名校
解题方法
1 . 如图,四棱锥
的底面
是矩形,
平面
为
的中点,
为PA上一点,且
.
平面BDQ;
(2)若二面角
为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19210d688c39eb13fdf214dc517b1556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571c3a99cf0b5225444cc5d2d586874d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb178784aa857d4d4683e650273f054.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2386b1cb84295ef95039af00cc76772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a4ccef06bd7c89746239123517347c3.png)
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2024-06-11更新
|
169次组卷
|
2卷引用:黑龙江省双鸭山市第一中学2024届高三下学期第五次模拟考试数学试卷
名校
2 . 已知函数
.
(1)当
时,讨论
的单调性;
(2)若
是
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774d43498b111ed9b5bafaa3fe8818d2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e1e62266f846674d6837fbff34e42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655c90990e13cac00d36d671272c69b.png)
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名校
解题方法
3 . 在平面直角坐标系
中,点E到点
的距离与其到x轴的距离相等,记动点E的轨迹为
.
(1)求
的方程;
(2)已知
,过点
的直线与
交于P,Q两点,直线AP,AQ与
分别交于M,N(异于P,Q)两点,若
,求直线PQ的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb14382e662a3afc482f89b61845bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ab0b3037b6c53f8004343e26b12b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f868900a3d9769db641900d0de582c.png)
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4 . 为了检测A、B两种型号的抗甲流病毒疫苗的免疫效果,某医疗科研机构对100名志愿者注射A型号疫苗,对另外100名志愿者注射B型号疫苗,一个月后,检测这200名志愿者他们血液中是否产生抗体,统计结果如下表:
(1)根据小概率值
的独立性检验,判断能否认为A型号疫苗比B型号疫苗效果好?
(2)志愿者中已产生抗体的不用接种第二针,没有产生抗体的志愿者需接种原型号抗甲流病毒疫苗第二针,且第二针接种
型号疫苗后每人产生抗体的概率为
,第二针接种B型号疫苗后每人产生抗体的概率为
,用样本频率估计概率,每名志愿者最多注射两针.现从注射A、B型号抗甲流病毒疫苗的志愿者中各随机抽取1人,X表示这2人中产生抗体的人数,求X分布列和数学期望.
参考公式:
(其中
).
疫苗 | 抗体情况 | |
有抗体 | 没有抗体 | |
A型号疫苗 | 80 | 20 |
B型号疫苗 | 75 | 25 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0298d106f2b72aadf3cffce041a25da6.png)
(2)志愿者中已产生抗体的不用接种第二针,没有产生抗体的志愿者需接种原型号抗甲流病毒疫苗第二针,且第二针接种
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc70b5e1ba847b9918a50f67bfbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356b05e46b10ee51c3e43546d73ec96c.png)
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解题方法
5 . 记
为数列
的前n项和,
是首项与公差均为1的等差数列.
(1)求数列
的通项公式;
(2)设
,求数列
的前2024项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ba2b14e2a43f387d78a33e77813f2a.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b0e1f31866a3fbfb90d92044202bcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3200f3cc24af2c9663b5c0de282810.png)
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解题方法
6 . 已知双曲线
的焦距为
,点
在
上.
(1)求
的方程;
(2)直线
与
的右支交于
,
两点,点
与点
关于
轴对称,点
在
轴上的投影为点
.
(ⅰ)求
的取值范围;
(ⅱ)求证:直线
过点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0c551cfc411bdb73d2d94e72a274ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51698f7095e795d4f0527b986ac1db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a771f2e80c8a29ed2ebd76498b0f49.png)
(ⅱ)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2024-05-13更新
|
1209次组卷
|
3卷引用:黑龙江省双鸭山市友谊县高级中学2024届高三下学期高考模拟(一)数学试题
名校
解题方法
7 . 已知数列
的前n项和为
.
(1)求
,
;
(2)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdee039c0b6771f1d11ed6e90b0bb628.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
您最近一年使用:0次
2024-05-08更新
|
519次组卷
|
2卷引用:黑龙江省双鸭山市第一中学2023-2024学年高二下学期4月月考数学试题
8 . 如图,在正三棱柱
中,
,点
为
的中点.
//平面
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8da7fd8e46e7db2d692486c252274cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
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9 . 中华茶文化源远流长,博大精深,不但包含丰富的物质文化,还包含深厚的精神文化.其中绿茶在制茶过程中,在采摘后还需要经过杀青、揉捻、干燥这三道工序.现在某绿茶厂将采摘后的茶叶进行加工,其中杀青、揉捻、干燥这三道工序合格的概率分别为
,每道工序的加工都相互独立,且茶叶加工中三道工序至少有一道工序合格的概率为
.三道工序加工都合格的绿茶为特级绿茶,恰有两道工序加工合格的绿茶为一级绿茶,恰有一道工序加工合格的绿茶为二级绿茶,其余的为不合格绿茶.
(1)在绿茶的三道工序中恰有两道工序加工合格的前提下,求杀青加工合格的概率;
(2)每盒绿茶(净重
)原材料及制作成本为30元,其中特级绿茶、一级绿茶、二级绿茶的出厂价分别为90元,60元,40元,而不合格绿茶则不进入市场.记经过三道工序制成的一盒绿茶的利润为
元,求随机变量
的分布列及数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26872e2d89a5f1b66c3f74ab63e1a881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca9afd7a2a73f5d471737836d5cc179.png)
(1)在绿茶的三道工序中恰有两道工序加工合格的前提下,求杀青加工合格的概率;
(2)每盒绿茶(净重
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba5b5b312d2889c239dd8ad89c57a7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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10 . 已知数列
的各项均为正整数,设集合
,
,记
的元素个数为
.
(1)若数列A:1,3,5,7,求集合
,并写出
的值;
(2)若
是递减数列,求证:“
”的充要条件是“
为等差数列”;
(3)已知数列
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f885247785940c5c849210fb6f8abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4884c506476f191d7919cd266c8c0212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a0c2bb484bf523189b093485eca999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(1)若数列A:1,3,5,7,求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ff5cb5a9d88ed7db2c06683c3e355.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3197c615558fee3993d2a8deb9091f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d509697c5391a7c24d9bbc2c82422b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff241fc46c23ac975c5b39e87a9e46a.png)
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2024-04-19更新
|
331次组卷
|
4卷引用:黑龙江省双鸭山市友谊县高级中学2024届高三下学期高考模拟(一)数学试题
黑龙江省双鸭山市友谊县高级中学2024届高三下学期高考模拟(一)数学试题吉林省长春市长春吉大附中实验学校2023-2024学年高二下学期5月期中考试数学试卷(已下线)2024年北京高考数学真题平行卷(基础)(已下线)集合与常用逻辑用语-综合测试卷B卷