名校
1 . (1)已知
为
中点,过点
作
于
,交
于点
,求
.
(2)已知
,过点
作
于
,交
于点
,求
.
(3)在(2)的条件下,
为常数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c4c49765e33742b4204d6904dc3a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5378a3867bf1a7386b1330aa8b36f0a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/1e748517-2524-4763-aeb1-30d7a2bd7e1d.png?resizew=155)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df89cefacfd826262825276a739ca4f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39b13d187b25461d85a3b8d10c7b678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5378a3867bf1a7386b1330aa8b36f0a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/7e2e9fd4-ce48-414d-8682-dee6f813a104.png?resizew=154)
(3)在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f03cab451843012fd80fa6cc698c648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe857997fa13837880f520673db7809.png)
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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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名校
3 . 单位向量
,
,
的两两夹角为
,若实数
,
,
满足
,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccfda9afde4441cfd1d4df5fe9622d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145ec8e9ef187afb4bf6d27a8ab8be22.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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名校
解题方法
4 . 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.![]() |
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解题方法
5 . 坐标系建立的方式不同,会导致曲线方程形式上的不同,如初中学过的反比例函数的图象也是双曲线.已知形如
的函数图象均为双曲线,则双曲线
的一个焦点坐标为
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6 . 定义
,其中
为奇素数.
(1)给出同余方程
的满足
的一组解;
(2)(代数基本定理)设
,且
,求证
在
内至多有
个解;
(3)(
小定理)求证:
;
(4)(原根存在定理)若正整数
满足:
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80754c6842db876978ab0c306640186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411837b4b3078d05b43cb0439259a362.png)
,则记
,则称
为
在
意义下的阶,求证:必定存在
,有
;
(5)求证,存在
,都存在
中必有一者成立;
(6)说明当
时,
必有一组非零解
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa82bc7122ca89b418d33b694350f987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(1)给出同余方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b2afe64159eac83151200719a5c815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a964cf4f45603e28dec030a286786750.png)
(2)(代数基本定理)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2b731f8e2eaa9ac5e3eff49f586820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59917a9390d454668b58a0c22c08b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6227f2f164910966f194fb857d5e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b75c20efa27f38e93e3ce9e00005ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(3)(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9362bb4f6acf4bf074d0b7bc7b7aba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34e11a5e27430447b806863c5fdc76e.png)
(4)(原根存在定理)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e026ac41c5502a4743b336845bae2d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1e84f1d28522a63e61283132d1af48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80754c6842db876978ab0c306640186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411837b4b3078d05b43cb0439259a362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097f1e1905c0034991b00c360c5d28f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bb4eb36d6c696377fe2e14bbb66858.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa75d323fa66f6320034f2c7f45a6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b657e7e787a785063afc56cb983ca56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e0f45eacebab3cc301c18df8fa0cd1.png)
(5)求证,存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66543500cdc7031573611000b1b5f85c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107ba654d76c8b754beb5d173c06c6a7.png)
(6)说明当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13b47dded788f1274064925d5f38384e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95730071c97ce5e4d33780626f52e23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bad85768515c66beee8beeb0556520.png)
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7 . 如图,在五面体
中,底面
为矩形,
和
均为等边三角形,
平面
,
,
,且二面角
和
的大小均为
.设五面体
的各个顶点均位于球
的表面上,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/9922bed7-bbff-4246-a837-64a6972fd2e9.png?resizew=215)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a04a2b317c5a6b8b7eb5d760fbd818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e2bf04b646d77e272034198d21a1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5219d5b2c63eded763670e5800dd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9abe6e8d1f4f1e8bdc46ddbae0cd789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ba310682e25a0c6d488e6aff816614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5292af357a9c81f104ff2237053a4d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c2044ecc165365634e21f3e95ec7f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8b7a29b332ac3a192a2c19efa1f886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadd8e8730b81d153ffa6c55a3ac68e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a04a2b317c5a6b8b7eb5d760fbd818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/21/9922bed7-bbff-4246-a837-64a6972fd2e9.png?resizew=215)
A.有且仅有一个![]() ![]() |
B.有且仅有两个![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() |
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8 . 我们称
为“花式集合”,如果它满足如下三个条件:
(a)
;
(b)
的每个元素都是包含于
中的闭区间(元素可重复);
(c)对于任意实数
中包含
的元素个数不超过1011.
对于“花式集合”
和区间
,用
表示使得
的对
的数量.求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(a)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4105c41b98ebc0e7144eff1ba792c76d.png)
(b)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
(c)对于任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7bfa1a59b3451a4379f7cbc074ef60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
对于“花式集合”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fc1c4dd7cb41e3342eb79054ef1a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6ceed58d644f9027ea60bd0f1f557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aeb55594a33f7ac1d8d93dc5b13cb82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1ac9030ad24307666928b511a0f45e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e6ceed58d644f9027ea60bd0f1f557.png)
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名校
9 . 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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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
10 . 已知一动圆与圆
外切,与圆
内切,该动圆的圆心的轨迹为曲线
.
(1)求曲线
的方程.
(2)已知点
在曲线
上,斜率为
的直线
与曲线
交于
两点(异于点
).记直线
和直线
的斜率分别为
,
,从下面①、②、③中选取两个作为已知条件,证明另外一个成立.
①
;②
;③
.
注:若选择不同的组合分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334eced457d4ba4b994fb8f90073a026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a195b6d605a528ae425ba2d641c1dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8115c09f801cf0bb02293baef7bf137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71471908991617852f8b27bceeb689cd.png)
注:若选择不同的组合分别解答,则按第一个解答计分.
您最近一年使用:0次
2023-01-05更新
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1268次组卷
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3卷引用:河北省张家口市2022-2023学年高二上学期期末数学试题