(7，①当点P的坐标为(1，0)时，
设经过D，P，C三点的抛物线表达式为y?ax?bx?c， 25?a?，?28?c?7，?221??，则?a?b?c?0， ∴?b?? 28??64a?8b?c?1．??c?7．??∴所求抛物线的表达式为：y?22528x?222128x?7． ·····················································9分
②当点P为(7，0)时，