山东省枣庄市2017届高三下学期第一次模拟考试数学（理）试题（扫描版）

高三数学（理科）答案第 1 页 共 12 页 二○一七届高三模拟考试 数学（理科）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 CACB AD 二、填空题：本大题共 5小题，每小题 5分，共 25分． 11. 24 12. 2 13. 2 14. 2 3 15. 1( , e ) e −∞ − − 三、解答题：本大题共 6小题，共 75分． 16.（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= 图象的对称轴方程为 π 5π 2 12 kx = + ， .k ∈ Z ································· 5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 − ∈ − 所以 π π2 3 3 A − = ，或 π 2π2 . 3 3 A − = 所以 π 3 A = ，或 π . 2 A = ······························· 7分 由正弦定理，得 sin sin b a B A = ，所以 sinsin .b AB a = 当 π 3 A = 时， 2 3 3 sin 13 2sin 2 2 b AB a × = = = ；·················································· 9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 17．解：（1）记M 与 1B 、 2B 、 3B 进行对抗赛获胜的事件分别为 A、B、C，M 至少获 胜两场的事件为D，则 4( ) 5 P A = ， 2( ) 3 P B = ， 1( ) 2 P C = . 则 .D ABC ABC ABC ABC= + + + ········································································· 1分 由于事件 A， B，C相互独立，所以 高三数学（理科）答案第 2 页 共 12 页 ( ) ( ) ( ) ( ) ( )P D P ABC P ABC P ABC P ABC= + + + 4 2 1 4 2 1 4 2 1 4 2 1 11(1 ) (1 ) (1 ) . 5 3 2 5 3 2 5 3 2 5 3 2 15 = × × + × × − + × − × + − × × = ··············· 5分 因为 11 7 15 10 > ，所以M 会入选下一轮. ······························································ 6分 （2）M 获胜场数 X 的可能取值为 0,1, 2, 3. 则 1 1 1 1( 0) ( ) 5 3 2 30 P X P ABC= = = × × = ； 4 1 1 1 2 1 1 1 1 7( 1) ( ) ( ) ( ) 5 3 2 5 3 2 5 3 2 30 P X P ABC P ABC P ABC= = + + = × × + × × + × × = ； 7( 2) ( ) ( ) ( ) 15 P X P ABC P ABC P ABC= = + + = ； 4 2 1 4( 3) ( ) . 5 3 2 15 P X P ABC= = = × × = ······