名校
1 . 如图,在直三棱柱
中,
,
,
,
.
时,求证:
平面
;
(2)设二面角
的大小为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42da806a6bd2472459f6c4ad1dab7b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b360c98bd3fd209525fd8fece4246590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
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3卷引用:福建省漳州市龙文区2024届高三6月模拟预测数学试题
名校
2 . 若函数
是
上的偶函数,
是
上的奇函数,且满足
.
(1)求
,
的解析式;
(2)令
,证明函数
有且只有
个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ea1f7cd5fd2d33bc2ff7e1866bfb1c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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5卷引用:福建省八县(市)一中2020-2021学年高二下学期期末联考数学试题
福建省八县(市)一中2020-2021学年高二下学期期末联考数学试题福建省永泰县第一中学2020-2021学年高二下学期期末数学试题重庆市清华中学2022届高三上学期7月月考数学试题(已下线)专题07函数期末8种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(人教B版2019)(已下线)专题09 导数与零点、不等式综合常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
解题方法
3 . 已知
的三个内角A,B,C的对边分别为a,b,c,且
.
(1)求证:
为等腰三角形;
(2)若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e65f3ca149022d8a0ee5f70e9fa776.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35639227440e8dc58074332230523d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
4 . 某高校为了提升学校餐厅的服务水平,组织4000名师生对学校餐厅满意度进行评分调查,按照分层抽样方法,抽取200位师生的评分(满分100分)作为样本,绘制如图所示的频率分布直方图,并将分数从低到高分为四个等级:
(2)设在样本中,学生、教师的人数分别为m,
,记所有学生的评分为
,
,…,
,其平均数为
,方差为
,所有教师的评分为
,
,…,
,其平均数为
,方差为
,总样本的平均数为
,方差为
,若
,
,求m的最小值.
满意度评分 | ||||
满意度等级 | 不满意 | 基本满意 | 满意 | 非常满意 |
(2)设在样本中,学生、教师的人数分别为m,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f484692e20c48d072680c1355b821c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad7f66c97bfce4c00c53d86700c961b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a63cadbf6b0d54955a3c3d1b7a62b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d80da4a6cb5f102be334006d875a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9289410bd35c9d57326b93cc7f4c4767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a46d3e5d140624c95403eed7a42a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ec853e7338e9329e76a11b73106f08.png)
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5 . 已知双曲线
,点
在
上,
为常数,
.按照如下方式依次构造点
:过
作斜率为
的直线与
的左支交于点
,令
为
关于
轴的对称点,记
的坐标为
.
(1)若
,求
;
(2)证明:数列
是公比为
的等比数列;
(3)设
为
的面积,证明:对任意正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a3771d89c653798f5164c8dcfc94137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7680911a1cc664a88db0a4260c4849c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffbb4e6b92463a41bd9460dac6b1ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85def4eebc99aecdc878cd7c4180b8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb90a2118db1e9945d7b5997bf2482a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6192139c2fa8ac2dcf92c777c93b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6192139c2fa8ac2dcf92c777c93b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c66751ff7fe93ebc69986088141e8c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a2a34b4317deffa40ba34e269c2b81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c788875fe76212a7c59d0a9cee345d7.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f33eb7bcdb380fa633771537843b525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968a2a65734098f665e104786ec7a990.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f14afef14d8198491b9c43b1b5a0192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b306ea5e1ebbb1c2ec9450b3aedb74.png)
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7卷引用:福建省泉州市安溪铭选中学2023-2024学年高二下学期6月份质量检测数学试题
福建省泉州市安溪铭选中学2023-2024学年高二下学期6月份质量检测数学试题2024年新课标全国Ⅱ卷数学真题(已下线)2024年高考数学真题完全解读(新高考Ⅱ卷)专题08平面解析几何(已下线)2024年新课标全国Ⅱ卷数学真题变式题16-19专题08[2837] 平面解析几何(已下线)平面解析几何-综合测试卷B卷
6 . 已知函数
且
.
(1)求实数a的值;
(2)若函数
在
上恰有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd535030ec92efe0b1a86a33b7306aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008925a3b60d366297f31efa54aa38c9.png)
(1)求实数a的值;
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5b9f57d3634f8337f1414f8a2a2dc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
7 . 二次函数
满足
,且
.
(1)求
的解析式;
(2)若
时,
的图象恒在
图象的上方,试确定实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42b6975b22e99c0148e6952d174ebba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17ee5f43412795671704ab0e8d0b2f5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6070f2ee5e48cce77eb4a2cb9f11ccfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a0ac4bfe4ded00b4400f913e0c9862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-06-14更新
|
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|
3卷引用:福建省龙岩市上杭县第一中学2024年6月普通高中学业水平合格性考试数学模拟卷
名校
8 . 根据历史数据,某种机床生产产品的一项指标遵循某种规律.现从该种机床生产的一批产品中随机抽取六件检测该指标,所得数据为20.3,20.2,19.9,20.1,a,19.6.
(1)若该组数据的平均数恰好为20,求a的值;
(2)在(1)的条件下,求该组数据的方差.(计算结果保留到0.001)
(1)若该组数据的平均数恰好为20,求a的值;
(2)在(1)的条件下,求该组数据的方差.(计算结果保留到0.001)
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2卷引用:福建省安溪铭选中学2023-2024学年高一下学期6月份质量检测数学试题
9 . 已知数列
中,
,
.
(1)证明:数列
为常数列;
(2)求数列
的前2024项和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e21735689ef7272d918da315cdb5c8a.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1e7b49d90dc3ec036367ae7567dce0.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
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解题方法
10 . 如图,正方体
的棱长为2,E为
的中点.
的体积;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b565e518d475a50358fedff2f0bb8dec.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb8c3e6d8e2843a2783a409e130bc0a.png)
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