名校
解题方法
1 . 若直线
与
交于
,
两点,则
面积的最大值为_________ ,写出满足“
面积最大”的
的一个值________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/816d1f63b737faba12ab856d7e5dc885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8159f28f6c287fb3479678d6e1424217.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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
2 . 命题:若
是等比数列,则前n项和
不存在最大值和最小值.写出一组说明此命题为假命题的首项![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
___________ 和公比![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7999465d0e871febde66296a0cbf058c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0d99fef1aa4dbcc6dc7b30b7d2c9a9.png)
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3 . 若数列
、
均为严格增数列,且对任意正整数n,都存在正整数m,使得
,则称数列
为数列
的“M数列”.已知数列
的前n项和为
,则下列结论中正确的是________ .
①存在等差数列
,使得
是
的“M数列”
②存在等比数列
,使得
是
的“M数列”
③存在等差数列
,使得
是
的“M数列”
④存在等比数列
,使得
是
的“M数列”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf49ec5ab0efb3c5dd2fe780e28e85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①存在等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
②存在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
③存在等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
④存在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
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解题方法
4 . 已知
,
,
,则三者大小关系为________ (按从小到大顺序)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23fdb560c7313628bd027a9c40f100ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a942b177b2126602a515359bfe4449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff52cb77bc96e5b391d0bd06b05bde6.png)
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5 . 汉代刘歆设计的“铜嘉量”是龠、合、升、斗、斛五量合一的标准量器,其中升量器、斗量器、斛量器的形状均可视为圆柱.若升、斗、斛量器的容积成公比为10的等比数列,底面直径依次为
,且斛量器的高为
,则斗量器的高为______
,升量器的高为________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d40bfea5eaefd08ce28476a2708262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5f863463679148ff8f85329744fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f3bf70722b22983c120d008d097602.png)
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2024-06-15更新
|
2531次组卷
|
6卷引用:2024年北京高考数学真题
2024年北京高考数学真题(已下线)2024年北京高考数学真题变式题11-15(已下线)五年北京专题06立体几何与空间向量(已下线)三年北京专题06立体几何与空间向量专题07立体几何与空间向量专题08立体几何与空间向量(第一部分)
名校
解题方法
6 . 已知函数
.
①若
,则
的最小正周期是______ ;,
②若
,则
的值域是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5272b3bd721b8794178a2573a20d7a75.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dcee772e6187ac31d7f8d69b0487000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05a467ddaa138590b3b56615c2c42a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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解题方法
7 . 已知等比数列
满足:
(
),请写出符合上述条件的一个等比数列
的通项公式:______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49708635be29b0a43b0708cbf8c5c4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60960a0a619043d7bfd89bbd6cd96dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
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8 . 已知函数
,若
是偶函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
__________ ;若圆面
恰好覆盖
图象的最高点或最低点共3个,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c69f724f57925d84d4dc5a29d6474491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac624f921a4282e16b160384c47414d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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2024-06-10更新
|
365次组卷
|
2卷引用:北京市中国人民大学附属中学2024届高三下学期5月热身练习数学试题(三模)
名校
9 . 已知数列
的前n项和为
且
,给出下列四个结论:①长度分别为
的三条线段可以构成一个直角三角形:②
;③
;④
.其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae734ad099abbb2f7efe7d7a6a4169fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3807e619b383425065eda0ae269ef81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4a02ca421084c3a93d42597bdffb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b3ee64ccd5bb72bbef0f514989c69a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62552c86435988206cdaee449df97a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4024050c475a5fd70d29314576c6d0a1.png)
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2024-06-10更新
|
309次组卷
|
2卷引用:北京市中国人民大学附属中学2024届高三下学期5月热身练习数学试题(三模)
名校
解题方法
10 . 数学上的符号函数可以返回一个整型变量,用来指出参数的正负号,一般用
来表示,其解析式为
.已知函数
,给出下列结论:
①函数
的最小正周期为
;
②函数
的单调递增区间为
;
③函数
的对称中心为
;
④在
上函数
的零点个数为4.
其中正确结论的序号是____________ .(写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165d88ea5812bd14de49f5e3436eefad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a3bd54753e4c1a5fc06b414cc44ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d436e42ddbacbbd0af82f0e4750e54.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d56bab4fdb876bd72d5c9c7a734375.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5760e7c1da0c80f6b8912406b6b75c.png)
④在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb66add53686f989fbbb057652cb6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3077b0cfb8a47439afc656af6cc889ad.png)
其中正确结论的序号是
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