名校
解题方法
1 . 如图1所示,在边长为3的正方形
中,将
沿
折到
的位置,使得平面
平面
,得到图2所示的三棱锥
.点
分别在
上,且
,
,
.记平面
与平面
的交线为l.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/a232b33a-64b7-48ee-ad75-468ec615404d.png?resizew=335)
(1)在图2中画出交线l,保留作图痕迹,并写出画法.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1095b030f441de5fb223781b00f3dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bb1063e139610045f3bca5ca0b2766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715ef932b72eb703f3e7a17ee2ce6a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828795d52174dd64fba1c9ebe61072b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cf0ee918f8c2f753302d3b5928d358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/a232b33a-64b7-48ee-ad75-468ec615404d.png?resizew=335)
(1)在图2中画出交线l,保留作图痕迹,并写出画法.
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7f9eca6d2aabe3f9e0f39b46106ce4.png)
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2023-04-25更新
|
510次组卷
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3卷引用:四川省南充市嘉陵第一中学2022-2023学年高二下学期期中理科数学试题
2 . 如图,正四面体
,
(1)找出依次排列的四个相互平行的平面
,
,
,
,使得
,且其中每相邻两个平面间的距离都相等.请在答卷上作出满足题意的四个平面,并简要说明并证明作图过程;
(2)若满足(1)的平面
,
,
,
中,每相邻两个平面间的距离都为1,求该正四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/21fc98e1-5dbe-46a9-9c60-2bb1802386ea.png?resizew=167)
(1)找出依次排列的四个相互平行的平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9177f43add5ca8480daa636afc5862b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a56eca8dc73a0e8f0c6d3a41bb26bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109c658897735fce605120061c38709d.png)
(2)若满足(1)的平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9177f43add5ca8480daa636afc5862b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a56eca8dc73a0e8f0c6d3a41bb26bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
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名校
解题方法
3 . 在棱长为1的正方体
中,
为底面
的中心,
是棱
上一点,且
,
,
为线段
的中点,给出下列命题:
①
,
,
,
四点共面;
②三棱锥
的体积与
的取值有关;
③当
时,
;
④当
时,过
三点的平面截正方体所得截面的面积为
.
其中正确的有______ (填写序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0424446817f60c18f8e4e3cc202ad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa920e346a3d79b7ecfa395b8e72b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/137312de-792b-4a5b-9b8b-846be4283e38.png?resizew=162)
①
![](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)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9933c392d85e51aba78e72468363579b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c1eccad7857ccae05562abaaf10d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4aee887d79c104f7d37fafa312aef6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58edfa8a9009058dfa6c9f1b2b8c8018.png)
其中正确的有
您最近一年使用:0次
2023-10-01更新
|
255次组卷
|
3卷引用:四川省通江中学2022-2023学年高二上学期期中文科数学试题
四川省通江中学2022-2023学年高二上学期期中文科数学试题北京市日坛中学2023-2024学年高二上学期期中考试数学试题(已下线)高二数学上学期期中模拟卷01(前三章:空间向量与立体几何、直线与圆、圆锥曲线)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)
4 . 如图,已知圆
的半径为定长
是圆
所在平面内一个定点,
是圆上任意一点,线段
的垂直平分线
和直线
相交于点
.当点
在圆上运动时:(1)当点A在圆
内且不与点
重合时,点
的轨迹是__________ (从圆、椭圆、抛物线中选择一个填写);(2)当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c0700b92ddfc927f81fa96059d70e9.png)
__________
(从>,=,<中选择一个填写)时,点
的轨迹是双曲线的一支.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694032f6e765cbb0391c87c41ad629f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c0700b92ddfc927f81fa96059d70e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/24/6d6582d9-f283-4315-9dd9-b57b5603cb14.png?resizew=96)
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|
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3卷引用:四川省内江市2023-2024学年高二上学期1月期末检测数学试题
解题方法
5 . 在棱长为1的正方体
中,
为底面
的中心,
是棱
上一点,且
,
,
为线段
的中点,给出下列命题:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/b3b303f8-4645-4fb4-aae0-da651ab57e9e.png?resizew=170)
①
四点共面;
②三棱锥
的体积与
的取值有关;
③当
时,
;
④当
时,过
三点的平面截正方体所得截面的面积为
.
其中正确的有__________ (填写序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0424446817f60c18f8e4e3cc202ad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa920e346a3d79b7ecfa395b8e72b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/b3b303f8-4645-4fb4-aae0-da651ab57e9e.png?resizew=170)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae45d5c4c2e34bf01e860748b1d22c7.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9933c392d85e51aba78e72468363579b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c1eccad7857ccae05562abaaf10d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4aee887d79c104f7d37fafa312aef6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e45dbe14b2b2e3bf724be3f391b8ddf.png)
其中正确的有
您最近一年使用:0次
2022-12-10更新
|
263次组卷
|
3卷引用:四川省遂宁市遂宁高级实验学校2022-2023学年高二上学期期中数学(理)试题
名校
解题方法
6 . 已知直线
与双曲线
相交于M、N两点,双曲线C的左、右顶点分别为A、B,若直线AM与BN相交于点P,则下列说法正确的有______ (填写正确命题的序号)
![](https://img.xkw.com/dksih/QBM/2022/1/8/2889999141822464/2912159608569856/STEM/34487f5d-4b1f-458b-bdcb-20c8b8eb0b0e.png?resizew=167)
①实数
的取值范围为
或
;②直线AM与直线BN的斜率之积为定值;③点P在椭圆
上;④三角形PAB的面积最大值为ab.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1331519fd9ca511b19148878b1cacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://img.xkw.com/dksih/QBM/2022/1/8/2889999141822464/2912159608569856/STEM/34487f5d-4b1f-458b-bdcb-20c8b8eb0b0e.png?resizew=167)
①实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb193ae31142011d07756aa27b75dad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86474b8b559afef08fa4ea228f84b77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
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2022-02-08更新
|
1772次组卷
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4卷引用:四川省内江市威远中学校2021-2022学年高二下学期第一次月考数学(文)试题
四川省内江市威远中学校2021-2022学年高二下学期第一次月考数学(文)试题安徽省示范高中2021-2022学年高三上学期冬季联赛理科数学试题(已下线)专题11 圆锥曲线第三定义与点差法 微点1 圆锥曲线第三定义的应用(已下线)第八章 解析几何 专题9 圆锥曲线第三定义的应用 高中数学优质试题一题多解和变式训练
名校
7 . 数学中有许多形状优美、寓意美好的曲线,曲线
就是其中之一.曲线C对应的图象如图所示,下列结论:
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
;
②曲线C与圆
有2个交点;
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:________ .(填写所有正确结论的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5a27e68ac82e560536b3bdefd4b08f.png)
![](https://img.xkw.com/dksih/QBM/2020/8/23/2534261485158400/2542441775185920/STEM/b8f87e4853394f57b71cb90416bb3efa.png?resizew=132)
①直线AB的方程为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6274852e643a635e7340efa732edddc4.png)
②曲线C与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd89a03660c85fb78bd7fe82ee3068c.png)
③曲线C所围成的“心形”区域的面积大于12;
④曲线C恰好经过4个整点(即横、纵坐标均为整数的点).
其中正确的是:
您最近一年使用:0次
2020-09-04更新
|
415次组卷
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3卷引用:四川省内江市第六中学2021-2022学年高二下学期第一次月考数学(文科)试题
名校
8 . 富华中学的一个文学兴趣小组中,三位同学张博源、高家铭和刘雨恒分别从莎士比亚、雨果和曹雪芹三位名家中选择了一位进行性格研究,并且他们选择的名家各不相同.三位同学一起来找图书管理员刘老师,让刘老师猜猜他们三人各自的研究对象.刘老师猜了三句话:“①张博源研究的是莎士比亚;②刘雨恒研究的肯定不是曹雪芹;③高家铭自然不会研究莎士比亚.”很可惜,刘老师的这种猜法,只猜对了一句.据此可以推知张博源、高家铭和刘雨恒分别研究的是__________ .(A莎士比亚、B雨果、C曹雪芹,按顺序填写字母即可.)
您最近一年使用:0次
2017-05-08更新
|
958次组卷
|
6卷引用:四川省凉山木里中学2017-2018学年高二下学期期中考试数学(文)试卷
名校
9 . 如图,三棱锥
及其正视图与俯视图如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/8f528d9e-33e5-4841-8da5-d2e45f032ad6.png?resizew=421)
(1)求证:
;
(2)若D是
的中点(未画出),求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/8f528d9e-33e5-4841-8da5-d2e45f032ad6.png?resizew=421)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e4b16c2c6c9bd089da78122e9d2511.png)
(2)若D是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
您最近一年使用:0次
名校
解题方法
10 . 椭圆规是画椭圆的一种工具,如图1所示,在十字形滑槽上各有一个活动滑标
,
,有一根旋杆将两个滑标成一体,
,
为旋杆上的一点且在
,
两点之间,且
,当滑标
在滑槽
内做往复运动,滑标
在滑槽
内随之运动时,将笔尖放置于
处可画出椭圆,记该椭圆为
.如图2所示,设
与
交于点
,以
所在的直线为
轴,以
所在的直线为
轴,建立平面直角坐标系.则椭圆
的普通方程为______ .
![](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/c4e00ad067ceaf3a8c0452e5cd52a506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/d17663aeb7b7594a6b3af7d1538bb750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/8ec20cdb-37a3-464e-a4ec-f4b67843bf45.png?resizew=402)
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2020-08-16更新
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4卷引用:四川省绵阳南山中学2022-2023学年高二上学期期末数学试题
四川省绵阳南山中学2022-2023学年高二上学期期末数学试题陕西省西安市西北工业大学附属中学2019-2020学年高二下学期5月月考数学(理)试题(已下线)【新教材精创】2.5.2+椭圆的几何性质(1)-B提高练-人教B版高中数学选择性必修第一册新疆生产建设兵团第六师五家渠高级中学2022-2023学年高二下学期开学考试数学试题