中考数学试卷精选合辑60之21-初中毕业学业考试数学题及参考答案(4)

方案一:装A种2辆车, 装B种6辆车, 装C种2辆车; 方案二:装A种3辆车, 装B种4辆车, 装C种3辆车; ···································· 7分 方案三:装A种4辆车, 装B种2辆车, 装C种4辆车． （3）设销售利润为W(万元),则

W=3?12x?4?10?(10?2x)?2?8x

=?28x?400 ···················································································· 9分 故W是 x是的一次函数,且x增大时,W减少．

故x?2时,Wmax=400-28?2?344(万元) ·················································· 10分

?25a?5b?c?0?26、解：（1）由题意得：?36a?6b?c?0 ············2分

?c?0??a??1? 解得?b?5 ···········································3分

?c?0?故抛物线的函数关系式为y??x?5x ············4分 （2）?C在抛物线上，??2?5?2?m,?m?6 ··5分

22y

6

4 2

D

C E

P

F

1 2 -2 G A

5

x

?C点坐标为（2，6），?B、C在直线y?kx?b?上

-4

?6?2k?b? 解得k??3,b??12 ?????6?6k?b-6

B

···························································· 6分 ?直线BC的解析式为y??3x?12 ·

设BC与x轴交于点G，则G的坐标为（4，0）

11?S?OBC??4?6??4??6?24 ························································· 7分

22（3）存在P，使得?OCD∽?CPE ··································································· 8分

设P(m,n)，??ODC??E?90? 故CE?m?2,EP?6?n 若要?OCD∽?CPE，则要

ODDCODDC??或 CEEPEPCE

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6262??或 m?26?n6?nm?2解得m?20?3n或n?12?3m

即

?m?20?3n?n?12?3m又?(m,n)在抛物线上，?或? 22n??m?5mn??m?5m??10?m???m?2?m2?6?13?m2?2,?,或?1解得? ,??n1?6?n2??6?n?50?n2?61?9?故P点坐标为(1050，)和(6,?6) ······························································ 10分 39（只写出一个点的坐标记9分）

其它解法参照此标准计分．

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