1 . 如图,在多面体
中,底面
为平行四边形,
,矩形
所在平面与底面
垂直,
为
的中点.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
平面
;
(2)若平面
与平面
夹角的余弦值为
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f066f86a3df01f4231ff63986d905c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
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3卷引用:江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题
解题方法
2 . 已知
,则是“
”的充分不必要条件有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
3 . 在平面直角坐标系
中,已知椭圆
经过点
,直线
与
轴交于点
,过
的直线
与
交于
两点(异于
),记直线
和直线
的斜率分别为
.
(1)求
的标准方程;
(2)求
的值;
(3)设直线
和直线
的交点为
,求证:
在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c118b51ab426bc1c1b56179094f146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec30037a621b23ade12cf58e42c4059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8533b4c6574df4f59b2ecc99e5c458db.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e3016db8a12fd848e8c4b93c11070d.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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3卷引用:江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题
江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题山东省东营市第一中学2023-2024学年高二下学期开学收心考试数学试题(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
解题方法
4 . 在平面直角坐标系
中,已知双曲线
的右焦点为
,过
的直线
与
的左、右两支分别交于
两点,若
,则
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07e50a212d5dbc74c9f564988918069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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4卷引用:江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题
江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题(已下线)最新模拟重组精华卷2 -模块一 各地期末考试精选汇编山东省威海市第一中学2024届高三下学期第一次月考数学试题广东省揭阳市普宁市华美实验学校2023-2024学年高二下学期第一次阶段考试数学试题
名校
解题方法
5 . 已知四棱锥
的底面为直角梯形,
平面
,
.
(1)若点
是棱
上的动点,且满足
,证明:
平面
;
(2)若点
为棱
上的一点(不含端点),试探究
上是否存在一点N,使得平面ADN
平面BDN?若存在,请求出
的值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2ed152f77be93446aa07ff443d3973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda1a7eeb84ee2f5f723c78de0867aa1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/28/ac13bef7-02ab-4624-9d24-f76e625cb19a.png?resizew=150)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5553dffc1e06f6d3a28e48bf320e6b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36222db36e348661eb5f616820e4e60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50cafe199913787a939fe9e100924023.png)
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解题方法
6 . 已知双曲线
的左、右焦点分别为
,过
且与
轴垂直的直线与
的一个交点为
的内心为
,若
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b85061f26e36a305b6fc8fd231ff3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40f98254a6193566587a70c7d95fdabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb31dea9dd55c0d0887cb985fcd4a4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222043220cbc910b9863b777f3a59f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.2 | B.![]() | C.![]() | D.![]() |
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2卷引用:江苏省苏州大学2024届高考新题型2月指导卷数学试题
名校
7 . 抛物线有一条重要性质:从焦点出发的光线,经过抛物线上一点反射后,反射光线平行于抛物线的对称轴.已知点F为抛物线C:
(
)的焦点,从点F出发的光线经抛物线上一点反射后,反射光线经过点
,若入射光线和反射光线所在直线都与圆E:
相切,则p的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dab9e79198239cda875305fd6809b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1ad196b56e055e7f85d9b95ddb9419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395610d6e4427cecbe3ba7fe066fe8b5.png)
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2卷引用:江苏省南京市、盐城市2024届高三上学期期末调研测试数学试题
解题方法
8 . 已知双曲线
的左、右顶点分别为
,离心率为
.过点
的直线l与C的右支交于M,N两点,设直线
的斜率分别为
.
(1)若
,求
;
(2)证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9c11cc36320090d0aaf0c621a63b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e4cfa2db814e7e2e8abdf033706420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e607c2f7ae494246768832acb0d54a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3342ecc389773431bc3f64410e41191.png)
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9 . 已知
是圆锥
的底面直径,C是底面圆周上的一点,
,平面
和平面
将圆锥截去部分后的几何体如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/ebb26a22-b021-4be1-82e4-8358117bcf72.png?resizew=153)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006da854daaec2ed7b17388f640057bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/ebb26a22-b021-4be1-82e4-8358117bcf72.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6d39135a2f8472d66ea00eda3b13ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
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10 . 已知椭圆
的左、右焦点分别为F1,F2,设P,Q是E上位于x轴上方的两点,且直线
.若
则E的离心率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a9dc208e4e9a1d015745bba83e45a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0319e91a45d3bd62d6f35a571c3725.png)
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