名校
解题方法
1 . 求作一个立方体,使其体积等于已知立方体体积的2倍,这就是历史上有名的立方倍积问题.1837年法国数学家闻脱兹尔证明了立方倍积问题不能只用直尺与圆规作图来完成,不过人们发现,跳出直尺与圆规作图的框框,可以找到不同的作图方法.如图是柏拉图(公元前427—公元前347年)的方法:假设已知立方体的边长为
,作两条互相垂直的直线,相交于点
,在一条直线上截取
,在另一条直线上截取
,在直线
上分别取点
,使
(只要移动两个直角尺,使一个直角尺的边缘通过点
,另一个直角尺的边缘通过点
,并使两直角尺的另一边重合,则两直角尺的直角顶点即为
),则线段
即为所求立方体的一边.以直线
、
分别为
轴、
轴建立直角坐标系,若圆
经过点
,则圆
的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fbeb2f1f6ee7279885520d889bfc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918e047b9e13bcc736020457b63b234f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7710395115caf148d930164732c89b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54ef00d2ac8ffd33af4722fb1c2908d5.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/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c40e45fdb98b87035089ba2d435eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/33f88743-ad56-4c33-bf55-10bf779ef839.png?resizew=167)
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2 . 侏罗纪蜘蛛网是一种非常有规律的蜘蛛网,它是由无数个正方形环绕而成.如图正方形
的边长为1,取其四边的三等分点
,
,
,
,作第二个正方形为
,然后再取正方形
各边的三等分点
,
,
,
,作第三个正方形
,依次方法持续下去…,则第7个正方形的周长是______ ,如果这个作图过程可以一直继续下去,则所有这些正方形的周长之和将趋于______ .(填数值)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2857fac4963b129d99e79dcb3e13d295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8ce8c07e34224e2d25130ed27c9a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c266cba73c7b8ad86e52aa34892e2239.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/22/1dc89f40-0ee9-4fe5-951d-e3705e0eafc5.png?resizew=191)
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解题方法
3 . 将正三角形(1)的每条边三等分,并以中间的那一条线段为底边向外作正三角形,然后去掉底边,得到图(2);将图(2)的每条边三等分,并以中间的那一条线段为底边向外作正三角形,然后去掉底边,得到图(3);如此类推,将图(
)的每条边三等分,并以中间的那一条线段为底边向外作三角形,然后去掉底边,得到图
.上述作图过程不断的进行下去,得到的曲线就是美丽的雪花曲线.若图(1)中正三角形的边长为1,则图(
)的周长为__________ ,图(
)的面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aceb113626093e0e431f30fa45c2c444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/cc4bbbc0-a228-404d-981c-94e842b746b2.png?resizew=216)
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|
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6卷引用:广东省2022届高三上学期8月阶段性质量检测数学试题
4 . 对于三元基本不等式请猜想:设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec197b8ab457cfee3d4733f3d7f8d6f3.png)
_________ ,当且仅当
时,等号成立(把横线补全).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec197b8ab457cfee3d4733f3d7f8d6f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44acc0ee22dc4b7750e8be825e7c1355.png)
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5 . 已知一组数据
的平均数为
,方差为
,则这组数据的平均数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd141a9d19473cab037c5e918f722e18.png)
______ ;若新增3个均为
的数据,方差记为
,那么![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926eac04c657327fe496fdf49f023e66.png)
______
(填写“
”、“
”或“
”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569962d9dfea9c5b893d88b1fee19085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80746e5e22851a0f1075374a3c3280ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd141a9d19473cab037c5e918f722e18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926eac04c657327fe496fdf49f023e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926eac04c657327fe496fdf49f023e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671f43c79d612c93a6d160335e86e177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392cdb9d30684cce244bef94b8d861b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7942da6c3fc4005256fb1458557c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6706fe00b4e231e62d9ecbec567d526b.png)
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解题方法
6 . 下列说法中不正确的是______ (只需填写序号)
①设集合
,则
;
②若集合
,
,则
;
③在集合A到
的映射中,对于集合
中的任何一个元素
,在集合A中都有唯一的一个元素
与之对应;
④函数
的单调减区间是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d028846b8614318fbf90387d13c75b5.png)
⑤设集合
,
,若
,则
①设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cec1a82f40122b306b15aa29da2f8c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a88caacdbf71fca44d1ca412c68fa66.png)
②若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5361ed288fa23f3b5d16cbc09d3293d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f808f81b6ea9da53d51c549be04f4267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
③在集合A到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c9320d009a17deba67f208c7d8be8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d028846b8614318fbf90387d13c75b5.png)
⑤设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a569ad6f0b7c49d11d7e167bb0527ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa7b8acbc8b0027cbe9e3986ad1d859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ad78dc8b8aed907b4fe9640c997454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
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名校
解题方法
7 . 函数
(
为常数)有下列结论:
无论
为何值,该函数都经过定点
;
若
,则当
时,
随
增大而减小;
该函数图象关于
轴对称;
若该函数图象与
轴有
个交点,则
.其中正确的结论是______ (填写序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5127c7e8124ea12706a0e00b7e01b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a3afc9fdb61b847e5cc12b57861ccaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f06408895febc126c2ae409e807349c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ccaa6e503b61e9ae78d8439cba2e328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82e415812cca9545611c0faa0c01b1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8b8edd94bc4d5d517ec77e56800e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3828868765caa2ebed51aca7dc594993.png)
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8 . 某同学做最后两道选择题,已知每道题均有4个选项,其中有且只有一个答案正确,该学生随意填写两个答案,则选对一题的概率是_______ .
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2023-06-09更新
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2卷引用:上海市川沙中学2022-2023学年高二下学期3月月考数学试题
名校
9 . 如图,若正方体的棱长为2,点
是正方体
的上底面
上的一个动点(含边界),
,
分别是棱
,
上的中点,有以下结论:
①
在平面
上的投影图形的面积为定值;
②平面
截该正方体所得的截面图形是五边形;
③
的最小值是
;
④若保持
,则点
在上底面内运动路径的长度为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
______ .(填写所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe40405cd7bd60d69dd535d6da85c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
②平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08204b03bc91a4218d3eff5843002fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01961669cd597f61fa48e9853d678bb8.png)
④若保持
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1f8fe0fa1ef60ef5e9aa34ed6dd57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
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2023-03-14更新
|
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3卷引用:贵州省六校联盟2023届高三下学期适应性考试(三)数学(理)试题
贵州省六校联盟2023届高三下学期适应性考试(三)数学(理)试题广东省东莞市东莞中学松山湖学校2022-2023学年高一下学期第二次检测数学试题(已下线)专题03 基本立体图形、直观图、表面积与体积-期末真题分类汇编(新高考专用)
10 . 设
,则满足
在
上恒正的
是__________ .(填写序号)
①
;②
;③
;④
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89a66279f77b21261b88012a6ac7818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfb6c182e6983236c9b3af89111dd17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934577743726d3fb09c2dea88430b991.png)
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2023-03-06更新
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5卷引用:广东省佛山市禅城实验高级中学2022-2023学年高二下学期3月月考数学试题
广东省佛山市禅城实验高级中学2022-2023学年高二下学期3月月考数学试题上海市2023届高三模拟数学试题湖南省长沙市师大附中梅溪湖中学(湖南师大附中梅溪湖中学)等2校2023届高三下学期3月联考数学试题甘肃省武威市凉州区2022-2023学年高二下学期期中考试数学试题(已下线)核心考点08导数的运算-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)