2013年南京市白下区中考一模数学试题及答案(6)

34

解得m＝．

15

14333

＋＝，15－5×＝12，即C（，12）． ··················································· 5分

315555 方法二：

BC对应的函数关系式为y＝45x－15．

AC对应的函数关系式为y＝－5x＋15． ···························································· 3分

3

BC与AC的交点C的坐标为（，12）． ························································· 5分

5

3

点C的实际意义为王老师在出发 h后，在距离车站12 km处接到甲． ··················· 6分

5

（2）预设方案2：

方法一：

设王老师把乙放下后，再经过n h与甲相遇． (45＋5)n＝45a－5a．

4

解得n＝a． ································································································ 7分

55454

由于王老师骑摩托车一共行驶 h，可得方程15－5(a＋a)＝45×[－(a＋

6565

a)]． ······························································································································ 9分

5

解得a＝． ······························································································ 10分

16 方法二：

根据题意，得点B（a，15－45a）． ································································· 7分

9

求得点C（a，15－9a）． ············································································· 8分

5 所以CD对应的函数关系式为y＝－45x＋72a＋15． ············································· 9分

55

将（，0）代入，解得a＝．······································································ 10分

61615

（说明：未经过任何说明，直接判断点E坐标为（，0），从而解得a＝只

216

得1分）

12

优化方案

（3）本题答案不唯一，以下方法供参考． y/km A 15 C 10

5 B E D 251 O 1 x/h 363

······································································································· 11分 图中折线A-B-C-D、线段AC、线段BE分别表示王老师、甲、乙离车站的路程y（km）与王老师所用时间x（h）之间的函数图象．

······································································································· 12分

（说明：没有图象或图象错误不得分．）

13

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