2009年广东省梅州市中考数学试题及答案(word版)(3)

1

． ···························································································································· 4 分

2

或画树状图如下： 开始

1 2 3 4 小张

小李 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

共有 16 种可能的结果，且每种的可能性相同，其中小张获得车票的结果有6种： （2，1），（3，1），（3，2），（4，1），（4，2），（4，3）， ∴小张获得车票的概率为P

6335

；则小李获得车票的概率为1 ． 16888

∴这个规则对小张、小李双方不公平． ························································ 8 分

21．本题满分 8 分．

（1）解：令x

0，得y

C(0． ························································ 1分

令y

0，得2，x2 3， xx0，解得x1 1

，，0)B(3，0)． ·∴A( 1································································································· 3分

（2

）法一：证明：因为AC2 12 2 4，

······················· 4分 BC 3 12，AB 16， ·

∴AB AC BC， ··············································· 5分 ∴△ABC是直角三角形． ·········································· 6分

法二：因为OC OA 1，OB 3，

22

2

2

M1 x

2222

321题图

OB， ·∴OC OA ·············································································································· 4分 OCOB ，又 AOC COB， OAOC

∴Rt△AOC∽Rt△COB． ································································································ 5分 ∴ ACO OBC， OCB OBC 90°， ∴ ACO OCB 90°，

∴ ACB 90°， 即△ABC是直角三角形． ····················································· 6 分

∴

（3

）M1(4

，M2( 4

，M3(2（只写出一个给1分，写出2个，得1.5．

分） ····································································· 8分

22．本题满分 10 分．

6 ···························