名校
1 . 已知三次函数
,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db966991f5c33aaed168f3c1424612c2.png)
__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa8b68e7afd95e024c29b908e9c8c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509a0c0790dcf553abd63eb5c1658c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6763b4c6f48b7962142218b8ea047b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c82634f3457b8dc8cd49544cfc48ad7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db966991f5c33aaed168f3c1424612c2.png)
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2022-10-27更新
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3卷引用:河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题
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解题方法
2 . 若函数
为奇函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975f579159d9e8ade04e84c4da7f6b8a.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b23650b569f9c465fa20f76708bed94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975f579159d9e8ade04e84c4da7f6b8a.png)
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2022-10-23更新
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469次组卷
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3卷引用:河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题
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3 . 函数
在
上的最大值与最小值的和为_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c19f257e9dc477d46a3b61dbcff161e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34759112630cb0ae42f62595eb4f130.png)
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4 . 对任意
,给定
,记函数
,例如,
,则
的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32a6e5b8aaed692d8be521e82df5a230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5987b86e917a3632a4146ad7129d0a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1f9475786bf94035afd91d3e9e0aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3381b439c55c9d81e5f24eeff89a851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3859cd3de4d6d485df050b0f5321d6c6.png)
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2022-10-23更新
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3卷引用:河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题
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5 . 已知菱形
的边长为2,且
,沿
把
折起,得到三棱锥
,且二面角
的平面角为
,则三棱锥
的外接球的表面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0790f09a7b2f33f4a39da395252550a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe70c6135cb07a6c93b274322ee3833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abe5c8e5c6dfdc6d3b480e77e84ecd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a40929e574cb5b79c3a448f2e4547347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62ea41785fef55d1c361fa846fb2fdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4abe5c8e5c6dfdc6d3b480e77e84ecd7.png)
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2022-10-22更新
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3卷引用:河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题
河南省驻马店市确山县第一高级中学2022-2023学年高二上学期数学竞赛试题江西省赣州厚德外国语学校、丰城中学2023届高三上学期10月联考数学(文)试题(已下线)专题06 一网打尽外接球与内切球问题(精讲精练)-2
6 . 已知点
为双曲线
上任一点,
为双曲线的右焦点,过
作直线
的垂线,垂足为A,连接
并延长交y轴于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6eb70376-cd94-4cc1-a517-ee193669a6df.png?resizew=238)
(1)求线段
的中点
的轨迹
的方程;
(2)已知
,过点
的直线l与轨迹E交于不同的两点M、N,设直线DM和直线DN的斜率分别为
和
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15be73296477fc390f8b438cfd52b452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5fd9b17a0ed5508c11547ea3fbb3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f1b40221f57567c67c1ba5ceb2f57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bfa8bf45e6d2d25a730a793d0cf5694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31889f8671f76ca924c9d86f6fdc929c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ec9341909c0edd74ee755543c4c35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/6eb70376-cd94-4cc1-a517-ee193669a6df.png?resizew=238)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10195cb8bc3cb0db5c76dd15d331a28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85acf3c73db7fad56a34b1f86f5bdbf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb1b7b68a0fcb11f39395f57cba1c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2562424a83aae7e4b3f8adf90307961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b58edb637c5dfa03794f3952de9d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8869f1b1c62e8e88f528a38d6d71968a.png)
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7 . 若函数
,则不等式
的解集是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbab52883c15f4e8f80a9e56d3f7851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20f29bb8aa8a0770c23f0d0006002c07.png)
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8 . 在棱长为1的正方体
中,球
同时与以A为公共顶点的三个面相切,球
同时与以
为公共顶点的三个面相切,且两球相切于点F.若以F为焦点,
为准线的抛物线经过
,设球
,
的半径分别为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd732d29ad074c6ffca30f06c0ddba98.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72545bef56c4e32d1b76489bd32c3842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d123b8eba45af84e79775bcf1cae55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387d9d276d567b5ec2db8613ba77aa2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e3ece4dce20324f55badd3d9225e19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387d9d276d567b5ec2db8613ba77aa2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d123b8eba45af84e79775bcf1cae55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387d9d276d567b5ec2db8613ba77aa2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2968618b299ee06c9c964765ebb6c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f9819f0dbc1754dadfb417b8a04e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd732d29ad074c6ffca30f06c0ddba98.png)
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9 . 定义在R上的函数
单调递减,且满足
,对于任意的
,满足
恒成立,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703cb377d00d889a7642ab0cd1ff1c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c9121cede0ee0562e23b8a26b34616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b70e1115fe0a3e26c0cdf17ff8f55e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96187825b08503f8e22b1bf92309d422.png)
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22-23高三上·四川·阶段练习
名校
解题方法
10 . 如图,某菜农有一块等腰三角形菜地,其中
,
米.现将该三角形菜地分成三块,其中
.
![](https://img.xkw.com/dksih/QBM/2022/10/13/3086739334479872/3088306730713088/STEM/993b986ca3c84604a6d80a2dc1e40313.png?resizew=216)
(1)若
,求
的长;
(2)求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86c589939053ce21ce0a67cf40054a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d55d2649a844e8619de4663a03c233f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16d84bc57102fb66122cfb54d763218.png)
![](https://img.xkw.com/dksih/QBM/2022/10/13/3086739334479872/3088306730713088/STEM/993b986ca3c84604a6d80a2dc1e40313.png?resizew=216)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499c4e9eda4fc946d0195adc93a9d82f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
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