2014高三·全国·专题练习
名校
解题方法
1 . 如图,在四棱锥
中,底面
是边长为
的正方形,侧面
底面
,且
,若
、
分别为
、
的中点,求证:
![](https://img.xkw.com/dksih/QBM/2022/3/28/2945825533640704/3000684830597120/STEM/885421cd9f364e55b187dfeb967bfa3e.png?resizew=209)
(1)
侧面
;
(2)
平面
.
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b7201f9eb7e7c10042c096e0c9f15c.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2945825533640704/3000684830597120/STEM/885421cd9f364e55b187dfeb967bfa3e.png?resizew=209)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
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2022-06-13更新
|
941次组卷
|
9卷引用:河南省扶沟县第二高级中学2021-2022学年高一上学期第二次考试数学试题
河南省扶沟县第二高级中学2021-2022学年高一上学期第二次考试数学试题(已下线)2014届高考数学总复习考点引领+技巧点拨第八章第3课时练习卷2017届江苏苏州市高三暑假自主学习测试数学试卷云南省南涧彝族自治县民族中学2017-2018学年高二9月月考数学(文)试题甘肃省武威第十八中学2017-2018学年高二下学期第二次月考数学(文)试题甘肃省武威第十八中学2018-2019学年高一上学期期末考试数学试题海南省海南枫叶国际学校2019-2020学年高二上学期期中数学试题云南省昆明市官渡区第一中学2021--2022学年高一6月月考数学试题福建省将乐县第一中学2022-2023学年高一下学期第三次月考数学试题
名校
解题方法
2 . 如图所示,在四棱锥
中,底面
为直角梯形,平面
平面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/7/2931316583587840/2932502327058432/STEM/5b6d3ec2-76e6-4d7c-af7e-b090164fea99.png?resizew=180)
(1)求证:
,并且求三棱锥
的体积;
(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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0e30c61f4433ca0d6b7c30d82632a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678069acbf21579b42a786385b154c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e628d8d153b597967cbcb6e02250b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2022/3/7/2931316583587840/2932502327058432/STEM/5b6d3ec2-76e6-4d7c-af7e-b090164fea99.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84733f9dc908ceb11459cc2aed580ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2022-03-09更新
|
296次组卷
|
2卷引用:河南省周口市周口恒大中学2023-2024学年高二上学期9月月考数学试题
名校
3 . 如图,在三棱锥S—ABC中,SC⊥平面ABC,点P、M分别是SC和SB的中点,设PM=AC=1,∠ACB=90°,直线AM与直线SC所成的角为60°.
(2)求二面角M—AC—B的平面角的正切值;
(2)求二面角M—AC—B的平面角的正切值;
您最近一年使用:0次
2022-03-29更新
|
2557次组卷
|
11卷引用:河南省周口市商水县实验高级中学2021-2022学年高一下学期期末考试数学试题
河南省周口市商水县实验高级中学2021-2022学年高一下学期期末考试数学试题宁夏银川一中2021-2022学年高一上学期期末考试数学试题(已下线)专题25 二面角相关问题训练-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)第12练 空间直线、平面的垂直-2022年【暑假分层作业】高一数学(人教A版2019必修第二册)(已下线)高一数学下学期期末精选50题(提升版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)广东省七区2021-2022学年高一下学期期末联考数学试题(已下线)第02讲 基本图形的位置关系(3)陕西省咸阳市武功县普集高级中学2022-2023学年高一下学期6月第三次月考数学试题福建省福州第四中学2022-2023学年高一下学期期末考试数学试题重庆市铁路中学校2023-2024学年高二上学期开学考试数学试题江西省南昌市第十九中学2022-2023学年高二下学期期中考试数学试卷
名校
4 . 如图,在三棱柱
中,
平面
,且D为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/166ff543-f29f-492e-860e-2157c6a26dc1.png?resizew=219)
(1)证明:
;
(2)若
到直线
的距离为
,求二面角
的余弦值.
![](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/a80b15c04ce645384a5334365d9ce972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/166ff543-f29f-492e-860e-2157c6a26dc1.png?resizew=219)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f752d8a27ed612c37ddc86e8b483a243.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de31a7b108b0fdc888133f701e7c79b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc832d36322699ef4400fe19c59c8808.png)
您最近一年使用:0次
2022-04-11更新
|
1031次组卷
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5卷引用:河南省周口市2022-2023学年高二上学期期中数学试题
名校
5 . 如图,在直四棱柱
中,底面
是边长为2的菱形,且
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/0456cc4d-780c-4ec0-aaa7-75fb15f18c6f.png?resizew=137)
(1)证明:
平面
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/12/0456cc4d-780c-4ec0-aaa7-75fb15f18c6f.png?resizew=137)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4cd2b33bd983a9ed6575b9de04a46a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f95ffa57b758ece1827087586090bf1.png)
您最近一年使用:0次
2021-04-17更新
|
1492次组卷
|
9卷引用:河南省周口市太康县第二高级中学2022-2023学年高二上学期11月月考理科数学试题
河南省周口市太康县第二高级中学2022-2023学年高二上学期11月月考理科数学试题河南省周口市太康县第二高级中学2022-2023学年高二上学期11月月考文科数学试题甘肃省2021届第二次高考诊断理科数学试题甘肃省2021届高三下学期二模试数学(理科)试题内蒙古通辽新城第一中学2021届高三第二次增分训练数学(理)试题吉林省松原市实验高级中学2021届高三5月月考数学试题(已下线)专题2.7 空间向量与立体几何-2021年高考数学解答题挑战满分专项训练(新高考地区专用)黑龙江省七台河市勃利县高级中学2022-2023学年高一下学期期末数学试题重庆市杨家坪中学2022-2023学年高二上学期期末数学试题
名校
解题方法
6 . 在矩形ABCD中,AB=1,BC=2,E为AD的中点,如图1,将
沿BE折起,使得点A到达点P的位置(如图2),且平面PBE⊥平面BCDE
(2)若M为PB的中点,N为PC的中点,求三棱锥M﹣CDN的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
(2)若M为PB的中点,N为PC的中点,求三棱锥M﹣CDN的体积.
您最近一年使用:0次
2020-09-23更新
|
1875次组卷
|
6卷引用:河南省周口市太康县第一高级中学2023-2024学年高一下学期5月月考数学试题
河南省周口市太康县第一高级中学2023-2024学年高一下学期5月月考数学试题2020届江西省赣州市高三上学期期末考试数学(文)试题(已下线)第08章+立体几何初步(A卷基础篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教A版)黑龙江省鹤岗市第一中学2021-2022学年高二上学期开学考试数学试题(已下线)专题13.3 空间图形的表面积和体积(基础练)-2020-2021学年高一数学十分钟同步课堂专练(苏教版2019必修第二册)(已下线)核心考点8 立体几何中综合问题 A基础卷 (高一期末考试必考的10大核心考点)
7 . 如图,在四棱锥
中,底面
为矩形且
,侧面
底面
,且侧面
是正三角形,
是
中点.
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446425576128512/2446495270666240/STEM/b84947ceb14f4c369496711dbad07afe.png?resizew=208)
(1)证明:
平面
;
(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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b929269c53a44907dba8ee298a0a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446425576128512/2446495270666240/STEM/b84947ceb14f4c369496711dbad07afe.png?resizew=208)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290a37874cd284fb1a8c864769ce50c9.png)
您最近一年使用:0次
2020-04-21更新
|
327次组卷
|
3卷引用:河南省周口市信阳市重点高中2019-2020学年高三2月质量检测数学(理科)试题
名校
解题方法
8 . 如图,在四棱锥
中,底面四边形
为矩形且
,平面
底面
,且
是正三角形,
是
中点.
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446426150010880/2446488291303424/STEM/c8c2570fda8b4691b919d3faeddbd5e3.png?resizew=237)
(1)证明:
平面
;
(2)求点
到平面
的距离.
![](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/585288e61871608f6ff8f7e4a0beafbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2020/4/21/2446426150010880/2446488291303424/STEM/c8c2570fda8b4691b919d3faeddbd5e3.png?resizew=237)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2020-04-21更新
|
781次组卷
|
5卷引用:河南省周口市信阳市重点高中2019-2020学年高三2月质量检测数学(文科)试题
名校
解题方法
9 . 如图,已知四棱锥
中,底面
为矩形且
,平面
平面
,
是等边三角形,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/2019/6/14/2225596843335680/2225653401608192/STEM/c0109f89-903e-4960-b797-c50ed5c4eec3.png)
(Ⅰ)求证:
;
(Ⅱ)求直线
与平面
所成的角的正弦值.
![](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/1b929269c53a44907dba8ee298a0a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2019/6/14/2225596843335680/2225653401608192/STEM/c0109f89-903e-4960-b797-c50ed5c4eec3.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d5ee2d6fcbcad17b69997ef0741d2d.png)
(Ⅱ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2019-06-14更新
|
1061次组卷
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6卷引用:河南省周口市淮阳一中2019-2020学年高一上学期第二次月考数学试题
河南省周口市淮阳一中2019-2020学年高一上学期第二次月考数学试题【区级联考】天津市宝坻区2018-2019学年高一下学期期中考试数学试题贵州省思南中学2019-2020学年高二9月月考数学试题内蒙古集宁一中(西校区)集宁一中2020-2021学年高三上学期期中考试数学(文)试题(已下线)对点练47 直线、平面垂直的判定及其性质-2020-2021年新高考高中数学一轮复习对点练内蒙古乌兰察布市集宁一中西校区2020-2021学年高三(上)期中数学(文科)试题
10 . 如图,在四棱锥
中,
底面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/b7a61586-c415-4115-8707-95df97a3c98a.png?resizew=239)
(1)求证:
平面
;
(2)若点
在线段
上,且满足
,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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1cb23cb7d9f22cfc31a6cd6fcb12e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26eba7e649fade39fd2d0b6ef4ac5ffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/b7a61586-c415-4115-8707-95df97a3c98a.png?resizew=239)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e8c1551d814f36aa6773ff5986c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
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