1 . 已知单位向量
,
,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb74499b8965b3f6c9acfbbb168df438.png)
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2 . 设复数
的实虚部
,
所形成的点
在椭圆
上.若
为实数,则复数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9e4a7572ce9d7f8041b6ec5a3c3ade.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/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa966b9eb79620e797a58435755814f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb45808ea3775efd522060ed9d97dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
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3 . 对于正整数
,若
展开式经同类项合并,
合并后至少有2021项,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/332f0883a0a2b871baa31fd1942c7048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965829b71df11e3d1160ce37fd8e3ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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4 . 设数列
,
,2,…,7这里
表示不超过
的最大整数.若
,则正整数
有______ 种可能的取值情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecda33137d5e32f470be5ead72b8a85b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1e55cb07aa8350755e0e4f54ca0fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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5 . 已知二次函数
有两个不同的零点.若
有四个不同的根
,且
,
,
,
成等差数列,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e0be5afa2a9e64ec663846e1b4c1404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7a9ef0a7eab052019086506c70bd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
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名校
6 . 给定实数集合
,
,定义运算
.设
,
,则
中的所有元素之和为______ .
![](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/99b868cd0eb21378c04e4556b1575385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663bec4eafb64f3cea43a210c8ad68f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f85224096b00d87bb811686e779dcc3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e37e656d05244fe3a5769cd1446725.png)
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2021-08-20更新
|
653次组卷
|
3卷引用:2021年全国高中数学联赛浙江赛区预赛试题
7 . 已知
三个顶点的坐标为
,
,
,过点
的直线分别与线段
,
交于
,
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d808b3a1027a2e517472a0497708b5b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb9e88d3e58141dba299dcd8edc4e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837468348b6c42f4280fe2a3b027210e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7089a4e568ed92b1230af589f4d47be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a036940a3405590f3c7ff0826041e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0133c4f2e267ccdab49e4c5bc6de3caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d808b3a1027a2e517472a0497708b5b.png)
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解题方法
8 . 设直角坐标平面上两个区域为
,
,记
与
的公共部分面积为
.当
时,则
的表达式为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7b4d2af45f4af001a08d49d1161ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6d5db1f2427972e79de8f6eee18082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23865ee52040331dee23621b4a15c244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
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9 . 设
为给定的正整数,
,
,…,
为满足对每个
都有
的一列实数,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff01d50db01ac3d5f605ac915992ac9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0707998daa4067326b2068a2c9bf2d52.png)
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10 . 设
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c8d0474f7d81ef8dbefaacfd5afe7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a960485f8c5b9bbd93ba135640475c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbbb0675675b7e24ab9d9514a552b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.png)
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