名校
1 . 已知圆
,直线
,方程
,则“圆
与直线
相切”是“方程
表示的曲线为椭圆”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cadc2a6ae4ac51ad58567d0a352befd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03c995df016f9f211f419995919d045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e11b62c6594899bbc96c1547210f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.充分非必要条件 | B.必要非充分条件 | C.充要条件 | D.既非充分也非必要条件 |
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2 . 棣莫弗定理:若
为正整数,则
,其中
为虚数单位,已知复数
, 则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b890700d682af673c0dd9f143a27ba7.png)
____ ,
的实部为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f679d4c4b3686ee3602923cda586377.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579743813856e2a9183f5ec6eaaefbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9c0e62c8d20f29175d3a633726898c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b890700d682af673c0dd9f143a27ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c5f55103d035451be62f54c0e12d05.png)
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3 . 如图所示数阵,第
行共有
个数,第m行的第1个数为
,第2个数为
,第
个数为
,规定:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96a1efc782c7cbbbd7ccd55ae6c06c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6442c68ee525e11e798702dcca3f4ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d80851ce143df1c3e1f7bd0bb28754d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8869622c406f60ca66f66cbf7e0f94cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c9cefa7564754d75af2709b98b559c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82123c3c62e343e06a547f58ea074bea.png)
…… … … … … …
(1)试判断每一行的最后两个数的大小关系,并证明你的结论;
(2)求证:每一行的所有数之和等于下一行的最后一个数;
(3)从第1行起,每一行最后一个数依次构成数列
,设数列
的前n项和为
是否存在正整数k,使得对任意正整数n,
恒成立?如存在,请求出k的最大值,如不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdd4f87e7e7e32d723d7e97d980db42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29a285201fd7e0ad70fa7431cb89a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0749c4129afc0c704155f522290b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae0b861522b18be1753acc4474cbc9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222268dda9dcb9b660f3cbedbb37757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f1e3925bda80e8223bf7e431585847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96a1efc782c7cbbbd7ccd55ae6c06c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6442c68ee525e11e798702dcca3f4ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d80851ce143df1c3e1f7bd0bb28754d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8869622c406f60ca66f66cbf7e0f94cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c9cefa7564754d75af2709b98b559c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82123c3c62e343e06a547f58ea074bea.png)
…… … … … … …
(1)试判断每一行的最后两个数的大小关系,并证明你的结论;
(2)求证:每一行的所有数之和等于下一行的最后一个数;
(3)从第1行起,每一行最后一个数依次构成数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e8660fb54ba32b037b392b75316087.png)
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4 . 已知函数
.
(1)求
的单调区间;
(2)若对于任意
,都有
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3b6c56aee4bb8a8131fd960415c745.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f909328384f9c52134243753d9c954ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88a527fde68b2bbeec4fe524dafff4b9.png)
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5 . 某果园产苹果,其中一堆苹果中大果与小果的比例为
.
(1)若选择分层抽样,抽出100个苹果,其中大果的单果平均质量为240克,方差为300,小果的单果平均质量为190克,方差为320,试估计果园苹果平均质量、方差;
(2)现用一台分选机筛选,已知这台分选机把大果筛选为小果的概率为
,把小果筛选为大果的概率为
,经过分选机筛选后,现从“大果”里随机抽取一个,求这个“大果”是真的大果的概率.
参考公式:样本划分为2层,各层的容量、平均数和方差分别为:
,
,
;
,
,
.记样本平均数为
,样本方差为
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320896d1b4b9217d9ba527604ac35d3d.png)
(1)若选择分层抽样,抽出100个苹果,其中大果的单果平均质量为240克,方差为300,小果的单果平均质量为190克,方差为320,试估计果园苹果平均质量、方差;
(2)现用一台分选机筛选,已知这台分选机把大果筛选为小果的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f733b1ceeead9ff892539d46a23f3626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad2925d2ce0e1e8ef352f9501f2590d.png)
参考公式:样本划分为2层,各层的容量、平均数和方差分别为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85481cd7e94130ef3aa05b4a39e79cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbc29b47b83fdc5368770b7b1acb439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d80da4a6cb5f102be334006d875a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1295cbd36fdc55a55b549aa2dd5887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82359e2d8f541e44c6be90a390f33ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b880e98674bab74e6068ef1861a8ddf.png)
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解题方法
6 . 已知椭圆E的中心在坐标原点O,焦点在x轴上,过E的右焦点且斜率为1的直线l交E于A,B两点,且原点O到直线l的距离等于E的短轴长,则E的离心率为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-24更新
|
1202次组卷
|
2卷引用:湖北省荆州市部分重点高中2024届高考适应性考试数学试题
2024·全国·模拟预测
7 . 如图(1),在
中,
,
,点
为
的中点.将
沿
折起到
的位置,使
,如图(2).
.
(2)在线段
上是否存在点
,使得
?若存在,求二面角
的余弦值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77254996f9c0b31d0cf5a4f01ac46041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd657e48b15b9b54a55817e2c26b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a916d31a199e250556fb7478d9f57f7.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9072b0fae4133badde0a221234cca8f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3507a1f894fac6b554a49b1167965bbb.png)
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8 . 对于函数
的导函数
,若在其定义域内存在实数
和
,使得
成立,则称
是“跃然”函数,并称
是函数
的“跃然值”.
(1)证明:当
时,函数
是“跃然”函数;
(2)证明:
为“跃然”函数,并求出该函数“跃然值”的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79faaa73be5986e48442dcd5e80bc0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189e0f9d87a2d5fc08838ef19dee6d6b.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1a851f8e1dcaa446c0afa18656dfa8.png)
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解题方法
9 . 已知
,
,M是圆O:
上任意一点,
关于点M的对称点为N,线段
的垂直平分线与直线
相交于点T,记点T的轨迹为曲线C.
(1)求曲线C的方程;
(2)设
(
)为曲线C上一点,不与x轴垂直的直线l与曲线C交于G,H两点(异于E点).若直线GE,HE的斜率之积为2,求证:直线l过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813f9a2814013e2407b5b1c216159359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd15503ee692f8286b0312f7c6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7272356beb98a7953a49651324cb6455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbdbe9a17a23c44cec8c7475c4dc1a9.png)
(1)求曲线C的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d54a59ba55d5e12ae8b643e60a1bb49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
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2024-05-14更新
|
583次组卷
|
3卷引用:湖北省荆州市部分重点高中2024届高考适应性考试数学试题
名校
解题方法
10 . 已知点
,若直线
与直线
垂直,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b745dafd341d69a510d371a5a5ff79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1da6cc56e762bd11aa8e10476bea394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.![]() | B.2 | C.3 | D.4 |
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