名校
解题方法
1 . 已知抛物线
的准线
与圆
相切.
(1)求
的方程;
(2)点
是
上的动点,且
,过点
作圆
的两条切线分别与
交于
两点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f702bfe1a376398286f1dc3daf8c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/2205cffebf8c4d5f81d15ed7b85c8936.png)
您最近一年使用:0次
名校
解题方法
2 . 已知
,则
在复平面内的对应点所在的象限为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa094b239cd409c489feb7ca84dc238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
您最近一年使用:0次
名校
3 . 已知函数
是
的导函数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9ca8d13fcffa6e9fb07efdd05e4a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.“![]() ![]() |
B.“![]() ![]() |
C.若不等式![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
4 . 已知函数
,其中
为自然对数的底数.
(1)讨论
的单调性;
(2)若方程
有两个不同的根
.
(i)求
的取值范围;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca6a47d8e2b8ff86f955f401ed47acc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04133adb6f1562d859510c9771b2e545.png)
您最近一年使用:0次
名校
5 . 某大型商场的所有饮料自动售卖机在一天中某种饮料的销售量
(单位:瓶)与天气温度
(单位:
)有很强的相关关系,为能及时给饮料自动售卖机添加该种饮料,该商场对天气温度
和饮料的销售量
进行了数据收集,得到下面的表格:
经分析,可以用
作为
关于
的经验回归方程.
(1)根据表中数据,求
关于
的经验回归方程(结果保留两位小数);
(2)若饮料自动售卖机在一天中不需添加饮料的记1分,需添加饮料的记2分,每台饮料自动售卖机在一天中需添加饮料的概率均为
,在商场的所有饮料自动售卖机中随机抽取3台,记总得分为随机变量
,求
的分布列与数学期望.
参考公式及数据:对于一组数据
,经验回归方程
的斜率和截距的最小二乘估计公式分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de96374212b9a5df820d78d10e7d1291.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![]() | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
![]() | 4 | 16 | 64 | 256 | 2048 | 4096 | 8192 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8029f44c190cd8ced93ed27ba0c18b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)根据表中数据,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若饮料自动售卖机在一天中不需添加饮料的记1分,需添加饮料的记2分,每台饮料自动售卖机在一天中需添加饮料的概率均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
参考公式及数据:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eafbe64ec9acf78f3624abbd06d516e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db6103cb0f1d2bd6b19235d53ee7e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666e172502a39172a8379934128101f8.png)
您最近一年使用:0次
名校
解题方法
6 . 2023年10月全国多地医院出现较多的支原体肺炎感染患者,患者多以儿童为主.某研究所在某小学随机抽取了46名儿童,得到他们是否接种流感疫苗和是否感染支原体肺炎的情况的相关数据,如下表所示,则( )
附:
.
感染情况 接种情况 | 感染支原体肺炎 | 未感染支原体肺炎 | 合计 |
接种流感疫苗 | |||
未接种流感疫苗 | |||
合计 | 46 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedb26578090f09dd6b9f18d9a47a235.png)
0.1 | 0.05 | 0.01 | 0.005 | 0.001 | |
2.706 | 3.841 | 6.635 | 7.879 | 10.828 |
A.![]() |
B.![]() |
C.认为是否接种流感疫苗与是否感染支原体肺炎有关联,此推断犯错的概率不大于0.1 |
D.没有充分的证据推断是否接种流感疫苗与是否感染支原体肺炎有关联 |
您最近一年使用:0次
7 . 在正四棱台
中,
,
,且该正四棱台的每个顶点均在表面积为
的球
上,则平面
截球
所得截面的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572d44de660d3975ee8c55a07cfa01b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d80f16c3278cd252725625dcf253cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
及其导函数
的定义域均为
,记
.
满足
,
的图象关于直线
对称,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205b6623a0158130a701284de57bd331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c36601834a9a0e473ff9b17cd66458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-05-23更新
|
664次组卷
|
2卷引用:福建省南平市2024届高三下学期第三次质量检测数学试题
解题方法
9 . 若数列
共有
项,对任意
都有
(
为常数,且
),则称数列
是
关于
的一个积对称数列.已知数列
是
关于
的一个积对称数列.
(1)若
,
,
,求
的值;
(2)已知数列
是公差为
的等差数列,
,若
,
,求
和
的值;
(3)若数列
是各项均为正整数的单调递增数列,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2ba64bfc61ec78a65944fb8247a937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11950e41ac5d26b212a972cc58a3d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c876f7c64d581afb4d1bb6063c48f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fe8fabd6b7f3547c18062c8781dbd45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bfe21c96489cb30c544d49ddb4c1c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b13bd7807908887b854773a4901da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dc22436b2a4edf3d6e15e1e5a15343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de06482cf6ed8f6c8bc13de27e736fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c95a5133241ba22e1c805480c1b02a.png)
您最近一年使用:0次
10 . 对任意非零实数
,当
充分小时,
.如:
,用这个方法计算
的近似值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc51e97939a8966daa015535a801561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e3ac443cac01e741f166e48cee9ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09e442f77601cb12c592d2b930fd8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9317a6b2be7cdf9b7979f008750678e7.png)
A.1.906 | B.1.908 | C.1.917 | D.1.919 |
您最近一年使用:0次