2024高三·全国·专题练习
1 . 四棱锥
满足下列条件之一:
(1)各侧面都是正三角形.
(2)各侧面都是全等的等腰三角形.
(3)各侧面的斜高相等.
(4)各侧面与底面所成角相等.
(5)各侧棱与底面所成角相等.
(6)各侧面都是等腰三角形且底面是正方形.
(7)相邻侧面所成的二面角都相等.
(8)相邻侧棱所成的角都相等.
问:哪几个条件是四棱锥成为正四棱锥的充要条件?哪几个是充分不必要条件?哪几个是必要不充分条件?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfcf34539673d516eb9b259951a81ed.png)
(1)各侧面都是正三角形.
(2)各侧面都是全等的等腰三角形.
(3)各侧面的斜高相等.
(4)各侧面与底面所成角相等.
(5)各侧棱与底面所成角相等.
(6)各侧面都是等腰三角形且底面是正方形.
(7)相邻侧面所成的二面角都相等.
(8)相邻侧棱所成的角都相等.
问:哪几个条件是四棱锥成为正四棱锥的充要条件?哪几个是充分不必要条件?哪几个是必要不充分条件?说明理由.
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2023高一·江苏·专题练习
2 . 指出下列各题中,
是
的什么条件:
(1)
数
能被6整除,
数
能被3整除;
(2)
,
;
(3)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
有两个角相等,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
是正三角形;
(4)
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3567dcfdb7139dde2ec0ef0670136132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457185351773eeb5d216b3e8726acbbe.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97cc93a719bed81790e2d440aa40503a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6adbcb574dccb9d347938124d62cba1c.png)
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2023高一·全国·专题练习
3 . 下列各小题中,
是
的什么条件?(在“充分非必要条件”,“必要非充分条件”,“充要条件”“既不充分也不必要条件”中选一种)
(1)
:
,
:
或
;
(2)
:
,
:
或
;
(3)
:
,
:关于
的方程
有实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d4c247fff3abc77449e22aa029cf57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629507dcfdeb6866da428c4f45e2b21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d16f50c58699f352885df1f7bc9132.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6e98344626d5f5c451137d6605845d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b5b0ec9102c38d1a393a469090b5fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e109d31afb394e01c438eaacb8fa3e0.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cfada8fd642ddf968bfd4228d48ec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99aaea5595db1e5a12c8a1113cfffe4.png)
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名校
解题方法
4 . 已知
.
(1)若
,则
是
的什么条件?
(2)若
的必要不充分条件是
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af85ec373a252beb969df490c411f14d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023高一·全国·专题练习
解题方法
5 . 若集合
,
,试写出:
(1)
的一个既充分也必要条件;
(2)
的一个必要条件但不是充分条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0611d021fc4efdf1d9b992a4bd14bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13ce10cef49af1cd341d0a7599a73c1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7f14bf7f60fe19b509223284455f05.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7f14bf7f60fe19b509223284455f05.png)
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2023高一·全国·专题练习
6 . 指出下列各组命题中,p是q的什么条件(充分不必要条件,必要不充分条件,充要条件,既不充分又不必要条件).
(1)p:
,q:
;
(2)p:
,q:
;
(3)p:
,q:方程
有实根;
(4)p:
,q:
.
(1)p:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3019b662e5dc2750bb6f9199d3250f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb20e291772c2614ad19f4cc919dfec.png)
(2)p:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efd32ba5030535598e979fd6d3a4d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f069e3c3295e0014d44cc276fb933d.png)
(3)p:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6df730bcff4bcda7f3e5178a8641a85.png)
(4)p:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f7c6d752d770babee942434e1e5e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da6d82d173ad18cc040e94c925b5ab9.png)
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7 . 设函数
.
(1)设
,求函数
的单调区间;
(2)求证:
是
有三个不同零点的必要而不充分条件;
(3)设
,
,
,证明:函数
恰有一个零点r,且存在唯一的严格递增正整数数列
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae06c488100e31570805778b1d322e4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d3469fb79917724365db2b2829d512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0c84cafbf166a261fa4dbf66df8c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baddffb31adacf907742ca666e32d664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea0e903fbb4c8ce04133b9969578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba5fb2a39d08006bf9dd4bb689d0f4c.png)
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解题方法
8 . 设
,
,命题
,命题![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdab1bada0ab2dc143e0bbf571efd55.png)
(1)当
时,试判断命题p是命题q的什么条件?
(2)求
的取值范围,使命题p是命题q的必要不充分条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f925518eaba9e770ef4c4b13b44c57ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504648799795df73cf7e0d39bdb73a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06285f87fc0f915e637db2d55c7e814f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdab1bada0ab2dc143e0bbf571efd55.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfc27d13b4d07ade4729b481cc95735.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-06-18更新
|
1169次组卷
|
6卷引用:模块四 专题1 暑期结束综合检测1(基础卷)
(已下线)模块四 专题1 暑期结束综合检测1(基础卷)(已下线)模块四 专题4 大题分类练 《集合与常用逻辑用语》基础夯实练(已下线)模块四 专题5 大题分类练 一元二次函数、方程与不等式 能力拔高练福建省福州市八县(市、区)一中2022-2023学年高一上学期11月期中联考数学试题四川省眉山市仁寿实验中学2023-2024学年高一上学期期末数学试题四川省眉山市东坡区冠城七中实验学校2023-2024学年高一下学期开学数学试题
名校
9 . 已知
定义域为R的函数,
,若对任意
,均有
,则称
是S关联.
(1)判断函数
是否是
关联,并说明理由:
(2)若
是
关联,当
时,
,解不等式:
;
(3)判断“
是
关联”是“
是
关联”的什么条件?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424f7073274d2bd132b4e1505f7b3320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4c1727e642025874a4a6626722444e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69530f171615d0d6a6fc9dfb8d455efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbae93aebd279adb0da856cb3b10a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff7e39b335e3b5250b7f727e16a4a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50af11c345056215054f7cfe679939da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2b53cd9892f6d174509740afbc69d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712c22cbe31bf46fcd964c8c30bcb660.png)
(3)判断“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff7e39b335e3b5250b7f727e16a4a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
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2021高一·全国·专题练习
10 . 判断下列各题中的条件p是结论q的什么条件.
(1)条件
:
,结论
:
;
(2)条件
:
是
真子集,结论
:
.
(1)条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc7b691f42a099f56801834081ce341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
(2)条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.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/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9d50619b779c1056602f46b2a95e90.png)
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