2023高一下·上海·专题练习
解题方法
1 . 已知
,
,且
,则
点的坐标是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc69a40908bb7d490e038d2742d83c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22924a3c487c5a1b5dee2a39a0aa9bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd11cd9057a3ebbdc8bfc4ed7383dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2 . 已知平面向量
,则
在
方向上的投影数量为 __ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874f16fff7b603cf7391668c023a65dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
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2024高一下·上海·专题练习
名校
解题方法
3 . 已知
均为单位向量,且
,则
与
的夹角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db69ec248c9382eb087b25facfd6a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb667795acdfafa436ee35e152adbc4.png)
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2024高一下·上海·专题练习
解题方法
4 . 若函数
的定义域是
,值域是
,则
的最大值是 __ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b7927df1090867d941a9904dffb2a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56002ab09438fcb642fde70b10ee9720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
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2024高一下·上海·专题练习
5 . 某同学用“五点法”画函数
,
在某一周期内的图象时,列表并填入的部分数据如下表:
(1)请填写上表的空格处,并写出函数
的解析式;
(2)将函数
的图象向右平移
个单位,再所得图象上各点的横坐标缩小为原来的
,纵坐标不变,得到函数
的图象,求
的单调递增区间;
(3)在(2)的条件下,若
在
上恰有奇数个零点,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fcd4082d14e5a26c6fccf782576856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1acd2d5f345bc859faaf9edc1036a6c7.png)
![]() | ![]() | ![]() | ![]() | ||
![]() | 0 | ![]() | ![]() | ![]() | ![]() |
![]() | 0 | 1 | 0 | ![]() | 0 |
![]() | 0 | ![]() | 0 | ![]() | 0 |
(1)请填写上表的空格处,并写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ca334d2ae1289b70941e6af9e336a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91609d305f182620aff2f5d85cc7e17f.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdb2704ea6bc44b5a75fb3c8a100353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3810fc5221a4e2e7095f945bb4a2e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024高一下·上海·专题练习
6 . 方程
在
内的解为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43183efe32be57d11b6cbc413e7599dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27794407a3d82a6746f7e0871051f486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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2024高一下·上海·专题练习
7 . 已知函数
.
(1)求
的单调递增区间;
(2)若
,求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7ff32644b78ce91ebcad5e5ef8b2c1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7a3e19a25b7564106a3d2cf3a59b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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名校
解题方法
8 . 已知
,
,
.
(1)若
与
垂直,求实数
的值;
(2)若
与
方向相反,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29276b43a2950ed71f0f9629a35dfa74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff265969988f1f138700129e5d7a6d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9192e812a914e8065329bd509aa6ccb9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0d6f45010a54e0bfa0b48c90376ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d108e523626be0b40be9b3543ce12524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0d6f45010a54e0bfa0b48c90376ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a12309c8aa2c9362c197de345aad7eeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
9 . 将函数
图像向左平移
个单位,得到的图像的解析式为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9008d1da153965d1210fee62f29fea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
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名校
10 . 函数
,
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3b449ffe9403b417444df7bd6c523a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386a3591657c19aa04d02f8a256cf9b5.png)
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