名校
解题方法
1 . 已知函数
及其导函数
的定义域均为
,记
.
满足
,
的图象关于直线
对称,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205b6623a0158130a701284de57bd331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c36601834a9a0e473ff9b17cd66458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2卷引用:福建省南平市2024届高三下学期第三次质量检测数学试题
名校
2 . 我们把方程
的实数解称为欧米加常数,记为
.
和
一样,都是无理数,
还被称为在指数函数中的“黄金比例”.下列有关
的结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c9c4849920f9b5d6be15d5e73e33b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.函数![]() ![]() |
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解题方法
3 . 记
的内角
的对边分别为
.已知
,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a92cfa82ed0e7652b482635e72a84ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc940e481607daedc1e83e98ec3bd4c0.png)
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解题方法
4 . 如图,在棱长为的正方体
中,已知
,
,
分别是棱
,
,
的中点,点
满足
,
,下列说法正确的是
( )
A.![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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5 . 已知函数
.
(1)讨论函数
的单调性;
(2)设
,若存在
,使得
.
①求
的取值范围;
②设
为整数,若当
时,相应的
总满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c207efd83d75c1f69237d97616c726.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67a5e2b17bebd7968ed279513fc6f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea708e5373993201a728ef80057cd55.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34308cf92d20690e6b2745d28ea5ff5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b5f36cbdb64b34f98763993dc0e972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1aa7f92634a3de5b9d89a86c4968f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
6 . 已知椭圆
的离心率为
,点
中恰有两个点在
上.
(1)求
的方程;
(2)设
的内角
的对边分别为
,
.若点
在
轴上且关于原点对称,问:是否存在
,使得点
都在
上,若存在,请求出
,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70325b83a7ba044734bf05e11e9c8d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5750d4c946764c8d82ce4f61cf9f1c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7e0cabca48a12ffefd4f8ef4621ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594af9fdf0ec161fafdc4214eca9b1c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cefac15fc86ed0a0a1cef62b103dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5393d976849cb83e09eb35764c67a541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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解题方法
7 . 双曲线C:
的离心率为
,点
在C上.
(1)求C的方程;
(2)设圆O:
上任意一点P处的切线交C于M、N两点,证明:以MN为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46529ee9b4550db1c12f187e1fbebde0.png)
(1)求C的方程;
(2)设圆O:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
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3卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
名校
解题方法
8 . 如图,在棱长为2的正方体
中,点E,F分别是
和
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.![]() |
B.![]() |
C.点F到平面EAC的距离为![]() |
D.过E作平面![]() ![]() ![]() |
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|
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4卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题(已下线)专题3 立体几何中的范围、最值问题【讲】(已下线)专题5 空间向量的应用问题【讲】广东省广州市广雅中学2024届高三下学期教学情况检测(一)数学试题
名校
解题方法
9 . 如图,
的半径等于2,弦BC平行于x轴,将劣弧BC沿弦BC对称,恰好经过原点O,此时直线
与这两段弧有4个交点,则m的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b74381f68eb1e33d412a7a3d62313f.png)
A.![]() | B.![]() | C.![]() | D.1 |
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|
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3卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
10 . 已知圆
和点
,点
是圆上任意一点,线段
的垂直平分线与线段
相交于点
,记点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)点
在直线
上运动,过点
的动直线
与曲线
相交于点
.
(ⅰ)若线段
上一点
,满足
,求证:当
的坐标为
时,点
在定直线上;
(ⅱ)过点
作
轴的垂线,垂足为
,设直线
的斜率分别为
,当直线
过点
时,是否存在实数
,使得
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ff31057ecaa627f515ba1695a3a220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb898663f98b8400a897913b4d3102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/7789a500686c7a73770404ead6af0590.png)
(ⅰ)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d620fe39012122d4f56b11f84d6e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410aad8f4e564c85102f18040d68b93a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(ⅱ)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d809e0ac2b18c7dc492c661c582e54e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff32d26c8d44f5fb4813a19c1030a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc0ee0a95fab04edf648026f14b9ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6卷引用:2024届福建省厦门第一中学高考模拟(最后一卷)数学试题
2024届福建省厦门第一中学高考模拟(最后一卷)数学试题2024届山东省聊城市高三三模数学试题(已下线)情境12 结论未知的证明命题(已下线)情境10 存在性探索命题江苏省无锡市辅仁高级中学2024届高三下学期高考前适应性练习数学试题海南省2023-2024学年高二下学期期末数学考试试题