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1 . 若圆
上恰有3个点到直线
的距离为
,则
的值为__________ ;若圆C上恰有
个点到直线
的距离为
,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea52e88c141737314ff41263b94b4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b0e963195605a67975c6f8f3caa0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b0e963195605a67975c6f8f3caa0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2023-10-31更新
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213次组卷
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2卷引用:湖北省襄阳市第一中学2023-2024学年高二上学期10月月考数学试题
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解题方法
2 . 已知集合
,对于集合
的两个非空子集
,若
,则称
为集合
的一组“互斥子集”.记集合
的所有“互斥子集”的组数为
(当且仅当
时,
与
为同一组“互斥子集”),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9471b4864932cd4ea3410c5bb85e71b.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e026ea1deb91944e0ae91bcf52d405f0.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d597abdedb59434ee462de238f443f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71bbe792268ddc7adc67b489a3c61927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9471b4864932cd4ea3410c5bb85e71b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e026ea1deb91944e0ae91bcf52d405f0.png)
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解题方法
3 . 已知
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
________ 时,
取最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e3ef10014584843ea896176597593a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4b56b0d6b88c443166485c74a28093.png)
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解题方法
4 . 如图,在矩形
中,
,
,
,
,
分别为
,
,
,
的中点,
与
交于点
,现将
,
,
,
分别沿
,
,
,
把这个矩形折成一个空间图形,使
与
重合,
与
重合,重合后的点分别记为
,
,
为
的中点,则多面体
的体积为_______ ;若点
是该多面体表面上的动点,满足
时,点
的轨迹长度为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62142d2d114ffd9f404be533b79e530b.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357bfca91c08ec1a3f18cf6ddbe36983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3bb70557998ae1576b8eab0cbcea486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/ac0bc380-7886-486e-98a6-23bcba92c06d.png?resizew=155)
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2023-09-22更新
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382次组卷
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6卷引用:湖北省襄阳市宜城市第一中学2023-2024学年高二上学期9月月考数学试题
湖北省襄阳市宜城市第一中学2023-2024学年高二上学期9月月考数学试题江苏省南京中华中学、南京师范大学附属中学江宁分校两校2022-2023学年高三下学期3月联考数学试题江苏省南京师范大学附属中学江宁分校等2校2023届高三一模数学试题湖北省宜昌市枝江市第一高级中学2023-2024学年高二上学期10月月考数学试题(已下线)专题突破卷21 立体几何的轨迹问题(已下线)第18讲 第八章 立体几何初步 章节验收测评卷-【帮课堂】(人教A版2019必修第二册)
名校
解题方法
5 . 现代建筑讲究的线条感,曲线之美让人称奇.衡量曲线弯曲程度的重要指标是曲率,曲线的曲率定义如下:若
是
的导函数,
是
的导函数,则曲线
在点
处的曲率
,若曲线
和
在
处的曲率分别为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff61ecc0e66164caaf60511ea9500a4.png)
______ ;设余弦曲线
的曲率为K,则
的最大值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7522a3f232bd0b7a7850ae674db43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/609bb564e7770d324aeca4eec8ed927a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15661be48657998b68a2b6afbcf108e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16cc94df25e2cb6735f16ef98f534e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e029cc1f7d07eeb136bd3946a7eb23e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32410867843f1a7ef11410da8f3f8dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff61ecc0e66164caaf60511ea9500a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e27fde05cc2a11caf3422875b58372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581192317ef233ccdccfc48ac29b52b.png)
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2023-03-16更新
|
446次组卷
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4卷引用:湖北省襄阳市部分学校2022-2023学年高二下学期3月联考数学试题
湖北省襄阳市部分学校2022-2023学年高二下学期3月联考数学试题(已下线)第五篇 向量与几何 专题21 曲率与曲率圆 微点3 曲率与曲率圆综合训练(已下线)第十章 导数与数学文化 微点3 导数与数学文化(三)山东省青岛第十九中学2023-2024学年高二下学期期中考试数学试卷
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解题方法
6 . 已知数列
的各项都是正数,
若数列
各项单调递增,则首项
的取值范围是__________
当
时,记
,若
,则整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe05bdfc2bc652fbd96c0d6ece062cf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352d9b76dcf639368fa68cae70149802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e542f906f67f78fb7e682990c9b206ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0cb61095ee5d3d043cd61381003ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
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2023-02-14更新
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780次组卷
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5卷引用:湖北省襄阳市第五中学2023届高三下学期适应性考试(一)数学试题
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7 . 有甲、乙两种产品共120件,现按比例分配的分层随机抽样的方法抽取10件进行产品质量调查,如果所抽取的甲产品的数量是乙产品数量的2倍还多1件,那么甲产品共有 _________ 件,乙产品共有__________ 件.
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2023-01-05更新
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2卷引用:湖北省襄阳市第四中学2021-2022学年高一下学期6月月考数学试题
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8 . 函数
的最大值为________ ,最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2715ae634230abde615d6f01ed92ddfa.png)
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9 . 如图是瑞典数学家科赫
在
年构造的能够描述雪花形状的图案.图形的作法是:从一个正三角形开始,把每条边分成三等份,然后以各边的中间一段为底边分别向外作正三角形,再去掉底边.反复进行这一过程,就得到一条“雪花”状的曲线.
![](https://img.xkw.com/dksih/QBM/2022/7/1/3013419259797504/3013814397329408/STEM/8bf0c22091fc48f3a342b812f9da488d.png?resizew=550)
设原三角形(图
)的边长为
,把图
,图
,图
,
中的图形依次记为
,
,
,
,
,
,则
的边数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9d07ab5583613dbe6bd34c3784252d.png)
__________ ,
所围成的面积![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a071ea3c1c6c186a81f7631dd429ddee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaec8896b1d932e78055491e55a5265.png)
![](https://img.xkw.com/dksih/QBM/2022/7/1/3013419259797504/3013814397329408/STEM/8bf0c22091fc48f3a342b812f9da488d.png?resizew=550)
设原三角形(图
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9d07ab5583613dbe6bd34c3784252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c2864e2ec3416cc4c081ac1f71a0af.png)
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2022-07-02更新
|
527次组卷
|
3卷引用:湖北省襄阳市第三中学2022-2023学年高二上学期12月月考数学试题
名校
10 . 某学校开展手工艺品展示活动,小明同学用塑料制作了如图所示的手工艺品,其外部为一个底面边长为6的正三棱柱,内部为一个球,球的表面与三棱柱的各面均相切,则该内切球的表面积为___________ ,三棱柱的顶点到球的表面的最短距离为___________ .
![](https://img.xkw.com/dksih/QBM/2022/5/30/2990548873371648/2992150942736384/STEM/7c434bc2-e1cd-4a87-ac3a-c2a8ad817f79.png?resizew=152)
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2022-06-01更新
|
1290次组卷
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5卷引用:湖北省襄阳市第五中学2022-2023学年高二上学期10月月考数学试题
湖北省襄阳市第五中学2022-2023学年高二上学期10月月考数学试题湖北省襄阳五中2022-2023学年高二上学期10月测试(二)数学试题山东省烟台市2022届高三三模数学试题(已下线)第07练 九种外接球与内切球模型-2022年【暑假分层作业】高一数学(苏教版2019必修第二册)(已下线)第01讲 基本立体图形、简单几何体的表面积与体积 (精讲)-3