[]山东省枣庄市2018届高三第一次模拟考试（上学期期末）数学（文）试题（图片版）

高三数学(文科) 答案 第 1 页 共 6 页 2017～2018 学年度第一学期期末考试 高三数学（文科）参考答案及评分标准 2018.1 一、选择题：本大题共 12 小题，每小题 5 分，共 60 分. DDCC ABBC BDAA 二、填空题：本大题共 4 小题，每小题 5 分，共 20 分． 13. 5 14. 1 15. 4 16. (−∞ ， 4 ] 15 − 三、解答题：本大题共 6 小题，共 70 分．解答应写出文字说明、证明过程或演算步骤． 17.（I）解： 2 1 ( ) sin sin cos 2 f x x x xω ω ω= − − 1 cos 2 1 1 sin 2 2 2 2 x x ω ω − = − − ························································· 2 分 1 (sin 2 cos 2 ) 2 x xω ω= − + 2 sin(2 ). 2 4 xω π = − + ······································································· 4 分 可见， max 2 ( ) . 2 f x = 由题意， 2 . 2 m = ······················································· 5 分 由题意，函数 ( )f x 的周期为π ，因此 2 . 2ω π = π 解得 1.ω = ···························· 6 分 （II） 由（I），得 2 ( ) sin(2 ). 2 4 f x x π = − + 由2 2 2 4 k x π π π − +� 2 2 k π π +� ，k ∈ Z， ·························································· 8 分 得 . 8 8 k x k 3π π π − π +� � 所以， ( )f x 的单调递减区间为[ , ] 8 8 k k 3π π π − π + ， .k ∈ Z ·························· 10 分 注：1. 不出现k ∈ Z，扣 1 分； 2. 减区间写成开区间，不扣分. 18. （I）解法一：由题意， 2 =3 0+4 1=4a × × ， 3 =3 4+4 2=20a × × . 设 n nb = a nλ µ+ + ，则 1b = λ µ+ ， 2 4 2b = λ µ+ + ， 3 20 3b = λ µ+ + .······ 3 分 由题意，知数列{ }nb 是公比为3的等比数列，所以有 4 2 = 3 20 3 =3 4 2 λ µ λ µ λ µ λ µ + + +  + + + + （ ）， （ ）. ··········································································· 5 分 解得 =2λ ， =1µ .经验证， =2λ ， =1µ 符合题意. ········································· 6 分 高三数学(文科) 答案 第 2 页 共 6 页 解法二：由题意， 1 ( 1) 3( )n na n a nλ µ λ µ+ + + + = + + ， ······································· 3 分 即 1 3 2 2 .n na a nλ µ λ+ = + + − 又 +1 =3 4n na a n+ ，所以2 4λ = ，2 0.µ λ− = ··············································· 5 分 解得 2λ = ， 1.µ = ·························································································· 6 分 （II）由（I），知数列{ }nb 是首项 1 3b = ，且公比为3的等比数列， 故 13 3 3n nnb = −× = ，即 2 1 3nna n =+ + ，故 3 2 1 n na = n− − .·························