解题方法
1 . 帕德近似是法国数学家亨利.帕德发明的用有理多项式近似特定函数的方法.给定两个正整数
,函数
在
处的
阶帕德近似定义为:
,且满足:
,
.(注:
为
的导数)已知
在
处的
阶帕德近似为
.
(1)求实数
的值;
(2)比较
与
的大小;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16563cfb206d0394cac2a0c2595dda6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5aafa80443bb1bf55659966bb030b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4573475f70860a3d99b92a329d0d07f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a48b674555390d3d52b5dca1b8efaae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea7fa65b493fc1bdf84e16d39ae07d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35dd621776dee688a0175a1abe39c258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40765d09390381658d5b4dc0160366cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/043b64b1ead1450d67a720cf18328ce4.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f589e92d29e40d559a9cb548829662c3.png)
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名校
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
时,求
的零点;
(2)若
恰有两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
7日内更新
|
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4卷引用:吉林省吉林市第一中学等校2023-2024学年高二下学期5月期中联考数学试题
名校
3 . 已知函数
,
.
(1)若
,讨论函数
的单调性;
(2)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd58e16598e6bdb3c35194af69951a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895938bc4691b6ad48f8b001dfcad102.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074408cfb3eedc559116996d57d5a087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4175c57c61b71897b10583ad32e5e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c95440ace01be940f1591eed18ab5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f78ae07b1452e4f9dd8ba93db61d17.png)
您最近一年使用:0次
2024-06-05更新
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282次组卷
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2卷引用:山东省泰安市2023-2024学年高二下学期期中考试数学试题
4 . 在探究
的展开式的二项式系数性质时,我们把二项式系数写成一张表,借助它发现二项式系数的一些规律,我们称这个表为杨辉三角(如图1),小明在学完杨辉三角之后进行类比探究,将
的展开式按x的升幂排列,将各项系数列表如下(如图2):
表示,即
展开式中
的系数为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9216a0f9d6e65ea4937ab7bf102c5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affdb56951c1eb5c394817b973cf4434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b87d2924395caf206ff6e6692c3cd0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affdb56951c1eb5c394817b973cf4434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdf138124aba5204739cafbf1b59d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83651456ad892247ebda19d98c40e9c.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2024-06-04更新
|
285次组卷
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2卷引用:山东省泰安市2023-2024学年高二下学期期中考试数学试题
5 . ①在高等数学中,关于极限的计算,常会用到:i)四则运算法则:如果
,
,则
,
,若
,则
;ii)洛必达法则1:若函数
,
的导函数分别为
,
,且
,
则
;②设
,k是大于1的正整数,若函数
满足:对
,均有
成立,则称函数
为区间
上的k阶无穷递降函数.结合以上两个信息,回答下列问题:
(1)计算:①
;
②
;
(2)试判断
是否为区间
上的2阶无穷递降函数;并证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89cbc2f466f483804905ea82d3faa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e137fd4fc65a5c3992e32db3060fa46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999ffb5fc2f7c0b3aca42e902db0f680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00ff879851addbfa7fa4f80e099a653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d52399e72456de84f0a42dd69da06fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a02774dbbbfb146d928384de500d8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090a91e4f3c8930674f98a9fa527709b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783c88951a458d5862557f2a041f817a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3927e9f1e25bfe84d4d03caa53d80196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f021edb6f6d256b0837b365db77b56d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0feda45cb840b1f30f3241998d82e5a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061e376df45ffecd571d89704684214f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c316dece56752ea4023ed51b09adcb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e1f6cf8990c217af7e109120f35cc3.png)
(1)计算:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7529d1357e6d9e2343b2bb7fcb9aaf55.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15d5f4feda6efd2af4f1be9180ae504.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e40e451ed5164bec837f978fddd6413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e88cf1590641c7a45d48dfcccad70e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664710185651593168e63b90188b718a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be1d8c6384d7fabddb693b2b7fcdf4a.png)
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6 . 对于正整数m,n,存在唯一的自然数a,b,使得
,其中
,我们记
.对任意正整数
,定义
的生成数列为
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874689ac8a6f70ecd93aa1aaf7d626f6.png)
.
(1)求
和
.
(2)求
的前3项.
(3)存在
,使得
,且对任意
成立.考虑
的值:当
时,定义数列
的变换数列
的通项公式为
当
时,定义数列
的变换数列
的通项公式为
若数列
和数列
相同,则定义函数
,其中函数
的定义域为正整数集.
(ⅰ)求证:函数
是增函数.
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad12b60594a6408ccc237cad2880088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff38a5b95f1fb452d87fce9c80b1249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574aa06d3d4f9952157c60ec8f40b839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874689ac8a6f70ecd93aa1aaf7d626f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57dbb663375b927f3c00d1be3fda1508.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37dbd8745cf6246eea337a1bf91258c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87dc8de41005802093ae66c08f46a7a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926145a2b2232a88ceed6e69dc050265.png)
(3)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623ebc0f0eba98e8f63b7cd982c11009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8144524289a76dadf88c02976acea2db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf0ce448d146abfcd0bd689b925d168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c20d94765a05ee86edf370dd64fcff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8121a889da1f3ecbecd5387a9473c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98b98330b62847c220ab2f127e11391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5914cd027a87542e12cfb0c92c0aa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf19212dd24556423636ce37034cdf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d054e320d843bf0ca4a620519f75ebaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96dbc1106da9238ec6300e13ca3d9b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46498efb2e485c1172abe2189e498613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88ba8e1dc91318d8a9e1856d8ae080e.png)
(ⅰ)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88ba8e1dc91318d8a9e1856d8ae080e.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee5e2ada7f1e99bf68508d21b8f6fb7.png)
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7 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a670e5d56fcdd3cc214064c5d3d3b1.png)
(1)当
时,解关于
的不等式
;
(2)若
有两个零点
,求
的值;
(3)当
时,
的最大值
,最小值为
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a670e5d56fcdd3cc214064c5d3d3b1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ef9f9f0a79e61a30f7da782cbb2fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5f18a08ed6cf92b894ea722af72862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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8 . 若
是一个集合,
是一个以
的某些子集为元素的集合,且满足:①
属于
,空集
属于
;②
中任意多个元素的并集属于
;③
中任意多个元素的交集属于
,则称
是集合
上的一个拓扑.已知函数
,其中[x]表示不大于
的最大整数,当
时,函数
值域为集合
,则集合
上的含有4个元素的拓扑
的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89d1c17a43495542eaade6426cf4c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668efc94065bc0b990673bf77c40eeeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2024-04-29更新
|
173次组卷
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2卷引用:浙江省温州新力量联盟2023-2024学年高二下学期4月期中考试数学试题
解题方法
9 . 三角形的布洛卡点是法国数学家、数学教育学家克洛尔于1816年首次发现,但他的发现并未被当时的人们所注意.1875年,布洛卡点被一个数学爱好者布洛卡重新发现,并用他的名字命名.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
,点
为
的布洛卡点,其布洛卡角为
.
.求证:
①
(
为
的面积);
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/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.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/9d7b9d9bf0d5fc25c99170ab27fa4045.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa010342528037783c29e6fc705d5bba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/31e02df6f963e47a894cce8b4ad469ec.png)
您最近一年使用:0次
2024-04-24更新
|
628次组卷
|
3卷引用:江苏省常州市教育学会2023-2024学年高一下学期4月学业水平监测数学试题
名校
10 . 已知函数
.
(1)若
,讨论
的零点个数;
(2)若
是函数
(
为
的导函数)的两个不同的零点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a441ed40dca1a0f8c5ed0253d1ca300.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab42358409a44ea7a55fe532fe66ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b550cb121a3346f8d46b7f7ee2117d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380beb181ed0a48cc486131bba4a4c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d106beb9c7a567f35e7f3407f41c963c.png)
您最近一年使用:0次
2024-03-27更新
|
613次组卷
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3卷引用:山东省淄博市高青县第一中学2023-2024学年高二下学期期中学分认定考试数学试题