名校
解题方法
1 . 正方体
的棱长为
为该正方体侧面
内的动点(含边界),若
分别与直线
所成角的正切值之和为
,则四棱锥
的体积的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc79c14b2ed75664547ddd8ba5b1be9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2024-06-11更新
|
236次组卷
|
2卷引用:上海市建平中学2024届高三下学期三模考试数学试题
名校
2 . 如图,这是某同学绘制的素描作品,图中的几何体由一个正四棱锥和一个正四棱柱贯穿构成,正四棱柱的侧棱平行于正四棱锥的底面,正四棱锥的侧棱长为
,底面边长为6,正四棱柱的底面边长为
是正四棱锥的侧棱和正四棱柱的侧棱的交点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8969b40b7ded338cec0128fa40a291df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611122254dad4daf2a77259b675342bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
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2023-11-08更新
|
851次组卷
|
3卷引用:上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试卷
上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试卷江西省赣州市十八县(市、区)二十三校2024届高三上学期11月期中联考数学试题(已下线)上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试题变式题11-16
2023·上海浦东新·模拟预测
名校
3 . 已知
,对任意
都有
,则实数
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d412dac90a9ecc9db4398f52ea8ce028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca29dc5a65c6c11fb356bbe115a8954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f48653f85f9190e55c4b0b5c392a36e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
解题方法
4 . 现要将一边长为101的正方体
,分割成两部分,要求如下:(1)分割截面交正方体各棱
,
,
,
于点P,Q,R,S(可与顶点重合);(2)线段
,
,
,
的长度均为非负整数,且线段
,
,
,
的每一组取值对应一种分割方式,则有___________ 种不同的分割方式.(用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb6fd2fa53b92a03d21f208b74e3857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b81f1bce5be292fb6968afc5e07864f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb6fd2fa53b92a03d21f208b74e3857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b81f1bce5be292fb6968afc5e07864f.png)
您最近一年使用:0次
2022-06-22更新
|
1995次组卷
|
2卷引用:上海市普陀区晋元高级中学2024届高三上学期秋考模拟数学试题
5 . 已知椭圆
的左、右焦点分别为
、
.经过点
且倾斜角为
的直线
与椭圆
交于
、
两点(其中点
在
轴上方),
的周长为8.
(1)求椭圆
的标准方程;
(2)如图,把平面
沿
轴折起来,使
轴正半轴和
轴确定的半平面,与
负半轴和
轴所确定的半平面互相垂直.
,求异面直线
和
所成角的大小;
②若折叠后
的周长为
,求
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d49bc14700562fee13af6a548e4eaef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5e56b5cbcf69756792fc934bcc20cb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)如图,把平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
②若折叠后
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5e56b5cbcf69756792fc934bcc20cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7163395f9aaa29be7f6b3106ba48b744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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