名校
1 . 公元前6世纪,古希腊的毕达哥拉斯学派通过研究正五边形和正十边形的作图,发现了黄金分割值约为0.618,这一数值也可以表示为
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b588160dd4d001ee342bbf5b18bba8.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8210744a62fc4cbe44921712064557e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49eb6bedcfb4324c4e7116f56b7f060f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b588160dd4d001ee342bbf5b18bba8.png)
您最近一年使用:0次
2022-09-14更新
|
1011次组卷
|
7卷引用:山东省临沂市第二十四中学2022-2023学年高一下学期6月月考数学试题
2 . 公元前6世纪,古希腊的毕达哥拉斯学派研究过正五边形和正十边形的作图方法,发现了“黄金分割”.“黄金分割”是工艺美术、建筑、摄影等许多艺术门类中审美的要素之一,它表现了恰到好处的和谐,其比值为
,这一比值也可以表示为
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38fe16f54adcc3e4f314b6fecb1ee47.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3feb6b6ef4069134061525264fab958a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8210744a62fc4cbe44921712064557e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e084f0c8ebbcd9fed4b32ce7b04d06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38fe16f54adcc3e4f314b6fecb1ee47.png)
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解题方法
3 . 有下列命题:
①不等式
的解集为
;
②若
,函数
的最小值是2;
③对于
,
恒成立,则实数
的取值范围是
;
④已知
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7c299ac496c0fb85c77eacab348e22.png)
,若
是
的充分不必要条件,则实数
的取值范围是
.
其中真命题的序号为________________ .(把所有正确答案的序号填写在横线上,多选、错选不给分)
①不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5d21732d8a22de752d615b46867f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796daaf8d1d5ebeab2d0d989dffe3716.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647e17f9be50dcaba45fa6b15d5d982a.png)
③对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b78b09b0bae2d4e347a8445393ac19f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8c8fd3bdee0551dd6048a131f9eeb7.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b964e01f15a297b8cc3cb564dea1cf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7c299ac496c0fb85c77eacab348e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9cd3690e7aa3debb1ed054a9f622da.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54209e68b27ab4c59f51aa1e6f3d6fd.png)
其中真命题的序号为
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解题方法
4 . 在棱长为2的正方体
中,点M是对角线
上的点(点M与A、
不重合),则下列结论正确的是______________ .(请填写序号)
①存在点M,使得平面
平面
;
②存在点M,使得
平面
;
③若
的面积为S,则
;
④若
、
分别是
在平面
与平面
的正投影的面积,则存在点M,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/8/ff785f15-c66b-43ee-bd82-a02f45c1820f.png?resizew=157)
①存在点M,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba49eb8ddd4dd38c1f994ccec93430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
②存在点M,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce447afe4b0bb57a844b2c103b55fc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42910d271417cc2435d0affa6c85afd5.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce447afe4b0bb57a844b2c103b55fc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31dd78e9156dcf6db93f6cbcc5b43b14.png)
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5 . 某同学回忆一次大型考试中的一道填空题,题目要求判断一条给定直线与给定圆的位置关系,该同学表示,题中所给直线与圆的方程形式分别为
,
,但他忘记了方程中的三个参数的具体值,只记得
,并且他填写的结果为直线与圆相交.若数组
的每一种赋值的可能性都相等,则该同学该题答对的概率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f24e616b5a35ff372c78c1472f156ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8fa64fec535f51aacbae6480e744d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243e4c9ec9393f4aa3d64da6136b9e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6c9703877376f2469faef45141cc73.png)
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解题方法
6 . 命题
在
单调增函数,命题
(
)在R上为增函数,则命题P是命题Q的________ .(在“充分不必要条件、必要不充分条件、充要条件、既不充分也不必要条件”中选择最合适的填写)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad3ace71c2241cf5b82590ce93b87dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b727d110f266970027c05d35967371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
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2023-12-27更新
|
224次组卷
|
2卷引用:江苏省苏州市苏大附中2023-2024学年高一上学期12月月考数学试题
2023高三·全国·专题练习
7 . 阅读下面题目及其解答过程.
如图,在直三棱柱
中,
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2023/12/1/3379858988621824/3380140028157952/STEM/925fc86dad1c48f09cf7adf52bb8d990.png?resizew=138)
(1)求证:
;
(2)求证:
.
解:(1)取
的中点
,连接
,
,如图所示.
![](https://img.xkw.com/dksih/QBM/2023/12/1/3379858988621824/3380140028157952/EXPLANATION/d8115a60a30b48ac99ac18fb6deb2ed9.png?resizew=139)
在
中,
,
分别为
,
的中点,
,
.
由题意知,四边形
为_ .
为
的中点,
,
.
,
.
四边形
为平行四边形,
.又_ ,
平面
,
.
(2)
为直三棱柱,
平面
.
又
平面
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
_ .
,且
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
_ .
又
平面
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
_ ,
.
以上题目的解答过程中,设置了①~⑤五个空格,如下的表格中为每个空格给出了两个选项,其中只有一个符合逻辑推理.请选出符合逻辑推理的选项(只需填写“A”或“B”).
如图,在直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.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/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2023/12/1/3379858988621824/3380140028157952/STEM/925fc86dad1c48f09cf7adf52bb8d990.png?resizew=138)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cce492aefef0c3a24fffcae3a3ccba.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9874eca4abea481fa84eb772a920f9c7.png)
解:(1)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735056c174e8dd7906257a2a50a962a7.png)
![](https://img.xkw.com/dksih/QBM/2023/12/1/3379858988621824/3380140028157952/EXPLANATION/d8115a60a30b48ac99ac18fb6deb2ed9.png?resizew=139)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.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/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1038fe742b2121709231eed48fcb11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcfbf154e19cbd0580d58ccc9bac077c.png)
由题意知,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c56afd59592dbb194c87cdd725b7dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adec13cc3d4b82438803ac7bfa18d61b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d0463b6e3d27b5cfc1df0e6c14fbef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/758d6c28ad9f09ae4c5dbe5649cdf9f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeeadcae4a2964c73187962918724ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d5a164bf56f8fb92527ad78bc10ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28e425314ef91a4b7d9522ac79fbed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e3ffd599e4fb57893b141bad96c66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625899f6b0246330b5ac95b6538f5ca6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215eb19188ab59c8ec06776d0aee2085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a753598c7dafac4e9f2841b8b9a7132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be509ef5101aae24609ff9941cb246fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bab896c46e21eade473ddabf245263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83499936f532ddce9068dd1ff8eb2b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
又
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e3ffd599e4fb57893b141bad96c66b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0375c6c592f61ee820127b9261e96d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f3d198e76391779fa3badc848c8ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691da5f9c37b146ea9abbc50b8560c51.png)
以上题目的解答过程中,设置了①~⑤五个空格,如下的表格中为每个空格给出了两个选项,其中只有一个符合逻辑推理.请选出符合逻辑推理的选项(只需填写“A”或“B”).
空格序号 | 选项 |
① | A.矩形 B.梯形 |
② | A.![]() ![]() ![]() ![]() |
③ | A.![]() ![]() |
④ | A.![]() ![]() ![]() ![]() |
⑤ | A.![]() ![]() |
您最近一年使用:0次
8 . 设函数
的定义域为
,如果对任意
,都存在唯一的
,使得
(
为常数)成立,那么称函数
在
上具有性质
.现有函数:
①
;②
;③
;④
.
其中,在其定义域上具有性质
的函数的是_______ .(请填写序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cb15d282a40c780c2b68287e47867e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63df36c6387aab1039bc431c5317941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28419dc9aa7bf189c07fd7363ae10.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2c1ac861aad057fbe7734cae19f1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246de316aacce5e2a1b482840ff02f82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d9b6c2e49d3b364792fda2cab1dd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd57ea26ad54a7381754ade671ef1ab4.png)
其中,在其定义域上具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28419dc9aa7bf189c07fd7363ae10.png)
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解题方法
9 . 现有如下命题:
①若
的展开式中含有常数项,且n的最小值为10;
②
;
③若有一个不透明的袋子内装有大小、质量相同的6个小球,其中红球有2个,白球有4个,每次取一个,取后放回,连续取三次,设随机变量
表示取出白球的次数,则
;
④若定义在R上的函数
满足
,则
的最小正周期为8.
则正确论断有__________ .(填写序号)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cd2ce1ccd251c09cc123fa0b3493fd.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f1e02b27ef0953ed4f88863f10ef4f.png)
③若有一个不透明的袋子内装有大小、质量相同的6个小球,其中红球有2个,白球有4个,每次取一个,取后放回,连续取三次,设随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92278194f93b54876e6b319995f5a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e730f59a2af75888cbdd95d383cc7a.png)
④若定义在R上的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacebd0ecba599d14456e23734c68860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
则正确论断有
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10 . 对非负实数x“四舍五入”到个位的值记为
,即当n为非负整数时,若
,则
(如
,
).
给出下列关于
的结论:
①若x,y为非负实数,则
;
②若
,则实数x的取值范围为
;
③当
,m为非负整数时,有
.
其中,正确的结论有______ (填写所有正确的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2efc4b458ea20c1acca4317505e9fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692f19277572dc695f32be2f6b683c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0e5caa2e092b270af84632d1d20f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b981f173bbe6277820123ea29fcd13f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ac76d41805e577ace55d0721b70ff5.png)
给出下列关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2efc4b458ea20c1acca4317505e9fd2.png)
①若x,y为非负实数,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30580d5da931d6e3a4762e050c13f0d9.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f206b7a60be2bd87575983a76c13dd6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404fed5585d3128e0fe18f782c586bf2.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e2b6f7ee0d7d0db08406578a7a883e.png)
其中,正确的结论有
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