名校
解题方法
1 . 已知△ABC中,
,双曲线E以B,C为焦点,且经过点A,则E的两条渐近线的夹角为_____________ ;
的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c572c23c972fbeffe8d385d50a147b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283e48bac57e110e164c5c57d39dc19d.png)
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2卷引用:2024届广东省深圳市二模数学试题
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解题方法
2 . 如图是某公园局部的平面示意图,图中的实线部分(它由线段
与分别以
为直径的半圆弧组成)表示一条步道.其中的点
是线段
上的动点,点O为线段
的中点,点
在以
为直径的半圆弧上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ef02d1d900149833eb39981945cbd7.png)
均为直角.若
百米,则此步道的最大长度为_________ 百米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82f2c927f42e299eec9616f2d4d7e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ba6d3a4b110f65a8d203aeadd03ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10ff911ab3353e9b8221d258d4112ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ef02d1d900149833eb39981945cbd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0629452691a52b84bfe315ef1af796f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f6626065b64760f8cd190948ff008d.png)
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|
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3卷引用:广东省广雅中学2024届高三下学期高考考前适应性考试数学试题
3 . 已知抛物线
:
的焦点
,直线
过
且交C于两点
,已知当
时,
中点纵坐标的值为
.
(1)求
的标准方程.
(2)令
,P为C上的一点,直线
,
分别交C于另两点A,B.证明:
.
(3)过
分别作
的切线
,
与
相交于
,同时与
相交于
,求四边形
面积取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901eaab225137c0db994996875667279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6a55260653d60c2157a15ce3aebc8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3198d4ac606acfd7c6d7f60d619336ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c2293f93791a597bf0162411f3395f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77451286f0f5e470162aaa7f00b55933.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81687c0af83f550bcb802e2d82c76a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8801df26d9cb76bc289b64a3a26902e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
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2卷引用:广东省东莞市东华高级中学 东华松山湖高级中学2024届高三下学期第三次模拟考试数学试题
名校
4 . 如果方程
能确定y是x的函数,那么称这种方式表示的函数是隐函数.隐函数的求导方法如下:在方程
中,把y看成x的函数
,则方程可看成关于x的恒等式
,在等式两边同时对x求导,然后解出
即可.例如,求由方程
所确定的隐函数的导数
,将方程
的两边同时对x求导,则
(
是中间变量,需要用复合函数的求导法则),得
.那么曲线
在点
处的切线方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2329774440278b274651ca465704a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2329774440278b274651ca465704a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d318c5ba5c7154bbcc95f8ec8e3d4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fe744d4980ba5e09c4074e0643e635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e70497c791fd23d1f37a544f2f73f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76f3dbccb8db423d81c796cf1e8f4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f58a44e22ec20612a8aacba7295e4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96932f0ba294e407eabb7b1e324e66c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100e975b1e92a21f9533b42f8cd7d258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:广东省揭阳市2024届高三下学期二模考试数学试题
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解题方法
5 . 下列命题为真命题的是( )
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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3卷引用:广东省湛江市2024届高三下学期二模考试数学试题
6 . 过抛物线外一点
作抛物线的两条切线,切点分别为A,B,我们称
为抛物线的阿基米德三角形,弦AB与抛物线所围成的封闭图形称为相应的“囧边形”,且已知“囧边形”的面积恰为相应阿基米德三角形面积的三分之二.如图,点
是圆
上的动点,
是抛物线
的阿基米德三角形,
是抛物线
的焦点,且
.
的方程;
(2)利用题给的结论,求图中“囧边形”面积的取值范围;
(3)设
是“圆边形”的抛物线弧
上的任意一动点(异于A,B两点),过D作抛物线的切线
交阿基米德三角形的两切线边PA,PB于M,N,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b501de0a6ebd0c2f8143ac70d8b66649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1cb81ad58dc0521d4692a0404ecad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf1a7bb97f1c79c3f7bf664b78c20b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)利用题给的结论,求图中“囧边形”面积的取值范围;
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6833e56be18e5a0123210cbcaa0df2b.png)
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5卷引用:广东省深圳市深圳高级中学(集团)2024届高三下学期适应性考试数学试卷
名校
解题方法
7 . 定义
,对于任意实数
,则
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5855d641a4f2d83e1bceb76311c2e24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b1e9af136e020f8b986df700601bb2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:广东省韶关市2024届高三综合测试(二)数学试题
8 . 现有一“v”型的挡板如图所示,一椭圆形物件的短轴顶点被固定在A点.物件可绕A点在平面内旋转.AP间距离可调节且与两侧挡板的角度固定为60°.已知椭圆长轴长为4,短轴长为2.
(1)在某个角度固定椭圆,则当椭圆不超过挡板时AP间距离最短为多少;
(2)为了使椭圆物件能自由绕A点自由转动,AP间距离最短为多少.求出最短距离并证明其可行性.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/21/0d7b8c50-52e4-4c1f-86eb-cece102920f9.png?resizew=191)
(1)在某个角度固定椭圆,则当椭圆不超过挡板时AP间距离最短为多少;
(2)为了使椭圆物件能自由绕A点自由转动,AP间距离最短为多少.求出最短距离并证明其可行性.
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名校
解题方法
9 . 已知在平面直角坐标系
中,
:
,
:
,平面内有一动点
,过
作
交
于
,
交
于
,平行四边形
面积恒为1.
(1)求点
的轨迹方程并说明它是什么图形;
(2)记
的轨迹为曲线
,
,当
在
轴右侧且不在
轴上时,在
轴右侧的
上一点
满足
轴平分
,且
不与
轴垂直或
是
的一条切线,求
与
,
围成的三角形的面积最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4407788e4dc88210bca71a2551d4f2f9.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/b22c9e62d7dfe7116965d5f809f54fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8565d467e55e50c9c999868ce289f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e089ac241dbeeda7d9172a394d6acb.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/488675b0c71bc75ccea45696c496080b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95cfffad86cdce753e3025437b6ef14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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2024-03-21更新
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3卷引用:广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
10 . 已知以下事实:反比例函数
(
)的图象是双曲线,两条坐标轴是其两条渐近线.
(1)(ⅰ)直接写出函数
的图象
的实轴长;
(ⅱ)将曲线
绕原点顺时针转
,得到曲线
,直接写出曲线
的方程.
(2)已知点
是曲线
的左顶点.圆
:
(
)与直线
:
交于
、
两点,直线
、
分别与双曲线
交于
、
两点.试问:点A到直线
的距离是否存在最大值?若存在,求出此最大值以及此时
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
(1)(ⅰ)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c190daf6e3d1cdd5019c3f50a4f842e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
(ⅱ)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff2f5d89e535bab877ad226f086742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
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2024-03-21更新
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5卷引用:广东省佛山市禅城区2024届高三统一调研测试(二)数学试题