名校
解题方法
1 . 在
中,内角
,
,
的对边分别为
,
,
,且
,
,则( )
![](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/2f44c181a2f6ae22d5d52b374768dc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67cf40b73e4b9b9bd9fffb7e85b95808.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
解题方法
2 . 假设在某种细菌培养过程中,正常细菌每小时分裂1次(1个正常细菌分裂成2个正常细菌和1个非正常细菌),非正常细菌每小时分裂1次(1个非正常细菌分裂成2个非正常细菌).若1个正常细菌经过14小时的培养,则可分裂成的细菌的个数为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知数列
满足,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83eb0330e4696b03f9dd70f276447a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bbf0a641cc462fbed00ff931ac38e6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:河北省邯郸市部分示范性高中2024届高三下学期三模数学试题
4 . 已知数列
满足
.
(1)证明:数列
为等差数列,并求
;
(2)令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef62488d673b7bdd89a1b3d3fa477535.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099a64d86bd0b4602578d910322adc1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/101a280c6657313aab9bdec6ba8d648a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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5 . 已知数列
满足:
.
(1)请写出
的值,给出一个你的猜想,并证明;
(2)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d7d401a56dd0f08554b5bea34c5592.png)
(1)请写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72d62b424b71cf30b320113f382a02a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0345bf91f399b8783634e731947dc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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6 . 已知数列
均为等差数列,其前
项和分别为
,满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed48c3e5c53eba20c2e262b7d2c09bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd97eb7f00e8436abc39632f69d2d700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041dfb275f51fea6376f2659741a3c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2daa3c696b3a624b5967d09c154783.png)
A.2 | B.3 | C.5 | D.6 |
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解题方法
7 . 记各项均为正数的数列
的前
项和为
,已知
是
与
的等差中项.
(1)求
的通项公式;
(2)设
,数列
的前
项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c2663aa2e69ddc18269e43c118c6bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f47bf843425ef0ba8baeb4fc156432e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2714dbbe4d40c868b1d7360239649ef.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c90f1350dec7e6efa49bd058a5245c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1262b0948a6caa98c91c24d1c752832.png)
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解题方法
8 . 在
中,角
的对边分别为
,已知
.
(1)求
;
(2)若
为
边的中点,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8da3561f20a8aa399418172ee725549.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc28736bfbaea0c11e0c7b890ef2ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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解题方法
9 . 已知函数
的最小正周期为
.
(1)求
的值;
(2)在锐角
中,角A,B,C所对的边分别为a,b,c.c为
在
上的最大值,再从条件①、条件②、条件③这三个条件中选择一个作为已知,求
的取值范围.条件①:
;条件②:
;条件③:
的面积为S,且
.注:如果选择多个条件分别解答,按第一个条件计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8927608114a249f8acb7da7901fc7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)在锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d51992c05a557cf6058664f1f8961e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f2416d1f75a45a314331146550832e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19dd0c2a4a1107ea28a418a7d281ef5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b86308eec25f94db0a5e7a58765206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bf72fe243ab7ba53a1679372f41793.png)
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10 . 已知数列
的前n项和为
且
,给出下列四个结论:①长度分别为
的三条线段可以构成一个直角三角形:②
;③
;④
.其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae734ad099abbb2f7efe7d7a6a4169fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3807e619b383425065eda0ae269ef81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4a02ca421084c3a93d42597bdffb4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b3ee64ccd5bb72bbef0f514989c69a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62552c86435988206cdaee449df97a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4024050c475a5fd70d29314576c6d0a1.png)
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