名校
解题方法
1 . 如图,弧AEC是半径为
的半圆,AC为直径,点
为弧AC的中点,点
和点
为线段AD的三等分点,平面AEC外一点
满足
平面
.
;
(2)求点
到平面FED的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b5a90e556da12d63b7f481bd8e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee332f9a2d473022aeb62e79cd8af705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36fe5c17d533c3bd30d6c32cbe94815c.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
名校
2 . 如图,空间六面体
中,
,
,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
平面
为正方形,平面
平面
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
;
(2)若
,求平面
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17d4a6cf11cda87b3dfafaecdec683f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec123fb520885455b57bf7613e1b9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa32bd49a6554a2722444d71315920f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cdffc89ee1fe3e56de89222ad3313cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0b950951cf1ebf3f04b77ca00301e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecad5f4090684e0c60fb228a2ba471c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378c9b0145b88657c2536e43d27123fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2024-03-14更新
|
480次组卷
|
3卷引用:甘肃省2024届高三下学期3月月考(一模)数学试题
3 . 已知椭圆
过点
,离心率为
.不过原点的直线
交椭圆
于
两点,记直线
的斜率为
,直线
的斜率为
,且
.
(1)求椭圆
的方程;
(2)证明:直线
的斜率
为定值;
(3)求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a350d44bf2b7ddfbfe23c754efa9c8d4.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
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2024-05-27更新
|
963次组卷
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2卷引用:甘肃省兰州市西北师大附中2024届高三第五次诊断考试(三模)数学试题
名校
解题方法
4 . 已知非零向量
,
不共线.
(1)如果
,
,
,求证:
,
,
三点共线;
(2)欲使
和
共线,试确定实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a932fca4d0861a21e9fb2b798ed8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94710ac591216841c4645a1e613e71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70d75273f4fa9ce168ec5a35ad8b5b38.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/8455657dde27aabe6adb7b188e031c11.png)
(2)欲使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75d6886724cfe164028aa4d151aa98f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51dbf7fb9e71618bf5031f91c8d86b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2024-03-11更新
|
2457次组卷
|
36卷引用:甘肃省甘南州卓尼县柳林中学2018-2019学年高一下学期期末数学试题
甘肃省甘南州卓尼县柳林中学2018-2019学年高一下学期期末数学试题甘肃省兰州新区贺阳高级中学2023-2024学年度高一下学期3月月考数学试题辽宁省瓦房店市实验高级中学2018-2019学年高一下学期月考数学试卷四川省自贡市田家炳中学2020-2021学年高二上学期开学考试数学试题江苏省淮安市盱眙县马坝高级中学2020-2021学年高三上学期期中数学试题专题6.3《平面向量初步》(A卷基础篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教B版)北京市昌平区新学道临川学校2020-2021学年高一上学期期末考试数学试题广东省外语外贸大学附设肇庆外国语学校2020-2021学年高一下学期第一次月考数学试题福建省建瓯市芝华中学2020-2021学年高一下学期期中考试数学试题内蒙古阿拉善盟第一中学2020-2021学年高二上学期开学考试理科数学试题苏教版(2019) 必修第二册 过关斩将 第9章 9.2.2 向量的数乘广东省增城区四校2021-2022学年高一下学期期中联考数学试题广西桂林市临桂区五通中学2021-2022学年高一下学期期中段考数学试题黑龙江省齐齐哈尔市三立高级中学2021-2022学年高一下学期4月月考数学试题辽宁省沈阳市沈抚育才实验学校2022-2023学年高一上学期期末数学试题(已下线)6.3.1 平面向量基本定理(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)6.2 平面向量的运算(学案)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)陕西省西安工业大学附属中学2022-2023学年高一下学期期中数学试题福建省福州日升中学2022-2023学年高一下学期期中考试数学试题1.3向量的数乘1.3向量的数乘江西省九江市德安县第一中学2022-2023学年高一下学期7月期末考试数学试题山西省忻州市名校2022-2023学年高一下学期4月期中联考数学试题广西玉林市第十一中学2022-2023学年高一下学期3月月考数学试题(已下线)核心考点01平面向量及其应用(1)北师大版(2019)必修第二册课本习题 习题2-3(已下线)第九章 平面向量(压轴题专练)-单元速记·巧练(苏教版2019必修第二册)(已下线)模块一 专题2 平面向量基本定理与坐标运算(A)(已下线)2.3 从速度的倍数到向量的数乘6种常见考法归类-【帮课堂】(北师大版2019必修第二册)河北省廊坊市文安县第一中学2023-2024学年高一下学期第一次集中练(3月月考)数学试题江苏省宿迁市泗阳县实验高级中学2023-2024学年高一下学期第一次调研测试(3月)数学试题贵州省遵义市桐梓县荣兴高级中学2023-2024学年高一下学期第一次(3月)月考数学试题河北省唐山市开滦第二中学2023-2024学年高一下学期4月月考数学试题(已下线)模块一 专题4 平面向量基本定理与坐标运算(A)北师大版高一期中(已下线)习题 2-3四川省泸州市龙马潭区2023-2024学年高一下学期5月期中考试数学试题
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
求曲线
在点
处的切线方程.
(2)若
证明:
在
上单调递增.
(3)当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20439836def79ea69d967d95e81320a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87676cc3ca413d9ba64fab2cd45c909c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec994bb92d9945a4369f1215d859ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-05-08更新
|
372次组卷
|
4卷引用:甘肃省白银市2023-2024学年高二下学期5月期中考试数学试题
名校
解题方法
6 . 已知函数
.
(1)若
对
恒成立,求
的取值范围;
(2)当
时,若关于
的方程
有三个不相等的实数根
,
,
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139ccda5ac5ed8c01bd0e87e84d30e09.png)
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25af1b7613f714301020bb09a33d8fe8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427ddc261e4aea13a25fa479749f4074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c5f6fe92b97f07fb31b118fa97b11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/139ccda5ac5ed8c01bd0e87e84d30e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebb401767499a3b5eedf56cb36b4127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9e12d9f9b1dbd7a1ad8fffe752f5e7.png)
您最近一年使用:0次
2024-05-22更新
|
217次组卷
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2卷引用:甘肃省武威第六中学2023-2024学年高三下学期第五次诊断数学试卷
名校
7 . 如图,在四棱锥
中,底面
为直角梯形,
//
,
,
,平面
平面
,
,
.
;
(2)求二面角
的余弦值.
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df3cbb0e21389791a038f7a9ce6a327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0530f462e5ec1e58c46e1f7644d0cc21.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02535e1a690ca111ca7a395a1bf48080.png)
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2024-03-06更新
|
1218次组卷
|
7卷引用:甘肃省平凉市庄浪县紫荆中学2024届高三上学期第一次模拟考试数学试题
甘肃省平凉市庄浪县紫荆中学2024届高三上学期第一次模拟考试数学试题2020届山东省济宁市嘉祥一中高三第四次质量检测数学试题(已下线)专题03 少丢分题目强化卷(第二篇)-备战2021年新高考数学分层强化训练(北京专版)(已下线)重难点12 立体几何必考经典解答题全归类【九大题型】广东省广州市四中2023-2024学年高二下学期3月月考数学试题内蒙古自治区呼和浩特市剑桥中学2023-2024学年高二下学期第一次(3月)月考数学试题(已下线)专题06 空间直线﹑平面的垂直(一-《知识解读·题型专练》(人教A版2019必修第二册)
名校
解题方法
8 . 如图正方形ACDE所在平面与平面ABC垂直,M是CE和AD的交点,且
,
.
(1)求证:
平面EBC;
(2)求锐二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/b1404641-05c8-4b55-bcd1-bc9a16d235fd.png?resizew=140)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
(2)求锐二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a351d71fa01d3f5920e374a8ee7b524.png)
您最近一年使用:0次
2023-12-11更新
|
225次组卷
|
7卷引用:甘肃省白银市会宁县第四中学2015-2016学年高二上学期期末考试数学(理)试题
9 . 十七世纪至十八世纪的德国数学家莱布尼兹是世界上第一个提出二进制记数法的人,用二进制记数只需数字0和1,对于整数可理解为逢二进一,例如:自然数1在二进制中就表示为
,2表示为
,3表示为
,5表示为
,发现若
可表示为二进制表达式
,则
,其中
,
或
.
(1)记
,求证:
;
(2)记
为整数
的二进制表达式中的0的个数,如
,
.
(ⅰ)求
;
(ⅱ)求
(用数字作答).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afac8d5ff689800b23006bfb787f830e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75d883ba9da001d5bbdb4f9f27ef5d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084e9bad43a8ba23cfe1f348d16e1f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05a2ad4181e34f4155bdc8e9c6613ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209559aca6bf32705588b6a40e0b7320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f4052daae3c3e9ad015e2179319f1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6c716342983f6ae1ffaf192994c4070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489340c9a2d70c00bae13b7018cad448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca64ef9e0c3dd14e99d113dbbe973ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/864f7082fc29a1eb3a51d3548ee34f1d.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce2d56b82e70f24100e6966cc9a5b600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c303cf3774ce07269def2ffd0e77b739.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cdfd430e34aa63094df2b23088cfa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbb3d9df6afb29bf9201fb32d425c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d37b93187edaea11bc4471f62aecfa2.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b965e4215123ce1905dd9a4f77fba4.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2bb483ec28b388bd875049a8bb6c1f.png)
您最近一年使用:0次
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解题方法
10 . 已知抛物线
上有一点
,
为抛物线
的焦点,
,且
.
(1)求抛物线
的方程;
(2)过点
向圆
(点
在圆外)引两条切线,交抛物线
于另外两点
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06d1663b8c2cfbe0308470a3b1c5d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091bb3c75e9827076e9fbd84685c260e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c2632c02415c656fb4bda6f89a8b08.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba90e580d1cad80017e2b197262c8de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-12-05更新
|
834次组卷
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2卷引用:甘肃省兰州市西北师范大学附属中学2024届高三第三次诊断考试数学试题