名校
1 . 下列说法错误的个数为( )
①已知
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08ca29db8f436e0eb09d367943a1502.png)
②已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5561372d2b22000e1bd1b275f7152d1.png)
③投掷一枚均匀的硬币5次,已知正面向上不少于3次,则出现5次正面向上的概率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8d1ca7682da10dc7f36e858593d51f.png)
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae41b4e83c79f13cb4d410ec6c642da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b1b910246ef656d8270529cf68e1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08ca29db8f436e0eb09d367943a1502.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f36e1cabd0972a7677f852793ef5e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5561372d2b22000e1bd1b275f7152d1.png)
③投掷一枚均匀的硬币5次,已知正面向上不少于3次,则出现5次正面向上的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8d1ca7682da10dc7f36e858593d51f.png)
A.0 | B.1 | C.2 | D.3 |
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2卷引用:浙江省金华市卓越联盟2023-2024学年高二下学期5月阶段联考数学试题
2 . 已知①设函数
的值域是
,对于
中的每个
,若函数
在每一处
都等于它对应的
,这样的函数
叫做函数
的反函数,记作
,我们习惯记自变量为
,因此
可改成
即为原函数的反函数.易知
与
互为反函数,且
.如
的反函数是
可改写成
即为
的反函数,
与
互为反函数.②
是定义在
且取值于
的一个函数,定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c5d65e0ccd27748fcbc420c6a2e22.png)
,则称
是函数
在
上的
次迭代.例如
,则
.对于一些相对复杂的函数,为求出其
次迭代函数,我们引入如下一种关系:对于给定的函数
和
,若函数
的反函数
存在,且有
,称
与
关于
相似,记作
,其中
称为桥函数,桥函数满足以下性质:
(i)若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e8a92152787274ed6e06a21ef1661.png)
(ii)若
为
的一个不动点,即
,则
为
的一个不动点.
(1)若函数
,求
(写出结果即可)
(2)证明:若
,则
.
(3)若函数
,求
(桥函数可选取
),若
,试选取恰当桥函数,计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f93e3581e920716e710e22b31006bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f93e3581e920716e710e22b31006bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63ced31d098cfb0cf14d906e97e6353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955f3c2b80eebc3f88c804112e5f41f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955f3c2b80eebc3f88c804112e5f41f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb87ce86e2c9a1a8188b03b74438fdd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb87ce86e2c9a1a8188b03b74438fdd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ef38135b0e7906687d8a4918a4cb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43737e3ca063dfc210d0c72924a4930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808bd2fc4b344e7669fca65b4fa122df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808bd2fc4b344e7669fca65b4fa122df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c5d65e0ccd27748fcbc420c6a2e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c110a1293773729278a214c7fe8d544e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052ddf3664af9ab2990f3ea622997e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ca4e4f009554b599eab90e1d94c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.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/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71567deb76e48f8a2424b06536cbe465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66b033ee7a03c7b3508583481465275.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/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e8a92152787274ed6e06a21ef1661.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f199ad3fad8657afa38f370b319a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192bb45bd15b200f40b34377bc58905b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99315f5b2ae9bea18e06401b41d3780c.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becd598a11b876d858728161a7a09705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ab7717944da2b6cc305b6a65f91408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85f9d9be0ba965ff7beb0e011267f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bee7f1ccd52c7d526b6d466b970e769.png)
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名校
3 . 以下说法正确的是( )
A.把8个相同的小球放到编号为1,2,3,4的4个盒子中,恰有1个空盒的放法共有84种 |
B.![]() |
C.![]() ![]() |
D.已知![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2024-05-08更新
|
536次组卷
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2卷引用:浙江省东阳市外国语学校2023-2024学年高二下学期5月月考数学试题
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4 . 已知
的三个角
的对边分别为
且
,点
在边
上,
是
的角平分线,设
(其中
为正实数).
(1)求实数
的取值范围;
(2)设函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736d82fce28c323d02a4183610777845.png)
①当
时,求函数
的极小值;
②设
是
的最大零点,试比较
与1的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe29c42302504e7fd8577dbc7d130ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9ecf347b1b8b1edd8f354a0fc1f152.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736d82fce28c323d02a4183610777845.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f627a70fa1006b30c2db5b1fcfaae82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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2024-04-29更新
|
774次组卷
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4卷引用:浙江省东阳市外国语学校2023-2024学年高二下学期5月月考数学试题
浙江省东阳市外国语学校2023-2024学年高二下学期5月月考数学试题湖南省岳阳市2024届高三教学质量监测(三)数学试题(已下线)压轴题07三角函数与正余弦定理压轴题9题型汇总-2(已下线)模块5 三模重组卷 第1套 全真模拟卷
名校
解题方法
5 . 若
,则
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b3e0f638a0dc902d959f7cf8303be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcefcd3f339935767c3d8d01774d7cb.png)
A.2 | B.0 | C.![]() | D.![]() |
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2024-03-23更新
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2卷引用:浙江省金华市东阳市外国语学校2023-2024学年高二下学期3月检测数学试题
名校
6 . 如图,点C是以AB为直径的圆O上的一个动点,点Q是以AB为直径的圆O的下半个圆(包括A,B两点)上的一个动点,
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a547a90936ff4635dd6d5f303e12986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32979e540e6770ffc0f6417395ec5c74.png)
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解题方法
7 . “阿基米德多面体”也称为半正多面体,是由边数不全相同的正多边形为面围成的多面体,它体现了数学的对称美.如图,是一个八个面为正三角形,六个面为正方形的“阿基米德多面体”,某玩具厂商制作一个这种形状棱长为
,重量为
的实心玩具,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7808a98cf04a37b0358c1e855ee4347.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/37fbe650-3516-418a-b898-3bb8c8825d10.png?resizew=161)
A.将玩具放到一个正方体包装盒内,包装盒棱长最小为![]() |
B.将玩具放到一个球形包装盒内,包装盒的半径最小为![]() |
C.将玩具以正三角形所在面为底面放置,该玩具的高度为![]() |
D.将玩具放至水中,其会飘浮在水面上. |
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2024-02-28更新
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898次组卷
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3卷引用:浙江省金华十校2023-2024学年高二上学期1月期末调研考试数学试题
8 . 如图,已知正方形
的边长为2,分别取边
的中点
,并连接形成正方形
,继续取边
的中点
,并连接形成正方形
,继续取边
的中点
,并连接形成正方形
,依此类推;记
的面积为
的面积为
,依此类推,
的面积为
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3d2faa297324af40f0ea27ac7e653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9651011a8533cfdd7988e61495bbf039.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d659d5601d47fc8e580788f8bfc2cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa87ea03c832e1f4ce4d3256055c721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d88169cf2f7701c7e6ed7c1ee32171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e55e287d09dfa42b27ac66a3ac808db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4abedd7d123e37eeb9188c7d64d072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf95b2e03d60a1ecc36447e2c25bd8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed4684aedf3debd9c5112d925ff78b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddabf77e63bb043fa06ce23b6a8bce0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c58e4415c09a8f9471ce7b806eba50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d923f48adfae8d66a75240e570371c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae160c36edf1f8025b4efe1b2355862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/4b0609ba-5937-479a-a046-434d345cfa21.png?resizew=269)
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解题方法
9 . 如图,某工艺品是一个多面体
,点
两两互相垂直,且
位于平面
的异侧,则下列命题正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/4282488c-6e93-44a9-9b14-609068202f32.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80d830b4d2dec742948fddabb2c605f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2882390b318b9972228bc34c0f347701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc793a6afea747370cae351b53efd46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/16/4282488c-6e93-44a9-9b14-609068202f32.png?resizew=166)
A.异面直线![]() ![]() ![]() |
B.当点![]() ![]() ![]() ![]() |
C.工艺品![]() ![]() |
D.工艺品![]() ![]() |
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2024-01-10更新
|
573次组卷
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2卷引用:浙江省武义第一中学2023-2024学年高二上学期1月检测数学试题
名校
解题方法
10 . 某用人单位招聘毕业大学生设置了笔试、面试两个环节,先笔试后面试.笔试有两次机会,若第一次笔试通过,则进入面试环节,若没有通过,进行第二次笔试,两次笔试相互独立,若第二次笔试通过则进入面试环节,若仍不通过,则淘汰不予录用.面试只有一次机会,通过后即可录用.已知考生甲通过笔试的概率均为,通过面试的概率为
.考生乙通过笔试的概率均为
,通过面试的概率为
.记“甲被录用”为事件A,“乙被录用”为事件B,事件A,B相互独立.求:
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b6f8cb2faaad82b53b2a66ee817a37.png)
(2)甲乙两人恰有一个人被该用人单位录用的概率.
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2023-11-11更新
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4卷引用:浙江省金华市武义第一中学2023-2024学年高二上学期11月检测2数学试题