1 . 在长方体
中,
,点
为侧面
内一动点,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
平面
,则
的最小值为__________ ,此时点
到直线
的距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febe773ba9273dc5668bdb3fbe039695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
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解题方法
2 . 已知等差数列
的前
项的和为
,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3195af2fcb60759ccf57336ed41d928.png)
,则正整数
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/35319aade43a0deae40f185b74f99e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3195af2fcb60759ccf57336ed41d928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea23457d29048051cfad1300ee0df2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 如图,在正三棱柱
中,
,
,则直线
与直线
所成角的正切值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
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3卷引用:河南省鹤壁市外国语学校2024届高三上学期11月检测考试数学试题
河南省鹤壁市外国语学校2024届高三上学期11月检测考试数学试题(已下线)核心考点7 立体几何中角和距离 B提升卷 (高一期末考试必考的10大核心考点)甘肃省武威市2023-2024学年高一下学期6月月考数学试题
名校
解题方法
4 . 已知
,且
,则函数
的零点为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c25d8f0fd3e907886c99aafd62c671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67653fd1430f8ad1445414070ddf3346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b9a9df7e92ea7a60b58ca18613b066.png)
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5 . 设
为双曲线
:
左、右焦点,点
在
的右支上,线段
与
的左支相交于点
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbcc5cd6c478374feb2f610cc81e9d4.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8264135ba3bc4e68f571ea9293b0fc5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8ad9e94d07405a6be585f81a0d623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3effb79e6b61f1c41ed56431f6fca175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbcc5cd6c478374feb2f610cc81e9d4.png)
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6 . 棱长为
的正方体
中,
为棱
的中点,
为正方形
内一个动点(包括边界),且
平面
,则当三棱锥
体积取最大时,其外接球的表面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a73120cd0988eb4a63436e7a4b9470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ea211a573491409cb60f9fbe9a65cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640aa89f8c302356d2dfe5ccf7c054b0.png)
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解题方法
7 . 给出下列结论:①一组数据
的第
百分位数为
;②若随机变量
,且
,则
;③若将一组数据中的每一个数都加上同一个正数
,则其平均数和方差都会发生变化.其中正确说法的序号为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdb1faf12a59889ef07f9aa0e2c2b3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f959e5f8d89390f0f136f6acc9f6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7795348ccc99540240f53b5d81a3333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d387ddc97b98af79ddf82cde8f4852b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66161fc8faea9eb09485adafcb5add5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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8 . 已知复数
,则
的值等于_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16852bb45d8c0ed0505f02e6841204c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cebcc45614dae664853e3e7a141c0a49.png)
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9 . 在
中,角
的对边分别为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7112e7ccb1eb90facfa5182ea763970a.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/a6cf7c342ca03223c26581d35f049a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7112e7ccb1eb90facfa5182ea763970a.png)
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10 . 已知圆
的面积为
,则实数
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a25551b7fdcfef454c716d57205294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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