四川省资阳市2013届高三第二次高考模拟考试数学(4)

15．①③．

三、解答题：本大题共6个小题，共75分．解答要写出文字说明，证明过程或演算步骤．

16．解析 （Ⅰ

2csinA 0及正弦定理，

A 2sinCsinA 0（sinA 0），

∴sinC ∴C

3

，∵△ABC是锐角三角形，

． ············································································································ 6分

3

（Ⅱ）

∵c C

，∴△ABC

的面积S ABC

12

absin

3

∴ ···························································································· 8分 ab 6． ①由余弦定理，a2 b2 2abcos

3 7，

即a2 b2 ab 7．② ··························································································· 10分 由①×3＋②，得(a b)2 25，故a b 5．···························································· 12分

····················································· 3分 频率分布直方图：

··························································································································· 3分 （Ⅱ）记幸福指数评分值在（80，90]的3人分别是A1，A2，A3，（90，100]的2人分别是B1，B2，则全部基本事件有（A1，B1），（A1，B2），（A2，B1），（A2，B2）（A3，B1），（A3，B2），（A1，A2），（A1，A3），（A2，A3），（B1，B2）共10个，

其中幸福指数评分值在(80，90]区间有1人被邀请的基本事件有6个． 故幸福指数评分值在(80，90]区间仅有1人被邀请的概率

P

610

35

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

14AB

18．（Ⅰ）证明：取AB的中点M， AF，