名校
1 . 设复数
为虚数单位,
.
(1)若
,且
,试确定虚数q的值,使得
,并计算
的值;
(2)若数列
是各项均为正数的等比数列,
,
,
,求
的值;
(3)若
,且
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a036e9ee70ced65188b33599f9c5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22214f48085c06e62521bf96c27191b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a58dcdbc4ba66c058b9c2ea0b66c78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cf89ab7d054f735048e3f2de3790952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e958699ed7f4ec14624af584b08869c.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a19c1b64ab0b0ddcf2392cdc57b3772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0dd3fb6af23def773e1b0032a4f3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d308b3a2305c0a30cd95d08e6b039986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621c88d8efebb14c021243cf153046bb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4638a75e65012bebf3684a34212a2ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93fb330f2c2ee620c57204e75f439e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900298ea19e2fd2d1c99e9744484b0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4914cce8e01442532dbcee3564708e85.png)
您最近一年使用:0次
名校
2 . 已知向量
,
,函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740710b92f3f3af8f447d1a12799ef81.png)
(1)求函数
的解析式和对称轴方程;
(2)若a,b,c分别为
三个内角A,B,C的对边,
,
,
,试判断这个三角形解的个数,并说明理由;
(3)若
时,关于x的方程
恰有三个不同的实根
,
,
,求实数
的取值范围及
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a26d7f318b199dd3b4ff8f1880ae122.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa763cf9e70b74a8505418aa944c782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/740710b92f3f3af8f447d1a12799ef81.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若a,b,c分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3c28e2fc237e76e757b8a82c619802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10cf0c037dc56bdd6814bd49bea77ca.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e703cfbd69ddc733b2643a6788072b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63fd76169a859bddc4f953358f70fc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b968823edce2368203562f6ac28f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35bacde908aec2c313978fc4309d82bc.png)
您最近一年使用:0次
2022-05-09更新
|
3610次组卷
|
7卷引用:上海市闵行中学2021-2022学年高一下学期5月月考数学试题
名校
解题方法
3 . 若
是
外接圆圆心,
是
的内角,若
,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60d289f9ca42a1c9437c8a29cd42ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cee1cf625d78bef2f80ef4a38f8d9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
4 . 已知函数
的最小正周期为
,且直线
是其图象的一条对称轴.将函数
的图象向右平移
个单位,再将所得的图象上每一点的纵坐标不变,横坐标变为原来的2倍所得的图象对应函数记作
,令函数
.
(1)求函数
的函数解析式;
(2)求函数
的最大值及相对应的
的值;
(3)若函数
在
内恰有2021个零点,其中常数
,
,求常数
与
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7501daded8b96ec174db11901ab903dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c366dcd7fdd83db8578a19499ffed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb336259c817f029b1a46b849be56a87.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb336259c817f029b1a46b849be56a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0b396c8cd1754fb25acce89a06d280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde96e6275b050dcde76403356d0eda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
5 . 如图所示:点
是
所在平面上一点,并且满足
,已知
.
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966484403830784/2968055034716160/STEM/026d9dd8-8802-492b-8527-ae6e631cc22a.png?resizew=96)
(1)若实数
,求证:
是
的重心;
(2)若
是
的外心,求
的值;
(3)如果
是
的平分线上某点,则当
达到最小值时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17af6a9b4cccc1270e4f76d1bd26801a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25fb4275fdf9c823c1169bd804fc1e6d.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966484403830784/2968055034716160/STEM/026d9dd8-8802-492b-8527-ae6e631cc22a.png?resizew=96)
(1)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77eaab695f740ba2b7396c083e340f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a959d24343ceaf3f6a954df71e51bd6d.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcba53f5ec39e5315c2db3ea2a7fbae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/949bad47ce0b2ccd8c63323a8eb12cbf.png)
您最近一年使用:0次
名校
6 . 非零向量
满足
,则
的最小值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96022a881e03e32d3483d997c3f170c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54398513aaa38d9e85b678a255dbefa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3f1671f7b5595953d53759e3964d6c.png)
您最近一年使用:0次
7 . 已知函数
, 若存在实数
, 使得对于定义域内的任意实数
,均有
成立, 则称函数
为 “可平衡” 函数, 有序数对
称为函数
的 “平衡” 数对;
(1)若
, 求函数
的 “平衡” 数对;
(2)若
, 判断
是否为 “可平衡” 函数, 并说明理由;
(3)若
, 且
均为函数
的 “平衡” 数对, 求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40d5295942e85ec07a3728c7ad308d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b35c9f4a622bfa1c0ac47e3e4743070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c996b4493eeffa33e4606dc8457c0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed8f7e2a6d5a7c94c41687c21afb48c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560e9ae1410234c91e018b932684d3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc304a55feec5d8312d3082f1bb91a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294fe9f85ca15496f9e63b2a8ece70ee.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b719f5d8298f9686861a1c7aaac005b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2cfbf73de206ae31160923e52efa653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f037d9cba880bcafab3283b2a3e9865c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0e414b032d05f06c58ae6e95874d10.png)
您最近一年使用:0次
名校
8 . 在
中,若
,则此三角形为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2dc5998f96f216d85a525d6eb747c5e.png)
A.等腰三角形 | B.直角三角形 |
C.等腰直角三角形 | D.等腰或直角三角形 |
您最近一年使用:0次
2022-04-28更新
|
462次组卷
|
5卷引用:上海市奉贤区致远高级中学2021-2022学年高一下学期期中在线教学评估数学试题
上海市奉贤区致远高级中学2021-2022学年高一下学期期中在线教学评估数学试题甘肃省兰州市第二十四中学2022-2023学年高一下学期期中数学试题(已下线)第10章 三角恒等变换 章末检测卷-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)第8章:向量的数量积与三角恒等变换章末重点题型复习(2)-【帮课堂】(人教B版2019必修第三册)江苏省徐州市第三中学2023-2024学年高一下学期3月月考数学试题
名校
解题方法
9 . 已知O是四边形ABCD所在平面上一点,并且这五点,任意三点不共线,若存在一组正实数
、
、
、
使得
,则关于这四个角
、
、
、
的判断,一定正确的是______ .
①一定存在钝角 ②可能有两个钝角 ③可能四个角都是钝角 ④可能没有钝角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7345f310975ddb40dca94b5135c35dad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061baa765d2939a416300de14c45b8ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf97cb5e2fa09745dbb21b9bcfe9e6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9a08cf5fee968d97f92555b8bd61ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed66570f697459aba9daa2eaf9460bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f51d0f39a59c3b7d6d8422c802fee1.png)
①一定存在钝角 ②可能有两个钝角 ③可能四个角都是钝角 ④可能没有钝角
您最近一年使用:0次
名校
解题方法
10 . 著名数学家欧拉提出了如下定理:三角形的外心、重心、垂心依次位于同一直线上,且重心到外心的距离是重心到垂心距离的一半,此直线被称为三角形的欧拉线,该定理被称为欧拉线定理.已知
的外心为O,重心为G,垂心为H,M为BC中点,且
,
,则下列各式正确的有______ .
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d13a088bc184bfefd8414284501aec4.png)
③
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4139319479a982d1a34187d00b0ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d13a088bc184bfefd8414284501aec4.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef5de81202c50e6a5f52b955af24722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f0c94583a65e896b2b246a4cd7c5c9e.png)
您最近一年使用:0次
2022-04-26更新
|
677次组卷
|
3卷引用:上海交通大学附属中学2021-2022学年高一下学期线上教学反馈数学试题