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解题方法
1 . 有4个外包装相同的盒子,其中2个盒子分别装有1个白球,另外2个盒子分别装有1个黑球,现准备将每个盒子逐个拆开,则恰好拆开2个盒子就能确定2个白球在哪个盒子中的概率为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-08更新
|
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9卷引用:浙江省强基联盟2024届高三下学期5月全国“优创名校”联考数学试题
浙江省强基联盟2024届高三下学期5月全国“优创名校”联考数学试题河北省保定市九校2024届高三下学期二模数学试题山西省晋城市2024届高三第三次模拟考试数学试题(已下线)江苏省苏锡常镇四市2024届高三下学期教学情况调研考试数学试题(已下线)第五套 艺体生新高考全真模拟 (二模重组卷)辽宁省抚顺市六校协作体2024届高三下学期5月模拟考试数学试卷山东省日照市五莲县第一中学2024届高三第三次模拟考试数学试题广西钦州市2024届高三年级第三次教学质量监测 数学山东省菏泽市鄄城县2023-2024学年高二下学期5月月考数学试题
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2 . 某学生通过计步仪器,记录了自己最近30天每天走的步数,数据从小到大排序如下:
5588 6054 8799 9851 9901 10111 11029 11207 12634 12901
13001 13092 13127 13268 13562 13621 13761 13801 14101 14172
14191 14292 14426 14468 14562 14621 15061 15601 15901 19972
估计该学生最近30天每天走的步数数据的第75百分位数为( )
5588 6054 8799 9851 9901 10111 11029 11207 12634 12901
13001 13092 13127 13268 13562 13621 13761 13801 14101 14172
14191 14292 14426 14468 14562 14621 15061 15601 15901 19972
估计该学生最近30天每天走的步数数据的第75百分位数为( )
A.14292 | B.14359 | C.14426 | D.14468 |
您最近一年使用:0次
2024-05-08更新
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1766次组卷
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10卷引用:浙江省强基联盟2024届高三下学期5月全国“优创名校”联考数学试题
浙江省强基联盟2024届高三下学期5月全国“优创名校”联考数学试题河北省保定市九校2024届高三下学期二模数学试题山西省晋城市2024届高三第三次模拟考试数学试题(已下线)江苏省苏锡常镇四市2024届高三下学期教学情况调研考试数学试题(已下线)第二套 艺体生新高考全真模拟 (三模重组卷)(已下线)山东省淄博实验中学2024届高三下学期第三次模拟考试数学试题辽宁省抚顺市六校协作体2024届高三下学期5月模拟考试数学试卷广西钦州市2024届高三年级第三次教学质量监测 数学(已下线)期末押题卷01(考试范围:苏教版2019必修第二册)-【帮课堂】(苏教版2019必修第二册)(已下线)专题05 高一下期末考前必刷卷03-期末考点大串讲(人教A版2019必修第二册)
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3 . 定义2*2数表
,
,
,其中
称为
中的元素.
和
属于复数集合. 我们定义
,其中
,
(共
个),
,
,
:
(1)证明:
(i)
.
(ii)
.
(2)若存在A,B,C,使得
,且
,
,
:
(ⅰ)请列出所有满足条件的有序数对
.
(ⅱ)对
,
,
,试验证其是否满足上述条件.
(3)(ⅰ) 在上一题的(ⅱ)中,
以及
合称为Pauli数表. 任意
均可以表示为:
,
为复数,试用
表示
.
(ⅱ) 设
,请证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b32cd779049dfa4b55b955e8885dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67236be30275de9ab515dc663ad9cc92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75a92b76b4b5ae3c4571525b102491d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba1bbe411bc71bca016d3fd82352f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cd9eab3d56d2fe1c6611ccf5be1695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fa3364d3a162682f50528680cf4403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af76198c7bcd4ba4661c8ecb1fbf7930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855e9b47dd2df4781211d458bbb2dd40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0d82117f3aeb73a48ad24e9b563e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0f9b77ac8d2930cf5bed9fd31aa3791.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04d42748ae6abf54a9ba61fb833a8fd.png)
(1)证明:
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82643b4b9e28d0227c419de4e66df227.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb3e9de425ba79559cd0a2feb7d2109a.png)
(2)若存在A,B,C,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163d61d1df6137585249c17bdf1aff0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce53a57261f19484bf9cda89208d87b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc07d8e94e79abf1a6f717096df42c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c904bea2eaec0153be54e2ca1abb75.png)
(ⅰ)请列出所有满足条件的有序数对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52aaa08d0d339d57f466de67d31f54c7.png)
(ⅱ)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021cb7c01071fa8fb9ae6bc4312d2e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/425989826f834d15fe877946eb5e674f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3ad3326af484fb2493e45b1d8a98b7.png)
(3)(ⅰ) 在上一题的(ⅱ)中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5d6bebc33fde49c8b270b1887de4a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b05e6ffe5ec0915b52dcaabe337a3c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3356935218122dea72e8a911cc4dd203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc11dc86b57dab7d0a07bace5ac7a13a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc80e3e48f5109325489205c77f742c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc11dc86b57dab7d0a07bace5ac7a13a.png)
(ⅱ) 设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225b723bf52d579f519c13c41074cbbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe37acacda21f0768703d5217cf14de.png)
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4 . 如图所示,四棱台
,底面
为一个菱形,且
. 底面与顶面的对角线交点分别为
,
.
,
,
与底面夹角余弦值为
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
平面
;
(2)现将顶面绕
旋转
角,旋转方向为自上而下看的逆时针方向. 此时使得底面与
的夹角正弦值为
,此时求
的值(
);
(3)求旋转后
与
的夹角余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07c321ebb740613ff53c1d6e496ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a61472439de1ba85cfe33840b775f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d76ce5fcc2291de26b44b4b082df5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb34d99a48c5d1d8f21af99c1b70ea49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)现将顶面绕
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2236f820e9625bcc1e81f101e9ab7713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4967af4c76d238fea5695537dfc9e91e.png)
(3)求旋转后
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
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5 . 对于任意的两点
,
,定义
间的折线距离
,反折线距离
,
表示坐标原点. 下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8531b72eeaab9286ca4131e1aac2565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153b4e560c31f5e9aaca7077dd0df7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若存在四个点![]() ![]() ![]() ![]() ![]() |
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6 . 下列条件能确定唯一一个三角形
的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.![]() ![]() ![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() |
D.![]() |
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7 . 空气膜等厚干涉是一个有趣的光学现象,如左图所示,当一块玻璃在另一块平板玻璃上方时,让光线垂直照射就会出现明暗相间的条纹.同一条纹上两玻璃之间的空气间隙厚度一致.现有一圆锥形玻璃,底面周长为24
,母线长为13.将其顶点朝下放置于平板玻璃上,并且使得底面与平板玻璃的夹角
近似满足sin
=
,用光垂直照射,则得到的条纹形状为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6faa377b82f7c39f03875874b78f922b.png)
A.椭圆 | B.双曲线 | C.抛物线 | D.圆 |
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8 . 对于集合A,B,定义A\B=
且
,则对于集合A={
},B={
},
且
,以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5988bf315a64166f60f5e83ee63dc44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bb7c317f907cd7fda5ae49b24f2d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7667c8b7c51a4dbec279efe37159c95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de17e720d2ff39869ca8ab1fa73e899e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdca3f0545c3796a22128874c78b0bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ef577bf5059fba198afb7eddb2f94c.png)
A.若在横线上填入”∩”,则C的真子集有212﹣1 个. |
B.若在横线上填入”∪”,则C中元素个数大于250. |
C.若在横线上填入”\”,则C的非空真子集有2153﹣2个. |
D.若在横线上填入”∪![]() ![]() |
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9 . 已知
,
,数列
和
的公共项由小到大排列组成数列
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8becb97e55f0db7e62abbb86aff80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
A.![]() |
B.![]() |
C.数列![]() ![]() ![]() |
D.![]() ![]() ![]() |
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2024-04-29更新
|
850次组卷
|
4卷引用:浙江省杭州师范大学附属中学2024届高三下学期高考适应性考试数学试卷
10 . 设p为素数,对任意的非负整数n,记
,
,其中
,如果非负整数n满足
能被p整除,则称n对p“协调”.
(1)分别判断194,195,196这三个数是否对3“协调”,并说明理由;
(2)判断并证明在
,
,
,…,
这
个数中,有多少个数对p“协调”;
(3)计算前
个对p“协调”的非负整数之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1538e59a0527883bb6ff5f5a5eb8e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0dd417ec70cf425efddea5f4c7ba7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ded2da98f74d955ff5dd8f9ac051968b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208ffeb1f7342c141f490e3185d11930.png)
(1)分别判断194,195,196这三个数是否对3“协调”,并说明理由;
(2)判断并证明在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366cfc0dec131eacf81cb194da71eb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60c0322d41827fa6dc18ee22de5e769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d950956eba112b45bb5b0a26393c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe9ad3cf2737677a9d3f1fb9fb2d2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ec16c7b0b7d25431d352d89215462.png)
(3)计算前
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223ec16c7b0b7d25431d352d89215462.png)
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