1 . 当
为何值时,不等式
恰有一个解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/399e7902cf319a4ecc40aebda074eda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e17a1c30f62f3dce43df74c310679a5.png)
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解题方法
2 . 设数列
的前
项和为
,对一切
,点
在函数
的图象上.
(1)求
的表达式;
(2)设
为数列
的前
项积,是否存在实数
,使得不等式
对一切
都成立?若存在,求出
的取值范围;若不存在,请说明理由;
(3)将数列
依次按1项、2项循环地分为
,分别计算各个括号内各数之和,设由这些和按原来括号的前后顺序构成的数列为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41f32693d25ece7f8e22c34a183537f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f762c96e3ac6d45248ff06ebd7a6e0d8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09953c3d3c8bb8566bb740c3a7d53e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8f5cff3bc3f6b86f68837d11106fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)将数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830e6579d84bd90321c7a87ba078f41e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c50b5f75c050e3b40f1e35fdc114e.png)
您最近一年使用:0次
2024-03-23更新
|
112次组卷
|
2卷引用:第六届高一试题(初赛)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
解题方法
3 . 设函数为
上的增函数,令
.
(1)判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5226c58ca852742dca2b380d1fd4042e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a4d51c0394ade8f125957afaa6e994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93e1aa555d1670dfed9c8861bed364d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
解题方法
4 . 已知
是不相等的正数,在
之间分别插入
个正数
和正数
,使
是等差数列,
是等比数列.
(1)若
求
的值;
(2)若
,如果存在
使得
,求
的最小值及此时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0deee56cdb3d71a61f33763d350845a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344cf4e3f76485610c06ecac578fcaa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52dd8d016bbb44d79ad41822313ae55.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59aaf088da5730d295f6aae8bf605ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e0e9e80b4ddc64a82434aa4828866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71942c9560b5789c8558f43d240b8470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca4ae8dc0a6859759d16555a7ed9c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
5 .
的整数部分是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f61f4f195149d7ff7eb304649c67a8.png)
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6 . 正实数
成等差数列,对
,
,已知方程
有两个相等的实根,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636995f2a3d0002f8770cf3c4b6fb466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0d90384477629ddc37da42903d72eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dea25a60975362c07560fecbd21a12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f9f27d26082d9c8f3f845e9aa87997.png)
您最近一年使用:0次
7 . 已知函数
,其中
,
为实数且
.
(1)当
时,根据定义证明
在
单调递增;
(2)求集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9021fa0cc7427f534fbf1ec1db79c4b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0070f5fd205c3c48a41bd865a7049b.png)
(2)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac3810dfe2b1eb718bae23bf0bab35e.png)
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8 . 将正整数集
中划掉所有与15不互素的数,记剩下的数由小到大排成数列
,再按照两项,一项,两项,一项,两项的顺序循环分组(5组为一个周期):
,那么2014在第( )组.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08bdede3aec46b55cb1ace4dfb8ec95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecf01c82540b89950db49f8f6324113.png)
A.672 | B.679 | C.680 | D.681 |
您最近一年使用:0次
9 . 定义:(i)
表示x的最小值;(ii)
表示不超过x的最大整数.设a,b,c为正数,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de36f09136a15d9f9ed3b0793d79860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c179da37f00a4188877d6a803fae508.png)
A.0 | B.2 | C.3 | D.4 |
您最近一年使用:0次
10 . 如图1,在平面直角坐标系中,直线
与直线
相交于点
,点A是直线
上的动点,过点A作
于点
,点
的坐标为
,连接
.设点A的纵坐标为
的面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://img.xkw.com/dksih/QBM/2023/12/14/3388901252603904/3389081626116096/STEM/db4cbdc765054195a84bec305037bfea.png?resizew=334)
(1)当
时,请直接写出点
的坐标;
(2)
关于
的函数解析式为
,其图象如图2所示,结合图1、2的信息,求出
与
的值;
(3)在
上是否存在点A,使得
是直角三角形?若存在,请求出此时点A的坐标和
的面积;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbb51096f4d54ad3cc2aa72a26151904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9f9375b79d1c2591bef9c147a9c441.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/fbd2d246f0850db73fe2e6b1e26eb549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e705301752424a492f6277ed7774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3c8c0d7a9eebcf92e49659a58a0a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://img.xkw.com/dksih/QBM/2023/12/14/3388901252603904/3389081626116096/STEM/db4cbdc765054195a84bec305037bfea.png?resizew=334)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486d75d269000f65978a4922abdd53f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次