名校
1 . 《见微知著》谈到:从一个简单的经典问题出发,从特殊到一般,由简单到复杂:从部分到整体,由低维到高维,知识与方法上的类比是探索发展的重要途径,是思想阀门发现新问题、新结论的重要方法,
阅读材料一:利用整体思想解题,运用代数式的恒等变形,使不少依照常规思路难以解决的问题找到简便解决方法,常用的途径有:(1)整体观察;(2)整体设元;(3)整体代入:(4)整体求和等.
例如,
,求证:
.
证明:原式
.
波利亚在《怎样解题》中指出:“当你找到第一个藤菇或作出第一个发现后,再四处看看,他们总是成群生长”类似问题,我们有更多的式子满足以上特征.
请根据阅读材料解答下列问题
(1)已知如
,求
___________.
(2)若
,解方程
.
(3)若正数
、
满足
,求
的最小值.
阅读材料一:利用整体思想解题,运用代数式的恒等变形,使不少依照常规思路难以解决的问题找到简便解决方法,常用的途径有:(1)整体观察;(2)整体设元;(3)整体代入:(4)整体求和等.
例如,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2764ccd2cfe6de0c53dce98e45b120.png)
证明:原式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87898da3367d13667477a10c9cc47ac2.png)
波利亚在《怎样解题》中指出:“当你找到第一个藤菇或作出第一个发现后,再四处看看,他们总是成群生长”类似问题,我们有更多的式子满足以上特征.
请根据阅读材料解答下列问题
(1)已知如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1440907008dbc815bd37e30cb09e8a6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9093a255130a938a4d84595c0c56ce.png)
(3)若正数
![](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/ca27cc54ca0332245f5167488daa3408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab1cbf887eca130c254f6e0cf3fdb2f.png)
您最近一年使用:0次
2023-10-17更新
|
230次组卷
|
2卷引用:贵州省贵阳市清镇市博雅实验学校2023-2024学年高一上学期第三次月考数学试卷
名校
解题方法
2 . 如图,四棱锥P-ABCD的底面ABCD是菱形,PA⊥AB,PA⊥AD,且E、F分别是AC、PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/69dda575-4b41-45c5-935a-6aa6fca009ce.png?resizew=160)
(1)证明:EF∥平面PCD;
(2)求证:平面PBD⊥平面PAC.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/69dda575-4b41-45c5-935a-6aa6fca009ce.png?resizew=160)
(1)证明:EF∥平面PCD;
(2)求证:平面PBD⊥平面PAC.
您最近一年使用:0次
2022-04-26更新
|
1074次组卷
|
3卷引用:贵州省遵义市桐梓县荣兴高级中学2023-2024学年高二上学期第三次月考数学试题
3 . (1)已知
是实数,求证:
.
(2)用分析法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d21cedbf84856328405de3bf6275ba.png)
(2)用分析法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c19d94ff48082c1cd213c82c99abf0.png)
您最近一年使用:0次
2020-08-04更新
|
107次组卷
|
10卷引用:贵州省兴仁市凤凰中学2019-2020学年高二下学期第一次月考数学(理)试题
贵州省兴仁市凤凰中学2019-2020学年高二下学期第一次月考数学(理)试题贵州省兴仁市凤凰中学2019-2020学年高二下学期第一次月考数学(文)试题江西省山江湖协作体2019-2020学年高二上学期第三次月考(统招班)数学(文)试题安徽省淮南一中2020-2021学年高二下学期第一次段考理科数学试题山西省怀仁市大地学校2020-2021学年高二下学期第三次月考数学(理)试题山西省怀仁市大地学校2020-2021学年高二下学期第三次月考数学(文)试题安徽省蚌埠二中2019-2020学年高二下学期开学检测文科数学试题(已下线)专题23 不等式选讲-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)专题23 不等式选讲-2020年高考数学(文)母题题源解密(全国Ⅲ专版)(已下线)2.2.1 直接证明-2020-2021学年高二数学(理)课时同步练(人教A版选修2-2)
14-15高三上·贵州遵义·阶段练习
4 . 如图,在直三棱柱
中,
,且
.
(1)求证:平面
⊥平面
;
(2)设
是
的中点,判断并证明在线段
上是否存在点
,使
‖平面
;若存在,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aba147ef7f44248b5002cebebc6644e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9007977155e06426eb6983775e0839af.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://img.xkw.com/dksih/QBM/2014/8/6/1571835590991872/1571835596881920/STEM/c93d1b395e744070af56f2a489e9df65.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2093e4e0580dd53e3d25769d05ab9f9c.png)
![](https://img.xkw.com/dksih/QBM/2014/8/6/1571835590991872/1571835596881920/STEM/881f511785094ef5aecbc3894e8afaa3.png)
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14-15高三上·贵州遵义·阶段练习
5 . 已知函数
.
(1)若曲线
在
处的切线为
,求
的值;
(2)设![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3d3eea81768840109f218466174f7983.png)
,
,证明:当
时,
的图象始终在
的图象的下方;
(3)当
时,设
,(
为自然对数的底数),
表示
导函数,求证:对于曲线
上的不同两点
,
,
,存在唯一的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
,使直线
的斜率等于
.
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/1b4c32a0cfb14de8bc6a26a54311fedd.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6513e7d1ad16ed0ba54da88b098dc1d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3d3eea81768840109f218466174f7983.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/136995a0dea24df88860330a01092f62.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/9d2148a4da27426cbc7db6e777e7a69c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/8df1a95edcd34a89b926fc168f2aa20d.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/df61580512c44e8691de8efbd7e5053c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/fea3e068dd124c0ca98cbceba9b3347f.png)
(3)当
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/d6b34f6dada044619914cecb62849103.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/76a965da5b87446a9308156fdaaf7d8b.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/3865acfd7def4e79b7d712d720b9c02c.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/52b6a1f9256449b882a840dfa9462d64.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/2ec2086f962d4e64be08cb307f6d031b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5300f2d0cdf34de189a6be1b518891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631f75b2df538cc121bad64d9deb774d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2015/1/12/1571959319609344/1571959325589504/STEM/e89b836c01ae46a68c19ed11ecb9cf6e.png)
您最近一年使用:0次
13-14高二上·湖北武汉·期中
名校
6 . 如图,在三棱锥S-ABC中,BC⊥平面SAC,AD⊥SC.
(Ⅰ)求证:AD⊥平面SBC;
(Ⅱ)试在SB上找一点E,使得平面ABS⊥平面ADE,并证明你的结论.
您最近一年使用:0次
2013·海南海口·二模
7 . 切线
与圆切于点
,圆内有一点
满足
,
的平分线
交圆于
,
,延长
交圆于
,延长
交圆于
,连接
.
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571400889901056/1571400896045056/STEM/cc90bcdfe8cb46ea88822b7ed471dbc9.png)
(Ⅰ)证明:
//
;
(Ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27f7309808e0c517168a2291cceee3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571400889901056/1571400896045056/STEM/cc90bcdfe8cb46ea88822b7ed471dbc9.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
(Ⅱ)求证:
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571400889901056/1571400896045056/STEM/27722750bb10488a97f33f51a063a9d9.png)
您最近一年使用:0次
名校
8 . 如图所示,四棱锥
底面
为矩形,且
,
分别为
的中点,点
为线段
上靠近点
的三等分点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/d48177e5-c273-42ae-857f-c2cfa69fee43.png?resizew=183)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)当
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a022a267cc64a3289317ef88494ae9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1a062aa55781bec93f54d85eaff8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/d48177e5-c273-42ae-857f-c2cfa69fee43.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0cbbcc3d79bf999588882e7b1b4324.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e267d11d17f33c2bcf3b6b1d4b55a5de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12b929019ca5c2a922a019e3f42b5e5.png)
您最近一年使用:0次
2024-01-02更新
|
387次组卷
|
2卷引用:贵州省贵阳市第一中学2024届高三上学期高考适应性月考(三)(11月)数学试卷
9 . 如图,在直角梯形
中,
,
,且
,现以
为一边向形外作正方形
,然后沿边
将正方形
翻折,使平面
与平面
互相垂直.
(1)求证:平面
平面
;
(2)求点
到平面
的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0046177466c78f08d45449dc5639bf38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/ed66e110-9d08-4051-bf6b-19e3241c7fa6.png?resizew=383)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
您最近一年使用:0次
解题方法
10 . 如图,在四棱锥
中,
平面ABCD,四边形ABCD是直角梯形,
,
,
,直线PB与平面ABCD所成的角为
,E是棱PD的中点.
(1)求证:平面
平面PCD;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88c0a7c459f1bab0b84cbb1cd935ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/426c502d-b785-4ce5-95cd-47b25dddb324.png?resizew=181)
(1)求证:平面
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(2)求二面角
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2023-11-27更新
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3卷引用:贵州省部分中学2024届高三上学期第四次月考数学试题