1 . 已知椭圆
,左、右顶点分别为P,Q,上顶点为K,原点为O,
的面积为
,两焦点与短轴的一个顶点构成等边三角形,过点
且斜率不为
的直线
与椭圆
交于不同的两点A,B.
(1)求椭圆
的标准方程;
(2)求
面积的最大值;
(3)直线PA与直线
交于点
,试问B,Q,
三点是否共线?若共线,请证明;若不共线,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306ff1069e500e89a9ffe9c7f18bd1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)直线PA与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2 . 已知函数
,若函数
恰有6个零点,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e205ba02c6f9795f0de51775cdd17b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d274a9a2bfafc648ec0e420a5777b9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-12-15更新
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3卷引用:天津市静海区第一中学2021-2022学年高三上学期第一次阶段检测数学试题
3 . 已知数列
为等差数列,数列
为等比数列,且
,
,
,
.
(1)求
,
的通项公式.
(2)已知
,求数列
的前2n项和
.
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f81b63fc0cffb75cc6aeae64591277c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a72a928a6bcde50c7e502669880892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c72dc9034f1aca2b4ef5afb4475c66.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdd37f8bb8b52db13ba5c48b878de23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5e7f98ec8f4ea9b9492405094c5380.png)
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2022-12-15更新
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6卷引用:天津市静海区第一中学2021-2022学年高三上学期第四次阶段检测数学试题
名校
解题方法
4 . 已知正实数a,b满足
,则
的最小值为___________ .
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d66a894fe1c8dddb41d9e4885e979a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c36723680999121c79ad8ee75d2b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b098834e9a4a77cb48ffcaa17858a8.png)
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3卷引用:天津市静海区第一中学2021-2022学年高三上学期第二次阶段检测数学试题
名校
5 . 设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c5c8af0f6d0a59247ed2f4ae1b90c2.png)
(1)若函数
在
上单调递增,求
的最小值.
(2)证明:当
时,
;
(3)若对于任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c5c8af0f6d0a59247ed2f4ae1b90c2.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468955192675ea33da77c042bb5664e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d74217631c5420650c5746bc9300e47b.png)
(3)若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08972617a44cef00eca0d4f98f4a383c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:天津市静海区第一中学2021-2022学年高三上学期第二次阶段检测数学试题
天津市静海区第一中学2021-2022学年高三上学期第二次阶段检测数学试题天津市实验中学2022-2023学年高三上学期第二阶段学习质量检测数学试题(已下线)江西省九所重点中学2023届高三第二次联考联合考试数学(文)试题变式题21-23
6 . 已知数列
是公差为2的等差数列,其前8项的和为64.数列
是公比大于0的等比数列,
,
.
(1)求数列
和
的通项公式;
(2)记
,求数列
的前
项和
;
(3)记
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4995fa0403e013d888c0935ebfe15024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd86fd3108963fbf87c75d504fa40cf.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9037368a39bb0bff26415939c77359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b9a0d7150fb24be3e28ef7f0e18be93.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cf77695058b0b8e6b8ac8fd090137d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2022-12-06更新
|
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7卷引用:天津市静海区第一中学2021-2022学年高三上学期第三次阶段检测数学试题
名校
解题方法
7 . 已知命题
是假命题.
(1)求实数
的取值集合
;
(2)设不等式
的解集为A,若
是
的必要不充分条件,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b8fc7707dd4583f3e221bb7bfbbc2a.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)设不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56878bb7b66cd8d85da45f6efd7fb8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-01-04更新
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16卷引用:天津市武清区英华国际学校2021-2022学年高一上学期第一次统练数学试题
天津市武清区英华国际学校2021-2022学年高一上学期第一次统练数学试题福建省福州外国语学校2021-2022学年高一10月月考学情评价一数学试题河南省开封市五县2021-2022学年高二上学期期中联考数学(理)试题辽宁省沈阳市东北育才双语学校2021-2022学年高一上学期期中数学试题广西桂林市逸仙中学2022-2023学年高一上学期10月月考数学试题河北省唐县第一中学2023-2024学年高一上学期第一次考试数学试题山东省青岛市青岛第五十八中学2023-2024学年高一上学期10月月考数学试题山东省实验中学2022-2023学年高一上学期期中数学试题浙江省杭师大附2022-2023学年高一上学期期中数学试题山东省郯城第二中学2022-2023学年高一上学期期末考试数学试题浙江省名校协作体2023-2024学年高二上学期开学适应性考试数学试题(已下线)2.3 二次函数与一元二次方程、不等式(精练)-《一隅三反》(已下线)高一上学期期中【易错60题考点专练】(必修一前三章)-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)第二章 一元二次函数、方程和不等式-单元速记·巧练(人教A版2019必修第一册)(已下线)专题02 一元二次函数、方程和不等式3-2024年高一数学寒假作业单元合订本(已下线)常用逻辑用语
名校
8 . 已知函数
.
(1)若
,讨论
的单调性;
(2)若
,
是
的极大值点.
①求实数a的取值范围;
②若存在实数
使得
成立,求b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898643e49e42b6289719d6e43372114b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①求实数a的取值范围;
②若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2af339f3ce60a4534d7e9dcbd0005f.png)
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名校
解题方法
9 . 如图,椭圆
(
)的离心率为
,其短轴和长轴的端点分别为A,B,C,D,且
.
![](https://img.xkw.com/dksih/QBM/2022/12/19/3134451182362624/3134861796286464/STEM/091444bd2e9448c28c13d8f0a112124e.png?resizew=511)
(1)求椭圆的方程;
(2)P是椭圆上位于x轴上方的动点,直线
,
与直线l:
分别交于G、H两点.若
,求点P的坐标;
(3)直线
,
分别与椭圆交于E,F两点,其中点
满足
且
.若
面积是
面积的5倍,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f371c0b1d573c06516ab1904d95ee49f.png)
![](https://img.xkw.com/dksih/QBM/2022/12/19/3134451182362624/3134861796286464/STEM/091444bd2e9448c28c13d8f0a112124e.png?resizew=511)
(1)求椭圆的方程;
(2)P是椭圆上位于x轴上方的动点,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e1e5a89003de4fda1dcf41565a9057.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba1b211aa0cb973622f3031462ad8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb14f5a795eb84d125e5f82e73fdbb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918db766afc11101b1e4584fcf6881f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f7c63d03656e40f914486ddf22de4.png)
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2022-12-20更新
|
378次组卷
|
2卷引用:天津市第四十七中学2021-2022学年高二上学期第二次月考数学试题
名校
解题方法
10 . 如图,在三棱锥
中,
底面
,
,点
分别为棱
的中点,
是线段
的中点,
.
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)已知点
在棱
上,且直线
与直线
所成角的余弦值为
,求线段AH的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b9a4cf42189f9ef786b3c549ecd93e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daffd3935e47228b252568a886df769c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4627df8ec5432214e7e9bda4ef87b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0701f67727b0fc8100cfb5e20ec27d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6221be113e161825e54d48a2fb16d516.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef1f7b9adab87736321e30949a4d668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e468f168f3657d84d44be5eb89a62d8.png)
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2022-11-06更新
|
1170次组卷
|
9卷引用:天津市南开中学2021-2022学年高三上学期第二次月考数学试题