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)
您最近一年使用:0次
2 . 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)
您最近一年使用:0次
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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名校
4 . 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)
您最近一年使用:0次
2021-08-20更新
|
654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
5 . 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)
您最近一年使用:0次
6 . 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
7 . 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)
您最近一年使用:0次
8 . 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)
您最近一年使用:0次
名校
解题方法
9 . 在
中,
,
,
,
分别在线段
和
上,
,
,直线
于
.现将三角形
沿着
对折,当平面
与平面
的二面角为
时,则线段
的长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43136f56e59f3f9e878d0c5d4ccbeecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98823cbc09ca52df1fbcc446eba3e44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c2b49d2e533b0e30f467e2660123e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1776d156423ea523de87fbca6c0b6019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d78fc7fcb2762de28dcef8aa3aa0e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2021-08-20更新
|
898次组卷
|
2卷引用:2021年全国高中数学联赛浙江赛区预赛试题
解题方法
10 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7fb476bdfddd8bd1ece52e71a26bc8.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7fb476bdfddd8bd1ece52e71a26bc8.png)
您最近一年使用:0次
2021-07-10更新
|
602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