名校
1 . 设向量集合
.若对于任意
、
以及任意
,都有
,则称集合S是“凸集”.现有四个命题:
①集合
是“凸集”;
②集合
是“凸集”;
③若集合
、
都是“凸集”,则
也是“凸集”;
④若集合
、
都是“凸集”,且交集非空,则
也是“凸集”.
其中,所有正确命题的序号是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a8aa6b0a40a2ef451c9f6c263662d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c1870a8601323a0fefb2f90c669f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304c5050fdb05bd5ccdf8bdfc00e8108.png)
①集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275e06e147f70046e6c91b1cac72bfc.png)
②集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f32c01a67d79efc9fb98afc8bd2fb8.png)
③若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
④若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
其中,所有正确命题的序号是
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名校
解题方法
2 . 从
,
,
,
中任取
个不同的数,则取出的
个数之和为5的概率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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名校
3 . 向量
在
方向上的数量投影为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09833c6f54f46d1c9b427d18c1725297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e3b2d37bb01fa4ccfb57bc364d8078.png)
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真题
解题方法
4 . 已知
,且
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e533b8b204982c7d42001a20b9548a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d76ee2e81f447f84a3e0b39c0388ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
5 . “用一个不垂直于圆锥的轴的平面截圆锥,当圆锥的轴与截面所成的角不同时,可以得到不同的截口曲线”,利用这个原理,小强在家里用两个射灯(射出的光锥视为圆锥)在墙上投影出两个相同的椭圆(图1),光锥的一条母线恰好与墙面垂直.图2是一个射灯投影的直观图,圆锥
的轴截面
是等边三角形,椭圆
所在平面为
,则椭圆
的离心率为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745e0525a41fe2e2a7739c75a942290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4b27f503ce08bc7851006a98f9ce32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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2024高三下·全国·专题练习
6 . 已知
,
,则
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620a6c0dd68965305f065ddd135266b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14714599c403e4e8a92196fcd2e4ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219ba6c8a1b54598db1a78cab28d9d30.png)
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解题方法
7 . 在四面体
中,且
,点
分别是线段
,
的中点,若直线
平面
,且
截四面体
形成的截面为平面区域
,则
的面积的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65505f39fe3f011d3d84437100363d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
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解题方法
8 . 若随机变量
服从正态分布
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3a07cfb65f627c51622b0d396b30a6.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d491a7726909c51fe40594c511a56220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f1b3ebbde4d94fb5e883cf263d44f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb3a07cfb65f627c51622b0d396b30a6.png)
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9 . 已知函数
,则
的值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c36520e5715681c64bf7a4bd31a176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383acb6637f314601906b2b617c823bc.png)
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