10-11高二下·福建·阶段练习
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f3d9088bfaafb7101cda7a59ec44f9.png)
(1)求证:函数
在
上为增函数;(2)证明:方程
没有负根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f3d9088bfaafb7101cda7a59ec44f9.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f00bba28ce932fbcc82ed562994f031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
您最近一年使用:0次
2 . 已知正项数列
满足
且
.
(I)证明数列
为等差数列;
(II)若记
,
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065054f4e163585d630aa42cb6323a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa071fc950b95abcbe700e7e10b95c8.png)
(I)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/065054f4e163585d630aa42cb6323a3e.png)
(II)若记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba48fdff8697fad80fbfd5904a613d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9463c0db452f630d8dae2065e000923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10180f539520729e97afb8223a7404c0.png)
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名校
解题方法
3 . 已知数列
,
,其前
项和
满足
,其中
.
(1)设
,证明:数列
是等差数列;
(2)设
,
为数列
的前
项和,求证:
;
(3)设
(
为非零整数,
),试确定
的值,使得对任意
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.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/851afb5fa82c3e4448ac7b674d143cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdb807b6968c2986392b64b4fca2d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.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/3819480e1e624208f729ad8653e4f24f.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18230ed18623e12c2d46d055cb16df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4a37ac219023581db07fe5961ae460.png)
您最近一年使用:0次
2016-12-03更新
|
1277次组卷
|
4卷引用:2016-2017年福建福州外国语学校高二理上月考一数学试卷
4 . 选修4-1:几何证明选讲
如图,
中,以
为直径的⊙
分别交
于点
,
交于点
.
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/e5acaef67a79443e920f3741d0ab2cfd.png)
(Ⅰ)判断过
点平行于
的直线是否是⊙
的切线,并加以证明;
(Ⅱ)求证:
.
如图,
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/d6807c36241c407dad59c9fc46c30d9a.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/95e2d901d53d4bb18798e31064a6d677.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/aae13e1353d54cd18da102345c8686e0.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/114e941569be42b9adfe1ae1aa9c5b01.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/19072bdfbbb74a3a81c264923d257b9d.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/3303c83dd3654e37903270de1cd4dfb5.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/3e07055d97a740cda3c8b9b9b4bbe5c4.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/e5acaef67a79443e920f3741d0ab2cfd.png)
(Ⅰ)判断过
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/5f0f88aab3d44c3db4a9e9dc64ee37d1.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/4da02b3018894144b4698953561cf4cc.png)
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/aae13e1353d54cd18da102345c8686e0.png)
(Ⅱ)求证:
![](https://img.xkw.com/dksih/QBM/2016/4/20/1572599536279552/1572599542439936/STEM/1c7c9fe0278b482b8a2ec0833cb58ee8.png)
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10-11高二下·福建三明·阶段练习
5 . 先阅读下列不等式的证法,再解决后面的问题:
已知
且
,求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c6c22cb280913922a6b95344ad0997.png)
证明:构造函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dba68d676bf9e77c974fb7cc1da4ee.png)
因为对一切
,恒有
,所以
,从而![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c6c22cb280913922a6b95344ad0997.png)
(1)若
,且
,请写出上述结论的推广式;
(2)参考上述证法,对你的结论加以证明;
(3)若
,求证
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c38216ac0eb2bcaa85fd8c61901f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e5dadfc7d9b12bea102cc0ce5bfcc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c6c22cb280913922a6b95344ad0997.png)
证明:构造函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dba68d676bf9e77c974fb7cc1da4ee.png)
因为对一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00148b121ca924133dfc93af99e7cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c6c22cb280913922a6b95344ad0997.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b2509af4d6b78ffe1fc3b4ca7301c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4b9eca505fbff0bff1d2724d7155eb.png)
(2)参考上述证法,对你的结论加以证明;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03858c5f3aef6ff80609692d4e4f6fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1244e50a8246eb77b35b19007fbb443.png)
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名校
6 . 如图,已知
平面ABC,
,
,
,
,
,点
为
的中点
平面
;
(2)求直线
与平面
所成角的大小;
(3)若点
为
的中点,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa742d9b84b537be10034553776400e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4f0c1c9cca0555906d8a53e1a6803d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133760237c0ccf2d6a83786925b6d23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab527e1b5f124429b532804ef3f870f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4eaac4ba87386eca79a4f8b5d99ec38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
7日内更新
|
432次组卷
|
2卷引用:福建省安溪第一中学2023-2024学年高一下学期5月份质量检测数学试题
名校
解题方法
7 . 如图,在直三棱柱
中,
,
分别为线段
,
上的点,且
平面
.
;
(2)当
为
的中点,
时,求证:
.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb66e4fa5ca4231b8ce2490eeb192b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489bc206882a18e50d4d5272e5b862ef.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e04a0ba8fe0c0a240669fd793b7cb7.png)
您最近一年使用:0次
2024-06-08更新
|
1209次组卷
|
3卷引用:福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题
福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题(已下线)6.5.1直线与平面垂直-【帮课堂】(北师大版2019必修第二册)
名校
8 . 如图,
,
是圆锥底面圆
的两条互相垂直的直径,过
的平面与
交于点
,若
为
的中点,
,圆锥的体积为
.
;
(2)若圆
上的点
满足
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813b03f3d13783ee2cb12a81ce6fd07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9c25a19759b50db93a7f4c6d750ff4.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ceaaa537fddde531dcae13a6ab412f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ef49a4fcf91b1c60bbd38ac51295fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
2024-06-03更新
|
1350次组卷
|
4卷引用:福建省龙岩市上杭县第一中学2024届高三下学期5月数学模拟试题
9 . 如图,在棱长为2的正方体
中,为
棱
的中点,
为棱
的中点,平面
与平面
将该正方体截成三个多面体,其中
,
分别在棱
,
上.
平面
;
(2)求异面直线
与
所成角的余弦值;
(3)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea5787b53322bbfd5a6300aac1b84c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311e9cc12153a72e0b5c9290204badff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8b96bc1fed9c66ef8ab465d7e5362c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311e9cc12153a72e0b5c9290204badff.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53330c107f8245290a5a42c3d356acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb837e11438f2cede53982203c4bd08.png)
您最近一年使用:0次
2024-06-08更新
|
605次组卷
|
4卷引用:福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题
福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题(已下线)第六章:立体几何初步章末综合检测卷(新题型)-【帮课堂】(北师大版2019必修第二册)(已下线)专题01 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)
名校
10 . 如图,在四棱锥
中,
,
,
,E为棱
的中点,
平面
.
平面
;
(2)若二面角
的大小为
,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/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639bec6242a4b3f7bfb4b7033a67328c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
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2024-06-08更新
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2卷引用:福建省南安市侨光中学2023-2024学年高一下学期第2次阶段考试(5月月考)数学试题