解题方法
1 . 已知数列
前
项和
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b982b2d1d703e124c0f2c5894bf908c.png)
(1)求数列
的通项公式;
(2)求数列
的前
项和
.
![](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/1b982b2d1d703e124c0f2c5894bf908c.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57c83d526ac308d1461e80fcca9f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2 . 已知复数
,且
,
(1)求
的实部与虚部;
(2)若
是关于
的方程
,且
的一个复数根,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21094e3ba9668654a9d3afea8de90548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f253ceacadcf3ee5640fb844eddaac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a120c3b2b8c82da2b4fb15fafee77bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1357f8541d064df1b9a7af0bf950c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
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解题方法
3 . 如图,这是某种型号的奖杯,它是用一个正四棱台、一个正四棱柱和一个球焊接而成的球的半径为
.正四棱柱的底面边长为
,高为
.正四棱台的上、下底面边长分别为
和
,斜高(即侧面梯形的高)为
.
表示,焊接处对面积的影响忽略不计);
(2)已知
,若为奖杯表面镀金所用的材料每
可以涂
,且该种型号的奖杯底面(图中正四棱台的下底面作为该种型号的奖杯的底面,一般底面采用其他村质)不需要镀金,则为100个这种型号的奖杯镀金约需要多少材料?(
取3.14,精确到
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7f30167e1135806fe9de641870b1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8531b57064ada226c3f3ca2c8cc6383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753d029529e96c18464e5649cc2019dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7083b5636c7b87bf31a95eb750668267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da165d3d3de8812ab633e6276ed907b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a413309ee88e7184c2e99b39feaa266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090c07aece85100f0733e9f0c9eb13b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37d3860a1a4144a424a27fd121742f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d22e6589811741967bbf91724ae49a.png)
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名校
解题方法
4 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212b6a14e1ed6a4168778f44c05a49aa.png)
(1)化简![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
(2)若
,且
,求
的值.
(3)若
是第三象限角,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/212b6a14e1ed6a4168778f44c05a49aa.png)
(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1ba6b6ee00c4b2763cb3fa59caa69f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c2fc88cb139f6353cc047eb21547bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3299b21e382a636eb29f5a436bb363f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8466f82bce73bcc59604cad0769d5d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e33f0449855a5f76bf061b24ea3c2433.png)
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5 . 在平面直角坐标系中,角
的顶点为坐标原点,始边为
的非负半轴,终边经过点
.
(1)求
与
的值:
(2)求
的值.
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cf818dd484cc4cebd40a5f28eb8e9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f798a9af75a091a8be0b71f2038260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6369cd1db768436809404b1f3c4132c0.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac02f345bcdadd676da7347d7f4c3a9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/155a98ed36f52e4bb266cdd915d805a1.png)
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解题方法
6 . 四边形ABCD为平行四边形,
,点M,N满足
,
.
,求
的值;
(2)若
,且
,点P是边AD上的动点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecb91d19a693299dcdad4059b6237a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aff459d6f6f3ebd003d6c830b33b2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f06233da1e067a94c5abfeeee6dcdbf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8ea703abfa6d8fb4eac0a39ec8192a.png)
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解题方法
7 . 已知函数
在一个周期内的图象如图所示.
的解析式和最小正周期;
(2)求函数
在区间
上的最值及对应的x的取值;
(3)当
时,写出函数
的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a396eff9db616a8ffbb22458e33b17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f085d3f0cd19354da8667c594d18dae.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47dd5fc03cf0d593fcf67b5d18d1c2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
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8 . 已知函数
.
(1)求函数
的最小正周期及其单调递增区间,
(2)若
为锐角
的内角,且
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4419b92ef5f197b949f5b55448a4b2.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5cdd4e9623a41c9f97aa82b106a8fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
9 . 已知函数
的部分图象如图所示.
的解析式;
(2)求
在
上的值域;
(3)求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8958a4b164d0c948463dbe9493f3b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec4ae67bb39e9b22415aa555f644bf6.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7a87f9b744e0c821a82f82ea50f390.png)
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解题方法
10 . 已知角
的终边经过点
.
(1)求
,
,
的值;
(2)若
,
,
,求角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cf818dd484cc4cebd40a5f28eb8e9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f90c4754e6b6fc862d72943fb35569.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7417822839d79bac81ef019ba12975ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d394016b9fecac73f38cbc4ff18dee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f07029c97c324d32f258f18a96654a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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