名校
1 . 有甲乙两个骰子,甲骰子正常且均匀,乙骰子不正常且不均匀,经测试,投掷乙骰子得到6点朝上的概率为
,若投掷乙骰子共6次,设恰有3次得到6点朝上的概率为
,
是
的极大值点.
(1)求
;
(2)若
且等可能地选择甲乙其中的一个骰子,连续投掷3次,在得到都是6点朝上的结果的前提下,求这个骰子是乙骰子的概率;
(3)若
且每次都等可能地选择其中一个骰子,共投掷了10次,在得到都是6点朝上的结果的前提下,设这10次中有
次用了乙骰子的概率为
,试问当
取何值时
最大?并求
的最大值(精确到0.01).(参考数据
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcbd28fefa404513768b10747e2291a.png)
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2024·江苏连云港·模拟预测
名校
解题方法
2 . 已知函数
(
,且
).
(1)若
,求函数
的最小值;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b02f7eb75c4920528be28f08541c276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b06387179d53c1e474fcfcb408b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467ebe7ef361ddf4cfab29baeefc66aa.png)
您最近一年使用:0次
名校
3 . 在棱长为2的正方体
中,点
满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167c13c894f6d448cda166ac5f2a81e7.png)
A.当![]() ![]() ![]() ![]() |
B.任意![]() ![]() |
C.存在![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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4 . 已知椭圆C的方程为
,其离心率为
,
,
为椭圆的左右焦点,过
作一条不平行于坐标轴的直线交椭圆于A,B两点,
的周长为8
(2)过B作x轴的垂线交椭圆于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e7170bb4a2ddcef39391a06c989162.png)
①试讨论直线AD是否恒过定点,若是,求出定点坐标;若不是,请说明理由.
②求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
(2)过B作x轴的垂线交椭圆于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e7170bb4a2ddcef39391a06c989162.png)
①试讨论直线AD是否恒过定点,若是,求出定点坐标;若不是,请说明理由.
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372629a8666de1e9bac3e7daadcac7b6.png)
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名校
解题方法
5 . 已知函数
在
上为奇函数,
,
.
(1)求实数
的值;
(2)若对任意
,
,不等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a761ce7b2ab701376593bda11531de.png)
都成立,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bbe38c0bfa0dcbb845a38777063b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5caabda288fc01cc168938846eec5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a761ce7b2ab701376593bda11531de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff98574f62933ec7220fd8e7b091458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-02-04更新
|
484次组卷
|
2卷引用:江苏省东海高级中学2023-2024学年高一下学期第一次检测数学试题
6 . 已知函数
(
).
(1)记
,讨论
的单调性;
(2)若对任意的
,都有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8521eff2f145b88056f337e335b606ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2259e91a333ecf7900f6289f1fc22759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
23-24高三上·北京西城·期末
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解题方法
7 . 给定正整数
,已知项数为
且无重复项的数对序列
:
满足如下三个性质:①
,且
;②
;③
与
不同时在数对序列
中.
(1)当
,
时,写出所有满足
的数对序列
;
(2)当
时,证明:
;
(3)当
为奇数时,记
的最大值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2477167a02872167b2a3760f09d6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc25d4213ca2eadce49e6d8ba805e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b730e2023809495f2bd7fbf48f07a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca986e62ec3a6e50e4e2cad639aa9201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd869b784314b8278f5d144b2d3a9fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302391681aa37ac20d6f533dbae9e137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a215612787e43d28bfebc840c3903b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a60302649eb940748da818199e55da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241d587c2e6f2f109a4e41b79f1c800f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926c16dd072c9ff8a560b003cfb47053.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4546b12ff89d1599427da82294afc09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4546b12ff89d1599427da82294afc09b.png)
您最近一年使用:0次
2024-01-19更新
|
2122次组卷
|
7卷引用:江苏省连云港高级中学2023-2024学年高二下学期第一次月考数学试卷
江苏省连云港高级中学2023-2024学年高二下学期第一次月考数学试卷(已下线)北京市西城区2024届高三上学期期末数学试题北京市西城区2024届高三上学期期末数学试题(已下线)高三数学开学摸底考 (北京专用)2024年普通高等学校招生全国统一考试数学冲刺卷二(九省联考题型)江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(四)广东省深圳市外国语学校2024届高三教学情况测试(一)数学试题
名校
8 . 已知函数
,若方程
有四个不等的实根
,
,
,
,且
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b2918f630b94549d2bf89adb421c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eb2e46f49adba6036e2624639a1b966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba4a5fa1464a5cb5efdc3b8792de3c8.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/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-11-02更新
|
1299次组卷
|
4卷引用:江苏省连云港市新海高级中学2023-2024学年高一上学期一月学情检测数学试题
9 . 已知函数
,其中
为实数.
(1)若
,求实数
的最小值;
(2)设函数
,若函数
存在极大值,且极大值小于0,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8717fae07088e84b949a713e58278b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
10 . 已知椭圆C:
的离心率为
,点
在椭圆上.直线
与椭圆交于
两点.且
,其中
为坐标原点.
(1)求椭圆
的方程;
(2)若过原点的直线
与椭圆
交于
两点,且过
的中点
.求四边形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca18783e2f3bf03b3fadd62473af700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过原点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
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2023-10-06更新
|
936次组卷
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4卷引用:江苏省连云港市华杰高级中学2023-2024学年高二上学期期中数学试题
江苏省连云港市华杰高级中学2023-2024学年高二上学期期中数学试题河北省2024届高三上学期学生全过程纵向评价(一)数学试题(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)山东省滨州市惠民县2023-2024学年高二上学期期中数学试题