名校
1 . 已知抛物线
的准线方程为
,焦点为
为抛物线上不同的三点,
成等差数列,且点
在
轴下方,若
,则直线
的方程为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65172437164e6d819b704ab28fa71c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb49231e548b2015d4199d96194e943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a432648c32cf1adc1f3156025dd6d49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
2016-12-04更新
|
1370次组卷
|
7卷引用:2016届河北省武邑中学高三下3.20周考文科数学试卷
解题方法
2 . 已知等比数列
的首项
,公比
,数列
前
项和记为
,前
项积记为
.
(1)证明:
;
(2)求
为何值时,
取得最大值;
(3)证明:若数列
中的任意相邻三项按从小到大排列,则总可以使其成等差数列;若所有这些等差数列的公差按从大到小的顺序依次记为
、
、
、
,则数列
为等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0a7a93f2c8c3527c9f9ccb55ee5d7ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb08ac8920645c616053c845978bdf1.png)
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63128fc7a6b65457980de79855180df6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(3)证明:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
您最近一年使用:0次
3 . 已知函数
,
(1)若a=1,试判断并用定义证明函数f(x)在[1,4]上的单调性;
(2)当
时,求函数f(x)的最大值的表达式M(a);
(3)是否存在实数a,使得f(x)=3有且仅有3个不等实根,且它们成等差数列,若存在,求出所有a的值,若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2015/2/5/1571982470914048/1571982476836864/STEM/dc73eb93c7964e82b5c611f3ae5170d1.png)
(1)若a=1,试判断并用定义证明函数f(x)在[1,4]上的单调性;
(2)当
![](https://img.xkw.com/dksih/QBM/2015/2/5/1571982470914048/1571982476836864/STEM/2aef6a7612a34a89a91cd7ecd72f3058.png)
(3)是否存在实数a,使得f(x)=3有且仅有3个不等实根,且它们成等差数列,若存在,求出所有a的值,若不存在,说明理由.
您最近一年使用:0次
13-14高三下·湖北黄冈·阶段练习
解题方法
4 . 抛物线
,直线
过抛物线
的焦点
,交
轴于点
.
![](https://img.xkw.com/dksih/QBM/2014/5/20/1571726671437824/1571726677393408/STEM/5323c8d974b3466b8c492ccceac1a9a6.png?resizew=242)
(1)求证:
;
(2)过
作抛物线
的切线,切点为
(异于原点),
(ⅰ)
,
,
是否恒成等差数列,请说明理由;
(ⅱ)
重心的轨迹是什么图形,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2014/5/20/1571726671437824/1571726677393408/STEM/5323c8d974b3466b8c492ccceac1a9a6.png?resizew=242)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0470c08f34bd48239b0c7a95dc9755ec.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(ⅰ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41e7650fc9f6005f51323324f74ca23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a284ce8c14b7b8192d7f9f68905bd02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255588378632caac0ad5229ff879e3db.png)
(ⅱ)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
您最近一年使用:0次
11-12高三·江苏无锡·阶段练习
解题方法
5 . 已知数列
,其前
项和为
,对任意
都有:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89afa9e6ebd3f9b7181c7a8fcdf59b41.png)
(1)求证:
是等比数列;
(2)若
构成等差数列,求实数
的值;
(3)求证:对任意大于1的实数
,
,
,
不能构成等差数列.
![](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/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89afa9e6ebd3f9b7181c7a8fcdf59b41.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e389c99d035fdedd476cf3c371509a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求证:对任意大于1的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6c1d854e8a338c9d5595ce35837138.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c154f135badb251d9680527f7e4cd2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4525fced01478716ab31bddf93166f.png)
您最近一年使用:0次
6 . 设等比数列
的首项为
,公比为
(
为正整数),且满足
是
与
的等差中项;数列
满足
(
).
(1)求数列
的通项公式;
(2)试确定
的值,使得数列
为等差数列;
(3)当
为等差数列时,对每个正整数
,在
与
之间插入
个2,得到一个新数列
. 设
是数列
的前
项和,试求满足
的所有正整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6fae41755ecb64ac239a5a2d767354.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d4dad2cc2f2ca8a60a86f11ce7cb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a650ebfa6fdf8a4b658fe8674693e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828d7f858879420ada468745fba68030.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(2)试确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217b927efe12a98e1082ecd7f035b921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c88a7ef007c78a93e33bd77c4396626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a9fa3fe6f0cb2c66dc7c864785368f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-02更新
|
1353次组卷
|
5卷引用:江苏省南京市第二十九中学2022-2023学年高三下学期4月月考数学试题
江苏省南京市第二十九中学2022-2023学年高三下学期4月月考数学试题(已下线)湖南省长沙市一中2010届高三第一次模拟考试理科数学试题(已下线)2014届江苏省灌云高级中学高三第一学期期中考试理科数学试卷(已下线)2014届江苏省灌云高级中学高三第一学期期中考试文科数学试卷上海市位育中学2021-2022学年高二上学期期末数学试题