1 . 已知向量
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
______ ;若
,则向量
与
的夹角为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157a894088b095cb5c82691d4d64314d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b958a367fa2f08b6202a5a6ebf5e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f622a667018a0a1b7b9334909c136090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b4cf9cd1d12fd577dad52f462b2bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
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2卷引用:河北省邢台市邢襄联盟2023-2024学年高一下学期第三次月考数学试题
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解题方法
2 . 已知关于
的不等式
恒成立,
的最小值为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
___________ ,并求
的最小值为___________ (其中
为自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f4c6d71c421736c61a36801e11d6da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbd815a77afa6bd88296afdf28c4ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
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3 . 已知
是定义在
上的函数,且对任意的
,同时满足下列条件:①
;②
,其中
是大于1的常数.记
,且对任意的
,存在常数
,恒有
,则
的一个值是__________ ;若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6343d83fcbf9ef2a2e3d63bcd7bf66.png)
__________
.(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46074d28f2f23e5026fff76594e32ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b26b0960f01533ae7c120f0d9831392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fafeae53499e1b6935c7f32d0a652516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b452e6fc74f3fd4dca0d7f68e719261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1017c3c983d190798812f082957888cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6691894fe61c7e78b94df72b8379130d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb6343d83fcbf9ef2a2e3d63bcd7bf66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b63663851c6911a194e531e6e7bd5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024高三下·全国·专题练习
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4 . 了解某中学学生的身高情况,采用分层随机抽样的方法抽取了30名男生,20名女生.已知男生身高的平均数为170cm,方差为16,女生身高的平均数为165 cm,方差为25,则可估计该校学生身高的平均数为______ cm,方差为______ .
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5 . 已知数列
满足:
,定义:
表示整数
除以4的余数与整数
除以4的余数相同,例:
.设
,其中
,数列
的前
项和为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f37c41b3d37ebff1242f840b5fe0c0.png)
______ ;满足
的
最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bd1701942436577888033dddab56db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770e90a2561b0d1d2b29a3b79826ce3d.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/e7f6d0719b5ca93d2c769cb1dfde76a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41483f8495363a91ed69f7ca4eb82e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f37c41b3d37ebff1242f840b5fe0c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb38963c8058ddefb44934c83ab6c86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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6 . 已知
分别为
的内角
的对边,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
__________ ;内角
的平分线交
于点
,若
,则
的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.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/0c5b386a51718bd4f23a85807e5af0a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de75fd1c3d03791f343ec88122275e2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
7 . 做一个容积为
的圆柱形封闭容器,要求所用材料最省,则该容器的底面半径为______
,表面积为______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d241087588fc0716eb9f5aa05eeb35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
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2024-05-08更新
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225次组卷
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3卷引用:河北省石家庄十五中2023-2024学年高二下学期期中数学试题
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8 . 已知
,过点
恰好只有一条直线与圆E:
相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
________ ,该直线的方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bdb225f362f150791f7483a96a18d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7312c19269a2073277bd07b9b2f4912c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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2024-04-18更新
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523次组卷
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2卷引用:河北省邢台市2024届高三下学期教学质量检测(一)数学试题
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9 . 已知双曲线
的左右顶点分别为
,点
是双曲线
上在第一象限内的点,直线
的倾斜角分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8330ddbd3affee70070c06c45a10b47.png)
__________ ;当
取最小值时,
的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b30352c43707c4e54b94ce5b61f2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8330ddbd3affee70070c06c45a10b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e66f073bcf645db516f96974a067462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2024-03-13更新
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2542次组卷
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7卷引用:河北省重点高中2024届高三下学期5月模拟考试数学试题(一)
河北省重点高中2024届高三下学期5月模拟考试数学试题(一)湖北省七市州2024届高三下学期3月联合统一调研测试数学试题山东省潍坊市昌乐北大公学学校2024届高三下学期3月监测数学试题(已下线)数学(新高考卷01,新题型结构)(已下线)湖北省七市州2024届高三下学期3月联合统一调研测试数学试题变式题11-15重庆市涪陵第五中学校2024届高三下学期第二次适应性考试数学试题新疆石河子第一中学2024届高三“天使计划”第二轮测试数学试题
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10 . 已知等差数列
的公差与等比数列
的公比相等,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
______ ;若数列
和
的所有项合在一起,从小到大依次排列构成一个数列
,数列
的前
项和为
,则使得
成立的
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684b935a7274130d081bfa7b2b938023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89b8821c758c29c8b02bd79425ecbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13624221ac7e06fc5ebd48b21ed0de10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414187fca31df508dbf88d7f2bb83662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055bd850286feebbeac5df481988b1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2024-03-08更新
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1240次组卷
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4卷引用:河北省部分学校联考2024届高三下学期3月模拟(二)数学试题