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1 . 已知复数
的实部为0,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982c2cd8fd33539bd313fe3ea373e6c0.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0d037cbc7584aefec1e2ffe58d0971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982c2cd8fd33539bd313fe3ea373e6c0.png)
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2024-06-07更新
|
1820次组卷
|
5卷引用:山东省菏泽第一中学三校区联考2024届高三下学期5月月考数学试题
2 . 若数列
满足
,则称数列
为牛顿数列,若
,数列
为牛顿数列,且
,
,数列
的前n项和为
,则满足
的最大正整数
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33610d2a46105e3c8456257221d3d07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/195fc747e2fc50cb6df2c844d51e4d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3bb631154bd03c814e8f6c0b39ea8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753cd148252b19cf3a164d6a15fa90c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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3 . 已知
的展开式中所有项的系数的和为1,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a353236f25792c996986eefb149af507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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4 . 设
,
在
方向上的投影向量为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ee058d80bf1f695e71ad49beb81f81.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3391576038a1782ce7283ddb46e6ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cdfd82868aefda05f52913dfd762a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ee058d80bf1f695e71ad49beb81f81.png)
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5 . 法国著名数学家加斯帕尔
蒙日在研究圆锥曲线时发现:椭圆的任意两条互相垂直的切线的交点
的轨迹是以坐标原点为圆心,
为半径的圆
为椭圆的长半轴长,
为椭圆的短半轴长
,这个圆称为蒙日圆.已知椭圆
,若
是直线
上的一点,过点
作椭圆
的两条切线与椭圆相切于
,
两点,
是坐标原点,连接
,当
为直角时,则
为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97ec04a1aa7ac6fce72d589864940a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c6ecdf8ced933e8e6657196acc924f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada970bdcc475ace8b63f4ea02db8446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2801bb773af735fc9c0239d19c20e6e4.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a8a837c11c07073da3ff751d70278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023037c7a3e31ba698c39f9b52db2515.png)
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6 . 已知
,
,
,则
的最小值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131ac7eb1e911c9a40e84235bf3742ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9900bd691d7782b7fced65d28ad5933b.png)
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7 . 已知单位向量
,
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d706bf6fdca693e77cfe740fa0baf06.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed91ca31038a09c86354d20ce62559d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d706bf6fdca693e77cfe740fa0baf06.png)
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8 . 已知样本
,
,
的平均数为2,方差为1,则
,
,
的平均数为_____________ .
![](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/66e6b07b90cf9928c2987d684c49cf60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c50aa5108c821f0c5939af277af900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc3ecc0e9a896e91a059d75a472ad5b.png)
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2024-04-26更新
|
2702次组卷
|
2卷引用:山东省菏泽第一中学三校区联考2024届高三下学期5月月考数学试题
名校
9 . 若当
时,
无限趋近于一个确定的值,则称这个确定的值为二元函数
在点
处对
的偏导数,记为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ff26e2362e1dec1a5a9b0ac01967ec.png)
若当
时,
无限趋近于一个确定的值,则称这个确定的值为二元函数
在点
处对
的偏导数,记为
,即
.已知二元函数
,则f'm,nx+f'm,ny的最小值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965e4bba42c1945bf711ef186027f52a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5bfc316ab38c6e4b8f5a9fa66cd29b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1595f06925491766c4e26be4c83085fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136620de908d460adedad82e773c2480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618932fbfef25e4dc46ed1e9bacefb9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ff26e2362e1dec1a5a9b0ac01967ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89c85c3e1599b32abfb0c110eeb8c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8942f9d432eef33b6859677bbe3693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1595f06925491766c4e26be4c83085fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136620de908d460adedad82e773c2480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d00c5eb079d0e588fba56ba585f2ee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fdd9174f63888a87df0aab6c3921824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f804c95319cc42dc5222ff088809bd4.png)
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10 . 已知集合
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19df635acc14579a821b408206549971.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3bf17e2189abda65de08b248b6155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440555e75c74af7ac1f03512f86ee363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19df635acc14579a821b408206549971.png)
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2024-04-20更新
|
641次组卷
|
2卷引用:山东省菏泽第一中学人民路校区2024届高三下学期3月月考数学试题