1 . 平面
上三点的坐标分别是
.小林同学在点
处休息,进而小猫沿着
所在直线来回跑动,小猫离小林同学最近时的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad939769ee081dd5ecf86533c36f5eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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2024-05-27更新
|
147次组卷
|
2卷引用:上海市进才中学2023-2024学年高一下学期期中数学试题
名校
解题方法
2 . 已知点
,
,若点
满足
,则点
的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1e95fb519f59c46f40e4ab44660073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/444c5d393b85df77fc5c8ca43374cc5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4079b9c1702107192ed48da27fd117a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024-05-27更新
|
356次组卷
|
2卷引用:上海市进才中学2023-2024学年高一下学期期中数学试题
名校
解题方法
3 . 某同学用“五点法”画函数
在某一个周期内的图像时,列表并填入了部分数据,如下表:
(1)请直接写出表中
的值,并求出函数
的解析式和最小正周期;
(2)若关于
的方程
在
上有两个不同的实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0bfe1c23b5467382e6c2df68106e60.png)
0 | |||||
![]() | |||||
0 | 1 | 0 |
(1)请直接写出表中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae615b3edf7b6d7208c02acd74ced3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da008a98340a4940ca753902937a688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . 矩形
中,
,
,动点
满足
,
,则下列说法中正确的是______ .
①若
,则
的面积为定值 ②若
,则
的最小值为4
③若
,则满足
的点
不存在 ④若
,
,则
的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9545017eee79a71befee621b52c8cae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535964b59870f898bf1907ee5a3c56f8.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2753dc1c83d54044b89e628a7eb247f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95494fff79fac79913879645730eba57.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76819195cffab10d81638dd673f3af98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66790293bccf6d4410e38dbcfe41f770.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa2e529ffee0c5b492279f588cd5576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
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解题方法
5 .
是平面上一定点,
,
,
平面上不共线的三个点,动点
满足
,
,则
的轨迹一定通过
的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524d7ee6c3ba2d8b77358c7281137a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.外心 | B.内心 | C.重心 | D.垂心 |
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6 . 扇形
的半径为1,圆心角所对的
长为3,则该扇形的面积是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d372c99450c4fbbbb0f397e5ecb82c.png)
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7 . 已知函数
的图象如图所示,点
为
与
轴的交点,点
,
分别为
的最高点和最低点,而函数
在
处取得最小值.
的值;
(2)若
,求向量
与向量
的夹角;
(3)若点
为
函数图象上的动点,当点
在
,
之间运动时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f46cd4bd8b4bc46633ba802c58d93d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596ae4e312cb437c68101c5eb8406063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c98a7f3a8bf384b1dfc1d34aebd46d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab12359ab934c34ef538d26ba946001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f610645d18735fd3554cbd784d6ebc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/030dc33149ae86b07e6d913b7b3df078.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c1ad29ca45a2cb1d86f41d597a8d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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8 .
在
上的值域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c68e6d6050b1c7e427865c9696cd154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c6c37ce441a8ed77c8e3953e8fe1f.png)
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9 . 已知函数
在区间
有且仅有3个零点,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b33fff0def2be3a5ac4a46904173f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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10 . 在
中,角
、
、
的对边分别为
、
、
,
,则角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.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/c5db41a1f31d6baee7c69990811edb9f.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0a00261de17444279e81a872fb52d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9fabbbe61a759e52ec975215e2e7c.png)
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