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# 温州市“摇篮杯——生活中的数学知识”大赛(3)答案

（1）填空（填“Ⅰ”或“Ⅱ”）：每次乘车用现金买票时，余额与乘车次数的函数图象是________；买成IC卡后，余额与乘车次数的函数图象是________．

（2）求出线段Ⅰ和线段Ⅱ所表示的函数关系式；

（3）如果张先生每月平均乘坐公交车70次，则他用IC卡消费比用现金消费可以省下多少钱？

（1）调配后，此汽车配件厂生产甲、乙两种配件的年利润分别为多少？（用含m，x的代数式表示）

（2）如果调配后，生产甲种配件的年利润不小于调配前年利润的4，生产乙种配件的年利润大于调5

1． ··································································································· 2分 1?x

1 （2）①若选择一次清洗，则清洗后残留农药为：． ·········································· 3分 1?a

12 ②若分两次清洗，则第一次清洗后残留农药为：． ······························ 6分 ?a2?a1?2 一、解：（1）

2

4 第二次清洗后残留农药为：?2． ·············································· 9分 a?2a?4?2?a2

14a2?2a?4?4a?4a2?2a?2?2?2 ． ························ 12分 1?aa?2a?4(a?2a?4)(1?a)(a?2a?4)(1?a)

∵a≥2，

∴14························································································ 14分 ?2≥0． 1?aa?2a?4

∴选择分两次的方法进行清洗，这样水果或蔬菜上的残留农药更少一些． ·············· 16分 如果水能平分三次清洗，水果或蔬菜上的残留农药会更少． ··································· 20分

（2）设Ⅱ的函数关系式为y?kx?b，因（0，80）和（100，0）满足关系式，

?b?80，?80?b，4? 即?解得? ∴． ····················· 10分 y??x?80（x取整数）45k??.?0?100k?b.?5?

z(1?． 20?%)，z?1（元）80． ?0.8（元）100

∴Ⅰ所代表的函数关系式为y??x?80（x取整数）． ·········································· 16分

（3）(1?0.8)?70?14（元）． ·················································································· 20分