2023·河北·模拟预测
名校
解题方法
1 . 已知椭圆
的两焦点为
,
,x轴上方两点A,B在椭圆上,
与
平行,
交
于P.过P且倾斜角为
的直线从上到下依次交椭圆于S,T.若
,则“
为定值”是“
为定值”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9ff12b7dbd1ed59bd9d75b4a0bf942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b5d3f74009a381e750b439a7e7f874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不必要也不充分条件 |
您最近一年使用:0次
2023-01-05更新
|
1997次组卷
|
5卷引用:河北省衡水中学2023届高三新高考模拟数学试题
(已下线)河北省衡水中学2023届高三新高考模拟数学试题(已下线)专题一 集合与常用逻辑用语-2福建省福州市四校2022-2023学年高二下学期期末联考数学试题重庆市第十八中学2023-2024学年高二上学期期末数学模拟试题(已下线)第五篇 向量与几何 专题4 极点与极线 微点3 极点与极线问题常见模型总结(一)
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2 . 已知函数
.
(1)若
有唯一零点,设满足条件的
值为
与![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
证明:①
与![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
互为相反数;②
;
(2)设
.若
存在两个不同的极值点
、
,证明
.
参考数据:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8093693f847ccd4f20327e6eba8bc1b0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67eb0f20778cd55f4c54fab483b9705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67eb0f20778cd55f4c54fab483b9705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7093c8dda76e3bb3c876d5329b6df432.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f8dfce0268a1167fe049730858f6d7.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3caa37456ad465972bea16d93d02e1ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c292239a48d1475428eeb9863d5dceb.png)
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3 . 已知抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
,点
为抛物线焦点.过点
作一条斜率为正的直线l从下至上依次交抛物线于点
与点
,过点
作与l斜率互为相反数的直线分别交x轴和抛物线于
、
.
(1)若直线
斜率为k,证明抛物线在点
处切线斜率为
;
(2)过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f26d721b107f8b2bc88f3eb0f42c70.png)
作直线分别交x轴和抛物线于
、
,过点
作直线分别交x轴和抛物线于
、
,且
,直线
斜率与直线
斜率互为相反数.证明数列
为等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75de1947893e5c7a4d98d4458398fd6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53fc303cfac1c7534451fb0789e68340.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f26d721b107f8b2bc88f3eb0f42c70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46104701a43ad89ef6e010080c1aa573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09ec2d93ba8c1e03c87f72847b2e0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786943ad927681a7669f7657189b8e94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786943ad927681a7669f7657189b8e94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/477ff751d24f8169d1530d681cb6238d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee309657bd64d532c45fa5bd2dd70e0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20bdc8acb733f90c754c77a24eeb62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bab86a8763fd18721a95f2ba200e233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de8570a13f722ac57f7d9d970082d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16eb52ba8bbc8988475dd96ca0858eb3.png)
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4 . 二元数列
中各项的值同时由
,
决定
.已知二元数列
满足
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94fffd5f64091fec3cc205174cbcaec.png)
.若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9284e374e1be252c38aab216aea45e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a469eded727914a137426c520ddb7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a9d9a8781f66ede54de1209d5c6d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d02f764c09b1f302f7e2e7488a75e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8741b67519a3eb141655491e128037a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94fffd5f64091fec3cc205174cbcaec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9dd5d10c8e5e5dff7d0e715fc4c8c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2e8892620ae1b3d5b2cd50697559ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6978a23dd12e241a078cfe58ddfa9f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
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解题方法
5 . 底边和腰长之比为
的等腰三角形被称为“黄金三角形”,四个面都为“黄金三角形”的四面体被称为“黄金四面体”.“黄金四面体”的外接球与内切球表面积之比为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
您最近一年使用:0次
2023-01-03更新
|
2577次组卷
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7卷引用:河北衡水中学2023届高三模拟数学试题
河北衡水中学2023届高三模拟数学试题(已下线)“8+4+4”小题强化训练(20)(已下线)第八章立体几何初步章末题型大总结(精讲)(1)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)专题7-1 立体几何压轴小题:截面与球(讲+练)-2(已下线)8.3.2 圆柱、圆锥、圆台、球的表面积和体积(2)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)专题强化三 多面体与球有关的内切、外接问题-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2019必修第二册)(已下线)专题强化二 与球有关的内切、外接问题-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)
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6 . 直线
、
为曲线
与
的两条公切线.
从左往右依次交
与
于A点、B点;
从左往右依次交
与
于C点、D点,且A点位于C点左侧,D点位于B点左侧.设坐标原点为O,
与
交于点P.则下列说法中正确的有( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6895afad6fca3165f077eb0176421109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cacaef9d61fb706067e893b9051fdc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26c23adc2a79b93771e113e0364e44fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c7d5aee3615cdb65b3dd4e24da7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2c2f3e635507d9fbe6323b1b6d4574.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4c7d5aee3615cdb65b3dd4e24da7bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-01-03更新
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4卷引用:河北衡水中学2023届高三模拟数学试题
河北衡水中学2023届高三模拟数学试题(已下线)专题9 函数与导数 第3讲 导数的几何意义及简单应用(已下线)模块八 专题4 以导数为背景的压轴小题辽宁省沈阳市东北育才学校2022-2023学年高三下学期高考适应性测试(三)数学试题
7 . 已知椭圆C:
,
上有三点
、
、
,
、
分别为其左、右焦点.则下列说法中正确的有( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434249d6640b0c1a712d215cf8b83d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.若线段![]() ![]() ![]() ![]() ![]() ![]() |
B.若直线![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.![]() ![]() |
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8 . 平面上有两组互不重合的点,
与![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d430a0dc60efb63a1ad85b186ba66c.png)
,
,
,
.则
的范围为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98aac8bdd051e7d6ec50aa15f14c1abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d430a0dc60efb63a1ad85b186ba66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0df76003c64180ca21cfd01e36ff2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51febf51bfec95470929e563ffe6fc1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e530a2cdd573241f605eb54bdb6efb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ddeab4652f210d5409b158e4f6eccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ec2385c445f7b630d6f1c173629b9f.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:河北衡水中学2023届高三模拟数学试题
名校
9 . 已知函数
且
.
(1)设
,讨论
的单调性;
(2)若
且
存在三个零点
.
1)求实数
的取值范围;
2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f26cc366989b203c047e13db8de54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47352a6ebe48c4d92e32275a4f32dc4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7803d86067299198e6d14b0c83947f58.png)
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2022-12-21更新
|
5085次组卷
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10卷引用:河北省衡水市第十三中学2023届高三上学期1月月考数学试题
河北省衡水市第十三中学2023届高三上学期1月月考数学试题广东省广州市2023届高三一模数学试题四川省南充高级中学2023届高考模拟检测(七)理科数学试题江苏省南通市海安高级中学2023届高三下学期一模数学试题江苏省盐城市亭湖高级中学2022-2023学年高三上学期期末数学试题江苏省连云港市赣榆智贤中学2023-2024学年高三上学期9月模拟考试数学试题天津市蓟州区第一中学2024届高三上学期第三次学情调研数学试题辽宁省辽东十一所重点高中联合教研体2024届高三高考适应性考试模拟数学试题(已下线)(新高考新结构)2024年高考数学模拟卷(三)(已下线)专题3 导数与函数的零点(方程的根)【练】
名校
解题方法
10 . 已知
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847a2ee57a8036adf66e4d2a3761ea64.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2022-12-21更新
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3219次组卷
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7卷引用:河北省衡水市第十三中学2023届高三上学期1月月考数学试题
河北省衡水市第十三中学2023届高三上学期1月月考数学试题广东省广州市2023届高三一模数学试题浙江省杭州市桐庐中学2022-2023学年高三上学期1月期末数学试题(已下线)“8+4+4”小题强化训练(7)江苏省徐州市新沂市第三中学2023届高三下学期3月月考数学试题福建省安溪一中、养正中学、惠安一中、泉州实验中学2022-2023学年高二下学期期中联考数学试题(已下线)第六章 导数与不等式恒成立问题 专题十二 恒成立问题综合训练