名校
解题方法
1 . 已知关于x的方程
有一个根为
.
(1)求证:方程
有一个根为
的充要条件是
;
(2)若
,解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fa32c1e926f40a0722d106563777ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
(1)求证:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fa32c1e926f40a0722d106563777ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c766352f0be38b719621052de92615bd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f84617aaab200384efeaec9a4fe71772.png)
您最近一年使用:0次
2022-10-15更新
|
322次组卷
|
3卷引用:贵州省贵阳市第一中学2022-2023学年高一上学期第一次摸底考试数学试题
名校
2 . 如图,三棱柱
的底面
是正三角形,侧面
是菱形,平面
平面
,
,
分别是棱
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/3976fbf4-0948-4b2f-b25f-5d27091a7b49.png?resizew=184)
(1)证明:
∥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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/3976fbf4-0948-4b2f-b25f-5d27091a7b49.png?resizew=184)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7758424f31d253e5f2a3b6b0a50728a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
2022-12-21更新
|
1034次组卷
|
7卷引用:贵州省毕节市部分学校2023届高三上学期12月联合考试数学(理)试题
名校
3 . 求证:
是一元二次方程
的一个根的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7152aea5d046953a8c931571be7c529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1cb29d065cd6c268fb37208d7d2e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b86960dc00d766405e25dc14bdd295.png)
您最近一年使用:0次
2022-10-23更新
|
573次组卷
|
5卷引用:贵州省贵阳市“三新”改革联盟校2022-2023学年高一上学期联考试题(二)数学试题
贵州省贵阳市“三新”改革联盟校2022-2023学年高一上学期联考试题(二)数学试题福建省霞浦第一中学2022-2023学年高一上学期期末线上质量检测数学试题陕西省西安市高新第七高级中学(长安区第七中学)2022-2023学年高二上学期第二次月考数学试题(已下线)1.4 充分必要条件(精讲)-《一隅三反》(已下线)2.1必要条件与充分条件-高一数学同步精品课堂(北师大版2019必修第一册)
解题方法
4 . 在直棱柱
中,点
为棱
的中点,底面
为等腰直角三角形,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/06483254-d810-4c3f-9f0c-81b366f98ce4.png?resizew=145)
(1)证明:
平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42066e0ef0cb9012bc93b6cfe978c80b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/06483254-d810-4c3f-9f0c-81b366f98ce4.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dddfef906818cc8ddd00f867b77f227.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
名校
解题方法
5 . 图1是直角梯形ABCD,
,
.以BE为折痕将
折起,使点C到达C1的位置,且
,如图2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/a66055ea-24cc-46a5-bb1b-d0e96905f228.png?resizew=269)
(1)证明:平面
平面ABED;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49da1d7617e7efe7ac562b322bff20a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9b02a4ece39842989088e56b1d988b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/a66055ea-24cc-46a5-bb1b-d0e96905f228.png?resizew=269)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570723ec1803bb3a69f220ad7df50226.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
您最近一年使用:0次
2022-11-24更新
|
449次组卷
|
9卷引用:贵州省普通高等学校招生2019-2020学年高三适应性测试理科数学试题
贵州省普通高等学校招生2019-2020学年高三适应性测试理科数学试题贵州省2019-2020学年高三(4月份)模拟数学(理科)试题湖南省怀化市2020届高三下学期6月第三次模拟考试理科数学试题(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)黑龙江省齐齐哈尔市实验中学2020-2021学年高三上学期期末数学(理科)试题安徽省六安市第一中学2020-2021学年高二下学期开学考试数学(理)试题湖南省邵阳市新邵县2021届高三下学期新高考适应性考试数学试题广东省阳江市四校2022-2023学年高二上学期期中联考数学试题福建省上杭县第二中学2023届高三上学期12月月考数学试题
名校
6 . 如图,四棱柱
的底面
为矩形,
为
中点,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d7c36398-c2fd-47ec-88ab-5e6ce625c309.png?resizew=177)
(1)证明:
平面
;
(2)求二面角
的平面角的余弦值.
![](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/8e5e29ca242ec45e8932247be58c633a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a45953045e613b97eeee15ac188ae2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb119c89f01ba89c7f1684f75957736b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/d7c36398-c2fd-47ec-88ab-5e6ce625c309.png?resizew=177)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530bca33e52e5d0108885ff4e6978863.png)
您最近一年使用:0次
2022-11-26更新
|
195次组卷
|
4卷引用:贵州省遵义市第一中学等校2022-2023学年高二下学期第一次月考数学试题
名校
解题方法
7 . 如图,四棱锥P-ABCD中,底面四边形ABCD为矩形,PD⊥平面ABCD,E为AB中点,F为PD中点,AB=2,PD=BC=1.
![](https://img.xkw.com/dksih/QBM/2023/1/9/3149182292484096/3151471576784896/STEM/055c49f5bf8d458a92dbce93816f27ab.png?resizew=179)
(1)证明:EF∥平面PBC;
(2)求点E到平面PBC的距离.
![](https://img.xkw.com/dksih/QBM/2023/1/9/3149182292484096/3151471576784896/STEM/055c49f5bf8d458a92dbce93816f27ab.png?resizew=179)
(1)证明:EF∥平面PBC;
(2)求点E到平面PBC的距离.
您最近一年使用:0次
2023-01-12更新
|
363次组卷
|
8卷引用:贵州省毕节市金沙县第五中学2023-2024学年高二上学期第八周(10月)考试数学试题
贵州省毕节市金沙县第五中学2023-2024学年高二上学期第八周(10月)考试数学试题吉林省白城市通榆县毓才高级中学2022-2023学年高二上学期第一次月考数学试题吉林省实验中学2022-2023学年高二上学期期中数学试题湖南师范大学附属中学2022-2023学年高二上学期期中数学试题江西省上饶市第四中学2022-2023学年高二上学期第三次月考数学试题(已下线)全册综合测试卷-提高篇-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)黑龙江省牡丹江市第三高级中学2023-2024学年高二上学期第一次月考数学试题河南省濮阳市第一高级中学2023-2024学年高二上学期第二次质量检测数学试题
8 . 已知抛物线
的焦点为
,点
在抛物线
上,且
.
(1)求抛物线
的方程;
(2)若直线
过F且与抛物线
交于A,B两点,线段
的垂直平分线交
轴于点N,交
于点M,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7251452d9c6c09b409f734cc48f4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360d86f0ec1c4d9d0dfc06a9064db0b1.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440c013a4909fa47e4a5b16ebf200a03.png)
您最近一年使用:0次
2022-11-14更新
|
483次组卷
|
3卷引用:贵州省贵阳市“三新”改革联盟校2022-2023学年高二上学期月考(六)数学试题
名校
9 . 如图,在四棱锥
中,底面
是正方形,
是等边三角形,平面
平面
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/98675300-9a0b-49fe-9a1a-0940f868083c.png?resizew=175)
(1)证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1c1db5140a973d87e2646d25ed4f91.png)
(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/55a675310c8ba418e5a59beb7317e21e.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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47891397990336f55f96bd66d367758b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/98675300-9a0b-49fe-9a1a-0940f868083c.png?resizew=175)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1c1db5140a973d87e2646d25ed4f91.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8424bdcf257367472c217c92d559f39f.png)
您最近一年使用:0次
2022-11-18更新
|
1104次组卷
|
8卷引用:贵州省部分学校2023届高三上学期11月联考数学(理)试题
10 . 在直棱柱
中,点
为棱
的中点,底面
为等腰直角三角形,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/6989d871-7674-4328-a9a9-0d7093462208.png?resizew=152)
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42066e0ef0cb9012bc93b6cfe978c80b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/6989d871-7674-4328-a9a9-0d7093462208.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dddfef906818cc8ddd00f867b77f227.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1f7689bff6644bfdeb9e36feb163.png)
您最近一年使用:0次