名校
解题方法
1 . 已知
均为实数.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eee188b2a8c3a2a8a0ffbdb1037aee4.png)
;
(2)若
,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eee188b2a8c3a2a8a0ffbdb1037aee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2139582631c4b9e01433e86a1fcdf15f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89dc8118d95d6c7bd5b7d38667a498e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fae565df8b59b23e54b8076daf82756.png)
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2 . 如图所示,在四棱锥P-ABCD中,底面ABCD是边长为a的正方形,侧面
底面ABCD,且
,若E,F分别为PC,BD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/b473e904-1e8f-471d-9119-293dad237ee3.jpg?resizew=188)
(I)求证:EF//平面PAD;
(II)求三棱锥F-DEC的体积;
(III)在线段CD上是否存在一点G,使得平面
平面PDC?若存在,请说明其位置,并加以证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b7201f9eb7e7c10042c096e0c9f15c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/b473e904-1e8f-471d-9119-293dad237ee3.jpg?resizew=188)
(I)求证:EF//平面PAD;
(II)求三棱锥F-DEC的体积;
(III)在线段CD上是否存在一点G,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5394d00a80a5900d7fd7d9961868bd22.png)
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3 . 已知递增数列
的前
项和为
,且满足
,
.
(1)求证:数列
为等差数列;
(2)试求所有的正整数
,使得
为整数;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b50924b095b150187e33b96ef2f1a80d.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)试求所有的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3644a9e687b6447f961dab6e49e37c3e.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01e345a8629e25e3de6324e432c6166.png)
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4 . 如图,已知棱柱
的底面是菱形,且
面ABCD,
,F为棱
的中点,M为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/7e407635-3100-43bd-a36a-08e65207cf2a.png?resizew=189)
(1)求证:
面ABCD;
(2)判断直线MF与平面
的位置关系,并证明你的结论;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1513b119d8c0cd29e0682350c79fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/7e407635-3100-43bd-a36a-08e65207cf2a.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7db6f84e9bf0a9ddbb47a6a1761607.png)
(2)判断直线MF与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce52a3a64b0cdcad86e979d31dc89536.png)
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2020-01-31更新
|
121次组卷
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3卷引用:重庆市北碚区2019-2020学年高二上学期期末数学试题
5 . 设等比数列
的最n项和
,首项
,公比
.
(1)证明:
;
(2)若数列
满足
,
,求数列
的通项公式;
(3)若
,记
,数列
的前项和为
,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e86d6e063e5eb63549db69c59d59813.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede7367099b2a4ffce48ae4ae240de3b.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a81749efea2e46b681adcfd187548e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ba223c5329c3e688cddad1e52fd46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107ab533d39b3bd0933429156ff33bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebdf072477557ad3dbc7acfa8088436d.png)
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名校
6 . 已知抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97afdeaa1d4433cffe5005446fcbbbb.png)
,过焦点F的直线l与抛物线交于S,T,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/11c4f48f-a06f-431f-8779-6966df187d6e.png?resizew=187)
(1)求抛物线C的方程;
(2)设点P是x轴下方(不含x轴)一点,抛物线C上存在不同的两点A,B满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203f6ea7bd3319d450fd957137942573.png)
,其中
为常数,且两点D,E均在C上,弦AB的中点为M.
①若点P坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb3d32f46af3841f098c82e30ec1462.png)
,抛物线过点A,B的切线的交点为N,证明:点N在直线MP上;
②若直线PM交抛物线于点Q,求证;
为定值(定值用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97afdeaa1d4433cffe5005446fcbbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75ed10db4b9747a4b6d865b774f6b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3405289647ead6ef2e86bc2e29a29b2d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/11c4f48f-a06f-431f-8779-6966df187d6e.png?resizew=187)
(1)求抛物线C的方程;
(2)设点P是x轴下方(不含x轴)一点,抛物线C上存在不同的两点A,B满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/203f6ea7bd3319d450fd957137942573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c306bcfd9225ab3637e3f307161e8f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
①若点P坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb3d32f46af3841f098c82e30ec1462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfec4233214c3a729c843dee0d186db.png)
②若直线PM交抛物线于点Q,求证;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184d0e916ff15d13036d0c40905ab22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2020-01-31更新
|
222次组卷
|
4卷引用:重庆市沙坪坝区南开中学校2019-2020学年高二上学期期末数学试题
重庆市沙坪坝区南开中学校2019-2020学年高二上学期期末数学试题重庆市南开中学2019-2020学年高二上学期期末数学试题(已下线)【新东方】高中数学20210304-003(已下线)【新东方】高中数学20210323-002【高二上】
7 . 如图所示,在四棱锥
中,四边形
是正方形,点
分别是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/684f0061-f471-44fa-b0ef-91fd3df2774a.png?resizew=140)
(1)求证:
;
(2)线段
上是否存在一点
,使得面
面
,若存在,请找出点
并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1e038b4e76b3a368731d3331522b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a003de8409231a347edebc8284be186c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85de410d85be189dfa5aabb33410b896.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/684f0061-f471-44fa-b0ef-91fd3df2774a.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da4cd5cd0de37a81455262f96acaca01.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f32299ca54d8b38967931d69a218c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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2019-01-26更新
|
2609次组卷
|
19卷引用:【全国百强校】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(理科)试题
【全国百强校】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(理科)试题【校级联考】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(文科)试题安徽省皖北名校2020-2021学年高二上学期第一次联考数学试题安徽省合肥市肥东县第二中学2020-2021学年高二上学期第一次月考数学(理)试题(已下线)2.2.4 平面与平面平行的性质-2020-2021学年高一数学课时同步练(人教A版必修2)福建省厦门一中2020-2021学年高一下学期期中考数学试题湖南省郴州市嘉禾县第一中学2020-2021学年高一下学期第二次月考数学试题湖北省鄂东南三校联考2021-2022学年高一下学期阶段考试(二)数学试题四川省峨眉第二中学校2022-2023学年高二上学期10月月考文科数学试题四川省眉山市2022-2023学年高二上学期期末教学质量检测数学(文)试题四川省眉山市2022-2023学年高二上学期期末教学质量检测理科数学试题安徽省芜湖市华星学校2021-2022学年高一下学期期中数学试题四川省眉山市2022-2023学年高二上学期期末数学(理)试题陕西省西安市鄠邑区2022-2023学年高一下学期期中数学试题陕西省渭南市韩城市新蕾中学2020-2021学年高一上学期第三次月考数学试题云南省红河州开远市第一中学校2022-2023学年高一下学期4月月考数学试题浙江省嘉兴八校联盟2020-2021学年高一下学期期中联考数学试题(已下线)核心考点07空间直线、平面的平行-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)江苏省无锡市江阴市三校联考2023-2024学年高一下学期4月期中数学试题
8 . 已知数列
满足
,
.
(1)设
,证明:
;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf1bca3fd14967acd9bdecdbb70e3e80.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a240f46dc675bab4fb80f6d6ecd9d71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26c9e479280aee190bf9188299547d9.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46359a8e4a2f88fed097ca8eebb38b16.png)
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2018-07-07更新
|
433次组卷
|
2卷引用:【全国市级联考】重庆市开州区2018年春高一(下)期末测试卷数学
名校
解题方法
9 . 证明:
(1)求证:当实数
时,
;
(2)已知
,
,如果
,
的图象有两个不同的交点
,
.求证:
.
(参考数据:
,
,
,
为自然对数的底数)
(1)求证:当实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af92d8f4c2e0fdf1ca1977eb66a970d8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27aea66daa96c2d48a0f72c9b58d9d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdef85d50578d84a92ffcc754f7afddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.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/0c6db82d582ec95916861fc8a917b02d.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c894b7d6baa55c80c64e74748dad898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405361d7be3c9e4d462a4e955d8fe3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a458f4716b7fb99418d762909eecab11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
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10 . 已知函数
,曲线
在原点处的切线为
.
(1)证明:曲线
与
轴正半轴有交点;
(2)设曲线
与
轴正半轴的交点为
,曲线在点
处的切线为直线
,求证:曲线
上的点都不在直线
的上方;
(3)若关于
的方程
(
为正实数)有不等实根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd14ea273c21800c00132219688c61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
(1)证明:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f82ff0d82fef6094b313ce8acfedd.png)
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