名校
1 . 如图,在四棱锥
中,
,
平面
,底面
为正方形,
,
分别为
,
的中点.
(1)求证:
平面
;
(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/1365206d14224e0b2d40a7bd8b7965ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/578e3534-c0e1-4c0f-8a35-d416eab64d16.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c2b786c64e6a9ed2ec5670cde74f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
您最近一年使用:0次
2023-10-17更新
|
389次组卷
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12卷引用:西藏拉萨市2020届高三第二次模拟考试数学(理)试题
西藏拉萨市2020届高三第二次模拟考试数学(理)试题2020届北京市高考适应性测试数学试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)专题20 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)北京师范大学亚太实验学校2021届高三上学期期中数学试题黑龙江省哈尔滨市第九中学校2020-2021学年高二上学期期中考试数学(理)试题北京市第四十三中学2021届高三1月月考数学试题天津市河西区梧桐中学2020-2021学年高二上学期第一次学情调研数学试题福建省尤溪县第五中学2021-2022学年高二上学期第一次月考数学试题北京市朝阳区北京工业大学附属中学2023-2024学年高二上学期10月月考数学试题云南省砚山县第三高级中学2021-2022学年高二上学期期末考试数学试题云南省昭通市一中教研联盟2023-2024学年高二上学期期末质量检测数学试题(B卷)
名校
解题方法
2 . 如图,正方体
的棱长为2.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f647de53756993a680347e8ce3c0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
2023-12-17更新
|
490次组卷
|
5卷引用:西藏自治区拉萨市2024届高三一模数学(文)试题
西藏自治区拉萨市2024届高三一模数学(文)试题(已下线)专题8.10 立体几何初步全章十三大基础题型归纳(基础篇)-举一反三系列(已下线)专题8.12 立体几何初步全章综合测试卷(基础篇)-举一反三系列(人教A版2019必修第二册)宁夏回族自治区石嘴山市第三中学2023-2024学年高一下学期期中考试数学试题(已下线)11.3.2直线与平面平行-同步精品课堂(人教B版2019必修第四册)
3 . 如图,正方体
的棱长为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/3fca0077-a488-4b95-82c9-fc72287e753f.png?resizew=174)
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/3fca0077-a488-4b95-82c9-fc72287e753f.png?resizew=174)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb96d9ea39bf7974143973559058dbec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
2023-12-17更新
|
181次组卷
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2卷引用:西藏自治区拉萨市2024届高三一模数学(理)试题
4 . 已知函数
.
(1)讨论函数
的单调区间;
(2)若
为函数
的极值点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a32017ba8a1d4613cfd9ec6d030d016.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd4a25c61167cd73dd176d2c39b4b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07238e4e1f21841ecc5a8daaf3b5ade.png)
您最近一年使用:0次
2023-08-20更新
|
470次组卷
|
2卷引用:西藏昌都市第一高级中学2023届高三高考全真仿真考试数学(理)试题
解题方法
5 . 已知函数
.
(1)求不等式
的解集;
(2)证明:
,
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8280663b3b97e534043b0f12ad6f46.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4827f79723c41bd35bf4871bcac58907.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988382a54d3c382a9cef7ed796551f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8645952ea14b25443f411d39bdec641e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ba8d2cbae3db03e83b60f5323d5b5c.png)
您最近一年使用:0次
2023-12-18更新
|
144次组卷
|
2卷引用:西藏自治区拉萨市2024届高三一模数学(文)试题
解题方法
6 . 如图,在直三棱柱
中,
,
,
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/18cb7c40-da00-4b9c-af58-96853a090169.png?resizew=171)
(1)求证:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de9b94a20b9d6ea37cfe135d790801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78f0b646ccbe31c8d4df21054f82003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a78f1bee29c69699ae6c7dd553c73c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/20/18cb7c40-da00-4b9c-af58-96853a090169.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a0a3bb566b5d2404e4bb823abddfa9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d025c1c91b88c7d9154a191b3c5c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e802c9457575dc36375a9a084d73f3d.png)
您最近一年使用:0次
2023-04-18更新
|
1570次组卷
|
4卷引用:西藏拉萨市2023届高三一模数学(文)试题
7 . 已知函数
.
(1)证明:
,有
;
(2)设
(
),讨论
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2827943eee7716dc5609485eef4f846a.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1635473a4200e29e0cd13dffa54f7571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
8 . 已知函数
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/2df7826f-196e-44a7-aae9-aed9746b03b5.png?resizew=197)
(1)请在图中画出
和
的图象;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8fd1a361027fa379a87075511718ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5d6457a2bd393a793f5840cb001814.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/18/2df7826f-196e-44a7-aae9-aed9746b03b5.png?resizew=197)
(1)请在图中画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f343d52d725b942a0634da681b02439a.png)
您最近一年使用:0次
解题方法
9 . 已知函数
.
(1)求曲线
在
处的切线方程
,并证明:当
时,
恒成立;
(2)若
有两个不同的实数根
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/586ac14c735533a982d8029c21e4f09b.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a06acf17d7c28fa264c03224226951b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684bcf84f0a266515bfafde0da903050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a797b151c88c427c45b142e4eb5405e1.png)
您最近一年使用:0次
10 . 如图,在直三棱柱
中,
,
,
分别为
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/2023/5/8/3233425156571136/3233909931556864/STEM/d151e1559e0741709f726664e877cdc8.png?resizew=137)
(1)求证:
平面
;
(2)若
,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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2023/5/8/3233425156571136/3233909931556864/STEM/d151e1559e0741709f726664e877cdc8.png?resizew=137)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f475878dd1b32b0486cbf7b5ffbedd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae80f09dae8acbe1e5e27bd5c4d8164.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb74eeb04f2f2f68095db616f14c971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae80f09dae8acbe1e5e27bd5c4d8164.png)
您最近一年使用:0次
2023-05-09更新
|
1799次组卷
|
3卷引用:西藏林芝市第二高级中学2023届高三第四次模拟考试数学(理)试题