名校
解题方法
1 . 数列
满足
则称数列
为下凸数列.
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
,其中
,
分别是公比为
,
的两个正项等比数列,且
,证明:
是下凸数列且不是等比数列;
(3)若正项下凸数列的前
项和为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0bee75d4d83c0b76421fd87113e4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)证明:任意一个正项等比数列均为下凸数列;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f67fc95a626251da11649acb5e1706f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c340d7d093dd4a275ffea4b87cd26827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755d7aa870e2f199d6c12264fc9be86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若正项下凸数列的前
![](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/0002f427eded1721f43d60dd0fd3ffe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd419dc0a6580ab97777b2cb8fd7cded.png)
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2024-06-12更新
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1149次组卷
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5卷引用:河南省鹤壁市高中2024届高三下学期高考适应性考试(二)数学试题
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2 . 已知函数
,其中e为自然对数的底数.
(1)若函数
在
上有2个极值点,求a的取值范围;
(2)设函数
,
),证明:
的所有零点之和大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ffabb66b55e415c2c864685fa5223d2.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef53a8a0375569abd516895e30fa350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddea382d8bece5514a9cbd6a225667e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
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名校
解题方法
3 . 甲、乙两个不透明的袋中各装有6个大小质地完全相同的球,其中甲袋中有3个红球、3个黄球,乙袋中有1个红球、5个黄球.
(1)若从两袋中各随机地取出1个球,求这2个球颜色相同的概率;
(2)若先从甲袋中随机地取出2个球放入乙袋中,再从乙袋中随机地取出2个球,记从乙袋中取出的红球个数为
,求
的分布列与期望.
(1)若从两袋中各随机地取出1个球,求这2个球颜色相同的概率;
(2)若先从甲袋中随机地取出2个球放入乙袋中,再从乙袋中随机地取出2个球,记从乙袋中取出的红球个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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2024-05-14更新
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831次组卷
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5卷引用:河南省鹤壁市高中2024届高三下学期高考适应性考试(二)数学试题
河南省鹤壁市高中2024届高三下学期高考适应性考试(二)数学试题2024届河南省新乡市高三第三次模拟考试数学试卷广东省江门市新会第一中学2024届高三下学期高考热身考试数学试题(已下线)专题04 随机变量及其分布类常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第二册)(已下线)核心考点6 离散型随机变量与分布列 B提升卷 (高二期末考试必考的10大核心考点)
名校
4 . 求适合下列条件的曲线的标准方程:
(1)焦点在
轴上,长轴长等于
,离心率等于
的椭圆标准方程;
(2)经过点
,并且对称轴都在坐标轴上的等轴双曲线的方程.
(1)焦点在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757f86c364eca9a6b15c9c9f516baf18.png)
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5 . 已知定义在R上的函数
满足
且
,
.
(1)求
的解析式;
(2)设
,若对任意的
,存在
,使得
,求实数m取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bb398270cd7329daacb2b398b9ced9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89bf799b3583871167114652404c2731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e111595ac59e1fb558b6a465a02829.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51524070a246dbab263a3121e9e51e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9624a4db0f489d1d75f29314915897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0db7eb2d7545d055f1cb6e8a7b5e1dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174426520dc1b3bbc366bca4deaa664.png)
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2023-12-10更新
|
305次组卷
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3卷引用:河南省鹤壁市高中2023-2024学年高一上学期第三次段考数学试题
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6 . 已知函数
,其中
.
(1)若存在
,使得
,求
的最小值;
(2)令
,若关于
的方程
有两个根
,求当
时,实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e349f49908801a73999320f7a49820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1937d83a1f8f6a980d407360e9e81efc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e522c7f5814c715334b01c532ef6de8a.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d480ff89c82f1e2c16526c2e41851b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2818807dce7e9ec5514de572c3cc644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03cfa6139f43d02631a50e42fc3b8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-09更新
|
250次组卷
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2卷引用:河南省鹤壁市高中2023-2024学年高一上学期第三次段考数学试题
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解题方法
7 . 已知集合
,
.
(1)求集合
;
(2)已知命题
:
,命题
:
,若
是
的充分不必要条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d4358315f066e761779a13dc85f03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39af6602d5c4a13f95e9ee17a0e1a88.png)
(1)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)已知命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-11-23更新
|
642次组卷
|
3卷引用:河南省鹤壁市高中2023-2024学年高一上学期第三次段考数学试题
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解题方法
8 . 已知数列
是公差为2的等差数列,它的前n项和为
,且以
,
,
为边长的三角形是直角三角形.
(1)求
的通项公式;
(2)求数列
的前n项和
.并证明:
.
![](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/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54fbf9c064d2259638f751e77686269.png)
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2023-09-26更新
|
218次组卷
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3卷引用:河南省鹤壁市外国语学校2024届高三上学期11月检测考试数学试题
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9 . 已知
为第二象限角,且
.
(1)化简
;
(2)若
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b442c723e66ce5c5b091491436a9af5.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d394016b9fecac73f38cbc4ff18dee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84c3a207bcced5750874ec3eec7c098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602487eb2d85eb721b409ce69c9b872e.png)
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2023-09-21更新
|
597次组卷
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2卷引用:河南省鹤壁市高中2023-2024学年高一上学期第三次段考数学试题
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解题方法
10 . 已知函数
是定义域为R的偶函数.
(1)求实数
的值;
(2)若对任意
,都有
成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322b4af34ce8d81a0c880216a9d5ccad.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f283f717d6ce3936cd46651293f924.png)
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2023-09-04更新
|
1002次组卷
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6卷引用:河南省鹤壁市高中2024届高三下学期高考适应性考试(二)数学试题