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1 . 已知命题:“
,使等式
成立”是真命题.
(1)求实数
的取值集合
;
(2)设不等式
的解集为
,若
是
的必要条件,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4ea13e43d05596446bcbf52a53031d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14c27da343aac13ea6dc870863b0bac.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c9379cd1f92f83da21bee1bdc3c676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca06304795e9c2c1fd0b4a52eb8d5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 如图,在四棱锥
中,
,
平面
分别为
的中点,
.
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f089b54ee14e369cf48b528477a64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bf40f6235d0231481c2598e2ba977b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb46aaae98bce8e66848e09c2c1cdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801cabc43c024b9c5fac34b7db5d69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5617a404c5a3356753136e5a6b6d51e5.png)
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解题方法
3 .
的内角
的对边分别为
,满足
.
(1)求
;
(2)
的角平分线与
交于点
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008a9e8912d20e215500cd5a2a2e3a73.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e14d71667c64ab37596ff76207c7a82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451be539a00c5a0fa9e00fc9bf4c39fd.png)
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4 . 设两个向量
满足
.
(1)若
,求
与
的夹角
;
(2)若
的夹角为(1)中的
,向量
与
的夹角为锐角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b904ee9b19e35b3fef137fb02a654f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d062b28cf7f9dbbba15c2d7769b98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12dfa2b2e9488107d07fdac71f433774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d7ba9c5074d45752fb01ade0f441d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bd9536fa068918321bc80abad38f7c.png)
(1)当
时,求函数
的最小值;
(2)
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bd9536fa068918321bc80abad38f7c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e81b4aac721bcd4a49593b48a28a8f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
6 . 已知数列
的前n项和为
,
,
,
.
(1)求数列
和
的通项公式;
(2)记数列
的前n项和为
,若
对任意
都成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65c44af8125cfd1e8c9a6d2985bcee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4aede2d0a9e7eb471b709438d11d4a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83de9a45d9b680da8835bac1fee9c9b.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bde034b0bb6767f923526db8a387c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b8a237d8f9dc2d57db4e8bea895796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
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7日内更新
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332次组卷
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3卷引用:贵州省铜仁市2023-2024学年高二下学期5月联考数学试题
贵州省铜仁市2023-2024学年高二下学期5月联考数学试题内蒙古自治区兴安盟2023-2024学年高二下学期学业水平质量检测数学试题(已下线)专题07 数列通项公式与数列求和--高二期末考点大串讲(人教B版2019选择性必修第三册)
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7 . 已知函数
在
上单调.
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12127664a2b33675602275cfce075879.png)
①写出
的一个对称中心;
②求
的值.
(2)若
在
上恰有3个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321d7c14d11ad1d72fe704b93cbe878e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ec440191e19ee3902e555c4816096a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12127664a2b33675602275cfce075879.png)
①写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57d02269f97ea73ebe6a9d756d3450a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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解题方法
8 . 某中学举行了一场诗词竞赛,组委会在赛后抽取了部分参赛选手的成绩(百分制)作为样本进行统计(每组为左闭、右开的区间),作出了图1的频率分布直方图和图2的茎叶图(中间三行污损,看不清数据).
(2)分数在
的参赛选手中,男生有3人,现从该组抽取3人“座谈”.请选择合适的表示方法写出样本空间,并求至少有1名女生的概率.
(2)分数在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328fcb58a789bd05648864910ede4d36.png)
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解题方法
9 . 在
中,内角A,B,C的对边分别为a,b,c,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba19f9dbd8a0a559a6844c54a2ae6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求C;
(2)若
,求
周长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba19f9dbd8a0a559a6844c54a2ae6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求C;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
10 . 当今社会面临职业选择时,越来越多的青年人选择通过创业、创新的方式实现人生价值.小明是一名刚毕业的大学生,通过直播带货的方式售卖自己家乡的特产,下面是他近5个月的家乡特产收入y(单位:万元)的情况,如表所示.
(1)根据5月至9月的数据,求y与t之间的样本相关系数(精确到0.001),并判断相关性;
(2)求出y关于t的经验回归方程(结果中
保留两位小数),并预测10月收入能否突破1.5万元,请说明理由.
附:样本相关系数
.一组数据
其经验回归方程
的斜率和截距的最小二乘估计公式分别为
,
.
,
,
,
.
月份 | 5 | 6 | 7 | 8 | 9 |
时间代号t | 1 | 2 | 3 | 4 | 5 |
家乡特产收入y | 3 | 2.4 | 2.2 | 2 | 1.8 |
(2)求出y关于t的经验回归方程(结果中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc5505526d11946ca7d3a4421a9e08f.png)
附:样本相关系数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bbf28285862b22bbaaca459f97d016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5c72368931a68474ffa15f956f252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa43a4f8ef0ba36500733936da24b8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22795ad9b6d308bb1449b8478c17c793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1563296b0804d4255b078bc223a1b7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939b286af0e5bd7595e27cf8812f971e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da02f185fd8229677fca5b6df7521ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab88c7f31aa09e4b09361d0f54eba7e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9828417417bb4cc4e0b5d58309748d8.png)
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