名校
1 . 已知曲线
和圆
有2个交点,则实数
的取值范围是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e35b9f4c6a8ad43e30a5834b0fd3705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-05-14更新
|
341次组卷
|
3卷引用:上海市实验学校2023-2024学年高三下学期四模数学试题
2 . 函数
的表达式为
.
(1)若
,直线
与曲线
相切于点
,求直线
的方程;
(2)函数
的最小正周期是
,令
,将函数
的零点由小到大依次记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c032d50e3dde09f453adc34a1c5353ea.png)
,证明:数列
是严格减数列;
(3)已知定义在
上的奇函数
满足
,对任意
,当
时,都有
且
.记
,
.当
时,是否存在
,使得
成立?若存在,求出符合题意的
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c0923a929dbc45520103daa8a889b60.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea3733e989ba820120027e2c3664285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba2967e52115b6f3f668116ed021199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c032d50e3dde09f453adc34a1c5353ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30af9e4dbb01b5db338a2cd88cb1cc01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bef0ef12869d633d4592adec26ea6a.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b8ca7bca7dd23fa9e18073ad4636dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344008f3ab39f3923a971a44c2c4bbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd5f68f8223717c5f9e7a35da919f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca34074d548c4b6c3cd3a1006895fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbda8d24ba7efec06837fc39824d7e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf88dc817c8fdbd8730f52ff5ed4cd43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8f180b0f0fcbf29811f39603ecaba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e34fd6b3b3243aa66337886d067021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
您最近一年使用:0次
解题方法
3 . 已知双曲线
的左、右顶点分别为
、
,设点
在第一象限且在双曲线上,
为坐标原点.
(2)若
,求
的取值范围;
(3)椭圆
的长轴长为
,且短轴的端点恰好是
、
两点,直线
与椭圆的另一个交点为
记
、
的面积分别为
、
求
的最小值,并写出取最小值时点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d34cf4ed961f4052ed35c7475c7d32e.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58a8ca834f54630a35eec57044a9376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b14123852c3e17f0a519282e076797.png)
(3)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a36a9dc09e4ed89c47993141ea124fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e534b545e86c02abd2a0dc75d32b407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a1568c0bf07f285b2e01c3a3a55900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b1ab746f3773e5989f4d18fb3072a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
4 . 如图:已知三点
、
、
都在椭圆
上.
、
、
都是椭圆的顶点,求
的面积;
(2)若直线
的斜率为1,求弦
中点
的轨迹方程;
(3)若直线
的斜率为2,设直线
的斜率为
,直线
的斜率为
,是否存在定点
,使得
恒成立?若存在,求出所有满足条件的点
,若不存在,说明理由.
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9626bd07f966ea26a51dcd8ceba04ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf32f4d595c02a8c0f7cc5f8fd0c931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39978841bdbe3d4d968557f8048f223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
5 . 若函数
的图象上的两个不同点处的切线互相重合,则称该切线为函数
的图象的“自公切线”,称这两点为函数
的图象的一对“同切点”.
(1)分别判断函数
与
的图象是否存在“自公切线”,并说明理由;
(2)若
,求证:函数
有唯一零点且该函数的图象不存在“自公切线”;
(3)设
,
的零点为
,
,求证:“存在
,使得点
与
是函数
的图象的一对‘同切点’”的充要条件是“
是数列
中的项”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2750eb2ffdae5d0be38bda2ebb51875b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c6e387dd234bb49f53df1668d5e63e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4157d7a3d18b13df5428790499406f7d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039124ad765f2a9d8d3382bdc60a3d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1551e58c685b32149bffcb9329e710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdab40c21646025ac21019cf6e883c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a943c3df48c0961838d083e1c34fdbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fa720a5bafa2bb6ec5c60197e74a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d2fad3eba14b645100f279cf2af2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
您最近一年使用:0次
解题方法
6 . 双曲线
的左右焦点分别为
,过坐标原点的直线与
相交于
两点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad57fe6cb71d66d7ae751dc326523fd.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b8cc61e5a4d80351e68f1c782fc954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de37e08ced0d780b98ba98a8cbef58b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad57fe6cb71d66d7ae751dc326523fd.png)
您最近一年使用:0次
7 . 已知双曲线
:
的渐近线为
,焦距为
,直线
与
的右支及渐近线的交点自上至下依次为
、
、
、
.
(1)求
的方程;
(2)证明:
;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10273b05ad8210d8db07639c4d149fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8455657dde27aabe6adb7b188e031c11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1af14f9a53cb0f07d5d28dceba30aa.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571664dafc35f8c9ee5cc20eebc80c9a.png)
您最近一年使用:0次
2024-04-29更新
|
798次组卷
|
2卷引用:上海市建平中学2024届高三下学期三模考试数学试题
8 . 抛物线
上一点到点
的距离最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
您最近一年使用:0次
解题方法
9 . 如图,两条足够长且互相垂直的轨道
相交于点
,一根长度为
的直杆
的两端点
分别在
上滑动(
两点不与
点重合,轨道与直杆的宽度等因素均可忽略不计),直杆上的点
满足
,则
面积的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d718b208bce3e2778a466b2ed8d5312f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
您最近一年使用:0次
解题方法
10 . 如图,在等腰梯形
中,
∥
,
,
,
.点
是线段
上的一点,点
在线段
上,
.
命题①:若
,则
随着
的增大而减少.
命题②:设
,若存在线段
把梯形
的面积分成上下相等的两个部分,那么
,
随着
的增大而减少.
则下列选项正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b716d411a9e865ba6e60a83cdf65879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff5a86745bfe1dfe7bc2683811210330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1813a040cdcd5c345538ab2a192718.png)
命题①:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1be1437712a3f286efb87481bb875a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2330ceffc14c92ff9804c54d9a9717c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
命题②:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29dfebefd907eed364f1aa95697786d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f4b20658d64d6b40520e96ef8c26ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84c4da43d045928eb1d4c19945e145f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
则下列选项正确的是( ).
A.命题①不正确,命题②正确 | B.命题①,命题②都不正确 |
C.命题①正确,命题②不正确 | D.命题①,命题②都正确 |
您最近一年使用:0次