解题方法
1 . 已知向量
与
的夹角为
,
,
,求:
(1)
;
(2)
.
![](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/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cbd3ad4cfa6d2a99a3cf2217f96134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2396cac4b185cf1f1a67dad9248481c.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93af88a7628c71d642d3a6df067c15f5.png)
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2 . 计算:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543520fe35d5b3e4114b3c09b1de2db1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0e67d903473bc5537ed99a74deb3a6.png)
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解题方法
3 . 已知
,记
在
方向上的投影向量为
.
(1)求
的值;
(2)若向量
与
的夹角为锐角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2bf34bc1ee12179b6010fd264cfc7e.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)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7b2495078012b4d16e812d1c9258a8.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838ed4ef3fbcaa43693e8c375da6c04e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3a63f9f11a11986ca5a34f8f0f0a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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4 . 函数
(
,
,
)的部分图象如图,
和
均在函数
的图象上,且Q是图象上的最低点.
的单调递增区间;
(2)若
,
,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/083169a97d6babe52eca51c2ed0aefb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c426f776a2e72a8300512bf52c35ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9271992646b7bb71e0841d9d57912cf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920f7b809091d270731c50849a4388ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f8c00c0bf7344ba3bc7984516d3d18.png)
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5 . 求值:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9574e1c06fd2dc9ccbae5d137fd0af5b.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac4d516a6f25f72b7b5ec791fee421b.png)
(3)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9574e1c06fd2dc9ccbae5d137fd0af5b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac4d516a6f25f72b7b5ec791fee421b.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1762dbbbf7d267b7332fe2706e754c.png)
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6 . 求下列函数的导数:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fa7e9b06586c44d92eb5fb49851365.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68663cb9418693cb1b605538c4b4e364.png)
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解题方法
7 . 为纪念五四青年运动105周年,进一步激励广大团员青年继承和发扬五四精神,宁波市教育局组织中小学开展形式多样、内容丰富、彰显青年时代风貌的系列主题活动.某中学开展“读好红色经典,争做强国少年”经典知识竞赛答题活动,现从该校参加竞赛的全体学生中随机选取100份学生的答卷作为样本,所有得分都分布在
,将得分数据按照
,
,…,
分成7组,得到如图所示的频率分布直方图.
(2)估计该中学参加竞赛学生成绩的第75百分位数(结果精确到0.1);
(3)若竞赛得分100分及以上的学生视为“强国少年”.根据选取的100份答卷数据统计;竞赛得分在
内学生的平均分和方差分别为110和9,竞赛得分在
内学生的平均分和方差分别为128和6,请估计该中学“强国少年”得分的方差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a7e364c77b4d20435807e38eaf3ccf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb3d99cbd744a9d742ea44c620784d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318526d0ebdb8f02a91b3903e48b42b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cdd8aba4640ef388fe2f27d191e384.png)
(2)估计该中学参加竞赛学生成绩的第75百分位数(结果精确到0.1);
(3)若竞赛得分100分及以上的学生视为“强国少年”.根据选取的100份答卷数据统计;竞赛得分在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8eafe01a09a99b8c42da263cfbce2a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cdd8aba4640ef388fe2f27d191e384.png)
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解题方法
8 . (1)解不等式:
.
(2)已知
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d9add53293d74de1036132da77482b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a7de5b70003502e40b95b3b7d3d933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a39ee003ce154b19561409afdddb7c.png)
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9 . 已知O为坐标原点,经过点
的直线l与抛物线C:
交于A,B(A,B异于点O)两点,且以AB为直径的圆过点O.
(1)求C的方程;
(2)已知M,N,P是C上的三点,若△MNP为正三角形,Q为△MNP的中心,求直线OQ斜率的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
(1)求C的方程;
(2)已知M,N,P是C上的三点,若△MNP为正三角形,Q为△MNP的中心,求直线OQ斜率的最大值.
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解题方法
10 . 在
中,A,B,C所对的边分别为a,b,c,且
.
(1)求B;
(2)若
,求
的周长l的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb62f4dc2f19d82ca862fd207b2cae95.png)
(1)求B;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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