解题方法
1 . 已知函数
,
,且有
,若关于
的方程
有8个相异实根,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fcf6b8e8c8c88295a6063a83c751d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24fc566eecaf9d74d0b5a32ec62400bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2855b7a6af3f75a8a2a3270e55cf3259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a644a520b56352a738309ee8592021d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2 . 已知
,若对任意的
,不等式
恒成立,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c66d815378b39ae395dd50173c684bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663bd8e0ed39cbe5dc8b5b7cdf7281f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:广东省汕头市潮阳实验学校2024届高三上学期第四次阶段测试数学试题
3 . 已知函数
,
,
.
(1)若
,函数
存在斜率为3的切线,求实数
的取值范围;
(2)若
,试讨论函数
的单调性;
(3)若
,设函数
的图象
与函数
的图象
交于两点
,过线段
的中点
作
轴的垂线分别交
于点
,问是否存在点
,使
在
处的切线与
在
处的切线平行?若存在,求出点
的横坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6263576e5c3f2324a8dac311476bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc15277c34c6247a76f88ff286cc62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/935b4035585dfe624ebdd0c758c6ea89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/880248fa1259b2600a87f09a61287d44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a51949f48ee8cf746851ba779b078e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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解题方法
4 . 某人在
次射击中击中目标的次数为
,
,其中
,
,击中奇数次为事件
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870528aa6be6f56bae0eb6b10a765c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c11f6c800b8e0410674a0c6d307d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
A.若![]() ![]() ![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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21卷引用:山东省泰安肥城市2023届高考适应性训练数学试题(三)
山东省泰安肥城市2023届高考适应性训练数学试题(三)山东省新高考质量检测联盟2024届高三第一次质量检测数学试题(A)(已下线)第四篇 概率与统计 专题7 常见分布 微点3 常见分布综合训练湖北省武昌实验中学2023-2024学年高三上学期10月月考数学试题(已下线)模块一 专题2 概率(北师大2019版)(已下线)模块一 专题4 随机变量及其分布 (人教A)(已下线)模块一 专题3 概率 (苏教版)(已下线)单元提升卷11 统计与概率(已下线)考点13 二项分布与超级几何分布 2024届高考数学考点总动员【练】(已下线)随机变量及其分布(已下线)黄金卷02(已下线)专题10.1 概率与统计的综合运用【十一大题型】(举一反三)(新高考专用)-1(已下线)概率、随机变量及其分布-综合测试卷A卷(已下线)第11讲 二项分布与超几何分布-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)(已下线)专题04 超几何分布+二项分布+正态分布压轴题(4)(已下线)7.4.1 二项分布(分层练习,6大题型)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第三册)(已下线)专题7.10 随机变量及其分布全章综合测试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)辽宁省大连市第八中学2023-2024学年高二下学期4月月考数学试题(已下线)第七章:随机变量及其分布章末重点题型复习-2023-2024学年高二数学题型分类归纳讲与练(人教A版2019选择性必修第三册)黑龙江省牡丹江市第一高级中学2023-2024学年高二下学期5月期中考试数学试题(已下线)高二下期末考前押题卷02--高二期末考点大串讲(人教B版2019选择性必修)
5 . 已知椭圆
经过
两点.
(1)求
的方程;
(2)斜率不为0的直线
与椭圆
交于
两点,且点A不在
上,
,过点
作
轴的垂线,交直线
于点
,与椭圆
的另一个交点为
,记
的面积为
,
的面积为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fece72f0129665f84fa70aa1d7bf2a8d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)斜率不为0的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f59747cee312ee5140643428cae79efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667dff25fdab1b5478467dd09b1669dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf66a5f30d94390f59c6a3d1ae6c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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7卷引用:陕西省安康市2024届高三上学期第二次质检数学(理科)试卷
6 . 等差数列
的前
项和为
,
(
且
),
.
(1)求
的通项公式与前
项和
;
(2)记
,当
,
时,试比较
与
的大小;
(3)若
,正项等比数列
中,首项
,数列
是公比为4的等比数列
,且
,求
的通项公式与
.
![](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/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3c9f09e932ad3cc1f3720d93b34c56.png)
(1)求
![](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)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1dcf4e0dd72f254d9eab961b892ae9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15520cf5be7c2685975aac51bc99ac4f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afef6271af7462ffa935a1846e3ec90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ba85f74cda4ddd621278e558bc036f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ee3a47bf7dfe538ae367cc006a69b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea2efac902bfb513a224c40faef2516.png)
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7 . 已知函数.
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70317d5b4128ca9fdd6573787d1db993.png)
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|
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4卷引用:广东省惠州市第一中学2024届高三上学期第三次阶段测试数学试题
广东省惠州市第一中学2024届高三上学期第三次阶段测试数学试题山东省滨州市2024届高三上学期期末数学试题(已下线)广东省佛山市2024届高三教学质量检测(一)数学试题变式题17-22(已下线)2023-2024学年高二下学期第一次月考解答题压轴题十六大题型专练(2)
8 . 已知抛物线
的焦点为
,过
的直线
交
于
两点,过
与
垂直的直线交
于
两点,其中
在
轴上方,
分别为
的中点.
(1)证明:直线
过定点;
(2)设
为直线
与直线
的交点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764c199d659322854377a92fee97642d.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102716b8d55b91adb37dfe019cc7231b.png)
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8卷引用:广东省惠州市第一中学2024届高三上学期第三次阶段测试数学试题
广东省惠州市第一中学2024届高三上学期第三次阶段测试数学试题2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-192024年九省联考试卷分析及真题鉴赏(已下线)专题18 圆锥曲线高频压轴解答题(16大题型)(练习)(已下线)专题07 双曲线与抛物线(分层练)(五大题型+12道精选真题)(已下线)专题08 圆锥曲线 第二讲 圆锥曲线中的定点、定直线与定值问题(解密讲义)福建省厦门双十中学2023-2024学年高二下学期开学考试数学试题
名校
9 . 已知函数
,若
存在两个不相等的实数根
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5f090340f798e2e4fb4331efde99d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
A.e | B.2e | C.![]() | D.![]() |
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解题方法
10 . 双曲函数是一类与三角函数类似的函数,基本的双曲函数有:双曲正弦函数
,双曲余弦函数
,双曲正切函数
.给出下列四个结论:
①函数
是偶函数,且最小值为2;
②函数
是奇函数,且在
上单调递增;
③函数
在
上单调递增,且值域为
;
④若直线
与函数
和
的图象共有三个交点,这三个交点的横坐标分别为
,
,
,则
.
其中所有正确结论的序号是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f45428262907786c0f71f8233820ce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64d8edcac9fb4dc0cdc8c952596b722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2bdd2bb1b5116dbd9642e734ee3040.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3fb37c1744eb0ccb23705a24320d2e0.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7901d406f0b87b937ae820be17bc90ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1895e23c9bf91b7b185b4d93e1a16ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b1af5d4b930f8989cf63d44768621e.png)
④若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ff39dd1dfc9caf911ad0d11ba21d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3fb37c1744eb0ccb23705a24320d2e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7901d406f0b87b937ae820be17bc90ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef6228a20e5bb30673a1ab701c4c3b2.png)
其中所有正确结论的序号是
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2024-01-19更新
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476次组卷
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3卷引用:广东省汕头市潮阳实验学校2024届高三上学期第一次调研数学试题