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)
您最近一年使用:0次
2023-04-25更新
|
510次组卷
|
3卷引用:贵州省凯里市第一中学2023届高三三模数学(理)试题
解题方法
2 . 已知正四棱锥
中,O为底面ABCD的中心,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/05dc9a6b-56ad-4274-a7b8-1b8fa142b1e1.png?resizew=162)
(1)作出过点O与平面PAD平行的截面,在答题卡上作出该截面与四棱锥表面的交线,写出简要作图过程及理由;
(2)设PD的中点为G,
,求AG与平面PAB所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/05dc9a6b-56ad-4274-a7b8-1b8fa142b1e1.png?resizew=162)
(1)作出过点O与平面PAD平行的截面,在答题卡上作出该截面与四棱锥表面的交线,写出简要作图过程及理由;
(2)设PD的中点为G,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
您最近一年使用:0次
2022-11-23更新
|
326次组卷
|
3卷引用:山东省潍坊市五县市2022-2023学年高二上学期期中数学试题
名校
解题方法
3 . 如图,已知正三棱柱
中,所有棱长均为2,点E,F分别为棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/d1da7309-f913-43e5-b38e-71b659098164.png?resizew=217)
(1)求
与平面AEF所成角的正弦值;
(2)过A、E、F三点作一个平面,则平面AEF与平面
有且只有一条公共直线,在图中作出这条公共直线,简略写清作图过程,并求这条公共直线在正三棱柱底面
内部的线段长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/d1da7309-f913-43e5-b38e-71b659098164.png?resizew=217)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
(2)过A、E、F三点作一个平面,则平面AEF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
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名校
解题方法
4 . 在正方体中,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/24a9bce2-7d5f-42f1-8210-4c66c9c498ec.png?resizew=161)
(1)作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc725182c2fd1413319fea35b95c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923189afc198d153c79059a827f63c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42b4e11e3d0c9f18c4f7bdc9404824e.png)
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名校
解题方法
5 . 如图,四边形
是正方形,
平面
,
,
,
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/dee0013d-4a39-4b68-af36-65913fee0109.png?resizew=141)
(1)若
平面
,请在图中画出点
,保留作图痕迹,并说明理由.
(2)是否存在点
,使得
与平面
所成角的正弦值为
,若存在,求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed04b01505bbd8a4ac0bc12e46f23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180868535d96d800625148a03a33e9d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bcf55cb4ea16c17f20e02190ffdff07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/dee0013d-4a39-4b68-af36-65913fee0109.png?resizew=141)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d30788a482598e638aea779ac14da12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)是否存在点
![](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/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383c681f398877a4589a389d19a0f2e6.png)
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名校
6 . 某同学利用图形计算器研究教材中一例问题“设点
,
,直线
,
相交于点M,且它们的斜率之积为
,求点M的轨迹方程”时,将其中已知条件“斜率之积为
”拓展为“斜率之积为常数
”之后,进行了如图所示的作图探究:
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/3d217257-3ca3-4ff8-9d6b-5c848d6d0799.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/6a6a6eb1-633d-48bd-9799-9be0469f6918.png?resizew=200)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/f74ddd64-f2df-496e-8e44-8a8665a02e35.png?resizew=190)
参考该同学的探究,下列结论正确的有:( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d71fb4d3db6c9922d3b605a6d40e529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fe2c124d5bbbbe666ee145cd454b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889efe020137b112bfafaa8e0becda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889efe020137b112bfafaa8e0becda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/3d217257-3ca3-4ff8-9d6b-5c848d6d0799.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/6a6a6eb1-633d-48bd-9799-9be0469f6918.png?resizew=200)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/f74ddd64-f2df-496e-8e44-8a8665a02e35.png?resizew=190)
参考该同学的探究,下列结论正确的有:( )
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2021-02-05更新
|
807次组卷
|
8卷引用:重庆市部分区2020-2021学年高二上学期期末联考数学试题
7 . (1)求右焦点坐标是
,且经过点
的椭圆的标准方程.
(2)已知椭圆
,设斜率为
的直线
交椭圆
于
两点,
的中点为
,证明:当直线
平行移动时,动点
在一条过原点的定直线上.
(3)利用(2)中所揭示的椭圆几何性质,用作图方法找出图中的定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/c28d9ef0eba44eeda5181dc7b083523c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/d8e5e6ac67eb4145853c8cf83a5f9119.png)
(2)已知椭圆
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/7477185b1fe941e981b8590cdca860b1.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/1f22135cfb4d452e8f4ff5c0ea89c38a.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/6966e45b096d44088b1f951176c7fe24.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/da9e63efc9b9427ca212f9b6cadd87f1.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/a101441825324af9bc98161496aa0fdd.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/e62465c4941e4c3a8fc7bedf9dddda98.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/1d13f72b19fb4a32b9be6a541eab2263.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/6966e45b096d44088b1f951176c7fe24.png)
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/1d13f72b19fb4a32b9be6a541eab2263.png)
(3)利用(2)中所揭示的椭圆几何性质,用作图方法找出图中的定椭圆的中心,简要写出作图步骤,并在图中标出椭圆的中心.
![](https://img.xkw.com/dksih/QBM/2015/1/5/1571947852431360/1571947857920000/STEM/82de281a98b141cc9bce4e539af0d4dc.png)
您最近一年使用:0次
解题方法
8 . 已知集合
,
.
(1)求集合A,B;
(2)已知
,
,若p是q的_________条件,求实数a的取值范围.
请在①必要不充分、②充分不必要、③充要,这三个条件中选择一个填在横线上(若多选,按第一个给分),补全第(2)题,并根据所选条件解答该题.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8c3be3b286a9811cc4cc45124a0b165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffa73b9fedbc89a54baa3e94762fa13.png)
(1)求集合A,B;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc11e9183ffccd297df4a1c18618bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218c5309e534904dc6bf768074965239.png)
请在①必要不充分、②充分不必要、③充要,这三个条件中选择一个填在横线上(若多选,按第一个给分),补全第(2)题,并根据所选条件解答该题.
您最近一年使用:0次
2021-01-29更新
|
316次组卷
|
3卷引用:北师大版(2019) 必修第一册 名校名师卷 第八单元 对数运算与对数函数B卷
名校
9 . 一种画双曲线的工具如图所示,长杆OB通过O处的铰链与固定好的短杆OA连接,取一条定长的细绳,一端固定在点A,另一端固定在点B,套上铅笔(如图所示).作图时,使铅笔紧贴长杆OB,拉紧绳子,移动笔尖M(长杆OB绕O转动),画出的曲线即为双曲线的一部分.若|OA|=10,|OB|=12,细绳长为8,则所得双曲线的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/33da8c9a-b96d-4635-8914-658eeefbcca5.png?resizew=177)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/33da8c9a-b96d-4635-8914-658eeefbcca5.png?resizew=177)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-01-17更新
|
445次组卷
|
6卷引用:【区级联考】北京市丰台区2019届高三第一学期期末考试数学(理)试题
【区级联考】北京市丰台区2019届高三第一学期期末考试数学(理)试题【市级联考】辽宁省沈阳市郊联体2019届高三第一次模拟考试数学(理科)试题苏教版(2019) 选修第一册 突围者 第3章 第二节 课时2 双曲线的几何性质(已下线)专题6.2 期中押题检测卷(考试范围:第1-3章)2(中)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册) 北京交通大学附属中学2022届高三12月月考数学试题2023版 苏教版(2019) 选修第一册 突围者 第3章 第二节 课时2 双曲线的几何性质
名校
10 . 如图,已知正方体
的棱长为2,P为正方形底面
内的一动点,则以下结论:
(1)三棱锥
的体积为定值;
(2)若点
为
的中点,满足
平面
的点
的轨迹长度为2;
(3)若
,则
点在正方形底面
内的运动轨迹是线段
;
(4)以点
为球心,
为半径的球面与面
的交线长为
.正确的有______ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e7361ffb6d22b31453f636ef5bf45a.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3123da0313d458c833e82aaa234b9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c58abd0988129da90c2caf256b37233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(4)以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3765f7d2a69e4ad0707e9283801dcfcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/622f6bb6-6184-4598-9b23-890b4444bc66.png?resizew=169)
您最近一年使用:0次
2023-11-16更新
|
527次组卷
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2卷引用:上海市七宝中学2023-2024学年高二上学期期中数学试题