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1 . 设
表示
中最大的一个,例如
,则
.方程
的解是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749c45521309ed059607c75ee9b4bc26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeff341463d78c21224ca78a9ee47496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27f27cbb8185c1974d715ff95f8801c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc16367f9a67e563c2dbbbae87b7fdd5.png)
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2023-05-20更新
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83次组卷
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2卷引用:安徽省蚌埠第二中学2020-2021学年高一上学期自主招生考试数学试题
2 . 公元前3世纪,古希腊数学家欧几里德把人们公认的一些几何知识作为定义和公理(公设),在此基础上研究图形的性质,推导出一系列定理,组成演绎体系,写出《几何原本》.它的问世是整个数学发展史上意义极其深远的大事,也是整个人类文明史上的里程碑.在这本书中,欧几里德提出“三角形的内角和是
”这一定理,根据这一定理,我们可以得出“三角形的一个外角等于与它不相邻的两个内角之和”的结论.进一步思考:多边形的一个外角和与它不相邻的内角之间又有怎样的关系呢?假设一个
边形的某一个外角的度数是
,与它不相邻的所有内角的和是
,那么
与
的关系是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e7a123c9cc0e058db28841fb0edcf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed093e8d3f9c75408897c07186ad4784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a7e1a4cd618c17fdc4d9d084066b378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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3 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9eb25a10c0f201dc81f81249c78e9d3.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08d209628e76267ad265a89516d1913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9eb25a10c0f201dc81f81249c78e9d3.png)
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4 . 我们引入记号
表示某个函数,用
表示
时的函数值.例如函数
可以记为
,并有
.狄利克雷是德国著名数学家,是最早倡导严格化方法的数学家之一.狄利克雷函数
的出现表示数学家对数学的理解开始了深刻的变化,从研究“算”到研究更抽象的“概念、性质和结构”.关于狄利克雷函数,下列说法:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9691880e6d44aa300399619ab2032944.png)
②对于任意的实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9aaa072c8960c94bfa12a596a5ba53.png)
③对于任意的实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a9e945cb7f64159a24c0ae16a3f304.png)
④存在一个不等于0的常数
,使得对于任意的
都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71f07867fc8b77dd490e88c530b0b59.png)
⑤对于任意两个实数
和
,都有
.
其中正确的有__________ (填序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f484115a9df1b6060d6b14df85c6f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04beea76c59a6c5b096d8c5a3b77f8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca0676718505851f1f6daaef35df7ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37695572935ea8db6d7683ab6555acd9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9691880e6d44aa300399619ab2032944.png)
②对于任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9aaa072c8960c94bfa12a596a5ba53.png)
③对于任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a9e945cb7f64159a24c0ae16a3f304.png)
④存在一个不等于0的常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71f07867fc8b77dd490e88c530b0b59.png)
⑤对于任意两个实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec485f7f68edac80e8758f5864e73d5.png)
其中正确的有
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5 . 已知不相等的实数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcffef0ab24dc35852500469bec2ef1.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f03cab451843012fd80fa6cc698c648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11272b3f738e5cc5ec7894a75bc4b3a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcffef0ab24dc35852500469bec2ef1.png)
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6 . 已知
与
的边
的延长线分别相切,若
,则
的度数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a58a576a3574db4ac1f64c845387a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66898d6c16bfd2e6df54160a1b493ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17e587b7fcc3f7ef52c0a542141daa2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/10/d99e97d6-d737-4f9d-a31c-6d0172733801.png?resizew=204)
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7 . 如图,扇形
的圆心角
,半径为5,正方形
内接于该扇形,连接
,则
的正切值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5de86f3dd3e58e0a94638db1f3e355.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/10/0ea95124-0a25-480e-b767-9d36575bbbf2.png?resizew=168)
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8 . 若函数
,则当自变量
取1、2、3、...100这100个自然数时,函数值的和是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e2f47dbc262fb3d68f6000b76025df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 .
四支足球队进行单循环赛(每两队都要比赛1场且只比赛1场),胜一场得3分,负1场得0分,平局各得1分.已知:①此赛结果没有两队的积分相同;②
没有平局,
平2局;③
净胜球
个;④
净胜球
个;⑤
净胜球1个.问
与
比赛的净胜球数为__________ (净胜球
进球数一失球数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db2ca6d163be93b18959beb75ac588b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
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10 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7493baf90cc08fba0cdaec7cdf9031e.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321d7954d41287894696886db78a0fcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7493baf90cc08fba0cdaec7cdf9031e.png)
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2022-05-16更新
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474次组卷
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7卷引用:安徽省蚌埠第三中学2021-2022学年高二下学期开学测试数学试题