2016年5月福州市普通高中毕业班综合测试文科数学试题(word 版含(2)

SnSn 1

1 1

所以 是以 2为首项，以1为公差的等差数列． ···································· 6分

SS1 n

1

2 n 1 n 1， （Ⅱ）由（Ⅰ）可得Sn

1.··························································································· 8分

n 1

1111

所以Sn ． ·································································· 10分

nn(n 1)nn 1所以Sn

1111 1 11 1

所以S1 S2 S3+ +Sn 1 + + ························ 11分 ·

23n 2 23 nn 1

1n

． ·············································· 12分 1

n 1n 1

（18）本小题主要考查等高条形图、独立性检验、古典概型等基础知识，考查数据处理能力、运算求解能力以及应用意识，考查必然与或然思想等．满分12分． 解：（Ⅰ）由题意得2 2列联表如下：

2016年5月7日福州高三质检文科数学含答案

································· 3分 假设H0:喜欢娱乐节目A与观众性别无关，

540

5.934 3.841， ···························· 5分

39 21 30 3091

所以能在犯错误的概率不超过0.05的前提下认为喜欢娱乐节目A与观众性别有关． ·············································································································· 6分

则K的观测值k=

2

60 24 15 15 6

2

（Ⅱ）利用分层抽样在男性观众30名中抽取5名，其中喜欢娱乐节目A的人数为24 不喜欢节目A的人数为6

5

4，30

5

································································· 7分 =1．

30

被抽取的喜欢娱乐节目A的4名分别记为a,b,c,d；不喜欢节目A的1名记为B． 则从5名中任选2人的所有可能的结果为： a,b , a,c , a,d , a,B , b,c , b,d , b,B ,

c,d , c,B , d,B ，共有10种．

·············································································································· 9分 其中恰有1名喜欢节目A和1名不喜欢节目A的有 a,B , b,B , c,B , d,B ，共4种． ············································································································ 10分

42

所以所抽取的观众中恰有1名喜欢节目A和1名不喜欢节目A的观众的概率是：=．

105

····················································