解题方法
1 . 在棱长为1的正方体
中,过面对角线
的平面记为
,以下四个命题:
,使
;
②若平面
与平面
的交线为
,则存在直线
,使
;
③若平面
截正方体所得的截面为三角形,则该截面三角形面积的最大值为
;
④若平面
过点
,点
在线段
上运动,则点
到平面
的距离为
.
其中真命题的序号为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b239e234d9ae31814af54bf27b7056ba.png)
②若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0c6947783608bd8f6dc7fdaadad2cb.png)
③若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
④若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b78c047642924fe864028c81b1f49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
其中真命题的序号为
您最近一年使用:0次
2 . 设函数
的定义域为D,若命题p:“
,
”为假命题,则a的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709f71dee194d3fe1fd68c1c896a45e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92cee8296180434323233402cad0567c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
您最近一年使用:0次
3 . 如图所示,平面中两条直线
与
相交于点
,对于平面上任意一点
,若
,
分别是
到直线
与
的距离,则称有序非负实数对
是点
的“距离坐标”,给出下列四个命题:
![](https://img.xkw.com/dksih/QBM/2021/4/23/2706077913825280/2707664354615296/STEM/9e15335e-6124-48a7-8b6a-2816d5519936.png)
①“距离坐标”为
的两点间距离为2;
②若
,则点
的轨迹是一条过
点的直线;
③若
,则“距离坐标”为
的点有且仅有4个;
④若直线
与
的夹角是60°,则
或
.
其中所有正确命题的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e257b2b02bcd57c116841807979bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2021/4/23/2706077913825280/2707664354615296/STEM/9e15335e-6124-48a7-8b6a-2816d5519936.png)
①“距离坐标”为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72583e4cbf9e64cf692ecf600983fdee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6c0ae5144fcc033002b54006a9cfdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e257b2b02bcd57c116841807979bbc.png)
④若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441347596788bcbd19dd6bbfb2ce7b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61a87cc610f1c8796f6c477c9fce58ec.png)
其中所有正确命题的序号为
您最近一年使用:0次
2021-04-25更新
|
568次组卷
|
2卷引用:山东省聊城市2021届高三二模联考数学试题
名校
4 . 给出以下四个命题:
①若
,则
;
②已知直线
与函数
,
的图像分别交于点
,则
的最大值为
;
③若数列
为单调递增数列,则
取值范围是
;
④已知数列
的通项
,前
项和为
,则使
的
的最小值为12.
其中正确命题的序号为__________ .
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d6063ee5703cb140dfc69c9cde0bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfa5bb8b7d70c8dbf01bbc01d2b2019.png)
②已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8feb6516836167daab0bad41689b5d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
③若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c33b314a69d8a715bfd7e1481f0463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb74292380b8df9519b9c33bfd564f8.png)
④已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c4593f37ce523cfa8fb5c102240319.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/49763402b2f2023f0ba64c37924267d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
其中正确命题的序号为
您最近一年使用:0次
2020-05-22更新
|
779次组卷
|
3卷引用:广西南宁市第三中学2019-2020学年高一期中段考数学试题
名校
5 . 已知不等式
的解集为A,
的解集为B,若“
”是“
”的充分不必要条件,那么实数m的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1692b640417d185337e205fdf285faed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1b78cdf527aa9294e94d5dbbc3d4da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
您最近一年使用:0次
2020-02-16更新
|
2417次组卷
|
7卷引用:安徽省芜湖市2019-2020学年高二上学期期末数学(文)试题
安徽省芜湖市2019-2020学年高二上学期期末数学(文)试题2020届江苏省南京师大附中高三下学期期初数学试题福建省福州教育学院第二附属中学2020-2021学年高二上学期期中考数学试题四川省邻水实验学校2020-2021学年高二上学期第三阶段考试数学(理)试题(已下线)专题1.2 由集合关系求参数取值范围 B卷-2021-2022学年高一数学单元卷模拟(易中难)(2019人教A版必修第一册)广西壮族自治区钦州市第四中学2023届高三上学期9月考试数学(文)试题广西南宁市广西大学附属中学2023-2024学年高一上学期期中段考数学试题
名校
6 . 如图所示,
是定义在区间
上的奇函数,令
,并有关于函数
的四个结论:
①若
,对于
内的任意实数
,
恒成立.
②函数
是奇函数的充要条件是
.
③若
,
,则方程
必有3个实数根.
④
,
的导函数
恰有两个零点.
其中所有正确结论的序号是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281d4324c2aa43ecf1cf21438ea112a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018a285b53e19be4d5ed03b4c570773f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69f434cc713ab1fe3286e2090f057f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711dea1b5286cff688f1bc521a8dbe1.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a915c1a8a9304aeb307d130faaeb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86eff5761f61a20c240a428f2a7ceda.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cdab65718a2348c2339da2ed817edd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15ff6bbd513644e730d4cf7b2e749fc.png)
其中所有正确结论的序号是
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/4fe3f172-7de1-4358-8345-98dbc1dfc72d.png?resizew=178)
您最近一年使用:0次
名校
7 . 下列四个命题,其中真命题的序号是_______________ .
(1)
得最小值为2;
(2)
且
,则
恒成立;
(3)
,则
恒成立;
(4)
,其中
表示
三数中最大的一个数,则
的最小值为
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a22f0df337cc77b4124546d1acb08ed4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077a31bd2b8e26c35bfd855e42b5d7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22404ecc9b3ef48f2674c905008521bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba81d5fb9b83fef07f1420e1a3ace59.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4267dc8e500cecea41f8c252af19e34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475bc2e5ea93f868daee34e44cc4c70e.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476a1cea8bb4fec33606f3f75a80ee73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62f3f1d721cbf7a5d3fb5678b9a6349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067988c058392f4132c82c13e7e7e4c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33732f816538fc8d3e5f587a362c8108.png)
您最近一年使用:0次
名校
8 . 下列命题:
①关于
、
的二元一次方程组
的系数行列式
是该方程组有解的必要非充分条件;
②已知
、
、
、
是空间四点,命题甲:
、
、
、
四点不共面,命题乙:直线
和
不相交,则甲成立是乙成立的充分非必要条件;
③“
”是“对任意的实数
,
恒成立”的充要条件;
④“
或
”是“关于
的方程
有且仅有一个实根”的充要条件;
其中,真命题序号是________
①关于
![](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/aa5bb0568678356157bfa5fac7f813ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c842b063ead04eabfb321906f95e28.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
③“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cfada8fd642ddf968bfd4228d48ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e714eb4233acc48bbb4f2c552c790460.png)
④“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d9880afb9e2262dbfcf20235e85a62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee4ee43bf33b641aadeba4dd939cfa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0cd9bfc69d090a062b7ccc1891fce5.png)
其中,真命题序号是
您最近一年使用:0次
9 . 已知有两个不相等的非零向量
,两组向量
和
均由2个
和3个
排列而成,记
,
表示
所有可能取值中的最小值,则下列命题中真命题的序号是_________________ (写出所有真命题的序号)
①
有5个不同的值;
②若
,则
与
无关;
③若
,则
与
无关;
④若
,则
;
⑤若
,
,则
与
的夹角为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116e2e7116a7b5cd0a912ec0699ca017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d652b98f2db3c3002c9ef6fdc060d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e142505aaa7b64eaba9421bd0fea9e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be118f18e17dc2420b2c7021268c6bda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494f173fed024b28d9e2bc7a96362d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ab55ce496dc3dfdf3f0c459ccf49cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494f173fed024b28d9e2bc7a96362d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70fbd20f1e059a8a7f95435278b5ac81.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac408a5d33731ec9026a0a0e21d071f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494f173fed024b28d9e2bc7a96362d3d.png)
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您最近一年使用:0次
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您最近一年使用:0次
2019-05-17更新
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1385次组卷
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3卷引用:【校级联考】广东省佛山一中、珠海一中、金山中学2018-2019学年高二下学期期中考试数学(理)试题
【校级联考】广东省佛山一中、珠海一中、金山中学2018-2019学年高二下学期期中考试数学(理)试题上海市西南位育中学2021-2022学年高二下学期期末数学试题(已下线)高二下期末真题精选(易错60题45个考点专练)(高中全部内容)(原卷版)