名校
1 . 如图,在棱长为
的正方体
中,
,
分别为
,
的中点,有以下四种说法:
![](https://img.xkw.com/dksih/QBM/2022/4/14/2958049529307136/2958818150686720/STEM/a716e0ce-ac0f-4111-ba4c-8aacf0d4c6d3.png?resizew=170)
①直线
与
的夹角为
;
②二面角
的正切值是
;
③经过三点
,
,
截正方体的截面是等腰梯形;
④点
到平面
的距离为
;
则正确命题的序号为_____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2022/4/14/2958049529307136/2958818150686720/STEM/a716e0ce-ac0f-4111-ba4c-8aacf0d4c6d3.png?resizew=170)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
②二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213d25b5ade550ec6afd3536e9eb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
③经过三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
④点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae7f4612c548b1f72a964ddb291cd2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
则正确命题的序号为
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2卷引用:四川省攀枝花市第七高级中学校2021-2022学年高三上学期入学考试理科数学试题
名校
解题方法
2 . 下列说法中正确的序号为___________ .
①在同一坐标系中,函数
与函数
的图象关于
轴对称;
②函数
(
且
)的图象经过定点
;
③函数
的单减区间为
;
④任意
,都有
.
①在同一坐标系中,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/463d84a4fbb7d0e1ca72911e70c4bacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa80ae0b0eab1f14cccf872500f0843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c34af900e0f2a076c26a5273d4f75b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95169f7287a6a0c9b6917eb2ceb245eb.png)
④任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20251bc82067179f013288b5c338856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f487f165f3ecce50cca5e3720c0891c.png)
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2021-11-21更新
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2卷引用:四川省成都市四川大学附属中学2021-2022学年高一上学期期中考试数学试题
名校
3 . 等差数列
的前
项和为
,若
,公差
,有以下结论:
①若
,则必有
; ②若
,
,则
;
③若
,则必有
; ④若
,则必有
.
其中所有正确结论的序号为______ .
![](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/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63911d261ebb75e0ab8f76b58cbb7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e93339c2793d3d8add8cd5770d20fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6c2e49c873187b12e90a7b4d5d906b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b043acaf51edc23e735492fa61e66f4.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea31d9dcfd7fba1b7c90d4c349525ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe9f984aaa409de0dde80189cda4d03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d77bb6b1a5ca128223c897cf09ba19d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9a959dda5985723ef15d5d31ea6a25.png)
其中所有正确结论的序号为
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3卷引用:四川省资阳市2020-2021学年高一下学期期末数学试题
名校
4 . 对于曲线C:
,给出下面四个命题:
①曲线C不可能表示椭圆;
②当1<k<4时,曲线C表示椭圆;
③若曲线C表示双曲线,则k< 1或k> 4;
④若曲线C表示焦点在x轴上的椭圆,则
,其中所有正确命题的序号为 _________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f5d8320cca3ff218e4ca903df259c4.png)
①曲线C不可能表示椭圆;
②当1<k<4时,曲线C表示椭圆;
③若曲线C表示双曲线,则k< 1或k> 4;
④若曲线C表示焦点在x轴上的椭圆,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0c195ebd4c1f74ca5498a46fc9750c.png)
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|
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5卷引用:四川省攀枝花市第三高级中学校2021-2022学年高二上学期第一次月考数学(文)试题
5 . 如图,在正方体
中,
、
、
分别为线段
、
、
的中点,下述四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/380cf2d1-93a8-4d36-be72-3fe8d216bfe1.png?resizew=179)
①直线
、
、
共点;
②直线
、
为异面直线;
③四面体
的体积为
;
④线段
上存在一点
使得直线
平面
.
其中所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/380cf2d1-93a8-4d36-be72-3fe8d216bfe1.png?resizew=179)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ad8115387158c8dda205d26968ba11.png)
③四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
④线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae39b47a4da24a0647620f09fd0029c0.png)
其中所有正确结论的序号为( )
A.① | B.①② | C.①③ | D.①②③ |
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6 . 给出下列命题:
①同时垂直于一条直线的两个平面互相平行﹔
②一条直线平行于一个平面,另一条直线与这个平面垂直,则这两条直线互相垂直;
③设
为平面,若
,则
;
④设
为平面,若
,则
.
其中所有正确命题的序号为_______________________ .
①同时垂直于一条直线的两个平面互相平行﹔
②一条直线平行于一个平面,另一条直线与这个平面垂直,则这两条直线互相垂直;
③设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/750323bb31800fd98396e7d4027ef1f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35a45cfcdfbda18b089ce6698ccdbcd.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd89e4d1b330f923f5dfae5073c4836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1fa7bf93449d7619e46cef970dbf7a.png)
其中所有正确命题的序号为
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|
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7卷引用:四川省资阳市2020-2021学年高三上学期第二次诊断性考试 数学(理)试题
名校
解题方法
7 . 已知正四棱柱
的底面边长为2,侧棱
为上底面
上的动点,给出下列四个结论:
①若PD=3,则满足条件的P点有且只有一个;
②若
,则点P的轨迹是一段圆弧;
③若PD∥平面
,则DP长的最小值为2;
④若PD∥平面
,且
,则平面BDP截正四棱柱
的外接球所得图形的面积为
.
其中所有正确结论的序号为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48eab2e9070bf8d094193ea52f1129a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
①若PD=3,则满足条件的P点有且只有一个;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71826134c3080aa75becc655a9089855.png)
③若PD∥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
④若PD∥平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cfdc6224181d44e63aab43ddaf07ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71826134c3080aa75becc655a9089855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b2dfd7c4a190b8dbbc56f2fcc2b2ce0.png)
其中所有正确结论的序号为
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4卷引用:四川省内江市第六中学2021届高三第七次月考理科数学试题