山东省枣庄市2017届高三下学期第一次模拟考试数学（文）试题（扫描版）

高三数学（文科）答案第 1 页 共 6 页 二○一七届高三模拟考试 数学（文科）参考答案及评分标准 2017.3 一、选择题：本大题共 10小题，每小题 5分，共 50分. BDAC CBAD AC 二、填空题：本大题共 5小题，每小题 5分，共 25分． 11.相交 12. 2 13. 1 14. 1{ | e λ λ = − ，或 0}λ� 15. 2 3 三、解答题：本大题共 6小题，共 75分． 16. 解：（1）分数在[50, 60)的频率为0.008 10 0.08× = . ········································· 2分 由茎叶图知，分数在[50, 60)内的频数为 2，所以全班人数为 2 25 0.08 = ． ······ 4分 分数在[80,90)内的频数为 25 22 3− = . ······························································· 6分 （2）将分数在[80,90)内的 3份试卷记为 1 2 3, ,a a a ，分数在[90,100)内的 2份试卷记为 1 2,b b ，在[80,100)之间的试卷中任取两份的基本事件为： 1 2( , )a a ， 1 3( , )a a ， 1 1( , )a b ， 1 2( , )a b ， 2 3( , )a a ， 2 1( , )a b ， 2 2( , )a b ， 3 1( , )a b ， 3 2( , )a b ， 1 2( , )b b ，共10个. ···· 10分 其中，至少有一份试卷的分数在[90,100)内的基本事件有7个. ·······················11分 故至少有一份试卷的分数在[90,100)内的概率是 7 10 ． ····································· 12分 注：第（2）问中，无论按有序，还是按无序，只要计算正确，均给分. 17．解（1）由题意， π( ) sin(2 ). 3 f x x= − ····································································· 2分 令 π π2 π 3 2 x k− = + ， .k ∈ Z ··············································································· 4分 解得 ( )y f x= 图象的对称轴方程 π 5π 2 12 kx = + ， .k ∈ Z ····································· 6分 （2）由 3( ) 2 f A = ，得 πsin(2 ) 3 3 . 2 A − = 由0 πA< < ，得 π π 5π2 ( , ). 3 3 3 A − ∈ − ·································································· 7分 所以 π π2 3 3 A − = ，或 π 2π2 . 3 3 A − = 所以 π 3 A = ，或 π . 2 A = ······························· 9分 由正弦定理，得 sin sin b a B A = ，所以 sinsin .b AB a = 高三数学（文科）答案第 2 页 共 6 页 O A B C D A1 B1 C1 D1 当 π 3 A = 时， 2 3 3 sin 13 2sin 2 2 b AB a × = = = ； ················································· 10分 当 π 2 A = 时， 2 3 1sin 33sin . 2 3 b AB a × = = = ·······················································11分 综上， sin B的值为 1 2 ，或 3 . 3 ············································································ 12分 18．证明：（1）在四棱台 1 1 1 1ABCD A B C D− 中，连接 1 1A C .