名校
解题方法
1 . 已知函数
(a为常数),若函数
有两个零点
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa8ea75ca2f775085b1838bef2c641d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-05-09更新
|
755次组卷
|
4卷引用:福建省福州市闽侯县第一中学2023-2024学年高二下学期第二次月考(5月)数学试题
名校
解题方法
2 . 在复数域内,大小成为了没有意义的量,那么我们能否赋予它一个定义呢,在实数域内,我们通常用绝对值来描述大小,而复数域中也相应的有复数的模长来代替绝对值,于是,我们只需定义复数的正负即可,我们规定复数的“长度”即为模长,规定在复平面
轴上方的复数为正,在
轴下方的复数为负,在
轴上的复数即为实数大小.“大小”用符号+“长度”表示,我们用
来表示复数的“大小”,例如:
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1668e5530289a3f96e4d64d5902d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ac6b062f7dba435dcbc2ac3d6d5b0f.png)
A.![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.复数![]() ![]() ![]() ![]() |
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3 . 对于向量集
,记向量
.如果存在向量
,使得
,那么称
是向量集
的“长向量”.
(1)设向量
,
.若
是向量集
的“长向量”,求实数x的取值范围;
(2)设向量
,
,则向量集
是否存在“长向量”?给出你的结论并说明理由;
(3)已知
均是向量集
的“长向量”,其中
,
.设在平面直角坐标系xOy中的点集
,其中
,
,且
与
关于点
对称,
与
关于点
对称
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93932ca99eac3f0663cde6482af92342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522e132d820f9f43d02d3bbfdf6cfbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde5bf9b63fbb9634f67a370a209c42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0653377e152bab90be30606f5a7e447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f50ecfa147131019f969c3bc78169f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814dc1e4c6160bbe16dae1d961ecc5bc.png)
(1)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c252e4eca6fb761476858b1fd43ce0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67dbe2e19d8960789ec873b687998b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04557534811083fb3dcabd339d0b3b1c.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a220774f46b5026df2ff61e142850a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ceb9949fa420aed75fe606ce29fcb8.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0aca31150d49fff8a60dc4d5df88a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04557534811083fb3dcabd339d0b3b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda59f49576061a1fc069a6bc3df592b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90626abcbca513539be197b9872b2193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95903a582b54cb1b478276319805275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829179938940431b33a92fb95adc665e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098727eaeaec66f5190f20492060b177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc4dc226800792c55eaa32134041837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f306a75051c9a11c92aa30a836a016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b5ea93b62e9b06f0060ab0d09e6633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc4dc226800792c55eaa32134041837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432001ad997d27e91c27da58c19ea3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1f68f8b7671e3b51536ef30d50d8c8.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
对定义域内任意
,都有
,则正实数
取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0803f73027eb1eda725c4af835fed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998300a677c3f657523a4071def9135a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
5 . 如图所示,在棱长为2的正方体
中,点
,
分别为棱
,
上的动点(包含端点),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.四面体![]() |
B.当![]() ![]() ![]() ![]() ![]() |
C.正方体![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
6 . 在
中,内角A,B,C的对边分别为a,b,c.已知
,
.
(1)求证:
是直角三角形;
(2)已知
,
,点P,Q是边AC上的两个动点(P,Q不重合),记
.
①当
时,设
且
,记
的面积为
,求
的最小值;
②记
,
.问:是否存在实常数
和
,对于所有满足题意的
,
,都有
成立?若存在,求出
和
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc02f69333db266eeb1e4d8a367726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e899c486dc49e560fc4aca05e16835b7.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96fbed3c855b8d52c669712a4410fd39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7fa79a550591eb9e1bd07bced3a08fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f68ade9c228169668792516571e28a.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a40d2cf43fce0c99dff3470d554eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6283da8b3b002401e671818c788abe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec5d200b561e4be52ccaaebdc3105d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c495b8fd7f7bb21c177c9d50fbf6919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c47acbb0d7d46a8de00fc59849feaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4049622421974f1501f377f0f4f4f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faac624f25ebbba44bf8f2c4a84791cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
7 . 记集合
,集合
,若
,则称直线
为函数
在
上的“最佳上界线”;若
,则称直线
为函数
在
上的“最佳下界线”.
(1)已知函数
,
.若
,求
的值;
(2)已知
.
(ⅰ)证明:直线
是曲线
的一条切线的充要条件是直线
是函数
在
上的“最佳下界线”;
(ⅱ)若
,直接写出集合
中元素的个数(无需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8ed79e83f9896873e80c3c4b5a935d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0bf53ee2722352957ab61f90a49daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54ade3f669537d031a2be1b4f24a626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165beb63772ec0f7797a71646d0a1ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7cc26a0fe4103db9229df034d5aa70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf2f55da363aa19912ee465d3eb2737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063bb2a5c220db357fa36417de213ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da66a74e8ab43f08d4b3949bb7d24e4.png)
(ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f4d45f004ca5fbf9a9bb4f0eef8232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a669064772daefdeb12c3ebaf01a581f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a494f5a36475e96c7bc69589f70c3a86.png)
您最近一年使用:0次
2024-05-07更新
|
484次组卷
|
2卷引用:福建省福州市2023-2024学年高三下学期4月末质量检测数学试卷
名校
8 . 已知
,函数
有两个极值点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cbf8bd2bb0cbf80c2c2aa450045fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
A.![]() |
B.![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若存在![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
9 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b70d8169a0264375fb4cc7b85a011.png)
(1)若函数
与
的图象存在公切线,求
的取值范围;
(2)若方程
有两个不同的实根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1b70d8169a0264375fb4cc7b85a011.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576469e4f51c1ede73f7f0458f504418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03fd662f69ce3e5449c08e00b963194.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
,
,下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e729f17846ca23b0e4a20a58cfc025b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f5ed72f10fcbe1dc8f8d933209ba77.png)
A.函数![]() ![]() |
B.![]() |
C.函数![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次