名校
1 . 已知函数
,若
是偶函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
__________ ;若圆面
恰好覆盖
图象的最高点或最低点共3个,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69f724f57925d84d4dc5a29d6474491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac624f921a4282e16b160384c47414d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次
2024-06-10更新
|
371次组卷
|
2卷引用:北京市中国人民大学附属中学2024届高三下学期5月热身练习数学试题(三模)
名校
解题方法
2 . 数学上的符号函数可以返回一个整型变量,用来指出参数的正负号,一般用
来表示,其解析式为
.已知函数
,给出下列结论:
①函数
的最小正周期为
;
②函数
的单调递增区间为
;
③函数
的对称中心为
;
④在
上函数
的零点个数为4.
其中正确结论的序号是____________ .(写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165d88ea5812bd14de49f5e3436eefad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a3bd54753e4c1a5fc06b414cc44ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d436e42ddbacbbd0af82f0e4750e54.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d56bab4fdb876bd72d5c9c7a734375.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5760e7c1da0c80f6b8912406b6b75c.png)
④在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb66add53686f989fbbb057652cb6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3077b0cfb8a47439afc656af6cc889ad.png)
其中正确结论的序号是
您最近一年使用:0次
名校
解题方法
3 . 已知向量
的夹角为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd8759a145547dbc5a95b372b5dd1f6.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/260200d547998bcac50a4a491382e7f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2850eea313be74c7208c60e9f257b357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd8759a145547dbc5a95b372b5dd1f6.png)
您最近一年使用:0次
4 . 已知函数
,且
.若两个不等的实数
满足
且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98df89690f652e7e89234466359bdc6.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe384eeccf4e3e198ebd1c10a9fe3d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66a8a9a00283050c96e2c8bcc1b21902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4838931562c2c74740ad378c3fb9b95b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6efc9d3d7790cbc990483cbe23d9ef50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98df89690f652e7e89234466359bdc6.png)
您最近一年使用:0次
名校
解题方法
5 . 已知向量
,
在
上的投影向量为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6fce004c47849c29ebd8d5d7c16e98.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22238115ca80d3911e87b7b992817f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cdfd82868aefda05f52913dfd762a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fe104fd11503cee654020a008e646a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6fce004c47849c29ebd8d5d7c16e98.png)
您最近一年使用:0次
2024高一下·上海·专题练习
名校
解题方法
6 . 已知
均为单位向量,且
,则
与
的夹角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db69ec248c9382eb087b25facfd6a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb667795acdfafa436ee35e152adbc4.png)
您最近一年使用:0次
名校
7 . 已知函数
的图象如图,点
,
在
的图象上,过
,
分别作
轴的垂线,垂足分别为
,
,若四边形
为平行四边形,且面积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdb3c1503af61ac7ec3b75bce03c908.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98469d60fd56fd3091290302fbeb3c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385ed0dbb1909ac5b6223c7f5e6df86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ca334d2ae1289b70941e6af9e336a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afdb3c1503af61ac7ec3b75bce03c908.png)
您最近一年使用:0次
名校
解题方法
8 . 下图是第19届杭州亚运会的会徽“潮涌”,可将其视为一扇环ABCD.已知
,
.且该扇环
的面积为
,若将该扇环作为侧面围成一圆台,则该圆台的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed081abe2926ff6153cca8fe590f26f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e95a79288fcb7e47fba4410722e2bc6.png)
您最近一年使用:0次
名校
解题方法
9 . 设
,
,
,若满足条件的
与
存在且唯一,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
_______ , ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8640aafe54018ba013295b68e2946a7a.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28a96ee1e62b7fbc1fb0257ad0deeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd61d59ee2dc6cc43b25b7ee39ca58d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243288f8315e8ea94bda2ec3fec6a984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8640aafe54018ba013295b68e2946a7a.png)
您最近一年使用:0次
名校
解题方法
10 . 已知
中,
,
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808382ba1d893826a026d85e0cd67609.png)
_________ ;若
,当
最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c95c6fedd33a4a8b2d25c4a2bd8d077.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dfe8aa4868de1181b5263f7a1ed995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f0877d52e0b256d24f1877c4f1d3dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d9e6ae2b22b22796fc2b4a648ae65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808382ba1d893826a026d85e0cd67609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2b622913dfd7d0c099db3bdfed61d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22df2977de56cc69be0c1e847653d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c95c6fedd33a4a8b2d25c4a2bd8d077.png)
您最近一年使用:0次