名校
1 . 对于函数
和
,设
,
,若存在m,n,使得
,则称
和
互为“零点关联函数”,若函数
与
互为“零点关联函数”,则实数a的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c6d9297f968746043ea3a18c2674074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c646c8703395cf86ce6cd928457c2bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95d329c460f6e152a76de7b9549bc147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b626f9a54e5ab6d0ce3e60b38d70003a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e97e0da487ce6b29300e15f7ef52b66.png)
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2023-04-22更新
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453次组卷
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3卷引用:新疆维吾尔自治区部分学校2023届高三二模数学(理)试题
2 . 已知函数
,其中
且
,若函数
图象上存在关于原点对称的点仅有两对,则实数a的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f0ba3aeb142d868d4436ddf5b125e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
3 . 已知函数
,
,其中
为自然对数的底数.
(1)若
有两个极值点,求
的取值范围;
(2)记
有两个极值点为
、
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732f6cdb4e530b09885eb10920e5bda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/b92a222c35021168dd2a750a27203c1a.png)
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解题方法
4 . 已知
,
是椭圆
的左、右焦点,点
是
上一点,
的中点在
轴上,
为坐标原点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/22/a5e23d32-c4f5-4b67-98da-9041b21f6281.png?resizew=189)
(1)求椭圆
的方程;
(2)过点
任意作两条倾斜角互补的直线交椭圆于B,C两点,设直线BC的斜率为
,证明:
为定值,并求
的值.
![](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/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/22/a5e23d32-c4f5-4b67-98da-9041b21f6281.png?resizew=189)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5 . 已知函数
,
,
,其中
为自然对数的底数.
(1)讨论
的单调性;
(2)当
时,证明:对于
,都有
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f4ce63ecec208598b23202ae211bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a638b5a60d9a3dc23e23b5472874f785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fad1dd76d5b72f10f5bb62693a2996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
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2023-04-21更新
|
476次组卷
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3卷引用:新疆维吾尔自治区乌鲁木齐市等5地莎车县第九中学等2校2023届高三二模数学(文)试题
6 . 已知在直三棱柱
中,E,F分别为
,
的中点,
,
,
,
,如图所示,若过A、E、F三点的平面作该直三棱柱
的截面,则所得截面的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea0df817e3e2cd95b9cd8f73386834c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-21更新
|
2060次组卷
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6卷引用:新疆维吾尔自治区乌鲁木齐市等5地莎车县第九中学等2校2023届高三二模数学(文)试题
新疆维吾尔自治区乌鲁木齐市等5地莎车县第九中学等2校2023届高三二模数学(文)试题新疆维吾尔自治区部分学校2023届高三二模数学(理)试题(已下线)重难点专题02 空间点直线平面之间的位置关系-【同步题型讲义】(已下线)第02讲 空间点、直线、平面之间的位置关系(六大题型)(讲义)-1四川省达州市宣汉县土黄中学2023-2024学年高二上学期第三次月考数学试题(已下线)13.2.1 平面的基本性质-【帮课堂】(苏教版2019必修第二册)
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解题方法
7 . 杜牧《羊栏浦夜陪安会》的诗句中“球来香袖依稀暖,酒凸觥心泛艳光”描述的是唐代酒宴上的助兴游戏“击鼓传花”,也称传彩球.游戏规则为:鼓响时,众人开始依次传花,至鼓停为止,此时花在谁手中,谁就上台表演节目.甲、乙、丙三人玩击鼓传花,鼓响时,第1次由甲将花传出,每次传花时,传花者都等可能地将花传给另外两人中的任何一人,经过8次传递后,花又在甲手中的概率为________ .
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2023-04-18更新
|
750次组卷
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2卷引用:新疆石河子第一中学2022-2023学年高二下学期5月月考数学试题
解题方法
8 . 已知定义在R上的函数
,满足
,函数
的图象关于点
中心对称,且对任意的
,不等式
恒成立,给出如下结论:①
是奇函数;②
;③
在
上单调递增;④不等式
的解集为
,其中正确的结论是______ (填序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fceb969de98e32f56f9610c213823489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c3dd8fa2dc8c0c7e255bfb054ad34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfdc88443cc238bdf14ca5483f71a69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c6713188fd50d4981823bd8ac19a931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2635c6e599f816c706e471a3c197d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e11755ed0a988c3ef721649fa598f3b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fa39ae8b5073e7667c40b6eba10225.png)
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名校
解题方法
9 . 已知函数
.
(1)若函数
存在零点,求实数
的最大值;
(2)当
时,函数
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a78f5bce61e2ff49633e7f32563d263.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27487d40b525c0727313b7842aee124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-04-16更新
|
768次组卷
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5卷引用:新疆维吾尔自治区2023届高三一模数学(文)试题
名校
10 . 已知函数
,且
,
,
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7caf2e37f27288eda203418010c352d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c08d37876250a440fd3268c452fe7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225c8d3791c5cec998740d1337217c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117f295249ed4700ced8470e3f25f640.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-15更新
|
480次组卷
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3卷引用:新疆巴音郭楞蒙古自治州若羌县中学2024届高三上学期6月摸底考后强化数学试题
新疆巴音郭楞蒙古自治州若羌县中学2024届高三上学期6月摸底考后强化数学试题河南省商丘市部分学校2022-2023学年高二下学期期中考试数学试题(已下线)第三章 利用导数比较大小 专题四 利用导数比较大小综合训练综合训练