名校
解题方法
1 . 数学上的符号函数可以返回一个整型变量,用来指出参数的正负号,一般用
来表示,其解析式为
.已知函数
,给出下列结论:
①函数
的最小正周期为
;
②函数
的单调递增区间为
;
③函数
的对称中心为
;
④在
上函数
的零点个数为4.
其中正确结论的序号是____________ .(写出所有正确结论的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165d88ea5812bd14de49f5e3436eefad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a3bd54753e4c1a5fc06b414cc44ac8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d436e42ddbacbbd0af82f0e4750e54.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d56bab4fdb876bd72d5c9c7a734375.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5760e7c1da0c80f6b8912406b6b75c.png)
④在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aeb66add53686f989fbbb057652cb6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3077b0cfb8a47439afc656af6cc889ad.png)
其中正确结论的序号是
您最近一年使用:0次
2 . 已知平面内点集
,A中任意两个不同点之间的距离都不相等. 设集合
,
. 给出以下四个结论:
①若
,则
;
②若
为奇数,则
;
③若
为偶数,则
;
④若
,则
.
其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041bc291bff24b4cee0b205da68db1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ebdde37c672e10fd4ffe741247e566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18faaff0b5622f33a1574103fed13edd.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdda00159c36552b8a9a9743324f82a0.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffaac03e1e452f075e86853fef2a33de.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdda00159c36552b8a9a9743324f82a0.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25df56dc9b8169cbf924f39bfa9f7c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb931a4b3eaa34e2c6f7dab5650f8af.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
3 . 在近期学校组织的论文展示大赛中,同学们发现数学在音乐欣赏中起着重要的作用
纯音的数学模型是三角函数
如音叉发出的纯音振动可表示为
,其中
表示时间,
表示纯音振动时音叉的位移
我们听到的每个音是由纯音合成的,若某合音的数学模型为函数
,且声音的质感与
的参数有关,比如:音调与声波的振动频率有关,频率低的声音低沉,频率高的声音尖利.
(1)当
时,函数
的对称中心坐标为______ ;
(2)当
时,合音
的音调比纯音![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a72ab550b89f838b0f71a24c20f4bb.png)
______ (填写“高”或“低”).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f0670a61f0274e80b47844cea59ac1.png)
![](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/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe5c8a68ce20e3b6551d9fb67ea85fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b87383da5b68e452263e205594f334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a72ab550b89f838b0f71a24c20f4bb.png)
您最近一年使用:0次
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解题方法
4 . 在现实生活中,一个符合实际的函数模型经常是将不同的函数组合得到的,如听音乐家演奏音乐时,我们听到的声音常常就是多种不同乐器产生的声波叠加的结果.在学习了向量和三角函数后,人大附中某研学小组利用所学知识研究若干振幅相同,同频同向的简谐波叠加后,得到新的简谐波的振幅和初相规律,该小组把
(N为正整数)叠加,研究
中的
和
,其中
.
(1)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
(2)当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2073aefa188a89d515b9d32de5d89c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e289d2f03b9a42c8f61858f1c3b32e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d52d236ed8d14f8135a0a63d41a351fe.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb55d413f1ab722e17747c8e99f6c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722068b39032dd59c01afdba985d65be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46626b75bd7bc420bf32b66e3253b40b.png)
您最近一年使用:0次
5 . 已知
.在
中,
设
,
定义:
.
设
或
.给出下列四个结论:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3216c7108baab2601471b965ecb5694a.png)
②
;
③若
,则
;
④
,都有
,则
最多有
个元素.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edec660383c08c26ff438d1b8c7a3177.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c852b101e577e4b7d3af668489b0ea5.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888390fce47b31855712344fd536bce1.png)
定义:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21090f6a3148c6c09a6946c4611fcd7.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2143cab296d997c652c495982e90cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ddbe12fb60130709d275f169dc99c22.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3216c7108baab2601471b965ecb5694a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71daa66564dc886bd4c4f19d83396fd4.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616cdc04ccc5cae9cf8b941ebeb45ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0430ebe2730db038a644d8939a0d73.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9d43ee737b96bb2cd0cc241d6e1efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2509cacc1596557ea46e0f94e84823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
6 . 一架飞机从北京向南飞行1935公里到达广州,假设在广州白云国际机场上空的等待航线是圆形,飞机到达机场上空后,继续沿原航线向南飞行20公里后,开始在直径40公里的圆形等待航线上飞行,飞机每15分钟飞行一周,如图所示,设飞机在等待航线上飞行的时间为t小时,飞机从北京出发向南的飞行距离 为
,
可以近似地 表示为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb17843c51402a1f7cd9b07542597b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb17843c51402a1f7cd9b07542597b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d43e4f18894a6b698cc313a052449e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f1e5d29de6e4d72bfed62d9c14dde5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9448bf1d6136b3a108e7ea60506ad39.png)
您最近一年使用:0次
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解题方法
7 . 在平面直角坐标系
中,
,
.集合
,下列结论正确的是______ .
①点
;
②若
,则
;
③若
,则
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8950c7bc835103d52ceffab14b6b31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6938eeb65411eeac15e140cf1db99773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e460725dacf5768aa8290aa52d9d24.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db7f7eb57e496985bfa77847f58345f.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be2bc0b0fb98f94b86546fe2ab85de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae985f4f5ce87b3105e222f94c77899.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193029805ef60186dcc6338d847b01ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58aeae4debbb8d0c43d5f526ec7c0532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab8e57da1a24cba8a5feb1388b2fba6.png)
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8 . 时间经过
(时),时针转了______ 度,等于______ 弧度;若时针长度是1厘米,则时针
(时)转出的扇形面积是______ 平方厘米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c63f6b1652d3e830ed2dbc65253d043.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15694733427d51a02995963186c5c427.png)
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解题方法
9 . 设是单位圆的一条直径,
的顶点
在该单位圆上,延长
到
(
在线段
),使得
,则
的最大值为
您最近一年使用:0次
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解题方法
10 . 函数
,关于函数
的零点情况有下列说法:
①当
取某些值时,无零点; ②当
取某些值时,恰有1个零点;
③当
取某些值时,恰有2个不同的零点; ④当
取某些值时,恰有3个不同的零点.
则正确说法的全部序号为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24bd5843cbfaff1885592a83275ad7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2853174cf50c71d58b7d57d7048088.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
则正确说法的全部序号为
您最近一年使用:0次
2024-03-27更新
|
163次组卷
|
2卷引用:北京市第一六六中学2023-2024学年高一上学期数学期末模拟试卷