1 . 已知点
和向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ee15f9bec0b0007c405385a69a45fa.png)
(1)若向量
与向量
同向,且
,求点
的坐标;
(2)若向量
与向量
的夹角是钝角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9b4081755dd5d63529f95fab4ca51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ee15f9bec0b0007c405385a69a45fa.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59719064db2579c7479960ff3c1051cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edfcaa682bd35146c55bef5c2c5bb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f49f461d57d35cebe267f62f2c5ec1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024-04-12更新
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2卷引用:山东省菏泽市外国语学校2022-2023学年高一下学期第一次月考数学试题
名校
解题方法
2 . 如图,在三棱柱
中,平面
平面
,点
为
的中点,点
在线段
上,且
.
与平面
的夹角的余弦值;
(2)点
在
上,若直线
在平面
内,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd18ab492e444901bbe9a5a5cb6252a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35182e303363ec2d2e15e76eb1a4ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
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2024-03-04更新
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819次组卷
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2卷引用:山东省烟台第一中学2023-2024学年高三上学期12月份月考数学试题
名校
解题方法
3 . 已知O为坐标原点,
,
,点P满足
,记点P的轨迹为曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e28ce60503fab70ce1797449d90dadc.png)
(1)求曲线E的方程;
(2)过点
的直线l与曲线E交于
两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bdeda4c7e7dfc44086dcf4f3297a94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bffb9cf70cdb3312c1e547c3cc4b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f204edcd6f54b84b22add0ee7a1167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e28ce60503fab70ce1797449d90dadc.png)
(1)求曲线E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bffb9cf70cdb3312c1e547c3cc4b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a704469569b68ee11ab166dba3f686f0.png)
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2024-02-03更新
|
1001次组卷
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5卷引用:山东省泰安市新泰市第一中学东校2023-2024学年高二上学期期末模拟数学试题(一)
山东省泰安市新泰市第一中学东校2023-2024学年高二上学期期末模拟数学试题(一)(已下线)专题12双曲线(3个知识点5个拓展2个突破8种题型5个易错点)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)四川省成都市第七中学2023-2024学年高二上学期期末复习数学试题(三)湖北省2023-2024学年高二上学期期末冲刺模拟数学试题(02)(已下线)模块6 平面几何篇 第3讲:平面向量的范围问题【讲】
名校
解题方法
4 . 已知集合
.
(1)若
,求实数
的取值范围;
(2)若“
”是“
”的必要非充分条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/738c7287058faaf96c706f1b950f14ce.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-22更新
|
376次组卷
|
2卷引用:山东省菏泽市第一中学2023-2024学年高一上学期第四次月考数学试题
名校
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa80ae0b0eab1f14cccf872500f0843.png)
且
的图象恒过定点
,且点
又在函数
的图象上.
(1)若
,求
的值;
(2)若
使得不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa80ae0b0eab1f14cccf872500f0843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b72044b1c0296cbcfaa676aa4bd8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc2e93cee2e6a921b66d250bd046b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df938fcb2a0a8f76bfba85ad2730200.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71260f3e5621fb6c18ecd0efe1d8f6d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521c5b64ec73de7b2f498f80f564583d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34cb6402ac1407ee3347e01fb2ba48a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024-01-22更新
|
564次组卷
|
2卷引用:山东省菏泽市第一中学2023-2024学年高一上学期第四次月考数学试题
2024·全国·模拟预测
6 . 已知函数
.
(1)当
时,求函数
的单调递增区间;
(2)若函数
在
上有且仅有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc3a9769dbd74b2160eeaafce83ead7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1613d377a07850c72cbec354b7a3000f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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7 . 已知a,b,c为三角形的三边.
(1)求证:
;
(2)若
,求证:
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756084350ee839aa662bb1b39fa962db.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09cad84c1fa1dbfdc03fb5441c039a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b6d7b31981b8dc5e2ac863e5a25fda.png)
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8 . 已知抛物线
,
为
的焦点,直线
与
交于不同的两点
、
,且点
位于第一象限.
(1)若直线
经过
的焦点
,且
,求直线
的方程;
(2)若直线
经过点
,
为坐标原点,设
的面积为
,
的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)若直线
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0907a673d52825cd7df84b400972d4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5b6926cdb99eb58070b8720718f71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c525358262126a51fbb598d58f3e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c21cbb1c2bcbcb8391ac5a879f2ae0.png)
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2024-01-06更新
|
669次组卷
|
7卷引用:山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题
名校
9 . 如图,在四棱锥
中,底面ABCD为梯形,
,
.
(1)求点
到平面ABCD的距离;
(2)在棱
上是否存在点
,使得平面DBF与平面PBC夹角的余弦值为
?若存在,求出点
的位置;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/5ffc1e754954a86924402a0bc14d34d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8720b7fc8488adfa47321caff2566.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/02942b9f-e566-4908-860b-341c1cbe05c2.png?resizew=167)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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2024-01-06更新
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6卷引用:山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题
山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题湘豫名校联考2023-2024学年高二上学期1月阶段性考试数学试题河南省商丘市第一高级中学2023-2024学年高二上学期1月份半月考数学试卷(已下线)专题13 空间向量的应用10种常见考法归类(3)(已下线)第6章 空间向量与立体几何 章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)河南省信阳市信阳高级中学2023-2024学年高二下学期易错题回顾测试(开学)数学试题
名校
10 . 已知函数
.
(1)若
在
处的切线
与直线
垂直,求
的方程;
(2)若
,且
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb221b680754e21912398a4544b17ea.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea9824af71c9da5db5a00ec06063024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d406340355cba74ae8a04702e7c3a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672b3ddf3bb965a8a946aec16d894dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-12-29更新
|
512次组卷
|
2卷引用:山东省泰安市新泰弘文中学2024届高三上学期第二次质量检测数学试题