1 . 对于函数
,
,若存在非零实数
以及
,使得
,则称函数
为“
伴和函数”.
(1)设
,
,判断是否存在非零实数
,使得函数
为“
伴和函数”?若存在,求出
的取值范围;若不存在,请说明理由;
(2)设
,证明:函数
,
为“
伴和函数”;
(3)设
,若函数
,
为“1伴和函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3102c0a2f53b80f9dddbf9352537e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe52219480b8d773bf4f016a709f581.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c9320d009a17deba67f208c7d8be8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4da605280ae7f9dd0310276013f1ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d92505f3a1168e8e11eeab4be680f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 如图,在长方体
中,点
、
分别在
、
上,且
,
.
平面
;
(2)设
,
,
,求平面
与平面
所成的锐二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4305d8d52fe2cc79c78129652e64bb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fccb37728702288d4be7148301ab685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3e58edd1f900ca82bb2a3058293f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
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解题方法
3 . 太曲线
由曲线
和曲线
组成,其中点
、
为曲线
所在圆锥曲线的焦点,点
、
为曲线
所在圆锥曲线的焦点.
,
,求曲线的方程;
(2)作曲线
第一象限中渐近线的平行线
,若与曲线
有两个公共点
、
,求证:弦
的中点
必在曲线
的另一条渐近线上;
(3)设
,
,若直线
过点
交曲线
于点
,求
的面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68294f6f91613d44dbd4b22c24a76220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abeacbd3604d4e926b8d2ffe370f5322.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1282962a17a48a18edf733204054d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43fc57c70b00a6f9906bf9369ef7c28.png)
(2)作曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcc480016747ca3595a20507ff3c2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287adcb739a4890d108dd974358345fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdbb45d7359537458736c9ea5bf9e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2024-03-12更新
|
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3卷引用:上海交通大学附属中学2023-2024学年高二下学期摸底数学试卷
上海交通大学附属中学2023-2024学年高二下学期摸底数学试卷上海市第二中学2023-2024学年高二下学期期中数学试题(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)
名校
4 . 如图所示,在梭长为6的正方体
中,点
是平面
内的动点,满足
,则直线
与平面
所成角的正切值的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e975f6c9fafab8fd7639dc0cd0f70a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74769e4e9f9570aeca28ffd14c168e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e975f6c9fafab8fd7639dc0cd0f70a4.png)
您最近一年使用:0次
2024-03-12更新
|
527次组卷
|
2卷引用:上海交通大学附属中学2023-2024学年高二下学期摸底数学试卷
名校
解题方法
5 . 已知等差数列共有
项,各项与公差
均不为零,若将此数列删去某一项后,得到的数列(按原来顺序)是等比数列,则所有数列
组成的集合为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49dac16bbcffa236fbee961ada16420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26206bb5dafe7e8f0ac3775a4b2029c5.png)
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2023-03-23更新
|
575次组卷
|
4卷引用:上海市南洋模范中学2023-2024学年高二上学期开学考数学试题
名校
6 . 将连续正整数1,2,3,
,
从小到大排列构成一个
,
为这个数的位数.例如:当
时,此时为123456789101112,共有15个数字,则
.现从这个数中随机取一个数字,
为恰好取到0的概率.
(1)求
;
(2)当
时,求
得表达式;
(3)令
为这个数中数字0的个数,
为这个数中数字9的个数,
,
,求当
时,
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4673710cd589e1b6cd3d2906e36791df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df313df25c54af0180e52424f480260b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081fad2749f3f201cf2c324c3d0dd190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadc4f26938f7a9d55006ab4d3c1e102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6df056ae0ceeac78f539e23aadd6fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6291d7b91f71daa0b3c4fa02dc7a5ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eaaa90099b6eb96a5730619ca2df08f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e464598d8d334b4d5a01c25f7ef9021c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081fad2749f3f201cf2c324c3d0dd190.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d85d20b743e236a83edb22d5229d05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13d06dcfd70149e4f495614f36b3a72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f44b482719577dde6fa146e44aa0c448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6291d7b91f71daa0b3c4fa02dc7a5ea.png)
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7 . 某工厂36名工人的年龄数据如下表.
(1)计算按随机抽样法抽取到样本44,40,36,43,36,37,44,43,37样本的平均值x和方差
;
(2)36名工人中年龄在
与
之间有多少人?所占的百分比是多少(精确到
)?
工人编号 年龄 | 工人编号 年龄 | 工人编号 年龄 | 工人编号 年龄 |
A.40 | J.36 | S.27 | AB.34 |
B.44 | K.31 | T.43 | AC.39 |
C.40 | L.38 | U.41 | AD.43 |
D.41 | M.39 | V.37 | AE.38 |
E.33 | N.43 | W.34 | AF.42 |
F.40 | O.45 | X.42 | AG.53 |
G.45 | P.39 | Y.37 | AH.37 |
H.42 | Q.38 | Z.44 | AI.49 |
I.43 | R.36 | AA.42 | AJ.39 |
(1)计算按随机抽样法抽取到样本44,40,36,43,36,37,44,43,37样本的平均值x和方差
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
(2)36名工人中年龄在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0fb3cd22f8dc765b750d01f8cdd910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e3f228a95a1cd5cda7d6787e5e17d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200863a7bb1eaf36a39fa36f595c156c.png)
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8 . 已知抛物线方程
,过点
的直线与抛物线只有一个交点,这样的直线有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530e5817131adf2c05b99ff18eb9060f.png)
A.0条 | B.1条 | C.2条 | D.3条 |
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2023-03-14更新
|
953次组卷
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8卷引用:上海市川沙中学2022-2023学年高二下学期开学考试数学试题
上海市川沙中学2022-2023学年高二下学期开学考试数学试题上海市复兴中学2022-2023学年高二下学期期中数学试题(已下线)专题3.7 直线与抛物线的位置关系【八大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)3.3 抛物线(精练)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)3.3.2 抛物线的几何性质(5大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试卷(已下线)上海市四校(复兴高级中学、松江二中、奉贤中学、金山中学)2024届高三下学期3月联考数学试题变式题11-16(已下线)专题5 圆锥曲线中满足条件的直线条数问题(高三压轴小题大全)【讲】
22-23高二下·上海浦东新·开学考试
名校
解题方法
9 . 已知异面直线
所成角为
,直线
与
均垂直,且垂足分别是点
.若动点
,则线段
中点
的轨迹围成的区域的面积是__________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0f303f211915cd7fc41b9d4e7695e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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22-23高二下·上海浦东新·开学考试
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解题方法
10 . 已知点
,点
是双曲线
的右焦点,点
是双曲线
右支上一动点,则当
的周长取得最小时
的面积为__________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62f236e5e8352ad0d65c1570747d9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1983309686915252c4efc8e4455b9d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceff3844281849df3e37a2e56e110549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceff3844281849df3e37a2e56e110549.png)
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