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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．?xy 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，33 x3?2?1． x?1x?1x3??1．····································································································· 1分 x?1(x?1)(x?1)方程两边同时乘以(x?1)(x?1)，得 x(x?1)?3?(x?1)(x?1)． ································································································ 2分 x2?x?3?x2?1．
x?2． ··································································································································· 3分
检验：当x?2时，(x?1)(x?1)?3?0．
∴x?2是分式方程的根． ···································································································· 4分
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因此，当x?2时，A?B． ································································································· 5分 18．解：（1）画图正确得4分． C?
B? C
B D A （第18题答案图） D? 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， ∴四边形ABCE是平行四边形． ·························································································· 5分 ∴CE?AB?3． ∴DA?DE?CE?CD?2． ····························································································· 6分 ······················································································· 7分 ∴S?ABCE?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 金额/亿元
140 120 100 80 60 40 20 0 124 119 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②）
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（第20题答案图①）
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（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
由题意，得??2100k?b?1800， ··························································································· 3分
2800k?b?2300，?5?k?，?解之，得?··············································································································· 5分 7 ·??b?300．∴y与x的函数关系式为y?（2）当x?5600时，y?5x?300． ··········································································· 6分 75?5600?300?4300元． ····················································· 7分 7∴王老师旅游这条线路的价格是4300元． ·········································································· 8分
，，，，(00)(1，?1)． ·22．解：（1）(?11)····················································································· 3分
（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?31?． ····················································································································· 8分 15523．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°．
E D A 1 2 O
（第23题答案图）
B ·········································································· 5分 ∴BD?AB2?AD2?102?82?6． ·
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∴△OAC∽△BDA． ········································································································· 6分 ∴OA:BD?AC:DA． 即5:6?AC:8． ·················································································································· 7分
20∴AC?． ························································································································ 8分
324．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?CE?10?8?6． ∴OD?DE?OE?7．
2222D 3 C 1 P 2 B x （第24题答案图） E O ∴C，D两点的坐标分别为C(81)，，D(0，7)． ···································································· 4分 （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)． ∴PO2?8PO?7?0． ∴PO?1，或PO?7． ∴点P的坐标为(1，0)． ······················································································· 6分 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， 225?a?，?28?c?7，?221??，则?a?b?c?0， ∴?b?? 28??64a?8b?c?1．??c?7．?? 9
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∴所求抛物线的表达式为：y?②当点P为(7，0)时，
252221x?x?7． ·························································· 9分 2828设经过D，P，C三点的抛物线表达式为y?ax2?bx?c，
1?a?，?4?c?7，?11??则?49a?7b?c?0， ∴?b??， 4?64a?8b?c?1．???c?7．??∴所求抛物线的表达式为：y?1211x?x?7． ···························································· 10分 44（说明：求出一条抛物线表达式给3分，求出两条抛物线表达式给4分） 25．解：（1）答案不唯一，如图①、②（只要满足题意，画对一个图形给2分，画对两个给3分） A D A B
O O
B C C
（第25题答案图①） （第25题答案图②） ················································································································································· 3分 （2）过点A，B分别作CD的垂线，垂足分别为M，N． 11∵S△ACD?CD·AM?CD·AE·sin?， 2211S△BCD?CD·BN?CD·BE·sin?． ············································································· 5分
22∴S四边形ACBD?S△ACD?S△BCD 11?CD·AE·sin??CD·BE·sin? 22
1?CD·(AE?BE·)sin? 21?CD·AB·sin? 2C A D NEM? O 10
B
（第25题答案图③）
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?12msin?． ··········································· 7分 2
（3）存在．分两种情况说明如下： ···················································································· 8分 ①当AB与CD相交时，
由（2）及AB?CD?2R知S四边形ACBD?②当AB与CD不相交时，如图④ 1AB·CD·sin??R2sin?． ······················· 9分 2A D 2 ∵AB?CD?2R，OC?OD?OA?OB?R， ∴?AOB??COD?90°，
而S四边形ABCD?SRt△AOB?SRt△OCD?S△AOD?S△BOC B O 3 1 H E C ?R?S△AOD?S△BOC2（第25题答案图④）
． ····································································································· 10分
延长BO交?O于点E，连接EC，则?1??3??2??3?90°． ∴?1??2． ∴△AOD≌△COE． ∴S△AOD?S△OCE． ∴S△AOD?S△BOC?S△OCE?S△BOC?S△BCE． 过点C作CH?BE，垂足为H， 则S△BCE?1BE·CH?R·CH． 2∴当CH?R时，S△BCE取最大值R2． ············································································ 11分
综合①、②可知，当?1??2?90°，即四边形ABCD是边长为2R的正方形时， ············································································ 12分 S四边形ABCD?R2?R2?2R2为最大值． ·
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