解题方法
1 . (1)已知
均为正数,证明:
,并确定
为何值时,等号成立.
(2)设函数
,若不等式
的解集非空,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68425cd896b6dbe2d57140f4722e3f26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2409d894290b1676bd387cd5ebb178c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a840c593c0160c93e4d307b1325eb17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 .
是满足下列条件的集合:①
定义域
;②存在
使
在
分别单调递增,
单调递减,下列函数
为常数
下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdd8bd3ea4d1976c3c80f22380789c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d64909036f0df48da362875fdf7388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e0b6a54ec501dbd0e6475fe1ef02c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda1e4811871368b1c2325be6947b7ff.png)
A.![]() | B.![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() ![]() | D.![]() ![]() ![]() ![]() |
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解题方法
3 . 如图,四棱锥P-ABCD的底面ABCD是正方形,PA⊥底面ABCD,E,F分别是AC,PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/326c6403-37af-4197-98e9-1b25b2c36562.png?resizew=154)
(1)证明:EF∥平面PCD;
(2)若PA=AB,求EF与平面PAC所成角的大小.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/326c6403-37af-4197-98e9-1b25b2c36562.png?resizew=154)
(1)证明:EF∥平面PCD;
(2)若PA=AB,求EF与平面PAC所成角的大小.
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4 . 不等式
的解集是_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f921341b2518207896f11e0e540b5be.png)
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5 . 设集合
,则集合M中所有元素的和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab9f7ad05c54aed536190ab61354318a.png)
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解题方法
6 .
、
满足约束条件:
,则
的最小值是_________ .
![](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/32c8c65efbd6e954fe0a17747eac62e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73192b1b3394925c0b6483fcd811f764.png)
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7 . 已知
为半圆
(
为参数,
)上的点,点
的坐标为
,
为坐标原点,点
在射线
上,弧
的长度为
,线段
的长为4.
(1)以
为极点,
轴的正半轴为极轴建立极坐标系,求点
的直角坐标和极坐标;
(2)求直线
的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d1edafc77ae98bb8cb9aed44420773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34281318027f1d9d7cffd42d2cca8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd9e314a9d0954be3d0a7b5191b316b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14f419e14bc30fe2fada469a0fbbb64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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8 . 定义在
上的函数
满足:
,且
时,
递增,
,
,则
的值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d5a559394b2c15bc7acd901c340350.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a3fbff400c5a336dc2e5c07cfa50e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56a7a9c21d44c55fb211ed0dec84bce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d58b0e00d782782712e3ba9076ad8f3.png)
A.恒为负数 | B.等于0 | C.恒为正数 | D.正、负都有可能 |
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9 . 有一种波,其波形为函数
的图象,在
上至少有
个波峰(图象的最高点),则正整数
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09a7845b7aa74d364eed36ee6cb2ba6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/424843950ee17f6f18b5c181c1f6ee34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.3 | B.4 | C.5 | D.6 |
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解题方法
10 . 已知四棱锥
的三视图如下,则四棱锥
的全面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/0a657ee6-5da0-4689-becf-974f7aa29aa5.png?resizew=180)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/0a657ee6-5da0-4689-becf-974f7aa29aa5.png?resizew=180)
A.![]() | B.![]() | C.5 | D.4 |
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