名校
解题方法
1 . 已知球
的表面积为
,正四棱锥
的所有顶点都在球
的球面上,则该正四棱锥
体积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9c176877b59cd7c34fcc0838b05493.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2024-01-15更新
|
1612次组卷
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6卷引用:云南省昆明市2024届高三“三诊一模”摸底诊断测试数学试题
云南省昆明市2024届高三“三诊一模”摸底诊断测试数学试题广东省广州市第六中学2024届高三第三次调研数学试题2024年普通高等学校招生全国统一考试数学模拟试题(一)(新高考九省联考题型)(已下线)云南省昆明市2024届高三“三诊一模”摸底诊断测试数学试题变式题11-16四川省绵阳市三台中学校2024届高三下学期三诊模拟数学(文)试题四川省雅安市神州天立学校2024届高三高考适应性考试(三)数学(文)试题
2 . 布劳威尔不动点定理是拓扑学里一个非常重要的不动点定理,它得名于荷兰数学家鲁伊兹·布劳威尔,简单地讲就是对于满足一定条件的连续函数
,存在点
,使得
,那么我们称该函数为“不动点”函数,而称
为该函数的一个不动点.现新定义:若
满足
,则称
为
的次不动点.
(1)求函数
的次不动点;
(2)若函数
在
上仅有一个不动点和一个次不动点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f4a89a3721dd8a4327af943f864262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9579ecce76691f7459198e8a69c0d13.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e00828f4891d233cb20a7329d2151f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8065c840ec2313396be36ed5c72c7c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-01-15更新
|
301次组卷
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2卷引用:云南省大理白族自治州2023-2024学年高一上学期期末数学试题
名校
3 . 已知函数
.
(1)若直线
与函数
的图象有且仅有4个交点,求实数
的取值范围;
(2)求函数
在区间
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e8114098c4a57deda4ec7d6d5a3aff.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431a9833f292cec2b85ebe93a3ced3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ec9d0f2e9d84337d0a5b7f90b9d184.png)
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名校
4 . 已知函数
,
,
.
(1)若
,使得方程
有解,求实数
的取值范围;
(2)若对任意的
,总存在
,使得
,求实数
的取值范围;
(3)设
,记
为函数
在
上的最大值,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7215124081342ba1d78c39b2c98d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56dcd5cbb109fd4cc909e7c41c9eefc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7260f35c0268062fb981e3d363e7dd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397ad4c2323b5707c72ef766c3803af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7292952acdfc807cf6668bc94b3e1a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da748bc6ad3b7a207db7a81858f4998a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e8dc00cdc96860c9cbf8ac09677fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2f83ba773b9501bc15b3666727ac67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a239d924a26dbc7f33052c63a20a327a.png)
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2024-01-14更新
|
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2卷引用:云南省昆明市云南师大附中2023-2024学年高一上学期教学测评期末数学试题
名校
5 . 设函数
,若
,且
,则
的值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ccae48b3fb42b5c9ac42dfc5b9d1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2714f1eb0e74a1a31fa2c35275d368e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd33cb49fbf42fc943fca109a629c016.png)
A.4 | B.5 | C.![]() | D.6 |
您最近一年使用:0次
2024-01-14更新
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2卷引用:云南省昆明市云南师大附中2023-2024学年高一上学期教学测评期末数学试题
6 . 设函数
,已知
在
单调递增,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2bb7354fb64b7bf5ae232a93747955.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff8872f9dff36b373313ebae391728b.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
7 . 已知抛物线
上的点
到焦点的距离为8,点
到
轴的距离为
.
(1)求抛物线的方程;
(2)取抛物线上一点
,过点
作两条斜率分别为
的直线与抛物线交于
两点,且
,则直线
是否经过一个定点?若经过定点,求出该点坐标,否则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8b928c60de1b77c0588a2503a7c565.png)
(1)求抛物线的方程;
(2)取抛物线上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/594d4b99d4c5c90fc2e8010cc198551d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a690a05dc243e3c6736a6de514106ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-01-12更新
|
873次组卷
|
3卷引用:云南省昆明市官渡区2023-2024学年高二上学期1月期末学业水平考试数学试题
名校
解题方法
8 . 任取一个正整数,若是奇数,就将该数乘3再加上1;若是偶数,就将该数除以2.反复进行上述两种运算,经过有限次步骤后,必进入循环圈
.这就是数学史上著名的“冰雹猜想”(又称“角谷猜想”).如取正整数
,根据上述运算法则得出
,共需经过8个步骤变成1(简称为8步“雹程”).现给出冰雹猜想的递推关系如下:已知数列
满足:
(
为正整数),
当
时,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a16f78ce0dab1ac8fa6abbd70f2b008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3967d620e2fef3ecc724c66e29f68a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73700b5135fc6a9c2d923a27a4c9b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999ac8c1ef39251e07a7fc54cbf7e26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4914df4e75585d5ff7709d64a23611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59097ad7c8f3fcff871ad48933d30498.png)
A.170 | B.168 | C.130 | D.172 |
您最近一年使用:0次
2024-01-12更新
|
920次组卷
|
4卷引用:云南省昆明市官渡区2023-2024学年高二上学期1月期末学业水平考试数学试题
解题方法
9 . 过抛物线
的焦点
的一条直线交抛物线于
两点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
A.![]() |
B.存在直线![]() ![]() ![]() |
C.若经过点![]() ![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
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2卷引用:云南省昆明市官渡区2023-2024学年高二上学期1月期末学业水平考试数学试题
解题方法
10 . 如图,已知在四棱锥
中,底面
是菱形,且
底面
分别是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/c50d0e4d-967b-4eb0-a037-45b168b9d224.png?resizew=178)
(1)求平面
与平面
所成二面角的余弦值;
(2)求平面
截四棱锥
所得的截面与
交于点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a6d262ba028e0b1c597154fa34ecd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b1722cac6830f571c71fd809b3b433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f805fba552962d3389267f0ddf7fcf87.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/25/c50d0e4d-967b-4eb0-a037-45b168b9d224.png?resizew=178)
(1)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd66687a8c0d2d00ba430b040e9f647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/8bc953f0be1dafec1b4d1836cbafbf59.png)
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