江苏省连云港市2020-2021学年高一上学期期中考试数学试题(PDF版,含答案）

$$ 高一数学参考答案 第 1 页 共 4 页 2020～2021 学年第一学期期中考试 高一数学参考答案及评分标准 一、单项选择题：共 8 小题，每小题 5 分，共 40 分． 1．A 2．B 3．D 4．C 5．B 6．A 7．C 8．B 二、多项选择题：共 4 小题，每小题 5 分，共 20 分．在每小题给出的四个选项中，有多项符合题目要求， 全部选对的得 5 分，部分选对的得 3 分，有选错的得 0 分． 9．AC 10．AC 11．BD 12．ABD 三、填空题：共 4 小题，每小题 5 分，共 20 分． 13．3 14．8 15．30 16．36 四、解答题：共 6 小题，共 70 分．解答时写出必要的文字说明、证明过程或演算步骤． 17．（本小题满分 10 分） 解：若选择①因为  ( )( 1) 0A x x a x a     ，故 ( , 1)A a a  ； ························· 3 分 A B B ，则 A B ， ········································································· 5 分 所以 1, 1 1, a a    ≥ ≤ ······················································································ 8 分 解得 1 0a ≤ ≤ 所以选择①，实数 a 的取值范围是[ 1, 0] ． ··············································· 10 分 若选择②因为  ( )( 1) 0A x x a x a     ，故 ( , 1)A a a  ； ······························· 3 分 因为 A B ， 所以 1 1a  ≤ 或 1a≥ ， ·········································································· 6 分 解得 2a ≤ 或 1a≥ ， ············································································· 8 分 所以选择②，实数 a 的取值范围是 ( , 2] [1, )   ． ································· 10 分 若选择③因为  ( )( 1) 0A x x a x a     ，故 ( , 1)A a a  ； ······························· 3 分 因为 A B B ，则 B A ······································································ 5 分 所以 1, 1 1, a a    ≤ ≥ ····················································································· 8 分 所以 a 所以选择③，实数 a 不存在． ································································· 10 分 高一数学参考答案 第 2 页 共 4 页 18．（本小题满分 12 分） 解：（1）由 3 0, 1 0 x x    ≥ ≥ 得 1 3x ≤ ≤ ，所以  1,3A   ； ········································· 3 分 又   22 ( ) 2 3 1 2 2g x x x x      ≥ ，所以  2,B   ． ······························ 6 分 （2）由（1）知      1,3 2, 1,A B       ； ······································ 9 分 因为  , 2U B   ， ·······························