1 . 设圆
的圆心为
,直线
过点
且与
轴不重合,
交圆
于
两点,过
作
的平行线交
于点
.
(1)设动点
的轨迹为曲线
,求曲线
的方程;
(2)曲线
与
轴交于
.点
在点
的右侧,直线
交曲线
于点
两点
不过点
,直线
与直线
的斜率分别是
且
,直线
和直线
交于点
.
①探究直线
是否过定点,若过定点求出该点坐标,若不过定点请说明理由;
②证明:
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714df7f0c804617e1c8832d2e91b496a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)设动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de562860972bdb1f46843689a14ae69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f75e8505a83e34c81dfa2b2996f6557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448eb7d301baa90fe59b05761830f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439c8a01a6626d7a3f53af31ef0bcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bb56032b37aaf40bfbac51f7fe2d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
①探究直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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2卷引用:安徽省皖北五校联盟2024届高三第二次联考数学试卷
名校
解题方法
2 . 现定义“
维形态复数
”:
,其中
为虚数单位,
,
.
(1)当
时,证明:“2维形态复数”与“1维形态复数”之间存在平方关系;
(2)若“2维形态复数”与“3维形态复数”相等,求
的值;
(3)若正整数
,
,满足
,
,证明:存在有理数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dc4e868a310c371ff88075d8a966a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9d830212489b316bb052455098108e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc8299790d98621b87e73212a2ebb91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
(2)若“2维形态复数”与“3维形态复数”相等,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c136aaf9b5dedec254a92ce302f4a70c.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94742ebbb028c50d7a58e3e8f4ab329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35490c12e57ecd91af9934cb17b5c927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ed110fbfeb14003270a1039ba174d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f02f2606180ffeda602ff9ae747af6f.png)
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2024-05-11更新
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3卷引用:安徽省合肥市第一中学2023-2024学年高一下学期5月期中联考数学试题
名校
3 . “阿基米德多面体”也称为半正多面体,是由边数不全相同的正多边形围成的多面体,它体现了数学的对称美.如图所示,将正方体沿交同一顶点的三条棱的中点截去一个三棱锥,共可截去八个三棱锥,得到八个面为正三角形、六个面为正方形的一种阿基米德多面体.已知
,则关于图中的半正多面体,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
A.该半正多面体的体积为![]() |
B.该半正多面体过![]() ![]() ![]() ![]() |
C.该半正多面体外接球的表面积为![]() |
D.该半正多面体的表面积为![]() |
您最近一年使用:0次
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3卷引用:安徽省合肥市第一中学2023-2024学年高一下学期5月期中联考数学试题
4 . 有6本不同的书,按下列方式进行分配,其中分配种数正确的是( )
A.分给甲、乙、丙三人,每人各2本,有15种分法 |
B.分给甲、乙、丙三人,一人4本,另两人各1本,有180种分法 |
C.分给甲、乙每人各2本,分给丙、丁每人各1本,有180种分法 |
D.分给甲、乙、丙、丁四人,两人各2本,另两人各1本,有1080种分法 |
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5 . 已知函数
,(
).
(1)若
,求函数
的单调区间;
(2)若函数
有两个零点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4880051ee1220015a95b641c237a4ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b69f19078966e4444b2731fa7ebf7da.png)
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名校
解题方法
6 . 如图,已知等腰梯形
的外接圆圆心
在底边
上,
,
,
,点
是上半圆上的动点(不包含
,
两点),点
是线段
上的动点,将半圆
所在的平面沿直径
折起,使得平面
平面
.
平面
时,求
的值;
(2)证明:
不可能垂直
;
(3)设
与平面
所成的角为
,二面角
的平面角为
(其中
),求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e01d3d6bd865e16908eb08dec78f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a6241af8eadb720f601ee48f74cb9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745e0525a41fe2e2a7739c75a942290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7fdfebdbaddc49e8991ec47d2fb076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9350ccf7500c62835c27f4b946b6db58.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ea10539215794cd76e8b211abd503f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cd47260d190dc5b89e5303879ab164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628560d39eeb0339fa00c9c15ab2c095.png)
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名校
7 . 已知函数
和
有相同的最大值
,直线
与两曲线
和
恰好有三个交点,从左到右三个交点横坐标依此为
,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/809d649d9ccf56f3b399057e9268d0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b740dd29cf742f63add0e26c9c22c7d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2905c472769b73313bd3258bae3f33dc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 已知函数
(
是自然对数的底数).
(1)当
时,求
的极值点;
(2)讨论函数
的单调性;
(3)若
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c207efd83d75c1f69237d97616c726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb37cae66e9ec725a1e35be4ab1c711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086f714608dfffd3ac8da92d12c26239.png)
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名校
解题方法
9 . 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
|
476次组卷
|
2卷引用:安徽省安庆市第一中学2024届高三下学期6月第四次模拟(热身考试)数学试卷
名校
解题方法
10 . 已知平面非零向量
和单位向量
,若
与
的夹角为
与
的夹角为
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc64abe49847ade9b78678ba1f8e0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc64abe49847ade9b78678ba1f8e0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a6a5c98d78050766cfbc8214179e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fb0321db0676af22be95f8a9cc9b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576536967639b1821f5e3b07be02c3ce.png)
您最近一年使用:0次
2024-05-07更新
|
527次组卷
|
2卷引用:安徽省亳州市第二完全中学2023-2024学年高一下学期第二次月考(5月)数学试题