名校
解题方法
1 . 若非零函数
对任意x,y均有
,且当
时,
.
(1)求
,并证明
;
(2)求证:
为
上的减函数;
(3)当
时,对
时恒有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6585b5af98d4c7801c1edaf2e6ead0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73ed206046205dc9e41285f74d81dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1dd6e7640a36050cbbbcc6449606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
解题方法
2 . (1)已知
,设
,
,比较
与
的大小;
(2)证明:已知
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec532f119aff0491334d43cf6b1adf70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1166d36cb26ddb11b666ad0faf6a8b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)证明:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a0aa068c979c53361d049ce49987a8.png)
您最近一年使用:0次
解题方法
3 . 如图:正方体ABCD-A1B1C1D1棱长为2,E,F分别为DD1,BB1的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/60878e38-b7e3-4e3a-9c9e-8bd906cfc333.png?resizew=160)
(1)求证:CF//平面A1EC1;
(2)过点D作正方体截面使其与平面A1EC1平行,请给以证明并求出该截面的面积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/18/60878e38-b7e3-4e3a-9c9e-8bd906cfc333.png?resizew=160)
(1)求证:CF//平面A1EC1;
(2)过点D作正方体截面使其与平面A1EC1平行,请给以证明并求出该截面的面积.
您最近一年使用:0次
2022-07-14更新
|
1437次组卷
|
6卷引用:福建省永春第二中学2022-2023学年高一下学期5月月考数学试题
福建省永春第二中学2022-2023学年高一下学期5月月考数学试题(已下线)专题08 空间直线与平面的平行问题(1)-期中期末考点大串讲湖南省衡阳市衡南县2021-2022学年高一下学期期末数学试题(A卷)重庆市缙云教育联盟2023届高三上学期8月质量检测数学试题(已下线)第03讲 空间直线、平面的平行 (精讲)-2(已下线)第八章 立体几何初步 讲核心 02
名校
4 . 如图,三棱柱
中,侧面
为矩形,若平面
平面
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/ea941d1a-dc83-4dd2-a7f7-beceaffe880d.png?resizew=147)
(1)求证:
;
(2)记平面
与平面
所成角为
,直线
与平面
所成角为
,异面直线
与
所成角
,试探求
与
的大小关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/ea941d1a-dc83-4dd2-a7f7-beceaffe880d.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82343ddf8316e0a9a50c21c422bdc930.png)
(2)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ffad8405936ce486b0068524b67e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abfb55e8443ecf97535f8e189a76c60.png)
您最近一年使用:0次
2022-01-11更新
|
134次组卷
|
2卷引用:福建省德化第二中学2023-2024学年高二上学期第一阶段考试数学试题
名校
解题方法
5 . 如图,在边长为
的正方体
中,
为
中点,
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f11f1840eb8b17e7b07c3fe7e987a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0625187f35c80fb49277693e6b41b021.png)
您最近一年使用:0次
2024-04-24更新
|
2768次组卷
|
20卷引用:福建省永春第二中学2022-2023学年高一下学期5月月考数学试题
福建省永春第二中学2022-2023学年高一下学期5月月考数学试题新疆昌吉回族自治州昌吉市昌吉州行知学校2022-2023学年高三上学期1月学业水平考试数学试题贵州省黔西南州2022-2023学年高一下学期期末教学质量检测数学试题浙江省绍兴蕺山外国语学校2022-2023学年高一下学期期中数学试题云南省文山州砚山县第三高级中学2022-2023学年高二下学期5月月考数学试题专题07B立体几何解答题重庆市梁平中学2023-2024学年高二上学期入学考试数学试题广西桂林市第十八中学2019-2020学年高一上学期期中数学试题河北省唐山市滦南县第一中学2020-2021学年高一下学期期中数学试题湖南省邵阳市第二中学2021-2022学年高一下学期期中数学试题河北省邯郸市大名县第一中学2021-2022学年高一下学期开学考试数学试题河南省信阳市信阳高级中学2021-2022学年高一下学期第四次月考数学试题云南省(新教材)2021-2022学年高一春季学期期末普通高中学业水平考试数学试题(已下线)第03讲 直线、平面平行的判定与性质(八大题型)(讲义)(已下线)8.5.2 直线与平面平行-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)第13章 立体几何初步(提升卷)-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)(已下线)第8.5.2讲 直线与平面平行-同步精讲精练宝典(人教A版2019必修第二册)(已下线)专题06 立体几何初步解答题热点题型-《期末真题分类汇编》(江苏专用)广东省茂名市信宜市第二中学2023-2024学年高一下学期5月月考数学试题
名校
解题方法
6 . 在直角梯形
中,
,
,
,如图(1).把
沿
翻折,使得平面
平面
.
;
(2)在线段BC上是否存在点N,使得AN与平面ACD所成角为60°?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbd8599cee48d867a73477d60b1f62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
(2)在线段BC上是否存在点N,使得AN与平面ACD所成角为60°?若存在,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48732e80ec3c3b6de906d598c69840d5.png)
您最近一年使用:0次
2024-03-16更新
|
2964次组卷
|
19卷引用:福建省泉州市第七中学2023-2024学年高二上学期期中考试数学试卷
福建省泉州市第七中学2023-2024学年高二上学期期中考试数学试卷宁夏回族自治区吴忠市吴忠中学2023-2024学年高二上学期11月期中考试数学试题江西省宜春市宜丰县宜丰中学2023-2024学年高二上学期12月月考数学试题江西省赣州市大余县部分学校联考2023-2024学年高二上学期12月月考数学试题广东省佛山市南海区第一中学2023-2024高二上学期第三次大测数学试卷广东省中山市中山纪念中学2024届高三上学期第三次模拟测试数学试题河北省石家庄市第二中学2024届高三上学期第一次模拟测试数学试题四川省成都市郫都区2024届高三上学期阶段检测(三)理科数学试卷(已下线)(新高考新结构)2024年高考数学模拟卷(一)(已下线)微考点5-1 新高考新试卷结构立体几何解答题中的斜体建坐标系问题(已下线)重难点12 立体几何必考经典解答题全归类【九大题型】(已下线)第1套 全真模拟篇复盘卷 【模块三】(已下线)信息必刷卷01四川省成都市第七中学2024届高三下学期4月分推考试数学(理科)试卷(已下线)模块3 第3套 复盘卷四川省成都市石室阳安学校2023-2024学年高三下学期4月月考数学(理)试题(已下线)模块4 二模重组卷 第2套 复盘卷四川省泸州高级中学校2024届高三下学期第二次月考理科数学试题四川省成都市金堂县淮口中学校2024届高三下学高考仿真冲刺卷(一)理科数学试题
名校
解题方法
7 . 已知正项数列
满足:对任意正整数
,都有
成等差数列,
成等比数列,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e719bd380ea9dd3ec2a20242bdf6380.png)
(1)求证:数列
是等差数列;
(2)设数列
的前项和为
,如果对任意正整数
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0197eeeeaafec6b1fdd7bb8509572f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a20dfd9c14d834c66b2070c41f66eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5b55761181faa05961286eedfebca4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e719bd380ea9dd3ec2a20242bdf6380.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4f93dca4192c87d1ac77a2456bf12e.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b01041691ad489f126f05c18ea8f0fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd0dc83494c84b81687cf8c38736b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-25更新
|
437次组卷
|
3卷引用:福建省泉州市第一中学2024届高三上学期12月月考数学试题
名校
解题方法
8 . 已知椭圆
,长轴长为4,
分别为椭圆的左焦点、右焦点,椭圆上一点
满足
垂直于
轴,且
.
(1)求椭圆
的标准方程;
(2)已知点
为该椭圆的左顶点,若斜率为
且不经过点
的直线
与椭圆
交于
两点,且点
在以线段
为直径的圆上,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0e9a9aaa49dee8866983f5e087da103.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
9 . 如图,在四棱锥
中,
为等边三角形,
,
,且
,
,
,
为
中点.
(1)求证:平面
平面
;
(2)若线段
上存在点
,使得二面角
的大小为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25eb757d05fbff80d50c3bb8dbcb8657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18120a244d3a1f9c1688bf53eb2ad775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a0c299356c26338d4153748e8a61d.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/editorImg/2024/1/10/f090b990-e56f-4d88-9053-950374bfddbe.png?resizew=170)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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2024-01-04更新
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1244次组卷
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3卷引用:福建省泉州市第一中学2024届高三上学期12月月考数学试题
23-24高二上·江苏南通·阶段练习
名校
10 . 如图,在多面体
中,
平面
,平面
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/7c0cee21-e7c6-4b47-82d3-8197be943829.png?resizew=156)
(1)若点
在
上,且
,求证:
平面
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72635020e310c76245bcf094a3ed6ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4959250cb4f4289b7c5400c7bee0426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75929268210da5976bc37d080da030dd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/7c0cee21-e7c6-4b47-82d3-8197be943829.png?resizew=156)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457eb716c608c6b4fb6e91c8fc2ed163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
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