名校
解题方法
1 . “
”表示实数
整除实数
,例如:
,已知数列
满足:
,若
,则
,否则
,那么下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ea1aed56c455d77bd3c96b9129d1e9.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/20e1c681b27df538bd4742f6cd8298ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cefeddf71dca8ae824328df3f0e5e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c185ce550ab6fa8f0226e237d6d881d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5520432944173c414edf716f22c41067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3172a2dfbce3ce32fd909ff548e75b26.png)
A.![]() | B.![]() |
C.对任意![]() ![]() | D.存在![]() |
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名校
解题方法
2 . 已知甲植物生长了一天,长度为
,乙植物生长了一天,长度为
.从第二天起,甲每天的生长速度是前一天的
倍,乙每天的生长速度是前一天的
,则甲的长度第一次超过乙的长度的时期是( )(参考数据:取
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ec1e326713ddcd6dd66a24a809bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294e71b833e7a7a4711b829ff3164fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279c21a22d6a7ac8faed319940fe69d5.png)
A.第6天 | B.第7天 | C.第8天 | D.第9天 |
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2024-02-27更新
|
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8卷引用:山东省济南第一中学等校2024届高三下学期阶段性检测(开学考试)数学试题
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名校
解题方法
3 . 平面内互不重合的点
、
、
、
、
、
、
,若
,其中
,2,3,4,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2857fac4963b129d99e79dcb3e13d295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a821e643d5fae24caed0faa6d423dad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae2c84ddd51f10d399401cbf91a1217.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d2f8b944ab6d21b77a1f52a0530654.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-02-27更新
|
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3卷引用:北京市清华大学附中2024届高三下学期开学考试数学试题
名校
4 . 正四面体
棱长为6,
,且
,以
为球心且半径为1的球面上有两点
,
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f462070bf390881ceee2519ac07604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/e49a1538831e007a0e47ec5e1069bff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5128656ad9b18360970d3f50cace2a7.png)
A.24 | B.25 | C.48 | D.50 |
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|
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10卷引用:湖南省岳阳市第一中学2023-2024学年高三下学期开学考试数学试题
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名校
5 . 设无穷等差数列
的公差为
,集合
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040b2d17eb8cc9c82983da549afd2663.png)
A.![]() |
B.当且仅当![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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名校
6 . 如图,点E是
的内心,AE的延长线和
的外接圆相交于点D,与BC相交于点G,则下列结论:①
;②若
,则
;③若点G为BC的中点,则
;④
.其中一定正确的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/e6fa31a7-d828-4c0b-943d-58d185b820ca.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba77f66ecad8eb4a7a63f169f28a3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ee8de2d272e8a3cad423ef206cd7eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2549a1964e7221d4b82698d0afa9ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e792b0ef3d542237ed0903194597651.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/22/e6fa31a7-d828-4c0b-943d-58d185b820ca.png?resizew=160)
A.1 | B.2 | C.3 | D.4 |
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7 . 如图在平面直角坐标系中,一次函数
与
轴交于点
,与二次函数交于点
、点
,点
、
、
三点的横坐标分别是
、
、
.已知四个等式:①
;②
;③
;④
;它们一定成立的是( )
![](https://img.xkw.com/dksih/QBM/2023/10/13/3345146078420992/3345349969346560/STEM/24af12bcb86748769dc5b008eee79f7f.png?resizew=141)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c1972246a0a3d1c987d25205dbdd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/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/da7a2eefaa058fcdc80860a653d8df2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781671e3d7d7fda3383cdbc475fd34cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c389cbbd2651ce26509c81a33586c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43a95c07c7e8460c5dd8aa78de0552b.png)
![](https://img.xkw.com/dksih/QBM/2023/10/13/3345146078420992/3345349969346560/STEM/24af12bcb86748769dc5b008eee79f7f.png?resizew=141)
A.①②③④ | B.①②③ | C.①②④ | D.②③④ |
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8 . 定义:在平面直角坐标系中,对于点
,当点
满足
时,称点
是点
的“倍增点”,已知点
,有下列结论:
①点
,
都是点
的“倍增点”;
②若直线
上的点A是点
的“倍增点”,则点A的坐标为
;
③抛物线
上存在两个点是点
的“倍增点”;
④若点
是点
的“倍增点”,则
的最小值是
.
其中,正确结论的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1185fe2ea3fc2bf6bb3b09dd6b690d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46354969c0613de82c366f1fa5459c4b.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d018a15fb86e6d4dc3082ef8b062b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b78847c6a80fdf0c258607cefc607bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5511a368692de27c58ec48ce968de4a4.png)
③抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353b27715b12c8020985cee29deffdbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
④若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2433e2ed7f3dcabd27312c728ca654a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98ee8ce2c56dccae6b63b5a9ca022b8.png)
其中,正确结论的个数是( )
A.1 | B.2 | C.3 | D.4 |
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2023-09-13更新
|
58次组卷
|
2卷引用:四川省蒲江县蒲江中学2023-2024学年高一上学期入学摸底数学试题
9 . 已知
,对多项式
任意添加绝对值运算(不可添加为单个字母的绝对值或绝对值中含有绝对值的情况)后仍只含减法运算,称这种操作为“绝对领域”,例如:
等,下列相关说法正确的个数是( )
①一定存在一种“绝对领域”操作使得操作后的式子化简的结果为非负数;
②一定存在一种“绝对领域”操作使得操作后的式子化简的结果与原式互为相反数;
③进行“绝对领域”操作后的式子化简的结果可能有11种结果.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec8b6ac4b79dce7c5f0fc650c52b3172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad5711fee1f68fb726ccc2cf8b688f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c68bb68760c48ce7a60415db1341d9.png)
①一定存在一种“绝对领域”操作使得操作后的式子化简的结果为非负数;
②一定存在一种“绝对领域”操作使得操作后的式子化简的结果与原式互为相反数;
③进行“绝对领域”操作后的式子化简的结果可能有11种结果.
A.0 | B.1 | C.2 | D.3 |
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10 . 一次函数
的图象与x轴、y轴分别交于点A,B,点C是OA的中点,过点C作
于C,CD交一次函数图象于点D,P是OB上一动点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de869ae6b6dc5b79fcae3de540b30bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affbe2d2ced2303d8c3d183746d0bcf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186dee1a1cf68677d143172a2a50709c.png)
A.4 | B.![]() | C.![]() | D.![]() |
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2023-09-05更新
|
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2卷引用:广东省佛山市第二中学2021-2022学年高一上学期新生入学考试数学试题