名校
1 . 已知实数,函数
有两个不同的零点
.
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c823090181be0e23e8e9d9f781cbd385.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fb4b017d21b7bbe006344156ec3458.png)
您最近一年使用:0次
2024-03-19更新
|
762次组卷
|
2卷引用:2024届高三下学期3月适应性考试数学试题(新高考金卷)
名校
解题方法
2 . 已知直线
与抛物线
:
交于
,
两点.
是线段
的中点,点
在直线
上,且
垂直于
轴.
(1)求证:
的中点在
上;
(2)设点
在抛物线
:
上,
,
是
的两条切线,
,
是切点.若
,且
位于
轴两侧,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf8085c9d6fc73d634c7c316a14df78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a498dc93f63f98990b8f63990d4fe2e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e52060a3cb5cde73c28264f4e08a3e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bdc0e53398b36c82db3808c68314621.png)
您最近一年使用:0次
名校
解题方法
3 . 设数列
的前
项和为
,
为等比数列,且
,
,
,
成等差数列.
(1)求数列
的通项公式:
(2)设
,数列
的前
项和为
,证明:
.
![](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/4dea1dd4ffcb4cf0697ca43079f6a1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f36fcd81142614c2393024e1950e5a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57908072f697998145c4605d891583fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6778d12ca088339e20cd712be581e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3860c78a8d25ac6b5c1cff5ebbd960fc.png)
您最近一年使用:0次
名校
解题方法
4 . 如图所示,在长方体
中,
,
在棱
上,且
.
,求平面
截长方体所得截面的面积
(2)若点
满足
,求平面
与
所成夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee52cea67e7d0a82c4b8ed1d9fcd55f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/901c9e0d6c246c195b65100f3f622899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74bd823200bb6dfb1c1721345f941ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bc0580c6c53d00438fcf63bcbc5179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533677cab68214d89c7f2ee1a63650a1.png)
您最近一年使用:0次
2024-03-10更新
|
644次组卷
|
3卷引用:2024届高三下学期3月适应性考试数学试题(新高考金卷)
名校
5 . 垃圾分类是普惠民生的一项重要国策.垃圾分类不仅能够减少有害垃圾对环境的破坏,减少污染,同时也能够提高资源循环利用的效率.垃圾分类共分四类,即有害垃圾,厨余垃圾,可回收垃圾与其他垃圾.某校为了解学生对垃圾分类的了解程度,按照了解程度分为
等级和
等级,随机抽取了100名学生作为样本进行调查.已知样本中
等级的男生人数占总人数的
,两个等级的女生人数一样多,在样本中随机抽取1名学生,该生是
等级男生的概率为
.
(1)根据题意,完成下面的二维列联表.并根据小概率值
独立性检验,判断学生对垃圾分类的了解程度是否与性别有关?
附:
,其中
.
(2)为了进一步加强垃圾分类工作的宣传力度,学校特举办垃圾分类知识问答比赛活动.每局比赛由二人参加,主持人
和
轮流提问,先赢3局者获得第一名并结束比赛.甲,乙两人参加比赛,已知主持人
提问甲赢的概率为
,主持人
提问甲赢的概率为
,每局比赛互相独立,且每局都分输赢.抽签决定第一局由主持人
提问.
(i)求比赛只进行3局就结束的概率;
(ii)设
为结束比赛时甲赢的局数,求
的分布列和数学期望
.
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33adb74906403b0b00fcbd9fa691d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
(1)根据题意,完成下面的二维列联表.并根据小概率值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead9d6ff51996f3ebace6f212e11a9e4.png)
男生 | 女生 | |
![]() | ||
![]() |
![]() | 0.05 | 0.025 | 0.01 | 0.005 |
![]() | 3.841 | 5.024 | 6.635 | 7.879 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2187714e660234f0b72f2b47d3ea685a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
(2)为了进一步加强垃圾分类工作的宣传力度,学校特举办垃圾分类知识问答比赛活动.每局比赛由二人参加,主持人
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(i)求比赛只进行3局就结束的概率;
(ii)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
您最近一年使用:0次