解题方法
1 . 如图,在四棱锥
中,
平面
,
,
,
.
,
分别为棱
,
上的动点(与端点不重合),且
.
平面
;
(2)若
,设平面
与平面
所成的角为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada414c44eda3553b2b8bd070511b965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3b18adacdc2379dff16946537ea0ff.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bff03bfdc11e703c0e8fd99133552fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cdd1acd5353365eb41cfc2cabad999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3a282d19bf2c827a98d4443330f7ca1.png)
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解题方法
2 . 建盏为宋代名瓷之一,是中国古代黑瓷的巅峰之作,其采用福建建阳特有的高铁黏土和天然釉矿为原料烧制而成,工艺难度大,成功率低.假设建盏烧制开窑后经检验分为成品和废品两类,现有建盏10个,其中5个由工匠甲烧制,3个由工匠乙烧制,2个由工匠丙烧制,甲、乙、丙三人烧制建盏的成品率依次为0.2,0.1,0.3.
(1)从这10个建盏中任取1个,求取出的建盏是成品的概率;
(2)每件建盏成品的收入为1000元,每件废品的收入为0元.乙烧制的这3件建盏的总收入为
元,求
的分布列及数学期望.
(1)从这10个建盏中任取1个,求取出的建盏是成品的概率;
(2)每件建盏成品的收入为1000元,每件废品的收入为0元.乙烧制的这3件建盏的总收入为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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名校
解题方法
3 . 如图,在四棱锥
中,底面ABCD为平行四边形,
为等边三角形,
,
,
,
.
;
(2)若
,
①判断直线
与直线
的位置关系,并说明理由;
②求平面
与平面
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d152a8b0a10e18aeb42252c9563f47f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a2989b09435d633d1eee54ed9b591f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0d25ba47ac8c9f111543460b8031de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ad7c46b97fbb2c7934636f6f1dc244.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106763481f13fbc37747abaf0d0f4594.png)
①判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
②求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7495688c046142f688c822209c0e968e.png)
您最近一年使用:0次
2024-05-17更新
|
442次组卷
|
2卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
名校
解题方法
4 . 双曲线C:
的离心率为
,点
在C上.
(1)求C的方程;
(2)设圆O:
上任意一点P处的切线交C于M、N两点,证明:以MN为直径的圆过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46529ee9b4550db1c12f187e1fbebde0.png)
(1)求C的方程;
(2)设圆O:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
您最近一年使用:0次
2024-05-17更新
|
546次组卷
|
3卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
5 . 已知
为等差数列
的前n项和,
,
,
.
(1)求
的通项公式;
(2)记
为数列
的前n项和,若
,求n的最小值.
![](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/d9a2f68f2557e24143cc6b02a950a30d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b29f337981e06ebf40b65ddce648841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5cc09a66cb35ef1ee5fce4dd3da8ca.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb4e0f132efa63a6a530788ac36414d.png)
您最近一年使用:0次
2024-05-17更新
|
962次组卷
|
3卷引用:福建省厦门市2024届高中毕业班第二次质量检查基础巩固练习数学试题
6 . 甲箱装有2个黑球和4个白球,乙箱装有2个黑球和3个白球,这些球除颜色外完全相同.某人先从两个箱子中任选一个箱子,再从中随机摸出一球.
(1)求摸出的球是黑球的概率;
(2)若已知摸出的球是黑球,用概率公式判断该球取自哪个箱子的可能性更大.
(1)求摸出的球是黑球的概率;
(2)若已知摸出的球是黑球,用概率公式判断该球取自哪个箱子的可能性更大.
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7 . 坐标平面
上的点
也可表示为
,其中
为
轴非负半轴绕原点
逆时针旋转到与OP重合的旋转角.将点
绕原点
逆时针旋转
后得到点
,这个过程称之为旋转变换.
(1)证明旋转变换公式:
并利用该公式,求点
绕原点
逆时针旋转
后的点
的坐标;
(2)旋转变换建立了平面上的每个点
到
的对应关系.利用旋转变换,可将曲线通过旋转转化为我们熟悉的曲线进行研究.
(i)求将曲线
绕原点
顺时针旋转
后得到的曲线方程,并求该曲线的离心率;
(ii)已知曲线
,点
,直线AB交曲线
于
,
两点,作
的外角平分线交直线AB于点
,求|FM|的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f769907ad11c909d27dd855bf0914592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1029aaebd18d54c2c4d83219ccabc17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3682b5a7157ec7cf8b265bf0d1025c.png)
(1)证明旋转变换公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623c5066668a603bb3d9a8fe05a9e5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca401344cfe39388623409fed20243b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f8906c9d7ce68defb89848faa531ca.png)
(2)旋转变换建立了平面上的每个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f8906c9d7ce68defb89848faa531ca.png)
(i)求将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89034582719fefec243548a3b5e5a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
(ii)已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a721040f609e2d77d72b5deba330e58f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecb5caa69f91798f56550bdba335c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/36719f1e764ee0e719b65c49fae84677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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解题方法
8 . 桌上有除颜色外其他没有任何区别的7个黑球和7个白球,现将3个黑球和4个白球装入不透明的袋中.第一次从袋中任取一个球,若取出的是黑球则放入一个白球,若取出的是白球则放入一个黑球,本次操作完成.第二次起每次取球、放球的规则和第一次相同.
(1)求第2次取出黑球的概率;
(2)记操作完成
次后袋中黑球的个数为变量
.
(i)求
的概率分布列及数学期望
;
(ii)求
的数学期望
.
(1)求第2次取出黑球的概率;
(2)记操作完成
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5031a3a951c4a1d1c5e9f80a5e26513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576074947c20baa9388a82b20d3bd4f2.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93d0f3799612b81e85b87241ec8eee68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/685a18e8694ab2c3243133d8a1988e68.png)
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9 . 在平行四边形
中,
,
,
.将
沿
翻折到
的位置,使得
.
平面
;
(2)在线段
上是否存在点
,使得二面角
的余弦值为
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd0e8f705192e7012805abde99adb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9524e3810e06dc781285f1289e75d653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f29c3e772e56008790298824122792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be449ac37995493404101ba7d474360e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d7ec7877f4ce3166c1a0c587de156f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943feac8392ab6ce588420d6aa866ae9.png)
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解题方法
10 . 在
中,角
的对边分别为
.已知
,且
.
(1)若
,垂足为
,求BD的长;
(2)若
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7b296d57f8134aa27d3910dad49e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80500f9866df4e15761a10e5e85e2ec1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70734a8e672376bb0bd1522e229f86a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b3722c29d3032abc99a8b1dd145e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
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