1 . 将函数
的图象上所有点的横坐标缩短到原来的
,纵坐标不变,得到
的图象.
(1)求
的解析式与最小正周期;
(2)求
图象的对称中心的坐标;
(3)设函数
,求
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a4025a394f30a4f8e7a58c921dbccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2595780da91e1c21306800e7fa7d2fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbae6c61828aa9d7a6a04535831151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45f644764b91e5d01e6f830b50d3942.png)
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2 . 对于平面向量
,定义“
变换”:
,其中
表示
中较大的一个数,
表示
中较小的一个数.若
,则
.记
.
(1)若
,求
及
;
(2)已知
,将
经过
次
变换后,
最小,求
的最小值;
(3)证明:对任意
,经过若干次
变换后,必存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fde5542ad04744c14f912648f3aa0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bd66e602e9c043218806708e943c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb00071815c94c090a4095b4964fefb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7bc9573b3a8758511c63731db18183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96340894e8fb63c00d778b4d654d0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7bc9573b3a8758511c63731db18183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701ab98a2bf1135cd989822b0738e11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484c1b7bc2fc5677406e20180f667200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0624499e16b73afec432dd1afd6153d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b162d1d5bfaa7760678ea3d624beb171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5c19921380da55f5f1a00809a34503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35234a3829d238ea479fef9cec166468.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aceb3666a9d49ef40c39eac116ccd5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cfb8c8707c3960bf1fd46b805e481d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a887552671e6d4df390320ee9a36150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f389ec068eb1d1aa586b79097d70a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd78ec8777a8e6e5b32222cdb15c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06296b9023c1dca6f44b8297842bef7c.png)
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解题方法
3 . 在平面直角坐标系中,已知向量
,
,向量
与
间的夹角为
.
(1)求
在
方向上的投影向量的坐标;
(2)求
的值;
(3)若向量
与
夹角为钝角,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436ea16dea6aec60b738a82db53ab520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555585ed301898b926716324cd4f0c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7a1df960feef63dec4790d63f52279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7a1df960feef63dec4790d63f52279.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93c717ffc9d866dd09cb8bc4e0bcc4.png)
(3)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b305a8827b510a53b657fb72a99ff27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c470c3e1dcf820cd4e64fea80940e3a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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名校
4 . 已知
,
,
.
(1)若
,求
,
;
(2)若
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e5eea5f7f98ca8632358b7e49ceb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbaef0985c61e59281963e2edc0c0ed1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788203620f5d6b035b7566c417dc09ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150fdec66e3bab1d73073d0f091f08ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
7日内更新
|
87次组卷
|
2卷引用:广西桂林市2023-2024学年高一下学期阶段性联合质量检测数学卷
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5a951a4a8df40e4779d213f33ee8e6.png)
在一个周期上的图象(先在所给的表格中填上所需的数字,再画图);
(2)求
在区间
上的最大值和最小值及相应的
值.
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5a951a4a8df40e4779d213f33ee8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
0 | |||||
x | |||||
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26ae54737caa621832628479fa0de30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705e64c6f20c5ba1bfeeb92eb2a31b04.png)
您最近一年使用:0次
2024-06-08更新
|
209次组卷
|
2卷引用:广西梧州市苍梧中学2023-2024学年高一下学期3月考数学试题
名校
6 . 化简求值:
(1)
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1036fbb266194b9cda9db34d62ad3e1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bee1b86a76c3ef65d5f61eb5798ef18.png)
您最近一年使用:0次
7 . 已知函数
.
(1)求函数
的最小正周期和对称轴方程;
(2)若函数
在
上有2个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/924c64a597302fb73dc44109fdc88de3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c053fa2da356f77df641d07c32b975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb617f10398c8c7d7df67e5ad0572094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 对于分别定义在
上的函数
以及实数
若存在
使得
则称函数
与
具有关系![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9902e568d7b1f5229f6ebf5c43e18ab.png)
(1)若
判断
与
是否具有关系
并说明理由;
(2)若
与
具有关系
求实数
的取值范围;
(3)已知
为定义在
上的奇函数,且满足:
①在
上,当且仅当
时,
取得最大值1;
②对任意
有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67cba3a83a7d7f44570a197db5c9111.png)
判断是否存在实数
使得
与
具有关系
若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5f7f88d327670ad628ace52f5b792f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e924e716802ea0e503812d4168de1ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb097db757dcce8d1e114eaa35cfb5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c9050bc59bcfe21e528bf1e336996.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/d9902e568d7b1f5229f6ebf5c43e18ab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4efcf59a67eda20aff6a74fd1b5102.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/c217be22ee74ee758755bc18917e3eae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67240f24d5be6db366b4f218003d8896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17a7dd0a9319f92eec1ac43eb93106d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea020f6ee69455b961fa9fed5e82dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0446794d4e31bb0bd3907b1dd27dbd6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a78355986534b6e50bd7cabc9290a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbce12f6911dacf78262ba950c0be55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67cba3a83a7d7f44570a197db5c9111.png)
判断是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed0e00c9b96bf8b70b3ea1de85852ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65353833b295abc6a7ddd390046f69c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b4942cf1c67cc84090c77e373809d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d869a4478e36efba14ec203efbd00342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024高三·全国·专题练习
名校
解题方法
9 . 已知函数
的图像关于直线
对称,且图像上相邻两个最高点的距离为
.
(1)求
和
的值;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ab247c7377354297f144ac986d690e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f56a20bc5fce6b02217627b42249854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21866550e6e52b0d7d747ec8ef7da64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f72fad1ca837804a83a3555da43e93.png)
您最近一年使用:0次
名校
解题方法
10 . 已知平面向量
满足
,
,
与
的夹角为
.
(1)求
;
(2)当实数
为何值时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fc7a342293983cc4865498c121493d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ec7096fee04d80cabd9e831a90fae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e6f98f23fea7db0f74897928024ca0.png)
(2)当实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d312345f0d2e37235fe50df09c0656.png)
您最近一年使用:0次