1 . 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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2 . 已知函数
的值域是
,若
,则m的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b0f1d2939633cba651b3646083f14e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f723e73e6e321c4a64e0f32f5a17fe.png)
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3 . 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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4 . 已知随机变量
,
,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d0088531480beef86ec5a94a67edf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cb9ddc3c0280ff97079c6fa07a5c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269868d6181db77628cfada89a0adf44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f9a761c10e3757dbea1b1f4d4e42ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5be1440d099f464ef46dee39de6010.png)
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5 . 已知的数
(
),若
的最小正周期为
,
的图象向左平移
个单位长度后,再把图象上各点的横坐标变为原来的2倍(纵坐标不变)得到函数
的图象,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74a01d149399210cc1ce429a5b2b20e.png)
____________ ;若
在区间
上有3个零点,则
的一个取值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d683bbf46f0e98c8a5b0879e4465b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8ae071199874d9d74a4919a58902f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74a01d149399210cc1ce429a5b2b20e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72728cdc6b1c5521eeba55ca804d2d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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6 . 如图,几何体是以正方形ABCD的一边BC所在直线为旋转轴,其余三边旋转90°形成的面所围成的几何体,点G是圆弧
的中点,点H是圆弧
上的动点,
,给出下列四个结论:
①不存在点H,使得平面
平面CEG;
②存在点H,使得
平面CEG;
③不存在点H,使得点H到平面CEG的距离大于
;
④存在点H,使得直线DH与平而CEG所成角的正弦值为
.
其中所有正确结论的序号是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb53e0fdf3ebeb96e4f69feacbd80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f986c181183d8e7e45655e6c5b5d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
①不存在点H,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac315b586b67bb46ad7ec0542984611.png)
②存在点H,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8feff4cac57f90fcca8c7e41e4fbaa7d.png)
③不存在点H,使得点H到平面CEG的距离大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
④存在点H,使得直线DH与平而CEG所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d74ef32584586ec4857acd0a3f4fe9.png)
其中所有正确结论的序号是
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7 . 已知数列
为等比数列,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
____________ ;数列
的前4项和为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cdfc4722a9dff9a8394b409ab9e6d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dbd9ff686703cad03aa383e5fec21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a080c94bf1ffea8d5af10f9688978fb5.png)
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8 . 已知点
为抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2106aa0e7563fe875d14d46f7c6d0f.png)
上一点,则点P到抛物线C的焦点的距离为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79771acd6ebfbcbb3c2057949571f434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2106aa0e7563fe875d14d46f7c6d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75de1947893e5c7a4d98d4458398fd6e.png)
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9 . 已知函数
的定义域为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd5ff41b59099c1d096098e7b5f7c17.png)
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2024-05-10更新
|
729次组卷
|
5卷引用:北京市通州区2023-2024学年高三下学期二模数学试题
北京市通州区2023-2024学年高三下学期二模数学试题广东省江门市新会第一中学2024届高三下学期高考热身考试数学试题(已下线)2.1 函数的概念及其表示 (高三一轮)【讲-基础版】(已下线)2.1函数的概念及其表示(高三一轮)【同步课时】基础卷(已下线)专题05 一轮复习函数的概念与性质--高二期末考点大串讲(人教A版2019)
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10 . 已知过点
的直线(不过原点)与圆
相切,且在
轴、
轴上的截距相等,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570a136ae27fe3ef6d3e0a4a1624486f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877e32adab7fbed8cfb12eef72ca3e65.png)
![](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/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-25更新
|
819次组卷
|
2卷引用:北京市通州区潞河中学2023-2024学年高三下学期第三次模拟数学试卷