名校
解题方法
1 . 已知
(
,
,
)的图象如图,则( )
![](https://img.xkw.com/dksih/QBM/2021/4/15/2700230200819712/2700257808252928/STEM/92f2fdd0-dc90-4fdd-877f-3a94704d4ce7.png?resizew=240)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5e2a383cb47eb87493e86c8c40caf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bccbff75027c4490ae472c2d7405e953.png)
![](https://img.xkw.com/dksih/QBM/2021/4/15/2700230200819712/2700257808252928/STEM/92f2fdd0-dc90-4fdd-877f-3a94704d4ce7.png?resizew=240)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2021-04-15更新
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3卷引用:百校联盟2021届高考复习全程精练模拟卷新高考(辽宁卷)数学(二)试题
2 . 在①
;②
的面积为
;③
这三个条件中任选一个,补充到下面的问题中,若问题中的三角形存在,求出
,若问题中三角形不存在,说明理由.
问题:
中内角
,
,
的对边分别为
,
,
,已知
,
,______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9be4380bdcef1c542604a6ad61642c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c337b7aaaf6fbc17283e0429f7b561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0577566dbcc526fb6f783491a4784902.png)
问题:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/79835bb7b07ad68c16af1f51f4516bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
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解题方法
3 . 椭圆
:
的左右焦点分别为
,
,过
且与
轴垂直的直线交椭圆于
,
两点,其中点
在第一象限,
,
.
(1)求椭圆
的标准方程;
(2)A为椭圆上顶点,过A引两条直线
,
,斜率分别为
,
,若
,
,
分别交椭圆另一点为
,
,求证:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58488d9c19d82a9d3741abef088a664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2644e9f73e5871db934fdafc431d675.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)A为椭圆上顶点,过A引两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b728c0e69820cdcd839e67ffdb1014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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4 . 已知
,
为双曲线
的左、右焦点,以
,
为直径的圆与双曲线在第一象限的交点为
,
,
,则双曲线的标准方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96f0155ccaa463d45dbdecda29b6636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd1f0eee7474e9dee3f112e7ef943f22.png)
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名校
5 . 已知函数
,
恰有四个不相等的实数根
,
,
,
且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8220382b7da945972fb57347614c2c41.png)
______ ;
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fb88378846d8e92cfc2ae713d7481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75faf121e3293a5d65a96e08db97675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3604274ad6707a906eba371a9e884144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8220382b7da945972fb57347614c2c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4342e4abbba8f8fb8bf7dca5f143dd83.png)
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2021-04-15更新
|
818次组卷
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2卷引用:百校联盟2021届高考复习全程精练模拟卷新高考(辽宁卷)数学(二)试题
6 . 新冠疫情期间,某省级示范学校统计高三年级走读生与寄宿生的学习状态,得如下表格,其中前200名定为优秀.
(1)是否有95%把握认为成绩优秀与是否寄宿有关;
(2)年级前10名中有寄宿生4人,现从这10人中随机选出3人去名校研学,选出的寄宿生人数记为
,写出
的分布列,并求
.
参考数据及公式:
.
优秀 | 非优秀 | 合计 | |
走读生 | 120 | 650 | 650 |
寄宿生 | 80 | 270 | 350 |
合计 | 200 | 800 | 1000 |
(2)年级前10名中有寄宿生4人,现从这10人中随机选出3人去名校研学,选出的寄宿生人数记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
![]() | 0.15 | 0.10 | 0.05 | 0.025 | 0.01 | 0.001 |
![]() | 2.072 | 2.706 | 3.841 | 5.024 | 6.635 | 10.828 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3821f70c08c5180e9b3086d3c9610f.png)
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7 . 已知数列
满足:
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11fd5ca18ee4f2d529f06ca7ec8e879f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50bd4d63c6ce2d1f4b6fde323462463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac326f9f4ad78d0053c113f823ea6d60.png)
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8 . 圆
:
与圆
:
交于
、
两点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232828303f062be7fdc8cff1cb4d24b5.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/f21b82181bf5d8655b7e818025ef86e9.png)
A.6 | B.5 | C.![]() | D.![]() |
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2021-04-15更新
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11卷引用:百校联盟2021届高考复习全程精练模拟卷新高考(辽宁卷)数学(二)试题
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9 . 已知
,
',若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8767d32dc7128a26bc3f61aace01fbab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d4d802eaa971a74d0ec3af38b80cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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解题方法
10 . 已知:对任意
,
恒成立
(1)求
的范围;
(2)证明:
.(参考数据:
,
,
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b155df33a4bcb95c57cd46187d63f24d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e063899064e3ce01c7117a131b61a137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8cfcfbd692fb51329bed98826d5bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43ff8e3167899f297bc0f1983c3d5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7888357d9ab75b4dc896db8e0107bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120d02fd2740c2f32cda05df801d412d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d707608aac4f1b08ee6b12102f4308c.png)
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