1 . 2022年北京冬奥会仪式火种台(如图①)以“承天载物”为设计理念,创意灵感来自中国传统青铜礼器——尊(如图②),造型风格与火炬、火种灯和谐一致.仪式火种台采用了尊的曲线造型,基座沉稳,象征“地载万物”.顶部舒展开阔,寓意着迎接纯洁的奥林匹克火种.祥云纹路由下而上渐化为雪花,象征了“双奥之城”的精神传承.红色丝带飘逸飞舞、环绕向上,与火炬设计和谐统一.红银交映的色彩,象征了传统与现代、科技与激情的融合.现建立如图③所示的平面直角坐标系,设图中仪式火种台外观抽象而来的曲线对应的函数表达式为
.
(1)求函数
的图象在点
处的切线方程;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ad93dc19938b18b0a9a7dcfe3a7bf1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/20/74fa53e3-3998-4d0f-8f9e-266b5d590b43.png?resizew=388)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714621c52d929e662febee72b9d68351.png)
您最近一年使用:0次
2023-10-30更新
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126次组卷
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2卷引用:海南省陵水黎族自治县陵水中学2024届高三上学期第三次模拟测试数学试题
2 . 设O为坐标原点,点M,N在抛物线
上,且
.
(1)证明:直线
过定点;
(2)设C在点M,N处的切线相交于点P,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964889aaf14b9ef1837a988c048788e4.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)设C在点M,N处的切线相交于点P,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3cbb23e45970803a178f2bc7806156.png)
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3 . 现有4个除颜色外完全一样的小球和3个分别标有甲、乙、丙的盒子,将4个球全部随机放入三个盒子中(允许有空盒).
(1)记盒子乙中的小球个数为随机变量
,求
的数学期望;
(2)对于两个不互相独立的事件
,若
,称
为事件
的相关系数.
①若
,求证:
;
②若事件
盒子乙不空,事件
至少有两个盒子不空,求
.
(1)记盒子乙中的小球个数为随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)对于两个不互相独立的事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0364f24642d4009e263e9e5da016963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189fc93d4bce27aba82ba2377518afe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711de316595750eed2fc6c8c05ddcbf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959fa756e735c1bc6395dc2fa0af8127.png)
②若事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a463744f6f85de0ff99bc2e3073b9e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6196de2008aef22c3cd85ec7e1bb64ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2acb46dc3fe51d506fe277f7b8451ae5.png)
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2023-05-29更新
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748次组卷
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3卷引用:海南省海南中学2022-2023学年高二下学期期末考试数学试题
4 . 已知椭圆
的左、右两个顶点分别为
、
,左、右两个焦点分别为
、
,
.动点
是
上异于
、
的一点,当
时,
.
(1)求椭圆
的标准方程;
(2)设直线
的方程为
,直线
和
分别交
于点
和点
.从以下三个条件中任选一个作为已知条件,证明另外两个条件成立:①
;②
;③以
为直径的圆与
相切于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0101351de91c730d1ca02e0ba18fde68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/3a04d414e949fb071588c2566a449dfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e8e73e9074525466ef59276d2d5de0.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.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/0f85fca60a11e1af2bf50138d0e3fe62.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/c68a67703e2ac17818d68d7ec4c8aab3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
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解题方法
5 . 将图(1)所示四棱锥E-ABCD展开得到如图(2)所示的平面展开图(点E的展开点分别为
,
,
,
),其中四边形ABCD是矩形,A,D是线段
的三等分点,F,G是线段
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/35a81fb5-7577-4ae6-a3fb-efc5fd2fd407.png?resizew=336)
(1)证明:平面
平面EAB;
(2)若二面角E-BC-A的正切值为
,点H,K满足
,
,求HK与平面ABCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4dbe5d5c8b9c28c6f5eb92278a9f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e9e14b826f3b534c237734392f5ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc4e7835cb8233c6c61097c5f6a2708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0004e13a8fb2b54f51d8ada09ffb70a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8085882b23d697348eae30de9739f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/23/35a81fb5-7577-4ae6-a3fb-efc5fd2fd407.png?resizew=336)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279e81eb8d5cb0435bcedcb3dc00b370.png)
(2)若二面角E-BC-A的正切值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c65ea66c7c4173a2720fc2f7826f3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068cacee8b8ac591b8ee4143c9bf7171.png)
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解题方法
6 . 已知如图甲所示,直角三角形SAB中,
,
,C,D分别为SB,SA的中点,现在将
沿着CD进行翻折,使得翻折后S点在底面ABCD的投影H在线段BC上,且SC与平面ABCD所成角为
,M为折叠后SA的中点,如图乙所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/bed5ceea-5766-4ecb-a1e1-8eb6b5000cd5.png?resizew=345)
(1)证明:
平面SBC;
(2)求平面ADS与平面SBC所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148649805098fe3c70919f18dceb5a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df5ee7d6f1a6eb46d93cb274e9fcac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c009f663ad2b0c3ba521daf4b86b066f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/1/bed5ceea-5766-4ecb-a1e1-8eb6b5000cd5.png?resizew=345)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
(2)求平面ADS与平面SBC所成锐二面角的余弦值.
您最近一年使用:0次
2023-03-31更新
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1378次组卷
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4卷引用:海南省琼海市嘉积中学2022-2023学年高二下学期5月期中数学试题
海南省琼海市嘉积中学2022-2023学年高二下学期5月期中数学试题重庆市巴蜀中学2023届高三下学期高考适应性月考(八)数学试题江西省铜鼓中学2022-2023学年高二下学期4月月考数学试题(已下线)重难点突破06 立体几何解答题最全归纳总结(九大题型)-1