解题方法
1 . 如图,
分别是等腰梯形
的边
上的动点,
,其中
为定值,
,设
,其中
.
,求出
的表达式;
(2)证明:
的余弦值与
的取值无关;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ced9844fe2e052c70486af0740afa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596d41b6556f383445536d1c534ac182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f07948e9258b482a2164ac871f90f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18fec3e4a4fbc7b3e0e037ce650023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d91513d2e546a5a0b5fd42379db8df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e72cf7374a65ced433b6fa113ef57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e2be3e9225c71609248299caa49432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192c2f1059f6e05d44df048f5fdca04b.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db625151987f893816de66b15d9e699.png)
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名校
解题方法
2 . 如图,用一个与圆柱底面成
角的平面截圆柱,截面是一个椭圆. 已知圆柱的底面半径为1,建立适当的平面直角坐标系
,可以得到椭圆
的标准方程:
.
的左、右焦点分别为
、
,过
作斜率为
的直线
,与
交于
、
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/910a9ca0-9455-4258-9775-8a47aaf079e4.png?resizew=208)
(1)求
的标准方程;
(2)若
,直线
与
的交点
在直线
上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7708c156249bb475564027f73313fa8.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/c663466d641b5fdfef1e529d6c330ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166afeb61d5a80366a8ae29c912cd644.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/910a9ca0-9455-4258-9775-8a47aaf079e4.png?resizew=208)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371217502820b6f1b615ee61cfa488d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80ecb6b5d5eca464b3f099513c08fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffacc89d6cec4b91e811782b0d667fd.png)
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名校
解题方法
3 . 已知双曲线
,点
,
分别在两条渐近线上(不与原点
重合),点
是
上的一个动点,且
,记直线
的斜率分别为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538724a2186d3433efeceb10e7f7b2d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef7d76b595a30a00dade6f3e1496e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416f71ce7c4353b22d83d04430e5b2b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e62161dffbcefd4cfdcee73b0a64b.png)
A.![]() | B.当![]() ![]() |
C.![]() | D.![]() |
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4 . 已知
是椭圆
上的两点,
关于原点
对称,
是椭圆
上异于
的一点,直线
和
的斜率满足
.
(1)求椭圆
的标准方程;
(2)若斜率存在且不经过原点的直线
交椭圆
于
两点
异于椭圆
的上、下顶点),当
的面积最大时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5ef74db95fc6d43ff7565f257539e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08df584945b1bc9961138b670327d536.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若斜率存在且不经过原点的直线
![](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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030d5205aabb757fb29e03704b4b26b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee89f7d493efc00cd703af6bc73f9ea9.png)
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2023-09-08更新
|
1469次组卷
|
8卷引用:河南省周口市项城市2024届高三5校青桐鸣大联考9月数学试题
河南省周口市项城市2024届高三5校青桐鸣大联考9月数学试题(已下线)河南省信阳高级中学2023-2024学年高三上学期9月一模数学试题(已下线)3.1.2 椭圆的简单的几何性质(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)专题突破卷23 圆锥曲线大题归类(已下线)考点16 解析几何中的定值问题 2024届高考数学考点总动员(已下线)重难点突破09 一类与斜率和、差、商、积问题的探究(四大题型)(已下线)考点18 解析几何中的范围、最值问题 2024届高考数学考点总动员(已下线)专题06 椭圆的压轴题(6类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)
名校
5 . 如图,某景区共有
五个景点,相邻景点之间仅设置一个检票口供出入,共有7个检票口,工作人员为了检测检票设备是否正常,需要对每个检票口的检票设备进行检测.若不重复经过同一个检票口,依次对所有检票口进行检测,则共有____________ 种不同的检测顺序.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d75df9d80ce1e0b7cb50464e293864.png)
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2023-04-20更新
|
979次组卷
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6卷引用:河南省周口市项城市第一高级中学等5校2022-2023学年高二下学期期中数学试题
河南省周口市项城市第一高级中学等5校2022-2023学年高二下学期期中数学试题重庆市部分学校2022-2023学年高二下学期期中数学试题重庆市北碚区西南大学附属中学校2022-2023学年高二下学期期中数学试题(已下线)专题01 两个计数原理与排列组合(7类压轴题型)-【常考压轴题】2023-2024学年高二数学压轴题攻略(人教A版2019选择性必修第三册)(已下线)黄金卷04专题07排列组合(第一部分)
名校
6 . 设集合
,若集合S中的元素同时满足以下条件:
①
,
恰好都含有3个元素;
②
,
,
为单元素集合;
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e5858ed377ffaf700c868a38e7256.png)
则称集合S为“优选集”.
(1)判断集合
,
是否为“优选集”;
(2)证明:若集合S为“优选集”,则
,
至多属于S中的三个集合;
(3)若集合S为“优选集”,求集合S的元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32fe32077f54b51282141c6f6217071.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296902bfc14bde752a4503d57351988a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866fcccdcf1d7bf2f73d4323b4c1c1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41e1766af890659ac91f4ed407f5a0f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f5e5858ed377ffaf700c868a38e7256.png)
则称集合S为“优选集”.
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7d06d943bfb67f20183899803ef150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a839a1d941f18f084505c7e8614c984b.png)
(2)证明:若集合S为“优选集”,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7060f36f24efe532ddd3f12084f36d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若集合S为“优选集”,求集合S的元素个数的最大值.
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2023-01-19更新
|
566次组卷
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4卷引用:河南省周口市周口恒大中学2023-2024学年高一上学期9月月考数学试题
河南省周口市周口恒大中学2023-2024学年高一上学期9月月考数学试题北京交通大学附属中学2021-2022学年高一上学期期中数学试题重庆市南开中学校2023-2024学年高一上学期九月测试数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)
名校
解题方法
7 . 德国数学家黎曼(Ricmann)提出的黎曼函数r(x)在分析学中有着广泛的应用.黎曼函数r(x)的定义为
,(p∈N*,q∈Z,q≠0且p,q互素),下列命题中,正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625aee779fe2f73449c464ad522f1eb0.png)
A.存在常数T > 0,使得对任意的x∈R,都有![]() |
B.对任意的x∈R,有![]() |
C.存在a,b,a + b∈[0,1],使得![]() |
D.给定正整数t,记S =![]() ![]() |
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2022-11-05更新
|
389次组卷
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2卷引用:河南省周口市恒大中学2023-2024学年高一上学期12月月考数学试题
8 . 将正方形
的边
绕点
逆时针旋转至
,记旋转角为
.连接
,过点
作
垂直于直线
,垂足为点
,连接
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/86367bb7-74ca-4052-a1c0-d24f5046afed.png?resizew=244)
(1)如图1,当
时,
的形状为 ,连接
,可求出
的值为 ;
(2)当
且
时,
①(1)中的两个结论是否仍然成立?如果成立,请仅就图2的情形进行证明;如果不成立,请说明理由;
②当以点
为顶点的四边形是平行四边形时,请直接写出
的值.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85c133d0a322e4012f7c0eb7f4c626c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/86367bb7-74ca-4052-a1c0-d24f5046afed.png?resizew=244)
(1)如图1,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cf714ffb3fd5917a76b191640b55fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c4851109ebad7d40fd6e8c0ed91cde6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbaeec6b78ac2dce4b20c3fee0139bc6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783d872617eed2bbd474035156b6caaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d15b7c09aac2543b8615aca6b62ee36d.png)
①(1)中的两个结论是否仍然成立?如果成立,请仅就图2的情形进行证明;如果不成立,请说明理由;
②当以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e723dd679f5659390e39777911c58c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff7201050b9d841420f6389dfd4663f.png)
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