1 . 如图所示为某企业员工年龄(岁)的频率分布直方图,从左到右依次为第一组、第二组、……、第五组,若第五组的员工有80人,则第二组的员工人数为( )
A.140 | B.240 | C.280 | D.320 |
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解题方法
2 . 直线
与圆
交于
、
两点,
、
两点的坐标分别为
,
,且
是方程
的两根.
(1)求弦
的长;
(2)若圆
的圆心为
,求圆
的一般方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2297db3c14c256b9691fbb8e5bba978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7b73af3dc8b4f5cbf01551ce6f78fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9d4f56dc2eb55aaebcb5dcc125eaf72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5b9c2aab0325a03c42c49903c1ebdf.png)
(1)求弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a6bfc0db98794026938ca2069d9cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2024-03-07更新
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203次组卷
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2卷引用:江西省九江市六校2023-2024学年高二上学期期末联考数学试题
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3 . 某公司食堂每天中午给员工准备套餐,套餐只有A、B、C三种,公司规定:每位员工第一天在3个套餐中任意选一种,从第二天起,每天都是从前一天没有吃过的2种套餐中任意选一种.
(1)若员工甲连续吃了3天的套餐,求第三天吃的是“套餐A”的概率;
(2)设员工甲连续吃了5天的套餐,其中选择“套餐B”的天数为X,求X的分布列及数学期望.
(1)若员工甲连续吃了3天的套餐,求第三天吃的是“套餐A”的概率;
(2)设员工甲连续吃了5天的套餐,其中选择“套餐B”的天数为X,求X的分布列及数学期望.
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4 . 已知
的半径是1,点P满足
,直线PA与
相切于点A,直线PB与
交于B,C两点,D为BC的中点,设
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
___________ 时,
取得最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2099708046b5e3f94e6500939ba5d05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a9f13126fc3789b2d8a585ef60535f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9251dff989f7d60db751b73033dee269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992907998c85cf872f6e66df0b0c1030.png)
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5 . 下列说法正确的是( )
A.向量![]() ![]() ![]() |
B.“![]() ![]() ![]() |
C.若正数a,b满足![]() ![]() ![]() |
D.已知![]() ![]() ![]() |
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6 . 在通信技术中由
和
组成的序列有着重要作用,序列中数的个数称为这个
序列的长度
如
是一个长度为
的
序列
长为
的
序列中任何两个
不相邻的序列个数设为
,长度为
的
序列为:
,
,都满足数列
,
长度为
且满足数列
的
序列为:
,
,
,
.
(1)求
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634e70033857b751723d34d1ca86f375.png)
(2)求数列
中
,
,
的递推关系![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(3)记
是数列
的前
项和,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aec18fcd4df134d5037dd56f3d82841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f43677db00ba65a7f96fc49627d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2581813c187d2e230d97567d649d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffaa8e2bd299bb83168cfac17137d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e222c99263ff290929466f52bdb07404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a3257d015e9b178850734cfc3a5b1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f43677db00ba65a7f96fc49627d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d786bde127368fd1b2ed7a7d233db866.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbeed5324c432101be517dd6f5c735b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634e70033857b751723d34d1ca86f375.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41ae64e37ebcddccabd64e12b0afc2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7085d141e33ba0188e58fa2177d89ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1c13936c1d87bc8fc19a215f8a138f.png)
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7 . 已知函数①
②
. 从这两个函数中选择一个、并完成以下问题.
(1)求
的解:
(2)在x轴上取两点
和
,设线段
的中点为C,过点A,B,C分别作x轴的垂线,与函数
的图象交于
,线段
中点为M.
(i)求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845a9625056f54e2b623118dcbde919c.png)
(ii)判断
与
的大小.并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbc261343fd5e5fb0b93e54ee23333f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6ff19c4f3d3360749a6c8e372feccc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c66230dc7e2664b7b038028978093d.png)
(2)在x轴上取两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032606f32e41a9c38c5371438855be3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2fbdadf087a4272514a0ca6ec8b4d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23fb90e09994fdc6ab02ed6ba664f31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/382b953ed3bf25b6757cf6c2ec946d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291e1f1ee182b6ef4183649790fe84c7.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845a9625056f54e2b623118dcbde919c.png)
(ii)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd0bc6527169af7f0ad452e640adae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108980d5833420777fa60c88cbd6c0f7.png)
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2024-03-07更新
|
331次组卷
|
4卷引用:北京市延庆区2023-2024学年高一上学期期末考试数学试卷
北京市延庆区2023-2024学年高一上学期期末考试数学试卷(已下线)8.1.3向量数量积的坐标运算-同步精品课堂(人教B版2019必修第三册)四川省广安市友实学校2023-2024学年高一下学期3月月考数学试题(已下线)第二章平面向量及其应用章末综合检测卷(新题型)-【帮课堂】(北师大版2019必修第二册)
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解题方法
8 . 为了了解某校高一学生一次体育健康测试的得分情况,一位老师采用分层抽样的方法选取了20名学生的成绩作为样本,来估计本校高一学生的得分情况,并以
,
,
,
,
分组,作出了如图所示的频率分布直方图,规定成绩不低于90分为“优秀”.
(2)从样本成绩优秀的
,
两组学生中任意选取2人,记为
,
中的学生为
,
中的学生为
,求这2人来自同一组的概率;
(3)从成绩在
的学生中任取3名学生记为A组,从成绩在
的学生它任取3名学生记为B组,这两组学生的得分记录如下:
A组:
; B组:
.
写出a为何值时,A、B两组学生得分的方差相等(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd6f1acdfc48fc594b25c027ce8e72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3634aec4ef008f6664f52a7a92d9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df77e82fba3b3fe79fb17760a541667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0738024abc1a0993ca12a6112d8ac5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f411d8be30cfa2912989e6b08990643a.png)
(2)从样本成绩优秀的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0738024abc1a0993ca12a6112d8ac5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f411d8be30cfa2912989e6b08990643a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a655e4aedad47c733a6c343f86b3ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0738024abc1a0993ca12a6112d8ac5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48eb9133a090469a50cb72b098f08d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f411d8be30cfa2912989e6b08990643a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcf0f2f5795f0b8a333a176b8706117.png)
(3)从成绩在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3634aec4ef008f6664f52a7a92d9b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df77e82fba3b3fe79fb17760a541667.png)
A组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99e6f3f3cd83f6762eab72fd88b7e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eceab3b65f2c1a09f190353e7b86686.png)
写出a为何值时,A、B两组学生得分的方差相等(结论不要求证明).
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2024-03-07更新
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491次组卷
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5卷引用:北京市延庆区2023-2024学年高一上学期期末考试数学试卷
北京市延庆区2023-2024学年高一上学期期末考试数学试卷(已下线)专题06 概率-期末真题分类汇编(人教A版2019必修第二册)(已下线)15.2 随机事件的概率-【帮课堂】(苏教版2019必修第二册)江西省宜春市丰城中学2023-2024学年高一下学期4月期中考试数学试题(已下线)重难点专题16 玩转古典概型-【帮课堂】(苏教版2019必修第二册)
9 . 若
,则
的可能取值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b00438433719b82971f9fe309e04b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd0415fb7f2ffa1d3a21346a2374fb0.png)
A.![]() | B.0 | C.1 | D.2 |
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10 . 已知函数
与
的图象关于直线
对称,若
,构造函数
.
(1)当
时,求函数
在点
处的切线与坐标轴围成三角形的面积;
(2)若
(其中
为
的导函数),当
时,
,证明:
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca5c70f5cb1caf91827aa7d3041f37a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a3f617721f69da3649d17ec9c59602.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c97d54952104950bfd7afc0176bbd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339416541b598f3c1fd390ef1b3251b3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752bf766bc202c8cb83e4c6a9abe989f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424ef928fdc9de964b00ad253701959e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fed1a157dd189c3a1f20868a121cad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac07d4b1e7127c7eb1fb914837256d70.png)
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