1 . 设数列
的前
项和为
,且
,
.
(1)求
;
(2)求
;
(3)若对任意的
,
成立,求
的取值范围.
![](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/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28db143f2d86f4db4470ca9e95667a27.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db8ef40d523242893ebbce537bf5d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 已知函数
.
(1)若
,
,求曲线
在
处的切线方程;
(2)当
时,曲线
过点
的切线有三条,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94daf1031a5e70ef28c527051536f531.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019eb94a6a2b38308811470d860e1a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 设正项等差数列
的前
项和为
,
,
,
,
成等比数列.
(1)求
;
(2)若
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceda82fbc56d664a5d8b8c9e8de1fd18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5f771e56e0e7305280b04aa1df687c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5df8a2e17c59db1724e263b887831ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
4 . 2023年秋季,支原体肺炎在我国各地流行,该疾病的主要感染群体为青少年和老年人.某市医院传染病科从该市各医院某段时间就医且年龄在70岁以上的老年人中随机抽查了200人,并调查其患病情况,将调查结果整理如下:
(1)完成
列联表,并根据小概率值
的独立性检验,分析70岁以上老年人感染支原体肺炎与自身慢性疾病是否有关?
(2)用样本估计总体,并用本次抽查中样本的频率代替概率,从本市各医院某段时间就医且年龄在70岁以上的老年人中随机抽取3人,设抽取的3人中感染支原体肺炎的人数为X,求X的分布列,数学期望
和方差
.
附:
,
.
有慢性疾病 | 没有慢性疾病 | 合计 | |
未感染支原体肺炎 | 40 | 80 | |
感染支原体肺炎 | 40 | ||
合计 | 120 | 200 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead9d6ff51996f3ebace6f212e11a9e4.png)
(2)用样本估计总体,并用本次抽查中样本的频率代替概率,从本市各医院某段时间就医且年龄在70岁以上的老年人中随机抽取3人,设抽取的3人中感染支原体肺炎的人数为X,求X的分布列,数学期望
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc79c66ebaacd709ec9965b90a22b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbcc48b311ff8cdad7b805c4f46eeab.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
0.10 | 0.05 | 0.025 | 0.010 | 0.001 | |
2.706 | 3.841 | 5.024 | 6.635 | 10.828 |
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昨日更新
|
463次组卷
|
3卷引用:广西重点高中联考2023-2024学年高二下学期五月联合调研测试数学试题
广西重点高中联考2023-2024学年高二下学期五月联合调研测试数学试题甘肃省天水市第一中学2023-2024学年高二下学期第二学段检测考试(6月)数学试题(已下线)专题05 一元线性回归模型与独立性检验常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第二册)
5 . 甲、乙等6名同学周末参加环保活动,活动结束后他们站成一排拍照留念.
(1)求甲、乙相邻的不同站法种数;
(2)求甲、乙都不站两端的不同站法种数.
(1)求甲、乙相邻的不同站法种数;
(2)求甲、乙都不站两端的不同站法种数.
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名校
解题方法
6 . 某
(应用软件)举行推广活动,新用户注册前7天内,每天登录可获得1元红包,前7天连续登录的新用户,还可进入抽奖活动页面领取红包,每位用户随机点击4个红包中的1个领取(领取前不知道红包金额),领取后看1分钟广告,可再次从剩余3个红包中领取1个,4个红包的金额分别为
元、
元、
元、
元
.
(1)若前7天连续登录且抽奖活动页面看1分钟广告的新用户获得的所有红包金额之和
(单位:元)的期望值为70元,求
的值;
(2)该
推广活动进行一个月后,对新用户登录方案进行了调整,调整为:新用户注册前7天内,连续登录第
天,当天可获得
元红包,中间中断再登录重新计算连续天数,若新注册用户甲前4天已经连续登录该
,后3天每天登录的概率均为
,求该用户前7天内通过登录获得红包金额之和
(单位:元)的分布列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba5bb5088efb59d57c36b919197126e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9878a063abcb6098d10560f2bf2d4b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073bd7cec3f5d4d0107a2b6affcf59c2.png)
(1)若前7天连续登录且抽奖活动页面看1分钟广告的新用户获得的所有红包金额之和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)该
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba5bb5088efb59d57c36b919197126e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba5bb5088efb59d57c36b919197126e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
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名校
解题方法
7 . 在
中,角A,B,C所对的边分别为a,b,c,且
.
(1)证明:
为等腰三角形.
(2)若D是边BC的中点,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2818bff73d7e297bfbcda3d22d1a153.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若D是边BC的中点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb9af00d442a5c693c970f30efcc916f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-06-11更新
|
1167次组卷
|
3卷引用:广西柳州市第一中学2023-2024学年高二下学期阶段性期中考试数学试题
8 . 已知定点
,动点N在直线
上,过点N作l的垂线,该垂线与NF的垂直平分线交于点T,记点T的轨迹为曲线C.
(1)求曲线C的方程;
(2)已知点P、A、B是曲线C上的点,且
.
(i)若点P的坐标为
,则动直线AB是否过定点?如果过定点,请求出定点坐标,反之,请说明理由;
(ii)若
,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42502a5730e1930d77d7100d1e34707.png)
(1)求曲线C的方程;
(2)已知点P、A、B是曲线C上的点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
(i)若点P的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7334402b0f5f606a82d027208e3e2c.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81529452eb2cb8578fd164db9e957ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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9 . 四棱锥
中,平面
平面
,
,
,
,
,
,
,M为PC的中点,N为PD靠近D的三等分点.
(2)求二面角
的余弦值;
(3)求平面ABMN截四棱锥
所得的上、下几何体的体积比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c8a72acdef14452a6c62f2a60a15fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e5570e6cac94018e08e6573942b3d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5679a74e9f5506266ab627894ab03243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb77e46b82b1edbf990e0d0577381932.png)
(3)求平面ABMN截四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
10 . 已知函数
,其中
.
(1)若
,求
在
处的切线方程;
(2)若函数
存在两个极值点
.
(i)求实数a的取值范围;
(ii)当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88d158cacab265da551bdb84fad5318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
(i)求实数a的取值范围;
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e156df320e6b84a4e18961440b1ca078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eec001bfec02deb84bb9f3f24cb50d5.png)
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