名校
解题方法
1 . 在长方形
中,
,
,点
在线段
上(不包含端点),沿
将
折起,使二面角
的大小为
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e231505648333857565accb0c3c898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3744ee15af01a8e7c0f126edb5f68132.png)
A.存在某个位置,使得![]() |
B.存在某个位置,使得直线![]() ![]() |
C.四棱锥![]() ![]() |
D.当![]() ![]() ![]() |
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2卷引用:河北省秦皇岛市青龙满族自治县第一中学2024届高三下学期5月模拟考试数学试题
名校
2 . 已知方程
的正根构成等差数列,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d688733a01b1bc9ac801100c50c60f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd707b69a11f8de5566f23c1a2a9ff5a.png)
A.![]() | B.![]() | C.2 | D.4 |
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2卷引用:河北省邯郸市部分示范性高中2024届高三下学期三模数学试题
名校
3 . 已知甲口袋有
个红球和2个白球,乙口袋有
个红球和2个白球,小明从甲口袋有放回地连续摸球2次,每次摸出一个球,然后再从乙口袋有放回地连续摸球2次,每次摸出一个球.
(1)当
时,
(i)求小明4次摸球中,至少摸出1个白球的概率;
(ii)设小明4次摸球中,摸出白球的个数为
,求
的数学期望;
(2)当
时,设小明4次摸球中,恰有3次摸出红球的概率为
,则当
为何值时,
最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0272c60cbea81dd30c4b5690ed9fd31c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc0db1f5bc1c43e4bd7231c7fe63d11.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8cc04da8dc0c2ae5bea4b8904567fd5.png)
(i)求小明4次摸球中,至少摸出1个白球的概率;
(ii)设小明4次摸球中,摸出白球的个数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a4480988244a9d04ec293975db2cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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4 . 甲、乙两人进行知识问答比赛,共有
道抢答题,甲、乙抢题的成功率相同.假设每题甲乙答题正确的概率分别为
和
,各题答题相互独立.规则为:初始双方均为0分,答对一题得1分,答错一题得﹣1分,未抢到题得0分,最后累计总分多的人获胜.
(1)若
,
,求甲获胜的概率;
(2)若
,设甲第
题的得分为随机变量
,一次比赛中得到
的一组观测值
,如下表.现利用统计方法来估计
的值:
①设随机变量
,若以观测值
的均值
作为
的数学期望,请以此求出
的估计值
;
②设随机变量
取到观测值
的概率为
,即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
;在一次抽样中获得这一组特殊观测值的概率应该最大,随着
的变化,用使得
达到最大时
的取值
作为参数
的一个估计值.求
.
表1:甲得分的一组观测值.
附:若随机变量
,
的期望
,
都存在,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fafbc94594b8c877de8883dea10e374c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69656b7a5085c9033cfb16a838c0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
①设随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88738de257f3fdf71154ebc8d4c1d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69656b7a5085c9033cfb16a838c0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe7f95b5d89f9409ec24536da9e826.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9383b6387e1a94d4929663769ab5ab7.png)
②设随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c69656b7a5085c9033cfb16a838c0a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927068f621940e6731e02a0db41060bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6d1a2a6340864352cd68261b26c682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58b2b4120cd1e093a9b3052779d5a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58b2b4120cd1e093a9b3052779d5a73.png)
题目 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
得分 | 1 | 0 | 0 | ﹣1 | 1 | 1 | ﹣1 | 0 | 0 | 0 |
题目 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
得分 | ﹣1 | 0 | 1 | 1 | ﹣1 | 0 | 0 | 0 | 1 | 0 |
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf3baba074e8aeb6f3ea117865bbd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71701db4b413f2364dbcbd612fbc8a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67962bdeee331b3e908dd05e3a8899c.png)
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|
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8卷引用:河北省重点高中2024届高三下学期5月模拟考试数学试题(一)
河北省重点高中2024届高三下学期5月模拟考试数学试题(一)浙江省天域全国名校协作体2023-2024学年高三二模数学试题山东省青岛第二中学2024届高三下学期二模考试数学试题(已下线)数学(江苏专用02)(已下线)模块4 二模重组卷 第6套 全真模拟卷广东省广州市执信中学2024届高三下学期教学情况检测(三)数学试题江苏省苏州实验中学2023-2024学年高二下学期5月月考数学试题(已下线)专题03 第七章 随机变量及其分布列--高二期末考点大串讲(人教A版2019)
名校
解题方法
5 . 已知函数
的定义域为
,其导函数为
,若函数
的图象关于点
对称,
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac87434324956e4145e38ad92a1aa95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac3b9f2559633b745717564096ead14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/959e5ab675f526dfb54b05f8f82151b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005761e387f7b83fe50ed6a97bdd7cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e365a0f474ad40f96239b08a1ef52d54.png)
A.![]() ![]() | B.![]() |
C.![]() | D.![]() |
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8卷引用:河北省邯郸市2024届高三下学期学业水平选择性模拟考试数学试题
6 . 若一个两位正整数
的个位数为4,则称
为“好数”,若
,且
,
为正整数,则称数对
为“友好数对”,规定:
,例如
,称数对
为“友好数对”,
,则小于70的“好数”中,所有“友好数对”的
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d13a6e30a21289e94fc277cf8837689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ac064230ab6367a96d893d90e2eb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c6dff41808d7155650360fd48aa667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70feb95addc50c555e2eb6ad82521ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75f0e4f8c5195728e3e7675586a8513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9317cb763ff70bd19b2950e7f3f74399.png)
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|
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2卷引用:河北省部分示范性高中2024届高三下学期一模数学试题
解题方法
7 . 已知正方体
的棱长为
为线段
上的动点,则三棱锥
外接球半径的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88f17dc8c547feb4fc581504a436657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5420c8c4cf105205deb4a1b8327e6de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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3卷引用:河北省名校联盟2024届高三下学期4月第二次联考数学试题
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解题方法
8 . 把底面为椭圆且母线与底面都垂直的柱体称为“椭圆柱”.如图,椭圆柱(
中椭圆长轴
,短轴
,
为下底面椭圆的左右焦点,
为上底面椭圆的右焦点,
, P为线段
上的动点,E 为线段
上的动点,MN 为过点
的下底面的一条动弦(不与AB重合),则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4836945f324c29ef818b423bcc017a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d8b20bcb61ee074d884ef80a3c4a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7479255f54d51b97e6314db1dc06eb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.当![]() ![]() ![]() ![]() |
B.三棱锥![]() ![]() |
C.若点Q是下底面椭圆上的动点,![]() ![]() ![]() ![]() ![]() ![]() |
D.三棱锥![]() |
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4卷引用:2024届河北省邢台市部分高中二模数学试题
2024届河北省邢台市部分高中二模数学试题河北省衡水中学2023-2024学年高三下学期期中自我提升测试数学试题山东省淄博市2024届高三下学期一模考试数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点3 平面法向量求法及其应用综合训练【培优版】
名校
9 . 英国著名物理学家牛顿用“作切线”的方法求函数零点.已知二次函数
有两个不相等的实根
,其中
.在函数
图象上横坐标为
的点处作曲线
的切线,切线与
轴交点的横坐标为
;用
代替
,重复以上的过程得到
;一直下去,得到数列
.记
,且
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b2139fd92090785e08fbdf814c41f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4eccd123923cc68bd52b20dbf17db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ab44c68cb5ca9cc745e230f0b3aa2a.png)
A.![]() ![]() | B.数列![]() |
C.![]() | D.数列![]() ![]() ![]() |
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2024-02-21更新
|
3055次组卷
|
5卷引用:信息必刷卷05
(已下线)信息必刷卷05广东省东莞中学、广州二中、惠州一中、深圳实验、珠海一中、中山纪念中学2024届高三第四次六校联考数学试题辽宁省沈阳市辽宁实验中学2024届高三下学期高考适应性测试(二)数学试题(已下线)压轴题05数列压轴题15题型汇总-1江苏省常州市华罗庚中学2024届高三下学期4月冲刺测试一数学试卷
解题方法
10 . 已知双曲线:
的左、右焦点为
,
,
,P为双曲线右支上一点,
,
的内切圆圆心为M,
与
的面积的差为1,则双曲线的离心率
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a315b9eb8434525846af742fa5ff2f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dfb22c6f1c155747100e7536cd1abd.png)
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3卷引用:河北省唐山市2024届高三上学期期末数学试题
河北省唐山市2024届高三上学期期末数学试题河北省衡水市枣强县名校协作2024届高三上学期期末数学试题(已下线)2.3.2 双曲线的性质(二十二大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)