解题方法
1 . 已知椭圆
过点
,离心率为
.
![](https://img.xkw.com/dksih/QBM/2022/1/22/2899774921129984/2909124976984064/STEM/12edb5da-9f0e-4a27-82d9-6bee0b2e1ae9.png?resizew=150)
(1)求椭圆的标准方程;
(2)过椭圆的上顶点作直线l交抛物线
于A,B两点,O为坐标原点.
①求证:
;
②设OA,OB分别与椭圆相交于C,D两点,过点O作直线CD的垂线OH,垂足为H,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4ca616e225686a236f7c2db3e16dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb7c44fbd558182e05b1f82e4c337c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://img.xkw.com/dksih/QBM/2022/1/22/2899774921129984/2909124976984064/STEM/12edb5da-9f0e-4a27-82d9-6bee0b2e1ae9.png?resizew=150)
(1)求椭圆的标准方程;
(2)过椭圆的上顶点作直线l交抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
②设OA,OB分别与椭圆相交于C,D两点,过点O作直线CD的垂线OH,垂足为H,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33a489fa920ff269b00784034def90a.png)
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解题方法
2 . 已知函数
满足下列条件:
①
,
,
;
②对任意
、
,都有
;
③当
时,
;当
时,
.
试解决下列问题:
(1)求证:当
时,
;
(2)判断
在
上的单调性,并给出证明;
(3)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f247866d4020ed309d4e4d121ce445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e8d83d513071a98b64427deb4e30ce.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cccdff49c3efe6e7a7dbbf69db9319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e25584d1b6fb628bfc6f8e1d024c1c8.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d5a0e25aebe1cc182d2247ed344652.png)
试解决下列问题:
(1)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3df50b5d7f4a2c4f343780e0cd1588c.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1402a79a993757d8b8323cb3fe23428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
3 . 如图,
是圆
的直径,点
是圆
上异于
的点,直线
平面
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/f7673e33-3c9c-4190-bb73-09d2d988c7ed.png?resizew=154)
(1)记平面
与平面
的交线为
,试判断直线
与平面
的位置关系,并加以证明;
(2)设(1)中的直线
与圆
的另一个交点为
,且点
满足
.记直线
与平面
所成的角为
,异面直线
与
所成的角为
,二面角
的大小为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1443bfe022f648f813fb1e15b2d78b6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/f7673e33-3c9c-4190-bb73-09d2d988c7ed.png?resizew=154)
(1)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)设(1)中的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd392c9dae5132e0f17c5520dc787e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c171ec70d3220e84f5bd7bd391b0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd506c8ce8db557d4808388b780f9d6.png)
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4 . 已知函数
,
.
(1)当
时,证明
;
(2)当
时,对于两个不相等的实数
、
有
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e8fac584f94d8e561b232404558573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b489414956363d8f61b115c198f88915.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.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/2037b0bad7c7a312bac1ac0653d9a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475c9073257b3d0760e2c6051a82d592.png)
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名校
5 . 用反证法证明命题①:“已知
,求证:
”时,可假设“
”;命题②:“若
,则
或
”时,可假设“
或
”.以下结论正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937559aeec06323cde8861b17024fc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be100015cff38b6dfba5080fa94d128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44dcfbe7130c760acae3703469dd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2053e1f50472a9fed67d4c84d9cb938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc335ee14fc0b1130900cb82bcb3061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d09b9fc9719ff6faf32254b9d48713.png)
A.①与②的假设都错误 | B.①与②的假设都正确 |
C.①的假设正确,②的假设错误 | D.①的假设错误,②的假设正确 |
您最近一年使用:0次
2018-07-12更新
|
761次组卷
|
9卷引用:安徽省宣城市郎溪中学2020-2021学年高二下学期第一次月考理科数学试题
安徽省宣城市郎溪中学2020-2021学年高二下学期第一次月考理科数学试题【全国市级联考】福建省三明市2017-2018学年高二下学期期末考试数学(文)试题湖北省咸宁市2018-2019学年高二下学期期末数学(文)试题黑龙江省大庆实验中学2021届高三得分训练(二)数学(理)试题四川省仁寿第一中学校北校区2020-2021学年高二6月期末数学(文)试题广西河池市九校2020-2021学年高二下学期第二次联考数学(理)试题(已下线)考点43 直接证明与间接证明-备战2022年高考数学(理)一轮复习考点微专题(已下线)数学(上海B卷)河南省灵宝市第五高级中学2021-2022学年高二下学期第一次月考数学文科试题
6 . 在数列
中,已知
,且
.
(1)用数学归纳法证明:
;
(2)求证
.
![](https://img.xkw.com/dksih/QBM/2015/7/6/1572165697462272/1572165702983680/STEM/04a2c8fe43bd449b94f647b90775b88d.png)
![](https://img.xkw.com/dksih/QBM/2015/7/6/1572165697462272/1572165702983680/STEM/28d4f450063e4d898ed0855ed9177d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa95682a54b38ee787a86498d2175c5.png)
(1)用数学归纳法证明:
![](https://img.xkw.com/dksih/QBM/2015/7/6/1572165697462272/1572165702983680/STEM/36877c228c1b42c9b8acbd33d2619fea.png)
(2)求证
![](https://img.xkw.com/dksih/QBM/2015/7/6/1572165697462272/1572165702983680/STEM/4b88960493b44c12a787e5e3a86b09e3.png)
您最近一年使用:0次
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7 . 如图,圆内接四边形ABCD中,G为对角线AC、BD的交点,过点D作
交AC于E,且
,F在线段GD上,且
,连接CF.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/4bd1187a-ba53-4a8b-9c6f-9dcef6fc6fb6.png?resizew=170)
(1)求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe7eaf967808dad0a184eeedfa27721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c16639200620d92e1a8c228b581dc57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7953310f793ba2a127772d593b41aff0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/4bd1187a-ba53-4a8b-9c6f-9dcef6fc6fb6.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f1b8f2d3052769ed15da4dcdaad203.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb4a99e41e4a30238de487e733e01ef.png)
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解题方法
8 . 如图,在直三棱柱
中,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/dceb8774-c9bc-4811-86ba-02d05ab18f5e.png?resizew=158)
(1)求证:
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5442ad21d42dbdd92d9aac9330edcfcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/dceb8774-c9bc-4811-86ba-02d05ab18f5e.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896e293411e2fd0da215ff20781cb36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
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9 . 如图,在五面体
中,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ce9e33b060a1feff58a7771698c1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/001846c1-663e-46f8-8aaf-c0dc2752787e.png?resizew=153)
(1)求证:平面
平面
;
(2)线段
上是否存在一点
,使得平面
与平面
夹角的余弦值等于
,若存在,求
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ce9e33b060a1feff58a7771698c1ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d05426a41ec7b22c0445bfe78d786c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7422660f0635be92e11838af5f4b4b5e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/001846c1-663e-46f8-8aaf-c0dc2752787e.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d4548c32861ade058b139a5b2ec801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72acf5ee54c89dede4358c61ecd7a101.png)
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解题方法
10 . 已知
分别是椭圆
的左、右焦点,
是椭圆
上的一点,当
时,
.
(1)求椭圆
的方程;
(2)记椭圆
的上下顶点分别为
,过点
且斜率为
的直线
与椭圆
交于
两点,证明:直线
与
的交点
在定直线上,并求出该定直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2377ea22862dee84fcd0038858de4dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/f434c9d1e243f90bd9c5eac037017802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5091d6fe81cfa32af60c5c266bcfec2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e705301752424a492f6277ed7774e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2024-02-16更新
|
174次组卷
|
2卷引用:安徽省宣城市2023-2024学年高二上学期1月期末考试数学试卷