名校
解题方法
1 . 如图,在四棱锥P-ABCD中,底面ABCD为菱形,E为棱AB的中点,AC⊥PE,PA=PD.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/df736301-4b5d-4bb5-9fd9-04ea9122b7f9.png?resizew=177)
(1)证明:平面PAD⊥平面ABCD;
(2)若PA=AD,∠BAD=60°,求二面角
的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/df736301-4b5d-4bb5-9fd9-04ea9122b7f9.png?resizew=177)
(1)证明:平面PAD⊥平面ABCD;
(2)若PA=AD,∠BAD=60°,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abca0f7f7f2f49d821be607579565963.png)
您最近一年使用:0次
2023-12-20更新
|
1225次组卷
|
12卷引用:东北三省三校2023届高三第一次联合模拟考试数学试题
(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题东北三省三校2023届高三第一次联合模拟考试数学试题(已下线)东北三省三校2023届高三第一次联合模拟考试数学试题江西省新余市2023届高三二模数学(理)试题江苏省苏州市部分学校2024届高三上学期第二次调研考试数学试题(已下线)2023年高考数学(理)终极押题卷陕西师范大学附属中学2022-2023学年高二下学期期末理科数学试题云南省昆明市官渡区尚品书院学校2022-2023学年高二下学期3月月考数学试题黑龙江省饶河县高级中学2022-2023学年高二下学期第一次月考数学试题辽宁省沈阳市五校协作体2023-2024学年高二上学期期末考试数学试题(已下线)专题13 空间向量的应用10种常见考法归类(2)河南省南阳市桐柏县2023-2024学年高二上学期期末质量检测数学试题
解题方法
2 . 如图,在三棱锥
中,
,
,
为点
在平面
的射影,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/aca4fd47-38e0-4342-8b90-885fb44eeea4.png?resizew=164)
(1)证明
平面
;
(2)若
,
,
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41ffdaecfb3c73d403179e5745c71a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1326e85ff750d882de9ea65c29e3d3b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/7/aca4fd47-38e0-4342-8b90-885fb44eeea4.png?resizew=164)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d85f14d046c7d50a349b9c1fcf717d1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26e32412868f3dcb5cad62c8a836778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6edb7e5ea744db95ac422fe2e2af3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df915a088300b53c298fecd10675e5b.png)
您最近一年使用:0次
3 . 在
中,
为
边上中线,
,
,
.
(1)求
的面积;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9ad150cb1e4cd8977d4cc3d99be17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7650cede07c4758a9b3bb1da4553acc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e3f46a3abb0168440e73ecaacafe5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec8d59223618af883de79a8ead82658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6282292819434a8905a212427613fd85.png)
您最近一年使用:0次
名校
解题方法
4 . 已知首项为1的数列
,其前
项利为
,且数列
是公差为1的等差数列
.
(1)求
的通项公式;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5bc2b05dc79b18ecb4ac3f9b5c492d4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a35442a56588e5317acdedc8e51582a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
2023-11-14更新
|
1793次组卷
|
2卷引用:吉林省长春市2024届高三质量监测(一)数学试题
5 . 过抛物线
焦点
,斜率为
的直线
与抛物线交于
、
两点,
.
(1)求抛物线
的方程;
(2)过焦点
的直线
,交抛物线
于
、
两点,直线
与
的交点是否在一条直线上.若是,求出该直线的方程;否则,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c348601813d70ba64ffca73cf2256f3.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
您最近一年使用:0次
解题方法
6 . 树人中学某班同学看到有关产品抽检的资料后,自己设计了一个模拟抽检方案的摸球实验.在一个不透明的箱子中放入10个小球代表从一批产品中抽取出的样本(小球除颜色外均相同),其中有
个红球(
,
),代表合格品,其余为黑球,代表不合格品,从箱中逐一摸出
个小球,方案一为不放回摸取,方案二为放回后再摸下一个,规定:若摸出的
个小球中有黑色球,则该批产品未通过抽检.
(1)若采用方案一,
,
,求该批产品未通过抽检的概率;
(2)(ⅰ)若
,试比较方案一和方案二,哪个方案使得该批产品通过抽检的概率大?并判断通过抽检的概率能否大于
?并说明理由.
(ⅱ)若
,
,现采用(ⅰ)中概率最大的方案,设在一次实验中抽得的红球为
个,求
的分布列及数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9952125a947b88e068d9d7a54583a7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c38f3baf9a34265fbdb5c65dd1664d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若采用方案一,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c7630484d76b37662fe1c4ebdf2f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
(2)(ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c4bf61e073c899494b2fb3b767b108.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c7630484d76b37662fe1c4ebdf2f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
您最近一年使用:0次
名校
解题方法
7 . 在平面直角坐标系
中,抛物线E:
的焦点为F,E的准线交
轴于点K,过K的直线l与拋物线E相切于点A,且交
轴正半轴于点P.已知
的面积为2.
(1)求抛物线E的方程;
(2)过点P的直线交E于M,N两点,过M且平行于y轴的直线与线段OA交于点T,点H满足
.证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3dda800348653ff51eb6b1c8318039.png)
(1)求抛物线E的方程;
(2)过点P的直线交E于M,N两点,过M且平行于y轴的直线与线段OA交于点T,点H满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84594e725612627ce035c87451ba3ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef1f7b9adab87736321e30949a4d668.png)
您最近一年使用:0次
2023-11-08更新
|
725次组卷
|
7卷引用:吉林省东北师范大学附中2023届高三下学期七模数学试题
名校
8 . 近几年以华为为代表的中国高科技企业正在不断突破科技封锁.多项技术已经“遥遥领先”.国产光刻机作为芯片制造的核心设备,也已经取得了突飞猛进的发展.已知一芯片生产商用某国产光刻机生产的
型芯片经过十项指标全面检测后,分为Ⅰ级和Ⅱ级,两种芯片的某项指标的频率分布如图所示:
,将该指标大于
的产品应用于A型手机,小于或等于
的产品应用于
型手机.假设数据在组内均匀分布,以事件发生的频率作为相应事件发生的概率.
(1)求
型芯片Ⅰ级品该项指标的第70百分位数;
(2)当临界值
时,求
型芯片Ⅱ级品应用于A型手机的概率;
(3)已知
,现有足够多的
型芯片Ⅰ级品、Ⅱ级品,分别应用于A型于机、
型手机各1万部的生产:
方案一:直接将
型芯片Ⅰ级品应用于A型手机,其中该指标小于等于临界值
的芯片会导致芯片生产商每部手机损失700元;直接将
型芯片Ⅱ级品应用于
型手机,其中该指标大于临界值
的芯片,会导致芯片生产商每部手机损失300元;
方案二:重新检测
型芯片Ⅰ级品,Ⅱ级品,会避免方案一的损失费用,但检测费用共需要101万元;
请从芯片生产商的成本考虑,选择合理的方案.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)当临界值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b615f9fbd653768f9e29dfec4a58e8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434e2b948927f63dd1ee9914decb986b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
方案一:直接将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
方案二:重新检测
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
请从芯片生产商的成本考虑,选择合理的方案.
您最近一年使用:0次
2023-10-28更新
|
810次组卷
|
5卷引用:吉林地区普通高中2023-2024学年高三上学期第一次模拟考试数学试题
吉林地区普通高中2023-2024学年高三上学期第一次模拟考试数学试题重庆市九龙坡区四川外国语大学附属外国语学校2024届高三上学期期中数学试题(已下线)3.2频率分布直方图-数学同步精品课堂(北师大版2019必修第一册)(已下线)模块三 专题6大题分类练(统计) 拔高能力练(已下线)第04讲 9.2.2 总体百分位数的估计-【帮课堂】(人教A版2019必修第二册)
解题方法
9 . 已知函数
.
(1)若函数
在
上单调递增,求正实数
的取值范围;
(2)求证:当
时,
在
上存在唯一极小值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2419c5bd99d1951cc2c2f00cb1b041.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5085c14cc9d275af1875b7f58575200e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/313660c7376dbff3e1a5e1757ff29ae0.png)
您最近一年使用:0次
解题方法
10 . 已知数列
的前
项和为
,
,
.
(1)请在①②中选择一个作答,并把序号填在答题卡对应位置的横线上,①求数列
的通项公式;②求
;
(2)令
,求数列
的前
项和
,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8bbc0d68bee8853da4576f00834b85.png)
(1)请在①②中选择一个作答,并把序号填在答题卡对应位置的横线上,①求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ef194395f3d5320ea74d799f0fb2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02e80983b88cdf6b540502816c87d13.png)
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