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(6)

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

············································································································ 12分 （19）本小题主要考查空间直线与直线、直线与平面的位置关系及三棱锥的高等基础知识，考查空间想象能力、推理论证能力、运算求解能力，考查化归与转化思想等．满分12分． （Ⅰ）证明：取AP的中点F，连结DF,EF，如图所示． 因为点E是PB中点，

AB

所以EF//AB且EF ． ······································ 1分

2AB

又因为AB//CD且CD ，

2

所以EF//CD且EF CD， ······································ 2分 所以四边形EFDC为平行四边形， 所以CE//DF， ····················································· 3分 因为AB 平面PAD，DF 平面PAD， 所以AB DF． ··········································

··········· 4分

所以CE AB． ······················································ 5分 （Ⅱ）解：设点O为PD的中点，连结AO，如图所示， 因为EC AB 4，

··········································· 6分 由（Ⅰ）知，DF ·

又因为AB 4，所以PD AD 2，

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