名校
1 . 已知
外接圆的圆心为点
,半径为
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2 . 向量外积(又称叉积)广泛应用于物理与数学领域.定义两个向量
与
的叉积
,规定
的模长为
,
与
、
所在平面垂直,其方向满足如图1所示规则,且须满足如图所示的排列顺序.已知向量外积满足分配律,且
.
;②
;
(2)空间直角坐标系中有向量
,
①若
,用含
的坐标表示
;
②
证明:
;
(3)如图2所示,平面直角坐标系
中有三角形OAB,
,试探究
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4b78561c1b513a90122730a126d585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcf3f31d18fa318e4f947d331ddd229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4813c1052e3e1a7f229c85156c61b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb30a9b89b6310c560c56a79a9bdb30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92fe31d138472bc7f4b99050b97007f.png)
(2)空间直角坐标系中有向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af4e5a239ec34b9dd46a8b9518f86658.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea61e69fd7a319942f48082c341ac2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb17664b1f6e969b1cf22e95cef9075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3680f37d3a0a5fb8038213ccf33f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d641794c36b9ab43f9dc5ba02a0f65ef.png)
(3)如图2所示,平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de77ee0b176035fd3a89edc2ad957a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a711bf44ed64556c72fbb0e7f42c27f.png)
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解题方法
3 .
的三条高交于一点H,
所对的边分别为
,下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfae2500c1deac438b720b191a122a5b.png)
A.![]() |
B.![]() |
C.![]() |
D.若![]() ![]() ![]() |
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解题方法
4 . 设
,我们常用
来表示不超过
的最大整数.如:
.
(1)求证:
;
(2)解方程:
;
(3)已知
,若对
,使不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9322dd8f56b5f8d2c667fdf0d4a9f9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f161c2a3717f1b6c62d0d7dae0b606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0147928001a2b80afcd6c28c8091cf91.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d959974d562cb9ef138676ae943bc19c.png)
(2)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8300c3dc2f5674dddbaa768109142592.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48da06492a0b0c8a31a5dc1531e8f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb945c963b0d56df9d784d3e3288c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a9d89ec3d1181091ea159b40952b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-13更新
|
567次组卷
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4卷引用:湖北省云学名校联盟2023-2024学年高一下学期3月联考数学试卷
名校
解题方法
5 . 如图是一种升降装置结构图,支柱
垂直水平地面,半径为1的圆形轨道固定在支柱
上,轨道最低点
,
,
.液压杆
、
,牵引杆
、
,水平横杆
均可根据长度自由伸缩,且牵引杆
、
分别与液压杆
、
垂直.当液压杆
、
同步伸缩时,铰点
在圆形轨道上滑动,铰点
在支柱
上滑动,水平横杆
作升降运动(铰点指机械设备中铰链或者装置臂的连接位置,通常用一根销轴将相邻零件连接起来,使零件之间可围绕铰点转动).
的长为
,求水平横杆
的长和
离水平地面的高度
(用
表示);
(2)在升降过程中,求铰点
距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0101a7b5c8a4aed0de2af363792e39a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0101a7b5c8a4aed0de2af363792e39a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f9651b17b98d75a87a7e502202d32e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a987d8689e9a5556f98c37ea485afeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62e8aadaadebf1454fde21a390ebdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b49022a6f55817b5d7e3ab443b5491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971b23e3ee827018557d6c88edd5369a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b49022a6f55817b5d7e3ab443b5491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971b23e3ee827018557d6c88edd5369a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62e8aadaadebf1454fde21a390ebdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7a3e520a16d4fdd73c4e6a4ce7be0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62e8aadaadebf1454fde21a390ebdea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f268424db595e480bbd58f1b7a2e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09af0df7030bbefc8711456da8d87b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0101a7b5c8a4aed0de2af363792e39a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107fd7b3176ecb59eba848fe8d87d114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598c4ff9fc8518fa4829e39254d3f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)在升降过程中,求铰点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09af0df7030bbefc8711456da8d87b38.png)
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2024-01-29更新
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3卷引用:湖北省襄阳市第四中学2023-2024学年高一下学期质量检测(一)数学试题
湖北省襄阳市第四中学2023-2024学年高一下学期质量检测(一)数学试题浙江省台州市2023-2024学年高一上学期1月期末数学试题(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
6 . 如图,边长为8的正方形
的两边在坐标轴上,以点
为顶点的抛物线经过点
,点
是抛物线上点A,
间的一个动点(含端点),过点
作
于点
,点
,
的坐标分别为
,
,连接
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/d4e245e4-d95a-4866-b024-9ad0198f26aa.png?resizew=193)
(1)小明探究点
的位置发现:当点
与点A或点
重合时,
与
的差为定值,进而猜想:对于任意一点
,
与
的差为定值,请你判断该猜想是否正确,并说明理由;
(2)小明进一步探究得出结论:若将“使
的面积为整数”的点
记作“特别点”,则存在多个“特别点”,且使
的周长最小的点
也是一个“特别点”.请直接写出 所有“特别点”的个数,并直接写出
周长最小时“特别点”的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edadd9995393ece0d7b7bf4801504bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daa67de3b8971d54ced0cac0cd11f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/d4e245e4-d95a-4866-b024-9ad0198f26aa.png?resizew=193)
(1)小明探究点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
(2)小明进一步探究得出结论:若将“使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
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7 . 定义:若
,则称
是函数
的
倍伸缩仿周期函数.设
,且
是
的2倍伸缩仿周期函数.若对于任意的
,都有
,则实数m的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0b3091b42b44084cce4d5910b778bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0141bb8bf02d72c043bf38a54d296842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa707810ce8900ca0551a8ecfa723718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee2d98ee1e205abf5b8111be23ba53b.png)
A.12 | B.![]() | C.![]() | D.![]() |
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2023-06-09更新
|
448次组卷
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3卷引用:湖北省新高考协作体2022-2023学年高一下学期5月联考数学试题
名校
8 . 已知正三棱锥
的侧棱长为3,
.过顶点
作底面
的垂线,垂足为
,过点
作侧面
的垂线,垂足为
,过点
作平面
的垂线,垂足为
,连接相关线段形成四面体
,则四面体
的外接球的表面积为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1dd92c99d24ecbba1f72fc8b422822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
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2023-06-08更新
|
399次组卷
|
2卷引用:湖北省高中名校联盟2022-2023学年高一下学期5月联合测评数学试题
名校
9 . 某公园有一块长方形空地ABCD,如图,
,
.为迎接“五一”观光游,在边界BC上选择中点E,分别在边界AB、CD上取M、N两点,现将三角形地块MEN修建为花圃,并修建观赏小径EM,EN,MN,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/28/a7ef926e-429b-4c15-b94f-515a293cf4a9.png?resizew=154)
(1)当
时,求花圃的面积;
(2)求观赏小径EM与EN长度和的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb1e3ba0d8f65254f44ca1a34685726.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/28/a7ef926e-429b-4c15-b94f-515a293cf4a9.png?resizew=154)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d57894299174fdcb815d746b770604.png)
(2)求观赏小径EM与EN长度和的取值范围.
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2023-04-27更新
|
1199次组卷
|
3卷引用:湖北省武汉市第十一中学2022-2023学年高一下学期6月月考数学试题
名校
解题方法
10 . 对于两个均不等于1的正数m和n,定义:
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb22b7e5510fd19faec8653ccca3e36d.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-04-08更新
|
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