名校
解题方法
1 . 函数
的图象关于坐标原点成中心对称图形的充要条件是函数
为奇函数,有同学发现可以将其推广为:函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数.
(1)求函数
图象的对称中心;
(2)根据第(1)问的结论,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830a9e13de1222eb9c3d5e4b636f50fa.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bcb66de09592e24d8f7ef0b5080f7b2.png)
(2)根据第(1)问的结论,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0000e2309bf522573511c8d2419290e.png)
您最近一年使用:0次
2024-03-06更新
|
91次组卷
|
2卷引用:云南省蒙自市第一高级中学2023-2024学年高一下学期开学考试数学试题
解题方法
2 . 我们把
(其中
,
)称为一元n次多项式方程.代数基本定理:任何复系数一元
次多项式方程(即
,
,
,…,
为实数)在复数集内至少有一个复数根;由此推得,任何复系数一元
次多项式方程在复数集内有且仅有n个复数根(重根按重数计算).那么我们由代数基本定理可知:任何复系数一元
次多项式在复数集内一定可以分解因式,转化为n个一元一次多项式的积.即
,其中k,
,
,
,
,……,
为方程
的根.进一步可以推出:在实系数范围内(即
,
,
,…,
为实数),方程
的有实数根,则多项式
必可分解因式.例如:观察可知,
是方程
的一个根,则
一定是多项式
的一个因式,即
,由待定系数法可知,
.
(1)解方程:
;
(2)设
,其中
,
,
,
,且
.
(i)分解因式:
;
(ii)记点
是
的图象与直线
在第一象限内离原点最近的交点.求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e138b0fc1c40ba1637098eb2a6efd580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6368fec0c2c25db7c29b014d60270e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6368fec0c2c25db7c29b014d60270e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b328845a4b1881eee38084d5501224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcde67e0b4461129e0c7e3a12df4634f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edffa0cf823fb77bb7e273db0e014743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483fd78fe6ed871ce859f4796ad7779c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b765718479c160ba61ec5c6f8c5f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e29bf5652f0d4f764c3606efcdb445f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3230af83e2c18650f1de0c88060c0b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e138b0fc1c40ba1637098eb2a6efd580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e138b0fc1c40ba1637098eb2a6efd580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf70f45c7f3a63a81001f87863f2c73c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2527822fd5ee6ded770ffc9857c41bff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b924d856924e8cf2b172d5cacffe0610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2c82aa40a712f2ef6fda7eaeb88a48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7344f58d5f08fab08d4e99baa13fa652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7126d6d76248996a222631cc9ea93c.png)
(1)解方程:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58fc8760f5b4612d0f76133d938f4e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536bbd87dd4193314aec2e214e5f05b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1cdb8081eb1b3390b3730c01b9afb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653588ca473b428b4a437d6a8ed7a76c.png)
(i)分解因式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e42787c800e5f9c7ac483bea80d8440.png)
(ii)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c520c63104bb6669c3591bd100b10e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51969fc1a8030cef11cab59267689e89.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
.
(1)求函数
的最小正周期和单调增区间;
(2)求函数
在区间
上的最小值和最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77f5a7e82a0dd771d7799682eb36fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851eae00e3369068e33a7e6420483883.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7466d2055b1e49baea19e7e13cf97b77.png)
您最近一年使用:0次
2024-03-03更新
|
755次组卷
|
2卷引用:云南省红河哈尼族彝族自治州蒙自市第一高级中学2023-2024学年高一下学期3月月考数学试题
4 . 函数
(
,
,
)的部分图象如图所示.
的解析式;
(2)将函数
的图象先向右平移
个单位,再将所有点的横坐标缩短为原来的
(纵坐标不变),得到函数
的图象,若关于
的方程
在
上有两个不等实根
,
,求实数
的取值范围,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fcd3cea5f5e2fe943490dcb65d74c73.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/29e1734dcc7697235124fbaba4ba6033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b97537de8e5111a3fd21a175577e504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c958b625e443b4c66517e37b4e015e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02011cb66995c65cab56f1ad00de0f21.png)
您最近一年使用:0次
2024-03-01更新
|
1869次组卷
|
6卷引用:云南省德宏州2023-2024学年高一上学期期末教学质量统一监测数学试卷
云南省德宏州2023-2024学年高一上学期期末教学质量统一监测数学试卷四川省泸州市泸县第五中学2023-2024学年高一下学期3月月考数学试题四川省眉山市彭山区第一中学2023-2024学年高一下学期4月月考数学试题海南省东方市东方中学2023-2024学年高一下学期第一次月考数学试题(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)(已下线)专题02 三角函数图形与性质的12种常考题型归类(2)-《期末真题分类汇编》(北师大版(2019))
名校
5 . 化简求值:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175925ff8de139467847bf3b4cba76b9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b794771c2a5e4f140965a6405f28d0ac.png)
您最近一年使用:0次
名校
解题方法
6 . 已知
是定义在R上的偶函数,当
时,
.
(1)求函数
在R上的解析式;
(2)若函数
在区间
单调递增,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5397ee1eb6d157f6ec1e7a878f8d16e.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/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828d05bf56d2ed565e971fcf8eb3826b.png)
您最近一年使用:0次
2024-02-27更新
|
626次组卷
|
4卷引用:云南省蒙自市第一高级中学2023-2024学年高一下学期开学考试数学试题
名校
7 . 已知函数
,
.
(1)求函数
的单调递减区间;
(2)求函数
在
上的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bbfbc332a4314ae7c426d8bf56bb43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a7ac80b964f5baf79f5faa7ac1e2983.png)
您最近一年使用:0次
名校
解题方法
8 . 已知集合
,集合
.
(1)求
;
(2)若集合
,
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af834e77de8eb10ca841f63c36cca3f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a172b529260cf95c9f7e662ee101ea.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6fc36161bbbdc9ed5b658cb57301c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07241606934d6c75cf04455979d0e1b0.png)
您最近一年使用:0次
名校
解题方法
9 . 某工厂生产某种产品,年固定成本为200万元,可变成本
万元与年产量
(件)的关系为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d18ad99956e0ba011f044c45bb45af.png)
每件产品的售价为90万元,且工厂每年生产的产品都能全部售完.
(1)将年盈利额
(万元)表示为年产量
(件)的函数;
(2)求年盈利额的最大值及相应的年产量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cc4a85bbf152031dc8ebd182e44ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d18ad99956e0ba011f044c45bb45af.png)
每件产品的售价为90万元,且工厂每年生产的产品都能全部售完.
(1)将年盈利额
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求年盈利额的最大值及相应的年产量.
您最近一年使用:0次
名校
10 . 已知
.
(1)化简
;
(2)若
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a5de91aacb2747776c36fe4c80730b.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29a22a8bdd026f1199a4e418afcd240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6658f2f63a5adf94396085625cb246b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda66aa0b85ddcfaefc6eaafbfd46bed.png)
您最近一年使用:0次