名校
解题方法
1 . 如图,直角三角形ABC所在平面外有一点
,且
,
为斜边
的中点.求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700f2f0f1cf306f7fc18d18fe91d0acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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2 . 如图,是一座“双塔钢结构自锚式悬索桥”,悬索的形状是平面几何中的悬链线,悬链线方程为
(
为参数,
),当
时,该方程就是双曲余弦函数
,类似的有双曲正弦函数
.
______.(用
,
表示)
(2)
,不等式
恒成立,求实数
的取值范围;
(3)设
,证明:
有唯一的正零点
,并比较
和
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98be08efebc64ff0fbc8d0ef819b0290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594663e98b797cdc4efbd098cc15854f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2705e42f28cd5e415655cb1fbecf728b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bd6153986cc8b26dd0e58cf92abc00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740eb38441fe1cc663275e9f84bacb26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/515599523e72afd87bb9f2929425f35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ff0b4309f7e59ab9c65410bdee9485.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745eb108da3e42138a93d1ce780317f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a197403d3d4d35f97c483db6a95a1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a4ba376c9dfa67cc027d683476368f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a858b8c19d4627c256c8fd524051221a.png)
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3 . 如图,在四棱锥
中,底面
是菱形,
平面
分别是棱
的中点.
.
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe554ccad89bcb941104fbb58722a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55928df632fc6f2b88a44afe37e5a4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df44d1ff1227c4de03ca21ac87f3f86a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8c9aedf70a0d7dae193ec00ca059565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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名校
解题方法
4 . 如图所示,
是圆柱下底面圆的直径,
是下底面圆周上异于
,
的动点,
,
是圆柱的两条母线.
平面
;
(2)若异面直线
与
所成的角为
,圆柱的表面积为
,求四棱锥
体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
(2)若异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5f9251b20115e4f9bfc2005ef26f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
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名校
解题方法
5 . 五一假期后,高二年级篮球赛进入白热化阶段,甲、乙、丙三支种子队在进入半决赛之前不会相遇.他们都需要在最后一轮小组赛中战胜对手从而进入淘汰赛,然后在淘汰赛中胜出才能进入半决赛.已知甲队在小组赛最后一轮和淘汰赛中获胜的概率分别为
和
;乙队在最后一轮和淘汰赛中获胜的概率分别为
和
;丙队在最后一轮和淘汰赛中获胜的概率分别为
和
,其中
.
(1)甲、乙、丙三队中,谁进入半决赛的可能性最大;
(2)若甲、乙、丙三队中恰有两队进入半决赛的概率为
,求
的值;
(3)在(2)的条件下,设甲、乙、丙三队中进入半决赛的队伍数为
,求
的分布列及期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa174dffdf8206c7c51b514769dd9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee34861e71a34cb0d9aa743f632c8c2.png)
(1)甲、乙、丙三队中,谁进入半决赛的可能性最大;
(2)若甲、乙、丙三队中恰有两队进入半决赛的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67958ae7600c53b0dbc7a28203a7bd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)在(2)的条件下,设甲、乙、丙三队中进入半决赛的队伍数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
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2024-06-05更新
|
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3卷引用:湖北省部分重点中学2023-2024学年高二下学期五月联考数学试卷
名校
6 . 已知函数
,
.
(1)若
,讨论函数
的单调性;
(2)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd58e16598e6bdb3c35194af69951a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895938bc4691b6ad48f8b001dfcad102.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074408cfb3eedc559116996d57d5a087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4175c57c61b71897b10583ad32e5e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c95440ace01be940f1591eed18ab5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f78ae07b1452e4f9dd8ba93db61d17.png)
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2024-06-05更新
|
293次组卷
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2卷引用:江西省临川第二中学2023-2024学年高二下学期6月月考数学试题
名校
解题方法
7 . 已知半径为2的圆
的圆心在射线
上,点
在圆
上.
(1)求圆
的标准方程;
(2)求过点
且与圆
相切的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43e1bea7019a76adbc8651256cdfdfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f20953302d861e6c698575bfbab1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e30645f36e8628b9e25d53598d5174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2卷引用:河北省郑口中学2023-2024学年高二第三次质量检测数学试题
名校
8 . 已知复数
.
(1)若
,求
;
(2)若
,且
是纯虚数,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28229f5b710ea4e52b618ae9d3d20e9b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a742fe334d93ce636a7e98d612f87678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bafa6921a0f5987d5f1fc568cf54e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26dd5edae8097274a8a4fd56bc1b4c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
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解题方法
9 . 某旅游景区在手机APP上推出游客竞答的问卷,题型为单项选择题,每题均有4个选项,其中有且只有一项是正确选项.对于游客甲,在知道答题涉及的内容的条件下,可选出唯一的正确选项;在不知道答题涉及的内容的条件下,则随机选择一个选项.已知甲知道答题涉及内容的题数占问卷总题数的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefddb6e7a2d015ccd7814aef1eabdd6.png)
(1)求甲任选一题并答对的概率;
(2)若问卷答题以题组形式呈现,每个题组由2道单项选择题构成,每道选择题答对得2分,答错扣1分,放弃作答得0分.假设对于任意一道题,甲选择作答的概率均为
,且两题是否选择作答及答题情况互不影响,记每组答题总得分为
,
①求
和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfb0a5b63c5d06f6daa91c74b106c13.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefddb6e7a2d015ccd7814aef1eabdd6.png)
(1)求甲任选一题并答对的概率;
(2)若问卷答题以题组形式呈现,每个题组由2道单项选择题构成,每道选择题答对得2分,答错扣1分,放弃作答得0分.假设对于任意一道题,甲选择作答的概率均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb5cb404bfca8ef22331d801608e4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfb0a5b63c5d06f6daa91c74b106c13.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97aece7763179494a38df81089f5b8b2.png)
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2卷引用:江苏省苏州外国语学校2023-2024学年高二下学期5月月考数学试题
解题方法
10 . 随着新高考改革,高中阶段学生选修分为物理方向和历史方向,为了判断学生选修物理方向和历史方向是否与性别有关,现随机抽取50名学生,得到如下列联表:
(1)计算a,b,c的值;
(2)问是否有95%的把握认为选修物理方向和历史方向与性别有关?
附:
,
.
物理方向 | 历史方向 | 总计 | |
男生 | 13 | a | 23 |
女生 | 7 | 20 | 27 |
总计 | b | c | 50 |
(2)问是否有95%的把握认为选修物理方向和历史方向与性别有关?
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1464ac47bf07fd36c0e7ee81a5a38b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.25 | 0.15 | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 | |
1.323 | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 7.879 | 10.828 |
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2024-06-05更新
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3卷引用:山西省朔州市怀仁市大地学校高中部2023-2024学年高二下学期第四次月考(6月)数学试题