解题方法
1 . 如图,在三棱柱
中,侧面
是菱形,
是边
的中点.平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2020/12/20/2618475349975040/2624805250342912/STEM/24b6f5e4fe6b480ba509d499fdc36ffc.png?resizew=275)
(1)求证:
平面
;
(2)在线段
上是否存在点
,使得
平面
,若存在,请说明
点的具体位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2e00a3b5d4f1e10a52058f148060d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb64353c99068a7a1a8508a22f5b25b4.png)
![](https://img.xkw.com/dksih/QBM/2020/12/20/2618475349975040/2624805250342912/STEM/24b6f5e4fe6b480ba509d499fdc36ffc.png?resizew=275)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a590a08b3823e01024de68e967cbf3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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 . 如图,在四棱锥
中,底面
是矩形,且
,
,
平面
,
、
分别是线段
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/8a7462c6-c92d-4ed5-a22b-ddd652e46b9b.png?resizew=168)
(1)证明:
;
(2)求直线
与平面
所成角的正弦值.
![](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/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96127e45e2dd2494fccb1c0905951f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/8a7462c6-c92d-4ed5-a22b-ddd652e46b9b.png?resizew=168)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d603566c74b1d5de510a2e8f7859010.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0901e2f5cefe6468cbbcaa332287d63.png)
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名校
4 . 如图,在棱长为a的正方体
中,点P为线段
上的一个动点,连接
.
(1)求证:
面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862c61f56f6cb449418756b1005ee1e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/5/0fb4ed26-13e6-46bc-afc3-b90ca077e1d9.png?resizew=154)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f844a41f79ea2b231b326f8633beac50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
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2023-07-28更新
|
509次组卷
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2卷引用:重庆市长寿中学校2022-2023学年高二上学期期中数学试题
名校
5 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)若
=0,求
的值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a136afa15ea25aba12111fd15f6340f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d7daa713ad26b1537eb66a0a35db9c.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d0532bf8ea573af0bc5bbda9e52154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08649488c4b6e75ded28491787ef7558.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22385a460e5c54a3736e2eccd185c418.png)
您最近一年使用:0次
2023-10-22更新
|
503次组卷
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12卷引用:重庆市长寿中学2020-2021学年高二下学期第一次月考数学试题
重庆市长寿中学2020-2021学年高二下学期第一次月考数学试题(已下线)【新东方】高中数学20210513-003【2021】【高二下】江苏省苏州市第一中学2020-2021学年高二下学期期中数学试题江西省八所重点中学2021届高三4月联考数学(理)试题(已下线)精做06 函数与导数-备战2021年高考数学(理)大题精做(已下线)2021年高考数学(理)押题预测卷(新课标III卷)01(已下线)专题4.15—导数大题(构造函数证明不等式2)-2022届高三数学一轮复习精讲精练(已下线)专题2.16 导数-不等式的证明-2021年高考数学解答题挑战满分专项训练(新高考地区专用)天津市河北区2022届高三下学期总复习质量检测(一)数学试题北京市广渠门中学2024届高三上学期开学考数学试题天津市汇文中学2023-2024学年高三上学期10月月考数学试题北京市海淀实验中学2024届高三上学期10月月考数学试题
解题方法
6 . 如图,四棱锥P﹣ABCD的底面ABCD为菱形,PB=PD,E,F分别为AB和PD的中点.
![](https://img.xkw.com/dksih/QBM/2023/6/29/3270194285666304/3274662805946368/STEM/5f538f37d2df4c978a94f1a0ba80379c.png?resizew=224)
(1)求证:EF∥平面PBC;
(2)求证:平面PBD⊥平面PAC.
(3)若
,求二面角
的平面角的余弦值.
![](https://img.xkw.com/dksih/QBM/2023/6/29/3270194285666304/3274662805946368/STEM/5f538f37d2df4c978a94f1a0ba80379c.png?resizew=224)
(1)求证:EF∥平面PBC;
(2)求证:平面PBD⊥平面PAC.
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d923ad55a426c935e1358b4a0523ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b33b7213d99a817bff19bcf740a0697c.png)
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名校
解题方法
7 . 三棱台
的底面是正三角形,
平面
,
,
,
,E是
的中点,平面
交平面
于直线l.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/05030a34-c5f6-4325-b827-139a37c4caf6.png?resizew=155)
(1)求证:
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f8b295ee0c7c60e6fe1dbf054ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/05030a34-c5f6-4325-b827-139a37c4caf6.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650f79ce93087959934d79c35b89582f.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d365ce9f4bacc4d4bb15dbdb5306a5.png)
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2022-12-27更新
|
1649次组卷
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8卷引用:重庆市长寿中学校2022-2023学年高二上学期期末数学试题
名校
解题方法
8 . 在数列
中,
,
,
.
(1)设
,求证:数列
是等比数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59fac0a027bc7005e8e4ed946017f0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655c46b33730f3a29b9ec3024df71375.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e760fd67663947e5bd1800efdae057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求数列
![](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)
您最近一年使用:0次
2022-12-26更新
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3486次组卷
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5卷引用:重庆市长寿中学校2022-2023学年高二上学期期末数学试题
名校
解题方法
9 . 如图甲,在矩形
中,
,E为线段
的中点,
沿直线
折起,使得
,O点为AE的中点,连接DO、OC,如图乙.
(1)求证:
;
(2)线段
上是否存在一点
,使得平面
与平面
所成的角为
?若不存在,说明理由;若存在,求出
点的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/100af11e6cb83b56437f2db7dadeb9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8110f066b294763b30456f7cd90d1e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/220b37b8-7b4a-412c-be13-4ab3ee79f955.png?resizew=438)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f4946f86dce1600096f79d7716ea03.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977a483bd52c08968f4097d10609be20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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2023-07-28更新
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784次组卷
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6卷引用:重庆市长寿中学校2022-2023学年高二上学期期中数学试题
名校
10 . 用数学归纳法证明“
≥
(
N*)”时,由
到
时,不等试左边应添加的项是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e363f30f06c5f37bc82f0119cf2340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7bc6db76331d42d477c4664badd57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5b0aafc603ba02b6702e785b00a5013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef7ca2b3e8061384501f668e59696a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-04-28更新
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291次组卷
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12卷引用:重庆市长寿中学2018-2019学年高二下学期第一学段考试数学试题
重庆市长寿中学2018-2019学年高二下学期第一学段考试数学试题云南省保山一中2017-2018学年高二下学期期末考试理数试卷四川省成都市树德中学2019-2020学年高二下学期定时检测(线上开学考试)数学试题浙江省“9+1”联盟2019-2020学年高二下学期期中数学试题浙江省宁波市奉化高中、慈溪市三山高中等六校2019-2020学年高二下学期期中联考数学试题四川省成都市树德中学2019-2020学年高二下学期开学考试数学试题江西省赣州市第一中学2020-2021学年高二3月第一次月考数学(理)试题安徽省黄山市屯溪第一中学2020-2021学年高二下学期期中理科数学试题陕西省咸阳市武功县普集高中2021-2022学年高二下学期第一次月考实验班理科数学试题四川省成都市嘉祥教育集团2022-2023学年高二下学期期中监测数学(理)试题1.5 数学归纳法7种常见考法归类(1)(已下线)专题4.4 数学归纳法(2个考点四大题型)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)