2024高三·全国·专题练习
解题方法
1 . 欧拉函数
的函数值等于所有不超过
且与
互质的正整数的个数(公约数只有1的两个整数称为互质整数),例如:
,
.记
,数列
的前
项和为
,若
恒成立,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f435d0e2319eb04b19bd4037129c470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2 . 已知
,那么
的近似值为______ .(保留小数点后一位数字)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2493a9847bdf4e7e0cb5da764d62a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf6d10885fb83ded00d4e39532fcd10.png)
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3 . 已知圆
,直线
,
为直线
上的动点,过点
作圆
的两条切线,切点分别为
,
,则直线
过定点______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f25834d8218c53cb975c2a2fe7442a.png)
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解题方法
4 . 切比雪夫不等式是19世纪俄国数学家切比雪夫(1821.5~1894.12)在研究统计规律时发现的,其内容是:对于任一随机变量
,若其数学期望
和方差
均存在,则对任意正实数
,有
.根据该不等式可以对事件
的概率作出估计.在数字通信中,信号是由数字“0”和“1”组成的序列,现连续发射信号
次,每次发射信号“0”和“1”是等可能的.记发射信号“1”的次数为随机变量
,为了至少有
的把握使发射信号“1”的频率在区间
内,估计信号发射次数
的值至少为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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5 . 若一组数据
的中位数为16,方差为64,则另一组数据
的中位数为__________ ,方差为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca53f1cceda4b9903a0dfd1ffd74a2af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e44bef1b4ee6a4b00ad5881b6b6bc72.png)
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670次组卷
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4卷引用:辽宁省沈阳市第二中学2024届高三下学期三模数学试题
(已下线)辽宁省沈阳市第二中学2024届高三下学期三模数学试题河南省部分重点高中2023-2024学年高三下学期5月联考数学试卷 (新高考)2024届青海省海南藏族自治州高考二模数学(理科)试卷内蒙古自治区锡林郭勒盟2024届高三下学期5月模拟考试理科数学试题
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6 . 在复数范围内,方程
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a02d6c7a7f2cb4c2d2552efabb8ccf.png)
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5卷引用:辽宁省沈阳市第二中学2024届高三下学期三模数学试题
(已下线)辽宁省沈阳市第二中学2024届高三下学期三模数学试题河南省部分重点高中2023-2024学年高三下学期5月联考数学试卷 (新高考)2024届青海省海南藏族自治州高考二模数学(理科)试卷内蒙古自治区锡林郭勒盟2024届高三下学期5月模拟考试理科数学试题(已下线)复数-综合测试卷B卷
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7 . 若点
在圆
外,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
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解题方法
8 . 已知向量
满足
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a035c8861e9fa9369d20d6b531d88dc.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
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3卷引用:辽宁省沈阳市2024届高三教学质量监测(三)数学试题
9 . 在三棱锥
中,
,
,
,
为
的中点,则异面直线
与
所成角的余弦值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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3卷引用:辽宁省部分学校2024届高三抢分卷(三)数学试题
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解题方法
10 . 在平面直角坐标系
中,已知双曲线
经过点
,点
与点
关于原点对称,
为
上一动点,且
异于
,
两点.若
的重心为
,点
,则
的最小值______ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
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