2024·全国·模拟预测
解题方法
1 . 已知四棱锥
的底面
是边长为
的正方形,
,
平面
,
为线段
的中点,若空间中存在平面
满足
,
,记平面
与直线
分别交于点
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90271643a96d65b3b092fbbdbd61eea0.png)
______ ,四边形
的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967f74b8993c61634ceed95edca05ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3dd3fc7dc95d1af9eafb1ea58dd48a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e049faf8852317b6c046904a39134c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211a44ffb09c7413dac58e9cea70fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90271643a96d65b3b092fbbdbd61eea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a255eabf4d401236e1f1a9f35667ba9.png)
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解题方法
2 . 已知三棱锥
的各顶点均在半径为2的球
表面上,
,
,则三棱锥
的内切球半径为__________ ;若
,则三棱锥
体积的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/418b19e808e7ac6acb2065b005595693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a621bfa70a014bdcdb58697f099b597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbddb854a1a634484936c64ab4a9102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5402d4268ec1028e5307063539c10d7.png)
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名校
3 . 已知等差数列
的公差与等比数列
的公比相等,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
______ ;若数列
和
的所有项合在一起,从小到大依次排列构成一个数列
,数列
的前
项和为
,则使得
成立的
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684b935a7274130d081bfa7b2b938023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89b8821c758c29c8b02bd79425ecbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13624221ac7e06fc5ebd48b21ed0de10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055bd850286feebbeac5df481988b1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-03-08更新
|
1240次组卷
|
4卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题
解题方法
4 . 已知正七边形ABCDEFG的外接圆为
且A为该圆上距离坐标原点最远的点,则关于这七个点的回归直线方程为__________ ;设CG,AD交于Q,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9132d70f647b0578d00678883d8c66.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175dd7ca22ea4f6a83530a746893624a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9132d70f647b0578d00678883d8c66.png)
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5 . 设双曲线Γ:
,
,B,C在Γ上且直线
经过A.设
分别为Γ在B,C处的切线,点D满足
,则D的轨迹方程是___________ ;若D的横纵坐标均为正整数,且二者之和大于2024,则D可以是_____ .(写出1个即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3674d64026a371b001453280477ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86de0e038b0304e34ca8c9b117fec917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e6aa92080d4e1f43a1ac2f9c2965fe.png)
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6 . 已知直线
与直线
,点
是
与
轴的交点.过
作
轴的垂线交
于点
,过
作
轴的垂线交
于点
,过
作
轴的垂线交
于点
,过
作
轴的垂线交
于点
,依此方法一直继续下去,可得到一系列点
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e9415f5db5744af7997ff9b6848b3a.png)
______ ;设
的坐标为
,则数列
的前
项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4073d527d4b14759a7cbaeabfb35a756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32818d2d58f6faacb562af468fe584a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e9415f5db5744af7997ff9b6848b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92abae836b8026511113ad8c3ea23028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f825318efdba0967b4ee4f1743a1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
7 . 如图,已知菱形中,
为边
的中点,将
沿
翻折成
(点
位于平面
上方),连接
和
为
的中点,则在翻折过程中,
与
的夹角为
的轨迹的长度为
您最近一年使用:0次
2023-11-01更新
|
664次组卷
|
3卷引用:第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点2 翻折、旋转中的基本问题(二)
(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点2 翻折、旋转中的基本问题(二)重庆市名校联盟2023-2024学年度高二上学期期中联考数学试题山东省普高大联考2023-2024学年高二上学期11月期中联合质量测评数学试卷
8 . 已知等边
的边长为2,将其绕着
边旋转角度
,使点
旋转到
位置.记四面体
的内切球半径和外接球半径依次为
,当四面体
的表面积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc414210eac238504494ce83becf6a8c.png)
__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187de07874b5370c4489cb4a2dff0b1.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0991d38c6edebb9740ab1061437c720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dce64d610e7f309e414d9abe7ff2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0991d38c6edebb9740ab1061437c720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc414210eac238504494ce83becf6a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187de07874b5370c4489cb4a2dff0b1.png)
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2023-07-25更新
|
664次组卷
|
4卷引用:第11章 简单几何体(压轴必刷30题专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
(已下线)第11章 简单几何体(压轴必刷30题专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点3 翻折、旋转中的基本问题(三)云南省保山市部分校2022-2023学年高二下学期期末模拟测试数学试题广东五校2022-2023学年高二下学期期末联考数学试题
2023高三·全国·专题练习
9 . (1)已知实数
,
,
满足
,
,则
的最大值是________ ;
(2)对于
,当非零实数
,
满足
,且使
最大时,
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f9223bc24df8d429d743692fff7c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0928f6318bbc075ba006638646f4403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dd633c8b370658878f9fc35a7a8877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9a74d1fb37b9b59e181ecb0a7f72ff.png)
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名校
10 .
,
,则
最小值为______ .若
与
无交点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6989cc6bc212764fc7c1dfe45d57bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24d7a51950ec8ef70c8db2b5b6fa794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.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/0a6936d370d6a238a608ca56f87198de.png)
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