名校
1 . 已知抛物线
为第一象限内
上任意一点,以
为切点作
的切线
与
轴交于点
,与
轴交于点
,过点
作垂直于
的直线
交
于
两点,其中点
在第一象限,设
与
轴交于点
.
(1)若点
的坐标为
,求切线
的方程;
(2)若
,求
的值;
(3)当
时,连接
,记
的面积分别为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4498a6eea5157b692de2c3ff77320d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441f75e926cf159eee619685312bb4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e81a1e6338c6da07a6e8dfaafdffb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7a95ad057dc0d06ab143b1282fbb56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9c48b75c90321b2051f20ac5e788ae.png)
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名校
解题方法
2 . 在直角坐标系中,绕原点将
轴的正半轴逆时针旋转角
交单位圆于
点、顺时针旋转角
交单位圆于
点,若
点的纵坐标为
,且
的面积为
,则
点的纵坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9558de44a388c3ae60833c42a6d21374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c5f94443d221e01555765ab9ea6996c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5756451881af4d6594c820652ebcc2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-11更新
|
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5卷引用:甘肃省白银市靖远县第一中学2024届高三下学期模拟预测数学试题
3 . 已知正方形
的边长为
,两个点
,
(两点不重合)都在直线
的同侧(但
,
与
在直线
的异侧),
,
关于直线
对称,若
,则
面积的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134c3d2c318a33a82da4134dd17fa57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.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/10109d34ef06c3e721fd2c7128c5b9ca.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7393358bb94b0df78fd4e29223257e1.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/902f97913e1af1e6c793f7edfe6b2114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6315136b2449842c9894529e25e3b445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9a99e6336047697901dd4a330ed634.png)
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2024-06-11更新
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4卷引用:甘肃省白银市靖远县第一中学2024届高三下学期模拟预测数学试题
名校
解题方法
4 . 已知函数
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f66bd602858b6b31b0888a69740099.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若对任意实数![]() ![]() ![]() ![]() |
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2024-06-11更新
|
627次组卷
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2卷引用:甘肃省白银市靖远县第一中学2024届高三下学期模拟预测数学试题
5 . 复数
的实部与虚部之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93855503890990278ea609b41b73ff93.png)
A.![]() | B.![]() | C.8 | D.6 |
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解题方法
6 . 人工智能发展迅猛,在各个行业都有应用.某地图软件接入了大语言模型后,可以为用户提供更个性化的服务,某用户提出:“请统计我早上开车从家到公司的红灯等待时间,并形成统计表.”地图软件就将他最近100次从家到公司的导航过程中的红灯等待时间详细统计出来,将数据分成了
,
,
,
,
(单位:秒)这5组,并整理得到频率分布直方图,如图所示.
(2)估计该用户红灯等待时间的中位数(结果精确到0.1);
(3)根据以上数据,估计该用户在接下来的10次早上从家到公司的出行中,红灯等待时间低于85秒的次数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ea59cdd39c1e893fb609d05f86ded7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56f3ccfe5a0b479ce64640a30b46520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc20387d18997336f432f9d6e81b560e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29efcdaa3eb04c3d96c0b87f57aa2903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88647001f30cdc14ba03d19ffe52ca0.png)
(2)估计该用户红灯等待时间的中位数(结果精确到0.1);
(3)根据以上数据,估计该用户在接下来的10次早上从家到公司的出行中,红灯等待时间低于85秒的次数.
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2024-06-06更新
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1837次组卷
|
4卷引用:甘肃省白银市2023-2024学年高一下学期5月阶段性检测数学试题
甘肃省白银市2023-2024学年高一下学期5月阶段性检测数学试题(已下线)专题14.1统计(1))--重难点突破及混淆易错规避(苏教版2019必修第二册)广东省四会中学、广信中学2023-2024学年高一下学期第二次月考数学试题(已下线)专题05 第九章 统计-期末考点大串讲(人教A版2019必修第二册)
7 . 如图,在△ABC中,
,
,其中
,CP的延长线与AB交于点F.已知
,
,
.
,请用向量
,
表示向量
,并求
的值;
(2)若
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64f1d0b5e4a6ebf4405b98a21a1ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23b8ba897a7bbf4a9c0c3d6f6ecd89f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d2919e5bd26b5e9be672a3ff7604cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7ce899eaa74017eda8a8f3903c943e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0226b54b8c18c97505c9e2d8eeef2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1371fe98a65d8ebd840c8d98346b6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7239b3f2d88c2e45e17e5de9ae1a332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187634c24754b576ae8293665f45f89b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1795d8255d1235d98159322d4b0cda5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd0ae3147ba748cafdac6c00ae77c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04af7d85462fc4f519090d5cbb8ae61.png)
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名校
解题方法
8 . 已知
的内角A,B,C的对边分别为a,b,c,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f46c7f89428617ae644d3521800b5ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ca634c6de8b034f395a2d452d152024.png)
A.充要条件 | B.充分不必要条件 |
C.必要不充分条件 | D.既不充分也不必要条件 |
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|
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|
2卷引用:甘肃省白银市2023-2024学年高一下学期5月阶段性检测数学试题
名校
解题方法
9 . 若函数
有2个零点,则m的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94dadacc20558af802e1f7a204b6d05.png)
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2卷引用:甘肃省白银市2023-2024学年高一下学期5月阶段性检测数学试题
名校
解题方法
10 . 已知函数
.
(1)证明:
的定义域与值域相同.
(2)若
,
,
,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fae876092b09e59fba7a55aee637b76.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796544207152c2e3ab7b9a82c750c48a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948a984f88914c7143a1d8e35f0d974b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253613b33837c169202b1e6c5c706b56.png)
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|
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