名校
解题方法
1 . 设集合
为满足
,
,
的空间向量
,
,
中可能出现的两两共线的向量组数组成的数集,集合
,若
,则
的取值范围为______ ,当
最小时,
的取值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee0b48b17112965d224bd169314f5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42725bfd7040b47a57faa633f163b856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd4c620c5f6235adcb1c148cad15080.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/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e61c7d643455ec2d0d4fdbc4ee4dd1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eac19737d882225c903054eb4863501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-21更新
|
536次组卷
|
2卷引用:广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
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 . 如图1,直线
与x轴,y轴分别相交于A,B两点,将
绕点O逆时针旋转90°得到
,过点A,B,D的抛物线
叫做l的关联抛物线,而直线l叫做
的关联直线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ef9d3ce4-d4b1-4552-a814-082583273cf8.png?resizew=458)
(1)若直线
,则抛物线
表示的函数解析式为________;若抛物线
,则直线l表示的函数解析式为______.
(2)求抛物线
的对称轴(用含m,n的代数式表示);
(3)如图2,若直线
,抛物线
的对称轴与
相交于点E,点F在l上,点Q在抛物线
的对称轴上.当以点C,E,Q,F为顶点的四边形是以
为一边的平行四边形时,求点Q的坐标;
(4)如图3,若直线
,G为
中点,H为
中点,连接
,M为
中点,连接
.若
,求直线l,抛物线
表示的函数解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a88699a9cab3fb5e061e722d1f60a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9a6eeeebf3cff569578d7366b755aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ef9d3ce4-d4b1-4552-a814-082583273cf8.png?resizew=458)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90717234dbf965e8cb5f8fe2e53776da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef60818f89bebb4ed87db774a5149fd9.png)
(2)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
(3)如图2,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ec899da04f19dca04bba10ffc4358a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(4)如图3,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a163a3df8d98950645d7a249141b679d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc91a53e2534ce7034372b0add103eac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
您最近一年使用:0次
名校
4 . 当
时,
恒成立,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46800232bd76c00bc7cd92bef26aaf63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92cc0272d865b05c086bbcdf29979fc0.png)
A.当![]() ![]() | B.当![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
您最近一年使用:0次
2022-05-13更新
|
631次组卷
|
2卷引用:浙江省“新高考名校联盟”2021-2022学年高一下学期5月检测数学试题
名校
解题方法
5 . 若函数
在
上的值域是
,则称
是第
类函数.
(1)若
,
是第
类函数,求
的取值范围;
(2)若
,
是第2类函数,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe276c0522839b1d37086d92612aa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c042bfa9459620418970f38c0cc7d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a0a547c81fe36ab8c3ea79622ce7ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/465c1b181a5d0d2f849340d279f3eb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8416c507d6a49354db02a11f6959dae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6600826b9264d15d6c1d96c579d5ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
您最近一年使用:0次
2024高三·全国·专题练习
解题方法
6 . 正四棱锥
的外接球半径为R,内切球半径为r,求证:
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff3606c7bf728b4f539261461cde677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,已知抛物线
与x轴交于点
和B,与y轴交于点C,对称轴为
.
(1)求抛物线的解析式;
(2)如图1,若点P是线段BC上的一个动点(不与点B,C重合),过点P作y轴的平行线交抛物线于点Q,连接OQ.当线段PQ长度最大时,判断四边形OCPQ的形状并说明理由;
(3)如图2,在(2)的条件下,D是OC的中点,过点Q的直线与抛物线交于点E,且
.在y轴上是否存在点F,使得
为等腰三角形?若存在,求点F的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a1b01c1a6d9a929a4e1d0d532ca8f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a61d77911527508524874b212a0937d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/8/e7235442-4de4-4daf-8c3d-87adf604d345.png?resizew=373)
(1)求抛物线的解析式;
(2)如图1,若点P是线段BC上的一个动点(不与点B,C重合),过点P作y轴的平行线交抛物线于点Q,连接OQ.当线段PQ长度最大时,判断四边形OCPQ的形状并说明理由;
(3)如图2,在(2)的条件下,D是OC的中点,过点Q的直线与抛物线交于点E,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163a88553a193e3e31f42a42def91c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
您最近一年使用:0次
名校
8 . 当且仅当
(其中
)时,函数
的图像在函数
图像的下方,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1698eb2b7eb35ba842bd4e9089d8f863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed71b5f6cf02b7e4c52c1181669a3879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26bfd6f4f114107a8531b97079725497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc9500da43d762652277fcc768e4bd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0f46282728fa51ff142a5ad59b06dc.png)
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