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解题方法
1 . 如图所示,
是边长为3正三角形,
,S是空间内一点,
分别是
,
的二面角,满足
,点D到直线SB的距离是1,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94139af43ead4e1498111c4ff9a2cc55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9146b7c16d81ccb92aef1e1f1788f00f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fe637f1537666932491637f9b3d3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a5d8831a9bef0f3d882d97d28e6d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5fb1f1420818dd0bc15b57bcdd3053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09c783b689f9be3f192e6e32469e816.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/15/4d976eff-e798-4042-a1d8-57a8711e0f12.png?resizew=170)
A.![]() | B.![]() | C.![]() | D.![]() |
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6卷引用:浙江省温州市2022-2023学年高二下学期学考模拟测试数学试题
浙江省温州市2022-2023学年高二下学期学考模拟测试数学试题湖北省武汉外国语学校2023-2024学年高二上学期9月月考数学试题(已下线)高二上学期第一次月考选择题压轴题50题专练-2023-2024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)辽宁省部分名校2023-2024学年高二上学期联考数学试题广东省中山市中山纪念中学2024届高三上学期第三次模拟测试数学试题(已下线)第四章 立体几何解题通法 专题三 参数法 微点1 参数法(一)【培优版】
2 . 如图所示的八面体的表面是由2个全等的等边三角形和6个全等的等腰梯形组成,设
,
,有以下四个结论:
①
平面
; ②
平面
;
③直线
与
成角的余弦值为
④直线
与平面
所成角的正弦值为
.
其中正确结论的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/34f390e6-ecea-44bc-8ad5-62f5deb3aaf8.png?resizew=195)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1bdb08d371f24f7b4aeae53f292050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c50346190b81576e0d891456af44490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d4680b5fd79c9734c4439e28cdf3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7312cd653ef43a6ab81dd5da81cac779.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c8b7a498f2fa0820ad123a8756ce64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6c7567972273b4ba733b47bf9d5408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd6a02542c1ee2d2a60ea0a9ce7e82d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
其中正确结论的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/34f390e6-ecea-44bc-8ad5-62f5deb3aaf8.png?resizew=195)
A.1 | B.2 | C.3 | D.4 |
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名校
3 . 已知正方体
的棱长为
,点
是
的中点,点
是侧面
内的动点,且满足
,下列选项正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/dd55d538-b3e8-4e1e-9c46-f324511596f3.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c6151468904c32d230da58dca8193a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80cc064d914c1b4191d00f4b00032aad.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/dd55d538-b3e8-4e1e-9c46-f324511596f3.png?resizew=162)
A.动点![]() ![]() |
B.三角形![]() ![]() |
C.直线![]() ![]() ![]() ![]() ![]() |
D.存在某个位置![]() ![]() ![]() ![]() |
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6卷引用:浙江省丽水市2020-2021学年高一下学期期末数学试题
浙江省丽水市2020-2021学年高一下学期期末数学试题(已下线)第一章 (综合培优)空间向量与立体几何 B卷-【双基双测】2021-2022学年高二数学同步单元AB卷(浙江专用)(人教A版2019选择性必修第一册)福建省福州黎明中学2021-2022学年高一下学期期末考试数学试题浙江省绍兴市诸暨市2021-2022学年高二下学期学考模拟(1)数学试题(已下线)突破1.1 空间向量及其运算(课时训练)江苏省南京市第一中学2023-2024学年高二上学期7月阶段性考试数学试题
4 . 已知椭圆
的中心在坐标原点
,焦点在
轴上,左、右焦点分别为
、
,离心率
,短轴长为2,.
(1)求椭圆
的标准方程;
(2)设过
且斜率不为零的直线
与椭圆
交于
、
两点,过
作直线
的垂线,垂足为
,证明:直线
恒过一定点,并求出该定点的坐标;
(3)过点
作另一直线
,与椭圆分别交于
、
两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ea9f5967c96e60f03f332fd792cd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e1ba8ef888dfe9a639dddd38d6d603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ae93479f71c86ffa37131326cfd993.png)
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3卷引用:2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题
2021年黑龙江省哈尔滨市第三中学校高二上学期期中数学试题江西省赣州市赣县第三中学2021-2022学年高二12月月考数学(理)试题(已下线)易错点12 圆锥曲线-备战2022年高考数学考试易错题(新高考专用)
5 .
:若
,则
;
:_____________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f735290691112deb4686a0b4e05ae7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d367a8feeea3de8199efbb404be16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc1bb9d53a27d484396ad74d6a26e0.png)
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6 . 下列命题是真命题的是( )
A.3能被2整除 | B.对顶角不相等 |
C.5是偶数 | D.![]() |
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7 . 如图所示,P(在函数的左边)与Q(在函数的右边)分别为函数
的两个点,F为该抛物线的焦点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/e83ec34e-fa4c-4005-890f-96d2920c5f6e.png?resizew=145)
(1)若P的坐标为(-2,t),连接PF交抛物线另一点于H点,求H点的坐标;
(2)记PQ直线为m,其在y轴上的截距为6,过P作抛物线的切线,交抛物线的准线于M点,连接QF,若QF恰好经过M点,求直线m的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/8/e83ec34e-fa4c-4005-890f-96d2920c5f6e.png?resizew=145)
(1)若P的坐标为(-2,t),连接PF交抛物线另一点于H点,求H点的坐标;
(2)记PQ直线为m,其在y轴上的截距为6,过P作抛物线的切线,交抛物线的准线于M点,连接QF,若QF恰好经过M点,求直线m的方程.
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