名校
解题方法
1 . 勒洛四面体是一个非常神奇的“四面体”,它能在两个平行平面间自由转动,并且始终保持与两平面都接触,因此它能像球一样来回滚动.勒洛四面体是以正四面体的四个顶点为球心,以正四面体的棱长为半径的四个球的公共部分,如图所示,若正四面体ABCD的棱长为a.则( )
A.能够容纳勒洛四面体的正方体的棱长的最小值为![]() |
B.勒洛四面体能够容纳的最大球的半径为![]() |
C.勒洛四面体中过![]() ![]() |
D.勒洛四面体的体积![]() |
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2024-04-23更新
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404次组卷
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2卷引用:浙江省绍兴市第一中学2023-2024学年高一下学期创新班期中考试数学试卷
名校
2 . 如图,四棱锥
的底面是平行四边形,平面
与直线
分别交于点
,且
,点
在直线
上运动,在线段
上是否存在一定点
,使得其满足:
;
(ii)对所有满足条件(i)的平面
,点
都落在某一条长为
的线段上,且
.若存在,求出点
的位置;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fd396e01e4539fc2f5924cdbde2a9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5301994be1239a80629b5f5a71c5760c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/716aabfe3eadf464549db269bb4cebf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d473e21a7b8c67711b727634721facfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e462bf86e68d6c8cd5c30cf781a3e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8bffc76218560809009e44db708d9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f063fac503d173b9d6e85a73c289c365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f148079427e6d8be6481dcbc955f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5c211c1161ec42b504cbe3834f3b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3052213185f1e92ff61bcd1b69031257.png)
(ii)对所有满足条件(i)的平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5301994be1239a80629b5f5a71c5760c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8bffc76218560809009e44db708d9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cbc323d0169375246bedae9e253846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0a9a28fb901d39a885b8c48a965dd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5c211c1161ec42b504cbe3834f3b50.png)
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解题方法
3 . 在三棱锥
中,二面角
的大小为
,
,
,则三棱锥外接球表面积的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf7116a47efeeb4f6805dc16b4e60f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48b30e5e72402f4f6a167a8f9f13651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a9f167f2cdb95e6f8d202f2783623dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed6723c07230927d593cbe278ee88e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df01d40611ad128b314244ac8090cd95.png)
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4 . 已知函数
.
(1)当
时,求
的单调区间;
(2)若函数
的值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48beb029095fec0e587f38ff9dde6bf3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d3ff22333351c909a37c1d1dd19f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
5 . 已知函数
是定义在
上的减函数,其导函数
满足
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05492bbe2597c7ad72568e26df413a4a.png)
A.![]() | B.当且仅当![]() ![]() |
C.![]() | D.当且仅当![]() ![]() |
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6 . 已知椭圆
的离心率为
,
、
分别为椭圆
的左、右顶点,
、
分别为椭圆
的左、右焦点,
.
(1)求椭圆
的方程;
(2)设与
轴不垂直的直线
交椭圆
于
、
两点(
、
在
轴的两侧),记直线
,
,
,
的斜率分别为
,
,
,
.
(i)求
的值;
(ii)若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1947517f9e58164fef799bf9d5afe398.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc48974114e23f5a801843710c7ae21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3307e11f7e6896e32aa510bbed949ac6.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ac9e4439b8f0c82427e410dbc86735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e43d5fd4e0175a366093cb1219067d57.png)
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解题方法
7 . 教材44页第17题:在空间直角坐标系中,已知向量
,点
,点
.(1)若直线l经过点
,且以
为方向向量,P是直线l上的任意一点,求证:
;(2)若平面
经过点
,且以
为法向量,P是平面
内的任意一点,求证:
.利用教材给出的材料,解决下面的问题:已知平面
的方程为
,直线
是平面
与
的交线,则直线
与平面
所成角的正弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448381ad5527aa15c9e69a049fc8c09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832b5312310a88bef6596496df8daa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4733a43364bdf78f59757c8f8c3fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f0582d9908f92f14cb02a6ccaf0eae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4733a43364bdf78f59757c8f8c3fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b523a8c1993478f6599680dc3b3dc45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa144c27f1deb376ce3ef53c1a86a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b818e1793be8d9213e903e5224987a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2888abfda58ff7563b34102d4d736d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-14更新
|
438次组卷
|
2卷引用:浙江省绍兴市第一中学2023-2024学年高二上学期期中数学试题
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解题方法
8 . 已知实数
,
满足
,则
的最小值是__________ .
![](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/9d5b348153da7b39bd95869d534f4f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dc8fb2ef00c16567bfefeab15b2065.png)
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2023-11-10更新
|
990次组卷
|
2卷引用:浙江省绍兴市第一中学2023-2024学年高一上学期期中数学试题
名校
解题方法
9 . 设函数
.
(1)若
在区间
上的最大值为
,求
的取值范围;
(2)存在实数
,使得当
时,
恒成立,求
的最大值及此时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd63ef3ff6d79668dbbdff129823f94.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1179338aaa7f469d91589dcda0b51197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb8ea0b94a4dfdca119d09234656878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-11-10更新
|
229次组卷
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2卷引用:浙江省绍兴市第一中学2023-2024学年高一上学期期中数学试题
名校
解题方法
10 . 如图,甲乙做游戏,两人通过划拳(剪刀、石头、布)比赛决胜谁首先登上第3个台阶,并规定从平地开始,每次划拳赢的一方登上一级台阶,输的一方原地不动,平局时两人都上一个台阶.如果一方连续赢两次,那么他将额外获得上一级台阶的奖励,除非已经登上第3个台阶,当有任何一方登上第3个台阶时游戏结束,则游戏结束时恰好划拳3次的概率为______ .
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2023-09-24更新
|
1258次组卷
|
8卷引用:浙江省绍兴市第一中学2023-2024学年高一下学期创新班期中考试数学试卷
浙江省绍兴市第一中学2023-2024学年高一下学期创新班期中考试数学试卷吉林省东北师范大学附属中学2023-2024学年高二上学期第一次月考数学试题(已下线)第12章 概率初步(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)(已下线)12.4 随机事件的独立性(四大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)4.1.2 乘法公式与全概率公式(分层练习)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第二册)(已下线)高一下学期期末复习填空题压轴题二十三大题型专练(2)-举一反三系列(人教A版2019必修第二册)(已下线)第06讲 第十章 概率 章末题型大总结-【帮课堂】(人教A版2019必修第二册)(已下线)【练】专题三 复杂背景的概率计算问题(压轴大全)