名校
1 . 已知函数
.
(1)若
,求
的值;
(2)若
,用函数单调性定义证明
在
上单调递减;
(3)设
,若方程
在
上有唯一实数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d09168c3b90d6da2eccc0bf347f59e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc04702be4996e6b89b656f5a7fc8b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189b2da6c420bf8f8900002d14f65f72.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a47ac48e9c15189074604656c7fe180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86eff5761f61a20c240a428f2a7ceda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-01-03更新
|
459次组卷
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6卷引用:安徽省池州市东至县第三中学2020-2021学年高一上学期12月月考数学试题
名校
解题方法
2 . 如图,四棱锥
中,四边形
为菱形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/eff6de9e-9dba-4f36-8969-9543d3c37bcd.png?resizew=152)
(1)证明:
平面
;
(2)求点
到平面PBC的距离h.
![](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/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea5d51ba341d1932dbf76f3d685a3dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967f74b8993c61634ceed95edca05ffd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/eff6de9e-9dba-4f36-8969-9543d3c37bcd.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2022-02-26更新
|
495次组卷
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5卷引用:安徽省安庆市怀宁县第二中学2022届高三上学期期末数学(文)试题
名校
3 . 在四棱锥
中,底面
是矩形,平面
平面
,
,M是
的中点.
,
.
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842370273591296/2844580709367808/STEM/3975f6ed-8551-43cd-9749-8e4eb2813c1b.png?resizew=291)
(1)求证;
;
(2)求直线
与平面
所成角的正弦值;
(3)在线段
上是否存在点P,使得面
面
,若存在,求
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4cab41e3c3e1b04f0cff21aca315238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a12542a57ca634c2a56325fb64408a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/2021/11/2/2842370273591296/2844580709367808/STEM/3975f6ed-8551-43cd-9749-8e4eb2813c1b.png?resizew=291)
(1)求证;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2919a92ec8fdae2a7b8511fff31fa65.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab82b60265f8b4cab1a83c6a5a7e2d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f26c0452401a81d02af85260a19fac.png)
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2021-11-05更新
|
535次组卷
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6卷引用:安徽省当涂第一中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
4 . 已知数列
满足
,
.
(1)求
,
;
(2)设
,求证:数列
是等比数列,并求其通项公式;
(3)已知
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41913e6c1df7a7b899f9d06692fd8848.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb3985a508c39462365428b00bc592d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fef5ca86c3787b25607b39ed81f8f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08eecb0065cb86128983d1a924b3666.png)
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2021-11-04更新
|
903次组卷
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8卷引用:安徽省宿州市泗县第一中学2020-2021学年高二上学期开学考试数学试题
安徽省宿州市泗县第一中学2020-2021学年高二上学期开学考试数学试题苏教版(2019) 选修第一册 突围者 第4章 第三节 课时1 等比数列的概念、等比数列的通项公式人教B版(2019) 选修第三册 突围者 第五章 第三节 课时1 等比数列北师大版(2019) 选修第二册 突围者 第一章 第三节 等比数列 课时1 等比数列(已下线)第4章 数列(基础卷)-2021-2022学年高二数学新教材单元双测卷(苏教版2019选择性必修第一册)(已下线)第4章 数列单元检测卷-2021-2022学年高二数学尖子生同步培优题典(苏教版2019选择性必修第一册)(已下线)第4章 数列(章末测试提高卷)-2021-2022学年高二数学同步单元测试定心卷(苏教版2019选择性必修第一册)2023版 苏教版(2019) 选修第一册 突围者 第4章 第三节 课时1 等比数列的概念、等比数列的通项公式
名校
5 . 用数学归纳法证明“
”的过程中,从
到
时,不等式的左边增加了( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a1c8aad40749a4e8422e31a8e2a886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3066193c7ca6373691077f9a53aeded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-02-21更新
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726次组卷
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4卷引用:安徽省六安市第一中学2020-2021学年高二下学期第一次阶段检测理科数学试题
名校
6 . 已知抛物线
,直线
交
于
、
两点,且当
时,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/0da7987d-2449-461a-bd27-1861581ba1a5.png?resizew=191)
(1)求
的值;
(2)如图,抛物线
在
、
两点处的切线分别与
轴交于
、
,
和
交于
,
.证明:存在实数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5882f28beb2955fb48a47366b7aae20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ed9d97b8745ed1c15349ea3fffc299.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/0da7987d-2449-461a-bd27-1861581ba1a5.png?resizew=191)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)如图,抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/d053b14c8588eee2acbbe44fc37a6886.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9f6c5d96bd5b71927e4b30630c7496.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d10a88115f033bd6c8d7fe1dc97da8.png)
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2022-01-07更新
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738次组卷
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7卷引用:安徽省六安外国语高级中学2021-2022学年高二上学期期末数学试题
安徽省六安外国语高级中学2021-2022学年高二上学期期末数学试题四川省凉山州2021-2022学年高三上学期第一次诊断性检测数学(理)试题四川省凉山州2021-2022学年高三上学期第一次诊断性检测数学(文)试题四川省泸州市泸县第一中学2022届高三二诊模拟考试数学(理)试题河南省顶尖名校2021-2022学年高三下学期第三次素养调研理科数学试题河南省温县第一高级中学2021-2022学年高三下学期4月月考理科数学试题(已下线)高二上学期期末【常考60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
名校
7 . 已知长方体
中,棱
,
,连结
,过
点作
的垂线交
于
,交
于
.
平面
;
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baa1c07becd03537beeb09a31745cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc416a5b8dc234628e7475387888d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d8a9d64ad3c8cba28840b41ed7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d682fd0344452998187cb6d48de3dd1.png)
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2021-08-26更新
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1118次组卷
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3卷引用:安徽省阜阳汇文中学2022-2023学年高一下学期第三次月考数学试题
名校
8 . 如图,在几何体
中,底面
是边长为2的正三角形,
平面
,
,且
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/11/12/2849700677296128/2854736996712448/STEM/c8ac534f-7086-40a8-9d0c-b0124277f4b3.png?resizew=216)
(1)求证:
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/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36723bd074d43a8c98d9bd416020042c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7bcb2d8a6172fe504c2c63e3ebc1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2021/11/12/2849700677296128/2854736996712448/STEM/c8ac534f-7086-40a8-9d0c-b0124277f4b3.png?resizew=216)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee3d16c7bd3fa91ce2848206816eec2.png)
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2021-11-19更新
|
564次组卷
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6卷引用:安徽省合肥市第八中学2021-2022学年高二上学期期中数学试题
名校
解题方法
9 . 如图,在四棱锥P-ABCD中,
平面ABCD,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/12/16/2873881732603904/2877184785719296/STEM/c2745f06b3344927b90306b25dafedee.png?resizew=168)
(1)证明:平面
平面PAC;
(2)求平面PCD与平面PAB夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae1e04eeb4de72e5750dae77bcb6f88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e713f0ba80e87438cf6273fb00cb81a7.png)
![](https://img.xkw.com/dksih/QBM/2021/12/16/2873881732603904/2877184785719296/STEM/c2745f06b3344927b90306b25dafedee.png?resizew=168)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
(2)求平面PCD与平面PAB夹角的余弦值.
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2021-12-21更新
|
844次组卷
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11卷引用:安徽省安庆市第二中学2021-2022学年高二上学期12月第二次段考数学试题
安徽省安庆市第二中学2021-2022学年高二上学期12月第二次段考数学试题广东省茂名市2020-2021学年高二下学期期末数学试题江苏省南京市中华中学2021-2022学年高三上学期期初数学试题辽宁省抚顺市第一中学2021-2022学年高二上学期入学考试数学试题天津外国语大学附属滨海外国语学校2021-2022学年高二上学期10月月考数学试题广东省东莞市七校2021-2022学年高二上学期12月联考数学试题广东省潮州市2021-2022学年高二上学期期末数学试题辽宁省抚顺市第一中学2021-2022学年高二上学期入学考试数学试题黑龙江省齐齐哈尔市恒昌中学校2022-2023学年高三上学期开学考试数学试题重庆市荣昌永荣中学校2021-2022学年高二上学期期末数学试题河南省洛阳市洛宁县第一高级中学2022-2023学年高二下学期2月月考数学文科试题
名校
解题方法
10 . 如图,DC⊥平面ABC,EA∥DC,AB=AC=AE
DC,M为BD的中点.
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779702243450880/2792536993030144/STEM/36ae26b6932f42d0b4bf5988721ad34f.png?resizew=175)
(1)求证:EM∥平面ABC;
(2)求证:平面AEM⊥平面BCD;
(3)若AB=BC=2,求三棱锥E﹣BCD的体积V.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50a39604477d1d9326eb455cda2e838.png)
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779702243450880/2792536993030144/STEM/36ae26b6932f42d0b4bf5988721ad34f.png?resizew=175)
(1)求证:EM∥平面ABC;
(2)求证:平面AEM⊥平面BCD;
(3)若AB=BC=2,求三棱锥E﹣BCD的体积V.
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2021-08-23更新
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3卷引用:安徽省巢湖市黄山中学2019-2020学年高二上学期第一次月考文科数学试题