名校
1 . 如图,已知正三棱锥
和正三棱锥
的侧棱长均为
.若将正三棱锥
绕
旋转,使得点
分别旋转至点
处,且
四点共面,点
分别位于
两侧,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d2ef6661d1808fed0cbd1b0fa53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13ba83790c5605647e39a560641061c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff571c72c041d8668b4d2754679f64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de83ce4d5ad4bb47d74cbd3bc3394ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e5d9f7e63d80a1969318ac999a3e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e925a4d4d706168d1ae69167483096c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.多面体![]() | B.![]() |
C.![]() ![]() | D.点![]() ![]() |
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2024-05-29更新
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593次组卷
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2卷引用:江西省南昌市第十九中学2024届高三下学期第四次模拟考试数学试卷
名校
2 . 已知函数
,
.
(1)当
时,求
在
处的切线方程;
(2)求
的单调区间:
(3)若
,
,使得
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d4ffe83140243af103c4d806e3ed1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ef7094c6c60a57532334ee3e8b4afe.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da60d3fead7b237c07e817a3801cafe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41f25aab93b2ceb283fca684e9b8d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8c626afbc95213849e8f122d9b1a13.png)
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3 . 英国科学家牛顿在数学、物理、天文学方面作出了巨大的贡献.他曾用“切线法”求函数零点的近似值,方法是不断通过作函数
图象的切线,这些切线与
轴的交点的横坐标就是函数
一个零点的不同程度的近似值;现在给定函数
,点
是曲线上的点,设
,以点
为切点作曲线
的切线,切线与
轴的交点的横坐标为
;又以点
为切点作曲线
的切线,切线与
轴的交点的横坐标为
,……,一直下去,得到数列
;又记
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f3aae3d8f8d6bdbbba7c7751f13882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5832c0296400f0a756634e912db3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d56247c3c62a79ec98290642268e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93f8e7f0cee389f9d8cbb0d812f8359.png)
A.![]() | B.![]() |
C.![]() | D.设数列![]() ![]() ![]() ![]() |
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解题方法
4 . 设抛物线C:
(
),直线l:
交C于A,B两点.过原点O作l的垂线,交直线
于点M.对任意
,直线AM,AB,BM的斜率成等差数列.
(1)求C的方程;
(2)若直线
,且
与C相切于点N,证明:
的面积不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b35f0b940c8422ef47edc3b7ce55e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d0aa9412dd7caf42cc71520e282328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
(1)求C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edc05c94ee6367e5551b219ac3168865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
您最近一年使用:0次
2024-05-26更新
|
3034次组卷
|
5卷引用:江西省南昌市八一中学2024届高三下学期三模测试数学试题
江西省南昌市八一中学2024届高三下学期三模测试数学试题2024届广东省深圳市二模数学试题(已下线)第30题 几何分析曲径通幽,代数推演水到渠成(优质好题一题多解)安徽省六安第一中学2023-2024学年高三下学期期末质量检测卷(二)数学试题(已下线)易错点8 圆锥曲线问题中未讨论直线斜率的特殊情况
5 . 已知抛物线
,圆
,
是抛物线
上一点(异于原点).
(1)若
为圆
上一动点,求
的最小值;
(2)过点
作圆
的两条切线,分别交抛物线
于A,B两点,切点分别为E,F,若四边形ABFE为梯形,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4931ada8e765288f878a0dac700e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96492592e9e1cbea8a86e4f85cc1f51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
6 . 已知关于
的不等式
在
上恒成立,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98658fb33b67f416a48a304f2c82eb14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
7 . 已知以点M为圆心的动圆经过点
,且与圆心为
的圆
相切,记点M的轨迹为曲线C.
(1)求曲线C的方程;
(2)若动直线l与曲线C交于
,
两点(其中
),点A关于x轴对称的点为A',且直线BA'经过点
.
(ⅰ)求证:直线l过定点;
(ⅱ)若
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ef1ff0b6addca3494d762c7602c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64b2a02270f4716fe1a5074fac1933c.png)
(1)求曲线C的方程;
(2)若动直线l与曲线C交于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddef7fc1094028667143de29690d9a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.png)
(ⅰ)求证:直线l过定点;
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e19ed32b8282e6f9eaf2fc08c4b366.png)
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解题方法
8 . 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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2024-05-23更新
|
664次组卷
|
2卷引用:江西省南昌市八一中学2024届高三下学期三模测试数学试题
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解题方法
9 . 已知方程
在
上有两个不相等的实数根,则实数m的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd3f360188fc8bea4ef0d31ebd0151e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
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10 . 如图,正方体
的棱长为2,设P是棱
的中点,Q是线段
上的动点(含端点),M是正方形
内(含边界)的动点,且
平面
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407eeb34204a1df967b8fbe481cb04d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98dbbf1a30ea54a46b903a9645debab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714ae984b13488d536f583f610e59945.png)
A.存在满足条件的点M,使![]() |
B.当点Q在线段![]() ![]() |
C.三棱锥![]() |
D.直线![]() ![]() ![]() |
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