解题方法
1 . 已知正方体
的棱长为2,
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/2021/3/9/2674139275198464/2677682265489408/STEM/1e7eb36395414108a4e9749b4856e6e6.png?resizew=260)
(1)画出平面
截正方体各个面所得的多边形,并说明多边形的形状和作图依据;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e21de25a662ba9e513dee5d6e34cb237.png)
![](https://img.xkw.com/dksih/QBM/2021/3/9/2674139275198464/2677682265489408/STEM/1e7eb36395414108a4e9749b4856e6e6.png?resizew=260)
(1)画出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5cf7b987c8da3b08450400484db716.png)
您最近一年使用:0次
2021-03-14更新
|
736次组卷
|
4卷引用:广西桂林、崇左市2021届高三二模数学(理)试题
广西桂林、崇左市2021届高三二模数学(理)试题(已下线)专题36 仿真模拟卷04-2021年高考数学二轮复习热点题型精选精练(新高考地区专用)(已下线)精做04 立体几何-备战2021年高考数学(理)大题精做宁夏银川市贺兰县景博中学2021届高三下学期二模数(理)试题
名校
解题方法
2 . 如图多面体
中,面
面
,
为等边三角形,四边形
为正方形,
,且
,
、
分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/2021/5/16/2722164997160960/2761320622317568/STEM/085ce249526c498d8827e0ed61295117.png?resizew=230)
(1)做出平面
与平面
的交线,记该交线与直线
交点为
,则
的值是多少?(不需说明理由,保留作图痕迹);
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1056cd2db035cbfcce4935ffec20030a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaceb8d6c6927e14d9ac7a557a2b11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d459cad63e3cd2aba10862800fa4832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbebf3b4b4f58588abd4d909f287011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2021/5/16/2722164997160960/2761320622317568/STEM/085ce249526c498d8827e0ed61295117.png?resizew=230)
(1)做出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ab40260ac9056153d14d70d2519371.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9b93a16e12288832564c6ffe82151e.png)
您最近一年使用:0次
2021-07-10更新
|
338次组卷
|
8卷引用:安徽省马鞍山市2021届高三下学期第三次教学质量监测理科数学试题
安徽省马鞍山市2021届高三下学期第三次教学质量监测理科数学试题江苏省泰州中学2021届高三下学期四模数学试题安徽省示范高中培优联盟2020-2021学年高二下学期春季联赛理科数学试题(已下线)专题1.11 空间向量与立体几何大题专项训练(30道)-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)专题24 立体几何解答题最全归纳总结-2(已下线)专题08 立体几何解答题常考全归类(精讲精练)-1(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)-2(已下线)专题15 立体几何解答题全归类(练习)
解题方法
3 . 用平行于圆锥底面的平面截圆锥,截面与底面之间的几何体称为圆台,也可称为“截头圆锥”.在如图的圆台
中,上底面半径为
,下底面半径为
,母线长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/dcbeb60f-10fe-4a9c-862d-16cfa7d0a6b9.png?resizew=177)
(I)结合圆台的定义,写出截面
的作图过程;
(II)圆台截面
与截面
是两个全等的梯形,若
,求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe2aba242716238b79c46bb1f40e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/dcbeb60f-10fe-4a9c-862d-16cfa7d0a6b9.png?resizew=177)
(I)结合圆台的定义,写出截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(II)圆台截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bebae04c72b934bfbbf0b4d01f164f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d25b5ade550ec6afd3536e9eb5d75.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,在棱长为2的正方体
中,
为棱
的中点,
,
分别是棱
,
上的动点(不与顶点重合).
![](https://img.xkw.com/dksih/QBM/2021/11/29/2861864413462528/2874316998737920/STEM/1f194ed5527b4c139b2ee3bd33a6b6c8.png?resizew=182)
(1)作出平面
与平面
的交线(要求写出作图过程),并证明:若平面
平面
,则
;
(2)若
为棱
的中点,是否存在
,使平面
平面
,若存在,求出
的所有可能值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2021/11/29/2861864413462528/2874316998737920/STEM/1f194ed5527b4c139b2ee3bd33a6b6c8.png?resizew=182)
(1)作出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abb06405623edb5c9d5f7350d79dc76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8b5a6dbcf05f572f83f51abf7d668c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/723fee86afab63b4aa7c826e19d6954a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d47e5be88e89d0d042c56d2d6942b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3709c4a29868ca0913bbffe73e8aaf43.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee2fa962e94c95769f29027ca71dd68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71defc7ee294da7b05b7c32728ec4a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0a36f8412d05e2a501cf3c5bdffd3a.png)
您最近一年使用:0次
名校
5 . 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:北京交通大学附属中学2022届高三12月月考数学试题
北京交通大学附属中学2022届高三12月月考数学试题【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) 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
6 . 下列说法正确的是___________ (填写序号)
①命题“若
,则
”的逆否命题是“若
,则
”;
②“
”是“
”的充分不必要条件;
③若
为假命题,则
均为假命题;
④命题
,使得
,则
,均有
.
①命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fdf7d28b97fb6fe731703f80e122ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8a2a94168af9b16ce89271a5d8dc6b.png)
②“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e38581b43f437454b86dae0daed9a2f.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13472bf0353e16784a22e1f890fba40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
④命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fac11dd95cb4b78adb817fad02dedb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264dab145ceba44696a6ee63b1e1549d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cd44731d509352f907c9773a42cab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1c77d129b56255baf3d76eb2a6c2ff.png)
您最近一年使用:0次
2021-10-10更新
|
682次组卷
|
3卷引用:宁夏平罗中学2022届高三上学期第一次月考数学(文)试题
名校
解题方法
7 . 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)
您最近一年使用:0次
2022-02-08更新
|
1770次组卷
|
4卷引用: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
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
名校
8 . 一条抛物线把平面划分为二个区域,如果一个平面图形完全落在抛物线含有焦点的区域内,我们就称此平面图形被该抛物线覆盖.那么下列命题中,正确的是___________ .(填写序号)
(1)任意一个多边形所围区域总能被某一条抛物线覆盖;
(2)与抛物线对称轴不平行、不共线的射线不能被该抛物线覆盖;
(3)射线绕其端点转动一个锐角所扫过的角形区域可以被某二条抛物线覆盖;
(4)任意有限多条抛物线都不能覆盖整个平面.
(1)任意一个多边形所围区域总能被某一条抛物线覆盖;
(2)与抛物线对称轴不平行、不共线的射线不能被该抛物线覆盖;
(3)射线绕其端点转动一个锐角所扫过的角形区域可以被某二条抛物线覆盖;
(4)任意有限多条抛物线都不能覆盖整个平面.
您最近一年使用:0次
2021高三下·全国·专题练习
解题方法
9 . 已知双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
的左、右焦点分别为
,过
的直线与双曲线的左支交于
两点,连接
.(1)
为定值;(2)若
轴,
为等边三角形,则双曲线C的离心率为
;(3)
的内切圆与
切于点
.则上述说法正确的有____ .(填写所有正确说法的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8294e87df18d712bc134a3ca2a716c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55d76bfd757b64517963cbc4662b366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24624dffd30b66a5e4de57362b32b2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
您最近一年使用:0次
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解题方法
10 . 如图,正方体
中,
,
,
,
分别是棱
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/2021/10/16/2830782191337472/2831116185968640/STEM/4b7ab31c717143ab80a3908eb4e1b3b8.png?resizew=193)
(1)画出平面
截正方体各个面所得的多边形,并计算此多边形的周长;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.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/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2021/10/16/2830782191337472/2831116185968640/STEM/4b7ab31c717143ab80a3908eb4e1b3b8.png?resizew=193)
(1)画出平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212ef48bb043b58681c8802c79622050.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d23790694b3a227fa15dbcda9546ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e06947327f4c41340b8713e8a6b4c87.png)
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