名校
1 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a2a540400311fff2fb2c8ed098e82d.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a45190981deec3afa7fa82e93f8004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a2a540400311fff2fb2c8ed098e82d.png)
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2 . 欧拉函数
的函数值等于所有不超过正整数
,且与
互质的正整数的个数(公约数只有1的两个正整数称为互质整数),例如:
,
,则数列
的前
项和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad13428d2891b2bccd870f2a8061f77d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8113f70737283a31ba1c5af62a8118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d53e72365953a1fb223b7255cc43e6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc96280ed7f6538a23bb7d3fec82a331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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3 . 在
中,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e993bde3f1931058eb2c08c3e5bccee6.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca9e90a095dc00ba3289f61892d5832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e993bde3f1931058eb2c08c3e5bccee6.png)
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解题方法
4 . 已知复数
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882bff376e1d71865bd23b747ef78a66.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c26e564110b612b04c59fd4fa8c9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882bff376e1d71865bd23b747ef78a66.png)
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名校
解题方法
5 . 已知函数
在
上单调递增,则实数
的值的范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8546d079488e2d2a171ee668204a97b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5511a368692de27c58ec48ce968de4a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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6 . 对于等差数列和等比数列,我国古代很早就有研究成果,北宋大科学家沈括在《梦溪笔谈》中首创的“隙积术”,就是关于高阶等差级数求和的问题.现有一货物堆,从上向下查,第一层有2个货物,第二层比第一层多3个,第三层比第二层多4个,以此类推,记第
层货物的个数为
,则数列
的前10项和![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241515dbec4be59ea1099bb33e3aa26f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af1f1b7e9e20d799ee3c06b89a0611c.png)
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7 . 已知抛物线
的焦点
与圆
的圆心重合,直线
与
交于
,
两点,且满足:
(其中
为坐标原点且
,
均不与
重合),对于下列命题:
①
,
;②直线
恒过定点
;③
,
中点轨迹方程:
;④
面积的最小值为16.
其中是真命题的有_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80535fc5458973560b8ccfeec4163571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd767240a603ca0c0db5567707eb704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e3dcb7f9fa27f3d07d18a61d4bb36e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c971815096aafba83743ab5e4c89d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adfcdcacf75272cb6a20385c8d06134e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b8b0499988ee9f02f3c0ef389deb1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f436117499e8ba9cb034e2704fc0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b646e7630de8a801824a1c37bb7741ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
其中是真命题的有
您最近一年使用:0次
名校
8 . 已知
,则
的值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e923760168689ca3369df6a2ae8699a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a367b21eea1088ab0174967f6d989421.png)
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2024-06-12更新
|
933次组卷
|
5卷引用:江西省南昌市第十九中学2024届高三下学期第五次模拟考试数学试卷
江西省南昌市第十九中学2024届高三下学期第五次模拟考试数学试卷河南省郑州市2024届高三第三次质量预测数学试题(已下线)四川省成都市外国语学校2024届高三高考模拟(五)理科数学试题天津市第三中学2023-2024学年高二下学期6月月考数学试题河南省许昌市许昌高级中学2024届高三下学期三模数学试题
解题方法
9 . 如图所示,在棱长为1的正方体
中,点E,F分别是棱BC,
的中点,
是侧面
内一点,若
平面AEF.则线段
长度的最大值与最小值之和为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac822b7a0307d1f9378f9da2f9a44d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
您最近一年使用:0次
2024-06-11更新
|
147次组卷
|
2卷引用:江西省南昌市江西科技师范大学附属中学2023-2024学年高一下学期第二次月考数学试卷
名校
10 . 如图,21个相同的正方形相接,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656187cb339306dc30333c58ab42a8c4.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656187cb339306dc30333c58ab42a8c4.png)
您最近一年使用:0次