名校
1 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93208bc770714ae8311ab2ba6274ea8d.png)
A.存在![]() ![]() ![]() |
B.对任意![]() ![]() ![]() |
C.对任意![]() ![]() ![]() |
D.存在![]() ![]() ![]() |
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5卷引用:河北省保定市部分学校2023-2024学年高二下学期5月期中考试数学试题
2 . 已知椭圆C的标准方程为
,梯形
的顶点在椭圆上.
(1)已知梯形
的两腰
,且两个底边
和
与坐标轴平行或在坐标轴上.若梯形一底边
,高为
,求梯形
的面积;
(2)若梯形
的两底
和
与坐标轴不平行且不在坐标轴上,判断该梯形是否可以为等腰梯形?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)已知梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d2530e7023b2345c651e8f53629ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
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名校
解题方法
3 . 曲率是曲线的重要性质,表征了曲线的“弯曲程度”,曲线曲率解释为曲线某点切线方向对弧长的转动率,设曲线
具有连续转动的切线,在点
处的曲率
,其中
为
的导函数,
为
的导函数,已知
.
(1)
时,求
在极值点处的曲率;
(2)
时,
是否存在极值点,如存在,求出其极值点处的曲率;
(3)
,
,当
,
曲率均为0时,自变量最小值分别为
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd817a1014876a72ad1971548ed6f52c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe7522a3f232bd0b7a7850ae674db43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad7aa241de8ac2738629f7361a7c8bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea058d082b5f7517c3b6a6359dbcb44a.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c51e20ceeca65fe6821130d94b794c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3387f1c69de6c2407212536b35150e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.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/6fb22f6880c74b35a8285cbb51a50fb1.png)
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名校
解题方法
4 . 下列说法正确的是( ).
A.函数![]() ![]() ![]() |
B.函数![]() ![]() |
C.已知函数![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2024-06-13更新
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300次组卷
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2卷引用:黑龙江省哈尔滨市第三中学校2023-2024学年高二下学期期中考试数学试卷
名校
解题方法
5 . 满足
的最小正整数
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a966f87c3c0797cc0402bdbf297cbbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.12 | B.13 | C.17 | D.18 |
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6 . 关于函数
有下列结论:
(1)函数
存在最小值但没有最大值;
(2)函数
存在两个零点,且两个零点的和小于1;
(3)函数
存在唯一的极小值点
,且
;
(4)函数
存在唯一的极大值点
,且
.
其中正确的是__________ .(填写所有正确结论的编号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2db29e99cb06dfd0d9dbdd3a0d387fd.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caae75ee744fa4662f1dc8fbe3995789.png)
(4)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f803d4aab3143f9e43d7a024aab305e9.png)
其中正确的是
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解题方法
7 . 我们知道,一个一元一次方程最多有一个根,一个一元二次方程最多有两个根,这些都是代数基本定理的简单表示,代数基本定理可以表述为:一元n次多项式方程最多有
个不同的根.由代数基本定理可以得到如下推论:若一个一元
次方程有不少于
个不同的根,则必有各项的系数均为0.已知函数
,函数
的图象上有四个不同的点A、B、C、D.利用代数基本定理及其推理回答下列问题:
(1)解关于x的方程
;
(2)是否存在实数
,使得关于
的方程
有三个以上不同的解,若存在,求出
的值,若不存在,请说明理由;
(3)若
按逆时针方向顺次构成菱形,设
,求代数式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8a18548e00a131abe2eca8c4c815c2.png)
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bc57a9ac3f82c3b8af4fe78e5c861b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)解关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b070bfc31cef4c001541af54d3c36cd3.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2158cfb945452be603a745510df299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0877194ab8760f54c35527177b03ff93.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b032796d46540441098204aa82c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8a18548e00a131abe2eca8c4c815c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c004d926a934cced9bc523a8ecde1df1.png)
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8 . 已知实数
,曲线
与曲线
的公共点个数为
,对于不同的
,
所有可能的值的集合为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d165046175c70690335c3c8ce97b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32648507646862a988143a7db906c1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f6a5f23d11b3e731b289615d991246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
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解题方法
9 . 已知函数
,则下列命题正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb8089fe6ddf39eeb0bc78801016578.png)
A.方程![]() |
B.方程![]() |
C.![]() ![]() |
D.![]() ![]() |
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10 . 设有甲、乙两个盒子,均分别装有编号依次为1,2,3,…n(
,且
)的n个球,学生
从甲盒子中随机选取
个球,学生
从乙盒子中随机选取
个球,其中
,且
.
(1)若
,且A在编号为1到m(m为给定的正整数,且
)的球中选取,B在编号为
到n的球中选取.记
是编号为u的球和编号为v的球同时被选中的概率.
①若
,求
的值;
②求所有的
的和;
(2)求学生
取到的球的编号不相同的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5d0a73f50b3e4583f1c1b6d6bf0d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f357273172ea138c4ce8afb4fbddea46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6d99dfbc36d9be71895dfdb732f321.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19c57cfa9b48005549163191246fe9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa49f362f32e992f53341d6374140e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993f4303eb1dc02447ae807127c4b86f.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac01b30a1e66795b4a43d7afd57829fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b920476a1d9bbd4f5ae785891cdf81fb.png)
②求所有的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6042caba179e3ed5f55793bc33d828a9.png)
(2)求学生
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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