1 . 在平面直角坐标系中,定义
为两点
,
的“切比雪夫距离”.又设点P及l上任意一点Q,称d(P,Q)的最小值为点P到直线l的“切比雪夫距离”,记作d(P,l).给出下列四个命题:①对任意三点A,B,C,都有
;②已知点P(3,1)和直线
,则
;③到原点的“切比雪夫距离”等于1的点的轨迹是正方形.其中正确的序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5579881e0d1530cc0a17cc5460acecb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efc72de5cceb54c6959af52491ca762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94922febcf02e84401ab8631890532df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0104da8625fcd6af63b19a37274a40.png)
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2023高三·全国·专题练习
2 . 已知
的面积为
,若
所对的三边分别为
,则
的最小值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68c1d20a422a363e356a160f096503c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3408fea2ea6b0013e271138827654ec8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d05a998f820239dea73572dc3d1884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d58e6afe3f5d81fa150e692444d1d5.png)
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2023高三·全国·专题练习
3 . 已知实数x,y,z满足:
,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ac09ffd9addc3dadf363152c3e39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470548d8f3a06c9c8b30d8e8a3ed738d.png)
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2023高三·全国·专题练习
4 . 因式分解 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a008fa154a09401a0bbf5213a63c8087.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a008fa154a09401a0bbf5213a63c8087.png)
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5 . 使得等式
成立的实数a的值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970c9e74426740893db5e390bacd35b8.png)
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6 . 若一个分数
(a,b均为正整数)化为小数后,小数部分出现了连续的“2020”,例如
,就称它为“好数”.则“好数”的分母的第二小的可能值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5260f366728ec86c56841944c4d65842.png)
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7 . 若
,则
的值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7a91e69eac781c4df9031b233cd1eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76844c76a3b73ba134118c1292757a8.png)
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8 . 英国数学家布鲁克泰勒通过研究发现了如下正、余弦公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ab08491d327ffd0cfabccb639e6030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c868fcf317426476af632cac3c028629.png)
其中
,
,
,例如:
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c510ee5e16312f9d01fb3e24cd28d8.png)
在
中,已知
,
弧度,
米,则BC的长约为_________ 米(精确到0.01米)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ab08491d327ffd0cfabccb639e6030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c868fcf317426476af632cac3c028629.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ef8db418ece9675eecd645717806ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306da3f46a4e2a78bb84727e26b5ea9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c510ee5e16312f9d01fb3e24cd28d8.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddda8bee262f17d51ee3d70cf63d6b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1cf0ae3ce752f851cceca482cbec31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71807a35b3170fce28ee6edf4c00d083.png)
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20-21高一上·广西南宁·阶段练习
9 . 分解因式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f25d0500b6a1a82b3a0f5b7b1be7bac.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f25d0500b6a1a82b3a0f5b7b1be7bac.png)
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10 . 把下列各式分解因式:
(1)x2-3x+2=________ ;
(2)x2+37x+36=________ ;
(3)(a-b)2+11(a-b)+28=________ ;
(4)4m2-12m+9=________ .
(1)x2-3x+2=
(2)x2+37x+36=
(3)(a-b)2+11(a-b)+28=
(4)4m2-12m+9=
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