名校
解题方法
1 . 过点
作斜率为
的直线
交圆
于
,
两点,动点
满足
,若对每一个确定的实数
,记
的最大值为
,则当
变化时,
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73d26e5a4e3472fd6b1dbc1ea628a3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3625e0824b902d21fc6ec07b6881b4ad.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffcef281db0f6e2f9b0b9580fa6eaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca9469ed1175cf3b1defc3f8eb5d810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca9469ed1175cf3b1defc3f8eb5d810.png)
A.1 | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
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4卷引用:浙江省台州市名校联盟2022-2023学年高二上学期11月五科联赛数学试题
浙江省台州市名校联盟2022-2023学年高二上学期11月五科联赛数学试题广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(二)(已下线)单元高难问题02数学思想方法在解决与圆有关问题中的应用(各大名校30题专项训练)(原卷版)(已下线)专题2 与圆有关的最值问题【练】(压轴小题大全)
2 . 已知数列
满足
(
且
),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec805491b68bcd47219f79e69e26b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
A.![]() ![]() |
B.若数列![]() ![]() |
C.数列![]() ![]() ![]() |
D.当n是奇数时,![]() |
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5卷引用:江西省宜春市铜鼓中学2023届高三上学期第三次阶段性测试数学试题
名校
3 . 已知函数
和
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求
在
处的切线方程;
(2)若当
时,
恒成立,求
的取值范围;
(3)若
与
有相同的最小值.
①求出
;
②证明:存在实数
,使得
和
共有三个不同的根
、
、
,且
、
、
依次成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d210070cc28a32cd9c3e848e195726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952a0cde9449eef7c5f11385c7432e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00d47ef1d331094530990ffe38e1d77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
①求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明:存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7aec235f9df6700f3cbc89c8bcecb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c8ad137a5bf6b24e0dd8dff417c31cc.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/d79fc0ce080b8ad8b63ba63259c680b6.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)
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|
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3卷引用:天津市滨海新区塘沽第一中学2022-2023学年高三上学期期末数学试题
天津市滨海新区塘沽第一中学2022-2023学年高三上学期期末数学试题江苏省南京市宁海中学2022-2023学年高三下学期二月检测数学试题(已下线)江苏省南京市六校联合体2023-2024学年高三上学期11月期中数学试题变式题19-22
名校
4 . 已知函数
,其中
,函数
在
上的零点为
,函数
.
(1)证明:
①
;
②函数
有两个零点;
(2)设
的两个零点为
,证明:
.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7495c0f25cf04e5e59bb4ae43ffc4fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c940cb46e4a6eae0b7172414c965b66f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c353f6bf5422164ef1496838ba1e6de0.png)
(1)证明:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffa38ec984cae2089a6061c5b231dc5.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f127c78da4fd62e8e98f2262400bda.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2995cf1665e01b853555e62aeaf0ac31.png)
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4卷引用:T8(华师一附中、湖南师大附中等)2023届高三上学期第一次学业质量评价数学试题
名校
5 . 已知
和
是各项均为正整数的无穷数列,如果同时满足下面两个条件:
①
和
都是递增数列;
②
中任意两个不同的项的和不是
中的项.
则称
被
屏蔽,记作
.
(1)若
,
.
(i)判断
是否成立,并说明理由;
(ii)判断
是否成立,并说明理由.
(2)设
是首项为正偶数,公差是
的无穷等差数列,判断是否存在数列
,使得
.如果存在,写出一个符合要求的数列
;如果不存在,说明理由;
(3)设
是取值于正整数集的无穷递增数列,且对任意正整数
,存在正整数
,使得
.证明:存在数列
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
则称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677e46ecd051c92489c0d1d458932f37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fef6975d285cabcf6be67c78f30d30.png)
(i)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
(ii)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5bb0902c0daf52fe26a78a250b96f7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33f575cee1cddd9bbc34dcd592a4e2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53442dcf82f93d94f20be6bf2c934cb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1284d81cf684a54e3070d2c69085c76e.png)
您最近一年使用:0次
2022-12-05更新
|
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2卷引用:北京市海淀区北大附中2023届高三预科部上学期12月阶段练习数学试题
2022·全国·模拟预测
名校
6 . 已知
,
,
是互不相等的非零向量,其中
,
是互相垂直的单位向量,
,记
,
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff983823af408d32b203381c8f86665d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14390e9b6b44472bdc7a131133ab39b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cd14dfc0024459f9d8e594c95c5106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07dcf0b16163e0e0e0c0f248466ee7e.png)
A.若![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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4卷引用:2023年普通高等学校招生全国统一考试数学领航卷(九)
(已下线)2023年普通高等学校招生全国统一考试数学领航卷(九)黑龙江省牡丹江市第一高级中学2022-2023学年高一下学期4月月考数学试题黑龙江省哈尔滨市第九中学校2023-2024学年高一下学期4月月考数学试题浙江省温州中学2023-2024学年高一下学期期中考试数学试题
名校
解题方法
7 . 如图,在正方体
中,E,F是底面正方形
四边上的两个不同的动点,过点
的平面记为
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/be42cb24-a40c-4f8d-af2f-c2e172820934.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd191d81c6f35dc5a014872771673c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/be42cb24-a40c-4f8d-af2f-c2e172820934.png?resizew=160)
A.![]() |
B.当E,F分别是![]() ![]() ![]() |
C.当E,F分别是![]() ![]() ![]() |
D.当F是![]() ![]() |
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4卷引用:江苏省苏州八校联盟2022-2023学年高三上学期第二次适应性检测数学试题
名校
8 . 设函数
.
(1)当
时,若直线
是曲线
的切线,求
的值;
(2)若函数
在区间
上严格增,求
的取值范围;
(3)若
且满足
,对任意的
,恒有
,求证:对任意的
,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e99b2155565e0832a2bc405cd29843.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a9b769d70cb6f29e965c800921c8ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e54c5da8061411e6659614a6511a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca83d5dea2d5c02ac18a9c9496ca57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1313a22f7070883f17d39700f383b504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe276c0522839b1d37086d92612aa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc3d1fe6dd2ff21f192e14fd85062fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8deeaabea77488158d0a98639e02ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af041a320a49a5db1828a26c0613ec89.png)
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2卷引用:上海市大同中学2021-2022学年高二下学期期末数学试题
名校
解题方法
9 . 如图,斜三棱柱
中,
,
为
的中点,
为
的中点,平面
⊥平面
.
平面
;
(2)设直线
与直线
的交点为点
,若三角形
是等边三角形且边长为2,侧棱
,且异面直线
与
互相垂直,求异面直线
与
所成角;
(3)若
,在三棱柱
内放置两个半径相等的球,使这两个球相切,且每个球都与三棱柱的三个侧面及一个底面相切.求三棱柱
的高.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1638cde11c9862af200115048a0177da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53cdc56590b42b154608b4cf19462fa0.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e190568dc620895856a72fca1a08ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770da0f9a22d31e40431208bb33ab8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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2022-11-29更新
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3531次组卷
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8卷引用:上海市复旦大学附属中学2021-2022学年高一下学期期末数学试题
名校
10 . 已知
分别为椭圆
的左、右焦点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475a3fdc7b27d5ffa8c864dc478903d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
A.若点![]() ![]() ![]() ![]() |
B.若椭圆上恰有6个不同的点![]() ![]() ![]() ![]() |
C.若圆![]() ![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() |
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2022-11-26更新
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3卷引用:湖北省武汉市华中师范大学第一附属中学2022-2023学年高二上学期期中数学试题
湖北省武汉市华中师范大学第一附属中学2022-2023学年高二上学期期中数学试题山东省青岛第二中学2022-2023学年高二下学期期初考试数学试题(已下线)专题4 求圆锥曲线的离心率(高三压轴小题大全)【练】