名校
1 . 已知函数
.
(1)当
时,证明:
有且仅有一个零点.
(2)当
时,
恒成立,求a的取值范围.
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467fb8a741acbbae9548afdc186cd686.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f6313f09d17496008ebe3cc1fca0ca.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade0e43ca66880fa7a94c2121bfd0df2.png)
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1015次组卷
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4卷引用:内蒙古自治区呼伦贝尔市2024届高三下学期二模理科数学试题
名校
解题方法
2 . 设抛物线
的焦点为
,已知点
到圆
上一点的距离的最大值为6.
(1)求抛物线
的方程.
(2)设
是坐标原点,点
是抛物线
上异于点
的两点,直线
与
轴分别相交于
两点(异于点
),且
是线段
的中点,试判断直线
是否经过定点.若是,求出该定点坐标;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6b513530b5311e8d1d83d750aa1b44.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe1bdd134c4d6b45b9925e5b18b122f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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6卷引用:内蒙古自治区呼伦贝尔市2024届高三下学期二模理科数学试题
3 . 南宋数学家杨辉在《详解九章算法》和《算法通变本末》中,提出了一些新的垛积公式,所讨论的数列与一般等差数列不同,前后两项之差并不相等,但是逐项差数之差或者高次差相等.对这类高阶等差数列的研究·杨辉之后一般被称为“垛积术”.现有高阶等差数列前几项分别为1,4,8,14,23,36,54,则该数列的第21项为________ .
(注:
)
(注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ee4f17114ccb24847c7228ae17ba8c.png)
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名校
解题方法
4 . 已知椭圆C:
的离心率是
,点
在椭圆C上.
(1)求椭圆C的标准方程.
(2)直线l:
与椭圆C交于A,B两点,在y轴上是否存在点P(点
不与原点重合),使得直线PA,PB与x轴交点的横坐标之积的绝对值为定值?若存在,求出P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cac72ae550626c8583e4466b8b33d24.png)
(1)求椭圆C的标准方程.
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2023-02-19更新
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6卷引用:内蒙古海拉尔第一中学2023届高三5月高考模拟数学(理)试题
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77fb3b218a67bd1fc2d1883f4fba546.png)
(1)讨论函数
的单调性;
(2)若
,是否存在整数
,都有
恒成立,若存在求出实数m的最小值,若不存在说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77fb3b218a67bd1fc2d1883f4fba546.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ae00bc991ca62ee9f382e802b42ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390c478e54e90cc1a9b5a1c3f843bca1.png)
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9卷引用:内蒙古满洲里市第一中学2022-2023学年高三上学期第一次模拟考试试题理科数学试题
内蒙古满洲里市第一中学2022-2023学年高三上学期第一次模拟考试试题理科数学试题四川省雅安市2021-2022学年高二下学期期末数学(理)试题四川省雅安市2021-2022学年高二下学期期末数学(文)试题四川省甘孜藏族自治州2021-2022学年高二下学期期末数学(理)试题重庆市重庆十八中两江实验中学校2023届高三上学期第一次适应性强化训练数学试题江苏省镇江市句容碧桂园学校2022-2023学年高三上学期期初数学试题四川省宜宾市第六中学2022-2023学年高二下学期5月月考数学(文)试题四川省眉山市彭山区第一中学2022-2023学年高二下学期第一次月考(4月)理科数学试题(已下线)福建省百校联考2023-2024学年高三上学期期中考试数学试题
6 . 已知椭圆
的两个焦点分别为
和
,椭圆
上一点到
和
的距离之和为
,且椭圆
的离心率为
.
(1)求椭圆
的方程;
(2)过左焦点
的直线
交椭圆于
、
两点,线段
的中垂线交
轴于点
(不与
重合),是否存在实数
,使
恒成立?若存在,求出
的值;若不存在,请说出理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过左焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8617192cefc29b5889faa06a4bee3b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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5卷引用:内蒙古呼伦贝尔市海拉尔第二中学2022届高三下学期第四次模拟考试数学(理)试题
内蒙古呼伦贝尔市海拉尔第二中学2022届高三下学期第四次模拟考试数学(理)试题内蒙古呼伦贝尔市海拉尔第二中学2022届高三下学期第四次模拟考试数学(文)试题河南省信阳高级中学2022-2023学年高三上学期开学考试数学(文)试题(已下线)专题24 圆锥曲线中的存在性、探索性问题 微点1 圆锥曲线中的存在性问题四川省成都市石室中学2021-2022学年高二下学期零诊模拟练习文科数学试题
名校
7 . 在
中,角A,B,C的对边分别为
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4273b46ab9663b1fe7daeb2874f8e32.png)
(1)当
,求
的值
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4273b46ab9663b1fe7daeb2874f8e32.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe7a93172d308a58200e3c722fe1072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed31db39e8125dbd38816f4f75f5d8f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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5卷引用:内蒙古呼伦贝尔市海拉尔第二中学2022届高三下学期第四次模拟考试数学(理)试题
名校
解题方法
8 . 已知函数
,若对任意实数
,不等式
总成立,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c132743eeffa79d59055058540303d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d6c3c9afddb6dd9e52087da94d00cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:内蒙古呼伦贝尔市海拉尔第二中学2022届高三下学期第四次模拟考试数学(理)试题
解题方法
9 . 已知函数
.
(1)当
时,求函数
的单调区间;
(2)若不等式
对于任意
成立,求正实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3636562730381f92ba1cbe2a06a027d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4220a46a29faa98377e29d579572b6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d94276919e84ac7ebdb0c3a7284120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2卷引用:内蒙古呼伦贝尔市部分校2022届高考模拟数学(理)试题
解题方法
10 . 已知
为椭圆
的下顶点,
,
分别为
的左,右焦点,已知
的短轴长为
,且
=
.
(1)求
的方程![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)设
为坐标原点,
,
为
上
轴同侧的两动点,两条不重合的直线
,
关于直线
对称,直线
与
轴交于点
,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae13b2a96f91ab64fb4948de2b0ae10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804c767ba8ba0ac1fc157fc345cea965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ec50574737a875dfaf7bf2141dda9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e051d14fd6a787387995331f5e6d026.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a50372516f22d51a364482ecb1a24f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9f732048c080db0255e033aa4eb6fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589a4d5f5fb135a3144644595774b896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7f8c63b08903f9d869c162e153998ad.png)
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