名校
1 . 设
是平面上的两个单位向量,
.若
,则
的最小值是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d194ecefc9101001d88d3cc0bc9d6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdd48d1ec8139120391e1ebbc35b452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e6186354ec4880544893ef0347bcc5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2017-05-21更新
|
1049次组卷
|
5卷引用:吉林省吉林大学附属中学2017届高三第八次模拟考试数学(理)试题
2 . 平面向量
与
的夹角为
,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f274dcd681627e3ae23ed8532c0edd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89811165d009e98e45fb96ca6a4404b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a4a010a31650b7a97a2ef7ff43e27e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 函数
(
,
,
)在
内只能取到一个最大值和一个最小值,且当
时,
有最大值4,当
时,
有最小值-4.
(1)求出此函数的解析式以及它的单调递增区间;
(2)是否存在实数
,满足不等式
?若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b659146043ee17e549578998318b2c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/decd18aa25232173ccc2a5cf975dad72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff4d664067707c153d4d164e2e8cda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff420ca0d6e2e7d434a933cf6c5792b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44397846321d52e425b5bc8aaeacbabd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)求出此函数的解析式以及它的单调递增区间;
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccf022ea4a95ecc51774563b625acf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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4 . (理) 如图,在平面直角坐标系
中,点
,
在单位圆上,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/f6871996-1733-4ecd-a0e8-ddd01706b867.png?resizew=163)
(1)若
,求
的值;
(2)过点
作
轴的垂线交单位圆于另一点
,过
作
轴的垂线,垂足为
,记
的面积为
,
的面积为
,设
,求函数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1703344522b8eb0a0fb0029d3f403b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66fd2378453d47e4b06f157de803724d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d162c29b1e484cfc87350dd68f00b85.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/f6871996-1733-4ecd-a0e8-ddd01706b867.png?resizew=163)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1f8e415bd363c32acffbb489412340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbf9680f74a9ac5d934304654ce2771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4686f39b38d5b90309ee73ed89a0640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665d9c6fc06ddd0e080e45ab858d1852.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
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5 . 已知平面直角坐标系内三点
、
、
在一条直线上,满足
,
,
,且
,其中
为坐标原点.
(1)求实数
,
的值;
(2)设
的重心为
,且
,求
的值.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71eb98f5fae49f695ea1beea0e9a1d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5ee132822fe177349733feee41a8ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ebeac315bb91b2d6ab40c7eb00d8a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfe4da6f357e55927d25d9d27ea8717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3304bc1372275307dce0bf4e98b8f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f29d6bb411a032e06a1f7ed0ea2eed22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316e85517919c422ecd81c95fb367d57.png)
您最近一年使用:0次
2017-05-10更新
|
736次组卷
|
4卷引用:吉林黑龙江八校联合体2016-2017学年高一下学期期中考试数学试题
6 . 如图是函数
(
,
,
)的一部分的图像.
![](https://img.xkw.com/dksih/QBM/2017/5/10/1683941195087872/1684173603282944/STEM/1ebba597a4864fad8bc58905ea91b388.png?resizew=302)
(1)求
的解析式;
(2)若将
的图像向右平移1个单位得到
的图像,求函数
的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec89c3bc454d209007c2b29baeeb3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a297d9b18487cde772be5c7d2676b0.png)
![](https://img.xkw.com/dksih/QBM/2017/5/10/1683941195087872/1684173603282944/STEM/1ebba597a4864fad8bc58905ea91b388.png?resizew=302)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
您最近一年使用:0次
名校
7 . 如图,
为线段
的中点,
,
,设
,
,试用
,
表示
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a9a7e9187a8d25b268bd4cc9342cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902679a5126443f3b184c141e0ed6694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93073e4f4e45258852e499bc2becf9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683339de2afddad19127f3cb480de6c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd0cecf5c102254b9755e42a80c3948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd98a891fa65f2fc6688001b03185d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f90e16e18b1e88ebb1ab811d06be76.png)
![](https://img.xkw.com/dksih/QBM/2017/5/10/1683941195087872/1684173603250176/STEM/8e1366ace73d46409084b2fe00a7eff1.png?resizew=194)
您最近一年使用:0次
2017-05-10更新
|
920次组卷
|
3卷引用:吉林黑龙江八校联合体2016-2017学年高一下学期期中考试数学试题
解题方法
8 . (1)化简:
;
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bce8e4b3c4a8ad6425ffd76b141d472.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73257f360fc19649630994f09d368f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd78668df259acf62449420fd108b1aa.png)
您最近一年使用:0次
9 . 已知点
,
,
,
,则向量
在
方向上的投影为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f20953302d861e6c698575bfbab1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a290a27cce9bd59bb6d79822473d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733ca3719874892ee4ffbbaa2030b2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cebdf6eefcc6e7c9afe932ab9c78b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b680f91c4a693cc9ab2c23f2e9114ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f54023fbb1f404b2e75d8d494159eae.png)
您最近一年使用:0次
2017-05-10更新
|
254次组卷
|
2卷引用:吉林黑龙江八校联合体2016-2017学年高一下学期期中考试数学试题
解题方法
10 . 已知
的终边过点
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9012ae3226e6f1d338f879c180ce63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed78980e8b456e7c3a53b81c72c15dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
您最近一年使用:0次