名校
解题方法
1 . 如图1,山形图是两个全等的直角梯形
和
的组合图,将直角梯形
沿底边
翻折,得到图2所示的几何体.已知
,
,点
在线段
上,且
在几何体
中,解决下面问题.
平面
;
(2)若平面
平面
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10de2459bc376f9a3de90f74cc18ca7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde387abe3ecba7cde65df9c58131b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a39a7453e6994a580038828513c68c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3b8602719b3d371bc9ec6c441bb9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7513c5dc6e1d35f76020f8f60c95669.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c897a54f2e36bc4b52fba74b41c89d2d.png)
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2023-11-24更新
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606次组卷
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8卷引用:山西省运城市盐湖区第五高级中学2024届高三上学期一轮复习成果检测数学试题
山西省运城市盐湖区第五高级中学2024届高三上学期一轮复习成果检测数学试题江西省部分地区2023-2024学年高三上学期11月质量检测数学试题河北省部分高中2024届高三上学期11月联考数学试题陕西省榆林市府谷县第一中学2024届高三上学期第五次月考数学(理)试题(已下线)热点6-1 线线、线面、面面的平行与垂直(6题型+满分技巧+限时检测)(已下线)第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)(已下线)13.2.4 平面与平面的位置关系(2)-【帮课堂】(苏教版2019必修第二册)(已下线)11.4.2平面与平面垂直-同步精品课堂(人教B版2019必修第四册)
名校
2 . 已知函数
在点
处的切线为
:
,函数
在点
处的切线为
:
.
(1)若
,
均过原点,求这两条切线斜率之间的等量关系.
(2)当
时,若
,此时
的最大值记为m,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb2fb6043949ffd4a0fc14967e23c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b3c8be9aee074c9a3203abace248ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e9d271392e54ef2055c434430a8dc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16552a1b3198b61e02f62592431cb583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f06443b381a16ea4a5e39e19794a27.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027830fc47290062692964077ee481e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f12c60294fc2faefcf22ab41369d6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd33f65db812076a6f22f2cd8fa0f4.png)
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2023-03-31更新
|
838次组卷
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3卷引用:山西省运城市2024届高三上学期期中数学试题
名校
3 . 甲、乙两人进行象棋比赛,赛前每人发3枚筹码.一局后负的一方,需将自己的一枚筹码给对方;若平局,双方的筹码不动,当一方无筹码时,比赛结束,另一方最终获胜.由以往两人的比赛结果可知,在一局中甲胜的概率为0.3、乙胜的概率为0.2.
(1)第一局比赛后,甲的筹码个数记为
,求
的分布列和期望;
(2)求四局比赛后,比赛结束的概率;
(3)若
表示“在甲所得筹码为
枚时,最终甲获胜的概率”,则
.证明:
为等比数列.
(1)第一局比赛后,甲的筹码个数记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)求四局比赛后,比赛结束的概率;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50edc9133039f8ce8c95569e8351546a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa7a53331277fdb07dc4cbe4463374a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23491ff646a3d254669eb36002a51f2c.png)
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2023-07-20更新
|
1828次组卷
|
6卷引用:山西省运城市运城中学2023届高三第二次模拟数学试题
山西省运城市运城中学2023届高三第二次模拟数学试题河北省张家口市2023届高三三模数学试题福建省福州市四校2022-2023学年高二下学期期末联考数学试题湖北省武汉市第四十九中学2024届高三上学期九月调考模拟数学试题(二)(已下线)微考点7-2 递推方法计算概率与一维马尔科夫过程(数列与概率结合)(已下线)2024届高三开学摸底考试
解题方法
4 . 已知
.
(1)求证:
恒成立;
(2)令
,讨论
在
上的极值点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6064ea5c9236e2ccbd91de0368c67a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ba34ec42d35224b021c44eecacbcb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1e76aaf12e83bd85df89b42ab2eef5.png)
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2023-01-10更新
|
375次组卷
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2卷引用:山西省运城市2022-2023学年高三上学期期末调研测试数学试题
解题方法
5 . 设函数
,且
.
(1)求
的取值范围;
(2)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef8a3b9e57e3e5266d5c6e2abf3b7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f730cbbb88355e0f2b8ba350ab6b1af1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d7d6e1124df72c7c1e86fcb466704c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c8c68cf8575f884b9db2603d23a02e.png)
您最近一年使用:0次
名校
解题方法
6 . 已知抛物线
上一动点G,过点G作x轴的垂线,垂足为D,M是
上一点,且满足
.
(1)求动点M的轨迹C;
(2)若
为曲线C上一定点,过点P作两条直线分别与抛物线交于A,B两点,若满足
,求证:直线
恒过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ca3b0aa32a947786e56e03358ed019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f887360a533f0a25b0b34fb11f0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c8f133f8a3560ff5a14137411740f2.png)
(1)求动点M的轨迹C;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4be3a55efb9e423e27ca1e6a43881788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce68b1c5f9158699c13bb406a5f20a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2022-11-29更新
|
755次组卷
|
3卷引用:山西省高中教育发展联盟2022-2023学年高二上学期11月期中检测数学试题
山西省高中教育发展联盟2022-2023学年高二上学期11月期中检测数学试题辽宁省锦州市渤海大学附属高级中学2022-2023学年高二上学期期末数学试题(已下线)专题05 抛物线8种常见考法归类(2)
解题方法
7 . 已知抛物线
的焦点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/9c3a29c6-c76c-45ba-b61c-be95080b7958.png?resizew=167)
(1)如图所示,线段
为过点
且与
轴垂直的弦,动点
在线段
上,过点
且斜率为1的直线
与抛物线交于
两点,请问
是否为定值,若是,求出该定值;若不是,说明理由;
(2)过焦点
作直线
与
交于
两点,分别过
作抛物线
的切线,已知两切线交于点
,求证:直线
、
、
的斜率成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/9c3a29c6-c76c-45ba-b61c-be95080b7958.png?resizew=167)
(1)如图所示,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8141a4a565a9b1e56bf710b84476a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6e75677951ef1388f76aee5a779149.png)
(2)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95add8635f609e7fdc0a423842f7d037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95add8635f609e7fdc0a423842f7d037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1ab8833d1823f3dc027a39bdb58e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1a6ce0b35896c8a1c687a4376e71f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75af77f184b8d76a881874298852081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ad3d1bc78e0ea7a5518f38c0cf5b30.png)
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2023-01-10更新
|
1211次组卷
|
4卷引用:山西省运城市2022-2023学年高三上学期期末调研测试数学试题
山西省运城市2022-2023学年高三上学期期末调研测试数学试题山西省吕梁市2023届高三上学期期末数学试题(已下线)专题3 解答题题型(已下线)安徽省江南十校2022届高三下学期3月一模理科数学试题变式题16-20
8 . 已知抛物线
的焦点为F,M为T上一动点,N为圆
上一动点,
的最小值为
.
(1)求T的方程;
(2)直线l交T于A,B两点,交x轴的正半轴于点C,点D与C关于原点O对称,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3331494c6e0b32c275c259a2e0cb3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a58ff7a13f16152401ca349421cb3b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04af52c1e7a1317cdd43636ba705bf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4fdc034b4d20f15869d4c79b8161a0b.png)
(1)求T的方程;
(2)直线l交T于A,B两点,交x轴的正半轴于点C,点D与C关于原点O对称,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e839df5bcb6e835d21ffbdff727342b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85c44a34eebda86f1688b7d29b5557d.png)
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