名校
1 . 某同学利用图形计算器研究教材中一例问题“设点
,
,直线
,
相交于点M,且它们的斜率之积为
,求点M的轨迹方程”时,将其中已知条件“斜率之积为
”拓展为“斜率之积为常数
”之后,进行了如图所示的作图探究:
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/3d217257-3ca3-4ff8-9d6b-5c848d6d0799.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/6a6a6eb1-633d-48bd-9799-9be0469f6918.png?resizew=200)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/f74ddd64-f2df-496e-8e44-8a8665a02e35.png?resizew=190)
参考该同学的探究,下列结论正确的有:( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d71fb4d3db6c9922d3b605a6d40e529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fe2c124d5bbbbe666ee145cd454b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889efe020137b112bfafaa8e0becda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889efe020137b112bfafaa8e0becda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/3d217257-3ca3-4ff8-9d6b-5c848d6d0799.png?resizew=195)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/6a6a6eb1-633d-48bd-9799-9be0469f6918.png?resizew=200)
![](https://img.xkw.com/dksih/QBM/2021/1/27/2645089272954880/2651693900840960/STEM/f74ddd64-f2df-496e-8e44-8a8665a02e35.png?resizew=190)
参考该同学的探究,下列结论正确的有:( )
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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2021-02-05更新
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807次组卷
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8卷引用:江苏省扬州市江都区2021-2022学年高二上学期期中数学试题
名校
2 . 已知函数
.
(1)下面是某同学讨论函数单调性并求解单调区间的过程:因为
,所以
.令
,得
或
,所以当
时,
单调递减.请判断是否正确,若正确,补全解答过程,若不正确,请写出正确的解答过程;
(2)若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b23bc0d370d74bdb6aefdcada5dc7b.png)
(1)下面是某同学讨论函数单调性并求解单调区间的过程:因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b23bc0d370d74bdb6aefdcada5dc7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d068bdf530a8e66d040d22575f2df51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/868a4cf0549507ca5f2a18b2d1070085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a06a856627857e788a9f613b4fa126.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c28f5a9453d0b47ebb45852d83000c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857f0eb507a711096e5f095a2f203ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-09-29更新
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166次组卷
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2卷引用:河北省深州市中学2023-2024学年高三上学期期中考试数学试题
名校
3 . 一种画双曲线的工具如图所示,长杆OB通过O处的铰链与固定好的短杆OA连接,取一条定长的细绳,一端固定在点A,另一端固定在点B,套上铅笔(如图所示).作图时,使铅笔紧贴长杆OB,拉紧绳子,移动笔尖M(长杆OB绕O转动),画出的曲线即为双曲线的一部分.若|OA|=10,|OB|=12,细绳长为8,则所得双曲线的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/33da8c9a-b96d-4635-8914-658eeefbcca5.png?resizew=177)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/33da8c9a-b96d-4635-8914-658eeefbcca5.png?resizew=177)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-01-17更新
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445次组卷
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6卷引用:专题6.2 期中押题检测卷(考试范围:第1-3章)2(中)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)
(已下线)专题6.2 期中押题检测卷(考试范围:第1-3章)2(中)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册) 【区级联考】北京市丰台区2019届高三第一学期期末考试数学(理)试题【市级联考】辽宁省沈阳市郊联体2019届高三第一次模拟考试数学(理科)试题苏教版(2019) 选修第一册 突围者 第3章 第二节 课时2 双曲线的几何性质北京交通大学附属中学2022届高三12月月考数学试题2023版 苏教版(2019) 选修第一册 突围者 第3章 第二节 课时2 双曲线的几何性质
4 . 设
,则“
”是“
”的______ 条件.(填写“充分不必要”、“必要不充分”、“充要”、“既不充分又不必要”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200849ce71f53c0321506e27de437b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
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5 .
是
的______ 条件.(请填写“充分不必要”、“必要不充分”或“充要”)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcf268fb9d95f033c196f72ca517351.png)
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6 . 以下关于命题的说法正确的有______ (填写所有正确命题的序号).
①“若
,则
”是真命题;
②命题“若
,则
”的否命题是“若
,则
”;
③命题“若
,
都是偶数,则
也是偶数”的逆命题为真命题;
④命题“若
,则
”与命题“若
,则
”等价.
①“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2c58e340ebcea00ef2a6d05a836301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
②命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3019b662e5dc2750bb6f9199d3250f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
③命题“若
![](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/b88584cf1df43e28d03592c7998b1653.png)
④命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582ad43edf388c096e7704d92340bf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5286186cb58bf265a2a96e5195d88d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27dd329517f0dd8f1d0dfade6138ed4.png)
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7 . 若条件
:
,条件
:
,则
是
的______ 条件.(填写“充分不必要”、“必要不充分”、“充分必要”和“既不充分也不必要”之一).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6749db809dd84c2cfe5c47bea121e356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c21c6260bcade05f3a432841f449b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffc1bb9d53a27d484396ad74d6a26e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e26b38e357c7d985656ba7bb3c794a5.png)
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解题方法
8 . 命题
在
单调增函数,命题
在
上为增函数,则命题
是命题
的__________ .(在“充分不必要条件、必要不充分条件、充要条件、既不充分也不必要条件”中选择最合适的填写)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c8268047d111633e348bbe61ec5ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e738ba791473e4eee10f187409744fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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9 . 以下关于命题的说法正确的有______ (填写所有正确命题的序号).
①“若
,则函数
在其定义域内是减函数”是真命题;
②命题“若
,则
”的否命题是“若
,则
”;
③命题“若x,y都是偶数,则
也是偶数”的逆命题为真命题;
④命题“若
,则
”与命题“若
,则
”等价.
①“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2c58e340ebcea00ef2a6d05a836301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12be5e0c1681b2f57e60a3fb0113b80.png)
②命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3019b662e5dc2750bb6f9199d3250f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eae9ba258299eb489b490594397e23c.png)
③命题“若x,y都是偶数,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
④命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/582ad43edf388c096e7704d92340bf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5286186cb58bf265a2a96e5195d88d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab92728b35ed5798e07a2b0095bfcc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27dd329517f0dd8f1d0dfade6138ed4.png)
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10 . 已知椭圆
:
的左、右焦点分别为
,
,点
在椭圆
上,则
的值可以是______ .(填写一个满足条件的值即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914075a4574c09bdb860d8f8f09a4e7a.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75436dfba3658f87e4c7830e508a752f.png)
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2022-11-15更新
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541次组卷
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4卷引用:江西省抚州七校(广昌一中、金溪一中、乐安实验学校、黎川一中、南城二中、南丰一中、宜黄一中)2022-2023学年高二上学期联考数学试题
江西省抚州七校(广昌一中、金溪一中、乐安实验学校、黎川一中、南城二中、南丰一中、宜黄一中)2022-2023学年高二上学期联考数学试题江西省2022-2023学年高二上学期11月期中调研测试数学试题(已下线)第05讲 椭圆 (高频考点,精讲)-2(已下线)模块四 专题7 高考新题型(劣构题专训)基础夯实练(人教A)