名校
解题方法
1 . 若
是定义在
上的增函数,其中
,存在函数
,
,且函数
图像上存在两点
,
图像上存在两点
,其中
两点横坐标相等,
两点横坐标相等,且
,则称
在
上可以对
进行“
型平行追逐”,即
是
在
上的“
型平行追逐函数”. 已知
是定义在
上的奇函数,
是定义在
上的偶函数.
(1)求满足
的
的值;
(2)设函数
,若不等式
对任意的
恒成立,求实数
的取值范围;
(3)若函数
是
在
上的“
型平行追逐函数”,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3df718662452f53034b6f702e46dcdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/958a7330503a10fecf9b6b6f4a30ea8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5ffb9d0b5dc940f53d7370419a08db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c33c52de7a2c9d148e44283eec3dbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdeb8cfadb41d94aaa1ba534aa040dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e257d683ceaca6c6c3ee5ada0e447b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d908675a3ce0661cf6b3d7823143d4b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(1)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb874a24bc2fa3d232070f16712aa05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86df4f1b31c51da3551a76606d553f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0bb6dbc79a74521af6338b0140b713b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86644d5b1157b35cf7b825f108d4c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
2 . 已知复数
的实部分别为
,虚部分别为
,其中
.
(1)求
的取值范围;
(2)
能否为纯虚数,若能,求
;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d860cb86e1467ac24010aecfc7a425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94794614e69f70a5a1daccbe0f25d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92923558626742c01a5c00f5e78673b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d1585d08f854e80e8172dd968cd21f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8b3f66119c2ce542984d12eb2b6b77.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da4e6752d8c8a0705194f2b2f16ab5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
您最近一年使用:0次
名校
解题方法
3 . (1)将向量运算式
化简为最简形式.
(2)已知
,且复数
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/062aada34504971d17391527cda76d6c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1497a47127503ee20141f3b37b01252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
4 . 某高一数学研究小组,在研究边长为1的正方形
某些问题时,发现可以在不作辅助线的情况下,用高中所学知识解决或验证下列有趣的现象.若
分别为边
上的动点,当
的周长为2时,
有最小值(图1)、
为定值(图2)、
到
的距离为定值(图3).请你分别解以上问题.
的最小值;
(2)如图2,证明:
为定值;
(3)如图3,证明:
到
的距离为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7473497fee0257402b6318033c1ef7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030314ca026d6b18481682f70f48d19b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)如图2,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030314ca026d6b18481682f70f48d19b.png)
(3)如图3,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2024-05-08更新
|
277次组卷
|
2卷引用:广东省广州市增城中学2023-2024学年高一下学期期中数学试题
名校
解题方法
5 . 对称轴都在坐标轴上的双曲线过点
,
,斜率为
的直线
过点
.
(1)求双曲线的标准方程;
(2)若直线
与双曲线有两个交点,求斜率
的取值范围;
(3)是否存在实数
使得直线
与双曲线交于A,B两点,且点P恰好为AB中点?为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3f986a4f053c576c8a58c7debc8829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b55968d5f6b29626b1303e3cfe3132f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd064fc631163ed5e461887aa53cf197.png)
(1)求双曲线的标准方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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6 . 有甲、乙两个不透明的罐子,甲罐有3个红球,2个黑球,球除颜色外大小完全相同.某人做摸球答题游戏.规则如下:每次答题前先从甲罐内随机摸出一球,然后答题.若答题正确,则将该球放入乙罐;若答题错误,则将该球放回甲罐.此人答对每一道题目的概率均为
.当甲罐内无球时,游戏停止.假设开始时乙罐无球.
(1)求此人三次答题后,乙罐内恰有红球、黑球各1个的概率;
(2)设第
次答题后游戏停止的概率为
.
①求
;
②
是否存在最大值?若存在,求出最大值;若不存在,试说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求此人三次答题后,乙罐内恰有红球、黑球各1个的概率;
(2)设第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8aca1d5e54fc609eeea858b9620d39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
您最近一年使用:0次
2024-04-08更新
|
1755次组卷
|
3卷引用:广东省惠州市惠东县2023-2024学年高二下学期5月期中数学试题
2024·全国·模拟预测
名校
7 . 某校为了解高三年级1200名学生对成语的掌握情况,举行了一次“成语测试”比赛.从中随机抽取120名学生,统计结果如下:获奖人数与不获奖人数之比为
,其中获奖人数中,女生占
,不获奖人数中,女生占
.
(1)现从这120名学生中随机抽取1名学生,求恰好是女生的概率;
(2)对获奖学生采用按性别分层随机抽样的方法选取8人,参加赛后经验交流活动.若从这8人中随机选取2人.
①求在2人中有女生入选的条件下,恰好选到1名男生和1名女生的概率;
②记
为入选的2人中的女生人数,求随机变量
的分布列及数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe103f073845122c66f22dcb14b711f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)现从这120名学生中随机抽取1名学生,求恰好是女生的概率;
(2)对获奖学生采用按性别分层随机抽样的方法选取8人,参加赛后经验交流活动.若从这8人中随机选取2人.
①求在2人中有女生入选的条件下,恰好选到1名男生和1名女生的概率;
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
2024-04-07更新
|
1168次组卷
|
4卷引用:广东省茂名市高州中学2023-2024学年高二下学期期中考试数学试题
名校
解题方法
8 . 设
是单位圆上不同的两个定点,点
为圆心,点
是单位圆上的动点,点
满足
(
为锐角)线段
交
于点
(不包括
),点
在射线
上运动且在圆外,过
作圆的两条切线
.
(1)求
的范围
(2)求
的最小值,
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/7818812e33052be4de712cbbbb21e2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8d5cf36f04941f4ad49fe4c5e26133.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8eb37a4dd75318dcbd836395e575bd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e438bc5acc5cc10b3e7138279949a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63a42e22f8bc63465f595caf10e5842.png)
您最近一年使用:0次
2024-04-01更新
|
840次组卷
|
4卷引用:广东省深圳市高级中学(集团)2023-2024学年高一下学期期中测试数学试题
名校
9 . 设
的所有可能取值为
,称
(
)为二维离散随机变量
的联合分布列,用表格表示为:
仿照条件概率的定义,有如下离散随机变量的条件分布列:定义
,对于固定的
,若
,则称
为给定
条件下的
条件分布列.
离散随机变量的条件分布的数学期望(若存在)定义如下:
.
(1)设二维离散随机变量
的联合分布列为
求给定
条件下的
条件分布列;
(2)设
为二维离散随机变量,且
存在,证明:
;
(3)某人被困在有三个门的迷宫里,第一个门通向离开迷宫的道,沿此道走30分钟可走出迷宫;第二个门通一条迷道,沿此迷道走50分钟又回到原处;第三个门通一条迷道,沿此迷道走70分钟也回到原处.假定此人总是等可能地在三个门中选择一个,试求他平均要用多少时间才能走出迷宫.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db95c4f9791ca04094be000bd6fc72e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef046c85a536174bec951a53d9f60b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0d5998482df4a2f66ac9e54c2a4dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f51736ae099adaa15ca47aa32ffa9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54260f9909300f9e72da4a7b14a5b40.png)
Y X | … | … | |||||
… | … | ||||||
… | … | ||||||
… | … | … | … | … | … | … | … |
… | … | ||||||
… | … | … | … | … | … | … | … |
… | … | ||||||
… | … | 1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49cc73ff3664ca80cfb518d272023d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a00892a44afbb626aabad4d9fc0b8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2279cab9c33270e284a26c51247273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dfe778b3e0bbd2220de99c382ec323b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
离散随机变量的条件分布的数学期望(若存在)定义如下:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f6b8d1f9426e6b710431b3a4e10638.png)
(1)设二维离散随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db95c4f9791ca04094be000bd6fc72e1.png)
Y X | 1 | 2 | 3 | |
1 | 0.1 | 0.3 | 0.2 | 0.6 |
2 | 0.05 | 0.2 | 0.15 | 0.4 |
0.15 | 0.5 | 0.35 | 1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ce9db5574a2df6184bdc7cd13b208a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db95c4f9791ca04094be000bd6fc72e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc79c66ebaacd709ec9965b90a22b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a507ed1895a2d0c93b01e994e36bb6e6.png)
(3)某人被困在有三个门的迷宫里,第一个门通向离开迷宫的道,沿此道走30分钟可走出迷宫;第二个门通一条迷道,沿此迷道走50分钟又回到原处;第三个门通一条迷道,沿此迷道走70分钟也回到原处.假定此人总是等可能地在三个门中选择一个,试求他平均要用多少时间才能走出迷宫.
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2024-03-29更新
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750次组卷
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4卷引用:广东省揭阳华侨高级中学2024届高三下学期第二次阶段(期中)考试数学试题
名校
10 . 已知函数
.
(1)证明:函数
有三个不同零点的必要条件是
;
(2)由代数基本定理,
次复系数多项式方程在复数域内有且只有
个根(重根按重数计算).
若
,证明:方程
至多有3个实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1571d19fbc9b6cd2d6367983eccf5036.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931659cbdc2fb03ff6afad699f75da4a.png)
(2)由代数基本定理,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9125e2bdcf01ce9995123cc540532e2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2c45d7141a1edb1c439e5c4f1cfc09.png)
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2024-03-29更新
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2卷引用:广东省揭阳华侨高级中学2024届高三下学期第二次阶段(期中)考试数学试题