解题方法
1 . 设空间区域
中存在四个点两两距离都是
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9d1a596177d93fe5303bf37ba9efcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
您最近一年使用:0次
名校
2 . 如图,点P为函数
的图象上一点,且到两坐标轴距离相等,
半径为
,
,点
是
上的动点,点
是
的中点,则
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245fcfd1a86d3a20f810682d7e148d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4958b4ab618db469586f695f628d7721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/1/5c766026-f0e0-41c3-ae74-8de2d990429d.png?resizew=168)
您最近一年使用:0次
解题方法
3 . 已知球O的直径为
,圆柱
的底面直径和高均为
,设球O的表面积为
,圆柱
的表面积为
,则
的值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7f30167e1135806fe9de641870b1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7f30167e1135806fe9de641870b1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
解题方法
4 . 设直线与三条坐标轴的夹角分别为
,与三个坐标平面的夹角分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d0a2241095464f835e3ce4574f66c.png)
_________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2361805faef1a259a987e224eb938635.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef72093f571da03c6580a5e5fa9b0d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/645d0a2241095464f835e3ce4574f66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2361805faef1a259a987e224eb938635.png)
您最近一年使用:0次
5 . 在平面直角坐标系
中,设
,向量
,其中
,动点P满足
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a96bda2f374f74cfa244983a1879e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450743dbe1916012643039cd87a72263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe0890043f34b4575bf7bb3a773e32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b768ea6a05cbf45b28fc46c501ba532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b683529d8299e73e36ef06d0b1463d.png)
您最近一年使用:0次
解题方法
6 . 已知正方体
,点O,P分别为面
的中心,则
与
夹角的正弦值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c658a0a981613142b31025cfc3164544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec275f823ae17afdba53301fcbd2aa43.png)
您最近一年使用:0次
7 . 如果把一个平面区域内两点间的距离的最大值称为此区域的直径,那么曲线
围成的平面区域的直径为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b79ffef55f4609e7d23a888e508464.png)
您最近一年使用:0次
解题方法
8 . 已知三棱锥
的六条棱中,
,其余棱长均为3,则三棱锥
的外接球直径为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d4f26a50d041f80a1816bc7a3883ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
9 . 已知一个四棱锥的三视图如下,该四棱锥的四个侧面中,直角三角形的个数为____________ .
![](https://img.xkw.com/dksih/QBM/2023/4/6/3210686638145536/3292606112202752/STEM/d6dffac078064c77988d3cda8305c165.png?resizew=228)
您最近一年使用:0次
10 . 已知空间一球,
为其直径且
.A,B为球上两点,满足
,且
,则四面体
的体积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6df8b81a114ee91e3f6483bc5ba0982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a944e0cbc23f379deb41c0188fe5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d18f11eaebee6480f29838eafbb6282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
您最近一年使用:0次
2023-07-31更新
|
153次组卷
|
2卷引用:2017年清华大学暑期学校测试数学试题