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1 . 在
中,
、
、
的对边分别为a、b、c,若
、
、
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb1606f91a55ec822fa19b28c441b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284e282bb1d9fbf8634b3506ee5358ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d39e8c6fc9149d6290c493a65bdc53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
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2024-04-07更新
|
299次组卷
|
2卷引用:天津市滨海新区田家炳中学2023-2024学年高一下学期第一次月考数学试题
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2 . 已知:向量
,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
______ ,此时![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d33ee1f52775bf9ba66e0fdf0ecbb35.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d769ab21af5365d3c00dc617375ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa19624a4f60481a476a995391d0878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d33ee1f52775bf9ba66e0fdf0ecbb35.png)
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解题方法
3 . 已知:点
和向量
,若
,则点B的坐标是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc9aa334c8a364cbc597127d60b2b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ef4988b025cdf296ea81d7ef05f404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17178285fc30b77c846391467d3b0348.png)
您最近一年使用:0次
2024-03-27更新
|
266次组卷
|
3卷引用:天津市滨海新区田家炳中学2023-2024学年高一下学期第一次月考数学试题
天津市滨海新区田家炳中学2023-2024学年高一下学期第一次月考数学试题山东省泰安市泰山国际学校2023-2024学年高一下学期3月月考数学试题(已下线)第二章平面向量及其应用章末十六种常考题型归类(1)-【帮课堂】(北师大版2019必修第二册)
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解题方法
4 . 已知
,
,则
与
的夹角为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3f5a708574ca78631988b5c00cae76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3694b22f0466d64cb2eb482adfddc246.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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2024-03-27更新
|
503次组卷
|
3卷引用:天津市滨海新区田家炳中学2023-2024学年高一下学期第一次月考数学试题
名校
解题方法
5 . 已知向量
,
,
,若B,C,D三点共线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55fcd6e54fa0ff9436cc514945d4a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc14d5a5f428add123b6a2aa07fc192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0ff7f373dac36cf1333729ae2f562f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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2024-03-27更新
|
801次组卷
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3卷引用:天津市滨海新区田家炳中学2023-2024学年高一下学期第一次月考数学试题
6 . 已知函数
.
(ⅰ)函数
的定义域为______ ;
(ⅱ)若
是斜三角形的一个内角,则使不等式
成立的
的集合为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c111ae39998037ad9c2eef5a892b3e6.png)
(ⅰ)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2aeda5c6f101566159dd4c460b943b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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7 . 已知集合
或
,
,其中
.
(ⅰ)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e60375f97ff7854f4d3a8b1108d2e3.png)
______ ;
(ⅱ)若
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6036b5f9fcc6f245ee1f0ff218839f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa3022e7435b36f3b4b088d0820a700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88592a427b6845d3d4c821218b3e2171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e60375f97ff7854f4d3a8b1108d2e3.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b05d2be27e8f53e4de3071846dffb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 2023年10月26日神舟十七号载人飞船在长征二号F遥十七运载火箭的托举下点火升空,成功进入预定轨道.我国在航天领域取得的巨大成就,得益于我国先进的运载火箭技术.根据火箭理想速度公式
,可以计算理想状态下火箭的最大速度
,其中
是喷流相对速度,
是火箭(除推进剂外)的质量,
是推进剂与火箭质量的总和,
称为总质比.已知甲型火箭喷流相对速度为
.
(ⅰ)当总质比为9时,甲型火箭的最大速度为______
;
(ⅱ)若经过材料更新和技术改进后,甲型火箭的喷流相对速度提高到原来的
倍,总质比变为原来的
.若要使火箭的最大速度至少增加
,则在材料更新和技术改进前总质比的最小值为______ .
(所有结果保留整数,参考数据:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801fb850c497a5e833e8c4b7c6035f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e90016eded560b57a129f28d03aee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df0e5de30429c62a5febe61fe45ef24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebee00d8ff03814d153038706ebd7943.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7524718b9f699c26c3ff742bfc8675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467f61f8d38c71fcb30f3f16d88650d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc73529ef6d4431646ca0bdbca09f608.png)
(ⅰ)当总质比为9时,甲型火箭的最大速度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22964de2a093c97a8755dbe70487735e.png)
(ⅱ)若经过材料更新和技术改进后,甲型火箭的喷流相对速度提高到原来的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4836d554eed2e9b666ba934090c2bd77.png)
(所有结果保留整数,参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50101047632b94dcd5cf8035b093cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afc32b1084af96113b5cd239607d8ce.png)
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9 . 已知
,
,则用
,
表示![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40da37f9dc8f3e3b5790e9d67da1be15.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a08a2a5540efcdb5a77aa4ea3049884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850df3e299d9b1ecbda7e3a59e2a255e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40da37f9dc8f3e3b5790e9d67da1be15.png)
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10 . 命题“
,
”的否定是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8645952ea14b25443f411d39bdec641e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072c300a8d75385dbe53caeb2514fa00.png)
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