名校
解题方法
1 . 如图,在棱长为1的正方体
中,M为平面
所在平面内一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若M在线段![]() ![]() ![]() |
B.过M点在平面![]() ![]() |
C.若平面![]() ![]() |
D.若![]() ![]() ![]() |
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2 .
为坐标原点,以
为准线,
为焦点的抛物线
的方程为:
.过
的直线交
于
两点,
于
于
为线段
的中点.下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e627296086a74b6bec2c13f48ce3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcd0a07c239333bc9245de3b833043b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e71abd446a59195761c7b1684d73dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5889e1f093f2c35273d3132ef8434e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
A.![]() ![]() |
B.![]() |
C.直线![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() |
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3 . 如图,已知圆
,圆心是点T,点G是圆T上的动点,点H的坐标为
,线段CH的垂直平分线交线段TC于点R,记动点R的轨迹为曲线E.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
,
,试探究
是否为定值?若是,求出该定值;若不是,请说明理由;
(3)过点
作两条直线MP,MQ,分别交曲线E于P,Q两点,使得
.且
,点D为垂足,证明:存在定点F,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ebdc37c4828abb80c0f3bffb9e54e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5510fbff7fdcc083ef172d4b401c2229.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/7f184f36-d38a-4a16-a68d-696afedbb746.png?resizew=152)
(1)求曲线E的方程;
(2)过点H作一条直线与曲线E相交于A,B两点,与y轴相交于点C,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9545ecde4068ea16914263cddb3e8f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cff2d267cabb5318d29e319fe65c90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b385adf402cd17bddace02fdb32030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ebcef3ed51c751de97752bbf40e87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b14463c252e686a3cd0a8c4e33c02b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0165236f973be829fd3dbabe9507243.png)
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4 . 在几何学常常需要考虑曲线的弯曲程度,为此我们需要刻画曲线的弯曲程度.考察如图所示的光滑曲线C:
上的曲线段
,其弧长为
,当动点从A沿曲线段
运动到B点时,A点的切线
也随着转动到B点的切线
,记这两条切线之间的夹角为
(它等于
的倾斜角与
的倾斜角之差).显然,当弧长固定时,夹角越大,曲线的弯曲程度就越大;当夹角固定时,弧长越小则弯曲程度越大,因此可以定义
为曲线段
的平均曲率;显然当B越接近A,即
越小,K就越能精确刻画曲线C在点A处的弯曲程度,因此定义
(若极限存在)为曲线C在点A处的曲率.(其中y',y''分别表示
在点A处的一阶、二阶导数)
(2)求椭圆
在
处的曲率;
(3)定义
为曲线
的“柯西曲率”.已知在曲线
上存在两点
和
,且P,Q处的“柯西曲率”相同,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427eceadd7bb569ff140ea73d650db1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636a11a086df66133bd50e43481a546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea61ddc41f927684c6dfaacdd7f8e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92877ce3543f19dc565dbeff9777ecc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505d83f4d34a8cd385577a6ce93a4b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a6ffded1e8b3dd5ef03b57aa2beacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a345c0ab9bc098efa03e17ea556fcb.png)
(3)定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117c39fe1b37a6862ad0e46282488210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6004e46d022f4976a52dc949691da232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75def50794f0b3c42765b1e43334fcd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0cc87bade827b694da4e6e5c020eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7add187842d3ee824ed3a501f392735f.png)
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9卷引用:山东省菏泽市定陶区第一中学2023-2024学年高二下学期第一次月考数学试题
山东省菏泽市定陶区第一中学2023-2024学年高二下学期第一次月考数学试题浙江省宁波市镇海中学2024届高三上学期期末数学试题湖北省武汉市武钢三中2024届高三下学期开学考试数学试题(已下线)第四套 九省联考全真模拟(已下线)压轴题函数与导数新定义题(九省联考第19题模式)练(已下线)新题型01 新高考新结构二十一大考点汇总-3(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编湖南省长沙外国语学校2023-2024学年高二下学期3月月考数学试题(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
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解题方法
5 . 已知数列
为有穷正整数数列.若数列A满足如下两个性质,则称数列A为m的k减数列:
①
;
②对于
,使得
的正整数对
有k个.
(1)写出所有4的1减数列;
(2)若存在m的6减数列,证明:
;
(3)若存在2024的k减数列,求k的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281440c5e428da28c0a40fecbb87a83a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed25314606b875ae6cdfa2d073c73c85.png)
②对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ae1214cc78e72fb613d7e649bc27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b3392579424244c50ddf416ee3434d.png)
(1)写出所有4的1减数列;
(2)若存在m的6减数列,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409ce4e6aa8638fe5880009dbb732f7.png)
(3)若存在2024的k减数列,求k的最大值.
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9卷引用:山东省日照市五莲县第一中学2024届高考模拟预测(一)数学试题
山东省日照市五莲县第一中学2024届高考模拟预测(一)数学试题北京市通州区2024届高三上学期期末摸底考试数学试题江西省赣州市南康中学2024届高三“九省联考”考后模拟训练数学试题(一)安徽省合肥一六八中学2024届高三“九省联考”考后适应性测试数学试题(二)2024届广东省新改革高三模拟高考预测卷一(九省联考题型)数学试卷(已下线)(新高考新结构)2024年高考数学模拟卷(三)(已下线)信息必刷卷01湖南省长沙市雅礼中学2024届高三下学期数学月考试卷(八)(已下线)数学(江苏专用01)
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解题方法
6 . 已知函数
.
(1)若
对于任意
恒成立,求a的取值范围;
(2)若函数
的零点按照从大到小的顺序构成数列
,
,证明:
;
(3)对于任意正实数
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707db95c67bd9bb4ff1f449903d40cbc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44ecf9a385b5f3a023a662b2e75a260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48350c9f896c18a64f27867ca81c9be2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef26e8f565520685e2dc2dca27752db.png)
(3)对于任意正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b4256756f1416ad35f2227a616b7a7.png)
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2024-01-25更新
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3卷引用:山东省济南市山东实验中学2024届高三上学期第一次模拟测试数学试题
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7 . 学习几何体结构素描是学习素描的重要一步.如图所示,这是一个用来练习几何体结构素描的石膏几何体,它是由一个圆柱
和一个正三棱锥
穿插而成的对称组合体.棱
和面
与圆柱侧而相切,点
是棱
与圆柱侧而的切点.直线
分别与面
,面
交于点
,圆柱
在面
,面
上分别截得椭圆
.在平面
和平面
中,椭圆
上分别有两组不重合的两点
和
(图中未画出).且满足关系
.已知三棱锥
的外接球表面积为
,圆柱的底面直径为
,请问平面
,平面
上是否分别存在点
,使得对于满足
的直线
分别恒过定点
.若存在,试求
和
夹角的余弦值:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096cd7bd8a5a2219fd7dd166bbb8460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c121f8f04b49c7036888316b5f35e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c121f8f04b49c7036888316b5f35e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8461e08e60b84222ef056f49e71fa20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad044057e3a5b2f033d9ad0006b6f50e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b46bf815a5a193e9f5fc73078fb39d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357e0872d9e98d662a780e7686de86ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af67b85b1c91d1b489332503f6aaa8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37d0645be8436fa5c7a6ee8ba7de527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357e0872d9e98d662a780e7686de86ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cefbad5a2e9e1e812b54c5e972cf98d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d1e25f3c8094bf9da6eabef95e8214.png)
![](https://img.xkw.com/dksih/QBM/2024/1/13/3410267677220864/3410816027746304/STEM/273256e47234495eaf4d1e8d41ba7a4a.png?resizew=183)
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8 . 如图所示的六面体中,
,
,
两两垂直,
连线经过三角形
的重心
,且
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/09457a3d-4a27-4e4f-acdc-aef9a4bd959c.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07e98f7a65097311e8d93bd9f2af26e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/09457a3d-4a27-4e4f-acdc-aef9a4bd959c.png?resizew=160)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() |
D.若点![]() ![]() ![]() |
您最近一年使用:0次
2023-12-20更新
|
771次组卷
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3卷引用:山东省潍坊市2024届高三上学期普通高中学科素养能力测评数学试题
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解题方法
9 . 已知函数
,
,则下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28bd8a100f995d01627c3cb6a2ae8c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b9d6be01fc9d47f5965f32d767b742.png)
A.函数![]() ![]() |
B.当![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若不等式![]() ![]() ![]() |
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3卷引用:山东省济宁市2024届高三上学期期中考试数学试题
10 . 抛物线
与y轴交于点A,
,顶点为D.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/5fd8d323-e143-4e18-9ba1-f23ac31b4cbf.png?resizew=132)
(1)若点A的坐标为(0,-2),求抛物线的顶点D和点P的坐标;
(2)如图,在(1)的条件下,连接AD,PD,在直线AD下方的抛物线上是否存在点N,满足
,若存在,请求出点N的坐标;若不存在,请说明理由;
(3)已知点
,若线段PQ与抛物线恰有1个交点,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7025380bef07df5f62056160e6ea85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cab321e76d7c4c521cdc77d2d27c407.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/5fd8d323-e143-4e18-9ba1-f23ac31b4cbf.png?resizew=132)
(1)若点A的坐标为(0,-2),求抛物线的顶点D和点P的坐标;
(2)如图,在(1)的条件下,连接AD,PD,在直线AD下方的抛物线上是否存在点N,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4742f5710314af955b8dd4e6ddfd7151.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5649ae59934da963ba37a37fdd0977ea.png)
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