名校
解题方法
1 . 我国魏晋时期的数学家刘徽(图a)创造了一个称为“牟合方盖”的立体图形,在正方体内作两个互相垂直的内切圆柱(图b),其相交的部外就是牟合方盖(图c).我国南北朝时期数学家祖暅基于“势幂既同则积不容异”这一观点和对牟合方盖性质的研究,推导出了球体体积公式.已知在一个棱长为2r的正方体内有一个牟合方盖(图1),设平行于水平面且与水平面距离为
的平面为
,则平面
截牟合方盖所得截面的形状为__________ (填“正方形”或“圆形”),设这个牟合方盖的体积为
(图2),并设半径为
的球的体积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa4c480d031dedac6e81872836d04cc.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5547c2bb8607c1dba2bb0881777dbb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa4c480d031dedac6e81872836d04cc.png)
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名校
解题方法
2 . 如图,在
中,角
所对的边分别为
,已知
,
的平分线
交边
于点
边上的高为
边上的高为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ada871ccdbd83b6ccbddbcd84521bc.png)
__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330af1eaa4fbb442ebc7b47be6b6d7a.png)
__________ .
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0d44899ceb7b3137a82f2498c6d9b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bea1b93dcf0514f157720793da1a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383d609af37a655a531e3e7441cd123e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa9e9cc8d1a0e6846523986552693cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d287c4df5c0cac5a4931edb43b01d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ada871ccdbd83b6ccbddbcd84521bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330af1eaa4fbb442ebc7b47be6b6d7a.png)
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2024-06-16更新
|
218次组卷
|
3卷引用:陕西省西安市第一中学2023-2024学年高三下学期高考考前模拟考试理科数学试题
名校
解题方法
3 . 如图
中,
,
分别为
,
上的两点,满足
,
,则直线
一定通过
的______ (在重心,垂心,内心,外心中选择一项),若线段
和
相交于点
,那么
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a431c7044c63fc06428d1dcd01d45f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111d0ddc5a28986f3bfcbd145aa574e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf66a22ef9eee85270d407cec1dae7e2.png)
您最近一年使用:0次
解题方法
4 . 如图,双曲线
的右焦点为
,点A在
的渐近线上,点A关于
轴的对称点为
为坐标原点),记四边形OAFB的面积为
,四边形OAFB的外接圆
的面积为
,则
的最大值为____________ ,此时双曲线的离心率为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](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/76b327a14dbffd4334ddfd133a5dfc17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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2024-04-12更新
|
344次组卷
|
3卷引用:陕西省安康市汉滨区2024届高三下学期高考模拟(五)文科数学试题
解题方法
5 . 已知
的角A,B,C的对边分别为a,b,c,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1813aa92d2379664c36eb440ef7506fc.png)
______ ,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c53ba20b6e6cfd43641211e0a8dda4.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1bc2d6672709f0b84d2eb80bcb594a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1813aa92d2379664c36eb440ef7506fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009836129d49a39a61afaeb0da0f272a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c53ba20b6e6cfd43641211e0a8dda4.png)
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名校
解题方法
6 . 已知函数
,其中
是
的导函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01cdb4a84f02a75eb447b54f73f7df6.png)
__________ ;
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6ffee15075ffa58a02823b508ff03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b01cdb4a84f02a75eb447b54f73f7df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
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2024-03-22更新
|
333次组卷
|
2卷引用:陕西省榆林市2024届高三第二次模拟考试文科数学试题
7 . 若一组数据
,
,
,
,
的平均数为3,方差为
,则
,
,
,
,
,9这6个数的平均数为______ ,方差为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a85a2c984df17f7ef91d014d931410d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
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2024-03-21更新
|
913次组卷
|
4卷引用:陕西省西安市部分学校2024届高三下学期二模考试理科数学试题
陕西省西安市部分学校2024届高三下学期二模考试理科数学试题河南省新乡市2024届高三第二次模拟考试数学试题(已下线)第六套 艺体生新高考全真模拟 (二模重组卷)(已下线)9.2.2总体百分位数的估计+9.2.3总体集中趋势的估计+9.2.4总体离散程度的估计【第三练】“上好三节课,做好三套题“高中数学素养晋级之路
解题方法
8 . 如图所示的数阵由数字1和2构成,将上一行的数字1变成1个2,数字2变成2个1,得到下一行的数据,形成数阵,设
是第
行数字1的个数,
是第
行数字2的个数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0c134f914b44e181db0154e3be7567.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769b2937ed0d97c73ffe527bbf344e4c.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0c134f914b44e181db0154e3be7567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769b2937ed0d97c73ffe527bbf344e4c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/2ad58421-da63-4b33-ba6d-7d210ce75142.png?resizew=183)
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2024-02-12更新
|
151次组卷
|
2卷引用:陕西省西安市莲湖区2023-2024学年高二上学期期末质量监测数学试题
名校
解题方法
9 . 如图,正方形与正方形
的中心重合,边长分别为3和1,
,
,
,
分别为
,
,
,
的中点,把阴影部分剪掉后,将四个三角形分别沿
,
,
,
折起,使
,
,
,
重合于P点,则四棱锥
的高为
内接于该四棱锥,其上底面四个顶点在四棱锥侧棱上,下底面四个顶点在面
内,则该直四棱柱
体积的最大值为
您最近一年使用:0次
2024-01-06更新
|
402次组卷
|
4卷引用:陕西省西安中学2024届高三模拟考试(一)数学(理科)试题
陕西省西安中学2024届高三模拟考试(一)数学(理科)试题江苏省镇江市句容高级中学2024届高三上学期12月学情调研数学试题(已下线)2024年高考数学二轮复习测试卷(新高考Ⅰ卷专用)江苏省常州市联盟学校2023-2024学年高二下学期3月阶段调研数学试题
名校
10 . 设
,
,且
,则a=______ ,b=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc2504b3dcc75009bd239b1d37876a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60714a0434a4f4ff6b9e5fead1305bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41533c82c9c3093d5e87ae3a4009ca3f.png)
您最近一年使用:0次