山东省枣庄市2017届高三下学期第二次模拟考试数学（理）试题（答案PDF版）

高三数学（理科）答案 第 1 页 共 12 页 2017届高三定时测试 数学（理科）参考答案及评分标准 一、选择题：本大题共 10小题，每小题 5分，共 50分. CBBC ADCA DB 二、填空题：本大题共 5小题，每小题 5分，共 25分． 11. 2 3 12. [ 1− ， 1 ] 5 13. 24 14. 1 15. 4 三、解答题：本大题共 6小题，共 75分． 16.解：（1） ( ) 3sin 2 (1 cos2 )f x x x= − − ···································································· 2分 π2sin(2 ) 1. 6 x= + − ············································································· 3分 因为 π π 6 3 x− < < ，所以 π π 5π2 . 6 6 6 x− < + < ······················································ 4分 所以 1 πsin(2 ) 1 2 6 x− < + � ，所以 π2 2sin(2 ) 1 1. 6 x− < + − � 所以函数 ( )f x 在 π( 6 − ， π ) 3 上的值域为 ( 2− ，1]. ·········································· 6分 （2）由 ( ) 0f C = ，得 π2sin(2 ) 1 0 6 C + − = ，即 π 1sin(2 ) . 6 2 C + = 在 ABC△ 中，0 πC< < ， π π 13π2 6 6 6 C< + < . 所以 π 5π2 6 6 C + = ，即 π 3 C = .··············································································· 8分 所以 2π 3 A B+ = ， 2π 3 B A= − . 因为 sin sin sinB A C= ，所以 2π 3sin( ) sin 3 2 A A− = ， 所以 2π2sin( ) 3sin 3 A A− = ，即 3 cos sin 3sin .A A A+ = 所以 ( 3 1)sin 3 cosA A− = . ··············································································11分 又 cos 0A ≠ （若 cos 0A = ，则 sin 0A = ，这与 2 2sin cos 1A A+ = 矛盾）， 所以 sin 3 3 3tan cos 23 1 AA A + = = = − . ································································· 12分 高三数学（理科）答案 第 2 页 共 12 页 17.解：(1)设等差数列{ }na 的公差为 d . 因为 1 2 4, , 2a a a + 成等比数列，所以 2 2 1 4( 2)a a a= + ············································· 1分 即 2(1 ) 1 (3 3 )d d+ = ⋅ + . ··························································································· 2分 解得 2d = ，或 1d = − . 若 1d = − ，则 2 0a = ，这与 1 2 4, , 2a a a + 成等比数列矛盾，所以 1d = − 舍去. 经验证， 2d = 符合题意. ······················································································ 3分 所以 1 2( 1) 2 1na n n= + − = − ，············································································