名校
解题方法
1 . 我国南北朝时期的数学家祖暅提出体积的计算原理(祖暅原理):“幂势既同,则积不容异.”“势”即是几何体的高,“幂”是截面积,意思是:如果两等高的几何体在同高处的截面积相等,那么这两个几何体的体积相等.已知双曲线
的焦点在
轴上,离心率为
,且过点
,则双曲线的渐近线方程为______ .若直线
与
在第一象限内与双曲线及其渐近线围成如图阴影部分所示的图形,则该图形绕
轴旋转一周所得几何体的体积为______ .
![](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/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24de2c921a76397efbc7cc3f46c78a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bbf68714436abcc9a8fdc01bd04895.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
解题方法
2 . 如图是飞行棋部分棋盘,飞机的初始位置为0号格,抛掷一枚质地均匀的骰子,若抛出的点数为1,2,飞机向前移一格;若抛出的点数为3,4,5,6,飞机向前移两格.直到飞机移到第
(
且
)格(失败集中营)或第
格(胜利大本营)时,游戏结束.则飞机移到第3格的概率为___________ ,游戏胜利的概率为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5d0a73f50b3e4583f1c1b6d6bf0d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56c561ae92deb820c04628859bb7543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
3 . 设函数
的极值点为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52461774f112577cb7439e4ebc50b5fb.png)
______ .已知数列
满足
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b7daadaea74c1a9d8f97fd0b4086f1.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82de9617e278cd3a6fd199c434db7cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52461774f112577cb7439e4ebc50b5fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70245565b95dd8f667af2bfdf2dd3f89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c14c2231171ce31f2cedea0307f34d53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b7daadaea74c1a9d8f97fd0b4086f1.png)
您最近一年使用:0次
2024-05-12更新
|
235次组卷
|
2卷引用:辽宁省沈阳市第二中学2023-2024学年下学期期中考试数学试卷
4 . 某学校数学实践小组为该校一块长方形空地设计种树方案,在坐标纸上设计如下:第
棵树种在点
处,其中
,当
时,
,[
]表示不大于x的最大整数,按此设计方案,第3株树种植点的坐标为___________ ;第2025棵树种植点的坐标为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a9ea0c17c1c1576541f981a202701b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e93eb05e988d2fd48fac631e479b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7437284d09b06a4e911be5feaf83dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-05-11更新
|
220次组卷
|
2卷引用:山东省潍坊市2023-2024学年高二下学期期中质量监测数学试题
名校
解题方法
5 . 假设视网膜为一个平面,光在空气中不折射,眼球的成像原理为小孔成像. 思考如下成像原理: 如图,地面内有圆
,其圆心在线段
上,且与线段
交于不与
重合的点
,
地面,且
,
点为人眼所在处,视网膜平面与直线
垂直. 过
点作平面
平行于视网膜平面. 科学家已经证明,这种情况下圆
上任意一点到
点的直线与平面
交点的轨迹(令为曲线
)为椭圆或圆,且由于小孔成像,曲线
与圆
在视网膜平面上的影像是相似的,则当视网膜平面上的圆
的影像为圆时,圆
的半径
为____________ . 当圆
的半径
满足
时,视网膜平面上的圆
的影像的离心率的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d33c8575602cb3480ba3825dece9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7442b64b37f685bc3ae88ff450c1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e92e4810c9461c39fae1acde95e489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dc6893e52bbca0d011ac46845334d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
您最近一年使用:0次
2024-05-09更新
|
99次组卷
|
2卷引用:四川省成都市实验外国语学校2023-2024学年高二上学期期末能力测评数学试题
名校
6 . 记
表示k个元素的有限集,
表示非空数集E中所有元素的和,若集合
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33af7985fac2b7c4865d2f799baad783.png)
_____ ,若
,则m的最小值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fcb5a22de0e05657a3af45a0739e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed7239671dbc4429371f31db3b1efc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a8f8aae48c1483815eff5a6e3fb7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33af7985fac2b7c4865d2f799baad783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817fc14a3ac8462a34b4b2f3bf07f13d.png)
您最近一年使用:0次
2024-05-04更新
|
432次组卷
|
2卷引用:福建省三明市2024届普通高中高三毕业班质量检测数学试题
名校
7 . 剪纸是一种用剪刀或刻刀在纸上剪刻花纹,用于装点生活或配合其他民俗活动的中国民间艺术.其传承赓续的视觉形象和造型格式,蕴涵了丰富的文化历史信息,表达了广大民众的社会认知、道德观念、实践经验、生活理想和审美情趣,具有认知、教化、表意、抒情、娱乐、交往等多重社会价值.现有如图所示剪纸图案,其花纹中就隐含方程为
的曲线C(称为星形线),则曲线C的内切圆半径为__________ ;以曲线C上点
为切点的直线被坐标轴截得的线段长等于__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bc1b7db92cb8d877c90ddafb3b3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc34e72b0801752d88ec762af4e0814f.png)
您最近一年使用:0次
2024-03-14更新
|
593次组卷
|
5卷引用:安徽省安庆市2024届高三模拟考试(二模)数学试题
安徽省安庆市2024届高三模拟考试(二模)数学试题(已下线)【一题多变】曲线方程 变形化简(已下线)专题8 函数新定义问题【讲】(压轴题大全)(已下线)模块三 易错点3 不会从情境题中抽象出数学图形广东省广州市执信中学2024届高三下学期教学情况检测(三)数学试题
名校
解题方法
8 . 在
中,M是边BC的中点,N是线段BM的中点.设
,
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
__________ ;若
,
的面积为
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a779e711b3900db89bd868360dcfaa.png)
__________ 时,
取得最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f386f5b56b07b96f2600da1be15414a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc51bdc8c2c18379db1affbb06f8923f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06393c604df2200ce9fd4bc9e67c2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a779e711b3900db89bd868360dcfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6f0e94393fc6bbd9b4b83ede534ac.png)
您最近一年使用:0次
2024-03-01更新
|
1447次组卷
|
6卷引用:天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷
天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷(已下线)第2套 新高考新结构全真模拟2(艺体生)天津市实验中学滨海学校2023-2024学年高一下学期随堂质量监测(月考)数学试题(已下线)信息必刷卷04(天津专用)(已下线)压轴题03不等式压轴题13题型汇总 -1(已下线)2024年天津高考数学真题平行卷(提升)
2024高三·全国·专题练习
名校
解题方法
9 . 已知
为坐标原点,
为椭圆
的左、右焦点,
是椭圆上异于顶点的一点,点
是以
为底的等腰三角形
的内切圆圆心,过
作
,垂足为
,则椭圆的离心率为______ .设内切圆与
轴相切于点
,则
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20537b56f64f6b7a808402981257c96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c3e0f50ddb6819979cf96cce25248e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57da117f4143ccf0d6d8b26829197813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30467196dfcb2cc2f388fb9b2ab15e8.png)
您最近一年使用:0次
名校
10 . 如图,椭圆
与双曲线
有公共焦点
,椭圆的离心率为
,双曲线的离心率为
,点
为两曲线的一个公共点,且
为
的内心,
三点共线,且
轴上点
满足
,则
的最小值为__________ ;
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29eb5ce3f09c49dfa489a3b0bd5beafb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65abb60103949a9cbe1e4890df8bd3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8597c617617900e3265b9eacb0fed1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadd9ffa5f17a464c7b1eba82f68f386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78385e289193ff6bea96956b1126295e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7da98a8220a45b0cc4a665ebac80ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120f812ad42739155a1337e7d5a7bcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c07b101a1a118c7558a9e59b13c95c.png)
您最近一年使用:0次