福州市2011届第一学期高三期末质量检查数学(文科)试卷

福州市2010—2011学年第一学期期末高三质量检查

数学（文科）试卷参考答案及评分标准

一、选择题（每小题5分，满分60分）

1.D 2.A 3.B 4.A 5. C 6.D 7.C 8.A 9.A 10.C 11.D 12.B 二、填空题(每小题4分，满分16分)

13. 6 14. 127 15. ①②③ 16.（－1,1）

三、解答题（本大题共6小题，共74分．解答写出文字说明、证明过程或演算步骤.） 17.（本小题满分12分） 17.解：（Ⅰ）依题意：an 2 (n 1) n 1 ····························································2分

n(n 1)n23n

Sn 2n 1= ······································································· 4分

222

（Ⅱ）由（Ⅰ）知 b1 2

a1

········································································· 5分 4 ·

bn 1

········· 7分 2an 1 an 21 2 bn 是首项为4,公比为2的等比数列 ·

bn

···················································································· 9分 bn 4 2n 1 2n 1 ·

4(1 2n)

Tn 2n 2 4 ················································································ 12分

1 2

18.（本小题满分12分）

18.解：

（Ⅰ）f(x) 1 cos2 x xcos x

1 cos 2x ··································································· 2分

3s inx 2

······························ 5分 2 x cos2 x 1 2sin(2 x ) 1 ·

6

因为函数f(x)的最小正周期为π，且 0， 所以

2π

π，解得 1． ··························································································7分 2

（Ⅱ）由（Ⅰ）得f(x) 2sin(2x

6

2πππ7π

因为0≤x≤，所以 ≤2x ≤， ····················································· 9分

3666

所以

) 1

1π

0 2sin(2x ) 1 3， ，因此≤sin 2x ≤1 626

即f(x)的取值范围为[0,3]． ···················································································· 12分 19.（本小题满分12分）

19.解：（Ⅰ）连续取两次所包含的基本事件有：（红，红），（红，白1），（红，白2），（红，黑）；（白1，红）（白1，白1）（白1，白2），（白1，黑）；（白2，红），

（白2，白1），（白2，白2），（白2，黑）；(黑，红)，(黑，白1)，(黑，白2)，(黑，黑)， 所以基本事件的总数M 16． ···································
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