名校
解题方法
1 . 要做一个长方体带盖的箱子,其体积为
,底面长方形长与宽的比为
,则当它的长为_______ 时,可使其表面积最小,最小表面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976f9e0944eb38d7a73ed079c8fb6276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84783b6ba0f36789519816101a437f46.png)
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7日内更新
|
13次组卷
|
2卷引用:甘肃省定西市临洮县第二中学2023-2024学年高二下学期第一次月考数学试题
名校
解题方法
2 . 已知抛物线
的焦点为
,直线
交抛物线于
两点,
为抛物线
的准线与
轴的交点,直线
分别交抛物线于
两点(点
异于点
,
),
为坐标原点,则实数
的取值范围为__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b21b94a2bb768ccbc65c33f9c4ed923.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c654f3bb56ece42d29a9f14cca37bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb2d74932ede98011219d319f5b9995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b21b94a2bb768ccbc65c33f9c4ed923.png)
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名校
解题方法
3 . 我们通常用“曲率”来衡量曲线弯曲的程度,曲率越大,表示曲线的弯曲程度越大.工程规划中常需要计算曲率,如高铁的弯道设计.若
是
的导函数,
是
的导函数,那么曲线
在点
处的曲率
.已知曲线
,则曲线
在点
处的曲率为__________ ;若
,则曲线
的曲率的平方
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853716ac1619a812f57099d841c5c309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587882ac081850caa4447c44a7dbb845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4959c819f37676b4f3fbc315e4ed9dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6283166f874ed2823ac7b8be04507870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581192317ef233ccdccfc48ac29b52b.png)
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解题方法
4 . 已知向量
,
的夹角为
,
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e310702748855c3edccd151aae0143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed7444ed9ccdd2dc5ac13be29f40fc68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9ee73e05c2ea6a4b937b7ff42ac925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ef2b20e067d1865108bdb4ac7c1095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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名校
解题方法
5 . 已知向量
,
满足
,
,则
最大值为________ ,最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51c62833bf755f6d77083f26444a88d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c00a7fed3deb0cad572efe49e08e62e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb74499b8965b3f6c9acfbbb168df438.png)
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6 . 过圆
外一点
向圆O引两条切线
和
(其中A,B为切点),使得
,则实数a,b满足的等量关系为__________ ,
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](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/1b1c20fa9466374ae5ae611c76f62ac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8115d5e4d5972c18fe5dd5752f107473.png)
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2024-04-17更新
|
310次组卷
|
2卷引用:甘肃省2024届高三下学期4月月考数学试卷
名校
解题方法
7 . 已知椭圆
的左、右焦点分别为
,过点
且斜率为
的直线与
交于
两点.若
,则
的离心率为_____ ;线段
的垂直平分线与
轴交于点
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d398e2747bec7d0d3900a32b34510da.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fab3d0b2d405613743fa68d5ccac76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d398e2747bec7d0d3900a32b34510da.png)
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8 . 一组样本数据
的众数为______ ,中位数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729e87b155891c93b478beb3e0102340.png)
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2024-04-12更新
|
644次组卷
|
7卷引用:甘肃省靖远县2024届高三第三次联考试题三模数学试题
甘肃省靖远县2024届高三第三次联考试题三模数学试题四川省成都市石室阳安学校2023-2024学年高三下学期4月月考数学(理)试题(已下线)9.2.3?总体集中趋势的估计——随堂检测四川省雅安市2024届高三下学期4月联考数学(理)试题四川省雅安市2024届高三下学期4月联考数学(文)试题(已下线)9.2 用样本估计总体-同步精品课堂(人教A版2019必修第二册)(已下线)专题05 第九章 统计-期末考点大串讲(人教A版2019必修第二册)
名校
9 . 已知平行四边形
的面积为
,
,且
.若F为线段
上的动点,且
,则实数
的值为___________ ;
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27567d43c5b91382ee3d7ca708ee422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e90f9f4e44173888a54c624852064a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea8abb4cab55296ca7fc63de0af0aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a03511c689527acfb497e69775d0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33fe25a156a25f00d47e1498eec473c2.png)
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2024-04-10更新
|
1258次组卷
|
2卷引用:甘肃省张掖中学2023-2024学年高一下学期4月月考数学试卷
20-21高一·全国·课后作业
名校
解题方法
10 . 已知向量
与
的夹角为120°,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ef55542504e8d147448cbfb6eaad7a.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/b660be471d5dbd000f5e1fcb996371da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ef55542504e8d147448cbfb6eaad7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0034e6960678180a622cce4c90e599e.png)
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