贵州省2006- 2011全国高考理科数学卷

2008年普通高等学校招生全国统一考试 理科数学试题（必修?选修Ⅱ）参考答案和评分参考

评分说明：

1．本解答给出了一种或几种解法供参考，如果考生的解法与本解答不同，可根据试题的主要 考查内容比照评分参考制订相应的评分细则．

2．对计算题，当考生的解答在某一步出现错误时，如果后继部分的解答未改变该题的内容和 难度，可视影响的程度决定后继部分的给分，但不得超过该部分正确解答应得分数的一半；如果后继部分的解答有较严重的错误，就不再给分．

3．解答右端所注分数，表示考生正确做到这一步应得的累加分数． 4．只给整数分数．选择题不给中间分．

一、选择题

1．B 2．A 3．C 4．C 5．D 6．D 7．B 8．B 9．B 10．C 11．A 12．C 二、填空题

13．2 14．2 5．3?22 16．两组相对侧面分别平行；一组相对侧面平行且全等；对角线交于一点；底面是平行四边形．

注：上面给出了四个充要条件．如果考生写出其他正确答案，同样给分． 三、解答题 17．解：

512，得sinB?， 131343由cosC?，得sinC?．

55（Ⅰ）由cosB??所以sinA?sin(B?C)?sinBcosC?cosBsinC?（Ⅱ）由S△ABC?33． ··············································· 5分 6533得 2133， ?AB?AC?sinA?2233由（Ⅰ）知sinA?，

65故 AB?AC?65， ··································································································· 8分

AB?sinB20又 AC??AB，

sinC132013故 AB2?65，AB?．

132

所以 BC?

18．解：

AB?sinA11·················································································· 10分 ?． ·

sinC2各投保人是否出险互相独立，且出险的概率都是p，记投保的10 000人中出险的人数为?， 则?~B(10，p)．

（Ⅰ）记A表示事件：保险公司为该险种至少支付10 000元赔偿金，则A发生当且仅当??0， ······························································································································· 2分

4P(A)?1?P(A)

?1?P(??0) ?1?(1?p)10，

10又P(A)?1?0.999，

44故p?0.001． ························································································································ 5分 （Ⅱ）该险种总收入为10000a元，支出是赔偿金总额与成本的和． 支出 10000??50000，

盈利 ??10000a?(10000??50000)， 盈利的期望为 E??1000a0?4?3100E?0?0?3······················································ 9分 5，0 010)知，E??10000?10， 由?~B(10，E??104a?104E??5?104

?104a?104?104?10?3?5?104． E?≥0?104a?104?10?5?104≥0

?a?10?5≥0 ?a≥15（元）．

故每位投保人应交纳的最低保费为15元．········································································· 12分