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1 . 若把第n个位置上的数记为
,则称
有限个有序放置的数为一个数列A.定义数列A的“伴生数列”B是:
,其中
是这个数列中第n个位置上的数
,2,3,
,k且
,并规定
,
.如果数列A只有四个数,且
依次为2,4,2,3,则其“伴生数列”B是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ae6558e11384a40f3a338b73385ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/262f1462719358f378982cbea31db65e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee7bb49247387a9028602315729f8d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4dce0247ca8aee11cdc8149baf6aabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de15039797b7480f81c32f0dd2d316ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdf726dbbd0c77ff86be13d02d8197e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
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解题方法
2 . (1)解方程
;
(2)对于函数
,若存在实数x0,使
成立,则称x0为
的固定点.
①当
时,求
的固定点;
②若对于任意实数b,函数
恒有两个不相同的固定点,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be8c43081ed7c4e647fb233aff87600.png)
(2)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcd4a9364f0c7c5e7c2b7de0493a02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb3e9800ad01d07578ee6cfa38620e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②若对于任意实数b,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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3 . 在平面直角坐标系
中,给出如下定义:对于点
,若点
坐标为
,则称点
为点
的“朋友点”.例如,点
的“朋友点”为点
.已知点
的坐标为
,点
的“朋友点”为点
,点
的“朋友点”为点
,点
的“朋友点”为点
,点
的“朋友点”为点
,则点
的坐标是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5e56e5b067c66d6b3e16ee4e934241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990eaf5dbba84f199bdc438da81fcfa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b104090ea2ac34be58a76a4e0e95cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df1d9b712b639c8b6809c9f3ae03706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349185b5825ece65b7b45d91003a5419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a40c26831b1ea4691c405ddffb3db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4dd0a24e4256bed5828b10a588b29e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4dd0a24e4256bed5828b10a588b29e6.png)
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解题方法
4 . 若一列不全为零的数除了第一个数和最后一个数外,每个数都等于与它相邻的前后两数之和,则称这列数具有“波动性质”.已知一列数共有2025个,第五个数为3,且具有“波动性质”,则这2025个数的和是__________ .
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5 . 如图,圆
的内接四边形
的顶点
关于
的对称点恰为
的内心
,
.则圆
的半径为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f01c4faacedfe56f5127d6c0cc63cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/2023/5/18/3240515094872064/3240976658817024/STEM/d5f71ea599f343f2bffcde925d57ec9e.png?resizew=127)
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6 . 已知二次函数
图象的顶点M在第二象限,且经过点A(1,0)和点B(0,1),与x轴的另一个交点为C.
(1)求实数
的取值范围;
(2)当△ABC面积等于
时,求△ABM的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当△ABC面积等于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
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7 . 若关于
的不等式
只有一个整数解2,则实数
的取值范围为 ____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06521f5d9b02a98fa97e0d11583c8cb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-02-15更新
|
613次组卷
|
4卷引用:安徽省宣城市泾县中学2020年强基夏令营选拔测试数学试题
安徽省宣城市泾县中学2020年强基夏令营选拔测试数学试题(已下线)第01讲 2.1等式性质与不等式性质-【帮课堂】(已下线)专题03 不等式与不等关系压轴题-【常考压轴题】【名校面对面】2023-2024学年高一上学期第一次月考数学试题
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8 . 直线
经过
,
两点,则不等式
的解集为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ea6b5f801158380a615c3f99f615e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c214fc7994f26613212cf71418d55bc5.png)
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9 . 若函数
中自变量x的取值范围为一切实数,则实数
的取值范围是______________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f229fcf8c50fd3bdbd7654e755177ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
10 . 已知二次函数
的值域为
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5415d0bfad22b6c55eaaf6e779e712a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b029e85e686623cdef977b2cb1f207a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d11970314471017a0e8b59255eaa0ba.png)
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2021-03-31更新
|
313次组卷
|
4卷引用:安徽省宣城市泾县中学2021年强基夏令营选拔测试数学试题