名校
解题方法
1 . 若非空实数集X中存在最大元素M和最小元素m,则记
.下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63cf0f3392d77db21347ed4e94812a6.png)
A.已知![]() ![]() ![]() |
B.已知![]() ![]() ![]() ![]() |
C.已知![]() ![]() |
D.已知![]() ![]() |
您最近一年使用:0次
7日内更新
|
93次组卷
|
3卷引用:上海市复旦大学附属中学2022届高三上学期9月月考数学试题
名校
解题方法
2 . 如图展示了一个区间
(
是一个给定的正实数)到实数集R的对应过程:区间
中的实数
对应线段
上的点
,如图1;将线段
弯成半圆弧,圆心为
,如图2;再将这个半圆置于直角坐标系中,使得圆心
坐标为
,直径
平行
轴,如图3;在图形变化过程中,图1中线段
的长度对应于图3中的圆弧
的长度,直线
与直线
相交于点
,则与实数
对应的实数就是
,记作
.给出下列命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/313061c7-d288-4888-987f-7f43859f1047.png?resizew=508)
(1)
;
(2)函数
是奇函数;
(3)
是定义域上的单调递增函数;
(4)
的图像关于点
对称;
(5)方程
的解是
.
其中正确命题序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54db6c82096015c2fd1cfa62a05fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54db6c82096015c2fd1cfa62a05fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a8588dc60a543ad70d6bc0d263dbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9d87b1d7a593ed9fd10206b87fa59a.png)
![](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/a9df0e576a3d75d66060bbdd1549ba4b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/313061c7-d288-4888-987f-7f43859f1047.png?resizew=508)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1f28b00526dcd8edd41600728e14ba3.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df0e576a3d75d66060bbdd1549ba4b.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df0e576a3d75d66060bbdd1549ba4b.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df0e576a3d75d66060bbdd1549ba4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26fca47de6a623818ef1f56594de500.png)
(5)方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce1b004f97ed12a5cad0bd5ccf7bf09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991c786a9434ba4ac8b1cd223933766c.png)
其中正确命题序号为
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名校
3 . 在物理中,我们已学习过匀加速直线运动以及如下式子:
,
,现小明以加速度
做匀加速直线运动,在
地处的速度为
,在
地处的速度为
,则它在
地和
地的中点处的速度
满足( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3d2b8d0068d64c2f6511b236c5caca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5800a9ee6b8ad07f0f4bfda028aa645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a12ea6f9d2bbcc5a3d7980dbe79922d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44c235d8b49207ad3f2d77dc5d6cf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814f55724f7ee57bd395eb3b95393c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f6ccbb4c090d2e66cda9e5acf44458.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 在平面直角坐标系中,二元方程
的曲线为
,若存在一个定点
和一个定角
,使得曲线
上的所有点以
为中心顺时针(或逆时针)旋转角
,所得到的图形与原曲线重合,则称曲线
为旋转对称曲线.给出以下方程及其对应的曲线:
; ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199da209c1d449712901f9d8fa751d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d69accbf3a6fb381616ae0a7c43b160.png)
其中是旋转对称曲线的是__ (填上所有符合题意的曲线).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a6af0c85c1a59c2b77b6e550e1ef54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de72548ccc62e6e15d1be4afcdf09ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199da209c1d449712901f9d8fa751d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55411ad607653d2077c4e6ca583f985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d69accbf3a6fb381616ae0a7c43b160.png)
其中是旋转对称曲线的是
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名校
解题方法
5 . 已知上海地处东经
至
,则上海所辖区域的经线对应的两半平面所成的二面角的大小是__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8190523bfcbf0a3cb22974c5f0909311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33b1ca056574a0230b4753be66f630f.png)
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解题方法
6 . 对于给定数列
,若存在一个常数
,对于任意
,使得
成立,则称数列
是周期数列,
是数列
的一个周期,若
是数列
的周期,且
均不是数列
的周期,则称
为数列
的最小周期.已知无穷数列
的前
项和为
,满足:
对一切
成立
(1)若数列
是最小周期为2的周期数列,求数列
的通项公式;
(2)求证:数列
不可能是周期为2021的周期数列;
(3)数列
是否可能是最小周期为2020的周期数列?若不可能,请说明理由;若可能,求最小的正实数
,使得对任意最小周期为2020的周期数列
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a11f7b5372fa92315ff97c5ac13b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4400c714e5d4cbb684a3e20848d9c5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3c057679906df73d7e756da4ceedfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaf344771df7e1f3801f3d817302fa.png)
您最近一年使用:0次
7 . 已知椭圆
的左、右焦点分别为
,点
为椭圆
上两点.
(1)若直线
过左焦点
,求
的周长;
(2)若直线
过点
,求
的取值范围;.
(3)若点
是椭圆
与抛物线
在第一象限的交点.是否存在点
,使得线段
的中点
在拋物线
上?若存在,求出所有满足条件的点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdce3deea7dc84d1a2119a34863b36ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1ae37530007d72ccab3c15ffbe4de0.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12769b05875896568efa75bddf287bf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2023-01-03更新
|
560次组卷
|
4卷引用:上海市复旦大学附属中学2021届高三下学期4月月考数学试题
名校
解题方法
8 . 已知直线和点
,点
到直线
的有向距离
用如下方法规定:若
,
,若
,
.
(1)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04cd247d6eb7602b2fb813e961cb0981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8daba713e9d94a65871022d310c8baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eb516bff5a0ec1cad530c8dce3cbc7.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea1f5bdd213c7c3a571b4c38850bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bc6e35f01f01a7b1afedb7b1b8c4bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4cb1e1e4befa6939d2c121fb0b4a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a6bc81f2ed0a56e65beefbe220da1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f36aa5f1ba38dad6932617f92ce1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f2813ee8f26cca880b6427f5f545d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/144d8ebcb3add5def7d045c73a5ba4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5c1168539f25962374b48170d46730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-01-02更新
|
680次组卷
|
7卷引用:上海市复旦大学附属中学2021-2022学年高二上学期10月月考数学试题
上海市复旦大学附属中学2021-2022学年高二上学期10月月考数学试题云南省昆明市西南大学官渡实验学校2023-2024学年高二上学期9月综合素质测评数学试题福建省厦门市第一中学2023-2024学年高二上学期10月月考数学试题(已下线)第1章 坐标平面上的直线 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)(已下线)第1章 坐标平面上的直线 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)1.1 直线与直线的方程 检测卷-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册(已下线)专题04 直线的方程压轴题(4类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)
名校
解题方法
9 . (1)求证:
是函数
的最小正周期;
(2)已知
都是实数,求证:
,并且等式成立的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f159dec6b1eee9270c47ba0f07812bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b672aad8cac57acdc9654d95699c00c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1befdda5f9e5055b0d2ae58b1b4b201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab138a74db444886abc7fe18947f7a3e.png)
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10 . 已知复数
、
对应的向量为
.
(1)若向量
,且
,
.求
对应的复数
;
(2)容易证明:
,类比到对应的向量,请写出类似的结论,并加以证明;
(3)设
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5cdedb6f4384fda29fb4508ba6fcc5.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c931438cd1de4180c622d66aee1de431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbf8cf890e1bab18f37152ef5da7dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c97d2a35ee85fa0b51eeaeb1ce1f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4302196fdb56536ddc2f2a3c2e9073e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
(2)容易证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8c8b8610bef469c87bb73919310477.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e294bd40af7a49ac1fadca723499c229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
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2022-12-03更新
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3卷引用:上海市曹杨第二中学2020-2021学年高一下学期5月月考数学试题
上海市曹杨第二中学2020-2021学年高一下学期5月月考数学试题(已下线)专题7.7 复数的运算大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)高一复数重难点提高卷-【同步题型讲义】