高二数学试题参考答案第1页共7页2019~2020学年度第一学期第一学段模块考试高二数学试题参考答案及评分标准一、单项选择题(每小题4分,共40分)题号12345678910答案ACDACBBDCA二、多项选择题(每小题4分,共12分)11.AD12.ACD13.ABC三、填空题(每小题4分,共16分)14.31015.516.322217.210xy;11(,)42三、解答题(共82分)(注意:答案仅提供一种解法,学生的其他正确解法应依据本评分标准,酌情赋分.)18.(本小题满分12分)解:(Ⅰ)因为关于x的不等式20xmxm的解集为R,所以240mm,.......................................................................................2分解得04m,所以实数m的取值范围为(0,4).......................................................................4分(Ⅱ)当1x时,不等式20xmxm恒成立,等价于21xmx对(1,)x恒成立,...........................................................6分因为1x,得10x,所以21xx2(1)2(1)11xxx1(1)21xx...............................................................................8分高二数学试题参考答案第2页共7页12(1)24(1)xx...........................................................10分当且仅当111xx,即2x时等号成立,所以,实数m的取值范围是(,4).............................................................12分19.(本小题满分14分)解:(Ⅰ)设圆C的方程为220xyDxEyF,...................................................1分则019301640FDEFDF,...............................................................................3分解得420DEF,.....................................................................................................5分所以圆C的方程为22420xyxy......................................................6分(Ⅱ)由(Ⅰ)知圆心坐标为(2,1),半径为5,弦长为4时,圆心到直线的距离为:1.①若直线斜率不存在,直线方程为3x,经检验符合题意;..........................8分②若直线斜率存在,设直线斜率为k,则直线方程6(3)ykx,即360kxyk,则2|5|11kk,解得125k,所以直线方程为126(3)5yx,即12560xy..................13分综上可知,直线方程为3x和12560xy........................................14分20.(本小题满分14分)解:(Ⅰ)当2n时,高二数学试题参考答案第3页共7页111(1)(21)(1)(21)66nnnSnnnnnnaS1[(1)(21)(1)(21)]6nnnnn2n......................................................................................................4分当1n时,2111aS....................................................................................5分综上所述:2nan()nN............................................................................6分(Ⅱ)2111111()4141(21)(21)22121nnbannnnn..............10分所以nT111111(1)23352121nn11(1)221n21nn...............................................................14分21.(本小题满分14分)解:(Ⅰ)当2a时,集合2{|(31)20}{|560}Axxaxaaxxx,{|23}xx...........................................................................2分集合2{|430}{|13}Bxxxxx.....................................4分故{|23}ABxx................................................................................5分(Ⅱ)若q是p的必要条件,则集合AB.............................................................6分集合2{|(31)20}Axxaxaa{|()[(21)]0}xx...