1 . 在锐角
中,角
的对边分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
为
的面积,且
,则
的取值范围为__________ .
![](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/7132c2d8b2ff504e6c2ba36c4f6dcfaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c28d53e229fcea80c26b22d9e1a94ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a6afd3e0a0ed112f0533119fbb35d0.png)
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2 . 类比于平面三角形中的余弦定理,我们得到三维空间中的三面角余弦定理:如图1,由射线
、
、
构成的三面角
,
,
,
,二面角
的大小为
,则
.
中,平面
平面
,
,
,求
的余弦值;
(2)当
时,证明以上三面角余弦定理;
(3)如图3,斜三棱柱
中侧面
,
,
的面积分别为
,
,
,记二面角
,二面角
,二面角
的大小分别为
,
,
,试猜想正弦定理在三维空间中推广的结论,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa26fadeee2becc192fa53d778445d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac229a5e782559ffb0f271cbfc01c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6ab2d197160f40b72fe0abb3fe527d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6a7725d31fb74e974e2e45ba56805a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73152c2b4298298c8b81dc16dc21f5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947c03e48c4be7485f1547817f890c53.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291e4e0dc7974f2ce1b59620e3ec0232.png)
(3)如图3,斜三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa84da7ead562cffd02afd5940f8aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1654dfe63f11563eadbaee32dae7b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0cebc1b9472488bfb8f0db1c723fef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
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解题方法
3 . 三角形的布洛卡点是法国数学家克洛尔于1816年首次发现.当
内一点
满足条件
时,则称点
为
的布洛卡点,角
为布洛卡角.如图,在
中,角
,
,
所对边长分别为
,
,
,记
的面积为
,点
为
的布洛卡点,其布洛卡角为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5301e013bcb05bbcce0ba5c8dfeb40.png)
.求证:
①
;
②
为等边三角形.
(2)若
求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec15e5cb6d4dc2cf6ba0bedd87514448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5301e013bcb05bbcce0ba5c8dfeb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d7b9d9bf0d5fc25c99170ab27fa4045.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fac4633c3e6bdc3426250ab4591e463.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6492fa033f83d0775b049476612b86ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ca890db371750d26ec7f049cfe4f714.png)
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解题方法
4 . 如图,A、B是单位圆上的相异两定点(O为圆心),且
.点C为单位圆上的动点,线段AC交线段OB于点M.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/13/7ccbf500-5fcf-4fe5-af60-c52eb5af6db3.png?resizew=125)
(1)设
,求
的取值范围;
(2)设
(
),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/5/13/7ccbf500-5fcf-4fe5-af60-c52eb5af6db3.png?resizew=125)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbec8352ce3dbfbf3b173045d0ba8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6da9ea780ba5e54f3be57b4a7bb12b1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ed415a27df301751b8a613ad95cf5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d61f98f7418eda31a1d7c457e3841c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7dabddea6b3477b11da3196a2db7a1.png)
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解题方法
5 . 如图,在棱长为1的正方体
中,
为平面
内一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若![]() ![]() ![]() ![]() |
B.平面![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.对于给定的点![]() ![]() ![]() ![]() |
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3卷引用:广东省东莞市东华高级中学、东华松山湖高级中学2023-2024学年高一下学期期中教学质量检查(二)数学试题
名校
6 . 如图,在棱长为2的正方体
中,已知
,
,
分别是棱
,
,
的中点,点
满足
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f36a6370254d829ad191cb5727ea32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79296cd4046a71e163a8f3e647a176ae.png)
A.![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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5卷引用:广东实验中学2023-2024学年高一下学期第二次段考数学试题
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解题方法
7 . 设
是单位圆上不同的两个定点,点
为圆心,点
是单位圆上的动点,点
满足
(
为锐角)线段
交
于点
(不包括
),点
在射线
上运动且在圆外,过
作圆的两条切线
.
(1)求
的范围
(2)求
的最小值,
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/7818812e33052be4de712cbbbb21e2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8d5cf36f04941f4ad49fe4c5e26133.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8eb37a4dd75318dcbd836395e575bd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e438bc5acc5cc10b3e7138279949a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63a42e22f8bc63465f595caf10e5842.png)
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|
840次组卷
|
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名校
8 . 已知函数
和
的定义域分别为
和
,若对任意
,恰好存在
个不同的实数
,使得
(其中
),则称
为
的“
重覆盖函数”.
(1)试判断
是否为
的“2重覆盖函数”?请说明理由;
(2)若
,为
,的“2重覆盖函数”,求实数
的取值范围;
(3)函数
表示不超过
的最大整数,如
.若
为
的“2024重覆盖函数”请直接写出正实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eddf991be37d25d033f78bd3511809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d5df7922a4e98e8e07bf418dd48a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44a5aed663a9b61ef7355b38c77d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d1a18f254577a0ce74ceb27364b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b96b909824873058aebdaa54f6c21ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a264b8541eddc8ae86058de027d1a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f246e5b05b68bb9fdeb12a319aa7136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa88c20e58953bba4ed04d3ce419df95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ca781ffd5d55cc9b7dd551879ce65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4987dca9120f6a58139fd3e412ed77c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a899e901b141a0a6d56e3387ecf9f047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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2卷引用:广东省广州市第六中学2023-2024学年高一下学期期中考试数学试题
名校
解题方法
9 . 已知
,用
表示不超过
的最大整数.若函数
,函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bed8a0505d06c0404469d92dd1be71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bc65abc5ba0ee635b3e81fa4e22d3c.png)
A.函数![]() | B.函数![]() ![]() |
C.函数![]() ![]() | D.方程![]() |
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4卷引用:广东省深圳市深圳实验学校光明部2023-2024学年高一上学期期末考试数学试题
广东省深圳市深圳实验学校光明部2023-2024学年高一上学期期末考试数学试题四川省内江市第二中学2023-2024学年高一下学期第一次月考数学试题(已下线)专题03y=Asin(ωx+φ)的综合性质期末8种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)江苏省南京外国语学校2023-2024学年高一下学期5月阶段性测试数学试题
10 . 对于函数
及实数m,若存在
,使得
,则称函数
与
具有“m关联”性质.
(1)若
与
具有“m关联”性质,求m的取值范围;
(2)已知
,
为定义在
上的奇函数,且满足;
①在
上,当且仅当
时,
取得最大值1;
②对任意
,有
.
求证:
与
不具有“4关联”性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf557bc0501acbf300fd4ae5993b7242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4870a0f8fee7a8357094ab4309263752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e1ce7071be0743ded4a087fd908eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96101eb5dce02c0213ad008413f3066.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/263b718b5b3cbc27f3e0ef94f4157f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18db64040b2fa9d65075b41ada928fa6.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9c839f85fe048ed0882889e22f5166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d2c5422d4b9f8c11a5ad1b62c6bb87.png)
您最近一年使用:0次
2024-01-24更新
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4卷引用:广东省华南师范大学附属中学2023-2024学年高一上学期期末数学试题
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