名校
解题方法
1 .
的内角
,
,
的对边分别为
,
,
,
为
平分线,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734e4bdd3d2a5d489dd863b17687e61.png)
;
(2)若
,
上存在点
,使得
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734e4bdd3d2a5d489dd863b17687e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0b5b7c4ecfb428a6a7bb52fbcdcaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab268845d3dbdbc9ef05e8b721e59c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907a78dce0556d07572d9fd12112ca9a.png)
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解题方法
2 . 设
、
、
为非零向量,若
,则
的最大值与最小值的差为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7328473182f501a7d331662c02f7ddb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9963fe377bb415d71d1fe599eee188ce.png)
A.0 | B.1 | C.2 | D.3 |
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解题方法
3 . 已知数列
满足:
,
,其中
为数列
的前n项和.
(1)求数列
的通项公式;
(2)设m为正整数,若存在首项为1且公比为正数的等比数列
(
),对任意正整数k,当
时,都有
成立,求m的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b11b53600b5f8795438b5071251fe32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(2)设m为正整数,若存在首项为1且公比为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3d686e972baa72df81389555897acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41075383e3b80a1ac8faf5edec08f620.png)
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4 . 在三棱台
中,
平面ABC,
,且
,
,M为AC的中点,P是CF上一点,且
,
.
平面PBM;
(2)若直线BC与平面PBM的所成角为
,求平面EFM与平面PBM所成夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8783bc74553bf44b61d999a0e4144bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e4a2df58a236c20df5df0d29a466c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2e870c95b1ed54b281f93e683578bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f14839cf7e3ec6e25b60765ca25b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3362a45b72536c714c5107b0ae94f1c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
(2)若直线BC与平面PBM的所成角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
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解题方法
5 . 在平面直角坐标系xOy中,已知F为抛物线C:
的焦点,O为坐标原点,M为C的准线l上一点,直线MF的斜率为
,
的面积为4.
(1)求C的方程;
(2)过点F的直线交C于A,B两点,过点B作y轴的垂线交直线AO于点D,过点A作直线DF的垂线与C的另一交点为E,AE的中点为G,证明:G,B,D三点纵坐标相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d2ce6d23fb52cc513580a8f0e6760c2.png)
(1)求C的方程;
(2)过点F的直线交C于A,B两点,过点B作y轴的垂线交直线AO于点D,过点A作直线DF的垂线与C的另一交点为E,AE的中点为G,证明:G,B,D三点纵坐标相等.
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6 . 已知
,且
,记随机变量X为x,y,z中的最小值,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223770da09feb2fc824764188e924d7e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960430a95fa214ab71f3bab114c22080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb603414e6b47ce46dbbcd3f955a424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/223770da09feb2fc824764188e924d7e.png)
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7 . 某公司需要把直径为
的实心铁球融化后浇注为一个棱长为30cm的正方体实心模具(不计损耗),则至少需要________ 个这样的实心铁球.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72cce4e3fd2d140747a82b5f90755f0.png)
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8 . 函数
(n为正整数)的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471d04fe39fb83045690bc090527f591.png)
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9 . 已知定义在R上的函数
满足
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96af1a2a26c4f4338a63ffa3b688a5b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8718f486c48b09ffd904ddbf1dc7037.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 在复数范围内,下列命题是假命题的为( )
A.若![]() ![]() | B.若![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() ![]() |
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