名校
1 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb80ae52c549e41f9128006ddb56a15b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e60375f97ff7854f4d3a8b1108d2e3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:江苏省无锡市辅仁高级中学2024届高三下学期高考前适应性练习数学试题
2 . 已知无穷数列
中,
是以10为首项,以
为公差的等差数列,
是以
为首项,以
为公比的等比数列
,对一切正整数
,都有
.设数列
的前
项和为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74eb8a7738402df52d4a97262b85ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142876945177d2d9621b6842e3d51f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0af2dc59419e7a5e2d093c3d0d42a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c453d55bd2873e4469273132c421e7b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.当![]() ![]() | B.当![]() ![]() |
C.当![]() ![]() | D.不存在![]() ![]() |
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2卷引用:江苏省无锡市辅仁高级中学2024届高三下学期高考前适应性练习数学试题
3 . 定义1:若数列
满足①
,②
,则称
为“两点数列”;定义2:对于给定的数列
,若数列
满足①
,②
,则称
为
的“生成数列”.已知
为“两点数列”,
为
的“生成数列”.
(1)若
,求
的前
项和
;
(2)设
为常数列,
为等比数列,从充分性和必要性上判断
是
的什么条件;
(3)求
的最大值,并写出使得
取到最大值的
的一个通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7adb08bda4066fef731e23bf79f1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5674d0988e7b344263916b230b844e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adee3a6709875bf6fd41f16b5115b486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73933032b1598f4b10870291db9538d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68773e9560d4ecb08dac2d8163ead0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a5ca8276537bb6d7ae288eb5795a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a5ca8276537bb6d7ae288eb5795a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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3卷引用:江苏省无锡市辅仁高级中学2024届高三下学期高考前适应性练习数学试题
2024·全国·模拟预测
名校
解题方法
4 . 已知三棱柱
的侧棱垂直于底面,且
,
,
,
,若该三棱柱的各顶点都在同一球面上,则此球的表面积等于( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae8221601c7bd5c51fd520615581fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a456120c701a4f8b22cf2ce7eb51f1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
5 . 已知数列
的各项均为正数,
满足
,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d048849a2c08bcf87d80ab7c98a3ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2849e8da76332a6a0f4e3d6d68bf3b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10卷引用:江苏省无锡市辅仁高级中学2023届高三下学期高考前适应性练习数学试题
江苏省无锡市辅仁高级中学2023届高三下学期高考前适应性练习数学试题浙江省温州市2023届高三下学期5月第三次适应性考试(三模)数学试题(已下线)广东省深圳中学2024届高三下学期二轮三阶段测数学试题江西省南昌市新建区第二中学2024届高三上学期8月开学学业水平检测数学试题江苏省南京市金陵中学2023-2024学年高三上学期10月检测数学试题湖北省黄石市部分学校2023-2024学年高二上学期12月阶段性训练数学试题(已下线)专题10 数列小题(已下线)专题6.1 等差数列及其前n项和【九大题型】(已下线)FHgkyldyjsx19广东省广雅中学2024届高三下学期高考考前适应性考试数学试题
名校
解题方法
6 . 已知
均是锐角,设
的最大值为
,则
=( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2adfb5704758c5fcae425fab30fad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab3a9d16c81861321984655cee26ac6.png)
A.![]() | B.![]() | C.1 | D.![]() |
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4卷引用:江苏省无锡市辅仁高级中学2024届高三下学期高考前适应性练习数学试题
江苏省无锡市辅仁高级中学2024届高三下学期高考前适应性练习数学试题山西省部分学校2023-2024学年高三年级阶段性测试(定位)数学试题(已下线)【一题多解】同角关系 不朽传奇(已下线)压轴题03不等式压轴题13题型汇总 -1
7 . 已知函数
.
(1)求函数
的最小正周期和单调递增区间;
(2)在
中,内角
所对的边分别是
,且
,若
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba68e6a15b8fec4ae1418ad067b44a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)在
![](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/09a55650f8b6b243e3774ea5bb8dc9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6e1389b87a903f0cd149bf2bac4f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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3卷引用:江苏省无锡市江阴市第二中学2023届高三下学期5月模拟数学试题
8 . 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
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95816c45341eb35d6bb2d6ac744349b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)试确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.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/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00136ab4fd69ba9c28b47cd38442dc3a.png)
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6卷引用:江苏省无锡市天一中学2023届高三考前最后一模数学试题
江苏省无锡市天一中学2023届高三考前最后一模数学试题(已下线)2023年新课标全国Ⅰ卷数学真题变式题19-22上海市华东师范大学第三附属中学2022-2023学年高一下学期期末数学试题湖南省长沙市第一中学2022-2023学年高二下学期期末数学试题(已下线)专题07 数列-2(已下线)重难点突破01 数列的综合应用 (十三大题型)-2
名校
解题方法
9 . 若等差数列
前
项和为
,且
,
,数列
的前10项的和为______ .
![](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/6f01828ef9f7dec29057350e75a6fe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2fefbae840ade8ca814c0e310b06eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9cc5f5df852d9bb6a214aa04579c56c.png)
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名校
解题方法
10 . 在锐角
中,内角
的对边分别为
,
,
,且
,
,则( )
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f150935ed9bdffb5fefa8ee2444216.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:江苏省无锡市天一中学2023届高三考前最后一模数学试题
江苏省无锡市天一中学2023届高三考前最后一模数学试题(已下线)第四章 三角函数与解三角形 第六节 第二课时 正弦定理与余弦定理(二)陕西省西安高新第一中学2023-2024学年高一下学期第一次月考数学试题