1 . 如图,在六面体
中,平面
平面
,四边形ABCD与四边形
是两个全等的矩形,
,
,
平面ABCD,
,
,
,则六面体
的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04de6e3d84ddf7da3dc4fab26e59df46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590dd3b109776fa5521dfc9eecdfb87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00194912b2521c3fe54d3b0af7563e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44c59421cc4ae05d95fec5ac13a761c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94ef1ff132a7d10e2ab527571e61612c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d0fdc5a00ca0e857b89a7e1420df29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.288 | B.376 | C.448 | D.600 |
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,
满足以下条件:
①
,
;
②
,
,
,
.
(1)求
,
的值.
(2)判断函数
,
的奇偶性,并说明理由.
(3)若
,
,试判断函数
的周期性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306984f0895ba32a7b3bb607065b1eaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83e9f562c10762097469dea27c1e109.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50ac027c6ebce491ae836524d89901c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ebeb1c1f2826da8a2e0761f2d2ba87d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98eb23b8c96a34dd720e00669aa8ed2b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a078165d75cfb890141845324a6173b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60cf12a81b11e33356fe7e1c9e3d0b9.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfaff6cfe1d15bd64c1fa76af5e52831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158fbbd2cbedeb9a6fa1a900630369f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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名校
3 . 已知函数
.
(1)求曲线
在
处的切线方程;
(2)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a44f951eba35ed9b8e78e098fa7d6d8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66d61d5f66d68b4c4a2a25fd7103621.png)
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解题方法
4 . 已知定义在
上的函数
满足
,且当
时,有
,若
,则不等式
的解集是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a053c31366873abc1740437cae8c321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cb52244e80d80aba05265cec591a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9da4fdfdddc259dcef9fdd4b826b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6042ff9aa8376f6bdf6f2c5a4dd1166.png)
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名校
解题方法
5 . 数列
中,从第二项起,每一项与其前一项的差组成的数列
称为
的一阶差数列,记为
,依此类推,
的一阶差数列称为
的二阶差数列,记为
,….如果一个数列
的p阶差数列
是等比数列,则称数列
为p阶等比数列
.
(1)已知数列
满足
,
.
(ⅰ)求
,
,
;
(ⅱ)证明:
是一阶等比数列;
(2)已知数列
为二阶等比数列,其前5项分别为
,求
及满足
为整数的所有n值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82c65a855b1eed9c43e6829f6c3bffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c599a8303d934678c8cae0ed864b776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c599a8303d934678c8cae0ed864b776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5452a758da0f722da03128a5eb3ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f88267cbc5e8e016b1a92bcf0fb27d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281cde49dcc279bdc6b2a99edafe19da.png)
(1)已知数列
![](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/3998df04d0a8ded946c3f39d545fdc7e.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f94c7bb2d2afc4196b15f6879ddf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e9e4a01bdaa1f768225e055b6c6d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13df1f8f074ab49fc065ed0da2d5aff.png)
(ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0965cc6a58c25d9ba7876da319a8cae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
您最近一年使用:0次
2024-05-07更新
|
965次组卷
|
4卷引用:北京市中国人民大学附属中学2023-2024学年高二下学期统练3数学试题
北京市中国人民大学附属中学2023-2024学年高二下学期统练3数学试题2024届山东省潍坊市二模数学试题吉林市第一中学2024届高三高考适应性训练(二)数学试题(已下线)专题04 高二下期末考前必刷卷02(提高卷)--高二期末考点大串讲(人教A版2019)
名校
解题方法
6 . 在平面直角坐标系
中,
,
.集合
,下列结论正确的是______ .
①点
;
②若
,则
;
③若
,则
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8950c7bc835103d52ceffab14b6b31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6938eeb65411eeac15e140cf1db99773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e460725dacf5768aa8290aa52d9d24.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db7f7eb57e496985bfa77847f58345f.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be2bc0b0fb98f94b86546fe2ab85de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae985f4f5ce87b3105e222f94c77899.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193029805ef60186dcc6338d847b01ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58aeae4debbb8d0c43d5f526ec7c0532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab8e57da1a24cba8a5feb1388b2fba6.png)
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名校
7 . 函数
图像上存在两点
,
满足
,则下列结论成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329d1214589aa92c8fe583d97a31f2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f56635924584077092ac3c7dd68837b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce32bcbc07c12f0d60a36403dcbf6872.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c803c3e37110d2541dfa3dc3eb8cbee0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 对于正整数集合
(
),如果任意去掉其中一个元素![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合A为“可分集合”;
(1)判断集合
和
是否是“可分集合”(不必写过程);
(2)求证:四个元素的集合
一定不是“可分集合”;
(3)若集合
是“可分集合”,证明:
为奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7694f1219e3a480e81f62b29915b03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cecc3d59296521ff4e1edc78a4ea67d7.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9859aa908844a32c0e1e069a046727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44d462b5c1b7b7ea6c0f36e5cab65b9.png)
(2)求证:四个元素的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a784e0ba1c17aba6990123fe39b89114.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbfa3e226e067ec597ebf0bbc2e87d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
解题方法
9 . 将平面直角坐标系中的一列点
记为
.设
,其中
为与
轴方向相同的单位向量,若对任意的正整数
,都有
,则称
为
点列.
(1)判断
是否为
点列,并说明理由;
(2)若
为
点列,且
.任取其中连续三点
,证明
为钝角三角形;
(3)若
为
点列,对于正整数
,比较
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/464ce8acfb3e25e4e96b70b2a4da3ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/622a4c88b39fa3d66f44cdacb0b1788f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2980a18e4d0a2a795b7983a1a1866db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e4525be9d715134956094f1f7c9b4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3dda9bc78ee05030be17ceccbcfab3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a443e3315a7fb6489b01fad7e3215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cce5a900e897b3c9bd7fff78a90022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb323b330f9af1c3b30ad20d3fbc4c5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a3d6f45e09539242033b717d891ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aaf329c01986874440a30a0fd7b1d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18eb9f4ba92ab0c1132bdeba722aae0.png)
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10 . 已知数列
:
,
,…,
(
,
)具有性质
:对任意
,
(
),
与
两数中至少有一个是该数列中的一项,
为数列
的前
项和.
(1)分别判断数列0,1,3与数列0,1,3,4是否具有性质
;
(2)证明:
,且
;
(3)证明:当
时,
,
,
,
,
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c1d125b49fe60bc9796cf7d72e9170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ae331839bce8f3c14d7efd7f9d8915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)分别判断数列0,1,3与数列0,1,3,4是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85c71dfc82732880ae7e5d41d04efc0.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
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